python programming problems

exercises 9.3， 9.7， 9.17

You can find them on pg 304, see attached pdf.

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INTRODUCTION TO
PROGRAMMING USING
PYTHON
Y. Daniel Liang
Armstrong Atlantic State University

Editorial Director, ECS: Marcia Horton
Editor-in-Chief: Michael Hirsch
Executive Editor: Tracy Dunkelberger
Associate Editor: Carole Snyder
Director of Marketing: Patrice Jones
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Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this textbook
appear on Credits page located in the end matter.
Microsoft® and Windows® are registered trademarks of the Microsoft Corporation in the U.S.A. and other coun-
tries. Screen shots and icons reprinted with permission from the Microsoft Corporation. This book is not sponsored
or endorsed by or affiliated with the Microsoft Corporation.
Copyright © 2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved. Manufactured in the
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have been printed in initial caps or all caps.
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ISBN 13: 978-0-13-274718-9
ISBN 10: 0-13-274718-9

www.pearsonhighered.com

This book is dedicated to my former colleagues
at the National Severe Storms Laboratory,
in Norman, Oklahoma.
To Samantha, Michael, and Michelle

vi
PREFACE
Dear Reader,
This book assumes that you are a new programmer with no prior knowledge of programming.
So, what is programming? Programming solves problems by creating solutions—writing
programs—in a programming language. The fundamentals of problem solving and programming
are the same regardless of which programming language you use. You can learn programming
using any high-level programming language such as Python, Java, C++, or C#. Once you know
how to program in one language, it is easy to pick up other languages, because the basic tech-
niques for writing programs are the same.
So what are the benefits of learning programming using Python? Python is easy to learn
and fun to program. Python code is simple, short, readable, intuitive, and powerful, and thus
it is effective for introducing computing and problem solving to beginners.
Beginners are motivated to learn programming so they can create graphics. A big reason
for learning programming using Python is that you can start programming using graphics on
day one. We use Python’s built-in Turtle graphics module in Chapters 1–6 because it is a good
pedagogical tool for introducing fundamental concepts and techniques of programming. We
introduce Python’s built-in Tkinter in Chapter 9, because it is a great tool for developing
comprehensive graphical user interfaces and for learning object-oriented programming. Both
Turtle and Tkinter are remarkably simple and easy to use. More importantly, they are valuable
pedagogical tools for teaching the fundamentals of programming and object-oriented
programming.
To give instructors flexibility to use this book, we cover Turtle at the end of Chapters 1–6
so they can be skipped as optional material.
The book teaches problem solving in a problem-driven way that focuses on problem solv-
ing rather than syntax. We stimulate student interests in programming by using interesting
examples in a broad context. While the central thread of the book is on problem solving,
appropriate Python syntax and library are introduced in order to solve the problems. To sup-
port the teaching of programming in a problem-driven way, the book provides a wide variety
of problems at various levels of difficulty to motivate students. In order to appeal to students
in all majors, the problems cover many application areas in math, science, business, financial
management, gaming, animation, and multimedia.
All data in Python are objects. We introduce and use objects from Chapter 3, but defining
custom classes are covered in the middle of the book starting from Chapter 7. The book
focuses on fundamentals first: it introduces basic programming concepts and techniques on
selections, loops, and functions before writing custom classes.
The best way to teach programming is by example, and the only way to learn programming
is by doing. Basic concepts are explained by example and a large number of exercises with
various levels of difficulty are provided for students to practice. Our goal is to produce a text
that teaches problem solving and programming in a broad context using a wide variety of
interesting examples and exercises.
Sincerely,
Y. Daniel Liang
y.daniel.liang@gmail.com
www.cs.armstrong.edu/liang
www.pearsonhighered.com/liang
what is programming?
why Python?
graphics
optional Turtle
problem-driven
fundamentals first
examples and exercises

www.cs.armstrong.edu/liang

www.pearsonhighered.com/liang

Preface vii
Pedagogical Features
The book uses the following elements to get the most from the material:
■ Objectives list what students should learn in each chapter. This will help them determine
whether they have met the objectives after completing the chapter.
■ The Introduction opens the discussion with representative problems to give the reader an
overview of what to expect from the chapter.
■ Key Points highlight the important concepts covered in each section.
■ Check Points provide review questions to help students track their progress and evaluate
their learning.
■ Problems, carefully chosen and presented in an easy-to-follow style, teach problem
solving and programming concepts. The book uses many small, simple, and stimulating
examples to demonstrate important ideas.
■ Key Terms are listed with a page number to give students a quick reference to the impor-
tant terms introducd in the chapter.
■ The Chapter Summary reviews the important subjects that students should understand
and remember. It helps them reinforce the key concepts they have learned in the chapter.
■ Test Questions are available online, grouped by sections for students to do self-test on
programming concepts and techniques.
■ Programming Exercises are grouped by sections to provide students with opportunities
to apply on their own the new skills they have learned. The level of difficulty is rated as
easy (no asterisk), moderate (*), hard (**), or challenging (***). The trick of learning
programming is practice, practice, and practice. To that end, the book provides a great
many exercises.
■ Notes, Tips, and Cautions are inserted throughout the text to offer valuable advice and
insight on important aspects of program development.
Note
Provides additional information on the subject and reinforces important concepts.
Tip
Teaches good programming style and practice.
Caution
Helps students steer away from the pitfalls of programming errors.
Flexible Chapter Orderings
Graphics is a valuable pedagogical tool for learning programming. The book uses Turtle
graphics in Chapters 1–6 and Tkinter in the rest of the book. However, the book is designed to
give the instructors the flexibility to skip the sections on graphics or to cover them later. The
following diagram shows the chapter dependencies.
Chapter 10, Lists can be covered right after Chapter 6, Functions. Chapter 14, Tuples,
Sets, and Dictionaries can be covered after Chapter 10.

viii Preface
Organization of the Book
The chapters can be grouped into three parts that, taken together, form a comprehensive intro-
duction to Python programming. Because knowledge is cumulative, the early chapters pro-
vide the conceptual basis for understanding programming and guide students through simple
examples and exercises; subsequent chapters progressively present Python programming in
detail, culminating with the development of comprehensive applications.
Part I: Fundamentals of Programming (Chapters 1–6)
The first part of the book is a stepping stone, preparing you to embark on the journey of learn-
ing programming. You will begin to know Python (Chapter 1) and will learn fundamental pro-
gramming techniques with data types, variables, constants, assignments, expressions,
operators, objects, and simple functions and string operations (Chapters 2–3), selection state-
ments (Chapter 4), loops (Chapter 5), and functions (Chapter 6).
Part II: Object-Oriented Programming (Chapters 7–13)
This part introduces object-oriented programming. Python is an object-oriented programming
language that uses abstraction, encapsulation, inheritance, and polymorphism to provide great
flexibility, modularity, and reusability in developing software. You will learn object-oriented
programming (Chapters 7–8), GUI programming using Tkinter (Chapter 9), lists (Chapter
10), multidimensional lists (Chapter 11), inheritance, polymorphism, and class design
(Chapter 12), and files and exception handling (Chapter 13).
Part III: Data Structures and Algorithms (Chapters 14–15 and Bonus Chapters 16–23)
This part introduces the main subjects in a typical data structures course. Chapter 14 intro-
duces Python built-in data structures: tuples, sets, and dictionaries. Chapter 15 introduces
Chapter 10 Lists
Chapter 4 Selections
Chapter 5 Loops
Chapter 1 Introduction to
Computers, Programs, and
Python
Chapter 2 Elementary
Programming
Chapter 7 Objects and Classes
Chapter 13 Files and Exception
Handling
Note: Chapters 16–23 are bonus
chapters available from the
Companion Website
Chapter 8 More on Strings and
Special Methods
Chapter 9 GUI Programming
Using Tkinter
Chapter 11 Multidimensional
Lists
Chapter 12 Inheritance and
Polymorphism
Chapter 14 Tuples, Sets, and
Dictionaries
Chapter 15 Recursion
Chapter 16 Developing Efficient
Algorithms
Chapter 17 Sorting
Chapter 18 Linked Lists, Stacks,
Queues, and Priority Queues
Chapter 19 Binary Search Trees
Chapter 20 AVL Trees
Chapter 21 Hashing:
Implementing Dictionaries and
Sets
Chapter 22 Graphs and
Applications
Chapter 23 Weighted Graphs
and Applications
Part I: Fundamentals of
Programming
Part II: Object-Oriented
Programming
Part III: Data Structures and
Algorithms
Chapter 3 Mathematical
Functions, Strings, and
Objects
Chapter 6 Functions

Preface ix
recursion to write functions for solving inherently recursive problems. Chapters 16–23 are
bonus chapters on the Companion Website. Chapter 16 introduces measurement of algorithm
efficiency and common techniques for developing efficient algorithms. Chapter 17 discusses
classic sorting algorithms. You will learn how to implement linked lists, queues, and priority
queues in Chapter 18. Chapter 19 presents binary search trees, and you will learn about AVL
trees in Chapter 20. Chapter 21 introduces hashing, and Chapters 22 and 23 cover graph algo-
rithms and applications.
Student Resource Website
The Student Resource Website (www.cs.armstrong.edu/liang/py) contains the following resources:
■ Answers to review questions
■ Solutions to even-numbered programming exercises
■ Source code for the examples in the book
■ Interactive self-test questions (organized by sections for each chapter)
■ Supplements on using Python IDEs, advanced topics, etc.
■ Resource links
■ Errata
Additional Supplements
The text covers the essential subjects. The supplements extend the text to introduce additional
topics that might be of interest to readers. The supplements listed in this table are available
from the Companion Website.
Part I. General Supplements
A. Glossary
B. Installing and Using Python
C. Python IDLE
D. Python on Eclipse
E. Python on Eclipse Debugging
F. Python Coding Style Guidelines
Part II. Advanced Python Topics
A. Regular Expressions
B. Obtaining Date and Time
C. The str Class’s format Method
D. Pass Arguments from Command Line
E. Database Programming
Instructor Resource Website
The Instructor Resource Website, accessible from www.cs.armstrong.edu/liang/py, contains the
following resources:
■ Microsoft PowerPoint slides with interactive buttons to view full-color, syntax-highlighted
source code and to run programs without leaving the slides.
■ Solutions to all the review questions and exercises. Students will have access to the solu-
tions of even-numbered programming exercises.
■ Web-based quiz generator. (Instructors can choose chapters to generate quizzes from a
large database of more than 800 questions.)

www.cs.armstrong.edu/liang/py

x Preface
■ Sample exams. In general, each exam has four parts:
■ Multiple-choice questions or short-answer questions
■ Correct programming errors
■ Trace programs
■ Write programs
■ Projects. In general, each project gives a description and asks students to analyze, design,
and implement the project.
Some readers have requested the materials from the Instructor Resource Website. Please
understand that these are for instructors only. Such requests will not be answered.
Online Practice and Assessment
with MyProgrammingLab
MyProgrammingLab helps students fully grasp the logic, semantics, and syntax of program-
ming. Through practice exercises and immediate, personalized feedback, MyProgrammingLab
improves the programming competence of beginning students who often struggle with the basic
concepts and paradigms of popular high-level programming languages.
A self-study and homework tool, a MyProgrammingLab course consists of hundreds of
small practice problems organized around the structure of this textbook. For students, the
system automatically detects errors in the logic and syntax of their code submissions and
offers targeted hints that enable students to figure out what went wrong—and why. For
instructors, a comprehensive gradebook tracks correct and incorrect answers and stores the
code inputted by students for review.
MyProgrammingLab is offered to users of this book in partnership with Turing’s Craft, the
makers of the CodeLab interactive programming exercise system. For a full demonstration, to
see feedback from instructors and students, or to get started using MyProgrammingLab in
your course, visit www.myprogramminglab.com.
VideoNotes
VideoNotes are Pearson’s new visual tool designed for teaching students key programming con-
cepts and techniques. These short step-by-step videos demonstrate how to solve problems from
design through coding. VideoNotes allow for self-placed instruction with easy navigation includ-
ing the ability to select, play, rewind, fast-forward, and stop within each VideoNote exercise.
Margin icons in your textbook let you know when a VideoNote video is available for a par-
ticular concept or homework problem.
LiveLab
This book is accompanied by a complementary Web-based course assessment and manage-
ment system for instructors. The system has four main components:
■ The Automatic Grading System can automatically grade programs.
■ The Quiz Creation/Submission/Grading System enables instructors to create and mod-
ify quizzes that students can take and be graded upon automatically.
■ The Peer Evaluation System enables peer evaluations.
■ Checking plagiarisms, tracking grades, attendance, etc., lets students track their grades,
and enables instructors to view the grades of all students, to check plagiarisms, and to track
students’ attendance.
VideoNote

www.myprogramminglab.com

Preface xi
The main features of the Automatic Grading System include:
■ Students can run and submit exercises. (The system checks whether their program runs
correctly—students can continue to run and resubmit the program before the due date.)
■ Instructors can review submissions, run programs with instructor test cases, correct them,
and provide feedback to students.
■ Instructors can create/modify their own exercises, create public and secret test cases, as-
sign exercises, and set due dates for the whole class or for individuals.
■ All the exercises in the text can be assigned to students. Additionally, LiveLab provides
extra exercises that are not printed in the text.
■ Instructors can sort and filter all exercises and check grades (by time frame, student,
and/or exercise).
■ Instructors can check plagiarisms for a programming exercise.
■ Instructors can delete students from the system.
■ Students and instructors can track grades on exercises.
The main features of the Quiz System are:
■ Instructors can create/modify quizzes from the test bank or a text file or create completely
new tests online.
■ Instructors can assign the quizzes to students and set a due date and test time limit for the
whole class or for individuals.
■ Students and instructors can review submitted quizzes.
■ Instructors can analyze quizzes and identify students’ weaknesses.
■ Students and instructors can track grades on quizzes.
The main features of the Peer Evaluation System include:
■ Instructors can assign/unassign exercises for peer evaluation.
■ Instructors can view peer evaluation reports.
Acknowledgments
I would like to thank Armstrong Atlantic State University for enabling me to teach what I
write and for supporting me in writing what I teach. Teaching is the source of inspiration for
the book. I am grateful to the instructors and students who have offered comments, sugges-
tions, bug reports, and praise.
This book has been greatly enhanced thanks to the outstanding reviewers. They are:
Claude Anderson – Rose-Hulman Institute of Technology
Lee Cornell – Minnesota State University – Mankato
John Magee – Boston University
Shyamal Mitra – University of Texas – Austin
Yenumula Reddy – Grambling State University
David Sullivan – Boston University
Hong Wang – University of Toledo
It is a great pleasure, honor, and privilege to work with Pearson. I would like to thank
Tracy Dunkelberger, Marcia Horton, Michael Hirsch, Matt Goldstein, Carole Snyder, Tim
Huddleston, Yez Alayan, Jeff Holcomb, Gillian Hall, Rebecca Greenberg, and their colleagues
for organizing, producing, and promoting this project.
As always, I am indebted to my wife, Samantha, for her love, support, and encouragement.

BRIEF CONTENTS
1 Introduction to Computers, Programs,
and Python 1
2 Elementary Programming 31
3 Mathematical Functions, Strings,
and Objects 63
4 Selections 91
5 Loops 133
6 Functions 171
7 Objects and Classes 215
8 More on Strings and Special Methods 241
9 GUI Programming Using Tkinter 271
10 Lists 313
11 Multidimensional Lists 361
12 Inheritance and Polymorphism 399
13 Files and Exception Handling 439
14 Tuples, Sets, and Dictionaries 475
15 Recursion 499
xii
Chapters 16–23 are bonus Web chapters
16 Developing Efficient Algorithms 16-1
17 Sorting 17-1
18 Linked Lists, Stacks, Queues,
and Priority Queues 18-1
19 Binary Search Trees 19-1
20 AVL Trees 20-1
21 Hashing: Implementing Dictionaries
and Sets 21-1
22 Graphs and Applications 22-1
23 Weighted Graphs and Applications 23-1
APPENDIXES
A Python Keywords 533
B The ASCII Character Set 534
C Number Systems 536
INDEX 541
CREDITS 557

CONTENTS
Chapter 1 Introduction to Computers, Programs,
and Python 1
1.1 Introduction 2
1.2 What Is a Computer? 2
1.3 Programming Languages 9
1.4 Operating Systems 12
1.5 The History of Python 13
1.6 Getting Started with Python 14
1.7 Programming Style and Documentation 18
1.8 Programming Errors 19
1.9 Getting Started with Graphics Programming 21
Chapter 2 Elementary Programming 31
2.1 Introduction 32
2.2 Writing a Simple Program 32
2.3 Reading Input from the Console 34
2.4 Identifiers 36
2.5 Variables, Assignment Statements, and Expressions 36
2.6 Simultaneous Assignments 38
2.7 Named Constants 39
2.8 Numeric Data Types and Operators 40
2.9 Evaluating Expressions and Operator Precedence 43
2.10 Augmented Assignment Operators 44
2.11 Type Conversions and Rounding 45
2.12 Case Study: Displaying the Current Time 46
2.13 Software Development Process 48
2.14 Case Study: Computing Distances 52
Chapter 3 Mathematical Functions, Strings,
and Objects 63
3.1 Introduction 64
3.2 Common Python Functions 64
3.3 Strings and Characters 67
3.4 Case Study: Minimum Number of Coins 72
3.5 Introduction to Objects and Methods 74
3.6 Formatting Numbers and Strings 76
3.7 Drawing Various Shapes 81
3.8 Drawing with Colors and Fonts 83
xiii

Chapter 4 Selections 91
4.1 Introduction 92
4.2 Boolean Types, Values, and Expressions 92
4.3 Generating Random Numbers 93
4.4 if Statements 95
4.5 Case Study: Guessing Birthdays 96
4.6 Two-Way if-else Statements 100
4.7 Nested if and Multi-Way if-elif-else Statements 102
4.8 Common Errors in Selection Statements 105
4.9 Case Study: Computing Body Mass Index 107
4.10 Case Study: Computing Taxes 108
4.11 Logical Operators 110
4.12 Case Study: Determining Leap Years 113
4.13 Case Study: Lottery 114
4.14 Conditional Expressions 116
4.15 Operator Precedence and Associativity 117
4.16 Detecting the Location of an Object 118
Chapter 5 Loops 133
5.1 Introduction 134
5.2 The while Loop 134
5.3 The for Loop 143
5.4 Nested Loops 145
5.5 Minimizing Numerical Errors 147
5.6 Case Studies 148
5.7 Keywords break and continue 151
5.8 Case Study: Displaying Prime Numbers 154
5.9 Case Study: Random Walk 156
Chapter 6 Functions 171
6.1 Introduction 172
6.2 Defining a Function 172
6.3 Calling a Function 173
6.4 Functions with/without Return Values 176
6.5 Positional and Keyword Arguments 179
6.6 Passing Arguments by Reference Values 180
6.7 Modularizing Code 183
6.8 Case Study: Converting Decimals to Hexadecimals 185
6.9 The Scope of Variables 187
6.10 Default Arguments 189
6.11 Returning Multiple Values 190
6.12 Case Study: Generating Random ASCII Characters 191
6.13 Function Abstraction and Stepwise Refinement 192
6.14 Case Study: Reusable Graphics Functions 199
xiv Contents

Chapter 7 Objects and Classes 215
7.1 Introduction 216
7.2 Defining Classes for Objects 216
7.3 UML Class Diagrams 222
7.4 Immutable Objects vs. Mutable Objects 225
7.5 Hiding Data Fields 227
7.6 Class Abstraction and Encapsulation 229
7.7 Object-Oriented Thinking 233
Chapter 8 More on Strings and Special Methods 241
8.1 Introduction 242
8.2 The str Class 242
8.3 Case Study: Checking Palindromes 253
8.4 Case Study: Converting Hexadecimals to Decimals 254
8.5 Operator Overloading and Special Methods 257
8.6 Case Study: The Rational Class 258
Chapter 9 GUI Programming Using Tkinter 271
9.1 Introduction 272
9.2 Getting Started with Tkinter 272
9.3 Processing Events 273
9.4 The Widget Classes 275
9.5 Canvas 280
9.6 The Geometry Managers 283
9.7 Case Study: Loan Calculator 287
9.8 Displaying Images 288
9.9 Menus 290
9.10 Popup Menus 292
9.11 Mouse, Key Events, and Bindings 294
9.12 Animations 297
9.13 Scrollbars 300
9.14 Standard Dialog Boxes 301
Chapter 10 Lists 313
10.1 Introduction 314
10.2 List Basics 315
10.3 Case Study: Lotto Numbers 325
10.4 Case Study: Deck of Cards 327
10.5 Deck of Cards GUI 329
10.6 Copying Lists 330
10.7 Passing Lists to Functions 332
10.8 Returning a List from a Function 334
10.9 Case Study: Counting the Occurrences of Each Letter 335
10.10 Searching Lists 338
Contents xv

10.11 Sorting Lists 341
10.12 Case Study: Bouncing Balls 345
Chapter 11 Multidimensional Lists 361
11.1 Introduction 362
11.2 Processing Two-Dimensional Lists 362
11.3 Passing Two-Dimensional Lists to Functions 365
11.4 Problem: Grading a Multiple-Choice Test 367
11.5 Problem: Finding the Closest Pair 368
11.6 GUI: Finding the Closest Pair 370
11.7 Problem: Sudoku 372
11.8 Case Study: Sudoku GUI 375
11.9 Multidimensional Lists 377
Chapter 12 Inheritance and Polymorphism 399
12.1 Introduction 400
12.2 Superclasses and Subclasses 400
12.3 Overriding Methods 405
12.4 The object Class 406
12.5 Polymorphism and Dynamic Binding 409
12.6 The isinstance Function 411
12.7 Case Study: A Reusable Clock 414
12.8 Class Relationships 418
12.9 Case Study: Designing the Course Class 421
12.10 Designing a Class for Stacks 423
12.11 Case Study: The FigureCanvas Class 425
Chapter 13 Files and Exception Handling 439
13.1 Introduction 440
13.2 Text Input and Output 440
13.3 File Dialogs 448
13.4 Case Study: Counting Each Letter in a File 451
13.5 Retrieving Data from the Web 452
13.6 Exception Handling 454
13.7 Raising Exceptions 457
13.8 Processing Exceptions Using Exception Objects 460
13.9 Defining Custom Exception Classes 460
13.10 Binary IO Using Pickling 465
13.11 Case Study: Address Book 467
Chapter 14 Tuples, Sets, and Dictionaries 475
14.1 Introduction 476
14.2 Tuples 476
14.3 Sets 479
14.4 Comparing the Performance of Sets and Lists 485
xvi Contents

14.5 Case Study: Counting Keywords 486
14.6 Dictionaries 487
14.7 Case Study: Occurrences of Words 492
Chapter 15 Recursion 499
15.1 Introduction 500
15.2 Case Study: Computing Factorials 500
15.3 Case Study: Computing Fibonacci Numbers 503
15.4 Problem Solving Using Recursion 505
15.5 Recursive Helper Functions 507
15.6 Case Study: Finding the Directory Size 510
15.7 Case Study: Towers of Hanoi 512
15.8 Case Study: Fractals 515
15.9 Case Study: Eight Queens 518
15.10 Recursion vs. Iteration 520
15.11 Tail Recursion 521
A detailed table of contents for the Web chapters is available on the
companion Website:
Chapter 16 Developing Efficient Algorithms 16–1
Chapter 17 Sorting 17–1
Chapter 18 Linked Lists, Stacks, Queues,
and Priority Queues 18–1
Chapter 19 Binary Search Trees 19–1
Chapter 20 AVL Trees 20–1
Chapter 21 Hashing: Implementing Dictionaries
and Sets 21–1
Chapter 22 Graphs and Applications 22-1
Chapter 23 Weighted Graphs and Applications 23-1
APPENDIXES
Appendix A Python Keywords 533
Appendix B The ASCII Character Set 534
Appendix C Number Systems 536
INDEX 541
CREDITS 557
Contents xvii

LOCATION OF VIDEONOTES IN THE TEXT
Chapter 1 Start with Python, p. 14
Start with Turtle graphics, p. 21
Chapter 2 Assignment statement, p. 37
Perform computation, p. 40
Chapter 3 String operations, p. 75
Draw shapes, p. 81
Chapter 4 Boolean expressions, p. 92
Coffee price, p. 123
Chapter 5 while loop, p. 134
for loop, p. 143
Chapter 6 Use functions, p. 172
Divide and conquer, p. 192
Chapter 7 Define and use classes, p. 217
Private data fields, p. 227
Chapter 8 String methods, p. 242
Define classes, p. 258
Chapter 9 Simple GUI, p. 273
Create GUI application, p. 287
Chapter 10 Use lists, p. 315
Search a list, p. 338
Chapter 11 Process a matrix, p. 362
Chessboard, p. 394
Chapter 12 Inheritance and polymorphism, p. 400
Dynamic binding, p. 409
Chapter 13 Process text file, p. 443
Handle exceptions, p. 454
Chapter 14 Use sets, p. 479
Use dictionaries, p. 488
Chapter 15 Function sum, p. 500
Function print numbers, p. 506
xviii Location of VideoNotes in the Text

INTRODUCTION
TO COMPUTERS,
PROGRAMS,
AND PYTHON
Objectives
■ To demonstrate a basic understanding of computer hardware,
programs, and operating systems (§§1.2–1.4).
■ To describe the history of Python (§1.5).
■ To explain the basic syntax of a Python program (§1.6).
■ To write and run a simple Python program (§1.6).
■ To explain the importance of, and provide examples of,
proper programming style and documentation (§1.7).
■ To explain the differences between syntax errors, runtime errors,
and logic errors (§1.8).
■ To create a basic graphics program using Turtle (§1.9).
CHAPTER
1

2 Chapter 1 Introduction to Computers, Programs, and Python
1.1 Introduction
The central theme of this book is to learn how to solve problems by writing a program.
This book is about programming. So, what is programming? The term programming means to
create (or develop) software, which is also called a program. In basic terms, software contains
the instructions that tell a computer—or a computerized device—what to do.
Software is all around you, even in devices that you might not think would need it. Of
course, you expect to find and use software on a personal computer, but software also plays a
role in running airplanes, cars, cell phones, and even toasters. On a personal computer, you
use word processors to write documents, Web browsers to explore the Internet, and e-mail
programs to send messages. These programs are all examples of software. Software develop-
ers create software with the help of powerful tools called programming languages.
This book teaches you how to create programs by using the Python programming
language. There are many programming languages, some of which are decades old. Each
language was invented for a specific purpose—to build on the strengths of a previous lan-
guage, for example, or to give the programmer a new and unique set of tools. Knowing that
there are so many programming languages available, it would be natural for you to wonder
which one is best. But, in truth, there is no “best” language. Each one has its own strengths
and weaknesses. Experienced programmers know that one language might work well in some
situations, whereas a different language may be more appropriate in other situations. For this
reason, seasoned programmers try to master as many different programming languages as
they can, giving them access to a vast arsenal of software-development tools.
If you learn to program using one language, you should find it easy to pick up other
languages. The key is to learn how to solve problems using a programming approach. That is
the main theme of this book.
You are about to begin an exciting journey: learning how to program. At the outset, it
is helpful to review computer basics, programs, and operating systems. If you are already
familiar with such terms as CPU, memory, disks, operating systems, and programming
languages, you may skip the review in Sections 1.2–1.4.
1.2 What Is a Computer?
A computer is an electronic device that stores and processes data.
A computer includes both hardware and software. In general, hardware comprises the visible,
physical elements of the computer, and software provides the invisible instructions that control
the hardware and make it perform specific tasks. Knowing computer hardware isn’t essential
to learning a programming language, but it can help you better understand the effects that a
program’s instructions have on the computer and its components. This section introduces com-
puter hardware components and their functions.
A computer consists of the following major hardware components (Figure 1.1):
■ A central processing unit (CPU)
■ Memory (main memory)
■ Storage devices (such as disks and CDs)
■ Input devices (such as the mouse and keyboard)
■ Output devices (such as monitors and printers)
■ Communication devices (such as modems and network interface cards)
A computer’s components are interconnected by a subsystem called a bus. You can think
of a bus as a sort of system of roads running among the computer’s components; data and
what is programming?
program
programming languages
hardware
software
bus
Key
Point
Key
Point

1.2 What Is a Computer? 3
power travel along the bus from one part of the computer to another. In personal computers,
the bus is built into the computer’s motherboard, which is a circuit case that connects all of
the parts of a computer together, as shown in Figure 1.2.
1.2.1 Central Processing Unit
The central processing unit (CPU) is the computer’s brain. It retrieves instructions from
memory and executes them. The CPU usually has two components: a control unit and an
arithmetic/logic unit. The control unit controls and coordinates the actions of the other
components. The arithmetic/logic unit performs numeric operations (addition, subtraction,
multiplication, division) and logical operations (comparisons).
Today’s CPUs are built on small silicon semiconductor chips that contain millions of tiny
electric switches, called transistors, for processing information.
Every computer has an internal clock, which emits electronic pulses at a constant rate.
These pulses are used to control and synchronize the pace of operations. A higher clock speed
enables more instructions to be executed in a given period of time. The unit of measurement of
clock speed is the hertz (Hz), with 1 hertz equaling 1 pulse per second. In the 1990s computers
measured clocked speed in megahertz, but CPU speed has been improving continuously, and
motherboard
CPU
Bus
Memory
Storage
Devices
Input
Devices
Output
Devices
Communication
Devices
FIGURE 1.1 A computer consists of a CPU, memory, storage devices, input devices, output
devices, and communication devices.
CPU
speed
hertz
megahertz

4 Chapter 1 Introduction to Computers, Programs, and Python
the clock speed of a computer is now usually stated in gigahertz (GHz). Intel’s newest proces-
sors run at about 3 GHz.
CPUs were originally developed with only one core. The core is the part of the processor
that performs the reading and executing of instructions. In order to increase CPU processing
power, chip manufacturers are now producing CPUs that contain multiple cores. A multicore
CPU is a single component with two or more independent processors. Today’s consumer
computers typically have two, three, and even four separate cores. Soon, CPUs with tens or
even hundreds of cores will be affordable.
1.2.2 Bits and Bytes
Before we discuss memory, let’s look at how information (data and programs) are stored in a
computer.
A computer is really nothing more than a series of switches. Each switch exists in two
states: on or off. Storing information in a computer is simply a matter of setting a sequence
of switches on or off. If the switch is on, its value is 1. If the switch is off, its value is 0.
These 0s and 1s are interpreted as digits in the binary number system and called bits (binary
digits).
The minimum storage unit in a computer is a byte. A byte is composed of eight bits. A
small number such as 3 can be stored as a single byte. To store a number that cannot fit
into a single byte, the computer uses several bytes.
Data of various kinds, such as numbers and characters, are encoded as a series of bytes. As
a programmer, you don’t need to worry about the encoding and decoding of data, which the
computer system performs automatically, based on the encoding scheme. An encoding
scheme is a set of rules that govern how a computer translates characters, numbers, and sym-
bols into data the computer can actually work with. Most schemes translate each character
into a predetermined string of numbers. In the popular ASCII encoding scheme, for example,
the character C is represented as 01000011 in one byte.
gigahertz
core
bits
CPU is placed
under the fan
Memory
Motherboard
FIGURE 1.2 The motherboard connects all parts of computer together.
byte
encoding scheme

1.2 What Is a Computer? 5
A computer’s storage capacity is measured in bytes and multiples of the byte, as follows:
■ A kilobyte (KB) is about 1,000 bytes.
■ A megabyte (MB) is about 1 million bytes.
■ A gigabyte (GB) is about 1 billion bytes.
■ A terabyte (TB) is about 1 trillion bytes.
A typical one-page word document might take 20 KB. So 1 MB can store 50 pages of doc-
uments and 1 GB can store 50000 pages of documents. A typical two-hour high-resolution
movie might take 8 GB. So it would require 160 GB to store 20 movies.
1.2.3 Memory
A computer’s memory consists of an ordered sequence of bytes for storing programs as well
as data that the program is working with. You can think of memory as the computer’s work
area for executing a program. A program and its data must be moved into the computer’s
memory before they can be executed by the CPU.
Every byte in the memory has a unique address, as shown in Figure 1.3. The address is
used to locate the byte for storing and retrieving the data. Since the bytes in the memory can
be accessed in any order, the memory is also referred to as random-access memory (RAM).
kilobyte (KB)
megabyte (MB)
gigabyte (GB)
terabyte (TB)
memory
unique address
RAM
01000011
01110010
01100101
01110111
00000011
Encoding for character ‘C’
Encoding for character ‘r’
Encoding for character ‘e’
Encoding for character ‘w’
Encoding for number 3
2000
2001
2002
2003
2004
Memory address Memory content
FIGURE 1.3 Memory stores data and program instructions in uniquely addressed memory
locations. Each memory location can store one byte of data.
Today’s personal computers usually have at least 1 gigabyte of RAM, but they more com-
monly have 2 to 4 GB installed. Generally speaking, the more RAM a computer has, the faster
it can operate, but there are limits to this simple rule of thumb.
A memory byte is never empty, but its initial content may be meaningless to your program.
The current content of a memory byte is lost whenever new information is placed in it.
Like the CPU, memory is built on silicon semiconductor chips that have millions of
transistors embedded on their surface. Compared to CPU chips, memory chips are less com-
plicated, slower, and less expensive.
1.2.4 Storage Devices
A computer’s memory is a volatile form of data storage: any information that hasn’t been stored
in memory (that is, saved) is lost when the system’s power is turned off. Programs and data are
permanently stored on storage devices and are moved, when the computer actually uses them, to
memory, which operates at much faster speeds than permanent storage devices can.
storage device

6 Chapter 1 Introduction to Computers, Programs, and Python
There are three main types of storage devices:
■ Magnetic disk drives
■ Optical disc drives (CD and DVD)
■ USB flash drives
Drives are devices for operating a medium, such as disks and CDs. A storage medium physi-
cally stores data or program instructions. The drive reads data from the medium and/or writes
data onto the medium.
Disks
A computer usually has at least one hard disk drive (Figure 1.4). Hard disks are used for per-
manently storing data and programs. Newer computers have hard disks that can store from 200
to 800 gigabytes of data. Hard disk drives are usually encased inside the computer, but remov-
able hard disks are also available.
drive
hard disk
CD-R
CD-RW
DVD
FIGURE 1.4 A hard disk is a device for permanently storing programs and data.
CDs and DVDs
CD stands for compact disc. There are two types of CD drives: CD-R and CD-RW. A CD-R
is for read-only permanent storage; the user cannot modify its contents once they are
recorded. A CD-RW can be used like a hard disk; that is, you can write data onto the disc,
and then overwrite that data with new data. A single CD can hold up to 700 MB. Most new
PCs are equipped with a CD-RW drive that can work with both CD-R and CD-RW discs.
DVD stands for digital versatile disc or digital video disc. DVDs and CDs look alike, and you
can use either to store data. A DVD can hold more information than a CD; a standard DVD’s
storage capacity is 4.7 GB. Like CDs, there are two types of DVDs: DVD-R (read-only) and
DVD-RW (rewritable).

1.2 What Is a Computer? 7
USB Flash Drives
Universal serial bus (USB) connectors allow the user to attach many kinds of peripheral devices
to the computer. You can use a USB to connect a printer, digital camera, mouse, external hard
disk drive, and other devices to the computer.
A USB flash drive is a device for storing and transporting data. A flash drive is small—
about the size of a pack of gum, as shown in Figure 1.5. It acts like a portable hard drive that
can be plugged into your computer’s USB port. USB flash drives are currently available with
up to 256 GB storage capacity.
FIGURE 1.5 USB flash drives are popular portable devices for storing data.
Function
Modifier
Numeric Keypad
Page Up
Insert
Delete
Page Down
Arrows
FIGURE 1.6 A computer keyboard consists of the keys for sending input to a computer.
1.2.5 Input and Output Devices
Input and output devices let the user communicate with the computer. The most common input
devices are keyboards and mice. The most common output devices are monitors and printers.
The Keyboard
A keyboard is a device for entering input. A typical keyboard is shown in Figure 1.6. Compact
keyboards are available without a numeric keypad.
Function keys are located across the top of the keyboard and are prefaced with the letter F.
Their functions depend on the software currently being used.
function key

8 Chapter 1 Introduction to Computers, Programs, and Python
A modifier key is a special key (such as the Shift, Alt, and Ctrl keys) that modifies the
normal action of another key when the two are pressed simultaneously.
The numeric keypad, located on the right side of most keyboards, is a separate set of keys
styled like a calculator to use for entering numbers quickly.
Arrow keys, located between the main keypad and the numeric keypad, are used to move
the mouse pointer up, down, left, and right on the screen in many kinds of programs.
The Insert, Delete, Page Up, and Page Down keys are used in word processing and other
programs for inserting text and objects, deleting text and objects, and moving up or down
through a document one screen at a time.
The Mouse
A mouse is a pointing device. It is used to move a graphical pointer (usually in the shape of an
arrow) called a cursor around the screen or to click on-screen objects (such as a button) to
trigger them to perform an action.
The Monitor
The monitor displays information (text and graphics). The screen resolution and dot pitch
determine the quality of the display.
The screen resolution specifies the number of pixels in horizontal and vertical dimensions
of the display device. Pixels (short for “picture elements”) are tiny dots that form an image on
the screen. A common resolution for a 17-inch screen, for example, is 1024 pixels wide and
768 pixels high. The resolution can be set manually. The higher the resolution, the sharper and
clearer the image is.
The dot pitch is the amount of space between pixels, measured in millimeters. The smaller
the dot pitch, the sharper the display.
1.2.6 Communication Devices
Computers can be networked through communication devices, such as a dial-up modem
(modulator/demodulator), a DSL or cable modem, a wired network interface card, or a wire-
less adapter.
■ A dial-up modem uses a phone line and can transfer data at a speed up to 56,000 bps
(bits per second).
■ A digital subscriber line (DSL) connection also uses a standard phone line, but it can
transfer data 20 times faster than a standard dial-up modem.
■ A cable modem uses the cable TV line maintained by the cable company and is
generally faster than DSL.
■ A network interface card (NIC) is a device that connects a computer to a local area
network (LAN), as shown in Figure 1.7. LANs are commonly used in universities,
businesses, and government agencies. A high-speed NIC called 1000BaseT can
transfer data at 1,000 million bits per second (mbps).
■ Wireless networking is now extremely popular in homes, businesses, and schools.
Every laptop computer sold today is equipped with a wireless adapter that enables
the computer to connect to a local area network and the Internet.
Note
Answers to checkpoint questions are on the Companion Website.
1.1 What are hardware and software?
1.2 List five major hardware components of a computer.
1.3 What does the acronym “CPU” stand for?
modifier key
numeric keypad
arrow keys
Insert key
Delete key
Page Up key
Page Down key
screen resolution
pixels
dot pitch
modem
digital subscriber line (DSL)
cable modem
network interface card (NIC)
local area network (LAN)
million bits per second
(mbps)
✓Point✓Check

1.3 Programming Languages 9
1.4 What unit is used to measure CPU speed?
1.5 What is a bit? What is a byte?
1.6 What is memory for? What does RAM stand for? Why is memory called RAM?
1.7 What unit is used to measure memory size?
1.8 What unit is used to measure disk size?
1.9 What is the primary difference between memory and a storage device?
1.3 Programming Languages
Computer programs, known as software, are instructions that tell a computer what to do.
Computers do not understand human languages, so programs must be written in a language a
computer can use. There are hundreds of programming languages, and they were developed to
make the programming process easier for people. However, all programs must be converted
into a language the computer can understand.
1.3.1 Machine Language
A computer’s native language, which differs among different types of computers, is its machine
language—a set of built-in primitive instructions. These instructions are in the form of binary
code, so if you want to give a computer an instruction in its native language, you have to enter
Network Interface Card
LAN
FIGURE 1.7 A local area network connects computers in close proximity to each other.
machine language
Key
Point

10 Chapter 1 Introduction to Computers, Programs, and Python
the instruction as binary code. For example, to add two numbers, you might have to write an
instruction in binary code, like this:
1101101010011010
1.3.2 Assembly Language
Programming in machine language is a tedious process. Moreover, programs written in
machine language are very difficult to read and modify. For this reason, assembly language
was created in the early days of computing as an alternative to machine languages. Assembly
language uses a short descriptive word, known as mnemonic, to represent each of the machine-
language instructions. For example, the mnemonic add typically means to add numbers and
sub means to subtract numbers. To add the numbers 2 and 3 and get the result, you might write
an instruction in assembly code like this:
add 2, 3, result
Assembly languages were developed to make programming easier. However, because the
computer cannot understand assembly language, another program—called an assembler—is
used to translate assembly-language programs into machine code, as shown in Figure 1.8.
assembly language
assembler
Assembly Source File
…
add 2, 3, result
…
Machine-Code File
…
1101101010011010
…
Assembler
FIGURE 1.8 An assembler translates assembly-language instructions into machine code.
Writing code in assembly language is easier than in machine language. However, it is still
tedious to write code in assembly language. An instruction in assembly language essentially
corresponds to an instruction in machine code. Writing in assembly requires that you know how
the CPU works. Assembly language is referred to as a low-level language, because assembly
language is close in nature to machine language and is machine dependent.
1.3.3 High-Level Language
In the 1950s, a new generation of programming languages known as high-level languages
emerged. They are platform-independent, which means that you can write a program in a high-
level language and run it in different types of machines. High-level languages are English-like
and easy to learn and use. The instructions in a high-level programming language are called
statements. Here, for example, is a high-level language statement that computes the area of a
circle with a radius of 5:
area = 5 * 5 * 3.1415
There are many high-level programming languages, and each was designed for a specific
purpose. Table 1.1 lists some popular ones.
A program written in a high-level language is called a source program or source code.
Because a computer cannot understand a source program, a source program must be translated
into machine code for execution. The translation can be done using another programming tool
called an interpreter or a compiler.
■ An interpreter reads one statement from the source code, translates it to the machine
code or virtual machine code, and then executes it right away, as shown in Figure 1.9a.
low-level language
high-level language
source program
source code
interpreter
compiler
statement

1.3 Programming Languages 11
TABLE 1.1 Popular High-Level Programming Languages
Language Description
Ada Named for Ada Lovelace, who worked on mechanical general-purpose computers. The Ada language was
developed for the Department of Defense and is used mainly in defense projects.
BASIC Beginner’s All-purpose Symbolic Instruction Code. It was designed to be learned and used easily by beginners.
C Developed at Bell Laboratories. C combines the power of an assembly language with the ease of use and portability
of a high-level language.
C++ C++ is an object-oriented language, based on C.
C# Pronounced “C Sharp.” It is a hybrid of Java and C++ and was developed by Microsoft.
COBOL COmmon Business Oriented Language. Used for business applications.
FORTRAN FORmula TRANslation. Popular for scientific and mathematical applications.
Java Developed by Sun Microsystems, now part of Oracle. It is widely used for developing platform-independent
Internet applications.
Pascal Named for Blaise Pascal, who pioneered calculating machines in the seventeenth century. It is a simple, structured,
general-purpose language primarily for teaching programming.
Python A simple general-purpose scripting language good for writing short programs.
Visual Basic Visual Basic was developed by Microsoft and it enables the programmers to rapidly develop Windows-based
applications.
Machine-Code File
…
0101100011011100
1111100011000100
…
High-Level Source File
…
area = 5 * 5 * 3.1415;
…
(b)
Compiler Executor
High-Level Source File
…
area = 5 * 5 * 3.1415;
…
(a)
Interpreter
Output
Output
FIGURE 1.9 (a) An interpreter translates and executes a program one statement at a time. (b) A compiler translates the entire
source program into a machine-language file for execution.
Note that a statement from the source code may be translated into several machine
instructions.
■ A compiler translates the entire source code into a machine-code file, and the
machine code file is then executed, as shown in Figure 1.9b.
Python code is executed using an interpreter. Most other programming languages are
processed using a compiler.
1.10 What language does the CPU understand?
1.11 What is an assembly language? ✓Point✓Check

12 Chapter 1 Introduction to Computers, Programs, and Python
operating system (OS)
User
Application Programs
Operating System
Hardware
FIGURE 1.10 Users and applications access the computer’s hardware via the operating system.
1.12 What is an assembler?
1.13 What is a high-level programming language?
1.14 What is a source program?
1.15 What is an interpreter?
1.16 What is a compiler?
1.17 What is the difference between an interpreted language and a compiled language?
1.4 Operating Systems
The operating system (OS) is the most important program that runs on a computer.
The OS manages and controls a computer’s activities.
The popular operating systems for general-purpose computers are Microsoft Windows, Mac
OS, and Linux. Application programs, such as a Web browser or a word processor, cannot run
unless an operating system is installed and running on the computer. Figure 1.10 shows the
interrelationship of hardware, operating system, application software, and the user.
The major tasks of an operating system are:
■ Controlling and monitoring system activities
■ Allocating and assigning system resources
■ Scheduling operations
1.4.1 Controlling and Monitoring System Activities
Operating systems perform basic tasks, such as recognizing input from the keyboard, sending
output to the monitor, keeping track of files and folders on storage devices, and controlling
peripheral devices, such as disk drives and printers. An operating system must also ensure that
different programs and users working at the same time do not interfere with each other. In
addition, the OS is responsible for security, ensuring that unauthorized users and programs do
not access the system.
1.4.2 Allocating and Assigning System Resources
The operating system is responsible for determining what computer resources a program
needs (such as CPU time, memory space, disks, input and output devices) and for allocating
and assigning them to run the program.
Key
Point

1.5 The History of Python 13
1.4.3 Scheduling Operations
The OS is responsible for scheduling programs’ activities to make efficient use of system
resources. Many of today’s operating systems support such techniques as multiprogramming,
multithreading, and multiprocessing to increase system performance.
Multiprogramming allows multiple programs to run simultaneously by sharing the same
CPU. The CPU is much faster than the computer’s other components. As a result, it is idle
most of the time—for example, while waiting for data to be transferred from a disk or waiting
for other system resources to respond. A multiprogramming OS takes advantage of this situa-
tion by allowing multiple programs to use the CPU when it would otherwise be idle. For
example, multiprogramming enables you to use a word processor to edit a file at the same
time as your Web browser is downloading a file.
Multithreading allows a single program to execute multiple tasks at the same time. For
instance, a word-processing program allows users to simultaneously edit text and save it to a
disk. In this example, editing and saving are two tasks within the same application. These two
tasks may run concurrently.
Multiprocessing, or parallel processing, uses two or more processors together to per-
form subtasks concurrently and then combine solutions of the subtasks to obtain a solution
for the entire task. It is like a surgical operation where several doctors work together on one
patient.
1.18 What is an operating system? List some popular operating systems.
1.19 What are the major responsibilities of an operating system?
1.20 What are multiprogramming, multithreading, and multiprocessing?
1.5 The History of Python
Python is a general-purpose, interpreted, object-oriented programming language.
Python was created by Guido van Rossum in the Netherlands in 1990 and was named after
the popular British comedy troupe Monty Python’s Flying Circus. Van Rossum developed
Python as a hobby, and Python has become a popular programming language widely used
in industry and academia due to its simple, concise, and intuitive syntax and extensive
library.
Python is a general-purpose programming language. That means you can use Python to
write code for any programming task. Python is now used in the Google search engine, in
mission-critical projects at NASA, and in transaction processing at the New York Stock
Exchange.
Python is interpreted, which means that Python code is translated and executed by an inter-
preter, one statement at a time, as described earlier in the chapter.
Python is an object-oriented programming (OOP) language. Data in Python are objects
created from classes. A class is essentially a type or category that defines objects of the same
kind with properties and methods for manipulating objects. Object-oriented programming is a
powerful tool for developing reusable software. Object-oriented programming in Python will
be covered in detail starting in Chapter 7.
Python is now being developed and maintained by a large team of volunteers and is avail-
able for free from the Python Software Foundation. Two versions of Python are currently
coexistent: Python 2 and Python 3. The programs written in Python 3 will not run in Python
2. Python 3 is a newer version, but it is not backward-compatible with Python 2. This means
that if you write a program using the Python 2 syntax, it may not work with a Python 3 inter-
preter. Python provides a tool that automatically converts code written in Python 2 into syntax
Python 3 can use. Python 2 will eventually be replaced by Python 3. This book teaches pro-
gramming using Python 3.
multiprogramming
multithreading
multiprocessing
general-purpose
programming language
interpreted
object-oriented programming
(OOP)
Python 2 vs. Python 3
✓Point✓Check
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Point

14 Chapter 1 Introduction to Computers, Programs, and Python
1.21 Python is interpreted. What does that mean?
1.22 Can a program written in Python 2 run in Python 3?
1.23 Can a program written using Python 3 run in Python 2?
1.6 Getting Started with Python
A Python program is executed from the Python interpreter.
Let’s get started by writing a simple Python program that displays the messages Welcome
to Python and Python is fun on the console. The word console is an old computer
term that refers to the text entry and display device of a computer. Console input means
to receive input from the keyboard and console output means to display output to the
monitor.
Note
You can run Python on the Windows, UNIX, and Mac operating systems. For informa-
tion on installing Python, see Supplement I.B, Installing and Using Python, on the
Companion Website.
1.6.1 Launching Python
Assume you have Python installed on the Windows OS. You can start Python in a com-
mand window by typing python at the command prompt, as shown in Figure 1.11, or by
using IDLE, as shown in Figure 1.12. IDLE (Interactive DeveLopment Environment) is an
integrated development environment (IDE) for Python. You can create, open, save, edit,
and run Python programs in IDLE. Both the command-line Python interpreter and IDLE
are available after Python is installed on your machine. Note that Python (command line)
console
install Python
IDLE
FIGURE 1.11 You can launch Python from the command window.
FIGURE 1.12 You can use Python from IDLE.
Key
Point
console input
console output
✓Point✓Check
VideoNote
Start with Python

1.6 Getting Started with Python 15
and IDLE can also be accessed directly from the Windows Start button by searching for
Python (command line) or IDLE (Python GUI) on Windows 7 or Vista, as shown in
Figure 1.13.
After Python starts, you will see the symbol >>>. This is the Python statement prompt, and
it is where you can enter a Python statement.
Note
Type the commands exactly as they are written in this text. Formatting and other rules
will be discussed later in this chapter.
Now, type print(“Welcome to Python”) and press the Enter key. The string Welcome
to Python appears on the console, as shown in Figure 1.11. String is a programming term
meaning a sequence of characters.
Note
Note that Python requires double or single quotation marks around strings to delineate
them from other code. As you can see in the output, Python doesn’t display those
quotation marks.
The print statement is one of Python’s built-in functions that can be used to display a
string on the console. A function performs actions. In the case of the print function, it dis-
plays a message to the console.
Note
In programming terminology, when you use a function, you are said to be “invoking a
function” or “calling a function.”
Next, type print(“Python is fun”) and press the Enter key. The string Python is
fun appears on the console, as shown in Figure 1.11. You can enter additional statements at
the statement prompt >>>.
Note
To exit Python, press CTRL+Z and then the Enter key.
Python IDLE
Python command line
Enter Python here
FIGURE 1.13 You can launch the Python IDLE and command line from the Start button.
Python statement prompt >>>
string
function
invoking a function
calling a function

16 Chapter 1 Introduction to Computers, Programs, and Python
1.6.2 Creating Python Source Code Files
Entering Python statements at the statement prompt >>> is convenient, but the statements are
not saved. To save statements for later use, you can create a text file to store the statements
and use the following command to execute the statements in the file:
python filename.py
The text file can be created using a text editor such as Notepad. The text file, filename, is
called a Python source file or script file, or module. By convention, Python files are named
with the extension .py.
Running a Python program from a script file is known as running Python in script mode.
Typing a statement at the statement prompt >>> and executing it is called running Python in
interactive mode.
Note
Besides developing and running Python programs from the command window, you can
create, save, modify, and run a Python script from IDLE. For information on using IDLE,
see Supplement I.C on the Companion Website. Your instructor may also ask you to use
Eclipse. Eclipse is a popular interactive development environment (IDE) used to develop
programs quickly. Editing, running, debugging, and online help are integrated in one
graphical user interface. If you want to develop Python programs using Eclipse, see
Supplement I.D, on the Companion Website.
Listing 1.1 shows you a Python program that displays the messages Welcome to Python
and Python is fun.
LISTING 1.1 Welcome.py
1 # Display two messages
2 print(“Welcome to Python”)
3 print(“Python is fun”)
In this text, line numbers are displayed for reference purposes; they are not part of the pro-
gram. So, don’t type line numbers in your program.
Suppose the statements are saved in a file named Welcome.py. To run the program, enter
python Welcome.py at the command prompt, as shown in Figure 1.14.
source file
script file
module
.py file
script mode
interactive mode
Python on Eclipse
comment
print a message
FIGURE 1.14 You can run a Python script file from a command window.
In Listing 1.1, line 1 is a comment that documents what the program is and how it is con-
structed. Comments help programmers communicate and understand a program. They are not
programming statements and thus are ignored by the interpreter. In Python, comments are
preceded by a pound sign (#) on a line, called a line comment, or enclosed between three con-
secutive single quotation marks (”’) on one or several lines, called a paragraph comment.
line numbers
execute the program
comment
line comment
paragraph comment

1.6 Getting Started with Python 17
When the Python interpreter sees #, it ignores all text after # on the same line. When it sees
”’, it scans for the next ”’ and ignores any text between the triple quotation marks. Here
are examples of comments:
# This program displays Welcome to Python
”’ This program displays Welcome to Python and
Python is fun
”’
Indentation matters in Python. Note that the statements are entered from the first column in
the new line. The Python interpreter will report an error if the program is typed as follows:
# Display two messages
print(“Welcome to Python”)
print(“Python is fun”)
Don’t put any punctuation at the end of a statement. For example, the Python interpreter
will report errors for the following code:
# Display two messages
print(“Welcome to Python”).
print(“Python is fun”),
Python programs are case sensitive. It would be wrong, for example, to replace print in
the program with Print.
You have seen several special characters (#, “, ()) in the program. They are used in
almost every program. Table 1.2 summarizes their uses.
TABLE 1.2 Special Characters
Character Name Description
() Opening and closing parentheses Used with functions.
# Pound sign Precedes a comment line.
” ” Opening and closing quotation marks Encloses a string (i.e., sequence of characters).
”’ ”’ Paragraph comments Encloses a paragraph comment.
The program in Listing 1.1 displays two messages. Once you understand the program, it is
easy to extend it to display more messages. For example, you can rewrite the program to dis-
play three messages, as shown in Listing 1.2.
LISTING 1.2 WelcomeWithThreeMessages.py
1 # Display three messages
2 print(“Welcome to Python”)
3 print(“Python is fun”)
4 print(“Problem Driven”)
Welcome to Python
Python is fun
Problem Driven
indentation
case sensitive
special characters
comment
print statement
BAD
CO
DE
BAD
CO
DE

18 Chapter 1 Introduction to Computers, Programs, and Python
1.6.3 Using Python to Perform Mathematical Computations
Python programs can perform all sorts of mathematical computations and display the result.
To display the addition, subtraction, multiplication, and division of two numbers, x and y, use
the following code:
print(x + y)
print(x – y)
print(x * y)
print(x / y)
Listing 1.3 shows an example of a program that evaluates and prints its result.
LISTING 1.3 ComputeExpression.py
1 # Compute expression
2 print((10.5 + 2 * 3) / (45 – 3.5))
10.5 + 2 * 3
45 – 3.5
comment
compute expression
0.397590361446
As you can see, it is a straightforward process to translate an arithmetic expression to a
Python expression. We will discuss Python expressions further in Chapter 2.
1.24 You can run Python in two modes. Explain these two modes.
1.25 Is Python case sensitive?
1.26 What is the Python source filename extension by convention?
1.27 What is the command to run a Python source file?
1.28 What is a comment? How do you denote a comment line and a comment paragraph?
1.29 What is the statement to display the message Hello world on the console?
1.30 Identify and fix the errors in the following code:
1 # Display two messages
2 print(“Welcome to Python”)
3 print(“Python is fun”).
1.31 Show the output of the following code:
print(“3.5 * 4 / 2 – 2.5 is”)
print(3.5 * 4 / 2 – 2.5)
1.7 Programming Style and Documentation
Good programming style and proper documentation make a program easy to read and
prevents errors.
Programming style deals with what programs look like. When you create programs with a
professional programming style, they not only execute properly but are easy for people to
read and understand. This is very important if other programmers will access or modify your
programs.
Documentation is the body of explanatory remarks and comments pertaining to a program.
These remarks and comments explain various parts of the program and help others understand
its structure and function. As you saw earlier in the chapter, remarks and comments are
programming style
documentation
✓Point✓Check
Key
Point

1.8 Programming Errors 19
embedded within the program itself; Python’s interpreter simply ignores them when the pro-
gram is executed.
Programming style and documentation are as important as coding. Here are a few guidelines.
1.7.1 Appropriate Comments and Comment Styles
Include a summary comment at the beginning of the program to explain what the program
does, its key features, and any unique techniques it uses. In a long program, you should also
include comments that introduce each major step and explain anything that is difficult to read.
It is important to make comments concise so that they do not crowd the program or make it
difficult to read.
1.7.2 Proper Spacing
A consistent spacing style makes programs clear and easy to read, debug (find and fix errors),
and maintain.
A single space should be added on both sides of an operator, as shown in the following
statement:
More detailed guidelines can be found in Supplement I.F, Python Coding Style Guidelines,
on the Companion Website.
1.8 Programming Errors
Programming errors can be categorized into three types: syntax errors, runtime errors,
and logic errors.
1.8.1 Syntax Errors
The most common error you will encounter are syntax errors. Like any programming lan-
guage, Python has its own syntax, and you need to write code that obeys the syntax rules. If
your program violates the rules—for example, if a quotation mark is missing or a word is
misspelled—Python will report syntax errors.
Syntax errors result from errors in code construction, such as mistyping a statement, incor-
rect indentation, omitting some necessary punctuation, or using an opening parenthesis with-
out a corresponding closing parenthesis. These errors are usually easy to detect, because
Python tells you where they are and what caused them. For example, the following print
statement has a syntax error:
common errors
syntax rules
syntax errors
print(3+4*4) Bad style
print(3 + 4 * 4) Good style
Key
Point

20 Chapter 1 Introduction to Computers, Programs, and Python
The string Programming is fun should be closed with a closing quotation mark.
Tip
If you don’t know how to correct a syntax error, compare your program closely, charac-
ter by character, with similar examples in the text. In the first few weeks of this course,
you will probably spend a lot of time fixing syntax errors. Soon, you will be familiar with
Python syntax and will be able to fix syntax errors quickly.
1.8.2 Runtime Errors
Runtime errors are errors that cause a program to terminate abnormally. They occur while a
program is running if the Python interpreter detects an operation that is impossible to carry
out. Input mistakes typically cause runtime errors. An input error occurs when the user
enters a value that the program cannot handle. For instance, if the program expects to read in
a number, but instead the user enters a string of text, this causes data-type errors to occur in
the program.
Another common source of runtime errors is division by zero. This happens when the divi-
sor is zero for integer divisions. For example, the expression 1 / 0 in the following statement
would cause a runtime error.
logic errors
Fahrenheit 35 is Celsius degree
-12.555555555555554
You will get Celsius –12.55 degrees, which is wrong. It should be 1.66. To get the correct
result, you need to use 5 / 9 * (35 – 32) rather than 5 / 9 * 35 – 32 in the expression.
That is, you need to add parentheses around (35 – 32) so Python will calculate that expression
first before doing the division.
In Python, syntax errors are actually treated like runtime errors because they are detected
by the interpreter when the program is executed. In general, syntax and runtime errors are
easy to find and easy to correct, because Python gives indications as to where the errors
came from and why they are wrong. Finding logic errors, on the other hand, can be very
challenging.
fix syntax errors
runtime errors
input errors
1.8.3 Logic Errors
Logic errors occur when a program does not perform the way it was intended to. Errors of this
kind occur for many different reasons. For example, suppose you wrote the program in
Listing 1.4 to convert a temperature (35 degrees) from Fahrenheit to Celsius.
LISTING 1.4 ShowLogicErrors.py
1 # Convert Fahrenheit to Celsius
2 print(“Fahrenheit 35 is Celsius degree “)
3 print(5 / 9 * 35 – 32)

1.9 Getting Started with Graphics Programming 21
turtle
Tkinter
1.32 What are three kinds of program errors?
1.33 If you forget to put a closing quotation mark on a string, what kind of error will be
raised?
1.34 If your program needs to read data from a file, but the file does not exist, an error
would occur when running this program. What kind of error is this?
1.35 Suppose you write a program for computing the perimeter of a rectangle and you
mistakenly write your program so that it computes the area of a rectangle. What kind
of error is this?
1.9 Getting Started with Graphics Programming
Turtle is Python’s built-in graphics module for drawing lines, circles, and other
shapes, including text. It is easy to learn and simple to use.
Beginners often enjoy learning programming by using graphics. For this reason, we provide a
section on graphics programming at the end of most of the chapters in the first part of the
book. However, these materials are not mandatory. They can be skipped or covered later.
There are many ways to write graphics programs in Python. A simple way to start graphics
programming is to use Python’s built-in turtle module. Later in the book, we will introduce
Tkinter for developing comprehensive graphical user interface applications.
1.9.1 Drawing and Adding Color to a Figure
The following procedure will give you a basic introduction to using the turtle module. Sub-
sequent chapters introduce more features.
1. Launch Python by choosing Python (command line) from the Windows Start button or
by typing python at the command prompt.
2. At the Python statement prompt >>>, type the following command to import the turtle
module. This command imports all functions defined in the turtle module and makes
them available for you to use.
>>> import turtle # Import turtle module
3. Type the following command to show the current location and direction of the turtle, as
shown in Figure 1.15a.
>>> turtle.showturtle()
Graphics programming using the Python Turtle module is like drawing with a pen. The
arrowhead indicates the current position and direction of the pen. turtle is initially
positioned at the center of the window. Here, turtle refers to the object for drawing
graphics (objects will be introduced in Chapter 3).
4. Type the following command to draw a text string:
>>> turtle.write(“Welcome to Python”)
Your window should look like the one shown in Figure 1.15b.
5. Type the following command to move the arrowhead 100 pixels forward to draw a line
in the direction the arrow is pointing:
>>> turtle.forward(100)
Your window should now look like the one shown in Figure 1.15c.
To draw the rest of Figure 1.15, continue with these steps.
VideoNote
Start with Turtle graphics
Key
Point
✓Point✓Check

22 Chapter 1 Introduction to Computers, Programs, and Python
6. Type the following commands to turn the arrowhead right 90 degrees, change the
turtle’s color to red, and move the arrowhead 50 pixels forward to draw a line, as
shown in Figure 1.15d:
>>> turtle.right(90)
>>> turtle.color(“red”)
>>> turtle.forward(50)
7. Now, type the following commands to turn the arrowhead right 90 degrees, set the color to
green, and move the arrowhead 100 pixels forward to draw a line, as shown in Figure 1.15e:
>>> turtle.right(90)
>>> turtle.color(“green”)
>>> turtle.forward(100)
8. Finally, type the following commands to turn the arrowhead right 45 degrees and move
it 80 pixels forward to draw a line, as shown in Figure 1.15f:
>>> turtle.right(45)
>>> turtle.forward(80)
9. You can now close the Turtle Graphics window and exit Python.
1.9.2 Moving the Pen to Any Location
When the Turtle program starts, the arrowhead is at the center of the Python Turtle Graphics
window at the coordinates (0, 0), as shown in Figure 1.16a. You can also use the goto(x, y)
command to move the turtle to any specified point (x, y).
Restart Python and type the following command to move the pen to (0, 50) from (0, 0), as
shown in Figure 1.16b.
>>> import turtle
>>> turtle.goto(0, 50)
(a) (b)
(d) (e) (f)
(c)
FIGURE 1.15 Graphics are dynamically displayed with each statement.

1.9 Getting Started with Graphics Programming 23
(a) (b)
(d) (e)
(c)
(0, 0)
(0, 50)
(50, –50)
Y-axis
X-axis(0, 0)
FIGURE 1.16 (a) The center of the Turtle Graphics window is at the coordinates (0, 0). (b) Move to (0, 50). (c) Move the
pen to (50, –50). (d) Set color to red. (e) Draw a circle using the circle command.
You can also lift the pen up or put it down to control whether to draw a line when the pen
is moved by using the penup() and pendown() commands. For example, the following
commands move the pen to (50, -50), as shown in Figure 1.16c.
>>> turtle.penup()
>>> turtle.goto(50, -50)
>>> turtle.pendown()
You can draw a circle using the circle command. For example, the following commands
set color red (Figure 1.16d) and draw a circle with radius 50 (Figure 1.16e).
>>> turtle.color(“red”)
>>> turtle.circle(50) # Draw a circle with radius 50
1.9.3 Drawing the Olympic Rings Logo
Listing 1.5 shows a program for drawing the Olympics rings logo, as shown in Figure 1.17.
LISTING 1.5 OlympicSymbol.py
1 import turtle
2
3 turtle.color(“blue”)
4 turtle.penup()
5 turtle.goto(-110, -25)
6 turtle.pendown()
7 turtle.circle(45)
8
9 turtle.color(“black”)
draw blue circle
draw black circle

24 Chapter 1 Introduction to Computers, Programs, and Python
10 turtle.penup()
11 turtle.goto(0, -25)
12 turtle.pendown()
13 turtle.circle(45)
14
15 turtle.color(“red”)
16 turtle.penup()
17 turtle.goto(110, -25)
18 turtle.pendown()
19 turtle.circle(45)
20
21 turtle.color(“yellow”)
22 turtle.penup()
23 turtle.goto(-55, -75)
24 turtle.pendown()
25 turtle.circle(45)
26
27 turtle.color(“green”)
28 turtle.penup()
29 turtle.goto(55, -75)
30 turtle.pendown()
31 turtle.circle(45)
32
33 turtle.done()
The program imports the turtle module to use the Turtle Graphics window (line 1). It
moves the pen to (line 5) and draws a blue circle with radius 45 (line 7). Similarly,
it draws a black circle (lines 9–13), a red circle (lines 15–19), a yellow circle (lines 21–25), and
a green circle (lines 27–31).
Line 33 invokes turtle’s done() command, which causes the program to pause until the
user closes the Python Turtle Graphics window. The purpose of this is to give the user time to
view the graphics. Without this line, the graphics window would be closed right after the pro-
gram is finished.
1.36 How do you import the turtle module?
1.37 How do you display text in Turtle?
1.38 How do you move the pen forward?
1.39 How do you set a new color?
1.40 How do you move the pen without drawing anything?
1.41 How do you draw a circle?
1.42 What is the purpose of turtle.done() in line 33 in Listing 1.5?
(-110, -25)
FIGURE 1.17 The program draws the Olympics rings logo.
draw yellow circle
draw green circle
pause
✓Point✓Check
draw red circle

Chapter Summary 25
KEY TERMS
.py file 16
assembler 10
assembly language 10
bit 4
bus 2
byte 4
cable modem 8
calling a function 15
central processing unit (CPU) 3
comment 16
compiler 10
console 14
dot pitch 8
DSL (digital subscriber line) 8
encoding scheme 4
function 15
hardware 2
high-level language 10
IDLE (Interactive DeveLopment
Environment) 14
indentation 17
interactive mode 16
interpreter 10
invoking a function 15
line comment 16
logic error 20
low-level language 10
machine language 9
memory 5
modem 8
module 16
motherboard 3
network interface card (NIC) 8
operating system (OS) 12
pixel 8
program 2
runtime errors 20
screen resolution 8
script file 16
script mode 16
software 2
source code 10
source file 16
source program 10
statement 10
storage device 5
syntax errors 19
syntax rules 19
Note
The above terms are defined in the present chapter. Supplement I.A, Glossary, lists
all the key terms and descriptions in the book, organized by chapters.
CHAPTER SUMMARY
1. A computer is an electronic device that stores and processes data.
2. A computer includes both hardware and software.
3. Hardware is the physical aspect of the computer that can be touched.
4. Computer programs, known as software, are the invisible instructions that control the
hardware and make it perform tasks.
5. Computer programming is the writing of instructions (i.e., code) for computers to
perform.
6. The central processing unit (CPU) is a computer’s brain. It retrieves instructions
from memory and executes them.
7. Computers use zeros and ones because digital devices have two stable electrical
states, off and on, referred to by convention as zero and one.
8. A bit is a binary digit 0 or 1.
Supplement I.A

26 Chapter 1 Introduction to Computers, Programs, and Python
9. A byte is a sequence of 8 bits.
10. A kilobyte is about 1,000 bytes, a megabyte about 1 million bytes, a gigabyte about
1 billion bytes, and a terabyte about 1,000 gigabytes.
11. Memory stores data and program instructions for the CPU to execute.
12. A memory unit is an ordered sequence of bytes.
13. Memory is volatile, because information that hasn’t been saved is lost when the
power is turned off.
14. Programs and data are permanently stored on storage devices and are moved to
memory when the computer actually uses them.
15. The machine language is a set of primitive instructions built into every computer.
16. Assembly language is a low-level programming language in which a mnemonic is
used to represent each machine-language instruction.
17. High-level languages are English-like and easy to learn and program.
18. A program written in a high-level language is called source code.
19. A compiler is a software program that translates the source program into a machine-
language program.
20. The operating system (OS) is a program that manages and controls a computer’s
activities.
21. You can run Python on Windows, UNIX, and Mac.
22. Python is interpreted, meaning that Python translates each statement and processes it
one at a time.
23. You can enter Python statements interactively from the Python statement prompt >>>
or store all your code in one file and execute it using one command.
24. To run a Python source file from the command line, use the python filename.py
command.
25. In Python, comments are preceded by a pound sign (#) on a line, called a line comment,
or enclosed between triple quotation marks (”’ and ”’) on one or several lines,
called a paragraph comment.
26. Python source programs are case sensitive.
27. Programming errors can be categorized into three types: syntax errors, runtime
errors, and logic errors. Syntax and runtime errors cause a program to terminate
abnormally. Logic errors occur when a program does not perform the way it was
intended to.
TEST QUESTIONS
Do test questions for this chapter online at www.cs.armstrong.edu/liang/py/test.html.

www.cs.armstrong.edu/liang/py/test.html

Programming Exercises 27
PROGRAMMING EXERCISES
Note
Solutions to even-numbered exercises in this book are on the Companion Website.
Solutions to all exercises are on the Instructor Resource Website. The level of difficulty
is rated easy (no star), moderate (*), hard (**), or challenging (***).
Section 1.6
1.1 (Display three different messages) Write a program that displays Welcome to
Python, Welcome to Computer Science, and Programming is fun.
1.2 (Display the same message five times) Write a program that displays Welcome to
Python five times.
*1.3 (Display a pattern) Write a program that displays the following pattern:
FFFFFFF U U NN NN
FF U U NNN NN
FFFFFFF U U NN N NN
FF U U NN N NN
FF UUU NN NNN
1.4 (Print a table) Write a program that displays the following table:
a a^2 a^3
1 1 1
2 4 8
3 9 27
4 16 64
1.5 (Compute expressions) Write a program that displays the result of
1.6 (Summation of a series) Write a program that displays the result of
1.7 (Approximate ) can be computed using the following formula:
Write a program that displays the result of
and
1.8 (Area and perimeter of a circle) Write a program that displays the area and
perimeter of a circle that has a radius of 5.5 using the following formulas:
perimeter = 2 * radius * p
area = radius * radius * p
4 * ¢1 – 1
3
+
1
5
–
1
7
+
1
9
–
1
11
+
1
13
–
1
15
≤ .
4 * ¢1 – 1
3
+
1
5
–
1
7
+
1
9
–
1
11
≤ .
p = 4 * ¢1 – 1
3
+
1
5
–
1
7
+
1
9
–
1
11
+ c ≤
pp
3 + 4 + 5 + 6 + 7 + 8 + 9.
1 + 2 +
9.5 * 4.5 – 2.5 * 3
45.5 – 3.5
level of difficulty

28 Chapter 1 Introduction to Computers, Programs, and Python
1.9 (Area and perimeter of a rectangle) Write a program that displays the area and
perimeter of a rectangle with the width of 4.5 and height of 7.9 using the follow-
ing formula:
1.10 (Average speed) Assume a runner runs 14 kilometers in 45 minutes and 30 sec-
onds. Write a program that displays the average speed in miles per hour. (Note that
1 mile is 1.6 kilometers.)
*1.11 (Population projection) The US Census Bureau projects population based on the
following assumptions:
One birth every 7 seconds
One death every 13 seconds
One new immigrant every 45 seconds
Write a program to display the population for each of the next five years. Assume the
current population is 312032486 and one year has 365 days. Hint: in Python, you
can use integer division operator // to perform division. The result is an integer. For
example, 5 // 4 is 1 (not 1.25) and 10 // 4 is 2 (not 2.5).
Section 1.9
1.12 (Turtle: draw four squares) Write a program that draws four squares in the center
of the screen, as shown in Figure 1.18a.
area = width * height
(a) (b) (c) (d)
FIGURE 1.18 Four squares are drawn in (a), a cross is drawn in (b), a triangle is drawn in (c), and two triangles are drawn
in (d).
1.13 (Turtle: draw a cross) Write a program that draws a cross as shown in Figure 1.18b.
1.14 (Turtle: draw a triangle) Write a program that draws a triangle as shown in
Figure 1.18c.
1.15 (Turtle: draw two triangles) Write a program that draws two triangles as shown in
Figure 1.18d.
1.16 (Turtle: draw four circles) Write a program that draws four circles in the center of
the screen, as shown in Figure 1.19a.
1.17 (Turtle: draw a line) Write a program that draws a red line connecting two points
(-39, 48) and (50, -50) and displays the coordinates of the two points, as shown
in Figure 1.19b.
**1.18 (Turtle: draw a star) Write a program that draws a star, as shown in Figure 1.19c.
(Hint: The inner angle of each point in the star is 36 degrees.)

Programming Exercises 29
1.20 (Turtle: display a rectanguloid) Write a program that displays a rectanguloid, as
shown in Figure 1.20b.
*1.21 (Turtle: display a clock) Write a program that displays a clock to show the time
9:15:00, as shown in Figure 1.20c.
(a) (b) (c)
FIGURE 1.20 (a) The program displays a polygon. (b) The program displays a rectanguloid. (c) The program displays a
clock for the time.
(a) (c)(b)
FIGURE 1.19 Four circles are drawn in (a), a line is drawn in (b), and a star is drawn in (c).
1.19 (Turtle: draw a polygon) Write a program that draws a polygon that connects the
points (40, -69.28), (-40, -69.28), (-80, -9.8), (-40, 69), (40, 69), and (80,
0) in this order, as shown in Figure 1.20a.

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ELEMENTARY
PROGRAMMING
Objectives
■ To write programs that perform simple computations (§2.2).
■ To obtain input from a program’s user by using the input function (§2.3).
■ To use identifiers to name elements such as variables and functions (§2.4).
■ To assign data to variables (§2.5).
■ To perform simultaneous assignment (§2.6).
■ To define named constants (§2.7).
■ To use the operators +, -, *, /, //, %, and ** (§2.8).
■ To write and evaluate numeric expressions (§2.9).
■ To use augmented assignment operators to simplify coding (§2.10).
■ To perform numeric type conversion and rounding with
the int and round functions (§2.11).
■ To obtain the current system time by using time.time() (§2.12).
■ To describe the software development process and apply it to develop
a loan payment program (§2.13).
■ To compute and display the distance between two points in graphics (§2.14).
CHAPTER
2

32 Chapter 2 Elementary Programming
2.1 Introduction
The focus of this chapter is on learning elementary programming techniques to solve
problems.
In Chapter 1 you learned how to create and run very basic Python programs. Now you will
learn how to solve problems by writing programs. Through these problems, you will learn
fundamental programming techniques, such as the use of variables, operators, expressions,
and input and output.
Suppose, for example, that you need to take out a student loan. Given the loan amount,
loan term, and annual interest rate, can you write a program to compute the monthly payment
and total payment? This chapter shows you how to write programs like this. Along the way,
you learn the basic steps that go into analyzing a problem, designing a solution, and imple-
menting the solution by creating a program.
2.2 Writing a Simple Program
Writing a program involves designing a strategy for solving the problem and then
using a programming language to implement that strategy.
Let’s first consider the simple problem of computing the area of a circle. How do we write a
program for solving this problem?
Writing a program involves designing algorithms and then translating them into program-
ming instructions, or code. When you code—that is, when you write a program—you translate
an algorithm into a program. An algorithm describes how a problem is solved by listing the
actions that need to be taken and the order of their execution. Algorithms can help the
programmer plan a program before writing it in a programming language. Algorithms can be
described in natural languages or in pseudocode (natural language mixed with some program-
ming code). The algorithm for calculating the area of a circle can be described as follows:
1. Get the circle’s radius from the user.
2. Compute the area by applying the following formula:
3. Display the result.
Tip
It’s always good practice to outline your program (or its underlying problem) in the form
of an algorithm before you begin coding.
In this problem, the program needs to read the radius, which the program’s user enters
from the keyboard. This raises two important issues:
■ Reading the radius.
■ Storing the radius in the program.
Let’s address the second issue first. The value for the radius is stored in the computer’s
memory. In order to access it, the program needs to use a variable. A variable is a name
that references a value stored in the computer’s memory. Rather than using x and y as
variable names, choose descriptive names: in this case, for example, you can use the name
radius for the variable that references a value for radius and area for the variable that
references a value for area.
The first step is to prompt the user to designate the circle’s radius. You will learn how to
prompt the user for information shortly. For now, to learn how variables work, you can assign
a fixed value to radius in the program as you write the code.
area = radius * radius * p
problem
algorithm
pseudocode
variable
descriptive names
Key
Point
Key
Point

line# radius area
2 20
5 1256.636
2.2 Writing a Simple Program 33
The second step is to compute area by assigning the result of the expression radius *
radius * 3.14159 to area.
In the final step, the program will display the value of area on the console by using
Python’s print function.
The complete program is shown in Listing 2.1.
LISTING 2.1 ComputeArea.py
1 # Assign a value to radius
2 radius = 20 # radius is now 20 radius 20
3
4 # Compute area
5 area = radius * radius * 3.14159 area 1256.636
6
7 # Display results
8 print(“The area for the circle of radius”, radius, “is”, area) display result
The area for the circle of radius 20 is 1256.636
Variables such as radius and area reference values stored in memory. Every variable has
a name that refers to a value. You can assign a value to a variable using the syntax as shown
in line 2.
radius = 20
This statement assigns 20 to the variable radius. So now radius references the value
20. The statement in line 5
area = radius * radius * 3.14159
uses the value in radius to compute the expression and assigns the result into the variable
area. The following table shows the value for radius and area as the program is executed.
Each row in the table shows the values of variables after the statement in the corresponding
line in the program is executed. This method of reviewing how a program works is called
tracing a program. Tracing programs are helpful for understanding how programs work, and
they are useful tools for finding errors in programs.
If you have programmed in other languages, such as Java, you know you have to declare a
variable with a data type to specify what type of values are being used, such as integers or text
characters. You don’t do this in Python, however, because Python automatically figures out
the data type according to the value assigned to the variable.
The statement in line 8 displays four items on the console. You can display any number of
items in a print statement using the following syntax:
print(item1, item2, …, itemk)
assign value
trace a program
data type
print(item1, …)

34 Chapter 2 Elementary Programming
If an item is a number, the number is automatically converted to a string for displaying.
2.1 Show the printout of the following code:
width = 5.5
height = 2
print(“area is”, width * height)
2.2 Translate the following algorithm into Python code:
■ Step 1: Use a variable named miles with initial value 100.
■ Step 2: Multiply miles by 1.609 and assign it to a variable named kilometers.
■ Step 3: Display the value of kilometers.
What is kilometers after Step 3?
2.3 Reading Input from the Console
Reading input from the console enables the program to accept input from the user.
In Listing 2.1, a radius is set in the source code. To use a different radius, you have to modify
the source code. You can use the input function to ask the user to input a value for the radius.
The following statement prompts the user to enter a value, and then it assigns the value to the
variable:
variable = input(“Enter a value: “)
The value entered is a string. You can use the function eval to evaluate and convert it to a
numeric value. For example, eval(“34.5”) returns 34.5, eval(“345”) returns 345,
eval(“3 + 4”) returns 7, and eval(“51 + (54 * (3 + 2))”) returns 321.
Listing 2.2 rewrites Listing 2.1 to prompt the user to enter a radius.
LISTING 2.2 ComputeAreaWithConsoleInput.py
1 # Prompt the user to enter a radius
2 radius =
3
4 # Compute area
5 area = radius * radius * 3.14159
6
7 # Display results
8 print(“The area for the circle of radius”, radius, “is”, area)
eval(input(“Enter a value for radius: “))
eval function
input radius
compute area
display result
Enter a value for radius:
The area for the circle of radius 2.5 is 19.6349375
2.5
Enter a value for radius:
The area for the circle of radius 23 is 1661.90111
23
Line 2 prompts the user to enter a value (in the form of a string) and converts it to a num-
ber, which is equivalent to
s = input(“Enter a value for radius: “) # Read input as a string
radius = eval(s) # Convert the string to a number
After the user enters a number and presses the Enter key, the number is read and assigned
to radius.
Key
Point
✓Point✓Check

2.3 Reading Input from the Console 35
Listing 2.2 shows how to prompt the user for a single input. However, you can prompt for
multiple inputs as well. Listing 2.3 gives an example of reading multiple inputs from the key-
board. This program reads three integers and displays their average.
LISTING 2.3 ComputeAverage.py
1 # Prompt the user to enter three numbers
2 number1 = eval(input(“Enter the first number: “))
3 number2 = eval(input(“Enter the second number: “))
4 number3 = eval(input(“Enter the third number: “))
5
6 # Compute average
7 average = (number1 + number2 + number3) / 3
8
9 # Display result
10 print(“The average of”, number1, number2, number3,
11 “is”, average)
input number1
input number2
input number3
Enter the first number:
Enter the second number:
Enter the third number:
The average of 1 2 3 is 2.0
3
2
1
The program prompts the user to enter three integers (lines 2–4), computes their average
(line 7), and displays the result (lines 10–11).
If the user enters something other than a number, the program will terminate with a runtime
error. In Chapter 13, you will learn how to handle the error so that the program can continue to run.
Normally a statement ends at the end of the line. In the preceding listing, the print state-
ment is split into two lines (lines 10–11). This is okay, because Python scans the print state-
ment in line 10 and knows it is not finished until it finds the closing parenthesis in line 11. We
say that these two lines are joined implicitly.
Note
In some cases, the Python interpreter cannot determine the end of the statement
written in multiple lines. You can place the line continuation symbol (\) at the end
of a line to tell the interpreter that the statement is continued on the next line. For
example, the following statement
sum = 1 + 2 + 3 + 4 +
5 + 6
is equivalent to
sum = 1 + 2 + 3 + 4 + 5 + 6
Note
Most of the programs in early chapters of this book perform three steps: Input, Process,
and Output, called IPO. Input is to receive input from the user. Process is to produce
results using the input. Output is to display the results.
2.3 How do you write a statement to prompt the user to enter a numeric value?
2.4 What happens if the user enters 5a when executing the following code?
radius = eval(input(“Enter a radius: “))
2.5 How do you break a long statement into multiple lines?
\
runtime error
split a long statement
joining lines explicitly
line continuation symbol
IPO
✓Point✓Check

36 Chapter 2 Elementary Programming
identifiers
identifier naming rules
case sensitive
descriptive names
variable naming convention
camelCase
why called variables?
2.4 Identifiers
Identifiers are the names that identify the elements such as variables and functions in a
program.
As you can see in Listing 2.3, number1, number2, number3, average, input, eval, and
print are the names of things that appear in the program. In programming terminology, such
names are called identifiers. All identifiers must obey the following rules:
■ An identifier is a sequence of characters that consists of letters, digits, and
underscores (_).
■ An identifier must start with a letter or an underscore. It cannot start with a digit.
■ An identifier cannot be a keyword. (See Appendix A, Python Keywords, for a list of
keywords.) Keywords, also called reserved words, have special meanings in Python.
For example, import is a keyword, which tells the Python interpreter to import a
module to the program.
■ An identifier can be of any length.
For example, area, radius, and number1 are legal identifiers, whereas 2A and d+4 are
not because they do not follow the rules. When Python detects an illegal identifier, it reports a
syntax error and terminates the program.
Note
Because Python is case sensitive, area, Area, and AREA are all different identifiers.
Tip
Descriptive identifiers make programs easy to read. Avoid using abbreviations for identi-
fiers. Using complete words is more descriptive. For example, numberOfStudents is
better than numStuds, numOfStuds, or numOfStudents. We use descriptive
names for complete programs in the text. However, we will occasionally use variables
names such as i, j, k, x, and y in the code snippets for brevity. These names also
provide a generic tone to the code snippets.
Tip
Use lowercase letters for variable names, as in radius and area. If a name consists of
several words, concatenate them into one, making the first word lowercase and capital-
izing the first letter of each subsequent word—for example, numberOfStudents.
This naming style is known as the camelCase because the uppercase characters in the
name resemble a camel’s humps.
2.6 Which of the following identifiers are valid? Which are Python keywords (see
Appendix A)?
miles, Test, a+b, b–a, 4#R, $4, #44, apps
if, elif, x, y, radius
2.5 Variables, Assignment Statements, and Expressions
Variables are used to reference values that may be changed in the program.
As you can see from the programs in the preceding sections, variables are the names that refer-
ence values stored in memory. They are called “variables” because they may reference different
values. For example, in the following code, radius is initially 1.0 (line 2) and then changed to
2.0 (line 7), and area is set to 3.14159 (line 3) and then reset to 12.56636 (line 8).
Key
Point
keyword
reserved word
✓Point✓Check
Key
Point

2.5 Variables, Assignment Statements, and Expressions 37
1 # Compute the first area
2 radius = 1.0 radius 1.0
3 area = radius * radius * 3.14159 area 3.14159
4 print(“The area is”, area, “for radius”, radius)
5
6 # Compute the second area
7 radius = 2.0 radius 2.0
8 area = radius * radius * 3.14159 area 12.56636
9 print(“The area is”, area, “for radius”, radius)
The statement for assigning a value to a variable is called an assignment statement. In
Python, the equal sign (=) is used as the assignment operator. The syntax for assignment state-
ments is as follows:
variable = expression
An expression represents a computation involving values, variables, and operators that,
taken together, evaluate to a value. For example, consider the following code:
y = 1 # Assign 1 to variable y
radius = 1.0 # Assign 1.0 to variable radius
x = 5 * (3 / 2) + 3 * 2 # Assign the value of the expression to x
x = y + 1 # Assign the addition of y and 1 to x
area = radius * radius * 3.14159 # Compute area
You can use a variable in an expression. A variable can also be used in both sides of the =
operator. For example,
x = x + 1
In this assignment statement, the result of x + 1 is assigned to x. If x is 1 before the state-
ment is executed, then it becomes 2 after the statement is executed.
To assign a value to a variable, you must place the variable name to the left of the assign-
ment operator. Thus, the following statement is wrong:
1 = x # Wrong
Note
In mathematics, x = 2 * x + 1 denotes an equation. However, in Python, x = 2 *
x + 1 is an assignment statement that evaluates the expression 2 * x + 1 and assigns
the result to x.
If a value is assigned to multiple variables, you can use a syntax like this:
i = j = k = 1
which is equivalent to
k = 1
j = k
i = j
Every variable has a scope. The scope of a variable is the part of the program where the
variable can be referenced. The rules that define the scope of a variable will be introduced
gradually later in the book. For now, all you need to know is that a variable must be created
before it can be used. For example, the following code is wrong:
assignment statement
assignment operator
expression
Assignment statement
VideoNote
scope of a variable

38 Chapter 2 Elementary Programming
But you can simplify the task using the following statement to swap the values of x and y.
>>> x, y = y, x # Swap x with y
Simultaneous assignment can also be used to obtain multiple input in one statement.
Listing 2.3 gives an example that prompts the user to enter three numbers and obtains their
average. This program can be simplified using a simultaneous assignment statement, as
shown in Listing 2.4.
count is not defined yet.
>>> count = count + 1
NameError: count is not defined
>>>
To fix it, you may write the code like this:
>>> count = 1 # count is not created
>>> count = count + 1 # Now increment count
>>>
Caution
A variable must be assigned a value before it can be used in an expression. For example,
interestRate = 0.05
interest = interestrate * 45
This code is wrong, because interestRate is assigned a value 0.05, but
interestrate is not defined. Python is case-sensitive. interestRate and
interestrate are two different variables.
2.6 Simultaneous Assignments
Python also supports simultaneous assignment in syntax like this:
var1, var2, …, varn = exp1, exp2, …, expn
It tells Python to evaluate all the expressions on the right and assign them to the corre-
sponding variable on the left simultaneously. Swapping variable values is a common opera-
tion in programming and simultaneous assignment is very useful to perform this operation.
Consider two variables: x and y. How do you write the code to swap their values? A common
approach is to introduce a temporary variable as follows:
>>> x = 1
>>> y = 2
>>> temp = x # Save x in a temp variable
>>> x = y # Assign the value in y to x
>>> y = temp # Assign the value in temp to y
simultaneous assignment

2.7 Named Constants 39
input numbers
Enter three numbers separated by commas:
The average of 1 2 3 is 2.0
1, 2, 3 enter input in one line
2.7 What is the naming convention for variables?
2.8 What is wrong in the following statement?
2 = a
2.9 What is x, y, and z after the following statement?
x = y = z = 0
2.10 Assume that a = 1 and b = 2. What is a and b after the following statement?
a, b = b, a
2.7 Named Constants
A named constant is an identifier that represents a permanent value.
The value of a variable may change during the execution of a program, but a named constant
(or simply constant) represents permanent data that never changes. In our ComputeArea
program, p is a constant. If you use it frequently, you don’t want to keep typing 3.14159;
instead, you can use a descriptive name PI for the value. Python does not have a special
syntax for naming constants. You can simply create a variable to denote a constant. However,
to distinguish a constant from a variable, use all uppercase letters to name a constant. For
example, you can rewrite Listing 2.1 to use a named constant for p, as follows:
# Assign a radius
radius = 20 # radius is now 20
# Compute area
PI = 3.14159
area = radius * radius * PI
# Display results
print(“The area for the circle of radius”, radius, “is”, area)
There are three benefits of using constants:
1. You don’t have to repeatedly type the same value if it is used multiple times.
2. If you have to change the constant’s value (e.g., from 3.14 to 3.14159 for PI), you
need to change it only in a single location in the source code.
3. Descriptive names make the program easy to read.
constant naming convention
Key
Point
✓Point✓Check
LISTING 2.4 ComputeAverageWithSimultaneousAssignment.py
1 # Prompt the user to enter three numbers
2 number1, number2, number3 = eval(input(
3 “Enter three numbers separated by commas: “))
4
5 # Compute average
6 average = (number1 + number2 + number3) / 3
7
8 # Display result
9 print(“The average of”, number1, number2, number3
10 “is”, average)
benefits of constants

40 Chapter 2 Elementary Programming
2.8 Numeric Data Types and Operators
Python has two numeric types—integers and floating-point numbers—for working
with the operators +, -, *, /, //, **, and %.
The information stored in a computer is generally referred to as data. There are two types
of numeric data: integers and real numbers. Integer types (int for short) are for represent-
ing whole numbers. Real types are for representing numbers with a fractional part. Inside
the computer, these two types of data are stored differently. Real numbers are represented
as floating-point (or float) values. How do we tell Python whether a number is an integer
or a float? A number that has a decimal point is a float even if its fractional part is 0. For
example, 1.0 is a float, but 1 is an integer. These two numbers are stored differently in the
computer. In the programming terminology, numbers such as 1.0 and 1 are called literals. A
literal is a constant value that appears directly in a program.
The operators for numeric data types include the standard arithmetic operators, as shown
in Table 2.1. The operands are the values operated by an operator.
floating-point numbers
integer
int
float
operands
operators +, -, *, /, //, **, %
unary operator
binary operator
/ operator
TABLE 2.1 Numeric Operators
Name Meaning Example Result
+ Addition 34 + 1 35
– Subtraction 34.0 – 0.1 33.9
* Multiplication 300 * 30 9000
/ Float Division 1 / 2 0.5
// Integer Division 1 // 2 0
** Exponentiation 4 ** 0.5 2.0
% Remainder 20 % 3 2
The +, -, and * operators are straightforward, but note that the + and – operators can be
both unary and binary. A unary operator has only one operand; a binary operator has two. For
example, the – operator in -5 is a unary operator to negate the number 5, whereas the – oper-
ator in 4 – 5 is a binary operator for subtracting 5 from 4.
2.8.1 The /, //, and ** Operators
The / operator performs a float division that results in a floating number. For example,
>>> 4 / 2
2.0
>>> 2 / 4
0.5
>>>
Key
Point
VideoNote
Perform computation
literal
>>> 5 // 2
2
>>> 2 // 4
0
>>>
The // operator performs an integer division; the result is an integer, and any fractional
part is truncated. For example,
// operator

2.8 Numeric Data Types and Operators 41
To compute (a with an exponent of b) for any numbers a and b, you can write a ** b
in Python. For example,
ab ** exponent operator
>>> 2.3 ** 3.5
18.45216910555504
>>> (-2.5) ** 2
6.25
>>>
2.8.2 The % Operator
The % operator, known as remainder or modulo operator, yields the remainder after division.
The left-side operand is the dividend and the right-side operand is the divisor. Therefore, 7 %
3 yields 1, 3 % 7 yields 3,12 % 4 yields 0, 26 % 8 yields 2, and 20 % 13 yields 7.
% operator
4 12
12
0
3
8 26
24
2
3
Remainder
Quotient
Divisor Dividend13 20
13
7
1
7 3
0
3
0
3 7
6
1
2
The remainder operator is very useful in programming. For example, an even number % 2
is always 0 and an odd number % 2 is always 1. Thus, you can use this property to determine
whether a number is even or odd. If today is Saturday, it will be Saturday again in 7 days. Sup-
pose you and your friends are going to meet in 10 days. What day is in 10 days? You can find
that the day is Tuesday using the following expression:
Listing 2.5 shows a program that obtains minutes and remaining seconds from an amount
of time in seconds. For example, 500 seconds contains 8 minutes and 20 seconds.
input seconds
get minutes
LISTING 2.5 DisplayTime.py
1 # Prompt the user for input
2 seconds = eval(input(“Enter an integer for seconds: “))
3
4 # Get minutes and remaining seconds
5 minutes = seconds // 60 # Find minutes in seconds
6 remainingSeconds = seconds % 60 # Seconds remaining
7 print(seconds, “seconds is”, minutes,
8 “minutes and”, remainingSeconds, “seconds”)
get remainingSeconds
Enter an integer for seconds:
500 seconds is 8 minutes and 20 seconds
500
(6 + 10) % 7 is 2
After 10 days
Day 2 in a week is Tuesday
Note: Day 0 in a week is Sunday
A week has 7 days
Day 6 in a week is Saturday

42 Chapter 2 Elementary Programming
Line 2 reads an integer for seconds. Line 5 obtains the minutes using seconds // 60. Line
6 (seconds % 60) obtains the remaining seconds after taking away the minutes.
2.8.3 Scientific Notation
Floating-point values can be written in scientific notation in the form of For example,
the scientific notation for 123.456 is and for 0.0123456 is
Python uses a special syntax to write scientific notation numbers. For example,
is written as 1.23456E2 or 1.23456E+2, and as 1.23456E-2. The letter E
(or e) represents an exponent and can be in either lowercase or uppercase.
Note
The float type is used to represent numbers with a decimal point. Why are they called
floating-point numbers? These numbers are stored in scientific notation in memory.
When a number such as 50.534 is converted into scientific notation, such as
5.0534E+1, its decimal point is moved (floated) to a new position.
Caution
When a variable is assigned a value that is too large (in size) to be stored in memory, it
causes overflow. For example, executing the following statement causes overflow.
1.23456 * 10-2
1.23456 * 102
1.23456 * 10-2.1.23456 * 102
a * 10b.scientific notation
why called floating point?
what is overflow?
line# seconds minutes remainingSeconds
2 500
5 8
6 20
>>> 245.0 ** 1000
OverflowError: ‘Result too large’
>>>
When a floating-point number is too small (that is, too close to zero), it causes
underflow and Python approximates it to zero. Therefore, usually you don’t need to be
concerned with underflow.
2.11 What are the results of the following expressions?
Expression Result
42 / 5 _____
42 // 5 _____
42 % 5 _____
40 % 5 _____
1 % 2 _____
2 % 1 _____
45 + 4 * 4 – 2 _____
45 + 43 % 5 * (23 * 3 % 2) _____
5 ** 2 _____
5.1 ** 2 _____
what is underflow?
✓Point✓Check

2.9 Evaluating Expressions and Operator Precedence 43
evaluate an expression
2.12 If today is Tuesday, what day of the week will it be in 100 days?
2.13 What is the result of 25 / 4? How would you rewrite the expression if you wished
the result to be an integer number?
2.9 Evaluating Expressions and Operator Precedence
Python expressions are evaluated in the same way as arithmetic expressions.
Writing a numeric expression in Python involves a straightforward translation of an arith-
metic expression using operators. For example, the arithmetic expression
can be translated into a Python expression as:
(3 + 4 * x) / 5 – 10 * (y – 5) * (a + b + c) / x +
9 * (4 / x + (9 + x) / y)
Though Python has its own way to evaluate an expression behind the scene, the results of
a Python expression and its corresponding arithmetic expression are the same. Therefore,
you can safely apply the arithmetic rules for evaluating a Python expression. Operators con-
tained within pairs of parentheses are evaluated first. Parentheses can be nested, in which
case the expression in the inner parentheses is evaluated first. When more than one operator
is used in an expression, the following operator precedence rule is used to determine the
order of evaluation.
■ Exponentiation (**) is applied first.
■ Multiplication (*), float division (/), integer division (//) , and remainder operators
(%) are applied next. If an expression contains several multiplication, division, and
remainder operators, they are applied from left to right.
■ Addition (+) and subtraction (-) operators are applied last. If an expression
contains several addition and subtraction operators, they are applied from left
to right.
Here is an example of how an expression is evaluated:
3 + 4x
5
–
10(y – 5)(a + b + c)
x
+ 9¢4
x
+
9 + x
y
≤
Key
Point
operator precedence rule
3 + 4 * 4 + 5 * (4 + 3) – 1
3 + 4 * 4 + 5 * 7 – 1
3 + 16 + 5 * 7 – 1
3 + 16 + 35 – 1
19 + 35 – 1
54 – 1
53
(1) inside parentheses first
(2) multiplication
(3) multiplication
(4) addition
(5) addition
(6) subtraction

44 Chapter 2 Elementary Programming
addition assignment operator
TABLE 2.2 Augmented Assignment Operators
Operator Name Example Equivalent
+= Addition assignment i += 8 i = i + 8
-= Subtraction assignment i -= 8 i = i – 8
*= Multiplication assignment i *= 8 i = i * 8
/= Float division assignment i /= 8 i = i / 8
//= Integer division assignment i //= 8 i = i // 8
%= Remainder assignment i %= 8 i = i % 8
**= Exponent assignment i **= 8 i = i ** 8
✓Point✓Check
Key
Point
augmented assignment
compound assignment
2.14 How would you write the following arithmetic expression in Python?
2.15 Suppose m and r are integers. Write a Python expression for mr2.
2.10 Augmented Assignment Operators
The operators +, -, *, /, //, %, and ** can be combined with the assignment operator
(=) to form augmented assignment operators.
Very often the current value of a variable is used, modified, and then reassigned back
to the same variable. For example, the following statement increases the variable count
by 1:
count = count + 1
Python allows you to combine assignment and addition operators using an augmented
(or compound) assignment operator. For instance, the preceding statement can be written
as:
count += 1
The += operator is called the addition assignment operator. All augmented assignment
operators are shown in Table 2.2.
4
3(r + 34)
– 9(a + bc) +
3 + d(2 + a)
a + bd
Caution
There are no spaces in the augmented assignment operators. For example, + = should be +=.
2.16 Assume that a = 1, and that each expression is independent. What are the results of
the following expressions?
a += 4
a -= 4
a *= 4
a /= 4
a //= 4
a %= 4
a = 56 * a + 6
✓Point✓Check

2.11 Type Conversions and Rounding 45
2.11 Type Conversions and Rounding
If one of the operands for the numeric operators is a float value, the result will be a
float value.
Can you perform binary operations with two operands of different types? Yes. If an integer
and a float are involved in a binary operation, Python automatically converts the integer to a
float value. This is called type conversion. So, 3 * 4.5 is the same as 3.0 * 4.5.
Sometimes, it is desirable to obtain the integer part of a fractional number. You can use the
int(value) function to return the integer part of a float value. For example,
>>> value = 5.6
>>> int(value)
5
>>>
Note that the fractional part of the number is truncated, not rounded up.
You can also use the round function to round a number to the nearest whole value. For
example,
>>> value = 5.6
>>> round(value)
6
>>>
We will discuss the round function more in Chapter 3.
Note
The functions int and round do not change the variable being converted. For exam-
ple, value is not changed after invoking the function in the following code:
>>> value = 5.6
>>> round(value)
6
>>> value
5.6
>>>
round function
type conversion
int function
Key
Point
Note
The int function can also be used to convert an integer string into an integer. For
example, int(“34”) returns 34. So you can use the eval or int function to
convert a string into an integer. Which one is better? The int function performs a sim-
ple conversion. It does not work for a non-integer string. For example, int(“3.4”)
will cause an error. The eval function does more than a simple conversion. It can be
used to evaluate an expression. For example, eval(“3 + 4”) returns 7. However,
there is a subtle “gotcha” for using the eval function. The eval function will pro-
duce an error for a numeric string that contains leading zeros. In contrast, the int
function works fine for this case. For example, eval(“003”) causes an error, but
int(“003”) returns 3.
int vs. eval functions

46 Chapter 2 Elementary Programming
format
Enter purchase amount:
Sales tax is 11.85
197.55
The value of the variable purchaseAmount is 197.55 (line 2). The sales tax is 6% of the
purchase, so the tax is evaluated as 11.853 (line 5). Note that
tax * 100 is 1185.3
int(tax * 100) is 1185
int(tax * 100) / 100.0 is 11.85
So, the statement in line 8 displays the tax 11.85 with two digits after the decimal point.
2.17 What does a conversion from a float to an integer do with the fractional part of the
float value? Does the int(value) function change the variable value?
2.18 Are the following statements correct? If so, show their printout.
value = 4.6
print(int(value))
print(round(value))
print(eval(“4 * 5 + 2”))
print(int(“04”))
print(int(“4.5”))
print(eval(“04”))
2.12 Case Study: Displaying the Current Time
You can use the time() function in the time module to obtain the current system time.
The problem is to develop a program that displays the current time in Greenwich Mean Time
(GMT) in the format hour:minute:second, such as 13:19:18.
The time() function in the time module returns the current time in seconds with
millisecond precision elapsed since the time 00:00:00 on January 1, 1970 GMT, as shown
in Figure 2.1. This time is known as the UNIX epoch. The epoch is the point when time
starts. 1970 was the year when the UNIX operating system was formally introduced. For
format numbers
UNIX epoch
line# purchaseAmount tax output
2 197.55
5 11.853
8 11.85
Listing 2.6 shows a program that displays the sales tax with two digits after the decimal point.
LISTING 2.6 SalesTax.py
1 # Prompt the user for input
2 purchaseAmount = eval(input(“Enter purchase amount: “))
3
4 # Compute sales tax
5 tax = purchaseAmount * 0.06
6
7 # Display tax amount with two digits after decimal point
8 print(“Sales tax is”, int(tax * 100) / 100.0)
input purchaseAmount
compute tax
✓Point✓Check
Key
Point

2.12 Case Study: Displaying the Current Time 47
time.time()example, time.time() returns 1285543663.205, which means 1285543663 seconds and
205 milliseconds.
You can use this function to obtain the current time, and then compute the current second,
minute, and hour as follows.
1. Obtain the current time (since midnight, January 1, 1970) by invoking time.time()
(for example, 1203183068.328).
2. Obtain the total seconds totalSeconds using the int function (int(1203183068.328)
1203183068).
3. Compute the current second from totalSeconds % 60 (1203183068 seconds %
60 8, which is the current second).
4. Obtain the total minutes totalMinutes by dividing totalSeconds by 60 (1203183068
seconds // 60 20053051 minutes).
5. Compute the current minute from totalMinutes % 60 (20053051minutes % 60 31,
which is the current minute).
6. Obtain the total hours totalHours by dividing totalMinutes by 60 (20053051
minutes // 60 334217 hours).
7. Compute the current hour from totalHours % 24 (334217 hours % 24 17, which
is the current hour).
Listing 2.7 gives the complete program.
LISTING 2.7 ShowCurrentTime.py
1 import time
2
3 currentTime = time.time() # Get current time
4
5 # Obtain the total seconds since midnight, Jan 1, 1970
6 totalSeconds = int(currentTime)
7
8 # Get the current second
9 currentSecond = totalSeconds % 60
10
11 # Obtain the total minutes
12 totalMinutes = totalSeconds // 60
13
14 # Compute the current minute in the hour
15 currentMinute = totalMinutes % 60
16
17 # Obtain the total hours
18 totalHours = totalMinutes // 60
19
20 # Compute the current hour
21 currentHour = totalHours % 24
=
=
=
=
=
=
import time module
currentTime
totalSeconds
currentSecond
UNIX epoch
01-01-1970
00:00:00 GMT
Elapsed
time
Current Time
time.time ()
Time
FIGURE 2.1 The time.time() function returns the seconds with millisecond precision
since the UNIX epoch.
totalMinutes
currentMinute
totalHours
currentHour

48 Chapter 2 Elementary Programming
display output
Current time is 17:31:8 GMT
Line 3 invokes time.time() to return the current time in seconds as a float value with
millisecond precision. The seconds, minutes, and hours are extracted from the current time using
the // and % operators (lines 6–21).
In the sample run, a single digit 8 is displayed for the second. The desirable output would
be 08. This can be fixed by using a function that formats a single digit with a prefix 0 (see
Exercise 6.48).
2.19 What is the UNIX epoch?
2.20 What does time.time() return?
2.21 How do you obtain the seconds from the returned value for time.time()?
2.13 Software Development Process
The software development life cycle is a multistage process that includes requirements
specification, analysis, design, implementation, testing, deployment, and maintenance.
Developing a software product is an engineering process. Software products, no matter
how large or how small, have the same life cycle: requirements specification, system
analysis, system design, implementation, testing, deployment, and maintenance, as shown
in Figure 2.2.
Requirements specification is a formal process that seeks to understand the problem that
the software will address and to document in detail what the software system needs to do.
This phase involves close interaction between users and developers. Most of the examples in
line#
variables
3 6 9 12 15 18 21
currentTime 1203183068.328
totalSeconds 1203183068
currentSecond 8
totalMinutes 20053051
currentMinute 31
totalHours 334217
currentHour 17
requirements specification
22
23 # Display results
24 print(“Current time is”, currentHour, “:”,
25 currentMinute, “:”, currentSecond, “GMT”)
✓Point✓Check
Key
Point

2.13 Software Development Process 49
system analysis
system design
this book are simple, and their requirements are clearly stated. In the real world, however,
problems are not always well defined. Developers need to work closely with their customers
(the individuals or organizations that will use the software) and study the problem carefully to
identify what the software needs to do.
System analysis seeks to analyze the data flow and to identify the system’s input and output.
When you do analysis, it helps to identify what the output is first, and then figure out what
input data you need in order to produce the output.
System design is to design a process for obtaining the output from the input. This phase
involves the use of many levels of abstraction to decompose the problem into manageable
components, and design strategies for implementing each component. You can view a compo-
nent as a subsystem that performs a specific function of the system. The essence of system
analysis and design is input, process, and output (IPO).
Implementation involves translating the system design into programs. Separate programs
are written for each component and then integrated to work together. This phase requires the
use of a programming language such as Python. The implementation involves coding, self
testing, and debugging (that is, finding errors, called bugs, in the code).
Testing ensures that the code meets the requirements specification and weeds out bugs. An
independent team of software engineers not involved in the design and implementation of the
product usually conducts such testing.
Deployment makes the software available for use. Depending on the type of the soft-
ware, it may be installed on each user’s machine or installed on a server accessible on the
Internet.
Maintenance is concerned with updating and improving the product. A software product
must continue to perform and improve in an ever-evolving environment. This requires periodic
upgrades of the product to fix newly discovered bugs and incorporate changes.
To see the software development process in action, we will now create a program that
computes loan payments. The loan can be a car loan, a student loan, or a home mortgage loan.
For an introductory programming course, we focus on requirements specification, analysis,
design, implementation, and testing.
Requirements
Specification
System Analysis
System
Design
Testing
Input, Process, Output
IPO
Implementation
Maintenance
Deployment
FIGURE 2.2 At any stage of the software development life cycle, it may be necessary to go
back to a previous stage to correct errors or deal with other issues that might prevent the
software from functioning as expected.
IPO
implementation
testing
deployment
maintenance

50 Chapter 2 Elementary Programming
Stage 1: Requirements Specification
The program must satisfy the following requirements:
■ It must let the user enter the interest rate, the loan amount, and the number of years
for which payments will be made.
■ It must compute and display the monthly payment and total payment amounts.
Stage 2: System Analysis
The output is the monthly payment and total payment, which can be obtained using the fol-
lowing formula:
So, the input needed for the program is the annual interest rate, the length of the loan in years,
and the loan amount.
Note
The requirements specification says that the user must enter the interest rate, the loan
amount, and the number of years for which payments will be made. During analysis,
however, it is possible that you may discover that input is not sufficient or that some
values are unnecessary for the output. If this happens, you can go back to modify the
requirements specification.
Note
In the real world, you will work with customers from all walks of life. You may develop
software for chemists, physicists, engineers, economists, and psychologists and of
course, you will not have (or need) the complete knowledge of all these fields. There-
fore, you don’t have to know how the mathematical formulas are derived. Nonetheless,
given the annual interest rate, number of years, and loan amount, you can use this for-
mula to compute the monthly payment. You will, however, need to communicate with
the customers and understand how the mathematic model works for the system.
Stage 3: System Design
During system design, you identify the steps in the program:
Step 1. Prompt the user to enter the annual interest rate, number of years, and loan amount.
Step 2. The input for the annual interest rate is a number in percent format, such as 4.5%.
The program needs to convert it into a decimal by dividing it by 100. To obtain the
monthly interest rate from the annual interest rate, divide it by 12, since a year has
12 months. So to obtain the monthly interest rate in decimal format, you need to
divide the annual interest rate in percentage by 1200. For example, if the annual
interest rate is 4.5%, then the monthly interest rate is
Step 3. Compute the monthly payment using the formula given in Stage 2.
Step 4. Compute the total payment, which is the monthly payment multiplied by 12 and
multiplied by the number of years.
Step 5. Display the monthly payment and total payment.
4.5/1200 = 0.00375.
totalPayment = monthlyPayment * numberOfYears * 12
monthlyPayment =
loanAmount * monthlyInterestRate
1 –
1
(1 + monthlyInterestRate)numberOfYears*12

2.13 Software Development Process 51
Stage 4: Implementation
Implementation is also known as coding (writing the code). In the formula, you have to com-
pute You can use the exponentiation operator to
write it as
(1 + monthlyInterestRate) ** (numberOfYears * 12)
Listing 2.8 gives the complete program.
LISTING 2.8 ComputeLoan.py
1 # Enter annual interest rate as a percentage, e.g., 7.25
2 annualInterestRate = eval(input(
3 “Enter annual interest rate, e.g., 7.25: “))
4 monthlyInterestRate = annualInterestRate / 1200
5
6 # Enter number of years
7 numberOfYears = eval(input(
8 “Enter number of years as an integer, e.g., 5: “))
9
10 # Enter loan amount
11 loanAmount = eval(input(“Enter loan amount, e.g., 120000.95: “))
12
13 # Calculate payment
14 monthlyPayment = loanAmount * monthlyInterestRate / (1
15 – 1 / (1 + monthlyInterestRate) ** (numberOfYears * 12))
16 totalPayment = monthlyPayment * numberOfYears * 12
17
18 # Display results
19 print(“The monthly payment is”, int(monthlyPayment * 100) / 100)
20 print(“The total payment is”, int(totalPayment * 100) /100)
(1 + monthlyInterestRate)numberOfYears*12.
enter interest rate
obtain monthly interest rate
enter years
enter loan amount
monthlyPayment
totalPayment
display result
line#
variables
2 4 7 11 14 16
annualInterestRate 5.75
monthlyInterestRate 0.0047916666666
numberOfYears 15
loanAmount 250000
monthlyPayment 2076.0252175
totalPayment 373684.539
Enter annual interest rate, e.g., 7.25:
Enter number of years as an integer, e.g., 5:
Enter loan amount, e.g., 120000.95:
The monthly payment is 2076.02
The total payment is 373684.53
250000
15
5.75

52 Chapter 2 Elementary Programming
incremental development and
testing
enter x1, y1
enter x2, y2
compute distance
Enter x1 and y1 for Point 1:
Enter x2 and y2 for Point 2:
The distance between the two points is 8.764131445842194
4, 5
1.5, -3.4
The program prompts the user to enter the coordinates of the first point (line 2) and the
second point (line 5). It then computes the distance between them (line 8) and displays it
(line 10).
Key
Point
Line 2 reads the annual interest rate, which is converted into the monthly interest rate in
line 4.
The formula for computing the monthly payment is translated into Python code in lines
14–15.
The variable monthlyPayment is 2076.0252175 (line 14). Note that
int(monthlyPayment * 100) is 207602.52175
int(monthlyPayment * 100) / 100.0 is 2076.02
So, the statement in line 19 displays the tax 2076.02 with two digits after the decimal
point.
Stage 5: Testing
After the program is implemented, test it with some sample input data and verify whether the
output is correct. Some of the problems may involve many cases as you will see in later chap-
ters. For this type of problems, you need to design test data that cover all cases.
Tip
The system design phase in this example identified several steps. It is a good approach
to develop and test these steps incrementally by adding them one at a time. This
process makes it much easier to pinpoint problems and debug the program.
2.14 Case Study: Computing Distances
This section presents two programs that compute and display the distance between two
points.
Given two points, the formula for computing the distance is
You can use a ** 0.5 to compute The program in Listing 2.9 prompts the user to enter
two points and computes the distance between them.
LISTING 2.9 ComputeDistance.py
1 # Enter the first point with two float values
2 x1, y1 = eval(input(“Enter x1 and y1 for Point 1: “))
3
4 # Enter the second point with two float values
5 x2, y2 = eval(input(“Enter x2 and y2 for Point 2: “))
6
7 # Compute the distance
8 distance = ((x1 – x2) * (x1 – x2) + (y1 – y2) * (y1 – y2)) ** 0.5
9
10 print(“The distance between the two points is”, distance)
2a. 2(x2 – x1 )2 + (y2 – y1)2.
format numbers

2.14 Case Study: Computing Distances 53
Figure 2.3 illustrates the program in Listing 2.10. This program
1. Prompts the user to enter two points.
2. Computes the distance between the points.
3. Uses Turtle graphics to display the line that connects the two points.
4. Displays the length of the line at the center of the line.
Listing 2.10 gives the program.
LISTING 2.10 ComputeDistanceGraphics.py
1 import turtle
2
3 # Prompt the user for inputting two points
4 x1, y1 = eval(input(“Enter x1 and y1 for point 1: “))
5 x2, y2 = eval(input(“Enter x2 and y2 for point 2: “))
6
7 # Compute the distance
8 distance = ((x1 – x2) ** 2 + (y1 – y2) ** 2) ** 0.5
9
10 # Display two points and the connecting line
11 turtle.penup()
12 turtle.goto(x1, y1) # Move to (x1, y1)
13 turtle.pendown()
14 turtle.write(“Point 1”)
15 turtle.goto(x2, y2) # Draw a line to (x2, y2)
16 turtle.write(“Point 2”)
17
18 # Move to the center point of the line
19 turtle.penup()
20 turtle.goto((x1 + x2) / 2, (y1 + y2) / 2)
21 turtle.write(distance)
22
23 turtle.done()
FIGURE 2.3 The program displays a line and its length.
Enter x1 and y1 for Point 1:
Enter x2 and y2 for Point 2: 49, -85
-50, 34
The program prompts the user to enter the value for two points (x1, y1) and (x2, y2),
and computes their distance (lines 4–8). It then moves to (x1, y1) (line 12), displays the
display distance
pause
import turtle
enter x1, y1
enter x2, y2
compute distance
move to point 1
display point 1
draw a line
display point 2
move to center

54 Chapter 2 Elementary Programming
CHAPTER SUMMARY
1. You can get input using the input function and convert a string into a numerical
value using the eval function.
2. Identifiers are the names used for elements in a program.
3. An identifier is a sequence of characters of any length that consists of letters, digits,
underscores (_), and asterisk signs (*). An identifier must start with a letter or an
underscore; it cannot start with a digit. An identifier cannot be a keyword.
4. Variables are used to store data in a program.
5. The equal sign (=) is used as the assignment operator.
6. A variable must be assigned a value before it can be used.
7. There are two types of numeric data in Python: integers and real numbers. Integer
types (int for short) are for whole numbers, and real types (also called float) are for
numbers with a decimal point.
8. Python provides assignment operators that perform numeric operations: + (addi-
tion), – (subtraction), * (multiplication), / (division), // (integer division), %
(remainder), and ** (exponent).
9. The numeric operators in a Python expression are applied the same way as in an arith-
metic expression.
10. Python provides augmented assignment operators: += (addition assignment), –=
(subtraction assignment), *= (multiplication assignment), /= (float division assign-
ment), //= (integer division assignment), and %= (remainder assignment). These
operators combine the +, -, *, /, //, and % operators and the assignment operator
into one augmented operators.
algorithm 32
assignment operator (=) 37
augmented assignment 44
camelCase 36
compound assignment 44
data type 33
expression 37
floating-point numbers 40
identifiers 36
incremental development and testing 52
input, process, output (IPO) 35
keyword 36
line continuation symbol 35
literal 40
operands 40
operators 40
pseudocode 32
reserved word 36
scope of a variable 37
simultaneous assignment 38
system analysis 49
system design 49
type conversion 45
variable 32
text Point 1 (line 14), draws a line from (x1, y1) to (x2, y2) (line 15), and displays the
text Point 2 (line 16). Finally, it moves to the center of the line (line 20) and displays the
distance (line 21).
KEY TERMS

Programming Exercises 55
11. When evaluating an expression with values of an int type and a float type, Python
automatically converts the int value to a float type value.
12. You can convert a float to an int using the int(value) function.
13. System analysis seeks to analyze the data flow and to identify the system’s input and
output.
14. System design is the stage when programmers develop a process for obtaining the
output from the input.
15. The essence of system analysis and design is input, process, and output. This is called
IPO.
TEST QUESTIONS
Do test questions for this chapter online at www.cs.armstrong.edu/liang/py/test.html.
PROGRAMMING EXERCISES
Pedagogical Note
Instructors may ask you to document analysis and design for selected exercises.
You should use your own words to analyze the problem, including the input, output,
and what needs to be computed, and describe how to solve the problem in
pseudocode.
Debugging Tip
Python usually gives a reason for a syntax error. If you don’t know how to correct it,
compare your program closely, character by character, with similar examples in the text.
Sections 2.2–2.10
2.1 (Convert Celsius to Fahrenheit) Write a program that reads a Celsius degree from
the console and converts it to Fahrenheit and displays the result. The formula for
the conversion is as follows:
fahrenheit = (9 / 5) * celsius + 32
Here is a sample run of the program:
Enter a degree in Celsius:
43 Celsius is 109.4 Fahrenheit
43
2.2 (Compute the volume of a cylinder) Write a program that reads in the radius and
length of a cylinder and computes the area and volume using the following formulas:
area = radius * radius * π
volume = area * length
Here is a sample run:
learn from examples
document analysis and design

www.cs.armstrong.edu/liang/py/test.html

56 Chapter 2 Elementary Programming
*2.5 (Financial application: calculate tips) Write a program that reads the subtotal and
the gratuity rate and computes the gratuity and total. For example, if the user
enters 10 for the subtotal and 15% for the gratuity rate, the program displays 1.5
as the gratuity and 11.5 as the total. Here is a sample run:
Enter the subtotal and a gratuity rate:
The gratuity is 2.35 and the total is 18.04
15.69, 15
**2.6 (Sum the digits in an integer) Write a program that reads an integer between 0 and
1000 and adds all the digits in the integer. For example, if an integer is 932, the
sum of all its digits is 14. (Hint: Use the % operator to extract digits, and use the //
operator to remove the extracted digit. For instance, 932 % 10 = 2 and 932 //
10 = 93.) Here is a sample run:
Enter a number between 0 and 1000:
The sum of the digits is 27
999
**2.7 (Find the number of years and days) Write a program that prompts the user to
enter the minutes (e.g., 1 billion), and displays the number of years and days for
the minutes. For simplicity, assume a year has 365 days. Here is a sample run:
Enter the number of minutes:
1000000000 minutes is approximately 1902 years and 214 days
1000000000
2.8 (Science: calculate energy) Write a program that calculates the energy needed to
heat water from an initial temperature to a final temperature. Your program should
2.4 (Convert pounds into kilograms) Write a program that converts pounds into
kilograms. The program prompts the user to enter a value in pounds, converts it to
kilograms, and displays the result. One pound is 0.454 kilograms. Here is a
sample run:
Enter a value in pounds:
55.5 pounds is 25.197 kilograms
55.5
Enter the radius and length of a cylinder:
The area is 95.0331
The volume is 1140.4
5.5, 12
2.3 (Convert feet into meters) Write a program that reads a number in feet, converts it
to meters, and displays the result. One foot is 0.305 meters. Here is a sample run:
Enter a value for feet:
16.5 feet is 5.0325 meters
16.5

Programming Exercises 57
Enter the amount of water in kilograms:
Enter the initial temperature:
Enter the final temperature:
The energy needed is 1625484.0
10.5
3.5
55.5
*2.9 (Science: wind-chill temperature) How cold is it outside? The temperature alone is
not enough to provide the answer. Other factors including wind speed, relative
humidity, and sunshine play important roles in determining coldness outside. In
2001, the National Weather Service (NWS) implemented the new wind-chill tem-
perature to measure the coldness using temperature and wind speed. The formula
is given as follows:
where is the outside temperature measured in degrees Fahrenheit and v is the
speed measured in miles per hour. is the wind-chill temperature. The formula
cannot be used for wind speeds below 2 mph or for temperatures below or
above 41°F.
Write a program that prompts the user to enter a temperature between and
41°F and a wind speed greater than or equal to 2 and displays the wind-chill tem-
perature. Here is a sample run:
-58 �F
-58 �F
twc
ta
twc = 35.74 + 0.6215ta – 35.75v0.16 + 0.4275tav0.16
prompt the user to enter the amount of water in kilograms and the initial and final
temperatures of the water. The formula to compute the energy is
Q = M * (finalTemperature – initialTemperature) * 4184
where M is the weight of water in kilograms, temperatures are in degrees Celsius,
and energy Q is measured in joules. Here is a sample run:
Enter the temperature in Fahrenheit between -58 and 41:
Enter the wind speed in miles per hour:
The wind chill index is -5.56707
6
5.3
*2.10 (Physics: find runway length) Given an airplane’s acceleration a and take-off
speed v, you can compute the minimum runway length needed for an airplane to
take off using the following formula:
Write a program that prompts the user to enter v in meters/second (m/s) and the
acceleration a in meters/second squared and displays the minimum runway
length. Here is a sample run:
(m/s2),
length =
v2
2a
Enter speed and acceleration:
The minimum runway length for this airplane is 514.286 meters
60, 3.5

58 Chapter 2 Elementary Programming
Enter final account value:
Enter annual interest rate in percent:
Enter number of years:
Initial deposit value is 808.8639197424636
5
4.25
1000
2.12 (Print a table) Write a program that displays the following table:
a b a ** b
1 2 1
2 3 8
3 4 81
4 5 1024
5 6 15625
*2.13 (Split digits) Write a program that prompts the user to enter a four-digit integer
and displays the number in reverse order. Here is a sample run:
Enter an integer:
3
1
2
5
3125
*2.14 (Geometry: area of a triangle) Write a program that prompts the user to enter the
three points (x1, y1), (x2, y2), and (x3, y3) of a triangle and displays its area.
The formula for computing the area of a triangle is
Here is a sample run:
area = 2s(s – side1)(s – side2)(s – side3) s = (side1 + side2 + side3) / 2
Enter three points for a triangle:
The area of the triangle is 33.6
9.5, -3.4
1.5, -3.4, 4.6, 5,
*2.11 (Financial application: investment amount) Suppose you want to deposit a
certain amount of money into a savings account with a fixed annual interest rate.
What amount do you need to deposit in order to have $5,000 in the account after
three years? The initial deposit amount can be obtained using the following
formula:
Write a program that prompts the user to enter final account value, annual interest
rate in percent, and the number of years, and displays the initial deposit amount.
Here is a sample run:
initialDepositAmount =
finalAccountValue
(1 + monthlyInterestRate)numberOfMonths

Programming Exercises 59
2.15 (Geometry: area of a hexagon) Write a program that prompts the user to enter the
side of a hexagon and displays its area. The formula for computing the area of a
hexagon is where s is the length of a side. Here is a sample run:Area =
323
2
s2,
Enter the side:
The area of the hexagon is 78.5895
5.5
2.16 (Physics: acceleration) Average acceleration is defined as the change of velocity
divided by the time taken to make the change, as shown in the following formula:
Write a program that prompts the user to enter the starting velocity in
meters/second, the ending velocity in meters/second, and the time span t in
seconds, and displays the average acceleration. Here is a sample run:
v1
v0
a =
v1 – v0
t
Enter v0, v1, and t:
The average acceleration is 10.0889
5.5, 50.9, 4.5
*2.17 (Health application: compute BMI) Body mass index (BMI) is a measure of health
based on weight. It can be calculated by taking your weight in kilograms and
dividing it by the square of your height in meters. Write a program that prompts
the user to enter a weight in pounds and height in inches and displays the BMI.
Note that one pound is 0.45359237 kilograms and one inch is 0.0254 meters.
Here is a sample run:
Enter weight in pounds:
Enter height in inches:
BMI is 26.8573
50
95.5
Sections 2.11–2.13
*2.18 (Current time) Listing 2.7, ShowCurrentTime.py, gives a program that displays the
current time in GMT. Revise the program so that it prompts the user to enter the
time zone in hours away from (offset to) GMT and displays the time in the speci-
fied time zone. Here is a sample run:
Enter the time zone offset to GMT:
The current time is 4:50:34
-5

60 Chapter 2 Elementary Programming
*2.20 (Financial application: calculate interest) If you know the balance and the annual
percentage interest rate, you can compute the interest on the next monthly pay-
ment using the following formula:
interest = balance * (annualInterestRate / 1200)
Write a program that reads the balance and the annual percentage interest rate
and displays the interest for the next month. Here is a sample run:
Enter balance and interest rate (e.g., 3 for 3%):
The interest is 2.91667
1000, 3.5
**2.21 (Financial application: compound value) Suppose you save $100 each month into
a savings account with an annual interest rate of 5%. Therefore, the monthly inter-
est rate is After the first month, the value in the account
becomes
100 * (1 + 0.00417) = 100.417
After the second month, the value in the account becomes
(100 + 100.417) * (1 + 0.00417) = 201.252
After the third month, the value in the account becomes
(100 + 201.252) * (1 + 0.00417) = 302.507
and so on.
Write a program that prompts the user to enter a monthly saving amount and
displays the account value after the sixth month. Here is a sample run of the
program:
0.05/12 = 0.00417.
*2.19 (Financial application: calculate future investment value) Write a program that
reads in an investment amount, the annual interest rate, and the number of years,
and displays the future investment value using the following formula:
For example, if you enter the amount 1000, an annual interest rate of 4.25%,
and the number of years as 1, the future investment value is 1043.33. Here is a
sample run:
futureInvestmentValue = investmentAmount * (1 + monthlyInterestRate)numberOfMonths
Enter investment amount:
Enter annual interest rate:
Enter number of years:
Accumulated value is 1043.33
1
4.25
1000

Programming Exercises 61
Enter the monthly saving amount:
After the sixth month, the account value is 608.81
100
2.22 (Population projection) Rewrite Exercise 1.11 to prompt the user to enter the
number of years and displays the population after that many years. Here is a
sample run of the program:
Enter the number of years:
The population in 5 years is 325932970
5
(a) (b) (c)
FIGURE 2.4 Four circles are drawn in (a), four hexagons are drawn in (b), and a rectangle is drawn in (c).
Section 2.14
2.23 (Turtle: draw four circles) Write a program that prompts the user to enter the
radius and draws four circles in the center of the screen, as shown in Figure 2.4a.
2.24 (Turtle: draw four hexagons) Write a program that draws four hexagons in the
center of the screen, as shown in Figure 2.4b.
**2.25 (Turtle: draw a rectangle) Write a program that prompts the user to enter the
center of a rectangle, width, and height, and displays the rectangle, as shown in
Figure 2.4c.
**2.26 (Turtle: draw a circle) Write a program that prompts the user to enter the
center and radius of a circle, and then displays the circle and its area, as shown
in Figure 2.5.
FIGURE 2.5 A circle and its area are displayed.

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MATHEMATICAL
FUNCTIONS,
STRINGS,
AND OBJECTS
Objectives
■ To solve mathematics problems by using the functions in the math
module (§3.2).
■ To represent and process strings and characters (§§3.3–3.4).
■ To encode characters using ASCII and Unicode (§§3.3.1–3.3.2).
■ To use the ord function to obtain a numerical code for a character and the
chr function to convert a numerical code to a character (§3.3.3).
■ To represent special characters using the escape sequence (§3.3.4).
■ To invoke the print function with the end argument (§3.3.5).
■ To convert numbers to a string using the str function (§3.3.6).
■ To use the + operator to concatenate strings (§3.3.7).
■ To read strings from the keyboard (§3.3.8).
■ To introduce objects and methods (§3.5).
■ To format numbers and strings using the format function (§3.6).
■ To draw various shapes (§3.7).
■ To draw graphics with colors and fonts (§3.8).
CHAPTER
3

64 Chapter 3 Mathematical Functions, Strings, and Objects
3.1 Introduction
The focus of this chapter is to introduce functions, strings, and objects, and to use
them to develop programs.
The preceding chapter introduced fundamental programming techniques and taught you how
to write simple programs to solve basic problems. This chapter introduces Python functions
for performing common mathematical operations. You will learn how to create custom func-
tions in Chapter 6.
Suppose you need to estimate the area enclosed by four cities, given the GPS locations (lat-
itude and longitude) of these cities, as shown in the following diagram. How would you write
a program to solve this problem? You will be able to write such a program after completing
this chapter.
problem
Orlando (28.5383355, –81.3792365)
Savannah (32.0835407, –81.0998342)
Charlotte (35.2270869, –80.8431267)
Atlanta
(33.7489954, –84.3879824)
Because all data in Python are objects, it is beneficial to introduce objects early so that you
can begin to use them to develop useful programs. This chapter gives a brief introduction to
objects and strings; you will learn more on objects and strings in Chapters 7 and 8.
3.2 Common Python Functions
Python provides many useful functions for common programming tasks.
A function is a group of statements that performs a specific task. Python, as well as other
programming languages, provides a library of functions. You have already used the func-
tions eval, input, print, and int. These are built-in functions and they are always avail-
able in the Python interpreter. You don’t have to import any modules to use these functions.
Additionally, you can use the built-in functions abs, max, min, pow, and round, as shown in
Table 3.1.
Key
Point
Key
Point
function
TABLE 3.1 Simple Python Built-in Functions
Function Description Example
abs(x) Returns the absolute value for x. abs(-2) is 2
max(x1, x2, …) Returns the largest among x1, x2, … max(1, 5, 2) is 5
min(x1, x2, …) Returns the smallest among x1, x2, … min(1, 5, 2) is 1
pow(a, b) Returns ab. Same as a ** b. pow(2, 3) is 8
round(x) Returns an integer nearest to x. If x
is equally close to two integers,
the even one is returned.
round(5.4) is 5
round(5.5) is 6
round(4.5) is 4
round(x, n) Returns the float value rounded to n
digits after the decimal point.
round(5.466, 2) is 5.47
round(5.463, 2) is 5.46

3.2 Common Python Functions 65
>>> abs(-3) # Returns the absolute value
3
>>> abs(-3.5) # Returns the absolute value
3.5
>>> max(2, 3, 4, 6) # Returns the maximum number
6
>>> min(2, 3, 4) # Returns the minimum number
2
>>> pow(2, 3) # Same as 2 ** 3
8
>>> pow(2.5, 3.5) # Same as 2.5 ** 3.5
24.705294220065465
>>> round(3.51) # Rounds to its nearest integer
4
>>> round(3.4) # Rounds to its nearest integer
3
>>> round(3.1456, 3) # Rounds to 3 digits after the decimal point
3.146
>>>
Many programs are created to solve mathematical problems. The Python math module
provides the mathematical functions listed in Table 3.2.
Two mathematical constants, pi and e, are also defined in the math module. They can be
accessed using math.pi and math.e. Listing 3.1 is a program that tests some math func-
tions. Because the program uses the math functions defined in the math module, the math
module is imported in line 1.
For example,
TABLE 3.2 Mathematical Functions
Function Description Example
fabs(x) Returns the absolute value for x as a float. fabs(-2) is 2.0
ceil(x) Rounds x up to its nearest integer and returns that integer. ceil(2.1) is 3
ceil(-2.1) is -2
floor(x) Rounds x down to its nearest integer and returns that integer. floor(2.1) is 2
floor(-2.1) is -3
exp(x) Returns the exponential function of x (ex). exp(1) is 2.71828
log(x) Returns the natural logarithm of x. log(2.71828) is 1.0
log(x, base) Returns the logarithm of x for the specified base. log(100, 10) is 2.0
sqrt(x) Returns the square root of x. sqrt(4.0) is 2
sin(x) Returns the sine of x. x represents an angle in radians. sin(3.14159 / 2) is 1
sin(3.14159) is 0
asin(x) Returns the angle in radians for the inverse of sine. asin(1.0) is 1.57
asin(0.5) is 0.523599
cos(x) Returns the cosine of x. x represents an angle in radians. cos(3.14159 / 2) is 0
cos(3.14159) is -1
acos(x) Returns the angle in radians for the inverse of cosine. acos(1.0) is 0
acos(0.5) is 1.0472
tan(x) Returns the tangent of x. x represents an angle in radians. tan(3.14159 / 4) is 1
tan(0.0) is 0
degrees(x) Converts angle x from radians to degrees. degrees(1.57) is 90
radians(x) Converts angle x from degrees to radians. radians(90) is 1.57

66 Chapter 3 Mathematical Functions, Strings, and Objects
You can use the math functions to solve many computational problems. Given the three
vertices of a triangle, for example, you can compute the angles by using the following formula:
import math module
enter three points
compute edges
A = acos((a * a – b * b – c * c) / (-2 * b * c))
B = acos((b * b – a * a – c * c) / (-2 * a * c))
C = acos((c * c – b * b – a * a) / (-2 * a * b))
LISTING 3.1 MathFunctions.py
1 # import math module to use the math functions
2
3 # Test algebraic functions
4 print(“exp(1.0) =”, )
5 print(“log(2.78) =”, )
6 print(“log10(10, 10) =”, )
7 print(“sqrt(4.0) =”, )
8
9 # Test trigonometric functions
10 print(“sin(PI / 2) =”, )
11 print(“cos(PI / 2) =”, )
12 print(“tan(PI / 2) =”, )
13 print(“degrees(1.57) =”, )
14 print(“radians(90) =”, )math.radians(90)
math.degrees(1.57)
math.tan(math.pi / 2)
math.cos(math.pi / 2)
math.sin(math.pi / 2)
math.sqrt(4.0)
math.log(10, 10)
math.log(math.e)
math.exp(1)
import math
exp(1.0) = 2.71828182846
log(2.78) = 1.0
log10(10, 10) = 1.0
sqrt(4.0) = 2.0
sin(PI / 2) = 1.0
cos(PI / 2) = 6.12323399574e-17
tan(PI / 2) = 1.63312393532e+16
degrees(1.57) = 89.9543738355
radians(90) = 1.57079632679
A
B
C
a
b
c
x1, y1
x2, y2
x3, y3
Don’t be intimidated by the mathematic formula. As we discussed early in Listing 2.8,
ComuteLoan.py, you don’t have to know how the mathematical formula is derived in order to
write a program for computing the loan payments. Here in this example, given the length of
three sides, you can use this formula to write a program to compute the angles without having
to know how the formula is derived. In order to compute the lengths of the sides, we need to
know the coordinates of three corner points and compute the distances between the points.
Listing 3.2 is an example of a program that prompts the user to enter the x- and y-coordinates
of the three corner points in a triangle and then displays the figure’s angles.
LISTING 3.2 ComputeAngles.py
1 import math
2
3 x1, y1, x2, y2, x3, y3 = eval(input(“Enter three points: “))
4
5 a = math.sqrt((x2 – x3) * (x2 – x3) + (y2 – y3) * (y2 – y3))
6 b = math.sqrt((x1 – x3) * (x1 – x3) + (y1 – y3) * (y1 – y3))
7 c = math.sqrt((x1 – x2) * (x1 – x2) + (y1 – y2) * (y1 – y2))
import math module
exp
log
log10
sqrt
sin
cos
tan
degrees
radians

3.3 Strings and Characters 67
compute angles
display result
Enter three points:
The three angles are 15.26 90.0 74.74
1, 1, 6.5, 1, 6.5, 2.5
The program prompts the user to enter three points (line 3). This prompting message is not
clear. You should give the user explicit instructions on how to enter these points as follows:
input(“Enter six coordinates of three points separated by commas\
like x1, y1, x2, y2, x3, y3: “)
The program computes the distances between the points (lines 5–7), and applies the for-
mula to compute the angles (lines 9–11). The angles are rounded to display up to two digits
after the decimal point (lines 13–14).
3.1 Evaluate the following functions:
3.2 True or false? The argument for trigonometric functions represents an angle in radians.
3.3 Write a statement that converts 47 degrees to radians and assigns the result to a variable.
3.4 Write a statement that converts π / 7 to an angle in degrees and assigns the result to
a variable.
3.3 Strings and Characters
A string (described in Chapter 1) is a sequence of characters. Python treats characters
and strings the same way.
In addition to processing numeric values, you can process strings in Python. A string is a
sequence of characters and can include text and numbers. String values must be enclosed in
matching single quotes (‘) or double quotes (“). Python does not have a data type for charac-
ters. A single-character string represents a character. For example,
letter = ‘A’ # Same as letter = “A”
numChar = ‘4’ # Same as numChar = “4”
message = “Good morning” # Same as message = ‘Good morning’
string
single quotes or double
quotes
8
9 A = math.degrees(math.acos((a * a – b * b – c * c) / (-2 * b * c)))
10 B = math.degrees(math.acos((b * b – a * a – c * c) / (-2 * a * c)))
11 C = math.degrees(math.acos((c * c – b * b – a * a) / (-2 * a * b)))
12
13 print(“The three angles are “, round(A * 100) / 100.0,
14 round(B * 100) / 100.0, round(C * 100) / 100.0)
(a) math.sqrt(4) (j) math.floor(-2.5)
(b) math.sin(2 * math.pi) (k) round(3.5)
(c) math.cos(2 * math.pi) (l) round(-2.5)
(d) min(2, 2, 1) (m) math.fabs(2.5)
(e) math.log(math.e) (n) math.ceil(2.5)
(f) math.exp(1) (o) math.floor(2.5)
(g) max(2, 3, 4) (p) round(-2.5)
(h) abs(-2.5) (q) round(2.6)
(i) math.ceil(-2.5) (r) round(math.fabs(-2.5))
✓Point✓Check
Key
Point

68 Chapter 3 Mathematical Functions, Strings, and Objects
The first statement assigns a string with the character A to the variable letter. The sec-
ond statement assigns a string with the digit character 4 to the variable numChar. The third
statement assigns the string Good morning to the variable message.
Note
For consistency, this book uses double quotes for a string with more than one character
and single quotes for a string with a single character or an empty string. This convention
is consistent with other programming languages, so it will be easy for you to convert a
Python program to a program written in other languages.
3.3.1 ASCII Code
Computers use binary numbers internally (see Section 1.2.2). A character is stored in a
computer as a sequence of 0s and 1s. Mapping a character to its binary representation is called
character encoding. There are different ways to encode a character. The manner in which
characters are encoded is defined by an encoding scheme. One popular standard is ASCII
(American Standard Code for Information Interchange), a 7-bit encoding scheme for repre-
senting all uppercase and lowercase letters, digits, punctuation marks, and control characters.
ASCII uses numbers 0 through 127 to represent characters. Appendix B, The ASCII Charac-
ter Set, shows the ASCII code for characters.
3.3.2 Unicode Code
Python also supports Unicode. Unicode is an encoding scheme for representing interna-
tional characters. ASCII is a small subset of Unicode. Unicode was established by the
Unicode Consortium to support the interchange, processing, and display of written texts
in the world’s diverse languages. A Unicode starts with \u, followed by four hexadecimal
digits that run from \u0000 to \uFFFF. (For information on hexadecimal numbers, see
Appendix C.) For example, the word “welcome” is translated into Chinese using
two characters, and . The Unicode representations of these two characters are
\u6B22\u8FCE.
The program in Listing 3.3 displays two Chinese characters and three Greek letters, as
shown in Figure 3.1.
LISTING 3.3 DisplayUnicode.py
1 import turtle
2
3 turtle.write(“\u6B22\u8FCE \u03b1 \u03b2 \u03b3”)
4
5 turtle.done()
character encoding
FIGURE 3.1 You can use Unicode to display international characters in a Python GUI
program.
If no Chinese font is installed on your system, you will not be able to see the Chinese char-
acters. In this case, delete \u6B22\u8FCE from your program to avoid errors. The Unicode
codes for the Greek letters and are \u03b1, \u03b2, and \u03b3.ga, b,

3.3 Strings and Characters 69
>>> ch = ‘a’
>>> ord(ch)
97
>>> chr(98)
‘b’
>>> ord(‘A’)
65
>>>
The ASCII code for a is 97, which is greater than the code for A (65). The ASCII code for
lowercase letters are consecutive integers starting from the code for a, then for b, c, and so on,
up to the letter z. The same is true for the uppercase letters. The difference between the ASCII
code of any lowercase letter and its corresponding uppercase letter is the same: 32. This is a
useful property for processing characters. For example, you can find the uppercase represen-
tation of any lowercase letter, as shown in the following code:
1 >>> ord(‘a’) – ord(‘A’)
2 32
3 >>> ord(‘d’) – ord(‘D’)
4 32
5 >>> offset = ord(‘a’) – ord(‘A’)
6 >>> lowercaseLetter = ‘h’
7 >>> uppercaseLetter = chr(ord(lowercaseLetter) – offset)
8 >>> uppercaseLetter
9 ‘H’
10 >>>
Line 6 assigns a lowercase letter to variable lowercaseLetter. Line 7 obtains its corre-
sponding uppercase letter.
3.3.4 Escape Sequences for Special Characters
Suppose you want to print a message with quotation marks in the output. Can you write a
statement like this?
print(“He said, “John’s program is easy to read””)
No, this statement has an error. Python thinks the second quotation mark is the end of the
string and does not know what to do with the rest of the characters.
To overcome this problem, Python uses a special notation to represent special characters,
as shown in Table 3.3. This special notation, which consists of a backslash (\) followed by a
letter or a combination of digits, is called an escape sequence.
The \n character is also known as a newline, line break or end-of-line (EOL) character,
which signifies the end of a line. The \f character forces the printer to print from the next
page. The \r character is used to move the cursor to the first position on the same line. The \f
and \r characters are rarely used in this book.
backslash (\)
escape sequence
newline
line break
end-of-line (EOL) character
3.3.3 The ord and chr Functions
Python provides the ord(ch) function for returning the ASCII code for the character ch
and the chr(code) function for returning the character represented by the code. For
example,

70 Chapter 3 Mathematical Functions, Strings, and Objects
TABLE 3.3 Python Escape Sequences
Character Escape Sequence Name Numeric Value
\b Backspace 8
\t Tab 9
\n Linefeed 10
\f Formfeed 12
\r Carriage Return 13
\\ Backslash 92
\’ Single Quote 39
\” Double Quote 34
Now you can print the quoted message using the following statement:
>>> print(“He said, \”John’s program is easy to read\””)
He said, “John’s program is easy to read”
3.3.5 Printing without the Newline
When you use the print function, it automatically prints a linefeed (\n) to cause the out-
put to advance to the next line. If you don’t want this to happen after the print function is
finished, you can invoke the print function by passing a special argument end =
“anyendingstring” using the following syntax:
print(item, end = “anyendingstring”)
For example, the following code
1 print(“AAA”, end = ‘ ‘)
2 print(“BBB”, end = ”)
3 print(“CCC”, end = ‘***’)
4 print(“DDD”, end = ‘***’)
displays
AAA BBBCCC***DDD***
Line 1 prints AAA followed by a space character ‘ ‘, line 2 prints BBB, line 3 prints CCC
followed by ***, and line 4 prints DDD followed by ***. Note that ” in line 2 means an
empty string. So, nothing is printed for ”.
You can also use the end argument for printing multiple items using the following syntax:
print(item1, item2, …, end = “anyendingstring”)
For example,
radius = 3
print(“The area is”, radius * radius * math.pi, end = ‘ ‘)
print(“and the perimeter is”, 2 * radius)
displays
The area is 28.26 and the perimeter is 6
Note that the symbols \ and ” together represent one character.

3.3 Strings and Characters 71
3.3.6 The str Function
The str function can be used to convert a number into a string. For example,
>>> s = str(3.4) # Convert a float to string
>>> s
‘3.4’
>>> s = str(3) # Convert an integer to string
>>> s
‘3’
>>>
3.3.7 The String Concatenation Operator
You can use the + operator to add two numbers. The + operator can be used to concatenate
two strings. Here are some examples:
1 >>> message = “Welcome ” + “to ” + “Python”
2 >>> message
3 ‘Welcome to Python’
4 >>> chapterNo = 3
5 >>> s = “Chapter ” + str(chapterNo)
6 >>> s
7 ‘Chapter 3’
8 >>>
Line 1 concatenates three strings into one. In line 5, the str function converts the numeric
value in variable chapterNo to a string. This string is concatenated with “Chapter ” to
obtain the new string “Chapter 3″.
The augmented assignment += operator can also be used for string concatenation. For
example, the following code concatenates the string in message with the string ” and
Python is fun”.
>>> message = “Welcome to Python”
>>> message
‘Welcome to Python’
>>> message += ” and Python is fun”
>>> message
‘Welcome to Python and Python is fun’
>>>
3.3.8 Reading Strings from the Console
To read a string from the console, use the input function. For example, the following code
reads three strings from the keyboard:
s1 = input(“Enter a string: “)
s2 = input(“Enter a string: “)
s3 = input(“Enter a string: “)
print(“s1 is ” + s1)
print(“s2 is ” + s2)
print(“s3 is ” + s3)

72 Chapter 3 Mathematical Functions, Strings, and Objects
Enter a string:
Enter a string:
Enter a string:
s1 is Welcome
s2 is to
s3 is Python
Python
to
Welcome
3.5 Use the ord function to find the ASCII code for 1, A, B, a, and b. Use the chr
function to find the character for the decimal codes 40, 59, 79, 85, and 90.
3.6 How do you display the characters \ and “?
3.7 How do you write a character in Unicode?
3.8 Suppose you entered A when running the following code. What is the output?
x = input(“Enter a character: “)
ch = chr(ord(x) + 3)
print(ch)
3.9 Suppose you entered A and Z when running the following code. What is the
output?
x = input(“Enter a character: “)
y = input(“Enter a character: “)
print(ord(y) – ord(x))
3.10 What is wrong in the following code? How do you fix it?
title = “Chapter ” + 1
3.11 Show the result of the following code:
sum = 2 + 3
print(sum)
s = ‘2’ + ‘3’
print(s)
3.4 Case Study: Minimum Number of Coins
Now let’s look at a sample program that uses the features covered in this section. Suppose you
want to develop a program that classifies a given amount of money into smaller monetary
units. The program lets the user enter an amount as a floating-point value representing a total
in dollars and cents, and then outputs a report listing the monetary equivalent in dollars, quar-
ters, dimes, nickels, and pennies, as shown in the sample run.
Your program should report the maximum number of dollars, then the number of quarters,
dimes, nickels, and pennies, in this order, to result in the minimum number of coins.
Here are the steps in developing the program:
1. Prompt the user to enter the amount as a decimal number, such as 11.56.
2. Convert the amount (11.56) into cents (1156).
3. Divide the cents by 100 to find the number of dollars. Obtain the remaining cents using
the cents remainder % 100.
4. Divide the remaining cents by 25 to find the number of quarters. Obtain the remaining
cents using the remaining cents remainder % 25.
minimum number of coins
✓Point✓Check

3.4 Case Study: Minimum Number of Coins 73
enter input
dollars
quarters
dimes
nickels
5. Divide the remaining cents by 10 to find the number of dimes. Obtain the remaining
cents using the remaining cents remainder % 10.
6. Divide the remaining cents by 5 to find the number of nickels. Obtain the remaining
cents using the remaining cents remainder % 5.
7. The remaining cents are the pennies.
8. Display the result.
The complete program is shown in Listing 3.4.
LISTING 3.4 ComputeChange.py
1 # Receive the amount
2 amount = eval(input(“Enter an amount, for example, 11.56: “))
3
4 # Convert the amount to cents
5 remainingAmount = int(amount * 100)
6
7 # Find the number of one dollars
8 numberOfOneDollars = remainingAmount // 100
9 remainingAmount = remainingAmount % 100
10
11 # Find the number of quarters in the remaining amount
12 numberOfQuarters = remainingAmount // 25
13 remainingAmount = remainingAmount % 25
14
15 # Find the number of dimes in the remaining amount
16 numberOfDimes = remainingAmount // 10
17 remainingAmount = remainingAmount % 10
18
19 # Find the number of nickels in the remaining amount
20 numberOfNickels = remainingAmount // 5
21 remainingAmount = remainingAmount % 5
22
23 # Find the number of pennies in the remaining amount
24 numberOfPennies = remainingAmount
25
26 # Display the results
27 print(“Your amount”, amount, “consists of\n”,
28 “\t”, numberOfOneDollars, “dollars\n”,
29 “\t”, numberOfQuarters, “quarters\n”,
30 “\t”, numberOfDimes, “dimes\n”,
31 “\t”, numberOfNickels, “nickels\n”,
32 “\t”, numberOfPennies, “pennies”)
Enter an amount, for example, 11.56:
Your amount 11.56 consists of
11 dollars
2 quarters
0 dimes
1 nickels
1 pennies
11.56
pennies
output

74 Chapter 3 Mathematical Functions, Strings, and Objects
The variable amount stores the amount entered from the console (line 2). This variable is
not changed, because the amount has to be used at the end of the program to display the
results. The program introduces the variable remainingAmount (line 5) to store the chang-
ing remainingAmount.
The variable amount is a float representing dollars and cents. It is converted to an integer
variable remainingAmount, which represents all the cents. For instance, if amount is
11.56, then the initial remainingAmount is 1156. 1156 // 100 is 11 (line 8). The
remainder operator obtains the remainder of the division. So, 1156 % 100 is 56 (line 9).
The program extracts the maximum number of quarters from remainingAmount and
obtains a new remainingAmount (lines 12–13). Continuing the same process, the program
finds the maximum number of dimes, nickels, and pennies in the remaining amount.
As shown in the sample run, 0 dimes, 1 nickels, and 1 pennies are displayed in the result.
It would be better not to display 0 dimes, and to display 1 nickel and 1 penny using the sin-
gular forms of the words. You will learn how to use selection statements to modify this pro-
gram in the next chapter (see Exercise 4.7).
Caution
One serious problem with this example is the possible loss of precision when converting a
float amount to the integer remainingAmount. This could lead to an inaccurate result. If
you try to enter the amount 10.03, 10.03 * 100 might be 1003.9999999999999.
You will find that the program displays 10 dollars and 2 pennies. To fix the problem, enter
the amount as an integer value representing cents (see Exercise 3.8).
3.5 Introduction to Objects and Methods
In Python, all data—including numbers and strings—are actually objects.
In Python, a number is an object, a string is an object, and every datum is an object. Objects
of the same kind have the same type. You can use the id function and type function to get
these pieces of information about an object. For example,
loss of precision
object
1 >>> n = 3 # n is an integer
2 >>> id(n)
3 505408904
4 >>> type(n)
5
6 >>> f = 3.0 # f is a float
line#
variables
2 5 8 9 12 13 16 17 20 21 24
amount 11.56
remainingAmount 1156 56 6 6 1
numberOfOneDollars 11
numberOfQuarters 2
numberOfDimes 0
numberOfNickels 1
numberOfPennies 1
Key
Point

3.5 Introduction to Objects and Methods 75
The id for the object is automatically assigned a unique integer by Python when the program
is executed. The id for the object will not be changed during the execution of the program.
However, Python may assign a different id every time the program is executed. The type for the
object is determined by Python according to the value of the object. Line 2 displays the id for a
number object n, line 3 shows the id Python has assigned for the object, and its type is dis-
played in line 4.
In Python, an object’s type is defined by a class. For example, the class for string is str
(line 15), for integer is int (line 5), and for float is float (line 10). The term “class” comes
from object-oriented programming, which will be discussed in Chapter 7. In Python, classes
and types are synonymous.
Note
The id and type functions are rarely used in programming, but they are good tools for
learning more about objects.
A variable in Python is actually a reference to an object. Figure 3.2 shows the relationship
between the variables and objects for the preceding code.
id function
type function
objects vs. object reference
variable
The object
for int 3
n
n = 3 f = 3.0 s = “Welcome”
The object
for float
3.0
The object
for str
“Welcome”
id: 505408904 id: 26647120 id: 36201472
f s
FIGURE 3.2 In Python, each variable is actually a reference to an object.
The statement n = 3 in line 1 assigns value 3 to n, which actually assigns 3 to an int
object referenced by variable n.
Note
For n = 3, we say n is an integer variable that holds value 3. Strictly speaking, n is a variable
that references an int object for value 3. For simplicity, it is fine to say n is an int variable
with value 3.
You can perform operations on an object. The operations are defined using functions. The
functions for the objects are called methods in Python. Methods can only be invoked from a
specific object. For example, the string type has the methods such as lower() and upper(),
methods
7 >>> id(f)
8 26647120
9 >>> type(f)
10
11 >>> s = “Welcome” # s is a string
12 >>> id(s)
13 36201472
14 >>> type(s)
15
16 >>>
VideoNote
String operations

76 Chapter 3 Mathematical Functions, Strings, and Objects
strip()
whitespace characters
>>> s = “\t Welcome \n”
>>> s1 = # Invoke the strip method
>>> s1
‘Welcome’
>>>
s.strip()
Note
If you use Python on Eclipse, Eclipse automatically appends \r in the string entered from
the input function. Therefore, you should use the strip() method to remove the \r
character as follows:
s = input(“Enter a string”).strip()
More details on processing strings and on object-oriented programming will be discussed
in Chapter 7.
3.12 What is an object? What is a method?
3.13 How do you find the id for an object? How do you find the type for an object?
3.14 Which of the following statements is the precise meaning for the statement n = 3?
(a) n is a variable that holds int value 3.
(b) n is a variable that references an object that holds int value 3.
3.15 Suppose s is “\tGeorgia\n”. What is s.lower() and s.upper()?
3.16 Suppose s is ” \tGood\tMorning\n”. What is s.strip()?
3.6 Formatting Numbers and Strings
You can use the format function to return a formatted string.
Often it is desirable to display numbers in a certain format. For example, the following code
computes interest, given the amount and the annual interest rate.
Python on Eclipse
Line 2 invokes s.lower() on object s to return a new string in lowercase and assigns it to s1.
Line 5 invokes s.upper() on object s to return a new string in uppercase and assigns it to s2.
As you can see from the preceding example, the syntax to invoke a method for an object is
object.method().
Another useful string method is strip(), which can be used to remove (strip) the
whitespace characters from both ends of a string. The characters ‘ ‘, \t, \f, \r, and \n are
known as the whitespace characters.
For example,
✓Point✓Check
Key
Point
which return a new string in lowercase and uppercase. Here are some examples of how to
invoke these methods:
1 >>> s = “Welcome”
2 >>> s1 = # Invoke the lower method
3 >>> s1
4 ‘welcome’
5 >>> s2 = # Invoke the upper method
6 >>> s2
7 ‘WELCOME’
8 >>>
s.upper()
s.lower()

3.6 Formatting Numbers and Strings 77
>>> amount = 12618.98
>>> interestRate = 0.0013
>>> interest = amount * interestRate
>>> print(“Interest is”, interest)
Interest is 16.404674
>>>
Because the interest amount is currency, it is desirable to display only two digits after the
decimal point. To do this, you can write the code as follows:
>>> amount = 12618.98
>>> interestRate = 0.0013
>>> interest = amount * interestRate
>>> print(“Interest is”, round(interest, ))
Interest is 16.4
>>>
2
However, the format is still not correct. There should be two digits after the decimal point
like 16.40 rather than 16.4. You can fix it by using the format function, like this: format
>>> amount = 12618.98
>>> interestRate = 0.0013
>>> interest = amount * interestRate
>>> print(“Interest is”, )
Interest is 16.40
>>>
format(interest, “.2f”)
The syntax to invoke this function is
format(item, format-specifier)
where item is a number or a string and format-specifier is a string that specifies how the
item is formatted. The function returns a string.
3.6.1 Formatting Floating-Point Numbers
If the item is a float value, you can use the specifier to give the width and precision of the
format in the form of width.precisionf. Here, width specifies the width of the resulting
string, precision specifies the number of digits after the decimal point, and f is called the
conversion code, which sets the formatting for floating point numbers. For example,
print(format(57.467657, “10.2f”))
print(format(12345678.923, “10.2f”))
print(format(57.4, “10.2f”))
print(format(57, “10.2f”))
displays
conversion code
2 f10 .
field width
precision
conversion code
format specifier
10
57.47
123456782.92
57.40
57.00
where a square box ( ) denotes a blank space. Note that the decimal point is counted as one
space.

78 Chapter 3 Mathematical Functions, Strings, and Objects
3.6.2 Formatting in Scientific Notation
If you change the conversion code from f to e, the number will be formatted in scientific
notation. For example,
print(format(57.467657, “10.2e”))
print(format(0.0033923, “10.2e”))
print(format(57.4, “10.2e”))
print(format(57, “10.2e”))
displays
10
5.75e+01
3.39e-03
5.74e+01
5.70e+01
The + and – signs are counted as places in the width limit.
3.6.3 Formatting as a Percentage
You can use the conversion code % to format a number as a percentage. For example,
print(format(0.53457, “10.2%”))
print(format(0.0033923, “10.2%”))
print(format(7.4, “10.2%”))
print(format(57, “10.2%”))
displays
10
53.46%
0.34%
740.00%
5700.00%
10
57.47
57.47
The format(“10.2f”) function formats the number into a string whose width is 10, includ-
ing a decimal point and two digits after the point. The number is rounded to two decimal places.
Thus there are seven digits allocated before the decimal point. If there are fewer than seven digits
before the decimal point, spaces are inserted before the number. If there are more than seven
digits before the decimal point, the number’s width is automatically increased. For example,
format(12345678.923, “10.2f”) returns 12345678.92, which has a width of 11.
You can omit the width specifier. If so, it defaults to 0. In this case, the width is automati-
cally set to the size needed for formatting the number. For example,
print(format(57.467657, “10.2f”))
print(format(57.467657, “.2f”))
displays
The format 10.2% causes the number to be multiplied by 100 and displayed with a % sign
following it. The total width includes the % sign counted as one space.

3.6 Formatting Numbers and Strings 79
10
59832
59832
e9b8
e9b8
3.6.4 Justifying Format
By default, the format of a number is right justified. You can put the symbol < in the format specifier to specify that the item be left-justified in the resulting format within the specified width. For example, print(format(57.467657, "10.2f")) print(format(57.467657, "<10.2f”)) displays 10 57.47 57.47 3.6.5 Formatting Integers The conversion codes d, x, o, and b can be used to format an integer in decimal, hexadecimal, octal, or binary. You can specify a width for the conversion. For example, print(format(59832, "10d")) print(format(59832, "<10d")) print(format(59832, "10x")) print(format(59832, "<10x")) displays The format specifier 10d specifies that the integer is formatted into a decimal with a width of ten spaces. The format specifier 10x specifies that the integer is formatted into a hexadeci- mal integer with a width of ten spaces. 3.6.6 Formatting Strings You can use the conversion code s to format a string with a specified width. For example, print(format("Welcome to Python", "20s")) print(format("Welcome to Python", "<20s")) print(format("Welcome to Python", ">20s”))
print(format(“Welcome to Python and Java”, “>20s”))
displays
20
Welcome to Python
Welcome to Python
Welcome to Python
Welcome to Python and Java
The format specifier 20s specifies that the string is formatted within a width of 20. By
default, a string is left justified. To right-justify it, put the symbol > in the format specifier. If
the string is longer than the specified width, the width is automatically increased to fit the
string.
Table 3.4 summarizes the format specifiers introduced in this section.

80 Chapter 3 Mathematical Functions, Strings, and Objects
3.17 What is the return value from invoking the format function?
3.18 What happens if the size of the actual item is greater than the width in the format
specifier?
3.19 Show the printout of the following statements:
print(format(57.467657, “9.3f”))
print(format(12345678.923, “9.1f”))
print(format(57.4, “.2f”))
print(format(57.4, “10.2f”))
3.20 Show the printout of the following statements:
print(format(57.467657, “9.3e”))
print(format(12345678.923, “9.1e”))
print(format(57.4, “.2e”))
print(format(57.4, “10.2e”))
3.21 Show the printout of the following statements:
print(format(5789.467657, “9.3f”))
print(format(5789.467657, “<9.3f")) print(format(5789.4, ".2f")) print(format(5789.4, "<.2f")) print(format(5789.4, ">9.2f”))
3.22 Show the printout of the following statements:
print(format(0.457467657, “9.3%”))
print(format(0.457467657, “<9.3%")) 3.23 Show the printout of the following statements: print(format(45, "5d")) print(format(45, "<5d")) print(format(45, "5x")) print(format(45, "<5x")) 3.24 Show the printout of the following statements: print(format("Programming is fun", "25s")) print(format("Programming is fun", "<25s")) print(format("Programming is fun", ">25s”))
TABLE 3.4 Frequently Used Specifiers
Specifier Format
“10.2f” Format the float item with width 10 and precision 2.
“10.2e” Format the float item in scientific notation with width 10 and precision 2.
“5d” Format the integer item in decimal with width 5.
“5x” Format the integer item in hexadecimal with width 5.
“5o” Format the integer item in octal with width 5.
“5b” Format the integer item in binary with width 5.
“10.2%” Format the number in decimal.
“50s” Format the string item with width 50.
“<10.2f” Left-justify the formatted item. ">10.2f” Right-justify the formatted item.
✓Point✓Check

3.7 Drawing Various Shapes 81
3.7 Drawing Various Shapes
The Python turtle module contains methods for moving the pen, setting the pen’s
size, lifting, and putting down the pen.
Chapter 1 introduced drawing with the turtle. A turtle is actually an object that is created
when you import the turtle module. You then invoke the turtle object’s methods to perform
operations. This section introduces more methods for the turtle object.
When a turtle object is created, its position is set at (0, 0)—the center of the window—and
its direction is set to go straight to the right. The turtle module uses a pen to draw shapes.
By default, the pen is down (like the tip of an actual pen touching a sheet of paper). When you
move the turtle, it draws a line from the current position to the new position if the pen is down.
Table 3.5 lists the methods for controlling the pen’s drawing state; Table 3.6 lists the methods
for moving the turtle.
turtle’s position and direction
turtle’s pen
TABLE 3.5 Turtle Pen Drawing State Methods
Method Description
turtle.pendown() Pulls the pen down—drawing when moving.
turtle.penup() Pulls the pen up—no drawing when moving.
turtle.pensize(width) Sets the line thickness to the specified width.
All these methods are straightforward. The best way to learn them is to write a test code to
see how each method works.
The circle method has three arguments: The radius is required, and extent and step
are optional. extent is an angle that determines which part of the circle is drawn. step
determines the number of steps to use. If step is 3, 4, 5, 6, …, the circle method will draw
a maximum regular polygon with three, four, five, six, or more sides enclosed inside the cir-
cle (that is, a triangle, square, pentagon, hexagon, etc.). If step is not specified, the circle
method will draw a circle.
TABLE 3.6 Turtle Motion Methods
Method Description
turtle.forward(d) Moves the turtle forward by the specified distance in the direction the turtle is headed.
turtle.backward(d) Moves the turtle backward by the specified distance in the opposite direction the turtle is
headed. The turtle’s direction is not changed.
turtle.right(angle) Turns the turtle right by the specified angle.
turtle.left(angle) Turns the turtle left by the specified angle.
turtle.goto(x, y) Moves the turtle to an absolute position.
turtle.setx(x) Moves the turtle’s x-coordinate to the specified position.
turtle.sety(y) Moves the turtle’s y-coordinate to the specified position.
turtle.setheading(angle) Sets the orientation of the turtle to a specified angle. 0-East, 90-North, 180-West, 270-South.
turtle.home() Moves the turtle to the origin (0, 0) and east direction.
turtle.circle(r, ext, step) Draws a circle with the specified radius, extent, and step.
turtle.dot(diameter, color) Draws a circle with the specified diameter and color.
turtle.undo() Undo (repeatedly) the last turtle action(s).
turtle.speed(s) Sets the turtle’s speed to an integer between 1 and 10, with 10 being the fastest.
Key
Point
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Draw shapes

82 Chapter 3 Mathematical Functions, Strings, and Objects
Listing 3.5 shows sample code for drawing a triangle, a square, a pentagon, a hexagon, and
a circle, as shown in Figure 3.3.
LISTING 3.5 SimpleShapes.py
1 import turtle
2
3 # Set pen thickness to 3 pixels
4 # Pull the pen up
5
6 # Pull the pen down
7 # Draw a triangle
8
9 turtle.penup()
10 turtle.goto(-100, -50)
11 turtle.pendown()
12 turtle.circle(40, steps = 4) # Draw a square
13
14 turtle.penup()
15 turtle.goto(0, -50)
16 turtle.pendown()
17 turtle.circle(40, steps = 5) # Draw a pentagon
18
19 turtle.penup()
20 turtle.goto(100, -50)
21 turtle.pendown()
22 turtle.circle(40, steps = 6) # Draw a hexagon
23
24 turtle.penup()
25 turtle.goto(200, -50)
26 turtle.pendown()
27 turtle.circle(40) # Draw a circle
28
29 turtle.done()
Line 1 imports the turtle module. Line 3 sets the pen’s thickness to 3 pixels. Line 4 pulls
the pen up so that you can reposition it to (-200, -50) in line 5. Line 6 puts the pen down to
draw a triangle in line 7. In line 7, the turtle object invokes the circle method with a
radius of 40 and 3 steps to draw a triangle. Similarly, the rest of the program draws a square
(line 12), a pentagon (line 17), a hexagon (line 22), and a circle (line 27).
3.25 How do you set the turtle to its original position (0, 0)?
3.26 How do you draw a red dot with diameter 3?
3.27 What figure will the following method draw?
turtle.circle(50, step = 4)
turtle.circle(40, steps = 3)
turtle.pendown()
turtle.goto(-200, -50)
turtle.penup()
turtle.pensize(3)
import turtle module
set pen size
FIGURE 3.3 The program draws five shapes.
penup
move pen
pendown
draw a triangle
pause
✓Point✓Check

3.8 Drawing with Colors and Fonts 83
3.28 How do you make the turtle move fast?
3.29 How do you undo the turtle’s last action?
3.8 Drawing with Colors and Fonts
A turtle object contains the methods for setting colors and fonts.
The preceding section showed you how to draw shapes with the turtle module. You learned
how to use the motion methods to move the pen and use the pen methods to raise the pen up,
set it down, and control its thickness. This section introduces more pen control methods and
shows you how to set colors and fonts and write text.
Table 3.7 lists the pen methods for controlling drawing, color, and filling. Listing 3.6 is a
sample program that draws a triangle, a square, a pentagon, a hexagon, and a circle in differ-
ent colors, as shown in Figure 3.4. The program also adds text to the drawing.
TABLE 3.7 Turtle Pen Color, Filling, and Drawing Methods
Method Description
turtle.color(c) Sets the pen color.
turtle.fillcolor(c) Sets the pen fill color.
turtle.begin_fill() Calls this method before filling a shape.
turtle.end_fill() Fills the shapes drawn before the last call to begin_fill.
turtle.filling() Returns the fill state: True if filling, False if not filling.
turtle.clear() Clears the window. The state and the position of the turtle are not affected.
turtle.reset() Clears the window and reset the state and position to the original default value.
turtle.screensize(w, h) Sets the width and height of the canvas.
turtle.hideturtle() Makes the turtle invisible.
turtle.showturtle() Makes the turtle visible.
turtle.isvisible() Returns True if the turtle is visible.
turtle.write(s, font=(“Arial”,
8, “normal”))
Writes the string s on the turtle position. Font is a triple consisting of fontname,
fontsize, and fonttype.
LISTING 3.6 ColorShapes.py
1
2
3 turtle.pensize(3) # Set pen thickness to 3 pixels
4 turtle.penup() # Pull the pen up
5 turtle.goto(-200, -50)
6 turtle.pendown() # Pull the pen down
7 # Begin to fill color in a shape
8
9 turtle.circle(40, steps = 3) # Draw a triangle
10 # Fill the shape
11
12 turtle.penup()
13 turtle.goto(-100, -50)
14 turtle.pendown()
15 turtle.begin_fill() # Begin to fill color in a shape
16 turtle.color(“blue”)
17 turtle.circle(40, steps = 4) # Draw a square
turtle.end_fill()
turtle.color(“red”)
turtle.begin_fill()
import turtle import turtle module
set pen size
penup
move pen
pendown
begin_fill
set a color
draw a triangle
end_fill
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Point

84 Chapter 3 Mathematical Functions, Strings, and Objects
18 turtle.end_fill() # Fill the shape
19
20 turtle.penup()
21 turtle.goto(0, -50)
22 turtle.pendown()
23 turtle.begin_fill() # Begin to fill color in a shape
24 turtle.color(“green”)
25 turtle.circle(40, steps = 5) # Draw a pentagon
26 turtle.end_fill() # Fill the shape
27
28 turtle.penup()
29 turtle.goto(100, -50)
30 turtle.pendown()
31 turtle.begin_fill() # Begin to fill color in a shape
32 turtle.color(“yellow”)
33 turtle.circle(40, steps = 6) # Draw a hexagon
34 turtle.end_fill() # Fill the shape
35
36 turtle.penup()
37 turtle.goto(200, -50)
38 turtle.pendown()
39 turtle.begin_fill() # Begin to fill color in a shape
40 turtle.color(“purple”)
41 turtle.circle(40) # Draw a circle
42 turtle.end_fill() # Fill the shape
43 turtle.color(“green”)
44 turtle.penup()
45 turtle.goto(-100, 50)
46 turtle.pendown()
47
48
49
50
51 turtle.done()
turtle.hideturtle()
font = (“Times”, 18, “bold”))
turtle.write(“Cool Colorful Shapes”,write text
pause
FIGURE 3.4 The program draws five shapes in different colors.
The program is similar to Listing 3.5. SimpleShapes.py, except that it fills each shape with
a color and writes a string. The turtle object invokes the begin_fill() method in line 7 to
tell Python to draw shapes filled with color. A triangle is drawn in line 9. Invoking the
end_fill() method (line 10) completes the color filling for the shape.
The write method writes a string with the specified font at the current pen position (lines
47–48). Note that drawing takes place when the pen is moved if the pen is down. To avoid
drawing, you need to pull the pen up. Invoking hideturtle() makes the turtle invisible
(line 49) so you will not see the turtle in the window.

Programming Exercises 85
backslash (\) 69
character encoding 68
end-of-line 69
escape sequence 69
line break 69
methods 75
newline 69
object 74
string 67
whitespace characters 76
CHAPTER SUMMARY
1. Python provides the mathematical functions abs, max, min, pow, and round in the
interpreter and the functions fabs, ceil, floor, exp, log, sqrt, sin, asin, cos,
acos, tan, degrees, and radians in the math module.
2. A string is a sequence of characters. String values can be enclosed in matching single
quotes (‘) or double quotes (“). Python does not have a data type for characters; a
single-character string represents a character.
3. An escape sequence is a special syntax that begins with the character \ followed by a
letter or a combination of digits to represent special characters, such as \’, \”, \t,
and \n.
4. The characters ‘ ‘, \t, \f, \r, and \n are known as the whitespace characters.
5. All data including numbers and strings are objects in Python. You can invoke
methods to perform operations on the objects.
6. You can use the format function to format a number or a string and return the result
as a string.
TEST QUESTIONS
Do test questions for this chapter online at www.cs.armstrong.edu/liang/py/test.html.
PROGRAMMING EXERCISES
Section 3.2
3.1 (Geometry: area of a pentagon) Write a program that prompts the user to enter the
length from the center of a pentagon to a vertex and computes the area of the pen-
tagon, as shown in the following figure.
3.30 How do you set the turtle’s color?
3.31 How do you fill a shape with color?
3.32 How do you make the turtle invisible?
KEY TERMS
r
✓Point✓Check

www.cs.armstrong.edu/liang/py/test.html

86 Chapter 3 Mathematical Functions, Strings, and Objects
Enter the length from the center to a vertex:
The area of the pentagon is 108.61
5.5
*3.2 (Geometry: great circle distance) The great circle distance is the distance between
two points on the surface of a sphere. Let (x1, y1) and (x2, y2) be the geographical
latitude and longitude of two points. The great circle distance between the two
points can be computed using the following formula:
Write a program that prompts the user to enter the latitude and longitude of two
points on the earth in degrees and displays its great circle distance. The average
earth radius is 6,371.01 km. Note that you need to convert the degrees into radians
using the math.radians function since the Python trigonometric functions use
radians. The latitude and longitude degrees in the formula are for north and west.
Use negative to indicate south and east degrees. Here is a sample run:
d = radius * arccos(sin(x1) * sin(x2) + cos(x1) * cos(x2) * cos(y1 – y2))
Enter point 1 (latitude and longitude) in degrees:
Enter point 2 (latitude and longitude) in degrees:
The distance between the two points is 10691.79183231593 km
41.5, 87.37
39.55, -116.25
*3.3 (Geography: estimate areas) Find the GPS locations for Atlanta, Georgia;
Orlando, Florida; Savannah, Georgia; and Charlotte, North Carolina from
www.gps-data-team.com/map/ and compute the estimated area enclosed by these
four cities. (Hint: Use the formula in Programming Exercise 3.2 to compute the
distance between two cities. Divide the polygon into two triangles and use the for-
mula in Programming Exercise 2.14 to compute the area of a triangle.)
3.4 (Geometry: area of a pentagon) The area of a pentagon can be computed using the
following formula (s is the length of a side):
Write a program that prompts the user to enter the side of a pentagon and displays
the area. Here is a sample run:
Area =
5 * s2
4 * tan¢p
5
≤
Enter the side:
The area of the pentagon is 53.04444136781625
5.5
The formula for computing the area of a pentagon is where s is
the length of a side. The side can be computed using the formula
where r is the length from the center of a pentagon to a vertex. Here is a sample
run:
s = 2r sin
p
5
,
Area =
323
2
s2,

www.gps-data-team.com/map/

Programming Exercises 87
*3.5 (Geometry: area of a regular polygon) A regular polygon is an n-sided polygon in
which all sides are of the same length and all angles have the same degree (i.e., the
polygon is both equilateral and equiangular). The formula for computing the area
of a regular polygon is
Here, s is the length of a side. Write a program that prompts the user to enter the
number of sides and their length of a regular polygon and displays its area. Here is
a sample run:
Area =
n * s2
4 * tan¢p
n
≤
Enter the number of sides:
Enter the side:
The area of the polygon is 73.69017017488385
6.5
5
Enter an ASCII code:
The character is E
69
3.7 (Random character) Write a program that displays a random uppercase letter
using the time.time() function.
*3.8 (Financial application: monetary units) Rewrite Listing 3.4, ComputeChange.py,
to fix the possible loss of accuracy when converting a float value to an int value.
Enter the input as an integer whose last two digits represent the cents. For exam-
ple, the input 1156 represents 11 dollars and 56 cents.
*3.9 (Financial application: payroll) Write a program that reads the following infor-
mation and prints a payroll statement:
Employee’s name (e.g., Smith)
Number of hours worked in a week (e.g., 10)
Hourly pay rate (e.g., 9.75)
Federal tax withholding rate (e.g., 20%)
State tax withholding rate (e.g., 9%)
A sample run is shown below:
Sections 3.3–3.6
*3.6 (Find the character of an ASCII code) Write a program that receives an ASCII
code (an integer between 0 and 127) and displays its character. For example, if the
user enters 97, the program displays the character a. Here is a sample run:
Enter employee’s name:
Enter number of hours worked in a week:
Enter hourly pay rate:
Enter federal tax withholding rate:
Enter state tax withholding rate:
Employee Name: Smith
0.09
0.20
9.75
10
Smith

88 Chapter 3 Mathematical Functions, Strings, and Objects
*3.10 (Turtle: display Unicodes) Write a program to display Greek letters
The Unicode of these characters are \u03b1 \u03b2 \u03b3 \u03b4 \u03b5
\u03b6 \u03b7 \u03b8.
3.11 (Reverse number) Write a program that prompts the user to enter a four-digit inte-
ger and displays the number in reverse order. Here is a sample run:
abgdPzhu.
Enter an integer:
The reversed number is 5213
3125
Sections 3.7–3.8
**3.12 (Turtle: draw a star) Write a program that prompts the user to enter the length of
the star and draw a star, as shown in Figure 3.5a. (Hint: The inner angle of each
point in the star is 36 degrees.)
*3.13 (Turtle: display a STOP sign) Write a program that displays a STOP sign, as
shown in Figure 3.5b. The hexagon is in red and the text is in white.
3.14 (Turtle: draw the Olympic symbol ) Write a program that prompts the user to
enter the radius of the rings and draws an Olympic symbol of five rings of the
same size with the colors blue, black, red, yellow, and green, as shown in
Figure 3.5c.
*3.15 (Turtle: paint a smiley face) Write a program that paints a smiley face, as shown in
Figure 3.6a.
(a) (b) (c)
FIGURE 3.5 The program (a) draws a star, (b) displays a STOP sign, and (c) draws an Olympic symbol.
Hours Worked: 10.0
Pay Rate: $9.75
Gross Pay: $97.5
Deductions:
Federal Withholding (20.0%): $19.5
State Withholding (9.0%): $8.77
Total Deduction: $28.27
Net Pay: $69.22

Programming Exercises 89
**3.16 (Turtle: draw shapes) Write a program that draws a triangle, square, pentagon,
hexagon, and octagon, as shown in Figure 3.6b. Note that the bottom edges of
these shapes are parallel to the x-axis. (Hint: For a triangle with a bottom line
parallel to the x-axis, set the turtle’s heading to 60 degrees.)
*3.17 (Turtle: triangle area) Write a program that prompts the user to enter the three
points p1, p2, and p3 for a triangle and display its area below the triangle, as
shown in Figure 3.7a. The formula for computing the area of a triangle is given
in Exercise 2.14.
(a) (b)
FIGURE 3.6 The program paints a smiley face in (a) and draws five shapes with bottom edges parallel to the x-axis in (b).
*3.18 (Turtle: triangle angles) Revise Listing 3.2, ComputeAngles.py, to write a pro-
gram that prompts the user to enter the three points p1, p2, and p3 for a triangle
and display its angles, as shown in Figure 3.7b.
**3.19 (Turtle: draw a line) Write a program that prompts the user to enter two points
and draw a line to connect the points and displays the coordinates of the points,
as shown in Figure 3.7c.
(a) (b) (c)
FIGURE 3.7 The program displays (a) the area of the triangle and (b) the angles for the triangle. (c) The program draws
a line.

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SELECTIONS
CHAPTER
4
Objectives
■ To write Boolean expressions using comparison operators (§4.2).
■ To generate random numbers using the random.randint(a, b) or
random.random() functions (§4.3).
■ To program with Boolean expressions (AdditionQuiz) (§4.3).
■ To implement selection control using one-way if statements (§4.4).
■ To program with one-way if statements (GuessBirthday) (§4.5).
■ To implement selection control using two-way if-else statements (§4.6).
■ To implement selection control with nested if and multi-way
if-elif-else statements (§4.7).
■ To avoid common errors in if statements (§4.8).
■ To program with selection statements (§§4.9–4.10).
■ To combine conditions using logical operators (and, or, and not) (§4.11).
■ To use selection statements with combined conditions (LeapYear,
Lottery) (§§4.12–4.13).
■ To write expressions that use the conditional
expressions (§4.14).
■ To understand the rules governing operator precedence
and associativity (§4.15).
■ To detect the location of an object (§4.16).

92 Chapter 4 Selections
4.1 Introduction
A program can decide which statements to execute based on a condition.
If you enter a negative value for radius in Listing 2.2, ComputeAreaWithConsoleInput.py,
the program displays an invalid result. If the radius is negative, the program cannot compute
the area. How can you deal with this situation?
Like all high-level programming languages, Python provides selection statements that let
you choose actions with two or more alternative courses. You can use the following selection
statement to replace line 5 in Listing 2.2:
if radius < 0: print("Incorrect input") else: area = radius * radius * math.pi print("Area is", area) Selection statements use conditions, which are Boolean expressions. This chapter introduces Boolean types, values, comparison operators, and expressions. 4.2 Boolean Types, Values, and Expressions A Boolean expression is an expression that evaluates to a Boolean value True or False. How do you compare two values, such as whether a radius is greater than 0, equal to 0, or less than 0? Python provides six comparison operators (also known as relational operators), shown in Table 4.1, which an be used to compare two values (the table assumes that a radius of 5 is being used). problem selection statements Boolean expressions comparison operators == vs. = TABLE 4.1 Comparison Operators Python Operator Mathematics Symbol Name Example (radius is 5) Result < < less than radius < 0 False <= < less than or equal to radius <= 0 False > > greater than radius > 0 True
>= > greater than or equal to radius >= 0 True
== = equal to radius == 0 False
!= � not equal to radius != 0 True
Boolean value
Caution
The equal to comparison operator is two equal signs (==), not a single equal sign (=).
The latter symbol is for assignment.
The result of the comparison is a Boolean value: True or False. For example, the follow-
ing statement displays the result True:
radius = 1
print(radius > 0)
Key
Point
Key
Point
VideoNote
Boolean expressions

4.3 Generating Random Numbers 93
A variable that holds a Boolean value is known as a Boolean variable. The Boolean data
type is used to represent Boolean values. A Boolean variable can hold one of the two values:
True or False. For example, the following statement assigns the value True to the variable
lightsOn:
lightsOn = True
True and False are literals, just like a number such as 10. They are reserved words and
cannot be used as identifiers in a program.
Internally, Python uses 1 to represent True and 0 for False. You can use the int function
to convert a Boolean value to an integer.
For example,
print(int(True))
displays 1 and
print(int(False))
displays 0.
You can also use the bool function to convert a numeric value to a Boolean value. The
function returns False if the value is 0; otherwise, it always returns True.
For example,
print(bool(0))
displays False and
print(bool(4))
displays True.
4.1 List six comparison operators.
4.2 Can the following conversions be allowed? If so, find the converted result.
i = int(True)
j = int(False)
b1 = bool(4)
b2 = bool(0)
4.3 Generating Random Numbers
The randint(a, b) function can be used to generate a random integer between a
and b, inclusively.
Suppose you want to develop a program to help a first grader practice addition. The
program randomly generates two single-digit integers, number1 and number2, and dis-
plays to the student a question such as What is 1 + 7, as shown in Listing 4.1. After the
student types the answer, the program displays a message to indicate whether it is true
or false.
To generate a random number, you can use the randint(a, b) function in the random
module. This function returns a random integer i between a and b, inclusively. To obtain a
random integer between 0 and 9, use randint(0, 9).
Boolean variable
Boolean literals
convert Boolean to int
bool function
Key
Point
✓Point✓Check

94 Chapter 4 Selections
The program may be set up to work as follows:
Step 1: Generate two single-digit integers for number1 (e.g., 4) and number2 (e.g., 5)
Step 2: Prompt the student to answer, “What is 4 + 5?”
Step 3: Check whether the student’s answer is correct.
LISTING 4.1 AdditionQuiz.py
1 import random
2
3 # Generate random numbers
4
5 number2 = random.randint(0, 9)
6
7 # Prompt the user to enter an answer
8 answer = eval(input(“What is ” + + ” + ”
9 + str(number2) + “? “))
10
11 # Display result
12 print(number1, “+”, number2, “=”, answer,
13 “is”, number1 + number2 == answer)
str(number1)
number1 = random.randint(0, 9)
import random module
generate number1
generate number2
show question
display result
What is 1 + 7?
1 + 7 = 8 is True
8
What is 4 + 8?
4 + 8 = 9 is False
9
The program uses the randint function defined in the random module. The import
statement imports the module (line 1).
Lines 4–5 generate two numbers, number1 and number2. Line 8 obtains an answer from the
user. The answer is graded in line 12 using a Boolean expression number1 + number2 ==
answer.
Python also provides another function, randrange(a, b), for generating a random inte-
ger between a and b – 1, which is equivalent to randint(a, b – 1). For example,
randrange(0, 10) and randint(0, 9) are the same. Since randint is more intuitive, the
book generally uses randint in the examples.
You can also use the random() function to generate a random float r such that 0 <= r < 1.0. For example random module randrange function random function line# number1 number2 answer output 4 4 5 8 8 9 12 4 + 8 = 9 is False 1 >>> import random
2 >>> random.random()
3 0.34343
4 >>> random.random()
5 0.20119
6 >>> random.randint(0, 1)
random.random()
random.random()
random.randint(a, b)

4.4 if Statements 95
random.randrange(a, b)
Invoking random.random() (lines 2 and 4) returns a random float number between 0.0 and
1.0 (excluding 1.0). Invoking random.randint(0, 1) (lines 6 and 8) returns 0 or 1.
Invoking random.randrange(0, 1) (line 10) always returns 0.
4.3 How do you generate a random integer i such that
4.4 How do you generate a random integer i such that
4.5 How do you generate a random integer i such that
4.6 How do you generate a random integer 0 or 1?
4.4 if Statements
A one-way if statement executes the statements if the condition is true.
The preceding program displays a message such as 6 + 2 = 7 is False. If you wish the
message to be 6 + 2 = 7 is incorrect, you have to use a selection statement to make
this minor change.
Python has several types of selection statements: one-way if statements, two-way if-
else statements, nested if statements, multi-way if-elif-else statements and conditional
expressions. This section introduces one-way if statements.
A one-way if statement executes an action if and only if the condition is true. The syntax
for a one-way if statement is:
if boolean-expression:
statement(s) # Note that the statement(s) must be indented
The statement(s) must be indented at least one space to the right of the if keyword
and each statement must be indented using the same number of spaces. For consistency, we
indent it four spaces in this book.
The flowchart in Figure 4.1a illustrates how Python executes the syntax of an if state-
ment. A flowchart is a diagram that describes an algorithm or process, showing the steps as
boxes of various kinds, and their order by connecting these with arrows. Process operations
are represented in these boxes, and arrows connecting them show flow of control. A diamond
box is used to denote a Boolean condition and a rectangle box is for representing statements.
If the boolean-expression evaluates to true, the statements in the if block are exe-
cuted. The if block contains the statements indented after the if statement. For example:
if radius >= 0:
area = radius * radius * math.pi
print(“The area for the circle of radius”, radius, “is”, area)
The flowchart of the preceding statement is shown in Figure 4.1b. If the value of radius
is greater than or equal to 0, then the area is computed and the result is displayed; otherwise,
these statements in the block are not executed.
The statements in the if block must be indented in the lines after the if line and each
statement must be indented using the same number of spaces. For example, the following
code is wrong, because the print statement in line 3 is not indented using the same number
of spaces as the statement for computing area in line 2.
1 if radius >= 0:
2 area = radius * radius * math.pi # Compute area
3 print(“The area for the circle of radius”, radius, “is”, area)
10 … i … 50?
10 … i 6 20?
0 … i 6 20?
if statements
if statement
7 0
8 >>> random.randint(0, 1)
9 1
10 >>> random.randrange(0, 1) # This will always be 0
11 0
12 >>>
if block
flowchart
✓Point✓Check
Key
Point
BAD
CO
DE

96 Chapter 4 Selections
Listing 4.2 is an example of a program that prompts the user to enter an integer. If the num-
ber is a multiple of 5, the program displays the result HiFive. If the number is divisible by 2,
the program displays HiEven.
LISTING 4.2 SimpleIfDemo.py
1 number = eval(input(“Enter an integer: “))
2
3 if :
4 print(“HiFive”)
5
6 if :
7 print(“HiEven”)
number % 2 == 0
number % 5 == 0
enter input
check 5
check even
Enter an integer:
HiEven
4
Enter an integer:
HiFive
HiEven
30
The program prompts the user to enter an integer (line 1) and displays HiFive if it is divis-
ible by 5 (lines 3–4) and HiEven if it is divisible by 2 (lines 6–7).
4.7 Write an if statement that assigns 1 to x if y is greater than 0.
4.8 Write an if statement that increases pay by 3% if score is greater than 90.
4.5 Case Study: Guessing Birthdays
Guessing birthdays is an interesting problem with a simple program solution.
You can find out the date of the month when your friend was born by asking five questions.
Each question asks whether the day is in one of the five sets of numbers.
Statement(s)
boolean-
expression
true
false
(a)
area = radius * radius * math.pi
print(“The area for the circle of”,
“radius”, radius, “is”, area)
radius >= 0?
true
false
(b)
FIGURE 4.1 An if statement executes statements if the boolean-expression evaluates
to True.
✓Point✓Check
Key
Point

4.5 Case Study: Guessing Birthdays 97
day to be determined
in question1?
in question2?
The birthday is the sum of the first numbers in the sets where the date appears. For exam-
ple, if the birthday is 19, it appears in Set1, Set2, and Set5. The first numbers in these three
sets are 1, 2, and 16. Their sum is 19.
Listing 4.3 is a program that prompts the user to answer whether the day is in Set1 (lines
4–13), in Set2 (lines 16–25), in Set3 (lines 28–37), in Set4 (lines 40–49), or in Set5 (lines
52–61). If the number is in the set, the program adds the first number in the set to day (lines 13,
25, 37, 49, and 61).
LISTING 4.3 GuessBirthday.py
1 # birth day to be determined
2
3 # Prompt the user to answer the first question
4 question1 = “Is your birthday in Set1?\n” +
5 ” 1 3 5 7\n” + \
6 ” 9 11 13 15\n” + \
7 “17 19 21 23\n” + \
8 “25 27 29 31” + \
9 “\nEnter 0 for No and 1 for Yes: ”
10 answer = eval(input(question1))
11
12 if :
13 day += 1
14
15 # Prompt the user to answer the second question
16 question2 = “Is your birthday in Set2?\n” +
17 ” 2 3 6 7\n” + \
18 “10 11 14 15\n” + \
19 “18 19 22 23\n” + \
20 “26 27 30 31” + \
21 “\nEnter 0 for No and 1 for Yes: ”
22 answer = eval(input(question2))
23
24 if :
25 day += 2
26
27 # Prompt the user to answer the third question
28 question3 = “Is your birthday in Set3?\n” + \
29 ” 4 5 6 7\n” + \
30 “12 13 14 15\n” + \
31 “20 21 22 23\n” + \
32 “28 29 30 31” + \
33 “\nEnter 0 for No and 1 for Yes: ”
34 answer = eval(input(question3))
35
36 if :
37 day += 4
answer == 1
answer == 1
\
answer == 1
\
day = 0
16 17 18 19
20 21 22 23
24 25 26 27
28 29 30 31
9 10 11
12 13 14 15
24 25 26 27
28 29 30 31
5 6 7
12 13 14 15
20 21 22 23
28 29 30 31
2 3 6 7
10 11 14 15
18 22 23
26 27 30 31
3 5 7
9 11 13 15
17 19 1921 23
25 27 29 31
Set1 Set2 Set3 Set4 Set5
= 19
841
+
in question3?

98 Chapter 4 Selections
38
39 # Prompt the user to answer the fourth question
40 question4 = “Is your birthday in Set4?\n” + \
41 ” 8 9 10 11\n” + \
42 “12 13 14 15\n” + \
43 “24 25 26 27\n” + \
44 “28 29 30 31” + \
45 “\nEnter 0 for No and 1 for Yes: ”
46 answer = eval(input(question4))
47
48 if :
49 day += 8
50
51 # Prompt the user to answer the fifth question
52 question5 = “Is your birthday in Set5?\n” + \
53 “16 17 18 19\n”+ \
54 “20 21 22 23\n” + \
55 “24 25 26 27\n” + \
56 “28 29 30 31” + \
57 “\nEnter 0 for No and 1 for Yes: ”
58 answer = eval(input(question5))
59
60 if :
61 day += 16
62
63 print(“\nYour birthday is “+ str(day) + “!”)
answer == 1
answer == 1
in question4?
in question5?
Is your birthday in Set1?
1 3 5 7
9 11 13 15
17 19 21 23
25 27 29 31
Enter 0 for No and 1 for Yes:
Is your birthday in Set2?
2 3 6 7
10 11 14 15
18 19 22 23
26 27 30 31
Enter 0 for No and 1 for Yes:
Is your birthday in Set3?
4 5 6 7
12 13 14 15
20 21 22 23
28 29 30 31
Enter 0 for No and 1 for Yes:
Is your birthday in Set4?
8 9 10 11
12 13 14 15
24 25 26 27
28 29 30 31
Enter 0 for No and 1 for Yes: 0
0
1
1

4.5 Case Study: Guessing Birthdays 99
Is your birthday in Set5?
16 17 18 19
20 21 22 23
24 25 26 27
28 29 30 31
Enter 0 for No and 1 for Yes:
Your birthday is 19!
1
The last character \ at the end of lines 4–8 is the line continuation symbol, which tells the
interpreter that the statement is continued on the next line (see Section 2.3).
This game is easy to program. You may wonder how the game was created. The
mathematics behind the game is actually quite simple. The numbers are not grouped
together by accident. The way they are placed in the five sets is deliberate. The starting
numbers in the five sets are 1, 2, 4, 8, and 16, which correspond to 1, 10, 100, 1000, and
10000 in binary. A binary number for decimal integers between 1 and 31 has at most
five digits, as shown in Figure 4.2a. Assume this number is So,
as shown in Figure 4.2b. If a day’s binary
number has a digit 1 in the number should appear in Setk. For example, number 19 is
binary 10011, so it appears in Set1, Set2, and Set5. It is binary 1 + 10 + 10000 = 10011
or decimal 1 + 2 + 16 = 19. Number 31 is binary 11111, so it appears in Set1, Set2, Set3,
Set4, and Set5. It is binary 1 + 10 + 100 + 1000 + 10000 = 11111 or decimal 1 + 2
+ 4 + 8 + 16 = 31.
bk,
b5b4b3b2b1 = b50000 + b4000 + b300 + b20 + b1,
b5b4b3b2b1.
mathematics behind the game
line# day answer output
1 0
10 1
13 1
22 1
25 2
34 0
46 0
58 1
61 19
63 Your birthday is 19
Decimal Binary
1 00001
2 00010
3 00011
…
19 10011
…
31 11111
b5 0 0 0 0 10000
b4 0 0 0 1000
b3 0 0 10000 100
b2 0 10 10
+ b1 + 1 + 1
b5b4b3b2b1 10011 11111
19 31
(a) A number between 1 and 31 can be represented using a 5-digit binary num-
ber. (b) A 5-digit binary number can be obtained by adding binary numbers 1, 10, 100,
1000, or 10000.
FIGURE 4.2
(a) (b)

100 Chapter 4 Selections
4.6 Two-Way if-else Statements
A two-way if-else statement decides which statements to execute based on whether
the condition is true or false.
A one-way if statement takes an action if the specified condition is True. If the condition is
False, nothing is done. But what if you want to take one or more alternative actions when the
condition is False? You can use a two-way if-else statement. The actions that a two-way
if-else statement specifies differ based on whether the condition is True or False.
Here is the syntax for a two-way if-else statement:
if boolean-expression:
statement(s)-for-the-true-case
else:
statement(s)-for-the-false-case
The flowchart of the statement is shown in Figure 4.3.
If the boolean-expression evaluates to True, the statement(s) for the true case are exe-
cuted; otherwise, the statement(s) for the false case are executed. For example, consider the
following code:
if radius >= 0:
area = radius * radius * math.pi
print(“The area for the circle of radius”, radius, “is”, area)
else:
print(“Negative input”)
If radius >= 0 is true, area is computed and displayed; if it is false, the message
Negative input is displayed.
Here is another example of the if-else statement. This one determines whether a num-
ber is even or odd, as follows:
if number % 2 == 0:
print(number, “is even.”)
else:
print(number, “is odd.”)
Suppose you want to develop a program for a first grader to practice subtraction. The pro-
gram randomly generates two single-digit integers, number1 and number2, with number1
>= number2 and asks the student a question such as “What is 9 – 2? ” After the student
enters the answer, the program displays a message indicating whether it is correct.
two-way if-else statement
Statement(s) for the true case Statement(s) for the false case
boolean-
expression
true false
FIGURE 4.3 An if-else statement executes statements for the true case if the Boolean
expression evaluates to True; otherwise, statements for the false case are executed.
Key
Point

4.6 Two-Way if-else Statements 101
The program may work as follows:
Step 1: Generate two single-digit integers for number1 and number2.
Step 2: If number1 < number2, swap number1 with number2. Step 3: Prompt the student to answer, “What is number1 – number2?” Step 4: Check the student’s answer and display whether the answer is correct. The complete program is shown in Listing 4.4. LISTING 4.4 SubtractionQuiz.py 1 import random 2 3 # 1. Generate two random single-digit integers 4 number1 = random.randint(0, 9) 5 number2 = random.randint(0, 9) 6 7 # 2. If number1 < number2, swap number1 with number2 8 if number1 < number2: 9 number1, number2 = number2, number1 # Simultaneous assignment 10 11 # 3. Prompt the student to answer "What is number1 - number2?" 12 answer = eval(input("What is "+ str(number1) + " - " + 13 str(number2) + "? ")) 14 15 # 4. Check the answer and display the result 16 if number1 - number2 == answer: 17 print("You are correct!") 18 else: 19 print("Your answer is wrong.\n", number1, '-', 20 number2, "is", number1 - number2, '.') import random module random numbers swap if necessary get answer check the answer What is 6 - 6? You are correct! 0 What is 9 - 2? Your answer is wrong. 9 - 2 is 7. 5 line# number1 number2 answer output 4 2 5 9 9 9 2 12 5 19 Your answer is wrong. 9 – 2 is 7. If number1 number2, the program uses simultaneous assignment to swap the two variables (lines 8–9). 4.9 Write an if statement that increases pay by 3% if score is greater than 90, other- wise it increases pay by 1%. 6 ✓Point✓Check 102 Chapter 4 Selections 4.10 What is the printout of the code in (a) and (b) if number is 30 and 35, respectively? nested if statement FIGURE 4.4 A preferred format for multiple alternatives is shown in (b) using a multi-way if-elif-else statement. if number % 2 == 0: print(number, "is even.") print(number, "is odd.") if number % 2 == 0: print(number, "is even.") else print(number, "is odd.") (a) (b) 4.7 Nested if and Multi-Way if-elif-else Statements One if statement can be placed inside another if statement to form a nested if statement. The statement in an if or if-else statement can be any legal Python statement, including another if or if-else statement. The inner if statement is said to be nested inside the outer if statement. The inner if statement can contain another if statement; in fact, there is no limit to the depth of the nesting. For example, the following is a nested if statement: if i > k:
if j > k:
print(“i and j are greater than k”)
else:
print(“i is less than or equal to k”)
The if j > k statement is nested inside the if i > k statement.
The nested if statement can be used to implement multiple alternatives. The statement
given in Figure 4.4a, for instance, assigns a letter value to the variable grade according to the
score, with multiple alternatives.
if score >= 90.0:
grade = ‘A’
else:
if score >= 80.0:
grade = ‘B’
else:
if score >= 70.0:
grade = ‘C’
else:
if score >= 60.0:
grade = ‘D’
else:
grade = ‘F’
if score >= 90.0:
grade = ‘A’
elif score >= 80.0:
grade = ‘B’
elif score >= 70.0:
grade = ‘C’
elif score >= 60.0:
grade = ‘D’
else:
grade = ‘F’
Equivalent
This is better
The execution of how this if statement proceeds is shown in Figure 4.5. The first condi-
tion (score >= 90) is tested. If it is True, the grade becomes A. If it is False, the second
condition (score >= 80) is tested. If the second condition is True, the grade becomes B. If
that condition is False, the third condition and the rest of the conditions (if necessary) are
tested until a condition is met or all of the conditions prove to be False. If all of the condi-
tions are False, the grade becomes F. Note that a condition is tested only when all of the con-
ditions that come before it are False.
(a) (b)
Key
Point

4.7 Nested if and Multi-Way if-elif-else Statements 103
The if statement in Figure 4.4a is equivalent to the if statement in Figure 4.4b. In fact, Figure
4.4b is the preferred coding style for multiple alternative if statements. This style, called multi-
way if statements, avoids deep indentation and makes the program easier to read. The multi-way
if statements uses the syntax if-elif-else; elif (short for else if ) is a Python keyword.
Now let’s write a program to find out the Chinese zodiac sign for a given year. The Chinese
zodiac sign is based on a 12-year cycle, and each year in this cycle is represented by an animal—
monkey, rooster, dog, pig, rat, ox, tiger, rabbit, dragon, snake, horse, and sheep—as shown in
Figure 4.6.
grade = ‘A’
true
false
false
false
false
grade = ‘B’
score >= 80
true
grade = ‘C’
score >= 70
true
grade = ‘D’
score >= 60
true
grade = ‘F’
score >= 90
FIGURE 4.5 You can use a multi-way if-elif-else statement to assign a grade.
rat
0: monkey
1: rooster
2: dog
3: pig
4: rat
5: ox
6: tiger
7: rabbit
8: dragon
9: snake
10: horse
11: sheep
ox
tiger
rabbit
dragon
snakehorse
sheep
monkey
rooster
dog
pig
year % 12 =
FIGURE 4.6 The Chinese zodiac is based on a 12-year cycle.
multi-way if statement

104 Chapter 4 Selections
The value of year % 12 determines the zodiac sign. 1900 is the year of the rat since
1900 % 12 is 4. Listing 4.5 shows a program that prompts the user to specify a year, and then
it displays the animal for that year.
LISTING 4.5 ChineseZodiac.py
1 year = eval(input(“Enter a year: “))
2 zodiacYear = year % 12
3 if zodiacYear == 0:
4 print(“monkey”)
5 elif zodiacYear == 1:
6 print(“rooster”)
7 elif zodiacYear == 2:
8 print(“dog”)
9 elif zodiacYear == 3:
10 print(“pig”)
11 elif zodiacYear == 4:
12 print(“rat”)
13 elif zodiacYear == 5:
14 print(“ox”)
15 elif zodiacYear == 6:
16 print(“tiger”)
17 elif zodiacYear == 7:
18 print(“rabbit”)
19 elif zodiacYear == 8:
20 print(“dragon”)
21 elif zodiacYear == 9:
22 print(“snake”)
23 elif zodiacYear == 10:
24 print(“horse”)
25 else:
26 print(“sheep”)
enter year
12-year cycle
determine zodiac sign
Enter a year:
rabbit
1963
Enter a year:
ox
1877
4.11 Suppose x = 3 and y = 2; show the output, if any, of the following code. What is
the output if x = 3 and y = 4? What is the output if x = 2 and y = 2? Draw a flow-
chart for the code.
if x > 2:
if y > 2:
z = x + y
print(“z is”, z)
else:
print(“x is”, x)
4.12 Suppose x = 2 and y = 4. Show the output, if any, of the following code. What is
the output if x = 3 and y = 2? What is the output if x = 3 and y = 3? (Hint: Indent
the statement correctly first.)
✓Point✓Check

4.8 Common Errors in Selection Statements 105
if x > 2:
if y > 2:
z = x + y
print(“z is”, z)
else:
print(“x is”, x)
4.13 What is wrong in the following code?
if score >= 60.0:
grade = ‘D’
elif score >= 70.0:
grade = ‘C’
elif score >= 80.0:
grade = ‘B’
elif score >= 90.0:
grade = ‘A’
else:
grade = ‘F’
4.8 Common Errors in Selection Statements
Most common errors in selection statements are caused by incorrect indentation.
Consider the following code in (a) and (b).
radius = -20
if radius >= 0:
area = radius * radius * math.pi
print(“The area is”, area)
radius = -20
if radius >= 0:
area = radius * radius * math.pi
print(“The area is”, area)
(a) Wrong (b) Correct
In (a), the print statement is not in the if block. To place it in the if block, you have to
indent it, as shown in (b).
Consider another example in the following code in (a) and (b). The code in (a) below has
two if clauses and one else clause. Which if clause is matched by the else clause? The
indentation indicates that the else clause matches the first if clause in (a) and the second if
clause in (b).
i = 1
j = 2
k = 3
if i > j:
i > k:
print(‘A’)
:
print(‘B’)
else
if
i = 1
j = 2
k = 3
if i > j:
i > k:
print(‘A’)
:
print(‘B’)
else
if
(a) (b)
Since (i > j) is false, the code in (a) displays B, but nothing is displayed from the state-
ment in (b).
Key
Point

106 Chapter 4 Selections
The code can be simplified by assigning the test value directly to the variable, as shown in (b).
4.14 Which of the following statements are equivalent? Which ones are correctly
indented?
if number % 2 == 0:
even = True
else:
even = False
even = number % 2 == 0
(a) (b)
Equivalent
This is shorter
if i > 0:
x = 0
y = 1
else:
y = 0
z = 0
if i > 0:
x = 0
y = 1
else:
y = 0
z = 0
(a) (b)
if i > 0:
x = 0
y = 1
else:
y = 0
z = 0
if i > 0:
x = 0
y = 1
else:
y = 0
z = 0
(c) (d)
4.15 Rewrite the following statement using a Boolean expression:
if count % 10 == 0:
newLine = True
else:
newLine = False
4.16 Are the following statements correct? Which one is better?
if age < 16: print("Cannot get a driver's license") if age >= 16:
print(“Can get a driver’s license”)
if age < 16: print("Cannot get a driver's license") else: print("Can get a driver's license") (a) (b) 4.17 What is the output of the following code if number is 14, 15, and 30? if number % 2 == 0: print(number, "is even") if number % 5 == 0: print(number, "is multiple of 5") if number % 2 == 0: print(number, "is even") elif number % 5 == 0: print(number, "is multiple of 5") (a) (b) Tip Often new programmers write the code that assigns a test condition to a Boolean variable, like the code in (a): assign Boolean variable ✓Point✓Check 4.9 Case Study: Computing Body Mass Index 107 Write a program that prompts the user to enter a weight in pounds and height in inches and then displays the BMI. Note that one pound is 0.45359237 kilograms and one inch is 0.0254 meters. Listing 4.6 gives the program. LISTING 4.6 ComputeBMI.py 1 # Prompt the user to enter weight in pounds 2 weight = eval(input("Enter weight in pounds: ")) 3 4 # Prompt the user to enter height in inches 5 height = eval(input("Enter height in inches: ")) 6 7 KILOGRAMS_PER_POUND = 0.45359237 # Constant 8 METERS_PER_INCH = 0.0254 # Constant 9 10 # Compute BMI 11 weightInKilograms = weight * KILOGRAMS_PER_POUND 12 heightInMeters = height * METERS_PER_INCH 13 bmi = weightInKilograms / (heightInMeters * heightInMeters) 14 15 # Display result 16 print("BMI is", format(bmi, ".2f")) 17 if bmi < 18.5: 18 print("Underweight") 19 elif bmi < 25: 20 print("Normal") 21 elif bmi < 30: 22 print("Overweight") 23 else: 24 print("Obese") 4.9 Case Study: Computing Body Mass Index You can use nested if statements to write a program that interprets body mass index. Body mass index (BMI) is a measure of health based on weight. It can be calculated by taking your weight in kilograms and dividing it by the square of your height in meters. The interpre- tation of BMI for people 16 years and older is as follows: BMI Interpretation Below 18.5 Underweight 18.5–24.9 Normal 25.0–29.9 Overweight Above 30.0 Obese input weight input height compute bmi display output Enter weight in pounds: Enter height in inches: BMI is 20.95 Normal 70 146 Key Point 108 Chapter 4 Selections The two named constants, KILOGRAMS_PER_POUND and METERS_PER_INCH, are defined in lines 7–8. Named constants were introduced in Section 2.6. Using named constants here makes programs easy to read. Unfortunately, there is no special syntax for defining named constants in Python. Named constants are treated just like variables in Python. This book uses the format of writing constants in all uppercase letters to distinguish them from variables, and separates the words in constants with an underscore (_). 4.10 Case Study: Computing Taxes You can use nested if statements to write a program for computing taxes. The United States federal personal income tax is calculated based on filing status and taxable income. There are four filing statuses: single filers, married filing jointly, married filing sepa- rately, and head of household. The tax rates vary every year. Table 4.2 shows the rates for 2009. If you are, say, single with a taxable income of $10,000, the first $8,350 is taxed at 10% and the other $1,650 is taxed at 15%. So, your tax is $1,082.50. You are to write a program to compute personal income tax. Your program should prompt the user to enter the filing status and taxable income and then compute the tax. Enter 0 for single filers, 1 for married filing jointly, 2 for married filing separately, and 3 for head of household. Your program computes the tax for the taxable income based on the filing status. The filing status can be determined using if statements outlined as follows: if status == 0: # Compute tax for single filers elif status == 1: # Compute tax for married filing jointly elif status == 2: named constants TABLE 4.2 2009 U.S. Federal Personal Tax Rates Marginal Tax Rate Single Married Filing Jointly Married Filing Separately Head of Household 10% $0 – $8,350 $0 – $16,700 $0 – $8,350 $0 – $11,950 15% $8,351 – $33,950 $16,701 – $67,900 $8,351 – $33,950 $11,951 – $45,500 25% $33,951 – $82,250 $67,901 – $137,050 $33,951 – $68,525 $45,501 – $117,450 28% $82,251 – $171,550 $137,051 – $208,850 $68,526 – $104,425 $117,451 – $190,200 33% $171,551 – $372,950 $208,851 – $372,950 $104,426 – $186,475 $190,201 – $372,950 35% $372,951+ $372,951+ $186,476+ $372,951+ line# weight height weightInKilograms heightInMeters bmi output 2 146 5 70 11 66.22448602 12 1.778 13 20.9486 16 BMI is 20.95 22 Normal Key Point 4.10 Case Study: Computing Taxes 109 # Compute tax for married filing separately elif status == 3: # Compute tax for head of household else: # Display wrong status For each filing status there are six tax rates. Each rate is applied to a certain amount of taxable income. For example, of a taxable income of $400,000 for single filers, $8,350 is taxed at 10%, (33,950 – 8,350) at 15%, (82,250 – 33,950) at 25%, (171,550 – 82,250) at 28%, (372,950 – 171,550) at 33%, and (400,000 – 372,950) at 35%. Listing 4.7 gives the solution to compute taxes for single filers. The complete solution is left as Programming Exercise 4.13 at the end of this chapter. LISTING 4.7 ComputeTax.py 1 import sys 2 3 # Prompt the user to enter filing status 4 status = eval(input( 5 "(0-single filer, 1-married jointly,\n" + 6 "2-married separately, 3-head of household)\n" + 7 "Enter the filing status: ")) 8 9 # Prompt the user to enter taxable income 10 income = eval(input("Enter the taxable income: ")) 11 12 # Compute tax 13 tax = 0 14 15 if status == 0: # Compute tax for single filers 16 if income <= 8350: 17 tax = income * 0.10 18 elif income <= 33950: 19 tax = 8350 * 0.10 + (income - 8350) * 0.15 20 elif income <= 82250: 21 tax = 8350 * 0.10 + (33950 - 8350) * 0.15 + \ 22 (income - 33950) * 0.25 23 elif income <= 171550: 24 tax = 8350 * 0.10 + (33950 - 8350) * 0.15 + \ 25 (82250 - 33950) * 0.25 + (income - 82250) * 0.28 26 elif income <= 372950: 27 tax = 8350 * 0.10 + (33950 - 8350) * 0.15 + \ 28 (82250 - 33950) * 0.25 + (171550 - 82250) * 0.28 + \ 29 (income - 171550) * 0.33 30 else: 31 tax = 8350 * 0.10 + (33950 - 8350) * 0.15 + \ 32 (82250 - 33950) * 0.25 + (171550 - 82250) * 0.28 + \ 33 (372950 - 171550) * 0.33 + (income - 372950) * 0.35; 34 elif status == 1: # Compute tax for married file jointly 35 print("Left as exercise") 36 elif status == 2: # Compute tax for married separately 37 print("Left as exercise") 38 elif status == 3: # Compute tax for head of household 39 print("Left as exercise") 40 else: 41 print("Error: invalid status") 42 sys.exit() 43 44 # Display the result 45 print("Tax is", format(tax, ".2f")) import sys module input status input income compute tax exit program display output 110 Chapter 4 Selections (0-single filer, 1-married jointly, 2-married separately, 3-head of household) Enter the filing status: Enter the taxable income: Tax is 117683.50 400000 0 The program receives the filing status and taxable income. The multiple alternative if statements (lines 15, 34, 36, 38, and 40) check the filing status and compute the tax based on the filing status. sys.exit() (line 42) is defined in the sys module. Invoking this function terminates the program. To test a program, you need to provide input that covers all cases. For this program, your input should cover all statuses (0, 1, 2, and 3). For each status, test the tax for each of the six brackets. So, there are a total of 24 cases. Tip For all programs, you should write a small amount of code and test it before moving on to add more code. This is called incremental development and testing. This approach makes debugging easier, because the errors are likely in the new code you just added. 4.18 Are the following two statements equivalent? line# status income tax output 4 0 10 400000 13 0 17 117683.5 45 Tax is 117683.50 if income <= 10000: tax = income * 0.1 elif income <= 20000: tax = 1000 + \ (income – 10000) * 0.15 4.19 What is wrong in the following code? income = 232323 if income <= 10000: tax = income * 0.1 elif income > 10000 and income <= 20000: tax = 1000 + (income - 10000) * 0.15 print(tax) 4.11 Logical Operators The logical operators not, and, and or can be used to create a composite condition. Sometimes, a combination of several conditions determines whether a statement is executed. You can use logical operators to combine these conditions to form a compound expression. sys.exit() test all cases incremental development and testing if income <= 10000: tax = income * 0.1 elif income > 10000 and
income <= 20000: tax = 1000 + \ (income – 10000) * 0.15 ✓Point✓Check Key Point 4.11 Logical Operators 111 Logical operators, also known as Boolean operators, operate on Boolean values to create a new Boolean value. Table 4.3 lists the Boolean operators. Table 4.4 defines the not operator, which negates True to False and False to True. Table 4.5 defines the and operator. The and of two Boolean operands is true if and only if both operands are true. Table 4.6 defines the or operator. The or of two Boolean operands is true if at least one of the operands is true. TABLE 4.3 Boolean Operators Operator Description not logical negation and logical conjunction or logical disjunction TABLE 4.4 Truth Table for Operator not p not p Example (assume age = 24, gender = 'F') True False not (age > 18) is False, because (age > 18) is True.
False True not (gender == ‘M’) is True, because (gender == ‘M’) is False.
TABLE 4.5 Truth Table for Operator and
p1 p2 p1 and p2 Example (assume age = 24, gender = ‘F’)
False False False (age > 18) and (gender == ‘F’) is True, because
(age > 18) and (gender == ‘F’) are both True.
False True False
True False False (age > 18) and (gender != ‘F’) is False, because
(gender != ‘F’) is False.
True True True
TABLE 4.6 Truth Table for Operator or
p1 p2 p1 and p2 Example (assume age = 24, gender = ‘F’)
False False False (age > 34) or (gender == ‘F’) is True, because
(gender == ‘F’) is True.
False True True
True False True (age > 34) or (gender == ‘M’) is False, because
(age > 34) and (gender == ‘M’) are both False.
True True True
The program in Listing 4.8 checks whether a number is divisible by 2 and 3, by 2 or 3, and
by 2 or 3 but not both.
LISTING 4.8 TestBooleanOperators.py
1 # Receive an input
2 number = eval(input(“Enter an integer: “))
3
4 if :
5 print(number, “is divisible by 2 and 3”)
number % 2 == 0 and number % 3 == 0
input
and

112 Chapter 4 Selections
6
7 if :
8 print(number, “is divisible by 2 or 3”)
9
10 if \
11 :
12 print(number, “is divisible by 2 or 3, but not both”)
not (number % 2 == 0 and number % 3 == 0)
(number % 2 == 0 or number % 3 == 0) and
number % 2 == 0 or number % 3 == 0or
Enter an integer:
18 is divisible by 2 and 3
18 is divisible by 2 or 3
18
Enter an integer:
15 is divisible by 2 or 3
15 is divisible by 2 or 3, but not both
15
In line 4, number % 2 == 0 and number % 3 == 0 checks whether the number is
divisible by 2 and 4. number % 2 == 0 or number % 3 == 0 (line 7) checks whether
the number is divisible by 2 or 4. The Boolean expression in lines 10–11
(number % 2 == 0 and number % 3 == 0) and
not (number % 2 == 0 and number % 3 == 0)
checks whether the number is divisible by 2 or 3 but not both.
Note
De Morgan’s law, named after Indian-born British mathematician and logician Augustus De
Morgan (1806–1871), can be used to simplify Boolean expressions. The law states that:
not (condition1 and condition2) is the same as
not condition1 or not condition2
not (condition1 or condition2) is the same as
not condition1 and not condition2
So, line 11 in the preceding example,
not (number % 2 == 0 number % 3 == 0)
can be simplified by using an equivalent expression:
(number % 2 != 0 or number % 3 != 0)
As another example,
not (number == 2 or number == 3)
is better written as
number != 2 and number != 3
If one of the operands of an and operator is False, the expression is False; if one of
the operands of an or operator is True, the expression is True. Python uses these proper-
ties to improve the performance of these operators. When evaluating p1 and p2, Python
first evaluates p1 and then, if p1 is True, evaluates p2; if p1 is False, it does not evalu-
ate p2. When evaluating p1 or p2, Python first evaluates p1 and then, if p1 is False,
and
De Morgan’s law

4.12 Case Study: Determining Leap Years 113
evaluates p2; if p1 is True, it does not evaluate p2. Therefore, and is referred to as the
conditional or short-circuit AND operator, and or is referred to as the conditional or
short-circuit OR operator.
4.20 Assuming that x is 1, show the result of the following Boolean expressions.
True and (3 > 4)
not (x > 0) and (x > 0)
(x > 0) or (x < 0) (x != 0) or (x == 0) (x >= 0) or (x < 0) (x != 1) == not (x == 1) 4.21 Write a Boolean expression that evaluates to True if variable num is between 1 and 100. 4.22 Write a Boolean expression that evaluates to True if variable num is between 1 and 100 or the number is negative. 4.23 Assuming x 4 and y 5, show the result of the following Boolean expressions: x >= y >= 0
x <= y >= 0
x != y == 5
(x != 0) or (x == 0)
4.24 Are the following expressions equivalent?
(a) (x >= 1) and (x < 10) (b) (1 <= x < 10) 4.25 What is the value of the expression ch >= ‘A’ and ch <= 'Z' if ch is 'A', 'p', 'E', or '5'? 4.26 Suppose, when you run the following program, you enter input 2, 3, 6 from the console. What is the output? x, y, z = eval(input("Enter three numbers: ")) print("(x < y and y < z) is", x < y and y < z) print("(x < y or y < z) is", x < y or y < z) print("not (x < y) is", not (x < y)) print("(x < y < z) is", x < y < z) print("not(x < y < z) is", not (x < y < z)) 4.27 Write a Boolean expression that evaluates true if age is greater than 13 and less than 18. 4.28 Write a Boolean expression that evaluates true if weight is greater than 50 or height is greater than 160. 4.29 Write a Boolean expression that evaluates true if weight is greater than 50 and height is greater than 160. 4.30 Write a Boolean expression that evaluates true if either weight is greater than 50 or height is greater than 160, but not both. 4.12 Case Study: Determining Leap Years A year is a leap year if it is divisible by 4 but not by 100 or if it is divisible by 400. You can use the following Boolean expressions to determine whether a year is a leap year: # A leap year is divisible by 4 isLeapYear = (year % 4 == 0) # A leap year is divisible by 4 but not by 100 isLeapYear = isLeapYear and (year % 100 != 0) == conditional operator short-circuit evaluation ✓Point✓Check Key Point 114 Chapter 4 Selections # A leap year is divisible by 4 but not by 100 or divisible by 400 isLeapYear = isLeapYear or (year % 400 == 0) or you can combine all these expressions into one, like this: isLeapYear = (year % 4 == 0 and year % 100 != 0) or (year % 400 == 0) Listing 4.9 is an example of a program that lets the user enter a year and then determines whether it is a leap year. LISTING 4.9 LeapYear.py 1 year = eval(input("Enter a year: ")) 2 3 # Check if the year is a leap year 4 isLeapYear = 5 6 7 # Display the result 8 print(year, "is a leap year?", isLeapYear) (year % 400 == 0) (year % 4 == 0 and year % 100 != 0) or \ input leap year? display result Enter a year: 2008 is a leap year? True 2008 Enter a year: 2002 is a leap year? False 2002 Enter a year: 1900 is a leap year? False 1900 4.13 Case Study: Lottery The lottery program in this case study involves generating random numbers, comparing digits, and using Boolean operators. Suppose you want to develop a program to play a lottery. The program randomly generates a two-digit number, prompts the user to enter a two-digit number, and determines whether the user wins according to the following rules: 1. If the user’s input matches the lottery in the exact order, the award is $10,000. 2. If all the digits in the user’s input match all the digits in the lottery number, the award is $3,000. 3. If one digit in the user’s input matches a digit in the lottery number, the award is $1,000. The complete program is shown in Listing 4.10. LISTING 4.10 Lottery.py 1 import random 2 3 # Generate a lottery number 4 5 6 # Prompt the user to enter a guess 7 guess = eval(input("Enter your lottery pick (two digits): ")) lottery = random.randint(0, 99)generate a lottery enter a guess Key Point 4.13 Case Study: Lottery 115 8 9 # Get digits from lottery 10 lotteryDigit1 = lottery // 10 11 lotteryDigit2 = lottery % 10 12 13 # Get digits from guess 14 guessDigit1 = guess // 10 15 guessDigit2 = guess % 10 16 17 print("The lottery number is", lottery) 18 19 # Check the guess 20 21 print("Exact match: you win $10,000") 22 23 24 print("Match all digits: you win $3,000") 25 26 or guessDigit1 == lotteryDigit2 27 or guessDigit2 == lotteryDigit1 28 or guessDigit2 == lotteryDigit2): 29 print("Match one digit: you win $1,000") 30 else: 31 print("Sorry, no match") elif (guessDigit1 == lotteryDigit1 guessDigit1 == lotteryDigit2): elif (guessDigit2 == lotteryDigit1 and \ if guess == lottery: Enter your lottery pick (two digits): The lottery number is 12 Sorry, no match 45 Enter your lottery pick (two digits): The lottery number is 34 Match one digit: you win $1,000 23 line# variable 4 7 10 11 14 15 29 lottery 34 guess 23 lotteryDigit1 3 lotteryDigit2 4 guessDigit1 2 guessDigit2 3 output Match one digit: you win $1,000 The program generates a lottery number using the random.randint(0, 99) function (line 4) and prompts the user to enter a guess (line 7). Note that guess % 10 obtains the last digit from guess and guess // 10 obtains the first digit from guess, since guess is a two- digit number (lines 14–15). exact match? match all digits? match one digit? conditional expression 116 Chapter 4 Selections The program checks the guess against the lottery number in this order: 1. First check whether the guess matches the lottery number exactly (line 20). 2. If not, check whether the reversal of the guess matches the lottery number (lines 22–23). 3. If not, check whether one digit is in the lottery number (lines 25–28). 4. If not, nothing matches and display Sorry, no match (lines 30–31). 4.14 Conditional Expressions A conditional expression evaluates an expression based on a condition. You might want to assign a value to a variable that is restricted by certain conditions. For example, the following statement assigns 1 to y if x is greater than 0, and -1 to y if x is less than or equal to 0. if x > 0:
y = 1
else:
y = -1
Alternatively, as in this next example, you can use a conditional expression to achieve the
same result.
y = 1 if x > 0 else -1
Conditional expressions are in a completely different style. The syntax is:
expression1 if boolean-expression else expression2
The result of this conditional expression is expression1 if boolean-expression is
true; otherwise, the result is expression2.
Suppose you want to assign the larger number of variables number1 and number2 to max.
You can simply write a statement using the conditional expression:
max = number1 if number1 > number2 else number2
For another example, the following statement displays the message number is even if
number is even, and otherwise displays number is odd.
print(“number is even” if number % 2 == 0 else “number is odd”)
4.31 Suppose that when you run the following program you enter the input 2, 3, 6 from
the console. What is the output?
x, y, z = eval(input(“Enter three numbers: “))
print(“sorted” if x < y and y < z else "not sorted") 4.32 Rewrite the following if statements using a conditional expression: if ages >= 16:
ticketPrice = 20
else:
ticketPrice = 10
4.33 Rewrite the following conditional expressions using if/else statements:
(a) score = 3 * scale if x > 10 else 4 * scale
(b) tax = income * 0.2 if income > 10000 else income * 0.17 + 1000
(c) print(i if number % 3 == 0 else j)
if count % 10 == 0:
print(count)
else:
print(count, end = ” “)
Key
Point
✓Point✓Check

4.15 Operator Precedence and Associativity 117
4.15 Operator Precedence and Associativity
Operator precedence and associativity determine the order in which operators are
evaluated.
Operator precedence and operator associativity determine the order in which Python evalu-
ates operators. Suppose that you have this expression:
3 + 4 * 4 > 5 * (4 + 3) – 1
What is its value? What is the execution order of the operators?
Arithmetically, the expression in the parentheses is evaluated first. (Parentheses can be
nested, in which case the expression in the inner parentheses is executed first.) When evaluat-
ing an expression without parentheses, the operators are applied according to the precedence
rule and the associativity rule.
The precedence rule defines precedence for operators. Table 4.7 contains the operators you
have learned so far, with the operators listed in decreasing order of precedence from top to
bottom. The logical operators have lower precedence than the relational operators and the
relational operators have lower precedence than the arithmetic operators. Operators with the
same precedence appear in the same group.
operator precedence
operator associativity
precedence
associativity
behind the scenes
TABLE 4.7 Operator Precedence Chart
Precedence Operator
+, – (Unary plus and minus)
** (Exponentiation)
not
*, /, //, % (Multiplication, division, integer division, and remainder)
+, – (Binary addition and subtraction)
<, <=, >, >= (Comparison)
==, != (Equality)
and
or
=, +=, -=, *=, /=, //=, %= (Assignment operators)
If operators with the same precedence are next to each other, their associativity determines
the order of evaluation. All binary operators are left-associative. For example, since + and –
are of the same precedence and are left-associative, the expression
a – b + c – d
is equivalent to
((a – b) + c) – d
Note
Python has its own way to evaluate an expression internally. The result of a Python eval-
uation is the same as that of its corresponding arithmetic evaluation.
4.34 List the precedence order of the Boolean operators. Evaluate the following expressions:
True or True and False
True and True or False
4.35 True or false? All the binary operators except = are left-associative.
Key
Point
✓Point✓Check

118 Chapter 4 Selections
4.36 Evaluate the following expressions:
2 * 2 – 3 > 2 and 4 – 2 > 5
2 * 2 – 3 > 2 or 4 – 2 > 5
4.37 Is (x > 0 and x < 10) the same as ((x > 0) and (x < 10))? Is (x > 0 or
x < 10) the same as ((x > 0) or (x < 10))? Is (x > 0 or x < 10 and y < 0) the same as (x > 0 or (x < 10 and y < 0))? 4.16 Detecting the Location of an Object Detecting whether an object is inside another object is a common task in game programming. In game programming, often you need to determine whether an object is inside another object. This section gives an example of testing whether a point is inside a circle. The pro- gram prompts the user to enter the center of a circle, the radius, and a point. The program then displays the circle and the point along with a message indicating whether the point is inside or outside the circle, as shown in Figure 4.7a–b. A point is in the circle if its distance to the center of the circle is less than or equal to the radius of the circle, as shown in Figure 4.7c. The formula for computing the distance is Listing 4.11 gives the program. LISTING 4.11 PointInCircle.py 1 import turtle 2 3 x1, y1 = eval(input("Enter the center of a circle x, y: ")) 4 radius = eval(input("Enter the radius of the circle: ")) 5 x2, y2 = eval(input("Enter a point x, y: ")) 6 7 # Draw the circle 8 turtle.penup() # Pull the pen up 9 turtle.goto(x1, y1 - radius) 10 turtle.pendown() # Pull the pen down 11 12 # Draw the point turtle.circle(radius) 2(x2 - x1)2 + (y2 - y1)2. import turtle enter input (a) (b) (c) (x1, y1) (x2, y2) radius FIGURE 4.7 The program displays a circle, a point, and a message indicating whether the point is inside or outside the circle. draw a circle Key Point Chapter Summary 119 13 turtle.penup() # Pull the pen up 14 turtle.goto(x2, y2) 15 turtle.pendown() # Pull the pen down 16 turtle.begin_fill() # Begin to fill color in a shape 17 turtle.color("red") 18 19 turtle.end_fill() # Fill the shape 20 21 # Display the status 22 turtle.penup() # Pull the pen up 23 turtle.goto(x1 - 70, y1 - radius - 20) 24 turtle.pendown() 25 26 27 if d <= radius: 28 29 else: 30 31 32 turtle.hideturtle() 33 34 turtle.done() The program obtains the circle’s center location and radius (lines 3–4) and the location of a point (line 5). It displays the circle (lines 8–11) and the point (lines 13–19). The program computes the distance between the center of the circle and the point (line 26) and determines whether the point is inside or outside the circle. The code in lines 16–19 draws a dot, which can be simplified using the dot method, pre- sented in Table 3.6, as follows: turtle.dot(6, "red") This method draws a red dot with diameter 6. KEY TERMS turtle.write("The point is outside the circle") turtle.write("The point is inside the circle") d = ((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1)) ** 0.5 turtle.circle(3) draw a point compute distance in the circle not in the circle pause Boolean expressions 92 Boolean value 92 operator associativity 117 operator precedence 117 random module 94 selection statements 92 short-circuit evaluation 113 CHAPTER SUMMARY 1. A Boolean type variable can store a True or False value. 2. The relational operators (<, <=, ==, !=, >, >=), which work with numbers and charac-
ters, yield a Boolean value.
3. The Boolean operators and, or, and not operate with Boolean values and variables.
4. When evaluating p1 and p2, Python first evaluates p1 and then evaluates p2 if p1 is
True; if p1 is False, it does not evaluate p2. When evaluating p1 or p2, Python
first evaluates p1 and then evaluates p2 if p1 is False; if p1 is True, it does not eval-
uate p2. Therefore, and is referred to as the conditional or short-circuit AND
operator, and or is referred to as the conditional or short-circuit OR operator.

120 Chapter 4 Selections
5. Selection statements are used for programming with alternative courses. There are
several types of selection statements: if statements, if-else statements, nested
if-elif-else statements, and conditional expressions.
6. The various if statements all make control decisions based on a Boolean expression.
Based on the True or False evaluation of the expression, these statements take one
of two possible courses.
7. The operators in arithmetic expressions are evaluated in the order determined by the
rules of parentheses, operator precedence, and operator associativity.
8. Parentheses can be used to force the order of evaluation to occur in any sequence.
9. Operators with higher precedence are evaluated earlier. For operators of the same
precedence, their associativity determines the order of evaluation.
TEST QUESTIONS
Do test questions for this chapter online at www.cs.armstrong.edu/liang/py/test.html.
PROGRAMMING EXERCISES
Pedagogical Note
For each exercise, you should carefully analyze the problem requirements and design
strategies for solving the problem before coding.
Debugging Tip
Before you ask for help, read and explain the program to yourself, and trace it using
several representative inputs by hand or using an IDE debugger. You learn how to pro-
gram by debugging your own mistakes.
Section 4.2
*4.1 (Algebra: solve quadratic equations) The two roots of a quadratic equation, for
example, can be obtained using the following formula:
is called the discriminant of the quadratic equation. If it is positive, the
equation has two real roots. If it is zero, the equation has one root. If it is negative,
the equation has no real roots.
Write a program that prompts the user to enter values for a, b, and c and displays
the result based on the discriminant. If the discriminant is positive, display two
roots. If the discriminant is 0, display one root. Otherwise, display The equa-
tion has no real roots. Here are some sample runs.
b2 – 4ac
r1 =
– ˛b + 2b2 – 4ac
2a
and r2 =
– ˛b – 2b2 – 4ac
2a
ax2 + bx + c = 0,
think before coding
learn from mistakes

www.cs.armstrong.edu/liang/py/test.html

Programming Exercises 121
Enter a, b, c:
The roots are -0.381966 and -2.61803
1.0, 3, 1
Enter a, b, c:
The root is -1
1, 2.0, 1
Enter a, b, c:
The equation has no real roots
1, 2, 3
*4.2 (Game: add three numbers) The program in Listing 4.1 generates two integers and
prompts the user to enter the sum of these two integers. Revise the program to gen-
erate three single-digit integers and prompt the user to enter the sum of these three
integers.
Sections 4.3–4.8
*4.3 (Algebra: solve linear equations) You can use Cramer’s rule to solve the
following system of linear equation:
Write a program that prompts the user to enter a, b, c, d, e, and f and display the
result. If ad – bc is 0, report that The equation has no solution.
ax + by = e
cx + dy = f
x =
ed – bf
ad – bc
y =
af – ec
ad – bc
2 * 2
2 * 2
Enter a, b, c, d, e, f:
x is -2.0 and y is 3.0
9.0, 4.0, 3.0, -5.0, -6.0, -21.0
Enter a, b, c, d, e, f:
The equation has no solution
1.0, 2.0, 2.0, 4.0, 4.0, 5.0
**4.4 (Game: learn addition) Write a program that generates two integers under 100 and
prompts the user to enter the sum of these two integers. The program then reports
true if the answer is correct, false otherwise. The program is similar to Listing 4.1.
*4.5 (Find future dates) Write a program that prompts the user to enter an integer for
today’s day of the week (Sunday is 0, Monday is 1, …, and Saturday is 6). Also
prompt the user to enter the number of days after today for a future day and dis-
play the future day of the week. Here is a sample run:
Enter today’s day:
Enter the number of days elapsed since today:
Today is Monday and the future day is Thursday
3
1

122 Chapter 4 Selections
Enter today’s day:
Enter the number of days elapsed since today:
Today is Sunday and the future day is Wednesday
31
0
*4.6 (Health application: BMI ) Revise Listing 4.6, ComputeBMI.py, to let users enter
their weight in pounds and their height in feet and inches. For example, if a person
is 5 feet and 10 inches, you will enter 5 for feet and 10 for inches. Here is a sam-
ple run:
Enter weight in pounds:
Enter feet:
Enter inches:
BMI is 20.087702275404553
You are Normal
10
5
140
4.7 (Financial application: monetary units) Modify Listing 3.4, ComputeChange.py,
to display the nonzero denominations only, using singular words for single units
such as 1 dollar and 1 penny, and plural words for more than one unit such as 2
dollars and 3 pennies.
*4.8 (Sort three integers) Write a program that prompts the user to enter three integers
and displays them in increasing order.
*4.9 (Financial: compare costs) Suppose you shop for rice and find it in two different-
sized packages. You would like to write a program to compare the costs of the
packages. The program prompts the user to enter the weight and price of each
package and then displays the one with the better price. Here is a sample run:
Enter weight and price for package 1:
Enter weight and price for package 2:
Package 1 has the better price.
25, 11.99
50, 24.59
4.10 (Game: multiplication quiz) Listing 4.4, SubtractionQuiz.py, randomly generates
a subtraction question. Revise the program to randomly generate a multiplication
question with two integers less than 100.
Sections 4.9–4.16
*4.11 (Find the number of days in a month) Write a program that prompts the user to
enter the month and year and displays the number of days in the month. For exam-
ple, if the user entered month 2 and year 2000, the program should display that
February 2000 has 29 days. If the user entered month 3 and year 2005, the pro-
gram should display that March 2005 has 31 days.
4.12 (Check a number) Write a program that prompts the user to enter an integer and
checks whether the number is divisible by both 5 and 6, divisible by 5 or 6, or just
one of them (but not both). Here is a sample run:
Enter an integer:
Is 10 divisible by 5 and 6? False
Is 10 divisible by 5 or 6? True
Is 10 divisible by 5 or 6, but not both? True
10

Programming Exercises 123
Coffee price
*4.13 (Financial application: compute taxes) Listing 4.7, ComputeTax.py, gives the
source code to compute taxes for single filers. Complete Listing 4.7 to give the
complete source code for the other filing statuses.
4.14 (Game: heads or tails) Write a program that lets the user guess whether a flipped
coin displays the head or the tail. The program randomly generates an integer 0 or
1, which represents head or tail. The program prompts the user to enter a guess
and reports whether the guess is correct or incorrect.
**4.15 (Game: lottery) Revise Listing 4.10, Lottery.py, to generate a three-digit lottery
number. The program prompts the user to enter a three-digit number and deter-
mines whether the user wins according to the following rules:
1. If the user input matches the lottery number in the exact order, the award is
$10,000.
2. If all the digits in the user input match all the digits in the lottery number, the
award is $3,000.
3. If one digit in the user input matches a digit in the lottery number, the award is
$1,000.
4.16 (Random character) Write a program that displays a random uppercase letter.
*4.17 (Game: scissor, rock, paper) Write a program that plays the popular scissor-rock-
paper game. (A scissor can cut a paper, a rock can knock a scissor, and a paper can
wrap a rock.) The program randomly generates a number 0, 1, or 2 representing
scissor, rock, and paper. The program prompts the user to enter a number 0, 1, or
2 and displays a message indicating whether the user or the computer wins, loses,
or draws. Here are sample runs:
scissor (0), rock (1), paper (2):
The computer is scissor. You are rock. You won.
1
scissor (0), rock (1), paper (2):
The computer is paper. You are paper too. It is a draw.
2
*4.18 (Financials: currency exchange) Write a program that prompts the user to enter
the currency exchange rate between U.S. dollars and Chinese Renminbi (RMB).
Prompt the user to enter 0 to convert from U.S. dollars to Chinese RMB and 1 for
vice versa. Prompt the user to enter the amount in U.S. dollars or Chinese RMB to
convert it to Chinese RMB or U.S. dollars, respectively. Here are some sample
runs:
Enter the exchange rate from dollars to RMB:
Enter 0 to convert dollars to RMB and 1 vice versa:
Enter the dollar amount:
$100.0 is 681.0 yuan
100
0
6.81
Enter the exchange rate from dollars to RMB:
Enter 0 to convert dollars to RMB and 1 vice versa:
Enter the RMB amount:
10000.0 yuan is $1468.43
10000
1
6.81
VideoNote

124 Chapter 4 Selections
Enter the exchange rate from dollars to RMB:
Enter 0 to convert dollars to RMB and 1 vice versa:
Incorrect input
5
6.81
**4.19 (Compute the perimeter of a triangle) Write a program that reads three edges for a
triangle and computes the perimeter if the input is valid. Otherwise, display that
the input is invalid. The input is valid if the sum of every pair of two edges is
greater than the remaining edge. Here is a sample run:
Enter three edges:
The perimeter is 3
1, 1, 1
Enter three edges:
The input is invalid
1, 3, 1
*4.20 (Science: wind-chill temperature) Exercise 2.9 gives a formula to compute the
wind-chill temperature. The formula is valid for temperatures in the range
between and 41°F and for wind speed greater than or equal to 2. Write a
program that prompts the user to enter a temperature and a wind speed. The pro-
gram displays the wind-chill temperature if the input is valid; otherwise, it dis-
plays a message indicating whether the temperature and/or wind speed is invalid.
Comprehensive
**4.21 (Science: day of the week) Zeller’s congruence is an algorithm developed by
Christian Zeller to calculate the day of the week. The formula is
where
■ h is the day of the week (0: Saturday, 1: Sunday, 2: Monday, 3: Tuesday,
4: Wednesday, 5: Thursday, 6: Friday).
■ q is the day of the month.
■ m is the month (3: March, 4: April, …, 12: December). January and February are
counted as months 13 and 14 of the previous year.
■ j is the century (i.e., ).
■ k is the year of the century (i.e., year % 100).
Write a program that prompts the user to enter a year, month, and day of the
month, and then it displays the name of the day of the week. Here are some sam-
ple runs:
j year
100
k
h = ¢q + j 26(m + 1)
10
k + k + j k
4
k + j j
4
k + 5j≤ % 7
– ˛58 �F
Enter year: (e.g., 2008):
Enter month: 1-12:
Enter the day of the month: 1-31:
Day of the week is Friday
25
1
2013

Programming Exercises 125
Enter year: (e.g., 2008):
Enter month: 1-12:
Enter the day of the month: 1-31:
Day of the week is Saturday
12
5
2012
(Hint: for a positive n. January and February are counted as 13 and 14
in the formula, so you need to convert the user input 1 to 13 and 2 to 14 for the
month and change the year to the previous year.)
**4.22 (Geometry: point in a circle?) Write a program that prompts the user to enter a
point (x, y) and checks whether the point is within the circle centered at (0, 0) with
radius 10. For example, (4, 5) is inside the circle and (9, 9) is outside the circle, as
shown in Figure 4.8a.
:n; = n//1
(Hint: A point is in the circle if its distance to (0, 0) is less than or equal to 10. The
formula for computing the distance is Test your
program to cover all cases.) Two sample runs are shown next.
2(x2 – x1)2 + (y2 – y1)2.
x-axis(0, 0)
(a) (b)
y-axis
(4, 5)
(9, 9)
(2, 2)
(6, 4)
x-axis
y-axis
(0, 0)
FIGURE 4.8 (a) Points inside and outside of the circle; (b) points inside and outside of the
rectangle.
Enter a point with two coordinates:
Point (4.0, 5.0) is in the circle
4, 5
Enter a point with two coordinates:
Point (9.0, 9.0) is not in the circle
9, 9
**4.23 (Geometry: point in a rectangle?) Write a program that prompts the user to enter
a point (x, y) and checks whether the point is within the rectangle centered at
(0, 0) with width 10 and height 5. For example, (2, 2) is inside the rectangle and
(6, 4) is outside the rectangle, as shown in Figure 4.8b. (Hint: A point is in the
rectangle if its horizontal distance to (0, 0) is less than or equal to 10 / 2 and
its vertical distance to (0, 0) is less than or equal to 5.0 / 2. Test your program
to cover all cases.) Here are two sample runs:
Enter a point with two coordinates:
Point (2.0, 2.0) is in the rectangle
2, 2

126 Chapter 4 Selections
Enter a point with two coordinates:
Point (6.0, 4.0) is not in the rectangle
6, 4
**4.24 (Game: pick a card ) Write a program that simulates picking a card from a deck of
52 cards. Your program should display the rank (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10,
Jack, Queen, King) and suit (Clubs, Diamonds, Hearts, Spades) of the card.
Here is a sample run of the program:
The card you picked is the Jack of Hearts
*4.25 (Geometry: intersecting point) Two points on line 1 are given as (x1, y1) and (x2,
y2) and on line 2 as (x3, y3) and (x4, y4), as shown in Figure 4.9a–b.
The intersecting point of the two lines can be found by solving the following lin-
ear equation:
This linear equation can be solved using Cramer’s rule (see Exercise 4.3). If the
equation has no solutions, the two lines are parallel (Figure 4.9c). Write a program
that prompts the user to enter four points and displays the intersecting point. Here
are sample runs:
(y3 – y4)x – (x3 – x4)y = (y3 – y4)x3 – (x3 – x4)y3
(y1 – y2)x – (x1 – x2)y = (y1 – y2)x1 – (x1 – x2)y1
(x1, y1)
(x2, y2) (x3, y3)
(x4, y4)
(a) (b) (c)
(x1, y1)
(x2, y2)
(x3, y3)
(x4, y4)
(x1, y1)
(x2, y2)
(x3, y3)
(x4, y4)
FIGURE 4.9 Two lines intersect in (a–b) and two lines are parallel in (c).
Enter x1, y1, x2, y2, x3, y3, x4, y4:
The intersecting point is at (2.88889, 1.1111)
2, 2, 5, -1, 4, 2, -1, -2
Enter x1, y1, x2, y2, x3, y3, x4, y4:
The two lines are parallel
2, 2, 7, 6, 4, 2, -1, -2
4.26 (Palindrome number) Write a program that prompts the user to enter a three-digit
integer and determines whether it is a palindrome number. A number is a palindrome

Programming Exercises 127
Enter a three-digit integer:
121 is a palindrome
121
Enter a three-digit integer:
123 is not a palindrome
123
**4.27 (Geometry: points in triangle?) Suppose a right triangle is placed in a plane as
shown below. The right-angle point is at (0, 0), and the other two points are at
(200, 0), and (0, 100). Write a program that prompts the user to enter a point with
x- and y-coordinates and determines whether the point is inside the triangle. Here
are some sample runs:
Enter a point’s x- and y-coordinates:
The point is in the triangle
100.5, 25.5
Enter a point’s x- and y-coordinates:
The point is not in the triangle
100.5, 50.5
**4.28 (Geometry: two rectangles) Write a program that prompts the user to enter the
center x-, y-coordinates, width, and height of two rectangles and determines
whether the second rectangle is inside the first or overlaps with the first, as shown
in Figure 4.10. Test your program to cover all cases.
if it reads the same from right to left and from left to right. Here is a sample run of
this program:
(a)
w1
(x1, y1)
(x2, y2)
w2
h2h1
(b)
w1
(x1, y1)
h2
h1
(x2, y2)
w2
FIGURE 4.10 (a) A rectangle is inside another one. (b) A rectangle overlaps another one.
(0, 100)
(0, 0) (200, 0)
p2
p1

128 Chapter 4 Selections
Enter r1’s center x-, y-coordinates, width, and height:
Enter r2’s center x-, y-coordinates, width, and height:
r2 overlaps r1
3, 4, 4.5, 5
1, 2, 3, 5.5
Enter r1’s center x-, y-coordinates, width, and height:
Enter r2’s center x-, y-coordinates, width, and height:
r2 does not overlap r1
40, 45, 3, 2
1, 2, 3, 3
**4.29 (Geometry: two circles) Write a program that prompts the user to enter the center
coordinates and radii of two circles and determines whether the second circle is
inside the first or overlaps with the first, as shown in Figure 4.11. (Hint: circle2 is
inside circle1 if the distance between the two centers <= | r1 - r2| and circle2 overlaps circle1 if the distance between the two centers <= r1 + r2. Test your program to cover all cases.) (a) (b) (x1, y1) (x2, y2) r2 r1 (x1, y1) r1 (x2, y2) r2 FIGURE 4.11 (a) A circle is inside another circle. (b) A circle overlaps another circle. Here are some sample runs: Enter circle1's center x-, y-coordinates, and radius: Enter circle2's center x-, y-coordinates, and radius: circle2 is inside circle1 1, 1.7, 4.5 0.5, 5.1, 13 Enter circle1's center x-, y-coordinates, and radius: Enter circle2's center x-, y-coordinates, and radius: circle2 overlaps circle1 6.7, 3.5, 3 4.4, 5.7, 5.5 Here are some sample runs: Enter r1's center x-, y-coordinates, width, and height: Enter r2's center x-, y-coordinates, width, and height: r2 is inside r1 1.5, 5, 0.5, 3 2.5, 4, 2.5, 43 Programming Exercises 129 Enter circle1's center x-, y-coordinates, and radius: Enter circle2's center x-, y-coordinates, and radius: circle2 does not overlap circle1 5.5, 7.2, 1 4.4, 5.5, 1 *4.30 (Current time) Revise Programming Exercise 2.18 to display the hour using a 12- hour clock. Here is a sample run: Enter the time zone offset to GMT: The current time is 4:50:34 AM -5 *4.31 (Geometry: point position) Given a directed line from point p0(x0, y0) to p1(x1, y1), you can use the following condition to decide whether a point p2(x2, y2) is on the left side of the line, on the right side of the line, or on the same line (see Figure 4.12): (x1 - x0)*(y2 - y0) - (x2 - x0)*(y1 - y0) c 70 p2 is on the left side of the line=0 p2 is on the same line 60 p2 is on the right side of the line p0 p2 p1 p0 p2 p1 p0 p2 p1 (a) (b) (c) FIGURE 4.12 (a) p2 is on the left side of the line. (b) p2 is on the right side of the line. (c) p2 is on the same line. Write a program that prompts the user to enter the x- and y-coordinates for the three points p0, p1, and p2 and displays whether p2 is on the left side of the line from p0 to p1, on the right side, or on the same line. Here are some sample runs: Enter coordinates for the three points p0, p1, and p2: p2 is on the left side of the line from p0 to p1 3.4, 2, 6.5, 9.5, -5, 4 Enter coordinates for the three points p0, p1, and p2: p2 is on the same line from p0 to p1 1, 1, 5, 5, 2, 2 Enter coordinates for the three points p0, p1, and p2: p2 is on the right side of the line from p0 to p1 3.4, 2, 6.5, 9.5, 5, 2.5 130 Chapter 4 Selections Enter coordinates for the three points p0, p1, and p2: (1.5, 1.5) is on the line segment from (1.0, 1.0) to (2.5, 2.5) 1, 1, 2.5, 2.5, 1.5, 1.5 Enter coordinates for the three points p0, p1, and p2: (3.5, 3.5) is not on the line segment from (1.0, 1.0) to (2.0, 2.0) 1, 1, 2, 2, 3.5, 3.5 *4.33 (Decimal to hex) Write a program that prompts the user to enter an integer between 0 and 15 and displays its corresponding hex number. Here are some sam- ple runs: Enter a decimal value (0 to 15): The hex value is B 11 Enter a decimal value (0 to 15): The hex value is 5 5 Enter a decimal value (0 to 15): Invalid input 31 *4.34 (Hex to decimal) Write a program that prompts the user to enter a hex character and displays its corresponding decimal integer. Here are some sample runs: Enter a hex character: The decimal value is 10 A Enter a hex character: The decimal value is 10 a Enter a hex character: The decimal value is 5 5 *4.32 (Geometry: point on line segment) Exercise 4.31 shows how to test whether a point is on an unbounded line. Revise Exercise 4.31 to test whether a point is on a line segment. Write a program that prompts the user to enter the x- and y-coordinates for the three points p0, p1, and p2 and displays whether p2 is on the line segment from p0 to p1. Here are some sample runs: Programming Exercises 131 Enter a hex character: Invalid input G *4.35 (Turtle: point position) Write a program that prompts the user to enter the x- and y-coordinates for the three points p0, p1, and p2, and displays a message to indicate whether p2 is on the left side, the right side, or on the line from p0 to p1, as shown in Figure 4.13. See Exercise 4.31 for determining the point position. **4.36 (Turtle: point in a circle?) Modify Listing 4.11 to let the program randomly gen- erate a point within the square whose center is the same as the circle center and whose side is the diameter of the circle. Draw the circle and the point. Display a message to indicate whether the point is inside the circle. **4.37 (Turtle: point in a rectangle?) Write a program that prompts the user to enter a point (x, y) and checks whether the point is within the rectangle centered at (0, 0) with width 100 and height 50. Display the point, the rectangle, and a message indicating whether the point is inside the rectangle in the window, as shown in Figure 4.14. (a) (b) (c) FIGURE 4.13 The program displays the point position graphically. (a) (b) FIGURE 4.14 The program displays the rectangle, a point, and a message whether a point is in or outside of the rectangle. *4.38 (Geometry: two rectangles) Write a program that prompts the user to enter the center x-, y-coordinates, width, and height of two rectangles and determines whether the second rectangle is inside the first or overlaps with the first, as shown in Figure 4.15. 132 Chapter 4 Selections *4.39 (Turtle: two circles) Write a program that prompts the user to enter the center coordinates and radii of two circles and determines whether the second circle is inside the first or overlaps with the first, as shown in Figure 4.16. (a) (b) (c) FIGURE 4.15 The program checks whether a rectangle is inside another one, overlaps another one, or does not overlap. (a) (b) (c) FIGURE 4.16 The program displays two circles and a status message. LOOPS Objectives ■ To write programs for executing statements repeatedly by using a while loop (§5.2). ■ To develop loops following the loop design strategy (§§5.2.1–5.2.3). ■ To control a loop with the user’s confirmation (§5.2.4). ■ To control a loop with a sentinel value (§5.2.5). ■ To obtain a large amount of input from a file by using input redirection instead of typing from the keyboard and to save output to a file by using output redirection (§5.2.6). ■ To use for loops to implement counter-controlled loops (§5.3). ■ To write nested loops (§5.4). ■ To learn the techniques for minimizing numerical errors (§5.5). ■ To learn loops from a variety of examples (GCD, FutureTuition, MonteCarloSimulation, PrimeNumber) (§§5.6, 5.8). ■ To implement program control with break and continue (§5.7). ■ To use a loop to simulate a random walk (§5.9). CHAPTER 5 134 Chapter 5 Loops 5.1 Introduction A loop can be used to tell a program to execute statements repeatedly. Suppose that you need to display a string (e.g., Programming is fun!) 100 times. It would be tedious to type the statement 100 times: print("Programming is fun!") print("Programming is fun!") ... print("Programming is fun!") problem loop why loop? loop body condition-controlled loop count-controlled loop while loop iteration loop-continuation- condition 100 times loop body loop-continuation-condition So, how do you solve this problem? Python provides a powerful construct called a loop, which controls how many times in suc- cession an operation (or a sequence of operations) is performed. By using a loop statement, you don’t have to code the print statement a hundred times; you simply tell the computer to display a string that number of times. The loop statement can be written as follows: count = 0 while count < 100: print("Programming is fun!") count = count + 1 The variable count is initially 0. The loop checks whether count < 100 is true. If so, it executes the loop body—the part of the loop that contains the statements to be repeated—to display the message Programming is fun! and increments count by 1. It repeatedly exe- cutes the loop body until count < 100 becomes false (i.e., when count reaches 100). At this point the loop terminates and the next statement after the loop statement is executed. A loop is a construct that controls the repeated execution of a block of statements. The con- cept of looping is fundamental to programming. Python provides two types of loop state- ments: while loops and for loops. The while loop is a condition-controlled loop; it is controlled by a true/false condition. The for loop is a count-controlled loop that repeats a specified number of times. 5.2 The while Loop A while loop executes statements repeatedly as long as a condition remains true. The syntax for the while loop is: while loop-continuation-condition: # Loop body Statement(s) Figure 5.1a shows the while-loop flowchart. A single execution of a loop body is called an iteration (or repetition) of the loop. Each loop contains a loop-continuation-condition, a Boolean expression that controls the body’s execution. It is evaluated each time to determine if the loop body should be executed. If its evaluation is True, the loop body is executed; otherwise, the entire loop terminates and the program control turns to the statement that follows the while loop. The loop that displays Programming is fun! 100 times is an example of a while loop. Its flowchart is shown in Figure 5.1b. The loop-continuation-condition is count < 100 and the loop body contains two statements: count = 0 while count < 100: print("Programming is fun!") count = count + 1 Key Point Key Point while loop VideoNote 5.2 The while Loop 135 loop- continuation- condition? true false (a) A while loop count < 100? true false (b) A while loop example count = 0 print("Programming is fun!") count = count + 1 Statement(s) (loop body) FIGURE 5.1 The while loop repeatedly executes the statements in the loop body as long as the loop-continuation-condition evaluates to True. Here is another example illustrating how a loop works: sum = 0 i = 1 while i < 10: sum = sum + i i = i + 1 print("sum is", sum) # sum is 45 If i < 10 is true, the program adds i to sum. The variable i is initially set to 1, then incre- mented to 2, 3, and so on, up to 10. When i is 10, i < 10 is false, and the loop exits. So sum is 1 + 2 + 3 + ... + 9 = 45. Suppose the loop is mistakenly written as follows: sum = 0 i = 1 while i < 10: sum = sum + i i = i + 1 Note that the entire loop body must be indented inside the loop. Here the statement i = i + 1 is not in the loop body. This loop is infinite, because i is always 1 and i < 10will always be true. Note Make sure that the loop-continuation-condition eventually becomes false so that the loop will terminate. A common programming error involves infinite loops (i.e., the loop runs forever). If your program takes an unusual long time to run and does not stop, it may have an infinite loop. If you run the program from the command window, press CTRL+C to stop it. Caution Programmers often mistakenly execute a loop one time more or less than intended. This kind of mistake is commonly known as the off-by-one error. For example, the following loop displays Programming is fun 101 times rather than 100 times. The error lies in the condition, which should be count < 100 rather than count <= 100. count = 0 while : print("Programming is fun!") count = count + 1 count <= 100 infinite loop off-by-one error BAD CO DE 136 Chapter 5 Loops Recall that Listing 4.4, SubtractionQuiz.py, gives a program that prompts the user to enter an answer for a question on subtraction. Using a loop, you can now rewrite the program to let the user enter a new answer until it is correct, as shown in Listing 5.1. LISTING 5.1 RepeatSubtractionQuiz.py 1 import random 2 3 # 1. Generate two random single-digit integers 4 number1 = random.randint(0, 9) 5 number2 = random.randint(0, 9) 6 7 # 2. If number1 < number2, swap number1 with number2 8 if number1 < number2: 9 number1, number2 = number2, number1 10 11 # 3. Prompt the student to answer "What is number1 - number2?" 12 answer = eval(input("What is " + str(number1) + " - " 13 + str(number2) + "? ")) 14 15 # 4. Repeatedly ask the question until the answer is correct 16 while : 17 answer = eval(input("Wrong answer. Try again. What is " 18 + str(number1) + " - " + str(number2) + "? ")) 19 20 print("You got it!") number1 - number2 != answer random number1 random number2 swap numbers enter answer check answer enter answer again What is 4 - 3? Wrong answer. Try again. What is 4 - 3? Wrong answer. Try again. What is 4 - 3? You got it! 1 5 4 The loop in lines 16–18 repeatedly prompts the user to enter an answer when number1 - number2 != answer is true. Once number1 - number2 != answer is false, the loop exits. 5.2.1 Case Study: Guessing Numbers The problem is to guess what number a computer has in mind. You will write a program that randomly generates an integer between 0 and 100, inclusive. The program prompts the user to enter numbers continuously until it matches the randomly generated number. For each user input, the program reports whether it is too low or too high, so the user can choose the next input intelligently. Here is a sample run: Guess a magic number between 0 and 100 Enter your guess: Your guess is too high Enter your guess: Your guess is too low Enter your guess: Your guess is too high Enter your guess: Yes, the number is 39 39 42 25 50 The magic number is between 0 and 100. To minimize the number of guesses, enter 50 first. If your guess is too high, the magic number is between 0 and 49. If your guess is too low, intelligent guess 5.2 The while Loop 137 think before coding code incrementally generate a number enter a guess correct guess? too high? too low? the magic number is between 51 and 100. So, after one guess, you can eliminate half the numbers from further consideration. How do you write this program? Do you immediately begin coding? No. It is important to think before coding. Think about how you would solve the problem without writing a pro- gram. You need to first generate a random number between 0 and 100, inclusive, then prompt the user to enter a guess, and then compare the guess with the random number. It is a good practice to code incrementally—that is, one step at a time. For programs involving loops, if you don’t know how to write a loop right away, you might first write the program so it executes the code once, and then figure out how to execute it repeatedly in a loop. For this program, you can create an initial draft, as shown in Listing 5.2. LISTING 5.2 GuessNumberOneTime.py 1 import random 2 3 # Generate a random number to be guessed 4 5 6 print("Guess a magic number between 0 and 100") 7 8 # Prompt the user to guess the number 9 10 11 12 print("Yes, the number is", number) 13 14 print("Your guess is too high") 15 16 print("Your guess is too low") When this program runs, it prompts the user to enter a guess only once. To let the user enter a guess repeatedly, you can change the code in lines 11–16 to create a loop, as follows: 1 2 # Prompt the user to guess the number 3 4 5 6 print("Yes, the number is", number) 7 8 print("Your guess is too high") 9 10 print("Your guess is too low") This loop repeatedly prompts the user to enter a guess. However, the loop still needs to ter- minate; when guess matches number, the loop should end. So, revise the loop as follows: 1 2 # Prompt the user to guess the number 3 guess = eval(input("Enter your guess: ")) 4 5 if guess == number: 6 print("Yes, the number is", number) 7 elif guess > number:
8 print(“Your guess is too high”)
9 else:
10 print(“Your guess is too low”)
The complete code is given in Listing 5.3.
while guess != number:
else:
elif guess > number:
if guess == number:
guess = eval(input(“Enter your guess: “))
while True:
else:
elif guess > number:
if guess == number:
guess = eval(input(“Enter your guess: “))
number = random.randint(0, 100)

138 Chapter 5 Loops
LISTING 5.3 GuessNumber.py
1 import random
2
3 # Generate a random number to be guessed
4 number = random.randint(0, 100)
5
6 print(“Guess a magic number between 0 and 100”)
7
8
9
10 # Prompt the user to guess the number
11 guess = eval(input(“Enter your guess: “))
12
13 if guess == number:
14 print(“Yes, the number is”, number)
15 elif guess > number:
16 print(“Your guess is too high”)
17 else:
18 print(“Your guess is too low”)
while guess != number:
guess = -1
generate a number
enter a guess
too high?
too low?
line# number guess output
4 39
8 –1
iteration 1 11 50
16 Your guess is too high
iteration 2 11 25
18 Your guess is too low
iteration 3 11 42
16 Your guess is too high
iteration 4 11 39
14 Yes, the number is 39
{
{
{
{
The program generates the magic number in line 4 and prompts the user to enter a guess
continuously in a loop (lines 9–18). For each guess, the program determines whether
the user’s number is correct, too high, or too low (lines 13–18). When the guess is correct,
the program exits the loop (line 9). Note that guess is initialized to -1. This is to avoid
initializing it to a value between 0 and 100, because that could be the number to be
guessed.
5.2.2 Loop Design Strategies
Writing a loop that works correctly is not an easy task for novice programmers. Consider the
three steps involved when writing a loop:
Step 1: Identify the statements that need to be repeated.
Step 2: Wrap these statements in a loop like this:
while True:
Statements

5.2 The while Loop 139
Step 3: Code the loop-continuation-condition and add appropriate statements for
controlling the loop.
while loop-continuation-condition:
Statements
Additional statements for controlling the loop
5.2.3 Case Study: Multiple Subtraction Quiz
The subtraction quiz program in Listing 4.4, SubtractionQuiz.py, generates just one question
for each run. You can use a loop to generate questions repeatedly. How do you write the code
to generate five questions? Follow the loop design strategy. First, identify the statements that
need to be repeated. These are the statements for obtaining two random numbers, prompting
the user with a subtraction question, and grading the question. Second, wrap the statements in
a loop. Third, add a loop-control variable and the loop-continuation-condition to execute the
loop five times.
Listing 5.4 is a program that generates five questions and, after a student answers all of
them, reports the number of correct answers. The program also displays the time spent on the
test, as shown in the sample run.
LISTING 5.4 SubtractionQuizLoop.py
1 import random
2 import time
3
4 # Count the number of correct answers
5 # Count the number of questions
6 # Constant
7
8 startTime = time.time() # Get start time
9
10
11 # Generate two random single-digit integers
12 number1 = random.randint(0, 9)
13 number2 = random.randint(0, 9)
14
15 # If number1 < number2, swap number1 with number2 16 if number1 < number2: 17 number1, number2 = number2, number1 18 19 # Prompt the student to answer "What is number1 - number2?" 20 answer = eval(input("What is " + str(number1) + " - " + 21 str(number2) + "? ")) 22 23 # Grade the answer and display the result 24 if number1 - number2 == answer: 25 print("You are correct!") 26 27 else: 28 print("Your answer is wrong.\n", number1, "-", 29 number2, "is", number1 - number2) 30 31 # Increase the count 32 33 34 endTime = time.time() # Get end time 35 testTime = int(endTime – startTime) # Get test time 36 print("Correct count is", correctCount, "out of", 37 NUMBER_OF_QUESTIONS, "\nTest time is", testTime, "seconds") count += 1 correctCount += 1 while count < NUMBER_OF_QUESTIONS: NUMBER_OF_QUESTIONS = 5 count = 0 correctCount = 0 correct count total count get start time loop display a question grade an answer increase correct count increase control variable get end time test time display result 140 Chapter 5 Loops What is 1 - 1? You are correct! What is 7 - 2? You are correct! What is 9 - 3? Your answer is wrong. 9 - 3 is 6 What is 6 - 6? You are correct! What is 9 - 6? Your answer is wrong. 9 - 6 is 3 Correct count is 3 out of 5 Test time is 10 seconds 2 0 4 5 0 The program uses the control variable count to control the execution of the loop. count is initially 0 (line 5) and is increased by 1 in each iteration (line 32). A subtraction question is displayed and processed in each iteration. The program obtains the time before the test starts in line 8 and the time after the test ends in line 34, and computes the test time in seconds in line 35. The program displays the correct count and test time after all the quizzes have been taken (lines 36–37). 5.2.4 Controlling a Loop with User Confirmation The preceding example executes the loop five times. If you want the user to decide whether to take another question, you can offer a user confirmation. The template of the program can be coded as follows: while continueLoop == : # Execute the loop body once ... # Prompt the user for confirmation continueLoop = input("Enter Y to continue and N to quit: ") You can rewrite Listing 5.4 with user confirmation to let the user decide whether to advance to the next question. 5.2.5 Controlling a Loop with a Sentinel Value Another common technique for controlling a loop is to designate a special input value, known as a sentinel value, which signifies the end of the input. A loop that uses a sentinel value in this way is called a sentinel-controlled loop. The program in Listing 5.5 reads and calculates the sum of an unspecified number of inte- gers. The input 0 signifies the end of the input. You don’t need to use a new variable for each input value. Instead, use a variable named data (line 1) to store the input value and use a vari- able named sum (line 5) to store the total. Whenever a value is read, assign it to data (line 9) and add it to sum (line 7) if it is not zero. 'Y' continueLoop = 'Y' confirmation sentinel value sentinel-controlled loop 5.2 The while Loop 141 LISTING 5.5 SentinelValue.py 1 data = eval(input("Enter an integer (the input ends " + 2 "if it is 0): ")) 3 4 # Keep reading data until the input is 0 5 sum = 0 6 7 sum += data 8 9 data = eval(input("Enter an integer (the input ends " + 10 "if it is 0): ")) 11 12 print("The sum is", sum) while data != 0: input data loop output result Enter an integer (the input ends if it is 0): Enter an integer (the input ends if it is 0): Enter an integer (the input ends if it is 0): Enter an integer (the input ends if it is 0): The sum is 9 0 4 3 2 line# data sum output 1 2 5 0 iteration 1 7 2 9 3 iteration 2 7 5 9 4 iteration 3 7 9 9 0 12 The sum is 9 { { { numeric error If data is not 0, it is added to the sum (line 7) and the next item of input data is read (lines 9–10). If data is 0, the loop body is no longer executed and the while loop terminates. The input value 0 is the sentinel value for this loop. Note that if the first input read is 0, the loop body never executes, and the resulting sum is 0. Caution Don’t use floating-point values for equality checking in a loop control. Since those values are approximated, they could lead to imprecise counter values. This example uses int value for data. Consider the following code for computing 1 + 0.9 + 0.8 + ... + 0.1: item = 1 sum = 0 while : # No guarantee item will be 0 sum += item item -= 0.1 print(sum) item != 0 142 Chapter 5 Loops The variable item starts with 1 and is reduced by 0.1 every time the loop body is executed. The loop should terminate when item becomes 0. However, there is no guar- antee that item will be exactly 0, because the floating-point arithmetic is approximated. This loop seems okay on the surface, but it is actually an infinite loop. 5.2.6 Input and Output Redirections In Listing 5.5, if you have a lot of data to enter, it would be cumbersome to type all the entries from the keyboard. You can store the data in a text file (named input.txt, for example) and run the program by using the following command: python SentinelValue.py < input.txt This command is called input redirection. Instead of having the user type the data from the keyboard at runtime, the program takes the input from the file input.txt. Suppose the file con- tains the following numbers, one number per line: 2 3 4 0 The program should get sum to be 9. Similarly, output redirection can send the output to a file instead of displaying it on the screen. The command for output redirection is: python Script.py > output.txt
Input and output redirection can be used in the same command. For example, the following
command gets input from input.txt and sends output to output.txt:
python SentinelValue.py < input.txt > output.txt
Run the program and see what contents show up in output.txt.
5.1 Analyze the following code. Is count < 100 always True, always False, or some- times True or sometimes False at Point A, Point B, and Point C? count = 0 while count < 100: # Point A print("Programming is fun!") count += 1 # Point B # Point C 5.2 What is wrong if guess is initialized to 0 in line 8 in Listing 5.3? 5.3 How many times are the following loop bodies repeated? What is the printout of each loop? input redirection output redirection i = 1 while i < 10: if i % 2 == 0: print(i) i = 1 while i < 10: if i % 2 == 0: print(i) i += 1 (a) (b) i = 1 while i < 10: if i % 2 == 0: print(i) i += 1 (c) ✓Point✓Check 5.3 The for Loop 143 5.4 Show the errors in the following code: count = 0 while count < 100: print(count) count = 0 while count < 100: print(count) count -= 1 (a) (b) count = 0 while count < 100: count += 1 (c) 5.5 Suppose the input is 2 3 4 5 0 (one number per line). What is the output of the fol- lowing code? number = eval(input("Enter an integer: ")) max = number while number != 0: number = eval(input("Enter an integer: ")) if number > max:
max = number
print(“max is”, max)
print(“number”, number)
5.3 The for Loop
A Python for loop iterates through each value in a sequence.
Often you know exactly how many times the loop body needs to be executed, so a control
variable can be used to count the executions. A loop of this type is called a counter-controlled
loop. In general, the loop can be written as follows:
i = initialValue # Initialize loop-control variable
while i < endValue: # Loop body ... i += 1 # Adjust loop-control variable A for loop can be used to simplify the preceding loop: for i in range(initialValue, endValue): # Loop body In general, the syntax of a for loop is: for var in sequence: # Loop body A sequence holds multiple items of data, stored one after the other. Later in the book, we will introduce strings, lists, and tuples. They are sequence-type objects in Python. The vari- able var takes on each successive value in the sequence, and the statements in the body of the loop are executed once for each value. The function range(a, b) returns the sequence of integers a, a + 1, ..., b - 2, and b - 1. For example, counter-controlled loop for loop range(a, b) function Key Point VideoNote for loop 144 Chapter 5 Loops >>> for v in range(4, 8):
… print(v)
…
4
5
6
7
>>>
The range function has two more versions. You can also use range(a) or range(a, b,
k). range(a) is the same as range(0, a). k is used as step value in range(a, b, k). The
first number in the sequence is a. Each successive number in the sequence will increase by the
step value k. b is the limit. The last number in the sequence must be less than b. For example,
range(a) function
range(a, b, k) function
>>> for v in range(3, 9, 2):
… print(v)
…
3
5
7
>>>
The step value in range (3, 9, 2) is 2, and the limit is 9. So, the sequence is 3, 5, and 7.
The range(a, b, k) function can count backward if k is negative. In this case, the
sequence is still a, a + k, a + 2k, and so on for a negative k. The last number in the
sequence must be greater than b. For example,
count backward
>>> for v in range(5, 1, -1):
… print(v)
…
5
4
3
2
>>>
Note
The numbers in the range function must be integers. For example, range(1.5,
8.5), range(8.5), or range(1.5, 8.5, 1) would be wrong.
5.6 Suppose the input is 2 3 4 5 0 (one number per line). What is the output of the fol-
lowing code?
number = 0
sum = 0
for count in range(5):
number = eval(input(“Enter an integer: “))
sum += number
print(“sum is”, sum)
print(“count is”, count)
5.7 Can you convert any for loop to a while loop? List the advantages of using for loops.
step value
✓Point✓Check

5.8 Convert the following for loop statement to a while loop:
sum = 0
for i in range(1001):
sum = sum + i
5.9 Can you always convert any while loop into a for loop? Convert the following
while loop into a for loop.
i = 1
sum = 0
while sum < 10000: sum = sum + i i += 1 5.10 Count the number of iterations in the following loops: count = 0 while count < n: count += 1 for count in range(n): print(count) (a) (b) count = 5 while count < n: count += 1 count = 5 while count < n: count = count + 3 (c) (d) 5.4 Nested Loops A loop can be nested inside another loop. Nested loops consist of an outer loop and one or more inner loops. Each time the outer loop is repeated, the inner loops are reentered and started anew. Listing 5.6 presents a program that uses nested for loops to display a multiplication table. LISTING 5.6 MultiplicationTable.py 1 print(" Multiplication Table") 2 # Display the number title 3 print(" |", end = '') 4 5 print(" ", j, end = '') 6 print() # Jump to the new line 7 print("——————————————————————————————————————————") 8 9 # Display table body 10 11 print(i, "|", end = '') 12 13 # Display the product and align properly 14 print(format(i * j, "4d"), end = '') 15 print() # Jump to the new line for j in range(1, 10): for i in range(1, 10): for j in range(1, 10): nested loops table title table body nested loop display a line 5.4 Nested Loops 145 Key Point 146 Chapter 5 Loops Multiplication Table 1 2 3 4 5 6 7 8 9 ————————————————————————————————————————— 1 | 1 2 3 4 5 6 7 8 9 2 | 2 4 6 8 10 12 14 16 18 3 | 3 6 9 12 15 18 21 24 27 4 | 4 8 12 16 20 24 28 32 36 5 | 5 10 15 20 25 30 35 40 45 6 | 6 12 18 24 30 36 42 48 54 7 | 7 14 21 28 35 42 49 56 63 8 | 8 16 24 32 40 48 56 64 72 9 | 9 18 27 36 45 54 63 72 81 The program displays a title (line 1) on the first line in the output. The first for loop (lines 4–5) displays the numbers 1 through 9 on the second line. A line of dashes (-) is dis- played on the third line (line 7). The next loop (lines 10–15) is a nested for loop with the control variable i in the outer loop and j in the inner loop. For each i, the product i * j is displayed on a line in the inner loop, with j being 1, 2, 3, . . ., 9. To align the numbers properly, the program formats i * j using format(i * j, "4d") (line 14). Recall that "4d" specifies a decimal integer format with width 4. Normally, the print function automatically jumps to the next line. Invoking print(item, end = '') (lines 3, 5, 11, and 14) prints the item without advancing to the next line. Note that the print function with the end argument was introduced in Section 3.3.5. Note Be aware that a nested loop may take a long time to run. Consider the following loop nested in three levels: for i in range(1000): for j in range(1000): for k in range(1000): Perform an action The action is performed 1,000,000,000 times. If it takes 1 millisecond to perform the action, the total time to run the loop would be more than 277 hours. 5.11 Show the output of the following programs. (Hint: Draw a table and list the variables in the columns to trace these programs.) end = '' for i in range(1, 5): j = 0 while j < i: print(j, end = " ") j += 1 i = 0 while i < 5: for j in range(i, 1, -1): print(j, end = " ") print("****") i += 1 (a) (b) i = 5 while i >= 1:
num = 1
for j in range(1, i + 1):
print(num, end = “xxx”)
num *= 2
print()
i -= 1
i = 1
while i <= 5: num = 1 for j in range(1, i + 1): print(num, end = "G") num += 2 print() i += 1 (c) (d) ✓Point✓Check 5.5 Minimizing Numerical Errors 147 5.5 Minimizing Numerical Errors Using floating-point numbers in the loop-continuation-condition may cause numeric errors. Numerical errors involving floating-point numbers are inevitable. This section provides an example showing you how to minimize such errors. The program in Listing 5.7 sums a series that starts with 0.01 and ends with 1.0. The numbers in the series will increment by 0.01, as follows: 0.01 + 0.02 + 0.03 and so on. LISTING 5.7 TestSum.py 1 # Initialize sum 2 sum = 0 3 4 # Add 0.01, 0.02, ..., 0.99, 1 to sum 5 i = 0.01 6 7 sum += i 8 i = i + 0.01 9 10 # Display result 11 print("The sum is", sum) while i <= 1.0: loop The sum is 49.5 The result displayed is 49.5, but the correct result is actually 50.5. What went wrong? For each iteration in the loop, i is incremented by 0.01. When the loop ends, the i value is slightly larger than 1 (not exactly 1). This causes the last i value not to be added into sum. The funda- mental problem is that the floating-point numbers are represented by approximation. To fix the problem, use an integer count to ensure that all the numbers are added to sum. Here is the new loop: # Initialize sum sum = 0 # Add 0.01, 0.02, ..., 0.99, 1 to sum i = 0.01 sum += i i = i + 0.01 # Increase count # Display result print("The sum is", sum) Or, use a for loop as follows: # Initialize sum sum = 0 # Add 0.01, 0.02, ..., 0.99, 1 to sum i = 0.01 for count in range(100): sum += i i = i + 0.01 # Display result print("The sum is", sum) After this loop, sum is 50.5. count += 1 while count < 100: count = 0 numeric error Key Point 148 Chapter 5 Loops 5.6 Case Studies Loops are fundamental in programming. The ability to write loops is essential in learning programming. If you can write programs using loops, you know how to program! For this reason, this section presents three additional examples of solving problems using loops. 5.6.1 Problem: Finding the Greatest Common Divisor The greatest common divisor (GCD) of the two integers 4 and 2 is 2. The greatest common divisor of the two integers 16 and 24 is 8. How do you find the greatest common divisor? Let the two input integers be n1 and n2. You know that number 1 is a common divisor, but it may not be the greatest common divisor. So you can check whether k (for k 2, 3, 4, and so on) is a common divisor for n1 and n2, until k is greater than n1 or n2. Store the common divisor in a variable named gcd. Initially, gcd is 1. Whenever a new common divisor is found, it becomes the new gcd. When you have checked all the possible common divisors from 2 up to n1 or n2, the value in the variable gcd is the greatest common divisor. The idea can be trans- lated into the following loop: gcd = 1 # Initial gcd is 1 int k = 2 # Possible gcd while k <= n1 and k <= n2: if n1 % k == 0 and n2 % k == 0: gcd = k k += 1 # Next possible gcd # After the loop, gcd is the greatest common divisor for n1 and n2 Listing 5.8 presents a program that prompts the user to enter two positive integers and finds their greatest common divisor. LISTING 5.8 GreatestCommonDivisor.py 1 # Prompt the user to enter two integers 2 n1 = eval(input("Enter first integer: ")) 3 n2 = eval(input("Enter second integer: ")) 4 5 gcd = 1 6 k = 2 7 while k <= n1 and k <= n2: 8 if n1 % k == 0 and n2 % k == 0: 9 gcd = k 10 k += 1 11 12 print("The greatest common divisor for", 13 n1, "and", n2, "is", gcd) = input input gcd output Enter first integer: Enter second integer: The greatest common divisor for 125 and 2525 is 25 2525 125 How would you approach writing this program? Would you immediately begin to write the code? No. It is important to think before you type. Thinking enables you to generate a logicalthink before you type GCD Key Point 5.6 Case Studies 149 multiple solutions erroneous solutions solution for the problem without wondering how to write the code. Once you have a logical solution, type the code to translate the solution into a program. A problem often has multiple solutions. The GCD problem can be solved in many ways. Exercise 5.16 at the end of this chapter suggests another solution. A more efficient solution is to use the classic Euclidean algorithm. See www.cut-the-knot.org/blue/Euclid.shtml for more information. 5.12 If you think that a divisor for a number n1 cannot be greater than n1 / 2, you might attempt to improve the program using the following loop: k = 2 while k <= and k <= : if n1 % k == 0 and n2 % k == 0: gcd = k k += 1 This revision is wrong. Can you find the reason? 5.6.2 Problem: Predicting the Future Tuition Suppose that the tuition for a university is $10,000 this year and increases 7% every year. In how many years will the tuition have doubled? Before you attempt to write a program, first consider how to solve this problem by hand. The tuition for the second year is the tuition for the first year * 1.07. The tuition for a future year is the tuition of its preceding year * 1.07. So, the tuition for each year can be computed as follows: year = 0 # Year 0 tuition = 10000 year += 1 # Year 1 tuition = tuition * 1.07 year += 1 # Year 2 tuition = tuition * 1.07 year += 1 # Year 3 tuition = tuition * 1.07 ... Keep computing tuition for a new year until it is at least 20000. By then you will know how many years it will take for the tuition to be doubled. You can now translate the logic into the following loop: year = 0 # Year 0 tuition = 10000 while tuition < 20000: year += 1 tuition = tuition * 1.07 The complete program is shown in Listing 5.9. LISTING 5.9 FutureTuition.py 1 year = 0 # Year 0 2 tuition = 10000 # Year 1 3 4 while tuition < 20000: n2 / 2n1 / 2 loop ✓Point✓Check www.cut-the-knot.org/blue/Euclid.shtml 150 Chapter 5 Loops The while loop (lines 4–6) is used to repeatedly compute the tuition for a new year. The loop terminates when tuition is greater than or equal to 20000. 5.6.3 Problem: Monte Carlo Simulation A Monte Carlo simulation uses random numbers and probability to solve problems. It has a wide range of applications in computational mathematics, physics, chemistry, and finance. We now look at an example of using a Monte Carlo simulation for estimating First, draw a circle with its bounding square. p. generate random points check inside circle estimate pi PI is 3.14124 5 year += 1 6 tuition = tuition * 1.07 7 8 print("Tuition will be doubled in", year, "years") 9 print("Tuition will be $" + format(tuition, ".2f"), 10 "in", year, "years") Tuition will be doubled in 11 years Tuition will be $21048.52 in 11 years next year’s tuition 1 –1 –1 1 x y Assume the radius of the circle is 1. So, the circle area is and the square area is 4. Ran- domly generate a point in the square. The probability that the point falls in the circle is circleArea / squareArea = π / 4. Write a program that randomly generates 1000000 points that fall in the square and let numberOfHits denote the number of points that fall in the circle. So, numberOfHits is approximately 1000000 * (π / 4). can be approximated as 4 * numberOfHits / 1000000. The complete program is shown in Listing 5.10. LISTING 5.10 MonteCarloSimulation.py 1 import random 2 3 NUMBER_OF_TRIALS = 1000000 # Constant 4 numberOfHits = 0 5 6 for i in range(NUMBER_OF_TRIALS): 7 x = random.random() * 2 - 1 8 y = random.random() * 2 – 1 9 10 if x * x + y * y <= 1: 11 12 13 14 15 print("PI is", pi) pi = 4 * numberOfHits / NUMBER_OF_TRIALS numberOfHits += 1 p p 5.7 Keywords break and continue 151 The program repeatedly generates a random point (x, y) in the square in lines 7–8: x = random.random() * 2 - 1 y = random.random() * 2 – 1 Recall that random() returns a random float r such that 0 <= r < 1.0. If the point is inside the circle and numberOfHits is incremented by 1. is approximately 4 * numberOfHits / NUMBER_OF_TRIALS (line 13). 5.7 Keywords break and continue The break and continue keywords provide additional controls to a loop. Pedagogical Note Two keywords, break and continue, can be used in loop statements to provide addi- tional controls. Using break and continue can simplify programming in some cases. Overusing or improperly using them, however, can make programs difficult to read and debug. (Note to readers: You may skip this section without affecting your understanding of the rest of the book.) You can use the keyword break in a loop to immediately terminate a loop. Listing 5.11 presents a program to demonstrate the effect of using break in a loop. LISTING 5.11 TestBreak.py 1 sum = 0 2 number = 0 3 4 while number < 20: 5 number += 1 6 sum += number 7 if sum >= 100:
8 break
9
10 print(“The number is”, number)
11 print(“The sum is”, sum)
px2 + y2 … 1,
break keyword
break out of the loop
The number is 14
The sum is 105
The program adds integers from 1 to 20 in this order to sum until sum is greater than or
equal to 100. Without lines 7–8, this program would calculate the sum of the numbers from 1
to 20. But with lines 7–8, the loop terminates when sum becomes greater than or equal to 100.
Without lines 7–8, the output would be:
The number is 20
The sum is 210
You can also use the continue keyword in a loop. When it is encountered, it ends the cur-
rent iteration and program control goes to the end of the loop body. In other words, continue
breaks out of an iteration, while the break keyword breaks out of a loop. The program in
Listing 5.12 shows the effect of using continue in a loop.
continue statement
Key
Point

152 Chapter 5 Loops
LISTING 5.12 TestContinue.py
1 sum = 0
2 number = 0
3
4 while number < 20: 5 number += 1 6 if number == 10 or number == 11: 7 continue 8 sum += number 9 10 print("The sum is", sum) jump to the end of the iteration The sum is 189 The program adds all the integers from 1 to 20 except 10 and 11 to sum. The continue statement is executed when number becomes 10 or 11. The continue statement ends the current iteration so that the rest of the statement in the loop body is not executed; therefore, number is not added to sum when it is 10 or 11. Without lines 6 and 7, the output would be as follows: The sum is 210 In this case, all the numbers are added to sum, even when number is 10 or 11. Therefore, the result is 210. You can always write a program without using break or continue in a loop (see Check- point Question 5.15). In general, it is appropriate to use break and continue if their use simplifies coding and makes programs easy to read. Suppose you need to write a program to find the smallest factor other than 1 for an integer n (assume n >= 2). You can write a simple and intuitive code using the break statement as
follows:
n = eval(input(“Enter an integer >= 2: “))
factor = 2
while factor <= n: if n % factor == 0: break factor += 1 print("The smallest factor other than 1 for", n, "is", factor) You may rewrite the code without using break as follows: n = eval(input("Enter an integer >= 2: “))
found = False
factor = 2
while factor <= n and not found: if n % factor == 0: found = True else: factor += 1 print("The smallest factor other than 1 for", n, "is", factor) Obviously, the break statement makes the program simpler and easier to read in this example. However, you should use break and continue with caution. Too many break 5.7 Keywords break and continue 153 goto and continue statements will produce a loop with many exit points and make the pro- gram difficult to read. Note Some programming languages have a goto statement. The goto statement indiscrimi- nately transfers control to any statement in the program and executes it. This makes your program vulnerable to errors. The break and continue statements in Python are different from goto statements. They operate only in a loop statement. The break statement breaks out of the loop, and the continue statement breaks out of the cur- rent iteration in the loop. 5.13 What is the keyword break for? What is the keyword continue for? Will the fol- lowing program terminate? If so, give the output. balance = 1000 while True: if balance < 9: break balance = balance - 9 print("Balance is", balance) balance = 1000 while True: if balance < 9: continue balance = balance - 9 print("Balance is", balance) (a) (b) 5.14 The for loop on the left is converted into the while loop on the right. What is wrong? Correct it. for i in range(4): if i % 3 == 0: continue sum += i i = 0 while i < 4: if i % 3 == 0: continue sum += i i += 1 Converted Wrong conversion 5.15 Rewrite the programs TestBreak and TestContinue in Listings 5.11 and 5.12 without using break and continue statements. 5.16 After the break statement in (a) is executed in the following loop, which statement is executed? Show the output. After the continue statement in (b) is executed in the following loop, which statement is executed? Show the output. for i in range(1, 4): for j in range(1, 4): if i * j > 2:
break
print(i * j)
print(i)
for i in range(1, 4):
for j in range(1, 4):
if i * j > 2:
continue
print(i * j)
print(i)
(a) (b)
✓Point✓Check

154 Chapter 5 Loops
5.8 Case Study: Displaying Prime Numbers
This section presents a program that displays the first fifty prime numbers in five lines,
each containing ten numbers.
An integer greater than 1 is prime if its only positive divisor is 1 or itself. For example, 2, 3,
5, and 7 are prime numbers, but 4, 6, 8, and 9 are not.
The problem can be broken into the following tasks:
■ Determine whether a given number is prime.
■ For number = 2, 3, 4, 5, 6, …, test whether the number is prime.
■ Count the prime numbers.
■ Display each prime number, and display ten numbers per line.
Obviously, you need to write a loop and repeatedly test whether a new number is prime. If
the number is prime, increase the count by 1. The count is 0 initially. When it reaches 50, the
loop terminates.
Here is the algorithm for the problem:
Set the number of prime numbers to be displayed as
a constant NUMBER_OF_PRIMES
Use count to track the number of prime numbers and
set an initial count to 0
Set an initial number to 2
Test if number is prime
if number is prime:
Display the prime number and increase count
Increment number by 1
To test whether a number is prime, check whether it is divisible by 2, 3, 4, …, up to
number/2. If a divisor is found, the number is not a prime. The algorithm can be described as
follows:
Use a Boolean variable isPrime to denote whether
the number is prime; Set isPrime to True initially
for divisor in range(2, number / 2 + 1):
if number % divisor == 0:
Set isPrime to False
Exit the loop
The complete program is given in Listing 5.13.
LISTING 5.13 PrimeNumber.py
1 NUMBER_OF_PRIMES = 50 # Number of primes to display
2 NUMBER_OF_PRIMES_PER_LINE = 10 # Display 10 per line
3 # Count the number of prime numbers
4 number = 2 # A number to be tested for primeness
5
6 print(“The first 50 prime numbers are”)
7
8 # Repeatedly find prime numbers
count = 0
while count < NUMBER_OF_PRIMES: count prime numbers Key Point 5.8 Case Study: Displaying Prime Numbers 155 9 while count < NUMBER_OF_PRIMES: 10 # Assume the number is prime 11 isPrime = True # Is the current number prime? 12 13 # Test if number is prime 14 divisor = 2 15 16 if number % divisor == 0: 17 # If true, the number is not prime 18 isPrime = False # Set isPrime to false 19 # Exit the for loop 20 divisor += 1 21 22 # Display the prime number and increase the count 23 if : 24 count += 1 # Increase the count 25 26 print(format(number, "5d"), end = '') 27 if count % NUMBER_OF_PRIMES_PER_LINE == 0: 28 # Display the number and advance to the new line 29 print() # Jump to the new line 30 31 # Check if the next number is prime 32 number += 1 isPrime break while divisor <= number / 2: check primeness exit loop display if prime This is a complex example for novice programmers. The key to developing a program- matic solution for this problem—and for many other problems—is to break it into sub- problems and develop solutions for each of them in turn. Do not attempt to develop a complete solution in the first trial. Instead, begin by writing the code to determine whether a given number is prime, and then expand the program to test whether other numbers are prime in a loop. To determine whether a number is prime, check whether it is divisible by a number between 2 and number/2 inclusive. If so, it is not a prime number; otherwise, it is a prime number. For a prime number, display it. If the count is divisible by 10, advance to a new line. The program ends when the count reaches 50. The program uses the break statement in line 19 to exit the for loop as soon as the num- ber is found to be a nonprime. You can rewrite the loop (lines 15–20) without using the break statement as follows: while divisor <= number / 2 : if number % divisor == 0: # If True, the number is not prime isPrime = False # Set isPrime to False divisor += 1 However, using the break statement makes the program simpler and easier to read in this case. and isPrime The first 50 prime numbers are 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 156 Chapter 5 Loops 5.9 Case Study: Random Walk You can use Turtle graphics to simulate a random walk. In this section, we will write a Turtle program that simulates a random walk in a lattice (e.g., like walking around a garden and turning to look at certain flowers) that starts from the center and ends at a point on the boundary, as shown in Figure 5.2. Listing 5.14 gives the program. FIGURE 5.2 The program simulates random walks in a lattice. LISTING 5.14 RandomWalk.py 1 import turtle 2 from random import randint 3 4 turtle.speed(1) # Set turtle speed to slowest 5 6 # Draw 16-by-16 lattice 7 turtle.color("gray") # Color for lattice 8 x = -80 9 10 turtle.penup() 11 turtle.goto(x, y) # Draw a horizontal line 12 turtle.pendown() 13 turtle.forward(160) 14 15 y = 80 16 turtle.right(90) 17 18 turtle.penup() 19 turtle.goto(x, y) # Draw a vertical line 20 turtle.pendown() 21 turtle.forward(160) 22 23 turtle.pensize(3) 24 turtle.color("red") 25 26 turtle.penup() 27 turtle.goto(0, 0) # Go to the center 28 turtle.pendown() 29 30 x = y = 0 # Current pen location at the center of lattice 31 32 r = randint(0, 3) 33 34 x += 10 # Walk right if r == 0: while abs(x) < 80 and abs(y) < 80: for x in range(-80, 80 + 1, 10): for y in range(-80, 80 + 1, 10): import turtle import randint set turtle speed set color draw horizontal lines draw vertical lines move to center current position check boundaries walk east Key Point Key Terms 157 35 turtle.setheading(0) 36 turtle.forward(10) 37 38 y -= 10 # Walk down 39 turtle.setheading(270) 40 turtle.forward(10) 41 42 x -= 10 # Walk left 43 turtle.setheading(180) 44 turtle.forward(10) 45 46 y += 10 # Walk up 47 turtle.setheading(90) 48 turtle.forward(10) 49 50 turtle.done() Assume the size of the lattice is 16 by 16 and the distance between two lines in the lattice is 10 pixels (lines 6–21). The program first draws the lattice in a gray color. It sets the color to gray (line 7), uses the for loop (lines 9–13) to draw the horizontal lines, and the for loop (lines 17–21) to draw the vertical lines. The program moves the pen to the center (line 27), and starts to simulate a random walk in a while loop (lines 31–48). The variables x and y are used to track the current position in the lattice. Initially, it is at (0, 0) (line 30). A random number from 0 to 3 is generated in line 32. These four numbers each correspond to a direction: east, south, west, and north. Con- sider four cases: ■ If a walk is to the east, x is increased by 10 (line 34) and the pen is moved to the right (lines 35–36). ■ If a walk is to the south, y is decreased by 10 (line 38) and the pen is moved down- ward (lines 39–40). ■ If a walk is to the west, x is decreased by 10 (line 42) and the pen is moved to the left (lines 43–44). ■ If a walk is to the north, y is increased by 10 (line 46) and the pen is moved upward (lines 47–48). The walk stops when abs(x) or abs(y) is 80 (i.e., the walk reaches the boundary of the lattice). A more interesting walk is called a self-avoiding walk. It is a random walk in a lattice that does not visit the same point twice. You will learn how to write a program to simulate a self- avoiding walk later in the book. KEY TERMS elif r == 3: elif r == 2: elif r == 1: walk south walk west walk north pause break keyword 151 condition-controlled loop 134 continue keyword 151 count-controlled loop 134 infinite loop 135 input redirection 142 iteration 134 loop 134 loop body 134 loop-continuation- condition 134 nested loop 145 off-by-one error 135 output redirection 142 sentinel value 140 158 Chapter 5 Loops CHAPTER SUMMARY 1. There are two types of repetition statements: the while loop and the for loop. 2. The part of the loop that contains the statements to be repeated is called the loop body. 3. A one-time execution of a loop body is referred to as an iteration of the loop. 4. An infinite loop is a loop statement that executes infinitely. 5. In designing loops, you need to consider both the loop-control structure and the loop body. 6. The while loop checks the loop-continuation-condition first. If the condi- tion is true, the loop body is executed; otherwise, the loop terminates. 7. A sentinel value is a special value that signifies the end of the input. 8. The for loop is a count-controlled loop and is used to execute a loop body a pre- dictable number of times. 9. Two keywords, break and continue, can be used in a loop. 10. The break keyword immediately ends the innermost loop, which contains the break. 11. The continue keyword ends only the current iteration. TEST QUESTIONS Do test questions for this chapter online at www.cs.armstrong.edu/liang/py/test.html. PROGRAMMING EXERCISES Pedagogical Note For each problem, read it several times until you understand it. Think how to solve the problem before coding. Translate your logic into a program. A problem often can be solved in many different ways. You should explore various solutions. Sections 5.2–5.7 *5.1 (Count positive and negative numbers and compute the average of numbers) Write a program that reads an unspecified number of integers, determines how many positive and negative values have been read, and computes the total and average of the input values (not counting zeros). Your program ends with the input 0. Display the average as a floating-point number. Here is a sample run: read and think before coding explore solutions Enter an integer, the input ends if it is 0: Enter an integer, the input ends if it is 0: Enter an integer, the input ends if it is 0: Enter an integer, the input ends if it is 0: 3 -1 2 1 www.cs.armstrong.edu/liang/py/test.html Programming Exercises 159 Enter an integer, the input ends if it is 0: The number of positives is 3 The number of negatives is 1 The total is 5 The average is 1.25 0 5.2 (Repeat additions) Listing 5.4, SubtractionQuizLoop.py, generates five random subtraction questions. Revise the program to generate ten random addition ques- tions for two integers between 1 and 15. Display the correct count and test time. 5.3 (Conversion from kilograms to pounds) Write a program that displays the follow- ing table (note that 1 kilogram is 2.2 pounds): Kilograms Pounds 1 2.2 3 6.6 ... 197 433.4 199 437.8 5.4 (Conversion from miles to kilometers) Write a program that displays the following table (note that 1 mile is 1.609 kilometers): Miles Kilometers 1 1.609 2 3.218 ... 9 15.481 10 16.090 *5.5 (Conversion from kilograms to pounds and pounds to kilograms) Write a program that displays the following two tables side by side (note that 1 kilogram is 2.2 pounds and that 1 pound is .45 kilograms): Kilograms Pounds | Pounds Kilograms 1 2.2 | 20 9.09 3 6.6 | 25 11.36 ... 197 433.4 | 510 231.82 199 437.8 | 515 235.09 *5.6 (Conversion from miles to kilometers and kilometers to miles) Write a program that displays the following two tables side by side (note that 1 mile is 1.609 kilo- meters and that 1 kilometer is .621 mile): Miles Kilometers | Kilometers Miles 1 1.609 | 20 12.430 2 3.218 | 25 15.538 ... 9 15.481 | 60 37.290 10 16.090 | 65 40.398 Enter an integer, the input ends if it is 0: You didn't enter any number 0 160 Chapter 5 Loops 5.7 (Use trigonometric functions) Print the following table to display the sin value and cos value of degrees from 0 to 360 with increments of 10 degrees. Round the value to keep four digits after the decimal point. Degree Sin Cos 0 0.0000 1.0000 10 0.1736 0.9848 ... 350 -0.1736 0.9848 360 0.0000 1.0000 5.8 (Use the math.sqrt function) Write a program that prints the following table using the sqrt function in the math module. Number Square Root 0 0.0000 2 1.4142 ... 18 5.2426 20 5.4721 **5.9 (Financial application: compute future tuition) Suppose that the tuition for a uni- versity is $10,000 this year and increases 5% every year. Write a program that computes the tuition in ten years and the total cost of four years’ worth of tuition starting ten years from now. 5.10 (Find the highest score) Write a program that prompts the user to enter the number of students and each student’s score, and displays the highest score. Assume that the input is stored in a file named score.txt, and the program obtains the input from the file. *5.11 (Find the two highest scores) Write a program that prompts the user to enter the number of students and each student’s score, and displays the highest and second- highest scores. 5.12 (Find numbers divisible by 5 and 6) Write a program that displays, ten numbers per line, all the numbers from 100 to 1,000 that are divisible by 5 and 6. The num- bers are separated by exactly one space. 5.13 (Find numbers divisible by 5 or 6, but not both) Write a program that displays, ten numbers per line, all the numbers from 100 to 200 that are divisible by 5 or 6, but not both. The numbers are separated by exactly one space. 5.14 (Find the smallest n such that n2 12,000) Use a while loop to find the smallest integer n such that n2 is greater than 12,000. 5.15 (Find the largest n such that n3 12,000) Use a while loop to find the largest integer n such that n3 is less than 12,000. *5.16 (Compute the greatest common divisor) For Listing 5.8, another solution to find the greatest common divisor of two integers n1 and n2 is as follows: First find d to be the minimum of n1 and n2, and then check whether d, d - 1, d - 2, ..., 2, or 1 is a divisor for both n1 and n2 in this order. The first such common divisor is the greatest common divisor for n1 and n2. Section 5.8 *5.17 (Display the ASCII character table) Write a program that displays the characters in the ASCII character table from ! to ~. Display ten characters per line. The char- acters are separated by exactly one space. 6 7 Programming Exercises 161 **5.18 (Find the factors of an integer) Write a program that reads an integer and displays all its smallest factors, also known as prime factors. For example, if the input inte- ger is 120, the output should be as follows: 2, 2, 2, 3, 5 **5.19 (Display a pyramid ) Write a program that prompts the user to enter an integer from 1 to 15 and displays a pyramid, as shown in the following sample run: Enter the number of lines: 1 2 1 2 3 2 1 2 3 4 3 2 1 2 3 4 5 4 3 2 1 2 3 4 5 6 5 4 3 2 1 2 3 4 5 6 7 6 5 4 3 2 1 2 3 4 5 6 7 7 *5.20 (Display four patterns using loops) Use nested loops that display the following patterns in four separate programs: Pattern A Pattern B Pattern C Pattern D 1 1 2 3 4 5 6 1 1 2 3 4 5 6 1 2 1 2 3 4 5 2 1 1 2 3 4 5 1 2 3 1 2 3 4 3 2 1 1 2 3 4 1 2 3 4 1 2 3 4 3 2 1 1 2 3 1 2 3 4 5 1 2 5 4 3 2 1 1 2 1 2 3 4 5 6 1 6 5 4 3 2 1 1 **5.21 (Display numbers in a pyramid pattern) Write a nested for loop that displays the following output: 1 1 2 1 1 2 4 2 1 1 2 4 8 4 2 1 1 2 4 8 16 8 4 2 1 1 2 4 8 16 32 16 8 4 2 1 1 2 4 8 16 32 64 32 16 8 4 2 1 1 2 4 8 16 32 64 128 64 32 16 8 4 2 1 *5.22 (Display prime numbers between 2 and 1,000) Modify Listing 5.13 to display all the prime numbers between 2 and 1,000, inclusive. Display eight prime numbers per line. Comprehensive **5.23 (Financial application: compare loans with various interest rates) Write a pro- gram that lets the user enter the loan amount and loan period in number of years and displays the monthly and total payments for each interest rate starting from 5% to 8%, with an increment of 1/8. Here is a sample run: 162 Chapter 5 Loops Loan Amount: Number of Years: Interest Rate Monthly Payment Total Payment 5.000% 188.71 11322.74 5.125% 189.28 11357.13 5.250% 189.85 11391.59 ... 7.875% 202.17 12129.97 8.000% 202.76 12165.83 5 10000 For the formula to compute monthly payment, see Listing 2.8, ComputeLoan.py. **5.24 (Financial application: loan amortization schedule) The monthly payment for a given loan pays the principal and the interest. The monthly interest is computed by multiplying the monthly interest rate and the balance (the remaining principal). The principal paid for the month is therefore the monthly payment minus the monthly interest. Write a program that lets the user enter the loan amount, number of years, and interest rate, and then displays the amortization schedule for the loan. Here is a sample run: Loan Amount: Number of Years: Annual Interest Rate: Monthly Payment: 865.26 Total Payment: 10383.21 Payment# Interest Principal Balance 1 58.33 806.93 9193.07 2 53.62 811.64 8381.43 ... 11 10.00 855.26 860.27 12 5.01 860.25 0.01 7 1 10000 Note The balance after the last payment may not be zero. If so, the last payment should be the normal monthly payment plus the final balance. Hint Write a loop to display the table. Since the monthly payment is the same for each month, it should be computed before the loop. The balance is initially the loan amount. For each iteration in the loop, compute the interest and principal and update the balance. The loop may look like this: for i in range(1, numberOfYears * 12 + 1): interest = monthlyInterestRate * balance principal = monthlyPayment - interest balance = balance - principal print(i, "\t\t", interest, "\t\t", principal, "\t\t", balance) Programming Exercises 163 *5.25 (Demonstrate cancellation errors) A cancellation error occurs when you are manipulating a very large number with a very small number. The large number may cancel out the smaller number. For example, the result of 100000000.0 + 0.000000001 is equal to 100000000.0. To avoid cancellation errors and obtain more accurate results, carefully select the order of computation. For example, in computing the following series, you will obtain more accurate results by comput- ing from right to left rather than from left to right: Write a program that compares the results of the summation of the preceding series, computing both from left to right and from right to left with n 50000. *5.26 (Sum a series) Write a program to sum the following series: **5.27 (Compute ) You can approximate by using the following series: Write a program that displays the value for i = 10000, 20000, . . ., and 100000. **5.28 (Compute e) You can approximate e by using the following series: Write a program that displays the e value for i = 10000, 20000, . . ., and 100000. (Hint: Since , then is Initialize e and item to be 1 and keep adding a new item to e. The new item is the previous item divided by i for i = 2, 3, 4, . . . .) 5.29 (Display leap years) Write a program that displays, ten per line, all the leap years in the twenty-first century (from year 2001 to 2100). The years are separated by exactly one space. **5.30 (Display the first days of each month) Write a program that prompts the user to enter the year and first day of the year, and displays the first day of each month in the year on the console. For example, if the user entered year 2013, and 2 for Tuesday, January 1, 2013, your program should display the following output: January 1, 2013 is Tuesday ... December 1, 2013 is Sunday **5.31 (Display calendars) Write a program that prompts the user to enter the year and first day of the year, and displays on the console the calendar table for the year. For example, if the user entered year 2005, and 6 for Saturday, January 1, 1 i(i - 1)! . 1 i! i! = i * (i - 1) * c * 2 * 1 e = 1 + 1 1! + 1 2! + 1 3! + 1 4! + c + 1 i! p p = 4¢1 - 1 3 + 1 5 - 1 7 + 1 9 - 1 11 + c + (-1)i+1 2i - 1 ≤ pp 1 3 + 3 5 + 5 7 + 7 9 + 9 11 + 11 13 + c + 95 97 + 97 99 = 1 + 1 2 + 1 3 + c + 1 n 164 Chapter 5 Loops 2005, your program should display the calendar for each month in the year, as follows: January 2005 Sun Mon Tue Wed Thu Fri Sat 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 ... December 2005 Sun Mon Tue Wed Thu Fri Sat 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 *5.32 (Financial application: compound value) Suppose you save $100 each month into a savings account with the annual interest rate 5%. So, the monthly interest rate is After the first month, the value in the account becomes 100 * (1 + 0.00417) = 100.417 After the second month, the value in the account becomes (100 + 100.417) * (1 + 0.00417) = 201.252 After the third month, the value in the account becomes (100 + 201.252) * (1 + 0.00417) = 302.507 and so on. Write a program that prompts the user to enter an amount (e.g., 100), the annual interest rate (e.g., 5), and the number of months (e.g., 6), and displays the amount in the savings account after the given month. *5.33 (Financial application: compute CD value) Suppose you put $10,000 into a CD with an annual percentage yield of 5.75%. After one month, the CD is worth 10000 + 10000 * 5.75 / 1200 = 10047.91 After two months, the CD is worth 10047.91 + 10047.91 * 5.75 / 1200 = 10096.06 After three months, the CD is worth 10096.06 + 10096.06 * 5.75 / 1200 = 10145.43 and so on. Write a program that prompts the user to enter an amount (e.g., 10,000), the annual percentage yield (e.g., 5.75), and the number of months (e.g., 18), and dis- plays a table as shown in the sample run. 0.05/12 = 0.00417. Programming Exercises 165 Enter the initial deposit amount: Enter annual percentage yield: Enter maturity period (number of months): Month CD Value 1 10047.91 2 10096.06 ... 17 10846.56 18 10898.54 18 5.75 10000 **5.34 (Game: lottery) Revise Listing 4.10, Lottery.py, to generate a lottery of a two-digit number. The two digits in the number are distinct. (Hint: Generate the first digit. Use a loop to continuously generate the second digit until it is different from the first digit.) **5.35 (Perfect number) A positive integer is called a perfect number if it is equal to the sum of all of its positive divisors, excluding itself. For example, 6 is the first per- fect number, because The next is There are four perfect numbers less than 10,000. Write a program to find these four numbers. ***5.36 (Game: scissor, rock, paper) Programming Exercise 4.17 gives a program that plays the scissor, rock, paper game. Revise the program to let the user play contin- uously until either the user or the computer wins more than two times. *5.37 (Summation) Write a program that computes the following summation: *5.38 (Simulation: clock countdown) You can use the time.sleep(seconds) function in the time module to let the program pause for the specified seconds. Write a program that prompts the user to enter the number of seconds, displays a message at every second, and terminates when the time expires. Here is a sample run: 1 1 + 22 + 122 + 23 + 123 + 24 + c + 12624 + 2625 28 = 14 + 7 + 4 + 2 + 1.6 = 3 + 2 + 1. Enter the number of seconds: 2 seconds remaining 1 second remaining Stopped 3 *5.39 (Financial application: find the sales amount) You have just started a sales job in a department store. Your pay consists of a base salary plus a commission. The base salary is $5,000. The following scheme shows how to determine the commission rate: Sales Amount Commission Rate $0.01–$5,000 8 percent $5,000.01–$10,000 10 percent $10,000.01 and above 12 percent Your goal is to earn $30,000 a year. Write a program that finds out the minimum amount of sales you have to generate in order to make $30,000. 166 Chapter 5 Loops 5.40 (Simulation: heads or tails) Write a program that simulates flipping a coin one million times and displays the number of heads and tails. **5.41 (Occurrence of max numbers) Write a program that reads integers, finds the largest of them, and counts its occurrences. Assume that the input ends with num- ber 0. Suppose that you entered 3 5 2 5 5 5 0; the program finds that the largest number is 5 and the occurrence count for 5 is 4. (Hint: Maintain two vari- ables, max and count. The variable max stores the current maximum number, and count stores its occurrences. Initially, assign the first number to max and 1 to count. Compare each subsequent number with max. If the number is greater than max, assign it to max and reset count to 1. If the number is equal to max, incre- ment count by 1.) Enter a number (0: for end of input): Enter a number (0: for end of input): Enter a number (0: for end of input): Enter a number (0: for end of input): Enter a number (0: for end of input): Enter a number (0: for end of input): Enter a number (0: for end of input): The largest number is 5 The occurrence count of the largest number is 4 0 5 5 5 2 5 3 **5.42 (Monte Carlo simulation) A square is divided into four smaller regions as shown in (a). If you throw a dart into the square one million times, what is the probability for the dart to fall into an odd-numbered region? Write a program to simulate the process and display the result. (Hint: Place the center of the square in the center of a coordinate system, as shown in (b). Randomly generate a point in the square and count the number of times for a point to fall in an odd-numbered region.) 1 2 1 3 ... ... The total number of all combinations is 21 **5.44 (Decimal to binary) Write a program that prompts the user to enter a decimal inte- ger and displays its corresponding binary value. *5.43 (Math: combinations) Write a program that displays all possible combinations for picking two numbers from integers 1 to 7. Also display the total number of com- binations. 1 4 3 2 (a) 1 4 3 2 (b) Programming Exercises 167 Enter ten numbers: The mean is 5.61 The standard deviation is 2.99794 10 9 8 7 6 5.6 5.5 3 2 1 **5.45 (Decimal to hex) Write a program that prompts the user to enter a decimal integer and displays its corresponding hexadecimal value. **5.46 (Statistics: compute mean and standard deviation) In business applications, you are often asked to compute the mean and standard deviation of data. The mean is simply the average of the numbers. The standard deviation is a statistic that tells you how tightly all the various data are clustered around the mean in a set of data. For example, what is the average age of the students in a class? How close are the ages? If all the students are the same age, the deviation is 0. Write a program that prompts the user to enter ten numbers, and displays the mean and standard devia- tions of these numbers using the following formula: Here is a sample run: deviation = aa n i=1 x2i - ¢an i=1 x i≤2 n n - 1 mean = a n i=1 x i n = x1 + x2 + c + xn n **5.47 (Turtle: draw random balls) Write a program that displays 10 random balls in a rectangle with width 120 and height 100, centered at (0, 0), as shown in Figure 5.3a. (a) (b) FIGURE 5.3 The program draws 10 random balls in (a), and 10 circles in (b). 168 Chapter 5 Loops **5.48 (Turtle: draw circles) Write a program that draws 10 circles with centers (0, 0), as shown in Figure 5.3b. **5.49 (Turtle: display a multiplication table) Write a program that displays a multiplica- tion table, as shown in Figure 5.4a. **5.50 (Turtle: display numbers in a triangular pattern) Write a program that displays numbers in a triangular pattern, as shown in Figure 5.4b. **5.51 (Turtle: display a lattice) Write a program that displays an 18-by-18 lattice, as shown in Figure 5.4c. **5.52 (Turtle: plot the sine function) Write a program that plots the sine function, as shown in Figure 5.5a. Hint The Unicode for p is \u03c0. To display –2p, use turtle.write("-2\u03c0"). For a trigonometric function like sin(x), x is in radians. Use the following loop to plot the sine function: for x in range(-175, 176): turtle.goto(x, 50 * math.sin((x / 100) * 2 * math.pi)) –2p is displayed at (–100, –15), the center of the axis is at (0, 0), and 2p is displayed at (100, –15). (a) (b) (c) FIGURE 5.4 (a) The program displays a multiplication table. (b) The program displays numbers in a triangular pattern. (c) The program displays an 18-by-18 lattice. Programming Exercises 169 **5.53 (Turtle: plot the sine and cosine functions) Write a program that plots the sine function in red and cosine in blue, as shown in Figure 5.5b. **5.54 (Turtle: plot the square function) Write a program that draws a diagram for the function (see Figure 5.6a).f(x) = x2 **5.55 (Turtle: chessboard) Write a program to draw a chessboard, as shown in Figure 5.6b. (a) (b) FIGURE 5.5 (a) The program plots a sine function. (b) The program plots sine function in blue and cosine function in red. FIGURE 5.6 (a) The program plots a diagram for function (b) The program draws a chessboard.f(x) = x2. (a) (b) This page intentionally left blank FUNCTIONS CHAPTER 6 Objectives ■ To define functions with formal parameters (§6.2). ■ To invoke functions with actual parameters (i.e., arguments) (§6.3). ■ To distinguish between functions that return and do not return a value (§6.4). ■ To invoke a function using positional arguments or keyword arguments (§6.5). ■ To pass arguments by passing their reference values (§6.6). ■ To develop reusable code that is modular and is easy to read, debug, and maintain (§6.7). ■ To create modules for reusing functions (§§6.7–6.8). ■ To determine the scope of variables (§6.9). ■ To define functions with default arguments (§6.10). ■ To define a function that returns multiple values (§6.11). ■ To apply the concept of function abstraction in software development (§6.12). ■ To design and implement functions using stepwise refinement (§6.13). ■ To simplify drawing programs with reusable functions (§6.14). 172 Chapter 6 Functions 6.1 Introduction Functions can be used to define reusable code and organize and simplify code. Suppose that you need to find the sum of integers from 1 to 10, 20 to 37, and 35 to 49. If you create a program to add these three sets of numbers, your code might look like this: sum = 0 for i in range(1, 11): sum += i print("Sum from 1 to 10 is", sum) sum = 0 for i in range(20, 38): sum += i print("Sum from 20 to 37 is", sum) sum = 0 for i in range(35, 50): sum += i print("Sum from 35 to 49 is", sum) You may have observed that the code for computing these sums is very similar, except that the starting and ending integers are different. Wouldn’t it be nice to be able to write com- monly used code once and then reuse it? You can do this by defining a function, which enables you to create reusable code. For example, the preceding code can be simplified by using functions, as follows: 1 def sum(i1, i2): 2 result = 0 3 for i in range(i1, i2 + 1): 4 result += i 5 6 return result 7 8 def main(): 9 print("Sum from 1 to 10 is", ) 10 print("Sum from 20 to 37 is", sum(20, 37)) 11 print("Sum from 35 to 49 is", sum(35, 49)) 12 13 main() # Call the main function Lines 1–6 define the function named sum with the two parameters i1 and i2. Lines 8–11 define the main function that invokes sum(1, 10) to compute the sum from 1 to 10, sum(20, 37) to compute the sum from 20 to 37, and sum(35, 49) to compute the sum from 35 to 49. A function is a collection of statements grouped together that performs an operation. In earlier chapters, you learned about such functions as eval("numericString") and random.randint(a, b). When you call the random.randint(a, b) function, for example, the system actually executes the statements in the function and returns the result. In this chapter, you will learn how to define and use functions and apply function abstraction to solve complex problems. 6.2 Defining a Function A function definition consists of the function’s name, parameters, and body. The syntax for defining a function is as follows: def functionName(list of parameters) # Function body sum(1, 10) problem why functions? define sum function define main function invoke sum functions Key Point Key Point Use functions VideoNote 6.3 Calling a Function 173 Let’s look at a function created to find which of two numbers is bigger. This function, named max, has two parameters, num1 and num2, the larger of which is returned by the func- tion. Figure 6.1 illustrates the components of this function. A function contains a header and body. The header begins with the def keyword, followed by the function’s name and parameters, and ends with a colon. The variables in the function header are known as formal parameters or simply parameters. A parameter is like a placeholder: When a function is invoked, you pass a value to the para- meter. This value is referred to as an actual parameter or argument. Parameters are optional; that is, a function may not have any parameters. For example, the random.random() function has no parameters. Some functions return a value, while other functions perform desired operations without returning a value. If a function returns a value, it is called a value-returning function. The function body contains a collection of statements that define what the function does. For example, the function body of the max function uses an if statement to determine which number is larger and return the value of that number. A return statement using the keyword return is required for a value-returning function to return a result. The function terminates when a return statement is executed. 6.3 Calling a Function Calling a function executes the code in the function. In a function’s definition, you define what it is to do. To use a function, you have to call or invoke it. The program that calls the function is called a caller. There are two ways to call a function, depending on whether or not it returns a value. If the function returns a value, a call to that function is usually treated as a value. For example, larger = max(3, 4) calls max(3, 4) and assigns the result of the function to the variable larger. Another example of a call that is treated as a value is print(max(3, 4)) which prints the return value of the function call max(3, 4). function header formal parameters parameters actual parameter argument value-returning function caller Define a function Invoke a function z = max(x, y) actual parameters (arguments) def max(num1, num2): if num1 > num2:
result = num1
else:
result = num2
return result
function name formal
parameters
return value
function
body
function
header
FIGURE 6.1 You can define a function and invoke it with arguments.
return value
Key
Point

174 Chapter 6 Functions
If a function does not return a value, the call to the function must be a statement. For example,
the print function does not return a value. The following call is a statement:
print(“Programming is fun!”)
Note
A value-returning function also can be invoked as a statement. In this case, the return value
is ignored. This is rare but is permissible if the caller is not interested in the return value.
When a program calls a function, program control is transferred to the called function. A
called function returns control to the caller when its return statement is executed or the func-
tion is finished.
Listing 6.1 shows a complete program that is used to test the max function.
LISTING 6.1 TestMax.py
1 # Return the max of two numbers
2
3 if num1 > num2:
4 result = num1
5 else:
6 result = num2
7
8
9
10 :
11 i = 5
12 j = 2
13 k = # Call the max function
14 print(“The larger number of”, i, “and”, j, “is”, k)
15
16 main() # Call the main function
max(i, j)
def main()
return result
def max(num1, num2):define max function
main function
invoke max
The larger number of 5 and 2 is 5
This program contains the max and main functions. The program script invokes the main
function in line 16. By convention, programs often define a function named main that con-
tains the main functionality for a program.
How is this program executed? The interpreter reads the script in the file line by line starting
from line 1. Since line 1 is a comment, it is ignored. When it reads the function header in line 2,
it stores the function with its body (lines 2–8) in the memory. Remember that a function’s defini-
tion defines the function, but it does not cause the function to execute. The interpreter then reads
the definition of the main function (lines 10–14) to the memory. Finally, the interpreter reads the
statement in line 16, which invokes the main function and causes the main function to be
executed. The control is now transferred to the main function, as shown in Figure 6.2.
main function
Line# i j k num1 num2 result
11 5
12 2
Invoke max
2 5 2
4 5
13 5
execution

6.3 Calling a Function 175
The execution of the main function begins in line 11. It assigns 5 to i and 2 to j (lines
11–12) and then invokes max(i, j) (line 13).
When the max function is invoked (line 13), variable i’s value is passed to num1 and vari-
able j’s value is passed to num2. The control is transferred to the max function, and the max
function is executed. When the return statement in the max function is executed, the max
function returns the control to its caller (in this case the caller is the main function).
After the max function is finished, the returned value from the max function is assigned to
k (line 13). The main function prints the result (line 14). The main function is now finished,
and it returns the control to its caller (line 16). The program is now finished.
Note
Here main is defined after max. In Python, functions can be defined in any order in a
script file as long as the function is in the memory when it is called. You can also define
main before max.
6.3.1 Call Stacks
Each time a function is invoked, the system creates an activation record that stores its argu-
ments and variables for the function and places the activation record in an area of memory
known as a call stack. A call stack is also known as an execution stack, runtime stack, or
machine stack, and is often shortened to just “the stack.” When a function calls another
function, the caller’s activation record is kept intact and a new activation record is created for
the new function call. When a function finishes its work and returns control to its caller, its
activation record is removed from the call stack.
A call stack stores the activation records in a last-in, first-out fashion. The activation record
for the function that is invoked last is removed first from the stack. Suppose function m1 calls
function m2, and then m3. The runtime system pushes m1’s activation record into the stack,
then m2’s, and then m3’s. After m3 is finished, its activation record is removed from the stack.
After m2 is finished, its activation record is removed from the stack. After m1 is finished, its
activation record is removed from the stack.
Understanding call stacks helps us comprehend how functions are invoked. When the
main function is invoked, an activation record is created to store variables i and j, as shown
in Figure 6.3a. Remember that all data in Python are objects. Python creates and stores
objects in a separate memory space called heap. Variables i and j actually contain reference
values to int objects 5 and 2, as shown in Figure 6.3a.
Invoking max(i, j) passes the values i and j to parameters num1 and num2 in the max
function. So now num1 and num2 reference int objects 5 and 2, as shown in Figure 6.3b. The
max function finds the maximum number and assigns it to result, so result now
references int object 5, as shown in Figure 6.3c. The result is returned to the main function
max function
order of functions
stack
def main():
i = 5
j = 2
k = max(i, j)

print(“The larger number or”,
i, “and”, j, “is”, k)
pass int 2
pass int 5
def max(num1, num2):
if num1 > num2:
result = num1
else:
result = num2
return result
main()
FIGURE 6.2 When a function is invoked, the control is transferred to the function. When the
function is finished, the control is returned to where the function was called.
heap
activation record

176 Chapter 6 Functions
and assigned to variable k. Now k references int object 5, as shown in Figure 6.3d. After the
main function is finished, the stack is empty, as shown in Figure 6.3e. The objects in the heap
are automatically destroyed by the Python interpreter when they are no longer needed.
6.4 Functions with/without Return Values
A function does not have to return a value.
The preceding section gives an example of a value-returning function. This section shows
how to define and invoke a function that does not return a value. Such a function is commonly
known as a void function in programming terminology.
The program in Listing 6.2 defines a function named printGrade and invokes it to print
the grade for a given score.
LISTING 6.2 PrintGradeFunction.py
1 # Print grade for the score
2
3 if score >= 90.0:
4 print(‘A’)
5 elif score >= 80.0:
6 print(‘B’)
7 elif score >= 70.0:
8 print(‘C’)
def printGrade(score):
void function
(a) The main function
is invoked.
This is the heap
for storing
objects.
stack stack stack
Space required for
the main function
j:
i:
int object
5
int object
2
(b) The max function
is invoked.
(c) The max function
is being executed.
This is the heap
for storing
objects.
Space required for
the main function
j:
i:
Space required for
the max function
num2:
num1:
int object
5
int object
2
Space required for
the main function
j:
i:
Space required for
the max function
result:
num2:
num1:
stack stack
(d) The max function
is finished and the
return value is sent
to k.
(e) The main
function is finished.
This is the heap
for storing
objects.
Space required for
the main function
k:
j: 2
i: 5
int object
5
int object
2
Stack is
now empty
FIGURE 6.3 When a function is invoked, an
activation record is created to store variables in
the function. The activation record is released
after the function is finished.
printGrade function
Key
Point

6.4 Functions with/without Return Values 177
9 elif score >= 60.0:
10 print(‘D’)
11 else:
12 print(‘F’)
13
14 :
15 score = eval(input(“Enter a score: “))
16 print(“The grade is “, end = ” “)
17
18
19 main() # Call the main function
printGrade(score)
def main() main function
invoke printGrade
Enter a score:
The grade is C
78.5
The printGrade function does not return any value. So, it is invoked as a statement in
line 17 in the main function.
To see the differences between a function that does not return a value and a function that
returns a value, let’s redesign the printGrade function to return a value. We call the new
function that returns the grade, getGrade, as shown in Listing 6.3.
LISTING 6.3 ReturnGradeFunction.py
1 # Return the grade for the score
2 :
3 if score >= 90.0:
4 return ‘A’
5 elif score >= 80.0:
6 return ‘B’
7 elif score >= 70.0:
8 return ‘C’
9 elif score >= 60.0:
10 return ‘D’
11 else:
12 return ‘F’
13
14 :
15 score = eval(input(“Enter a score: “))
16 print(“The grade is”, )
17
18 main() # Call the main function
getGrade(score)
def main()
def getGrade(score) getGrade function
main function
invoke getGrade
Enter a score:
The grade is C
78.5
The getGrade function defined in lines 2–12 returns a character grade based on the
numeric score value. It is invoked in line 16.
The getGrade function returns a character, and it can be invoked and used just like a
character. The printGrade function does not return a value, and it must be invoked as a
statement.

178 Chapter 6 Functions
None function
Note
Technically, every function in Python returns a value whether you use return or not. If
a function does not return a value, by default, it returns a special value None. For this
reason, a function that does not return a value is also called a None function. The None
value can be assigned to a variable to indicate that the variable does not reference any
object. For example, if you run the following program:
def sum(number1, number2):
total = number1 + number2
print(sum(1, 2))
you will see the output is None, because the sum function does not have a return state-
ment. By default, it returns None.
Note
A return statement is not needed for a None function, but it can be used for ter-
minating the function and returning control to the function’s caller. The syntax is
simply
return
or
return None
This is rarely used, but it is sometimes useful for circumventing the normal flow of con-
trol in a function that does not return any value. For example, the following code has a
return statement to terminate the function when the score is invalid.
# Print grade for the score
def printGrade(score):
print(“Invalid score”)
# Same as return None
if score >= 90.0:
print(‘A’)
elif score >= 80.0:
print(‘B’)
elif score >= 70.0:
print(‘C’)
elif score >= 60.0:
print(‘D’)
else:
print(‘F’)
6.1 What are the benefits of using a function?
6.2 How do you define a function? How do you invoke a function?
6.3 Can you simplify the max function in Listing 6.1 by using a conditional
expression?
6.4 True or false? A call to a None function is always a statement itself, but a call to a
value-returning function is always a component of an expression.
6.5 Can you have a return statement in a None function? Does the return statement in
the following function cause syntax errors?
def xFunction(x, y):
print(x + y)
return
return
if score < 0 or score > 100:
✓Point✓Check
return in None function

6.5 Positional and Keyword Arguments 179
6.6 Define the terms function header, parameter, and argument.
6.7 Write function headers for the following functions (and indicate whether the function
returns a value):
■ Computing a sales commission, given the sales amount and the commission rate.
■ Printing the calendar for a month, given the month and year.
■ Computing a square root.
■ Testing whether a number is even, and returning true if it is.
■ Printing a message a specified number of times.
■ Computing the monthly payment, given the loan amount, number of years, and
annual interest rate.
■ Finding the corresponding uppercase letter, given a lowercase letter.
6.8 Identify and correct the errors in the following program:
1 def function1(n, m):
2 function2(3.4)
3
4 def function2(n):
5 if n > 0:
6 return 1
7 elif n == 0:
8 return 0
9 elif n < 0: 10 return –1 11 12 function1(2, 3) 6.9 Show the output of the following code: 1 def main(): 2 print(min(5, 6)) 3 4 def min(n1, n2): 5 smallest = n1 6 if n2 < smallest: 7 smallest = n2 8 9 main() # Call the main function 6.10 What error will occur when you run the following code? def main(): print(min(min(5, 6), (51, 6))) def min(n1, n2): smallest = n1 if n2 < smallest: smallest = n2 main() # Call the main function 6.5 Positional and Keyword Arguments A function’s arguments can be passed as positional arguments or keyword arguments. The power of a function is its ability to work with parameters. When calling a function, you need to pass arguments to parameters. There are two kinds of arguments: positional arguments and keyword arguments. Using positional arguments requires that the arguments be passed in positional arguments Key Point 180 Chapter 6 Functions the same order as their respective parameters in the function header. For example, the follow- ing function prints a message n times: def nPrintln(message, n): for i in range(n): print(message) You can use nPrintln('a', 3) to print a three times. The nPrintln('a', 3) statement passes a to message, passes 3 to n, and prints a three times. However, the state- ment nPrintln(3, 'a') has a different meaning. It passes 3 to message and a to n. When we call a function like this, it is said to use positional arguments. The arguments must match the parameters in order, number, and compatible type, as defined in the func- tion header. You can also call a function using keyword arguments, passing each argument in the form name value. For example, nPrintln(n = 5, message = "good") passes 5 to n and "good" to message. The arguments can appear in any order using keyword arguments. It is possible to mix positional arguments with keyword arguments, but the positional argu- ments cannot appear after any keyword arguments. Suppose a function header is def f(p1, p2, p3): You can invoke it by using f(30, p2 = 4, p3 = 10) However, it would be wrong to invoke it by using f(30, p2 = 4, 10) because the positional argument 10 appears after the keyword argument p2 = 4. 6.11 Compare positional arguments and keyword arguments. 6.12 Suppose a function header is as follows: def f(p1, p2, p3, p4): Which of the following calls are correct? f(1, p2 = 3, p3 = 4, p4 = 4) f(1, p2 = 3, 4, p4 = 4) f(p1 = 1, p2 = 3, 4, p4 = 4) f(p1 = 1, p2 = 3, p3 = 4, p4 = 4) f(p4 = 1, p2 = 3, p3 = 4, p1 = 4) 6.6 Passing Arguments by Reference Values When you invoke a function with arguments, each argument's reference is passed by value to the parameter in the function. Because all data are objects in Python, a variable for an object is actually a reference to the object. When you invoke a function with arguments, the reference value of each argument is passed to the parameter. This is referred to as pass-by-value in programming terminology. For simplicity, we say that the value of an argument is passed to a parameter when invoking a function. The value is actually a reference value to the object. = keyword arguments mixing keyword and positional arguments pass-by-value ✓Point✓Check Key Point 6.6 Passing Arguments by Reference Values 181 If the argument is a number or a string, the argument is not affected, regardless of the changes made to the parameter inside the function. Listing 6.4 gives an example. LISTING 6.4 Increment.py 1 def main(): 2 x = 1 3 print("Before the call, x is", x) 4 5 print("After the call, x is", x) 6 7 def increment(n): 8 9 print("\tn inside the function is", n) 10 11 main() # Call the main function n += 1 increment(x) invoke increment increment n Before the call, x is 1 n inside the function is 2 After the call, x is 1 As shown in the output for Listing 6.4, the value of x (1) is passed to the parameter n to invoke the increment function (line 4). The parameter n is incremented by 1 in the function (line 8), but x is not changed no matter what the function does. The reason is that numbers and strings are known as immutable objects. The contents of immutable objects cannot be changed. Whenever you assign a new number to a variable, Python creates a new object for the new number and assigns the reference of the new object to the variable. Consider the following code: immutable objects >>> x = 4
>>> y = x
>>> id(x) # The reference of x
505408920
>>> id(y) # The reference of y is the same as the reference of x
505408920
>>>
You assign x to y, and both x and y now point to the same object for integer value 4, as
shown in Figure 6.4a–b. But if you add 1 to y, a new object is created and assigned to y, as
shown in Figure 6.4c. Now y refers to a new object, as shown in the following code:
>>> y = y + 1 # y now points to a new int object with value 5
>>> id(y)
505408936
>>>

182 Chapter 6 Functions
6.13 What is pass-by-value?
6.14 Can the argument have the same name as its parameter?
6.15 Show the result of the following programs:
(a) (b) (c)
The object
for int 4
x
x = 4
id: 505408920
The object
for int 4
y = x
id: 505408920
x
y
y = y + 1
id: 505408920
x The object
for int 4
id: 505408936
y The object
for int 5
FIGURE 6.4 (a) 4 is assigned to x; (b) x is assigned to y; (c) y + 1 is assigned to y.
def main():
max = 0
getMax(1, 2, max)
print(max)
def getMax(value1, value2, max):
if value1 > value2:
max = value1
else:
max = value2
main()
def main():
i = 1
while i <= 6: print(function1(i, 2)) i += 1 def function1(i, num): line = "" for j in range(1, i): line += str(num) + " " num *= 2 return line main() (a) (b) def main(): # Initialize times times = 3 print("Before the call, variable", "times is", times) # Invoke nPrintln and display times nPrint("Welcome to CS!", times) print("After the call, variable", "times is", times) # Print the message n times def nPrint(message, n): while n > 0:
print(“n = “, n)
print(message)
n -= 1
main()
(c)
def main():
i = 0
while i <= 4: function1(i) i += 1 print("i is", i) def function1(i): line = " " while i >= 1:
if i % 3 != 0:
line += str(i) + ” ”
i -= 1
print(line)
main()
(d)
✓Point✓Check

6.7 Modularizing Code 183
6.16 For (a) in the preceding question, show the contents of the stack just before the func-
tion max is invoked, just as max is entered, just before max is returned, and right after
max is returned.
6.7 Modularizing Code
Modularizing makes code easy to maintain and debug, and enables the code to be
reused.
Functions can be used to reduce redundant code and enable code reuse. Functions can also
be used to modularize code and improve a program’s quality. In Python, you can place the
function definition into a file called module with the file-name extension .py. The module
can be later imported into a program for reuse. The module file should be placed in the
same directory with your other programs. A module can contain more than one function.
Each function in a module must have a different name. Note that the turtle, random, and
math are the modules defined in the Python library, and thus they can be imported into any
Python program.
Listing 5.8, GreatestCommonDivisor.py, shows a program that prompts the user to
enter two integers and displays their greatest common divisor. You can rewrite the pro-
gram to use a function and place it into a module named GCDFunction.py, as shown in
Listing 6.5.
LISTING 6.5 GCDFunction.py
1 # Return the gcd of two integers
2 :
3 gcd = 1 # Initial gcd is 1
4 k = 2 # Possible gcd
5
6 while k <= n1 and k <= n2: 7 if n1 % k == 0 and n2 % k == 0: 8 gcd = k # Update gcd 9 k += 1 10 11 # Return gcd Now we write a separate program to use the gcd function, as shown in Listing 6.6. LISTING 6.6 TestGCDFunction.py 1 # Import the gcd function 2 3 # Prompt the user to enter two integers 4 n1 = eval(input("Enter the first integer: ")) 5 n2 = eval(input("Enter the second integer: ")) 6 7 print("The greatest common divisor for", n1, 8 "and", n2, "is", )gcd(n1, n2) from GCDFunction import gcd return gcd def gcd(n1, n2) module Enter the first integer: Enter the second integer: The greatest common divisor for 45 and 75 is 15 75 45 define gcd function return gcd import gcd get input invoke gcd Key Point 184 Chapter 6 Functions Line 1 imports the gcd function from the GCDFunction module, which enables you to invoke gcd in this program (line 8). You can also import it using the following statement: import GCDFunction Using this statement, you would have to invoke gcd using GCDFunction.gcd. By encapsulating the code for obtaining the gcd in a function, this program has several advantages: 1. It isolates the problem for computing the gcd from the rest of the code in the program. Thus, the logic becomes clear and the program is easier to read. 2. Any errors for computing the gcd are confined to the gcd function, which narrows the scope of debugging. 3. The gcd function now can be reused by other programs. What happens if you define two functions with the same name in a module? There is no syntax error in this case, but the latter function definition prevails. Listing 6.7 applies the concept of code modularization to improve Listing 5.13, PrimeNumber.py. The program defines two new functions, isPrime and printPrimeNumbers. The isPrime function determines whether a number is prime, and the printPrimeNumbers function prints prime numbers. LISTING 6.7 PrimeNumberFunction.py 1 # Check whether number is prime 2 def isPrime(number): 3 divisor = 2 4 while divisor <= number / 2: 5 if number % divisor == 0: 6 # If true, number is not prime 7 return False # number is not a prime 8 divisor += 1 9 10 return True # number is prime 11 12 def printPrimeNumbers(numberOfPrimes): 13 NUMBER_OF_PRIMES = 50 # Number of primes to display 14 NUMBER_OF_PRIMES_PER_LINE = 10 # Display 10 per line 15 count = 0 # Count the number of prime numbers 16 number = 2 # A number to be tested for primeness 17 18 # Repeatedly find prime numbers 19 while count < numberOfPrimes: 20 # Print the prime number and increase the count 21 if : 22 count += 1 # Increase the count 23 24 print(number, end = " ") 25 if count % NUMBER_OF_PRIMES_PER_LINE == 0: 26 # Print the number and advance to the new line 27 print() 28 29 # Check if the next number is prime 30 number += 1 31 32 def main(): 33 print("The first 50 prime numbers are") isPrime(number) import from module isPrime function printPrimeNumbers function invoke isPrime 6.8 Case Study: Converting Decimals to Hexadecimals 185 34 35 36 main() # Call the main function printPrimeNumbers(50) invoke printPrimeNumbers The first 50 prime numbers are 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 This program divides a large problem into two subproblems. As a result, the new program is easier to read and easier to debug. Moreover, the functions printPrimeNumbers and isPrime can be reused by other programs. 6.8 Case Study: Converting Decimals to Hexadecimals This section presents a program that converts a decimal number to a hexadecimal number. Hexadecimal numbers (introduced in Chapter 3) are often used in computer systems pro- gramming (see Appendix C for information on number systems). To convert a decimal number d to a hexadecimal number, you have to find the hexadecimal digits and such that These hexadecimal digits can be found by successively dividing d by 16 until the quotient is 0. The remainders are and The hexadecimal digits include the decimal digits 0,1,2,3,4,5,6,7,8,9 plus A which is the decimal value 10, B which is the decimal value 11, C which is 12, D which is 13, E which is 14, and F which is 15. For example, the decimal number 123 is 7B in hexadecimal. The conversion is done as shown below: hn.h0, h1, h2, c , hn-2, hn-1, + h2 * 162 + h1 * 161 + h0 * 160 d = hn * 16n + hn-1 * 16n-1 + hn-2 * 16n-2 + c h0hn, hn-1, hn-2, c, h2, h1, Remainder h0 Quotient 16 123 112 11 7 h1 16 7 0 7 0 The remainder of dividing 123 by 16 is 11, which is B in hexadecimal. The quotient of this division is 7. The remainder of dividing 7 by 16 is 7 and the quotient is 0. So, 7B is the hexa- decimal number for 123. The program in Listing 6.8 prompts the user to enter a decimal number and converts it into a hex number as a string. LISTING 6.8 Decimal2HexConversion.py 1 # Convert a decimal to a hex as a string 2 def decimalToHex(decimalValue): define decimalToHex Key Point 186 Chapter 6 Functions define toHexChar get a letter input decimal Enter a decimal number: The hex number for decimal 1234 is 4D2 1234 The hex string is initially empty (line 3). The program uses the decimalToHex function (lines 2–10) to convert a decimal integer to a hex number as a string. The function gets the remainder of the division of the decimal integer by 16 (line 6). The remainder is converted into a character by invoking the toHexChar function and then appending to the hex string (line 7). Dividing the decimal number by 16 removes a hex digit from the number (line 8). The function repeatedly performs these operations in a loop until the quotient becomes 0 (lines 5–8). The toHexChar function (lines 13–17) converts a hexValue between 0 and 15 into a hex character. If hexValue is between 0 and 9, it is converted to chr(hexValue + ord('0')) (line 15). For example, if hexValue is 5, chr(hexValue + ord('0')) returns 5. Similarly, if line# decimalValue hex hexValue toHexChar(hexValue) 21 1234 3 "" 6 2 iteration 1 7 "2" "2" 8 77 6 13 iteration 2 7 "D2" "D" 8 4 6 4 iteration 3 7 "4D2" "4" 8 0 3 hex = " " 4 5 while decimalValue != 0: 6 hexValue = decimalValue % 16 7 hex = + hex 8 decimalValue = decimalValue // 16 9 10 return hex 11 12 # Convert an integer to a single hex digit as a character 13 14 if 0 <= hexValue <= 9: 15 return 16 else: # 10 <= hexValue <= 15 17 return 18 19 def main(): 20 # Prompt the user to enter a decimal integer 21 decimalValue = eval(input("Enter a decimal number: ")) 22 23 print("The hex number for decimal", 24 decimalValue, "is", ) 25 26 main() # Call the main function decimalToHex(decimalValue) chr(hexValue - 10 + ord('A')) chr(hexValue + ord('0')) def toHexChar(hexValue): toHexChar(hexValue) 6.9 The Scope of Variables 187 hexValue is between 10 and 15, it is converted to chr(hexValue - 10 + ord('A')) (line 17). For example, if hexValue is 11, chr(hexValue - 10 + ord('A')) returns B. 6.9 The Scope of Variables The scope of a variable is the part of the program where the variable can be referenced. Chapter 2 introduced the scope of variables. This section discusses the scope of variables in the context of functions. A variable created inside a function is referred to as a local variable. Local variables can only be accessed within a function. The scope of a local variable starts from its creation and continues to the end of the function that contains the variable. In Python, you can also use global variables. They are created outside all functions and are accessible to all functions in their scope. Consider the following examples. Example 1 1 2 def f1(): 3 4 print(globalVar) 5 print(localVar) 6 7 f1() 8 print(globalVar) 9 print(localVar) # Out of scope, so this gives an error A global variable is created in line 1. It is accessed within the function in line 4 and outside the function in line 8. A local variable is created in line 3. It is accessed within the function in line 5. Attempting to access the variable from outside of the function causes an error in line 9. Example 2 1 2 def f1(): 3 4 print(x) # Displays 2 5 6 f1() 7 print(x) # Displays 1 Here a global variable x is created in line 1 and a local variable with the same name (x) is created in line 3. From this point on, the global variable x is not accessible in the function. Outside the function, the global variable x is still accessible. So, it prints 1 in line 7. Example 3 1 x = eval(input("Enter a number: ")) 2 if x > 0:
3
4
5 # This gives an error if y is not created
Here the variable y is created if x > 0. If you enter a positive value for x (line 1), the program
runs fine. But if you enter a nonpositive value, line 5 produces an error because y is not created.
Example 4
1 sum = 0
2 for i in range(5):
print(y)
y = 4
x = 2
x = 1
localVar = 2
globalVar = 1
scope of a variable
local variable
global variable
create a global variable
create a local variable
create a global variable
create a local variable
create a variable
Key
Point
variable i created

188 Chapter 6 Functions
3 sum += i
4
5 print(i)
Here the variable i is created in the loop. After the loop is finished, i is 4, so line 5
displays 4.
You can bind a local variable in the global scope. You can also create a variable in a func-
tion and use it outside the function. To do either, use a global statement, as shown in the
following example.
Example 5
1 x = 1
2 def increase():
3
4 x = x + 1
5 print(x) # Displays 2
6
7 increase()
8 print(x) # Displays 2
Here a global variable x is created in line 1 and x is bound in the function in line 3, which
means that x in the function is the same as x outside of the function, so the program prints 2
in line 5 and in line 8.
Caution
Although global variables are allowed and you may see global variables used in other
programs, it is not a good practice to allow them to be modified in a function, because
doing so can make programs prone to errors. However, it is fine to define global con-
stants so all functions in the module can share them.
6.17 What is the printout of the following code?
global x
global statement
global variable x
binding global variable
def function(x):
print(x)
x = 4.5
y = 3.4
print(y)
x = 2
y = 4
function(x)
print(x)
print(y)
def f(x, y = 1, z = 2):
return x + y + z
print(f(1, 1, 1))
print(f(y = 1, x = 2, z = 3))
print(f(1, z = 3))
(a) (b)
✓Point✓Check
6.18 What is wrong in the following code?
1 def function():
2 x = 4.5
3 y = 3.4
4 print(x)
5 print(y)
6
7 function()

6.10 Default Arguments 189
8 print(x)
9 print(y)
6.19 Can the following code run? If so, what is the printout?
x = 10
if x < 0: y = -1 else: y = 1 print("y is", y) 6.10 Default Arguments Python allows you to define functions with default argument values. The default values are passed to the parameters when a function is invoked without the arguments. Listing 6.9 demonstrates how to define functions with default argument values and how to invoke such functions. LISTING 6.9 DefaultArgumentDemo.py 1 def printArea( ): 2 area = width * height 3 print("width:", width, "\theight:", height, "\tarea:", area) 4 5 # Default arguments width = 1 and height = 2 6 # Positional arguments width = 4 and height = 2.5 7 # Keyword arguments width 8 # Default height = 2 9 # Default width = 1printArea(height = 6.2) printArea(width = 1.2) printArea(height = 5, width = 3) printArea(4, 2.5) printArea() width = 1, height = 2 default argument default argument default arguments positional arguments keyword arguments mixed arguments mixed arguments width: 1 height: 2 area: 2 width: 4 height: 2.5 area: 10.0 width: 3 height: 5 area: 15 width: 1.2 height: 2 area: 2.4 width: 1 height: 6.2 area: 6.2 Line 1 defines the printArea function with the parameters width and height. width has the default value 1 and height has the default value 2. Line 5 invokes the function with- out passing an argument, so the program uses the default value 1 assigned to width and 2 to height. Line 6 invokes the function by passing 4 to width and 2.5 to height. Line 7 invokes the function by passing 3 to width and 5 to height. Note that you can also pass the argument by specifying the parameter name, as shown in lines 8 and 9. Note A function may mix parameters with default arguments and non-default arguments. In this case, the non-default parameters must be defined before default parameters. Note Many programming languages support a useful feature that allows you to define two functions with the same name in a module, but it is not supported in Python. With default arguments, you can define a function once, and call the function in many Key Point 190 Chapter 6 Functions return multiple values receiving returned values n1 is 2 n2 is 3 The sort function returns two values. When it is invoked, you need to pass the returned values in a simultaneous assignment. 6.23 Can a function return multiple values? Show the printout of the following code: 1 def f(x, y): 2 return x + y, x - y, x * y, x / y 3 4 t1, t2, t3, t4 = f(9, 5) 5 print(t1, t2, t3, t4) different ways. This achieves the same effect as defining multiple functions with the same name in other programming languages. If you define multiple functions in Python, the later definition replaces the previous definitions. 6.20 Show the printout of the following code: def f(w = 1, h = 2): print(w, h) f() f(w = 5) f(h = 24) f(4, 5) 6.21 Identify and correct the errors in the following program: 1 def main(): 2 nPrintln(5) 3 4 def nPrintln(message = "Welcome to Python!", n): 5 for i in range(n): 6 print(message) 7 8 main() # Call the main function 6.22 What happens if you define two functions in a module that have the same name? 6.11 Returning Multiple Values The Python return statement can return multiple values. Python allows a function to return multiple values. Listing 6.10 defines a function that takes two numbers and returns them in ascending order. LISTING 6.10 MultipleReturnValueDemo.py 1 def sort(number1, number2): 2 if number1 < number2: 3 4 else: 5 6 7 n1, n2 = 8 print("n1 is", n1) 9 print("n2 is", n2) sort(3, 2) return number2, number1 return number1, number2 ✓Point✓Check Key Point ✓Point✓Check 6.12 Case Study: Generating Random ASCII Characters 191 6.12 Case Study: Generating Random ASCII Characters A character is coded using an integer. Generating a random character is to generate an integer. Computer programs process numeric data and characters. You have seen many examples involving numeric data. It is also important to understand characters and how to process them. This section gives an example of generating random ASCII characters. As introduced in Section 3.3, every ASCII character has a unique ASCII code between 0 and 127. To generate a random ASCII character, first generate a random integer between 0 and 127, and then use the chr function to obtain the character from the integer using the fol- lowing code: chr(randint(0, 127)) Let’s consider how to generate a random lowercase letter. The ASCII codes for lowercase let- ters are consecutive integers starting with the code for a, then for b, c, ..., and z. The code for a is ord('a') So a random integer between ord('a') and ord('z') is randint(ord('a'), ord('z')) Therefore, a random lowercase letter is chr(randint(ord('a'), ord('z'))) Thus, a random character between any two characters ch1 and ch2 with ch1 < ch2 can be generated as follows: chr(randint(ord(ch1), ord(ch2))) This is a simple but useful discovery. In Listing 6.11 we create a module named RandomCharacter.py with five functions that randomly generate specific types of charac- ters. You can use these functions in your future projects. LISTING 6.11 RandomCharacter.py 1 from random import randint # import randint 2 3 # Generate a random character between ch1 and ch2 4 : 5 return 6 7 # Generate a random lowercase letter 8 : 9 return getRandomCharacter('a', 'z') 10 11 # Generate a random uppercase letter 12 : 13 return getRandomCharacter('A', 'Z') 14 15 # Generate a random digit character 16 : 17 return getRandomCharacter('0', '9') 18 19 # Generate a random character 20 : 21 return chr(randint(0, 127)) def getRandomASCIICharacter() def getRandomDigitCharacter() def getRandomUpperCaseLetter() def getRandomLowerCaseLetter() chr(randint(ord(ch1), ord(ch2))) def getRandomCharacter(ch1, ch2) Key Point 192 Chapter 6 Functions Listing 6.12 is a test program that displays 175 random lowercase letters. LISTING 6.12 TestRandomCharacter.py 1 2 3 NUMBER_OF_CHARS = 175 # Number of characters to generate 4 CHARS_PER_LINE = 25 # Number of characters to display per line 5 6 # Print random characters between 'a' and 'z', 25 chars per line 7 for i in range(NUMBER_OF_CHARS): 8 print( , end = " ") 9 if (i + 1) % CHARS_PER_LINE == 0: 10 print() # Jump to the new line RandomCharacter.getRandomLowerCaseLetter() import RandomCharacter constants lowercase letter gmjsohezfkgtazqgmswfclrao pnrunulnwmaztlfjedmpchcif lalqdgivxkxpbzulrmqmbhikr lbnrjlsopfxahssqhwuuljvbe xbhdotzhpehbqmuwsfktwsoli cbuwkzgxpmtzihgatdslvbwbz bfesoklwbhnooygiigzdxuqni Line 1 imports the RandomCharacter module, because the program invokes the function defined in this module. Invoking getRandomLowerCaseLetter() returns a lowercase letter (line 8). Note that the function getRandomLowerCaseLetter() does not have any parameters, but you still have to use the parentheses when defining and invoking it. 6.24 Write an expression that returns a random integer between 34 and 55, inclusively. 6.25 Write an expression that returns a random character between B and M, inclusively. 6.26 Write an expression that returns a random number between 6.5 and 56.5 (excluding 56.5). 6.27 Write an expression that returns a random lowercase letter. 6.13 Function Abstraction and Stepwise Refinement Function abstraction is achieved by separating the use of a function from its implementation. The key to developing software is to apply the concept of abstraction. You will learn many levels of abstraction from this book. Function abstraction separates the use of a function from its implementation. A client program, called simply the client, can use a function without knowing how it is implemented. The details of the implementation are encapsulated in the function and hidden from the client that invokes the function. This is known as information hiding or encapsulation. If you decide to change the implementation, the client program will not be affected, provided that you do not change the function header. The implementation of the function is hidden from the client in a “black box,” as shown in Figure 6.5. You have already used many of Python’s built-in functions; you used these in client pro- grams. You know how to write the code to invoke these functions in your program, but as a user of these functions, you are not required to know how they are implemented. The concept of function abstraction can be applied to the process of developing programs. When writing a large program, you can use the “divide-and-conquer” strategy, also known as parentheses required function abstraction information hiding divide and conquer ✓Point✓Check Key Point Divide and conquer VideoNote 6.13 Function Abstraction and Stepwise Refinement 193 Function Header Black box Optional arguments for input Optional return value Function Body FIGURE 6.5 The function body can be thought of as a black box that contains the detailed implementation of the function. stepwise refinement, to break down the problem into subproblems. The subproblems can be further divided into smaller, more manageable ones. Suppose you write a program that displays the calendar for a given month of the year. The program prompts the user to enter the year and the month, and then it displays the entire cal- endar for the month, as shown in the following sample run: Enter full year (e.g., 2001): Enter month as number between 1 and 12: September 2011 ————————————————————————————————- Sun Mon Tue Wed Thu Fri Sat 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 9 2011 Let’s use this example to demonstrate the divide-and-conquer approach. 6.13.1 Top-Down Design How would you get started writing such a program? Would you immediately start coding? Beginning programmers often start by trying to work out the solution to every detail. Although details are important in the final program, concern for detail in the early stages may block the problem-solving process. To make problem solving flow as smoothly as possible, this example begins by using function abstraction to isolate details from design and only later implements the details. For this example, the problem is first broken into two subproblems: (1) get input from the user and (2) print the calendar for the month. At this stage, you should be concerned with what the subproblems will achieve, not with how to get input and print the calendar for the month. You can draw a structure chart to help visualize the decomposition of the problem (see Figure 6.6a). You can use the input function to read input for the year and the month. The problem of printing the calendar for a given month can be broken into two subproblems: (1) print the month title and (2) print the month body, as shown in Figure 6.6b. The month title consists of three lines: month and year, a dashed line, and the names of the seven days of the week. You need to get the month name (e.g., January) from the numeric month (e.g., 1). This is accom- plished in getMonthName (see Figure 6.7a). stepwise refinement 194 Chapter 6 Functions In order to print the month body, you need to know which day of the week is the first day of the month (getStartDay) and how many days the month has (getNumberOfDaysInMonth), as shown in Figure 6.7b. For example, December 2005 has 31 days, and December 1, 2005, is a Thursday. How would you get the start day for the first date in a month? There are several ways to do so. Assume you know that the start day for January 1, 1800, was Wednesday (START_DAY_FOR_JAN_1_1800 = 3). You could compute the total number of days (totalNumberOfDays) between January 1, 1800, and the first date of the calendar month. The start day for the calendar month is (totalNumberOfDays + startDay1800) % 7, since every week has seven days. Thus, the getStartDay problem can be further refined as getTotalNumberOfDays, as shown in Figure 6.8a. printCalendar (main) (a) (b) printMonthBodyprintMonthTitlereadInput printMonth printMonth FIGURE 6.6 The structure chart shows that the printCalendar problem is divided into two subproblems, readInput and printMonth, and that printMonth is divided into two smaller subproblems, printMonthTitle and printMonthBody. To get the total number of days, you need to know whether the year is a leap year and the number of days in each month. Therefore, getTotalNumberOfDays needs to be further refined into two subproblems: isLeapYear and getNumberOfDaysInMonth, as shown in Figure 6.8b. The complete structure chart is shown in Figure 6.9. (b)(a) getNumberOfDaysInMonthgetStartDaygetMonthName printMonthTitle printMonthBody FIGURE 6.7 (a) To printMonthTitle, you need getMonthName. (b) The printMonthBody problem is refined into several smaller problems. getTotalNumberOfDays getStartDay isLeapYear (a) (b) getNumberOfDaysInMonth getTotalNumberOfDays FIGURE 6.8 (a) To getStartDay, you need getTotalNumberOfDays. (b) The getTotalNumberOfDays problem is refined into two smaller problems. 6.13 Function Abstraction and Stepwise Refinement 195 6.13.2 Top-Down and/or Bottom-Up Implementation Now let’s turn our attention to implementation. In general, a subproblem corresponds to a function in the implementation, although some are so simple that this is unnecessary. You need to decide which modules to implement as functions and which to combine in other functions. Decisions of this kind should be based on the way that the overall program will be easier to read. In this example, the subproblem readInput can be simply implemented in the main function. You can use either a “top-down” or a “bottom-up” approach. The top-down approach implements one function in the structure chart at a time from the top to the bottom. A stub, which is a simple but incomplete version of a function, can be used for the functions waiting to be implemented. Stubs enable you to build the framework of a program quickly. Implement the main function first, then use a stub for the printMonth function. For example, let printMonth display the year and the month in the stub. Thus, your program may begin like this: # A stub for printMonth may look like this : print(year, month) # A stub for printMonthTitle may look like this : print("printMonthTitle") # A stub for getMonthBody may look like this : print("getMonthBody") # A stub for getMonthName may look like this : print("getMonthName") def getMonthName(month) def getMonthBody(year, month) def printMonthTitle(year, month) def printMonth(year, month) printCalendar (main) getTotalNumberOfDays getNumberOfDaysInMonth isLeapYear printMonthreadInput printMonthTitle getMonthName printMonthBody getStartDay FIGURE 6.9 The structure chart shows the hierarchical relationship of the subproblems in the program. top-down approach stub 196 Chapter 6 Functions # A stub for getStartDay may look like this : print("getStartDay") # A stub for getTotalNumberOfDays may look like this : print("getTotalNumberOfDays") # A stub for getNumberOfDaysInMonth may look like this : print("getNumberOfDaysInMonth") # A stub for isLeapYear may look like this : print("isLeapYear") def main(): # Prompt the user to enter year and month year = eval(input("Enter full year (e.g., 2001): ")) month = eval(input(( "Enter month as number between 1 and 12: "))) # Print calendar for the month of the year main() # Call the main function Run and test the program, and fix any errors. You can now implement the printMonth function. For functions invoked from the printMonth function, you can again use stubs. The bottom-up approach implements one function in the structure chart at a time from the bot- tom to the top. For each function implemented, write a test program, known as the driver, to test it. The top-down and bottom-up approaches are both fine. Both approaches implement func- tions incrementally, help to isolate programming errors, and make debugging easy. They can be used together. 6.13.3 Implementation Details The isLeapYear(year) function can be implemented using the following code (see Section 4.12): return year % 400 == 0 or (year % 4 == 0 and year % 100 != 0) Use the following facts to implement getTotalNumberOfDaysInMonth(year, month): ■ January, March, May, July, August, October, and December have 31 days. ■ April, June, September, and November have 30 days. ■ February has 28 days during a regular year and 29 days during a leap year. A regular year, therefore, has 365 days, and a leap year has 366 days. To implement getTotalNumberOfDays(year, month), you need to compute the total number of days (totalNumberOfDays) between January 1, 1800, and the first day of the calendar month. You could find the total number of days between the year 1800 and the cal- endar year and then figure out the total number of days prior to the calendar month in the cal- endar year. The sum of these two totals is totalNumberOfDays. To print the calendar’s body, first pad some space before the start day and then print the lines for every week. The complete program is given in Listing 6.13. printMonth(year, month) def isLeapYear(year) def getNumberOfDaysInMonth(year, month) def getTotalNumberOfDays(year, month) def getStartDay(year, month) bottom-up approach driver 6.13 Function Abstraction and Stepwise Refinement 197 LISTING 6.13 PrintCalendar.py 1 # Print the calendar for a month in a year 2 3 # Print the headings of the calendar 4 5 6 # Print the body of the calendar 7 8 9 # Print the month title, e.g., May 1999 10 11 print(" ", getMonthName(month), " ", year) 12 print("——————————————————————————————————————————") 13 print(" Sun Mon Tue Wed Thu Fri Sat") 14 15 # Print month body 16 17 # Get start day of the week for the first date in the month 18 startDay = getStartDay(year, month) 19 20 # Get number of days in the month 21 numberOfDaysInMonth = getNumberOfDaysInMonth(year, month) 22 23 # Pad space before the first day of the month 24 i = 0 25 for i in range(0, startDay): 26 print(" ", end = " ") 27 28 for i in range(1, numberOfDaysInMonth + 1): 29 print(format(i, "4d"), end = " ") 30 31 if (i + startDay) % 7 == 0: 32 print() # Jump to the new line 33 34 # Get the English name for the month 35 36 if month == 1: 37 monthName = "January" 38 elif month == 2: 39 monthName = "February" 40 elif month == 3: 41 monthName = "March" 42 elif month == 4: 43 monthName = "April" 44 elif month == 5: 45 monthName = "May" 46 elif month == 6: 47 monthName = "June" 48 elif month == 7: 49 monthName = "July" 50 elif month == 8: 51 monthName = "August" 52 elif month == 9: 53 monthName = "September" 54 elif month == 10: 55 monthName = "October" 56 elif month == 11: 57 monthName = "November" def getMonthName(month): def printMonthBody(year, month): def printMonthTitle(year, month): printMonthBody(year, month) printMonthTitle(year, month) def printMonth(year, month): printMonth printMonthTitle printMonthBody getMonthName 198 Chapter 6 Functions 58 else: 59 monthName = "December" 60 61 return monthName 62 63 # Get the start day of month/1/year 64 65 START_DAY_FOR_JAN_1_1800 = 3 66 67 # Get total number of days from 1/1/1800 to month/1/year 68 totalNumberOfDays = getTotalNumberOfDays(year, month) 69 70 # Return the start day for month/1/year 71 return (totalNumberOfDays + START_DAY_FOR_JAN_1_1800) % 7 72 73 # Get the total number of days since January 1, 1800 74 75 total = 0 76 77 # Get the total days from 1800 to 1/1/year 78 for i in range(1800, year): 79 if isLeapYear(i): 80 total = total + 366 81 else: 82 total = total + 365 83 84 # Add days from Jan to the month prior to the calendar month 85 for i in range(1, month): 86 total = total + getNumberOfDaysInMonth(year, i) 87 88 return total 89 90 # Get the number of days in a month 91 92 if (month == 1 or month == 3 or month == 5 or month == 7 or 93 month == 8 or month == 10 or month == 12): 94 return 31 95 96 if month == 4 or month == 6 or month == 9 or month == 11: 97 return 30 98 99 if month == 2: 100 return 29 if isLeapYear(year) else 28 101 102 return 0 # If month is incorrect 103 104 # Determine if it is a leap year 105 106 return year % 400 == 0 or (year % 4 == 0 and year % 100 != 0) 107 108 def main(): 109 # Prompt the user to enter year and month 110 year = eval(input("Enter full year (e.g., 2001): ")) 111 month = eval(input(("Enter month as number between 1 and 12: "))) 112 113 # Print calendar for the month of the year 114 printMonth(year, month) 115 116 main() # Call the main function def isLeapYear(year): def getNumberOfDaysInMonth(year, month): def getTotalNumberOfDays(year, month): def getStartDay(year, month):getStartDay getTotalNumberOfDays getNumberOfDaysInMonth isLeapYear 6.14 Case Study: Reusable Graphics Functions 199 This program does not validate user input. For instance, if the user enters either a month not in the range between 1 and 12 or a year before 1800, the program displays an erroneous calendar. To avoid this error, add an if statement to check the input before printing the calendar. This program prints calendars for a month but could easily be modified to print calendars for a whole year. Although it can print months only after January 1800, it could be modified to print months before 1800. 6.13.4 Benefits of Stepwise Refinement Stepwise refinement breaks a large problem into smaller manageable subproblems. Each sub- problem can be implemented using a function. This approach makes the program easier to write, reuse, debug, test, modify, and maintain. Simpler Program The print calendar program is long. Rather than writing a long sequence of statements in one function, stepwise refinement breaks it into smaller functions. This simplifies the program and makes the whole program easier to read and understand. Reusing Functions Stepwise refinement promotes code reuse within a program. The isLeapYear function is defined once and invoked from the getTotalNumberOfDays and getNumberOfDasInMonth functions. This reduces redundant code. Easier Developing, Debugging, and Testing Since each subproblem is solved in a function, a function can be developed, debugged, and tested individually. This isolates the errors and makes developing, debugging, and testing easier. When implementing a large program, use the top-down and/or bottom-up approach. Do not write the entire program at once. Using these approaches seems to take more development time (because you repeatedly run the program), but it actually saves time and makes debug- ging easier. Better Facilitating Teamwork Since a large problem is divided into subprograms, the subproblems can be assigned to pro- grammers. This makes it easier for programmers to work in teams. 6.14 Case Study: Reusable Graphics Functions You can develop reusable functions to simplify coding in the turtle module. Often you need to draw a line between two points, display text or a small point at a speci- fied location, depict a circle with a specified center and radius, or create a rectangle with a specified center, width, and height. It would greatly simplify programming if these func- tions were available for reuse. Listing 6.14 defines these functions in a module named UsefulTurtleFunctions. LISTING 6.14 UsefulTurtleFunctions.py 1 import turtle 2 3 # Draw a line from (x1, y1) to (x2, y2) 4 5 turtle.penup() def drawLine(x1, y1, x2, y2): incremental development and testing import turtle function drawLine Key Point 200 Chapter 6 Functions 6 turtle.goto(x1, y1) 7 turtle.pendown() 8 turtle.goto(x2, y2) 9 10 # Write a string s at the specified location (x, y) 11 12 turtle.penup() # Pull the pen up 13 turtle.goto(x, y) 14 turtle.pendown() # Pull the pen down 15 turtle.write(s) # Write a string 16 17 # Draw a point at the specified location (x, y) 18 19 turtle.penup() # Pull the pen up 20 turtle.goto(x, y) 21 turtle.pendown() # Pull the pen down 22 turtle.begin_fill() # Begin to fill color in a shape 23 turtle.circle(3) 24 turtle.end_fill() # Fill the shape 25 26 # Draw a circle centered at (x, y) with the specified radius 27 28 turtle.penup() # Pull the pen up 29 turtle.goto(x, y - radius) 30 turtle.pendown() # Pull the pen down 31 turtle.circle(radius) 32 33 # Draw a rectangle at (x, y) with the specified width and height 34 35 turtle.penup() # Pull the pen up 36 turtle.goto(x + width / 2, y + height / 2) 37 turtle.pendown() # Pull the pen down 38 turtle.right(90) 39 turtle.forward(height) 40 turtle.right(90) 41 turtle.forward(width) 42 turtle.right(90) 43 turtle.forward(height) 44 turtle.right(90) 45 turtle.forward(width) Now that you have written this code, you can use these functions to draw shapes. Listing 6.15 gives a test program to use these functions from the UsefulTurtleFunctions module to draw a line, write some text, and create a point, a circle, and a rectangle, as shown in Figure 6.10. LISTING 6.15 UseCustomTurtleFunctions.py 1 import turtle 2 from UsefulTurtleFunctions import * 3 4 # Draw a line from (-50, -50) to (50, 50) 5 drawLine(-50, -50, 50, 50) 6 7 # Write text at (-50, -60) 8 writeText("Testing useful Turtle functions", -50, -60) 9 10 # Draw a point at (0, 0) 11 drawPoint(0, 0) 12 13 # Draw a circle at (0, 0) with radius 80 def drawRectangle(x = 0, y = 0, width = 10, height = 10): def drawCircle(x = 0, y = 0, radius = 10): def drawPoint(x, y): def writeText(s, x, y): draw a line function writeText write string function drawPoint draw a tiny circle function drawCircle draw a circle function drawRectangle import turtle import UsefulTurtleFunctions draw a line write text string draw a point Chapter Summary 201 14 drawCircle(0, 0, 80) 15 16 # Draw a rectangle at (0, 0) with width 60 and height 40 17 drawRectangle(0, 0, 60, 40) 18 19 turtle.hideturtle() 20 turtle.done() FIGURE 6.10 The program draws shapes using the custom functions. The asterisk (*) in line 2 imports all functions from the UsefulTurtleFunctions mod- ule into the program. Line 5 invokes the drawLine function to draw a line, and line 8 invokes the writeText function to write a text string. The drawPoint function (line 11) draws a point, and the drawCircle function (line 14) draws a circle. Line 17 invokes the drawRectangle function to draw a rectangle. KEY TERMS actual parameter 173 argument 173 caller 173 default argument 189 divide and conquer 192 formal parameters (i.e., parameter) 173 functions 172 function abstraction 192 function header 173 global variable 187 immutable objects 181 information hiding 192 keyword arguments 180 local variable 187 None function 178 parameters 173 pass-by-value 180 positional arguments 179 return value 173 scope of a variable 187 stepwise refinement 193 stub 195 CHAPTER SUMMARY 1. Making programs modular and reusable is one of the central goals in software engi- neering. Functions can help to achieve this goal. 2. A function header begins with the def keyword followed by function’s name and parameters, and ends with a colon. 3. Parameters are optional; that is, a function does not have to contain any parameters. draw a circle draw a rectangle pause 202 Chapter 6 Functions 4. A function is called a void or None function if it does not return a value. 5. A return statement can also be used in a void function for terminating the function and returning to the function’s caller. This is useful occasionally for circumventing the normal flow of control in a function. 6. The arguments that are passed to a function should have the same number, type, and order as the parameters in the function header. 7. When a program calls a function, program control is transferred to the called func- tion. A called function returns control to the caller when its return statement is exe- cuted or when the last statement in the function is executed. 8. A value-returning function can also be invoked as a statement in Python. In this case, the function’s return value is ignored. 9. A function’s arguments can be passed as positional arguments or keyword arguments. 10. When you invoke a function with a parameter, the reference value of the argument is passed to the parameter. This is referred to as pass-by-value in programming terminology. 11. A variable created in a function is called a local variable. The scope of a local vari- able starts from its creation and exists until the function returns. A variable must be created before it is used. 12. Global variables are created outside all functions and are accessible to all functions in their scope. 13. Python allows you to define functions with default argument values. The default val- ues are passed to the parameters when a function is invoked without the arguments. 14. The Python return statement can return multiple values. 15. Function abstraction is achieved by separating the use of a function from its imple- mentation. The client can use a function without knowing how it is implemented. The details of the implementation are encapsulated in the function and hidden from the client that invokes the function. This is known as information hiding or encapsulation. 16. Function abstraction modularizes programs in a neat, hierarchical manner. Programs written as collections of concise functions are easier to write, debug, maintain, and modify than would otherwise be the case. This writing style also promotes function reusability. 17. When implementing a large program, use the top-down and/or bottom-up coding approach. Do not write the entire program at once. This approach may seem to take more time for coding (because you are repeatedly running the program), but it actu- ally saves time and makes debugging easier. TEST QUESTIONS Do test questions for this chapter online at www.cs.armstrong.edu/liang/py/test.html. www.cs.armstrong.edu/liang/py/test.html Programming Exercises 203 PROGRAMMING EXERCISES Sections 6.2–6.9 6.1 (Math: pentagonal numbers) A pentagonal number is defined as for and so on. So, the first few numbers are 1, 5, 12, 22, .... Write a function with the following header that returns a pentagonal number: def getPentagonalNumber(n): Write a test program that uses this function to display the first 100 pentagonal numbers with 10 numbers on each line. *6.2 (Sum the digits in an integer) Write a function that computes the sum of the digits in an integer. Use the following function header: def sumDigits(n): For example, sumDigits(234) returns 9 (Hint: Use the % operator to extract digits, and the // operator to remove the extracted digit. For instance, to extract 4 from 234, use 234 % 10 To remove 4 from 234, use 234 // 10 Use a loop to repeatedly extract and remove the digits until all the digits are extracted.) Write a test program that prompts the user to enter an integer and displays the sum of all its digits. **6.3 (Palindrome integer) Write the functions with the following headers: # Return the reversal of an integer, e.g. reverse(456) returns # 654 def reverse(number): # Return true if number is a palindrome def isPalindrome(number): Use the reverse function to implement isPalindrome. A number is a palin- drome if its reversal is the same as itself. Write a test program that prompts the user to enter an integer and reports whether the integer is a palindrome. *6.4 (Display an integer reversed) Write the following function to display an integer in reverse order: def reverse(number): For example, reverse(3456) displays 6543. Write a test program that prompts the user to enter an integer and displays its reversal. *6.5 (Sort three numbers) Write the following function to display three numbers in increasing order: def displaySortedNumbers(num1, num2, num3): Write a test program that prompts the user to enter three numbers and invokes the function to display them in increasing order. Here are some sample runs: (= 23). (= 4). (2 + 3 + 4). n = 1, 2, c , n(3n - 1)/2 Enter three numbers: The sorted numbers are 2.4 3 5 3, 2.4, 5 204 Chapter 6 Functions 6.8 (Conversions between Celsius and Fahrenheit) Write a module that contains the following two functions: # Converts from Celsius to Fahrenheit def celsiusToFahrenheit(celsius): # Converts from Fahrenheit to Celsius def fahrenheitToCelsius(fahrenheit): The formulas for the conversion are: celsius = (5 / 9) * (fahrenheit – 32) fahrenheit = (9 / 5) * celsius + 32 The amount invested: Annual interest rate: Years Future Value 1 1093.80 2 1196.41 ... 29 13467.25 30 14730.57 9 1000 Enter three numbers: The sorted numbers are 12.4 15 31 31, 12.4, 15 *6.6 (Display patterns) Write a function to display a pattern as follows: 1 2 1 3 2 1 ... n n-1 ... 3 2 1 The function header is def displayPattern(n): Write a test program that prompts the user to enter a number n and invokes displayPattern(n) to display the pattern. *6.7 (Financial application: compute the future investment value) Write a function that computes a future investment value at a given interest rate for a specified number of years. The future investment is determined using the formula in Exercise 2.19. Use the following function header: def futureInvestmentValue( investmentAmount, monthlyInterestRate, years): For example, futureInvestmentValue(10000, 0.05/12, 5) returns 12833.59. Write a test program that prompts the user to enter the investment amount and the annual interest rate in percent and prints a table that displays the future value for the years from 1 to 30. Here is a sample run: Programming Exercises 205 Write a test program that invokes these functions to display the following tables: Celsius Fahrenheit | Fahrenheit Celsius 40.0 104.0 | 120.0 48.89 39.0 102.2 | 110.0 43.33 ... 32.0 89.6 | 40.0 4.44 31.0 87.8 | 30.0 -1.11 6.9 (Conversions between feet and meters) Write a module that contains the following two functions: # Converts from feet to meters def footToMeter(foot): # Converts from meters to feet def meterToFoot(meter): The formulas for the conversion are: foot = meter / 0.305 meter = 0.305 * foot Write a test program that invokes these functions to display the following tables: Feet Meters | Meters Feet 1.0 0.305 | 20.0 66.574 2.0 0.610 | 26.0 81.967 ... 9.0 2.745 | 60.0 196.721 10.0 3.050 | 66.0 213.115 6.10 (Use the isPrime Function) Listing 6.7, PrimeNumberFunction.py, provides the isPrime(number) function for testing whether a number is prime. Use this function to find the number of prime numbers less than 10,000. 6.11 (Financial application: compute commissions) Write a function that computes the commission, using the scheme in Exercise 5.39. The header of the function is: def computeCommission(salesAmount): Write a test program that displays the following table: Sales Amount Commission 10000 900.0 15000 1500.0 ... 95000 11100.0 100000 11700.0 6.12 (Display characters) Write a function that prints characters using the following header: def printChars(ch1, ch2, numberPerLine): This function prints the characters between ch1 and ch2 with the specified numbers per line. Write a test program that prints ten characters per line from 1 to Z. 206 Chapter 6 Functions *6.13 (Sum series) Write a function to compute the following series: Write a test program that displays the following table: i m(i) 1 0.5000 2 1.1667 ... 19 16.4023 20 17.3546 *6.14 (Estimate ) can be computed using the following series: Write a function that returns m(i) for a given i and write a test program that dis- plays the following table: i m(i) 1 4.0000 101 3.1515 201 3.1466 301 3.1449 401 3.1441 501 3.1436 601 3.1433 701 3.1430 801 3.1428 901 3.1427 *6.15 (Financial application: print a tax table) Listing 4.7, ComputeTax.py, gives a program to compute tax. Write a function for computing tax using the following header: def computeTax(status, taxableIncome): Use this function to write a program that prints a tax table for taxable income from $50,000 to $60,000 with intervals of $50 for all four statuses, as follows: Taxable Single Married Married Head of Income Joint Separate a House 50000 8688 6665 8688 7352 50050 8700 6673 8700 7365 ... 59950 11175 8158 11175 9840 60000 11188 8165 11188 9852 *6.16 (Number of days in a year) Write a function that returns the number of days in a year using the following header: def numberOfDaysInAYear(year): Write a test program that displays the number of days in the years from 2010 to 2020. m(i) = 4¢1 - 1 3 + 1 5 - 1 7 + 1 9 - 1 11 + c + (-1)i+1 2i - 1 ≤ pp m(i) = 1 2 + 2 3 + c + i i + 1 Programming Exercises 207 Enter n: 0 1 0 0 0 0 1 1 1 3 *6.19 (Geometry: point position) Exercise 4.31 shows how to test whether a point is on the left side of a directed line, on the right, or on the same line. Write the follow- ing functions: # Return true if point (x2, y2) is on the left side of the # directed line from (x0, y0) to (x1, y1) def leftOfTheLine(x0, y0, x1, y1, x2, y2): # Return true if point (x2, y2) is on the same # line from (x0, y0) to (x1, y1) def onTheSameLine(x0, y0, x1, y1, x2, y2): # Return true if point (x2, y2) is on the # line segment from (x0, y0) to (x1, y1) def onTheLineSegment(x0, y0, x1, y1, x2, y2): Sections 6.10–6.11 *6.17 (The MyTriangle module) Create a module named MyTriangle that contains the following two functions: # Returns true if the sum of any two sides is # greater than the third side. def isValid(side1, side2, side3): # Returns the area of the triangle. def area(side1, side2, side3): Write a test program that reads three sides for a triangle and computes the area if the input is valid. Otherwise, it displays that the input is invalid. The formula for com- puting the area of a triangle is given in Exercise 2.14. Here are some sample runs: Enter three sides in double: Input is invalid 1, 3, 1 Enter three sides in double: The area of the triangle is 0.4330127018922193 1, 1, 1 *6.18 (Display matrix of 0s and 1s) Write a function that displays an n-by-n matrix using the following header: def printMatrix(n): Each element is 0 or 1, which is generated randomly. Write a test program that prompts the user to enter n and displays an n-by-n matrix. Here is a sample run: 208 Chapter 6 Functions Write a program that prompts the user to enter the three points for p0, p1, and p2 and displays whether p2 is on the left of the line from p0 to p1, on the right, on the same line, or on the line segment. The sample runs of this program are the same as in Exercise 4.31. *6.20 (Geometry: display angles) Rewrite Listing 2.9, ComputeDistance.py, using the following function for computing the distance between two points. def distance(x1, y1, x2, y2): **6.21 (Math: approximate the square root) There are several techniques for implement- ing the sqrt function in the math module. One such technique is known as the Babylonian function. It approximates the square root of a number, n, by repeatedly performing a calculation using the following formula: nextGuess = (lastGuess + (n / lastGuess)) / 2 When nextGuess and lastGuess are almost identical, nextGuess is the approximated square root. The initial guess can be any positive value (e.g., 1). This value will be the starting value for lastGuess. If the difference between nextGuess and lastGuess is less than a very small number, such as 0.0001, you can claim that nextGuess is the approximated square root of n. If not, nextGuess becomes lastGuess and the approximation process continues. Implement the following function that returns the square root of n. def sqrt(n): Sections 6.12–6.13 **6.22 (Display current date and time) Listing 2.7, ShowCurrentTime.py, displays the current time. Enhance this program to display the current date and time. (Hint: The calendar example in Listing 6.13, PrintCalendar.py, should give you some ideas on how to find the year, month, and day.) **6.23 (Convert milliseconds to hours, minutes, and seconds) Write a function that con- verts milliseconds to hours, minutes, and seconds using the following header: def convertMillis(millis): The function returns a string as hours:minutes:seconds. For example, convertMillis(5500) returns the string 0:0:5, convertMillis(100000) returns the string 0:1:40, and convertMillis(555550000) returns the string 154:19:10. Write a test program that prompts the user to enter a value for milliseconds and displays a string in the format of hours:minutes:seconds. **6.24 (Palindromic prime) A palindromic prime is a prime number that is also palin- dromic. For example, 131 is a prime and also a palindromic prime, as are 313 and 757. Write a program that displays the first 100 palindromic prime numbers. Dis- play 10 numbers per line and align the numbers properly, as follows: 2 3 5 7 11 101 131 151 181 191 313 353 373 383 727 757 787 797 919 929 Programming Exercises 209 **6.25 (Emirp) An emirp ( prime spelled backward) is a nonpalindromic prime number whose reversal is also a prime. For example, both 17 and 71 are prime numbers, so 17 and 71 are emirps. Write a program that displays the first 100 emirps. Display 10 numbers per line and align the numbers properly, as follows: 13 17 31 37 71 73 79 97 107 113 149 157 167 179 199 311 337 347 359 389 ... **6.26 (Mersenne prime) A prime number is called a Mersenne prime if it can be written in the form for some positive integer p. Write a program that finds all Mersenne primes with and displays the output as follows: p 2^p - 1 2 3 3 7 5 31 ... **6.27 (Twin primes) Twin primes are a pair of prime numbers that differ by 2. For exam- ple, 3 and 5, 5 and 7, and 11 and 13 are twin primes. Write a program to find all twin primes less than 1,000. Display the output as follows: (3, 5) (5, 7)... **6.28 (Game: craps) Craps is a popular dice game played in casinos. Write a program to play a variation of the game, as follows: Roll two dice. Each die has six faces representing values 1, 2, ..., and 6, respec- tively. Check the sum of the two dice. If the sum is 2, 3, or 12 (called craps), you lose; if the sum is 7 or 11 (called natural), you win; if the sum is another value (i.e., 4, 5, 6, 8, 9, or 10), a point is established. Continue to roll the dice until either a 7 or the same point value is rolled. If 7 is rolled, you lose. Otherwise, you win. Your program acts as a single player. Here are some sample runs. p … 31 2p - 1 You rolled 5 + 6 = 11 You win You rolled 1 + 2 = 3 You lose You rolled 4 + 4 = 8 point is 8 You rolled 6 + 2 = 8 You win You rolled 3 + 2 = 5 point is 5 You rolled 2 + 5 = 7 You lose 210 Chapter 6 Functions **6.29 (Financial: credit card number validation) Credit card numbers follow certain patterns: It must have between 13 and 16 digits, and the number must start with: ■ 4 for Visa cards ■ 5 for MasterCard credit cards ■ 37 for American Express cards ■ 6 for Discover cards In 1954, Hans Luhn of IBM proposed an algorithm for validating credit card num- bers. The algorithm is useful to determine whether a card number is entered cor- rectly or whether a credit card is scanned correctly by a scanner. Credit card numbers are generated following this validity check, commonly known as the Luhn check or the Mod 10 check, which can be described as follows (for illustra- tion, consider the card number 4388576018402626): 1. Double every second digit from right to left. If doubling of a digit results in a two-digit number, add up the two digits to get a single-digit number. 4388576018402626 2 * 2 = 4 2 * 2 = 4 4 * 2 = 8 1 * 2 = 2 6 * 2 = 12 (1 + 2 = 3) 5 * 2 = 10 (1 + 0 = 1) 8 * 2 = 16 (1 + 6 = 7) 4 * 2 = 8 2. Now add all single-digit numbers from Step 1. 3. Add all digits in the odd places from right to left in the card number. 4. Sum the results from Steps 2 and 3. 5. If the result from Step 4 is divisible by 10, the card number is valid; otherwise, it is invalid. For example, the number 4388576018402626 is invalid, but the number 4388576018410707 is valid. Write a program that prompts the user to enter a credit card number as an integer. Display whether the number is valid or invalid. Design your program to use the following functions: # Return true if the card number is valid def isValid(number): # Get the result from Step 2 def sumOfDoubleEvenPlace(number): # Return this number if it is a single digit, otherwise, return # the sum of the two digits def getDigit(number): # Return sum of odd place digits in number def sumOfOddPlace(number): 37 + 38 = 75 6 + 6 + 0 + 8 + 0 + 7 + 8 + 3 = 38 4 + 4 + 8 + 2 + 3 + 1 + 7 + 8 = 37 Programming Exercises 211 # Return true if the digit d is a prefix for number def prefixMatched(number, d): # Return the number of digits in d def getSize(d): # Return the first k number of digits from number. If the # number of digits in number is less than k, return number. def getPrefix(number, k): **6.30 (Game: chance of winning at craps) Revise Exercise 6.28 to run it 10,000 times and display the number of winning games. ***6.31 (Current date and time) Invoking time.time() returns the elapsed time in sec- onds since midnight of January 1, 1970. Write a program that displays the date and time. Here is a sample run: Current date and time is May 16, 2012 10:34:23 **6.32 (Print calendar) Exercise 4.21 uses Zeller’s congruence to calculate the day of the week. Simplify Listing 6.13, PrintCalendar.py, using Zeller’s algorithm to get the start day of the month. **6.33 (Geometry: area of a pentagon) Rewrite Exercise 3.4 using the following func- tion to return the area of a pentagon: def area(s): *6.34 (Geometry: area of a regular polygon) Rewrite Exercise 3.5 using the following function to return the area of a regular polygon: def area(n, side): *6.35 (Compute the probability) Use the functions in RandomCharacter in Listing 6.11 to generate 10,000 uppercase letters and count the occurrence of A. *6.36 (Generate random characters) Use the functions in RandomCharacter in Listing 6.11 to print 100 uppercase letters and then 100 single digits, printing ten per line. Section 6.14 *6.37 (Turtle: generate random characters) Use the functions in RandomCharacter in Listing 6.11 to display 100 lowercase letters, fifteen per line, as shown in Figure 6.11a. **6.38 (Turtle: draw a line) Write the following function that draws a line from point (x1, y1) to (x2, y2) with color (default to black) and line size (default to 1). def drawLine(x1, y1, x2, y2, color = "black", size = 1): **6.39 (Turtle: draw a star) Write a program that draws a star, as shown in Figure 6.11b. Use the drawLine function defined in Exercise 6.38. 212 Chapter 6 Functions (a) (b) (c) FIGURE 6.11 (a) The program displays random lowercase letters. (b) The program draws a star. (c) The program draws random points in a rectangle and in a circle. **6.40 (Turtle: filled rectangle and circle) Write the following functions that fill a rectan- gle with the specified color, center, width, and height, and a circle with the specified color, center, and radius. # Fill a rectangle def drawRectangle(color = "black", x = 0, y = 0, width = 30, height = 30): # Fill a circle def drawCircle(color = "black", x = 0, y = 0, radius = 50): **6.41 (Turtle: draw points, rectangles, and circles) Use the functions defined in Listing 6.14 to write a program that displays a rectangle centered at with width and height 100 and a circle centered at (50, 0) with radius 50. Fill 10 random points inside the rectangle and 10 inside the circle, as shown in Figure 6.11c. **6.42 (Turtle: plot the sine function) Simplify the code for Exercise 5.52 by using the functions in Listing 6.14. **6.43 (Turtle: plot the sine and cosine functions) Simplify the code for Exercise 5.53 by using the functions in Listing 6.14. **6.44 (Turtle: plot the square function) Simplify the code for Exercise 5.54 by using the functions in Listing 6.14. **6.45 (Turtle: draw a regular polygon) Write the following function to draw a regular polygon: def drawPolygon(x = 0, y = 0, radius = 50, numberOfSides = 3): The polygon is centered at (x, y) with a specified radius for the bounding circle for the polygon and the number of sides. Write a test program that displays a triangle, square, pentagon, hexagon, heptagon, and octagon, as shown in Figure 6.12a. *6.46 (Turtle: connect all points in a hexagon) Write a program that displays a hexagon with all the points connected, as shown in Figure 6.12b. *6.47 (Turtle: two chessboards) Write a program that displays two chessboards, as shown in Figure 6.13. Your program should define at least the following function: # Draw one chessboard whose upper-left corner is at # (startx, starty) and bottom-right corner is at (endx, endy) def drawChessboard(startx, endx, starty, endy): (-75, 0) Programming Exercises 213 (a) (b) FIGURE 6.12 (a) The program displays several n-sided polygons. (b) The program displays a hexagon with all points connected. FIGURE 6.13 The program draws two chessboards. *6.48 (Format an integer) Write a function with the following header to format the inte- ger with the specified width. def format(number, width): The function returns a string for the number with prefix 0s. The size of the string is the width. For example, format(34, 4) returns "0034" and format(34, 5) returns "00034". If the number is longer than the width, the function returns the string representation for the number. For example, format(34, 1) returns "34". Write a test program that prompts the user to enter a number and its width and dis- plays a string returned from invoking format(number, width). Here is a sample run: Enter an integer: Enter the width: The formatted number is 000453 6 453 This page intentionally left blank OBJECTS AND CLASSES CHAPTER 7 Objectives ■ To describe objects and classes, and use classes to model objects (§7.2). ■ To define classes with data fields and methods (§7.2.1). ■ To construct an object using a constructor that invokes the initializer to create and initialize data fields (§7.2.2). ■ To access the members of objects using the dot operator (.) (§7.2.3). ■ To reference an object itself with the self parameter (§7.2.4). ■ To use UML graphical notations to describe classes and objects (§7.3). ■ To distinguish between immutable and mutable objects (§7.4). ■ To hide data fields to prevent data corruption and make classes easy to maintain (§7.5). ■ To apply class abstraction and encapsulation to software development (§7.6). ■ To explore the differences between the procedural paradigm and the object-oriented paradigm (§7.7). 216 Chapter 7 Objects and Classes 7.1 Introduction Object-oriented programming enables you to develop large-scale software and GUIs effectively. Having learned the material in the preceding chapters, you are now able to solve many pro- gramming problems by using selections, loops, and functions. However, these features are not sufficient for developing a graphical user interface (GUI, pronounced goo-ee) or a large-scale software system. Suppose you want to develop the GUI shown in Figure 7.1. How would you program it? This chapter introduces object-oriented programming, which will build a foundation that enables you to develop GUIs and large-scale software systems in the upcoming chapters. 7.2 Defining Classes for Objects A class defines the properties and behaviors for objects. Section 3.5 introduced objects and methods, and showed you how to use objects. Objects are created from classes. This section shows you how to define custom classes. Object-oriented programming (OOP) involves the use of objects to create programs. An object represents an entity in the real world that can be distinctly identified. For example, a student, a desk, a circle, a button, and even a loan can all be viewed as objects. An object has a unique identity, state, and behavior. ■ An object’s identity is like a person’s Social Security number. Python automatically assigns each object a unique id for identifying the object at runtime. ■ An object’s state (also known as its properties or attributes) is represented by vari- ables, called data fields. A circle object, for example, has a data field radius, which is a property that characterizes a circle. A rectangle object has the data fields width and height, which are properties that characterize a rectangle. ■ Python uses methods to define an object’s behavior (also known as its actions). Recall that methods are defined as functions. You make an object perform an action by invoking a method on that object. For example, you can define methods named getArea() and getPerimeter() for circle objects. A circle object can then invoke the getArea() method to return its area and the getPerimeter() method to return its perimeter. Objects of the same kind are defined by using a common class. The relationship between classes and objects is analogous to that between an apple-pie recipe and apple pies. You can make as many apple pies (objects) as you want from a single recipe (class). A Python class uses variables to store data fields and defines methods to perform actions. A class is a contract—also sometimes called a template or blueprint—that defines what an object’s data fields and methods will be. why OOP? object-oriented programming object identity state properties attributes data fields behavior actions Button Entry (text field) Radio ButtonLabel Check Button FIGURE 7.1 You can create GUI objects like this using object-oriented programming. class contract Key Point Key Point 7.2 Defining Classes for Objects 217 An object is an instance of a class, and you can create many instances of a class. Creating an instance of a class is referred to as instantiation. The terms object and instance are often used interchangeably. An object is an instance and an instance is an object. Figure 7.2 shows a class named Circle and its three objects. 7.2.1 Defining Classes In addition to using variables to store data fields and define methods, a class provides a special method, __init__. This method, known as an initializer, is invoked to initialize a new object’s state when it is created. An initializer can perform any action, but initializers are designed to per- form initializing actions, such as creating an object’s data fields with initial values. Python uses the following syntax to define a class: class ClassName: initializer methods Listing 7.1 defines the Circle class. The class name is preceded by the keyword class and followed by a colon (:). The initializer is always named __init__ (line 5), which is a special method. Note that init needs to be preceded and followed by two underscores. A data field radius is created in the initializer (line 6). The methods getPerimeter and getArea are defined to return the perimeter and area of a circle (lines 8–12). More details on the initializer, data fields, and methods will be explained in the following sections. LISTING 7.1 Circle.py 1 import math 2 3 class Circle: 4 # Construct a circle object 5 def __init__(self, radius = 1): 6 self.radius = radius 7 8 def getPerimeter(self): 9 return 2 * self.radius * math.pi 10 11 def getArea(self): 12 return self.radius * self.radius * math.pi 13 14 def setRadius(self, radius): 15 self.radius = radius instantiation object instance methods initializer class definition class name Class Name: Circle Data Fields: radius is _____ Methods: getArea getPerimeter setRadius Circle Object 1 Data Fields: radius is 1 Circle Object 2 Data Fields: radius is 25 Circle Object 3 Data Fields: radius is 125 A class template Three objects of the Circle class FIGURE 7.2 A class is a template—or contract—for creating objects. initializer create data field getPerimeter() method getArea() method Define and use classes VideoNote 218 Chapter 7 Objects and Classes Note The naming style for class names in the Python library is not consistent. In this book, we will adopt a convention that capitalizes the first letter of each word in the class name. For example, Circle, LinearEquation, and LinkedList are correct class names according to our convention. 7.2.2 Constructing Objects Once a class is defined, you can create objects from the class with a constructor. The con- structor does two things: ■ It creates an object in the memory for the class. ■ It invokes the class’s __init__ method to initialize the object. All methods, including the initializer, have the first parameter self. This parameter refers to the object that invokes the method. The self parameter in the __init__ method is auto- matically set to reference the object that was just created. You can specify any name for this parameter, but by convention self is usually used. We will discuss the role of self more in Section 7.2.4. The syntax for a constructor is: ClassName(arguments) Figure 7.3 shows how an object is created and initialized. After the object is created, self can be used to reference the object. The arguments of the constructor match the parameters in the __init__ method without self. For example, since the __init__ method in line 5 of Listing 7.1 is defined as __init__(self, radius = 1), to construct a Circle object with radius 5, you should use Circle(5). Figure 7.4 shows the effect of constructing a Circle object using Circle(5). First, a Circle object is created in the memory, and then the initializer is invoked to set radius to 5. class naming convention constructor self parameter __init__ method FIGURE 7.3 Constructing an object creates the object in the memory and invokes its initializer. object Data Fields: _ _init_ _(self, …) 2. It invokes the class’s _ _init_ _ method to initialize the object. The self parameter in the _ _init_ _ method is automatically set to reference the object that was just created. 1. It creates an object in the memory for the class. Circle object 2. Invokes _ _init_ _(self, radius) 1. Creates a Circle object. Circle object radius: 5 FIGURE 7.4 A circle object is constructed using Circle(5). 7.2 Defining Classes for Objects 219 The initializer in the Circle class has a default radius value of 1. The following con- structor creates a Circle object with default radius 1: Circle() 7.2.3 Accessing Members of Objects An object’s member refers to its data fields and methods. Data fields are also called instance variables, because each object (instance) has a specific value for a data field. Methods are also called instance methods, because a method is invoked by an object (instance) to perform actions on the object such as changing the values in data fields for the object. In order to access an object’s data fields and invoke an object’s methods, you need to assign the object to a variable by using the following syntax: objectRefVar = ClassName(arguments) For example, c1 = Circle(5) c2 = Circle() You can access the object’s data fields and invoke its methods by using the dot operator (.), also known as the object member access operator. The syntax for using the dot operator is: objectRefVar.datafield objectRefVar.method(args) For example, the following code accesses the radius data field (line 3), and then invokes the getPerimeter method (line 5) and the getArea method (line 7). Note that line 1 imports the Circle class defined in the Circle module in Listing 7.1, Circle.py. default values instance methods dot operator (.) object member access operator 1 >>> from Circle import Circle
2 >>> c = Circle(5)
3 >>> c.radius
4 5
5 >>> c.getPerimeter()
6 31.41592653589793
7 >>> c.getArea()
8 78.53981633974483
9 >>>
Note
Usually you create an object and assign it to a variable. Later you can use the variable to
reference the object. Occasionally an object does not need to be referenced later. In this
case, you can create an object without explicitly assigning it to a variable, as shown below:
print(“Area is”, Circle(5).getArea())
The statement creates a Circle object and invokes its getArea method to return its
area. An object created in this way is known as an anonymous object.
7.2.4 The self Parameter
As mentioned earlier, the first parameter for each method defined is self. This parameter is
used in the implementation of the method, but it is not used when the method is called. So,
what is this parameter self for? Why does Python need it?
why self?
anonymous object

220 Chapter 7 Objects and Classes
self is a parameter that references the object itself. Using self, you can access object’s
members in a class definition. For example, you can use the syntax self.x to access the
instance variable x and syntax self.m1() to invoke the instance method m1 for the object
self in a class, as illustrated in Figure 7.5.
The scope of an instance variable is the entire class once it is created. In Figure 7.5, self.x
is an instance variable created in the __init__ method. It is accessed in method m2. The
instance variable self.y is set to 2 in method m1 and set to 3 in m2. Note that you can also cre-
ate local variables in a method. The scope of a local variable is within the method. The local
variable z is created in method m1 and its scope is from its creation to the end of method m1.
7.2.5 Example: Using Classes
The preceding sections demonstrated the concept of class and objects. You learned how to
define a class with the initializer, data fields, and methods, and how to create an object with
constructor. This section presents a test program that constructs three circle objects with radii
of 1, 25, and 125, and then displays the radius and area of each circle in Listing 7.2. The pro-
gram then changes the radius of the second object to 100 and displays its new radius and area.
LISTING 7.2 TestCircle.py
1 from Circle import Circle
2
3 def main():
4 # Create a circle with radius 1
5
6 print(“The area of the circle of radius”,
7 , “is”, )
8
9 # Create a circle with radius 25
10
11 print(“The area of the circle of radius”,
12 , “is”, )
13
14 # Create a circle with radius 125
15
16 print(“The area of the circle of radius”,
17 , “is”, )
18
circle3.getArea()circle3.radius
circle3 = Circle(125)
circle2.getArea()circle2.radius
circle2 = Circle(25)
circle1.getArea()circle1.radius
circle1 = Circle()
FIGURE 7.5
def ClassName:
def __init__(self, …):
self.x = 1 # Create/modify x
…
def m1(self, …):
self.y = 2 # Create/modify y
…
z = 5 # Create/modify z
… Scope of z
def m2(self, …):
self.y = 3 # Create/modify y
…
u = self.x + 1 # Create/modify u
self.m1(…) # Invoke m1
The scope of an instance variable is the entire class.
Scope of self.x
and self.y
import Circle
main function
create object
invoke methods
create object
create object
scope of an instance variable

7.2 Defining Classes for Objects 221
set a new radius
The area of the circle of radius 1.0 is 3.141592653589793
The area of the circle of radius 25.0 is 1963.4954084936207
The area of the circle of radius 125.0 is 49087.385212340516
The area of the circle of radius 100.0 is 31415.926535897932
The program uses the Circle class to create Circle objects. Such a program that uses
the class (such as Circle) is often referred to as a client of the class.
The Circle class is defined in Listing 7.1, Circle.py, and this program imports it in line 1
using the syntax from Circle import Circle. The program creates a Circle object
with a default radius 1 (line 5) and creates two Circle objects with the specified radii (lines
10, 15), and then retrieves the radius property and invokes the getArea() method on the
objects to obtain the area (lines 7, 12, and 17). The program sets a new radius property on
circle2 (line 20). This can also be done by using circle2.setRadius(100).
Note
An variable that appears to hold an object actually contains a reference to that object.
Strictly speaking, a variable and an object are different, but most of the time the distinction
can be ignored. So it is fine, for simplicity, to say that “circle1 is a Circle object”
rather than use the longer-winded description that “circle1 is a variable that contains a
reference to a Circle object.”
7.1 Describe the relationship between an object and its defining class.
7.2 How do you define a class?
7.3 How do you create an object?
7.4 What is the name of the initializer method?
7.5 The first parameter in the initializer method is named self by convention. What is
the role of self?
7.6 What is the syntax for constructing an object? What does Python do when construct-
ing an object?
7.7 What are the differences between an initializer and a method?
7.8 What is the object member access operator for?
7.9 What problem arises in running the following program? How do you fix it?
class A:
def __init__(self, i):
self.i = i
def main():
a = A()
print(a.i)
main() # Call the main function
7.10 What is wrong with the following programs?
client
object vs. variable
19 # Modify circle radius
20 # or circle2.setRadius(100)
21 print(“The area of the circle of radius”,
22 , “is”, )
23
24 main() # Call the main function
circle2.getArea()circle2.radius
circle2.radius = 100
✓Point✓Check

222 Chapter 7 Objects and Classes
UML
1 class A:
2 # Construct an object of the class
3 def A(self):
4 radius = 3
1 class A:
2 # Construct an object of the class
3 def __init__(self):
4 radius = 3
5
6 def setRadius(radius):
7 self.radius = radius
(a) (b)
7.3 UML Class Diagrams
UML class diagrams use graphical notation to describe classes.
The illustration of class templates and objects in Figure 7.2 can be standardized using UML (Uni-
fied Modeling Language) notation. This notation, as shown in Figure 7.6, called a UML class dia-
gram or simply a class diagram, is language independent; that is, other programming languages
use this same modeling and notation. In UML class diagrams, data fields are denoted as:
dataFieldName: dataFieldType
Constructors are shown as:
ClassName(parameterName: parameterType)
Methods are represented as:
methodName(parameterName: parameterType): returnType
Class nameCircle
radius: float
Circle(radius = 1: float)
getArea(): float
getPerimeter(): float
setRadius(radius: float): None
Data fields
Constructor
Methods
UML Class Diagram
UML notation
for objects
circle2: Circle
radius = 25
circle3: Circle
radius = 125
circle1: Circle
radius = 1
FIGURE 7.6 Classes and objects can be represented using UML notation.
The method definition in the class always has the special self parameter, but don’t
include it in the UML diagram, because the client does not need to know this parameter and
does not use this parameter to invoke the methods.
The __init__ method does not need to be listed in the UML diagram either, because it is
invoked by the constructor and its parameters are the same as the constructor’s parameters.
The UML diagram serves as the contract (template) for the client so that it will know how to
use the class. The diagram describes for the client how to create objects and how to invoke the
methods on the objects.
As an example, consider TV sets. Each TV is an object with states (that is, current chan-
nel, current volume level, and power on or off are its properties that are represented by data
fields) and behaviors (change channels, adjust volume, and turn on/off are the actions each
Key
Point

7.3 UML Class Diagrams 223
TV object implements with methods). You can use a class to define TV sets. The UML dia-
gram for the TV class is shown in Figure 7.7.
TV
The current channel (1 to 120) of this TV.
The current volume level (1 to 7) of this TV.
Indicates whether this TV is on/off.
channel: int
volumeLevel: int
on: bool
TV()
turnOn(): None
turnOff(): None
getChannel(): int
setChannel(channel: int): None
getVolume(): int
setVolume(volumeLevel: int): None
channelUp(): None
channelDown(): None
volumeUp(): None
volumeDown(): None
Constructs a default TV object.
Turns on this TV.
Turns off this TV.
Returns the channel for this TV.
Sets a new channel for this TV.
Gets the volume level for this TV.
Sets a new volume level for this TV.
Increases the channel number by 1.
Decreases the channel number by 1.
Increases the volume level by 1.
Decreases the volume level by 1.
FIGURE 7.7 The TV class defines TV sets.
Listing 7.3 gives the Python code for defining the TV class.
LISTING 7.3 TV.py
1
2
3 # Default channel is 1
4 # Default volume level is 1
5 # Initially, TV is off
6
7
8 self.on = True
9
10 :
11 self.on = False
12
13
14 return self.channel
15
16
17 if self.on and 1 <= self.channel <= 120: 18 self.channel = channel 19 20 21 return self.volumeLevel 22 23 24 if self.on and \ 25 1 <= self.volumeLevel <= 7: 26 self.volumeLevel = volumeLevel 27 28 def channelUp(self): def setVolume(self, volumeLevel): def getVolumeLevel(self): def setChannel(self, channel): def getChannel(self): def turnOff(self) def turnOn(self): self.on = False self.volumeLevel = 1 self.channel = 1 def __init__(self): class TV: define a class define initializer create instance variables turn on TV turn off TV get the channel set a new channel get the volume set a new volume increase channel 224 Chapter 7 Objects and Classes 29 if self.on and self.channel < 120: 30 self.channel += 1 31 32 33 if self.on and self.channel > 1:
34 self.channel -= 1
35
36
37 if self.on and self.volumeLevel < 7: 38 self.volumeLevel += 1 39 40 41 if self.on and self.volumeLevel > 1:
42 self.volumeLevel -= 1
The initializer creates the instance variables channel, volumeLevel, and on for the data
fields in a TV object (lines 2–5). Note that this initializer does not have any argument except
self.
The channel and volume level are not changed if the TV is not on (lines 16–18 and 23–26).
Before either of these is changed, its current value is checked to ensure that it is within the
correct range.
Listing 7.4 is a program that uses the TV class to create two objects.
LISTING 7.4 TestTV.py
1 from TV import TV
2
3 def main():
4
5 tv1.turnOn()
6 tv1.setChannel(30)
7 tv1.setVolume(3)
8
9
10 tv2.turnOn()
11 tv2.channelUp()
12 tv2.channelUp()
13 tv2.volumeUp()
14
15 print(“tv1’s channel is”, ,
16 “and volume level is”, )
17 print(“tv2’s channel is”, tv2.getChannel(),
18 “and volume level is”, tv2.getVolumeLevel())
19
20 main() # Call the main function
tv1.getVolumeLevel()
tv1.getChannel()
tv2 = TV()
tv1 = TV()
def volumeDown(self):
def volumeUp(self):
def channelDown(self):decrease channel
increase volume
decrease volume
import TV class
main function
create a TV
turn on
set a new channel
set a new volume
create a TV
turn on
increase channel
increase volume
display state
tv1’s channel is 30 and volume level is 3
tv2’s channel is 3 and volume level is 2
The program creates two TV objects tv1 and tv2 (lines 4 and 9), and invokes the methods
on the objects to perform actions for setting channels and volume levels and for increasing
channels and volumes. tv1 is turned on by invoking tv1.turnOn() in line 5, its channel is
set to 30 by invoking tv1.setChannel(30) in line 6, and its volume level is set to 3 in line
7. tv2 is turned on in line 10, its channel is increased by 1 by invoking tv2.channelUp()
in line 11, and again by another 1 in line 12. Since the initial channel is set to 1 (line 3 in

7.4 Immutable Objects vs. Mutable Objects 225
TV.py), tv2’s channel is now 3. tv2’s volume is increased by 1 by invoking
tv2.volumeUp() in line 13. Since the initial volume is set to 1 (line 4 in TV.py), tv2’s vol-
ume is now 2.
The program displays the state of the objects in lines 15–18. The data fields are read using
the getChannel() and getVolumeLevel() methods.
7.4 Immutable Objects vs. Mutable Objects
When passing a mutable object to a function, the function may change the contents of
the object.
Recall that numbers and strings are immutable objects in Python. Their contents cannot be
changed. When passing an immutable object to a function, the object will not be changed.
However, if you pass a mutable object to a function, the contents of the object may change.
The example in Listing 7.5 demonstrates the differences between an immutable object and
mutable object arguments in a function.
LISTING 7.5 TestPassMutableObject.py
1 from Circle import Circle
2
3 def main():
4 # Create a Circle object with radius 1
5 myCircle = Circle()
6
7 # Print areas for radius 1, 2, 3, 4, and 5
8 n = 5
9
10
11 # Display myCircle.radius and times
12 print(“\nRadius is”, myCircle.radius)
13 print(“n is”, n)
14
15 # Print a table of areas for radius
16 def printAreas(c, times):
17 print(“Radius \t\tArea”)
18 while times >= 1:
19 print(c.radius, “\t\t”, c.getArea())
20
21
22
23 main() # Call the main function
times = times – 1
c.radius = c.radius + 1
printAreas(myCircle, n)
import Circle
create object
invoke printAreas
display radius
display n
Radius Area
1 3.141592653589793
2 12.566370614359172
3 29.274333882308138
4 50.26548245743669
5 79.53981633974483
Radius is 6
n is 5
The Circle class is defined in Listing 7.1. The program passes a Circle object
myCircle and an int object n to invoke printAreas(myCircle, n) (line 9), which
prints a table of areas for radii 1, 2, 3, 4, and 5, as shown in the sample output.
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226 Chapter 7 Objects and Classes
immutable object vs. mutable
object
When you pass an object to a function, the reference of the object is passed to the function.
However, there are important differences between passing immutable objects and mutable
objects.
■ For an argument of an immutable object such as a number or string, the original
value of the object outside the function is not changed.
■ For an argument of a mutable object such as a circle, the original value of the object
is changed if the contents of the object are changed inside the function.
In line 20, the radius property of the Circle object c is incremented by 1. c.radius
+ 1 creates a new int object, which is assigned to c.radius. myCircle and c both point to
the same object. When the printAreas function is finished, c.radius is 6. So, the printout
for myCircle.radius is 6 from line 12.
In line 21, times – 1 creates a new int object, which is assigned to times. Outside of
the printAreas function, n is still 5. So, the printout for n is 5 from line 13.
7.11 Show the output of the following program:
class Count:
def __init__(self, count = 0):
self.count = count
def main():
c = Count()
times = 0
for i in range(100):
increment(c, times)
print(“count is”, c.count)
print(“times is”, times)
def increment(c, times):
c.count += 1
times += 1
main() # Call the main function
7.12 Show the output of the following program:
class Count:
def __init__(self, count = 0):
self.count = count
def main():
c = Count()
n = 1
m(c, n)
print(“count is”, c.count)
print(“n is”, n)
def m(c, n):
c = Count(5)
n = 3
main() # Call the main function
✓Point✓Check

7.5 Hiding Data Fields 227
7.5 Hiding Data Fields
Making data fields private protects data and makes the class easy to maintain.
You can access data fields via instance variables directly from an object. For example, the fol-
lowing code, which lets you access the circle’s radius from c.radius, is legal:
>>> c = Circle(5)
>>> c.radius = 5.4 # Access instance variable directly
>>> print(c.radius) # Access instance variable directly
5.4
>>>
However, direct access of a data field in an object is not a good practice—for two reasons:
■ First, data may be tampered with. For example, channel in the TV class has a value
between 1 and 120, but it may be mistakenly set to an arbitrary value (e.g.,
tv1.channel = 125).
■ Second, the class becomes difficult to maintain and vulnerable to bugs. Suppose you
want to modify the Circle class to ensure that the radius is nonnegative after other
programs have already used the class. You have to change not only the Circle class
but also the programs that use it, because the clients may have modified the radius
directly (e.g., myCircle.radius = -5).
To prevent direct modifications of data fields, don’t let the client directly access data fields.
This is known as data hiding. This can be done by defining private data fields. In Python, the
private data fields are defined with two leading underscores. You can also define a private
method named with two leading underscores.
Private data fields and methods can be accessed within a class, but they cannot be accessed
outside the class. To make a data field accessible for the client, provide a get method to return
its value. To enable a data field to be modified, provide a set method to set a new value.
Colloquially, a get method is referred to as a getter (or accessor), and a set method is
referred to as a setter (or mutator).
A get method has the following header:
If the return type is Boolean, the get method is defined as follows by convention:
A set method has the following header:
Listing 7.6 revises the Circle class in Listing 7.1 by defining the radius property as pri-
vate by placing two underscores in front of the property name (line 6).
LISTING 7.6 CircleWithPrivateRadius.py
1 import math
2
3 class Circle:
4 # Construct a circle object
5 def __init__(self, radius = 1):
6 self.__radius = radius
7
def setPropertyName(self, propertyValue):
def isPropertyName(self):
def getPropertyName(self):
data hiding
private data fields
private method
accessor
mutator
Boolean accessor
class name
Private data fields
VideoNote
Key
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initializer
private radius

228 Chapter 7 Objects and Classes
8 def getRadius(self):
9 return self.__radius
10
11 def getPerimeter(self):
12 return 2 * self.__radius * math.pi
13
14 def getArea(self):
15 return self.__radius * self.__radius * math.pi
The radius property cannot be directly accessed in this new Circle class. However, you
can read it by using the getRadius() method. For example:
getRadius()
1 >>> from CircleWithPrivateRadius import Circle
2 >>> c = Circle(5)
3 >>> c.__radius
4 AttributeError: no attribute ‘__radius’
5 >>> c.getRadius()
6 5
7 >>>
Line 1 imports the Circle class, which is defined in the CircleWithPrivateRadius
module in Listing 7.6. Line 2 creates a Circle object. Line 3 attempts to access the property
__radius. This causes an error, because __radius is private. However, you can use the
getRadius() method to return the radius (line 5).
Tip
If a class is designed for other programs to use, to prevent data from being tampered with
and to make the class easy to maintain, define data fields as private. If a class is only
used internally by your own program, there is no need to hide the data fields.
Note
Name private data fields and methods with two leading underscores, but don’t end the
name with more than one underscores. The names with two leading underscores and
two ending underscores have special meaning in Python. For example, __radius is a
private data field, but, __radius__ is not a private data field.
7.13 What problem arises in running the following program? How do you fix it?
class A:
def __init__(self, i):
self.__i = i
def main():
a = A(5)
print(a.__i)
main() # Call the main function
7.14 Is the following code correct? If so, what is the printout?
1 def main():
2 a = A()
3 a.print()
4
✓Point✓Check

7.6 Class Abstraction and Encapsulation 229
5 class A:
6 def __init__(self, newS = “Welcome”):
7 self.__s = newS
8
9 def print(self):
10 print(self.__s)
11
12 main() # Call the main function
7.15 Is the following code correct? If not, fix the error.
class A:
def __init__(self, on):
self.__on = not on
def main():
a = A(False)
print(a.on)
main() # Call the main function
7.16 What are the benefits of data hiding? How is it done in Python?
7.17 How do you define a private method?
7.6 Class Abstraction and Encapsulation
Class abstraction is a concept that separates class implementation from the use of a
class. The class implementation details are invisible from the user. This is known as
class encapsulation.
There are many levels of abstraction in software development. In Chapter 6, you learned
about function abstraction and used it in stepwise refinement. Class abstraction is the separa-
tion of class implementation from the use of a class. The creator of a class describes the
class’s functions and lets the client know how the class can be used. The class’s collection of
methods, together with the description of how these methods are expected to behave, serves
as the class’s contract with the client.
As shown in Figure 7.8, the user of the class does not need to know how the class is
implemented. The details of implementation are encapsulated and hidden from the user. This
is known as class encapsulation. In essence, encapsulation combines data and methods into
a single object and hides the data fields and method implementation from the user. For exam-
ple, you can create a Circle object and find the area of the circle without knowing how the
area is computed. For this reason, a class is also known as an abstract data type (ADT).
class abstraction
class’s contract
class encapsulation
abstract data type
Class’s Contract
(headers of
initializer and
methods)
Class
Class implementation
is like a black box
hidden from the clients
Clients use the
class through the
class’s contract
FIGURE 7.8 Class abstraction separates class implementation from the use of the class.
Class abstraction and encapsulation are two sides of the same coin. Many real-life exam-
ples illustrate the concept of class abstraction. Consider, for instance, building a computer
system. Your personal computer has many components—a CPU, memory, disk, motherboard,
fan, and so on. Each component can be viewed as an object that has properties and methods.
To get the components to work together, you need to know only how each component is used
and how it interacts with the others. You don’t need to know how the components work
Key
Point

230 Chapter 7 Objects and Classes
internally. The internal implementation is encapsulated and hidden from you. You can even
build a computer without knowing how a component is implemented.
The computer-system analogy precisely mirrors the object-oriented approach. Each com-
ponent can be viewed as an object of the class for the component. For example, you might
have a class that defines fans for use in a computer, with properties such as fan size and speed
and methods such as start and stop. A specific fan is an instance of this class with specific
property values.
As another example, consider getting a loan. A specific loan can be viewed as an object of
a Loan class. The interest rate, loan amount, and loan period are its data properties, and com-
puting monthly payment and total payment are its methods. When you buy a car, a loan object
is created by instantiating the class with your loan interest rate, loan amount, and loan period.
You can then use the methods to find the monthly payment and total payment of your loan. As
a user of the Loan class, you don’t need to know how these methods are implemented.
Listing 2.8, ComputeLoan.py, presented a program for computing loan payments. The
program as it is currently written cannot be reused in other programs. One way to fix this
problem is to define functions for computing monthly payment and total payment. However,
this solution has limitations. Suppose you wish to associate a borrower with the loan. There is
no good way to tie a borrower with a loan without using objects. The traditional procedural
programming paradigm is action-driven; data are separated from actions. The object-oriented
programming paradigm focuses on objects, so actions are defined along with the data in
objects. To tie a borrower with a loan, you can define a loan class with borrower along with
other properties of the loan as data fields. A loan object would then contain data and actions
for manipulating and processing data, with loan data and actions integrated in one object.
Figure 7.9 shows the UML class diagram for the Loan class. Note that the – (dash) in the
UML class diagram denotes a private data field or method of the class.
Loan
The annual interest rate of the loan (default 2.5).
Returns the annual interest rate of this loan.
Sets a new annual interest rate for this loan.
Sets a new number of years for this loan.
Sets a new amount for this loan.
Sets a new borrower for this loan.
Returns the monthly payment of this loan.
The number of years for the loan (default 1).
The loan amount (default 1000).
The borrower of this loan (default ” “).
Returns the number of the years of this loan.
Returns the amount of this loan.
Returns the borrower of this loan.
Returns the total payment of this loan.
Loan(annualInterestRate: float,
numberOfYears: int,loanAmount
float, borrower: str)
getAnnualInterestRate(): float
setNumberOfYears(
numberOfYears: int): None
setLoanAmount(
loanAmount: float): None
setBorrower(borrower: str): None
setAnnualInterestRate(
annualInterestRate: float): None
getNumberOfYears(): int
getLoanAmount(): float
getBorrower(): str
setMonthlyPayment(): float
getTotalPayment(): float
Constructs a Loan object with the
specified annual interest rate, number of years, loan
amount, and borrower.
-annualInterestRate: float
-numberOfYears: int
-loanAmount: float
-borrower: str
The � sign denotes a private data field.
FIGURE 7.9 The UML diagram for the Loan class models (shows) the properties and behaviors of loans.

7.6 Class Abstraction and Encapsulation 231
The UML diagram in Figure 7.9 serves as the contract for the Loan class. That is, the user
can use the class without knowing how the class is implemented. Assume that the Loan class
is available. We begin by writing a test program that uses the Loan class in Listing 7.7.
LISTING 7.7 TestLoanClass.py
1 from Loan import Loan
2
3 def main():
4 # Enter yearly interest rate
5 annualInterestRate = eval(input
6 (“Enter yearly interest rate, for example, 7.25: “))
7
8 # Enter number of years
9 numberOfYears = eval(input(
10 “Enter number of years as an integer: “))
11
12 # Enter loan amount
13 loanAmount = eval(input(
14 “Enter loan amount, for example, 120000.95: “))
15
16 # Enter a borrower
17 borrower = input(“Enter a borrower’s name: “)
18
19 # Create a Loan object
20 loan =
21
22
23 # Display loan date, monthly payment, and total payment
24 print(“The loan is for”, )
25 print(“The monthly payment is”,
26 format( , “.2f”))
27 print(“The total payment is”,
28 format( , “.2f”))
29
30 main() # Call the main function
loan.getTotalPayment()
loan.getMonthlyPayment()
loan.getBorrower()
loanAmount, borrower)
Loan(annualInterestRate, numberOfYears, create Loan object
invoke instance method
invoke instance method
invoke instance method
Enter yearly interest rate, for example, 7.25:
Enter number of years as an integer:
Enter loan amount, for example, 120000.95:
Enter a borrower’s name:
The loan is for John Jones
The monthly payment is 17.75
The total payment is 1064.84
John Jones
1000
5
2.5
The main function (1) reads the interest rate, payment period (in years), and loan amount,
(2) creates a Loan object, and then (3) obtains the monthly payment (line 26) and total pay-
ment (line 28) using the instance methods in the Loan class.
The Loan class can be implemented as in Listing 7.8.
LISTING 7.8 Loan.py
1 :
2
3 :
4 self.__annualInterestRate = annualInterestRate
5 self.__numberOfYears = numberOfYears
6 self.__loanAmount = loanAmount
numberOfYears = 1, loanAmount = 1000, borrower = ” “)
def __init__(self, annualInterestRate = 2.5,
class Loan
initializer

232 Chapter 7 Objects and Classes
7 self.__borrower = borrower
8
9
10 return self.__annualInterestRate
11
12
13 return self.__numberOfYears
14
15
16 return self.__loanAmount
17
18
19 return self.__borrower
20
21
22 self.__annualInterestRate = annualInterestRate
23
24
25 self.__numberOfYears = numberOfYears
26
27
28 self.__loanAmount = loanAmount
29
30
31 self.__borrower = borrower
32
33
34 monthlyInterestRate = self.__annualInterestRate / 1200
35 monthlyPayment = \
36 self.__loanAmount * monthlyInterestRate / (1 – (1 /
37 (1 + monthlyInterestRate) ** (self.__numberOfYears * 12)))
38 return monthlyPayment
39
40
41 totalPayment = self.getMonthlyPayment() * \
42 self.__numberOfYears * 12
43 return totalPayment
Because the data fields annualInterestRate, numberOfYears, loanAmount, and
borrower are defined as private (with two leading underscores), they cannot be accessed
from outside the class by a client program.
From a class developer’s perspective, a class is designed for use by many different cus-
tomers. In order to be useful in a wide range of applications, a class should provide a variety
of ways for users to customize the class with methods.
Important Pedagogical Tip
The UML diagram for the Loan class is shown in Figure 7.9. You should first write a test
program that uses the Loan class even though you don’t know how the Loan class is
implemented. This has three benefits:
■ It demonstrates that developing a class and using a class are two separate
tasks.
■ It enables you to skip the complex implementation of certain classes without
interrupting the sequence of the book.
■ It is easier to learn how to implement a class if you are familiar with the
class through using it.
For all the class development examples from now on, first create an object from the class
and try to use its methods and then turn your attention to its implementation.
def getTotalPayment(self):
def getMonthlyPayment(self):
def setBorrower(self, borrower):
def setLoanAmount(self, loanAmount):
def setNumberOfYears(self, numberOfYears):
def setAnnualInterestRate(self, annualInterestRate):
def getBorrower(self):
def getLoanAmount(self):
def getNumberOfYears(self):
def getAnnualInterestRate(self):get methods
set methods
getMonthlyPayment
getTotalPayment

7.7 Object-Oriented Thinking 233
7.7 Object-Oriented Thinking
The procedural paradigm for programming focuses on designing functions. The
object-oriented paradigm couples data and methods together into objects. Software
design using the object-oriented paradigm focuses on objects and operations on
objects.
This book’s approach is to teach problem solving and fundamental programming techniques
before object-oriented programming. This section shows how procedural and object-oriented
programming differ. You will see the benefits of object-oriented programming and learn to
use it effectively. We will improve the solution for the BMI problem introduced in Chapter 4
by using the object-oriented approach. From the improvements, you will gain insight into the
differences between procedural and object-oriented programming and see the benefits of
developing reusable code using objects and classes.
Listing 4.6, ComputeBMI.py, presents a program for computing body mass index. The
code as it is cannot be reused in other programs. To make it reusable, define a standalone
function to compute body mass index, as follows:
def getBMI(weight, height):
This function is useful for computing body mass index for a specified weight and height.
However, it has limitations. Suppose you need to associate the weight and height with a per-
son’s name and birth date. You could create separate variables to store these values, but these
values are not tightly coupled. The ideal way to couple them is to create an object that con-
tains them. Since these values are tied to individual objects, they should be stored in data
fields. You can define a class named BMI, as shown in Figure 7.10.
BMI
-name: str
-age: int
-weight: float
-height: float
BMI(name: str, age: int, weight:
float, height: float)

getBMI(): float
getStatus(): str
The name of the person.
The age of the person.
The weight of the person in pounds.
The height of the person in inches.
Creates a BMI object with the specified
name, age (the default is 20), weight,
and height.
Returns the BMI.
Returns the BMI status (e.g., Normal,
Overweight, etc.).
The get methods for these data fields
are provided in the class, but are omitted in
the UML diagram for brevity.
FIGURE 7.10 The BMI class encapsulates BMI data and methods.
Assume that the BMI class is available. Listing 7.9 is a test program that uses this class.
LISTING 7.9 UseBMIClass.py
1 from BMI import BMI
2
3 def main():
4
5 print(“The BMI for”, , “is”,bmi1.getName()
bmi1 = BMI(“John Doe”, 18, 145, 70)
import BMI class
create an object
invoke method
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234 Chapter 7 Objects and Classes
6 , )
7
8
9 print(“The BMI for”, , “is”,
10 , )
11
12 main() # Call the main function
bmi2.getStatus()bmi2.getBMI()
bmi2.getName()
bmi2 = BMI(“Peter King”, 50, 215, 70)
bmi1.getStatus()bmi1.getBMI()
create an object
invoke method
The BMI for John Doe is 20.81 Normal
The BMI for Peter King is 30.85 Obese
Line 4 creates an object bmi1 for John Doe and line 8 creates an object bmi2 for Peter
King. You can use the methods getName(), getBMI(), and getStatus() to return the
BMI information in a BMI object (lines 5 and 9).
The BMI class can be implemented as in Listing 7.10.
LISTING 7.10 BMI.py
1 class BMI:
2 def __init__(self, name, age, weight, height):
3 self.__name = name
4 self.__age = age
5 self.__weight = weight
6 self.__height = height
7
8
9 KILOGRAMS_PER_POUND = 0.45359237
10 METERS_PER_INCH = 0.0254
11 bmi = self.__weight * KILOGRAMS_PER_POUND / \
12 ((self.__height * METERS_PER_INCH) * \
13 (self.__height * METERS_PER_INCH))
14 return round(bmi * 100) / 100
15
16 def
17 bmi = self.getBMI()
18 if bmi < 18.5: 19 return "Underweight" 20 elif bmi < 25: 21 return "Normal" 22 elif bmi < 30: 23 return "Overweight" 24 else: 25 return "Obese" 26 27 def getName(self): 28 return self.__name 29 30 def getAge(self): 31 return self.__age 32 33 def getWeight(self): 34 return self.__weight 35 36 def getHeight(self): 37 return self.__height getStatus(self): def getBMI(self): initializer getBMI getStatus Chapter Summary 235 The mathematical formula for computing the BMI using weight and height is given in Section 4.9. The method getBMI() returns the BMI. Since the weight and height are data fields in the object, the getBMI() method can use these properties to compute the BMI for the object. The method getStatus() returns a string that interprets the BMI. The interpretation is also given in Section 4.9. This example demonstrates the advantages of the object-oriented paradigm over the proce- dural paradigm. The object-oriented approach combines the power of the procedural para- digm with an added dimension that integrates data with operations into objects. In procedural programming, data and operations are separate, and this methodology requires sending data to methods. Object-oriented programming places data and the opera- tions that pertain to them together in an object. This approach solves many of the problems inherent in procedural programming. The object-oriented programming approach organizes programs in a way that mirrors the real world, in which all objects are associated with both attributes and activities. Using objects improves software reusability and makes programs easier to develop and easier to maintain. Programming in Python involves thinking in terms of objects; a Python program can be viewed as a collection of cooperating objects. 7.18 Describe the differences between procedural and object-oriented paradigms. KEY TERMS procedural vs. object-oriented paradigms abstract data type (ADT) 229 accessor (getter) 227 actions 216 anonymous object 219 attributes 216 behavior 216 class 216 class abstraction 229 class encapsulation 229 class’s contract 229 client 221 constructor 218 data fields 216 data hiding 227 dot operator (.) 219 identity 216 initializer 217 instance 217 instance method 219 instance variable 220 instantiation 217 mutator (setter) 227 object-oriented programming (OOP) 216 private data fields 227 private method 227 property 216 state 216 Unified Modeling Language (UML) 222 CHAPTER SUMMARY 1. A class is a template, a blueprint, a contract, and a data type for objects. It defines the properties of objects and provides an initializer for initializing objects and methods for manipulating them. 2. The initializer is always named __init__. The first parameter in each method including the initializer in the class refers to the object that calls the method. By con- vention, this parameter is named self. 3. An object is an instance of a class. You use the constructor to create an object, and the dot operator (.) to access members of that object through its reference variable. ✓Point✓Check 236 Chapter 7 Objects and Classes 4. An instance variable or method belongs to an instance of a class. Its use is associated with individual instances. 5. Data fields in classes should be hidden to prevent data tampering and to make classes easy to maintain. 6. You can provide a get method or a set method to enable clients to see or modify the data. Colloquially, a get method is referred to as a getter (or accessor), and a set method as a setter (or mutator). TEST QUESTIONS Do test questions for this chapter online at www.cs.armstrong.edu/liang/py/test.html. PROGRAMMING EXERCISES Sections 7.2–7.3 7.1 (The Rectangle class) Following the example of the Circle class in Section 7.2, design a class named Rectangle to represent a rectangle. The class contains: ■ Two data fields named width and height. ■ A constructor that creates a rectangle with the specified width and height. The default values are 1 and 2 for the width and height, respectively. ■ A method named getArea() that returns the area of this rectangle. ■ A method named getPerimeter() that returns the perimeter. Draw the UML diagram for the class, and then implement the class. Write a test program that creates two Rectangle objects—one with width 4 and height 40 and the other with width 3.5 and height 35.7. Display the width, height, area, and perimeter of each rectangle in this order. Sections 7.4–7.7 7.2 (The Stock class) Design a class named Stock to represent a company’s stock that contains: ■ A private string data field named symbol for the stock’s symbol. ■ A private string data field named name for the stock’s name. ■ A private float data field named previousClosingPrice that stores the stock price for the previous day. ■ A private float data field named currentPrice that stores the stock price for the current time. ■ A constructor that creates a stock with the specified symbol, name, previous price, and current price. ■ A get method for returning the stock name. ■ A get method for returning the stock symbol. ■ Get and set methods for getting/setting the stock’s previous price. ■ Get and set methods for getting/setting the stock’s current price. ■ A method named getChangePercent() that returns the percentage changed from previousClosingPrice to currentPrice. Draw the UML diagram for the class, and then implement the class. Write a test program that creates a Stock object with the stock symbol INTC, the name Intel www.cs.armstrong.edu/liang/py/test.html Programming Exercises 237 Corporation, the previous closing price of 20.5, and the new current price of 20.35, and display the price-change percentage. 7.3 (The Account class) Design a class named Account that contains: ■ A private int data field named id for the account. ■ A private float data field named balance for the account. ■ A private float data field named annualInterestRate that stores the current interest rate. ■ A constructor that creates an account with the specified id (default 0), initial balance (default 100), and annual interest rate (default 0). ■ The accessor and mutator methods for id, balance, and annualInterestRate. ■ A method named getMonthlyInterestRate() that returns the monthly interest rate. ■ A method named getMonthlyInterest() that returns the monthly interest. ■ A method named withdraw that withdraws a specified amount from the account. ■ A method named deposit that deposits a specified amount to the account. Draw the UML diagram for the class, and then implement the class. (Hint: The method getMonthlyInterest() is to return the monthly interest amount, not the interest rate. Use this formula to calculate the monthly interest: balance * monthlyInterestRate. monthlyInterestRate is annualInterestRate / 12. Note that annualInterestRate is a percent (like 4.5%). You need to divide it by 100.) Write a test program that creates an Account object with an account id of 1122, a balance of $20,000, and an annual interest rate of 4.5%. Use the withdraw method to withdraw $2,500, use the deposit method to deposit $3,000, and print the id, balance, monthly interest rate, and monthly interest. 7.4 (The Fan class) Design a class named Fan to represent a fan. The class contains: ■ Three constants named SLOW, MEDIUM, and FAST with the values 1, 2, and 3 to denote the fan speed. ■ A private int data field named speed that specifies the speed of the fan. ■ A private bool data field named on that specifies whether the fan is on (the default is False). ■ A private float data field named radius that specifies the radius of the fan. ■ A private string data field named color that specifies the color of the fan. ■ The accessor and mutator methods for all four data fields. ■ A constructor that creates a fan with the specified speed (default SLOW), radius (default 5), color (default blue), and on (default False). Draw the UML diagram for the class and then implement the class. Write a test program that creates two Fan objects. For the first object, assign the maximum speed, radius 10, color yellow, and turn it on. Assign medium speed, radius 5, color blue, and turn it off for the second object. Display each object’s speed, radius, color, and on properties. *7.5 (Geometry: n-sided regular polygon) An n-sided regular polygon’s sides all have the same length and all of its angles have the same degree (i.e., the polygon is both equilateral and equiangular). Design a class named RegularPolygon that contains: ■ A private int data field named n that defines the number of sides in the polygon. ■ A private float data field named side that stores the length of the side. ■ A private float data field named x that defines the x-coordinate of the center of the polygon with default value 0. 238 Chapter 7 Objects and Classes ■ A private float data field named y that defines the y-coordinate of the center of the polygon with default value 0. ■ A constructor that creates a regular polygon with the specified n (default 3), side (default 1), x (default 0), and y (default 0). ■ The accessor and mutator methods for all data fields. ■ The method getPerimeter() that returns the perimeter of the polygon. ■ The method getArea() that returns the area of the polygon. The formula for computing the area of a regular polygon is Draw the UML diagram for the class, and then implement the class. Write a test pro- gram that creates three RegularPolygon objects, created using RegularPolygon(), using RegularPolygon(6, 4) and RegularPolygon(10, 4, 5.6, 7.8). For each object, display its perimeter and area. *7.6 (Algebra: quadratic equations) Design a class named QuadraticEquation for a quadratic equation The class contains: ■ The private data fields a, b, and c that represent three coefficients. ■ A constructor for the arguments for a, b, and c. ■ Three get methods for a, b, and c. ■ A method named getDiscriminant() that returns the discriminant, which is ■ The methods named getRoot1() and getRoot2() for returning the two roots of the equation using these formulas: These methods are useful only if the discriminant is nonnegative. Let these meth- ods return 0 if the discriminant is negative. Draw the UML diagram for the class, and then implement the class. Write a test program that prompts the user to enter values for a, b, and c and displays the result based on the discriminant. If the discriminant is positive, display the two roots. If the discriminant is 0, display the one root. Otherwise, display “The equation has no roots.” See Exercise 4.1 for sample runs. *7.7 (Algebra: linear equations) Design a class named LinearEquation for a system of linear equations: The class contains: ■ The private data fields a, b, c, d, e, and f with get methods. ■ A constructor with the arguments for a, b, c, d, e, and f. ■ Six get methods for a, b, c, d, e, and f. ■ A method named isSolvable() that returns true if is not 0. ■ The methods getX() and getY() that return the solution for the equation. Draw the UML diagram for the class, and then implement the class. Write a test program that prompts the user to enter a, b, c, d, e, and f and displays the result. If is 0, report that “The equation has no solution.” See Exercise 4.3 for sample runs. ad - bc ad - bc ax + by = e cx + dy = f x = ed - bf ad - bc y = af - ec ad - bc 2 * 2 2 * 2 r1 = -b + 2b2 - 4ac 2a and r2 = -b - 2b2 - 4ac 2a b2 - 4ac. ax2 + bx + x = 0. Area = n * s2 4 * tan¢p n ≤ . Programming Exercises 239 *7.8 (Stopwatch) Design a class named StopWatch. The class contains: ■ The private data fields startTime and endTime with get methods. ■ A constructor that initializes startTime with the current time. ■ A method named start() that resets the startTime to the current time. ■ A method named stop() that sets the endTime to the current time. ■ A method named getElapsedTime() that returns the elapsed time for the stop watch in milliseconds. Draw the UML diagram for the class, and then implement the class. Write a test program that measures the execution time of adding numbers from 1 to 1,000,000. **7.9 (Geometry: intersection) Suppose two line segments intersect. The two endpoints for the first line segment are (x1, y1) and (x2, y2) and for the second line segment are (x3, y3) and (x4, y4). Write a program that prompts the user to enter these four endpoints and displays the intersecting point. (Hint: Use the LinearEquation class from Exercise 7.7.) Enter the endpoints of the first line segment: Enter the endpoints of the second line segment: The intersecting point is: (1.0, 1.0) 0, 2.0, 2.0, 0 2.0, 2.0, 0, 0 *7.10 (The Time class) Design a class named Time. The class contains: ■ The private data fields hour, minute, and second that represent a time. ■ A constructor that constructs a Time object that initializes hour, minute, and second using the current time. ■ The get methods for the data fields hour, minute, and second, respectively. ■ A method named setTime(elapseTime) that sets a new time for the object using the elapsed time in seconds. For example, if the elapsed time is 555550 seconds, the hour is 10, the minute is 19, and the second is 12. Draw the UML diagram for the class, and then implement the class. Write a test program that creates a Time object and displays its hour, minute, and second. Your program then prompts the user to enter an elapsed time, sets its elapsed time in the Time object, and displays its hour, minute, and second. Here is a sample run: Current time is 12:41:6 Enter the elapsed time: The hour:minute:second for the elapsed time is 22:41:45 55550505 (Hint: The initializer will extract the hour, minute, and second from the elapsed time. The current elapsed time can be obtained using time.time(), as shown in Listing 2.7, ShowCurrentTime.py.) This page intentionally left blank MORE ON STRINGS AND SPECIAL METHODS Objectives ■ To learn how to create strings (§8.2.1). ■ To use the len, min, and max functions to obtain the length of a string or the smallest or largest character in a string (§8.2.2). ■ To access string elements by using the index operator ([]) (§8.2.3). ■ To get a substring from a larger string by using the slicing str[start : end] operator (§8.2.4). ■ To concatenate strings by using the + operator and to duplicate strings by using the * operator (§8.2.5). ■ To use the in and not in operators to determine whether a string is contained within another string (§8.2.6). ■ To compare strings by using comparison operators (==, !=, <, <=, >,
and >=) (§8.2.7).
■ To iterate characters in a string by using a for loop (§8.2.8).
■ To test strings by using the methods isalnum, isalpha, isdigit,
isidentifier, islower, isupper, and isspace (§8.2.9).
■ To search for substrings by using the methods endswith, startswith,
find, rfind, and count (§8.2.10).
■ To convert strings by using the methods capitalize, lower, upper,
title, swapcase, and replace (§8.2.11).
■ To strip whitespaces from the left and/or right of a string by using
the methods lstrip, rstrip, and strip (§8.2.12).
■ To format strings by using the methods center, ljust, rjust, and
format (§8.2.13).
■ To apply strings in the development of applications (CheckPalindrome,
HexToDecimalConversion) (§§8.3–8.4).
■ To define special methods for operators (§8.5).
■ To design the Rational class for representing rational numbers (§8.6).
CHAPTER
8

242 Chapter 8 More on Strings and Special Methods
>>> s1 = “Welcome”
>>> s2 = “Welcome”
>>> id(s1)
505408902
>>> id(s2)
505408902
>>>
str object for “Welcome”
s1
s2
: str
FIGURE 8.1 Strings with the same content are actually the same object.
8.1 Introduction
The focus of this chapter is on class design using Python’s str class as an example
and exploring the role of special methods in Python.
The preceding chapter introduced the important concepts of objects and classes. You learned
how to define classes as well as how to create and use objects. The str class is not only useful
for processing strings, but it is also a good example of class design. This class was introduced
in Chapter 3. We will discuss the str class in depth in this chapter.
The special methods play an important role in Python. This chapter will also introduce
special methods and operator overloading, and design classes using special methods.
8.2 The str Class
A str object is immutable; that is, its content cannot be changed once the string is
created.
In Chapter 7, you learned how to define the classes Loan and BMI and create objects from
these classes. You will frequently use the classes that come with the Python library to develop
programs. This section introduces the Python str class.
Strings are fundamental in computer science, and processing strings is a common task in
programming. Strings are the objects of the str class. So far, you have used strings in input
and output. The input function returns a string from the keyboard and the print function
displays a string on the monitor.
8.2.1 Creating Strings
You can create strings by using the constructor, as follows:
s1 = str() # Create an empty string object
s2 = str(“Welcome”) # Create a string object for Welcome
Python provides a simple syntax for creating a string object by using a string value. For
example,
s1 = ” ” # Same as s1 = str()
s2 = “Welcome” # Same as s2 = str(“Welcome”)
A string object is immutable: once it is created, its contents cannot be changed. To opti-
mize performance, Python uses one object for strings that have the same content. As
shown in Figure 8.1, both s1 and s2 refer to the same string object and have the same id
number.
This behavior is true for all immutable objects in the Python library. For example, int is
an immutable class. Two int objects with the same value actually share the same object, as
shown in Figure 8.2.
Key
Point
Key
Point
VideoNote
String methods

8.2 The str Class 243
len
max
min
1 >>> s = “Welcome”
2 >>> len(s)
3 7
4 >>> max(s)
5 ‘o’
6 >>> min(s)
7 ‘W’
8 >>>
>>> x = 10
>>> y = 10
>>> id(x)
35747680
>>> id(y)
35747680
>>>
int object for 10
x
y
: int
FIGURE 8.2 All immutable objects with the same content are stored in one object.
8.2.2 Functions for Strings
Several of Python’s built-in functions can be used with strings. You can use the len function
to return the number of the characters in a string, and the max and min functions (introduced
in Chapter 3) to return the largest or smallest character in a string. Here are some examples:
Since s has 7 characters, len(s) returns 7 (line 3). Note that the lowercase letters have a
higher ASCII value than the uppercase letters, so max(s) returns o (line 5) and min(s)
returns W (line 7).
Here is another example:
s = input(“Enter a string: “)
if len(s) % 2 == 0:
print(s, “contains an even number of characters”)
else:
print(s, “contains an odd number of characters”)
If you enter computer when running the code, it displays
computer contains an even number of characters
8.2.3 Index Operator [ ]
A string is a sequence of characters. A character in the string can be accessed through the
index operator using the syntax:
s[index]
The indexes are 0 based; that is, they range from 0 to len(s)-1, as shown in Figure 8.3. 0 based
s[10]
0 1 2 3 4 5 6 7 8 9 10
P r o g r a m m i n g
s[1]s[0]
s
FIGURE 8.3 The characters in a string can be accessed via an index operator.

244 Chapter 8 More on Strings and Special Methods
For example,
>>> s = “Welcome”
>>> for i in range(0, len(s), 2):
… print(s[i], end = ”)
Wloe
>>>
In the for loop, i is 0, 2, 4, and 6. So, s[0], s[2], s[4], and s[6] are displayed.
Python also allows the use of negative numbers as indexes to reference positions relative to
the end of the string. The actual position is obtained by adding the length of the string with the
negative index. For example,
1 >>> s = “Welcome”
2 >>> s[-1]
3 ‘e’
4 >>> s[-2]
5 ‘m’
6 >>>
In line 2, s[-1] is the same as s[-1 + len(s)], which is the last character in the string. In
line 4, s[-2] is the same as s[-2 + len(s)], which is the second last character in the string.
Note that since strings are immutable, you cannot change their contents. For example, the
following code is illegal:
s[2] = ‘A’
8.2.4 The Slicing Operator [start : end]
The slicing operator returns a slice of the string using the syntax s[start : end]. The slice
is a substring from index start to index end – 1. For example,
1 >>> s = “Welcome”
2 >>> s[1 : 4]
3 ‘elc’
s[1 : 4] returns a substring from index 1 to index 3.
The starting index or ending index may be omitted. In this case, by default the starting
index is 0 and the ending index is the last index. For example,
1 >>> s = “Welcome”
2 >>> s[ : 6]
3 ‘Welcom’
4 >>> s[4 : ]
5 ‘ome’
6 >>> s[1 : -1]
7 ‘elcom’
8 >>>
slicing operator

8.2 The str Class 245
In line 2, s[ : 6] is the same as s[0 : 6], which returns a substring from index 0 to
index 5. In line 4, s[4 : ] is the same as s[4 : 7], which returns a substring from index 4
to index 6. You can also use a negative index in slicing. For example, in line 6, s[1 : -1] is
the same as s[1 : -1 + len(s)].
Note
If index (i or j) in the slice operation s[i : j] is negative, replace the index with
len(s) + index. If j > len(s), j is set to len(s). If i >= j, the slice is
empty.
8.2.5 The Concatenation (+) and Repetition (*) Operators
You can join, or concatenate, two strings by using the concatenation operator (+). You can
also use the repetition operator (*) to concatenate the same string multiple times. Here are
some examples:
negative index
1 >>> s1 = “Welcome”
2 >>> s2 = “Python”
3 >>> s3 = s1 + ” to ” + s2
4 >>> s3
5 ‘Welcome to Python’
6 >>> s4 = 3 * s1
7 >>> s4
8 ‘WelcomeWelcomeWelcome’
9 >>> s5 = s1 * 3
10 >>> s5
11 ‘WelcomeWelcomeWelcome’
12 >>>
Note that 3 * s1 and s1 * 3 have the same effect (lines 6–11).
8.2.6 The in and not in Operators
You can use the in and not in operators to test whether a string is in another string. Here are
some examples:
>>> s1 = “Welcome”
>>> “come” in s1
True
>>> “come” not in s1
False
>>>
Here is another example:
s = input(“Enter a string: “)
if “Python” in s:
print(“Python”, “is in”, s)
repetition operator
concatenation operator

246 Chapter 8 More on Strings and Special Methods
>>> “green” == “glow”
False
>>> “green” != “glow”
True
>>> “green” > “glow”
True
>>> “green” >= “glow”
True
>>> “green” < "glow" False >>> “green” <= "glow" False >>> “ab” <= "abc" True >>>
Here is another example:
1 s1 = input(“Enter the first string: “)
2 s2 = input(“Enter the second string: “)
3 if s2 < s1: 4 s1, s2 = s2, s1 5 6 print("The two strings are in this order:", s1, s2) If you run the program by entering Peter and then John, s1 is Peter and s2 is John (lines 1–2). Since s2 < s1 is True (line 3), they are swapped in line 4. Therefore the pro- gram displays the following message in line 6. The two strings are in this order: John Peter else: print("Python", "is not in", s) If you run the program by entering Welcome to Python as the string, the program should display python is in Welcome to Python. 8.2.7 Comparing Strings You can compare strings by using the comparison operators (==,!=, >, >=, <, and <=, intro- duced in Section 4.2). Python compares strings by comparing their corresponding characters, and it does this by evaluating the characters’ numeric codes. For example, a is larger than A because the numeric code for a is larger than the numeric code for A. See Appendix B, The ASCII Character Set, to find the numeric codes for characters. Suppose you need to compare the strings s1 ("Jane") with s2 ("Jake"). The first two characters (J vs. J) from s1 and s2 are compared. Because they are equal, the second two characters (a vs. a) are compared. Because they are equal, the third two characters (n vs. k) are compared. Since n has a greater ASCII value than k, s1 is greater than s2. Here are some examples: 8.2 The str Class 247 for loop iterable 8.2.8 Iterating a String A string is iterable. This means that you can use a for loop to traverse all characters in the string sequentially. For example, the following code displays all the characters in the string s: for ch in s: print(ch) You can read the code as “for each character ch in s, print ch.” The for loop does not use indexes to access characters. However, you still have to use indexes if you wish to traverse the characters in the string in a different order. For example, the following code displays the characters at odd-numbered positions in the string: for i in range(0, len(s), 2): print(s[i]) The code uses variable i as the index for string s. i is initially 0, then increment by 2 suc- cessively, before it reaches or exceeds len(s). For each value i, s[i] is printed. 8.2.9 Testing Strings The str class has many useful methods. The methods in Figure 8.4 test the characters in the string. str isalnum(): bool isalpha(): bool isdigit(): bool isidentifier(): bool islower(): bool isupper(): bool isspace(): bool Returns True if characters in this string are alphanumeric and there is at least one character. Returns True if characters in this string are alphabetic and there is at least one character. Returns True if all characters in this string are lowercase lettters and there is at least one character. Returns True if all characters in this string are uppercase lettters and there is at least one character. Returns True if this string contains only number characters. Returns True if this string contains only whitespace characters. Returns True if this string is a Python identifier. FIGURE 8.4 The str class contains these methods for testing its characters. 1 >>> s = “welcome to python”
2 >>> s.isalnum()
3 False
4 >>> “Welcome”.isalpha()
5 True
6 >>> “2012”.isdigit()
7 True
8 >>> “first Number”.isidentifier()
9 False
Here are some examples of using the string testing methods:

248 Chapter 8 More on Strings and Special Methods
10 >>> s.islower()
11 True
12 >>> s.isupper()
13 False
14 >>> s.isspace()
15 False
16 >>>
s.isalnum() returns False (line 2), because s contains spaces, which are not letters or
numerals. Welcome contains all letters (line 4), so “Welcome”.isalpha() returns True.
Since 2012 contains all numerals, “2012”.isdigit() returns True (line 6). And because
first Number contains a space, it is not an identifier, so “first Number”.isidentifier()
returns False (line 8).
Here is another example:
s = “2011”
if s.isdigit():
print(s, “is a numeric string”)
The code displays
2011 is a numeric string
8.2.10 Searching for Substrings
You can search for a substring in a string by using the methods in Figure 8.5.
string search methods
1 >>> s = “welcome to python”
2 >>> s.endswith(“thon”)
3 True
4 >>> s.startswith(“good”)
5 False
6 >>> s.find(“come”)
str
endswith(s1: str): bool
startswith(s1: str): bool
find(s1): int
rfind(s1): int
count(substring): int
Returns True if the string ends with the substring s1.
Returns True if the string starts with the substring s1.
Returns the lowest index where s1 starts in this string, or –1 if
s1 is not found in this string.
Returns the highest index where s1 starts in this string, or –1 if
s1 is not found in this string.
Returns the number of non-overlapping occurrences of this
substring.
FIGURE 8.5 The str class contains these methods for searching substrings.
Here are some examples of using the string search methods:

8.2 The str Class 249
7 3
8 >>> s.find(“become”)
9 -1
10 >>> s.rfind(“o”)
11 17
12 >>> s.count(“o”)
13 3
14 >>>
Since come is found in string s at index 3, s.find(“come”) returns 3 (line 7). Because
the first occurrence of substring o from the right is at index 17, s.rfind(“o”) returns 17
(line 11). In line 8, s.find(“become”) returns -1, since become is not in s. In line 12,
s.count(“o”) returns 3, because o appears three times in s.
Here is another example:
s = input(“Enter a string: “)
if s.startswith(“comp”):
print(s, “begins with comp”)
if s.endswith(“er”):
print(s, “ends with er”)
print(‘e’, “appears”, s.count(‘e’), “time in”, s)
If you enter computer when running the code, it displays
computer begins with comp
computer ends with er
e appears 1 time in computer
8.2.11 Converting Strings
You can make a copy of a string by using the methods shown in Figure 8.6. These methods
let you control the capitalization of letters in the string’s copy, or to replace the string
entirely.
str
capitalize(): str
lower(): str
upper(): str
Returns a copy of this string with only the first character capitalized.
Returns a copy of this string with all letters converted to lowercase.
Returns a copy of this string with all letters converted to uppercase.
title(): str
swapcase(): str
replace(old, new): str
Returns a copy of this string with the first letter capitalized in each word.
Returns a copy of this string in which lowercase letters are converted to
uppercase and uppercase to lowercase.
Returns a new string that replaces all the occurrences of the old string
with a new string.
FIGURE 8.6 The str class contains these methods for converting letter cases in strings and for replacing one string with
another.

250 Chapter 8 More on Strings and Special Methods
The capitalize() method returns a copy of the string in which the first letter in the
string is capitalized. The lower() and upper() methods return a copy of the string in
which all letters are in lowercase or uppercase. The title() method returns a copy of the
string in which the first letter in each word is capitalized. The swapCase() method returns
a copy of the string in which the lowercase letters are converted to uppercase and the upper-
case letters are converted to lowercase. The replace(old, new) method returns a new
string that replaces the substring old with substring new. Here are some examples of using
these methods:
1 >>> s = “welcome to python”
2 >>> s1 = s.capitalize()
3 >>> s1
4 ‘Welcome to python’
5 >>> s2 = s.title()
6 >>> s2
7 ‘Welcome To Python’
8 >>> s = “New England”
9 >>> s3 = s.lower()
10 >>> s3
11 ‘new england’
12 >>> s4 = s.upper()
13 >>> s4
14 ‘NEW ENGLAND’
15 >>> s5 = s.swapcase()
16 >>> s5
17 ‘nEW eNGLAND’
18 >>> s6 = s.replace(“England”, “Haven”)
19 >>> s6
20 ‘New Haven’
21 >>> s
22 ‘New England’
23 >>>
Note
As stated earlier, a string is immutable. None of the methods in the str class changes
the contents of the string; instead, these methods create new strings. As shown in the
preceding script, s is still New England (lines 21–22) after applying the methods
s.lower(), s.upper(), s.swapcase(), and s.replace(“England”,
“Haven”).
8.2.12 Stripping Whitespace Characters from a String
You can use the methods in Figure 8.7 to strip whitespace characters from the front, end, or
both the front and end of a string. Recall that the characters ‘ ‘, \t, \f, \r, and \n are called
the whitespace characters (Section 3.5).

8.2 The str Class 251
Here are some examples of using the string stripping methods:
1 >>> s = ” Welcome to Python\t”
2 >>> s1 = s.lstrip()
3 >>> s1
4 ‘Welcome to Python\t’
5 >>> s2 = s.rstrip()
6 >>> s2
7 ‘ Welcome to Python’
8 >>> s3 = s.strip()
9 >>> s3
10 ‘Welcome to Python’
11 >>>
In line 2, s.lstrip() strips the whitespace characters in s from the left. In line 5,
s.rstrip() strips the whitespace characters in s from the right. In line 8, s.strip() strips
the whitespace characters in s from both the left and right.
Note
The stripping methods only strip the whitespace characters in the front and end of a
string. The whitespace characters surrounded by non-whitespace characters are not
stripped.
Tip
It is a good practice to apply the strip() method on an input string to ensure that any
unwanted whitespace characters at the end of the input are stripped.
8.2.13 Formatting Strings
You can use the methods in Figure 8.8 to return a formatted string.
str
lstrip(): str
rstrip(): str
strip(): str
Returns a string with the leading whitespace characters removed.
Returns a string with the trailing whitespace characters removed.
Returns a string with the starting and trailing whitespace characters
removed.
FIGURE 8.7 The str class contains these methods for stripping leading and trailing white-
space characters.
str
center(width): str
ljust(width): str
rjust(width): str
format(items): str
Returns a copy of this string centered in a field of the given width.
Returns a string left justified in a field of the given width.
Returns a string right justified in a field of the given width.
Formats a string.
FIGURE 8.8 The str class contains these formatting methods.

252 Chapter 8 More on Strings and Special Methods
Here are some examples that use the center, ljust, and rjust methods:
1 >>> s = “Welcome”
2 >>> s1 = s.center(11)
3 >>> s1
4 ‘ Welcome ‘
5 >>> s2 = s.ljust(11)
6 >>> s2
7 ‘Welcome ‘
8 >>> s3 = s.rjust(11)
9 >>> s3
10 ‘ Welcome’
11 >>>
In line 2, s.center(11) places s in the center of a string with 11 characters. In line 5,
s.ljust(11) places s at the left of a string with 11 characters. In line 8, s.rjust(11)
places s at the right of a string with 11 characters.
Section 3.6 introduced the format function for formatting a number or a string. The str
class has a format method, covered in Supplement II.C, which is very similar to the format
function.
8.1 Suppose that s1, s2, s3, and s4 are four strings, given as follows:
s1 = “Welcome to Python”
s2 = s1
s3 = “Welcome to Python”
s4 = “to”
What are the results of the following expressions?
a. s1 == s2
b. s2.count(‘o’)
c. id(s1) == id(s2)
d. id(s1) == id(s3)
e. s1 <= s4 f. s2 >= s4
g. s1 != s4
h. s1.upper()
i. s1.find(s4)
j. s1[4]
k. s1[4 : 8]
l. 4 * s4
m. len(s1)
n. max(s1)
o. min(s1)
p. s1[-4]
q. s1.lower()
r. s1.rfind(‘o’)
s. s1.startswith(“o”)
t. s1.endswith(“o”)
u. s1.isalpha()
v. s1 + s1
8.2 Suppose that s1 and s2 are two strings. Which of the following statements or expres-
sions are incorrect?
s1 = “programming 101”
s2 = “programming is fun”
s3 = s1 + s2
s3 = s1 – s2
s1 == s2
s1 >= s2
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8.3 Case Study: Checking Palindromes 253
i = len(s1)
c = s1[0]
t = s1[ : 5]
t = s1[5 : ]
8.3 What is the printout of the following code?
s1 = “Welcome to Python”
s2 = s1.replace(“o”,”abc”)
print(s1)
print(s2)
8.4 Let s1 be ” Welcome ” and s2 be ” welcome “. Write the code for the following
statements:
(a) Check whether s1 is equal to s2 and assign the result to a Boolean variable
isEqual.
(b) Check whether s1 is equal to s2, ignoring case, and assign the result to a
Boolean variable isEqual.
(c) Check whether s1 has the prefix AAA and assign the result to a Boolean variable b.
(d) Check whether s1 has the suffix AAA and assign the result to a Boolean variable b.
(e) Assign the length of s1 to a variable x.
(f) Assign the first character of s1 to a variable x.
(g) Create a new string s3 that combines s1 with s2.
(h) Create a substring of s1 starting from index 1.
(i) Create a substring of s1 from index 1 to index 4.
(j) Create a new string s3 that converts s1 to lowercase.
(k) Create a new string s3 that converts s1 to uppercase.
(l) Create a new string s3 that trims whitespace characters on both ends of s1.
(m) Replace e with E in s1.
(n) Assign the index of the first occurrence of character e in s1 to a variable x.
(o) Assign the index of the last occurrence of string abc in s1 to a variable x.
8.5 Does any method in the string object change the contents of the string?
8.6 Suppose string s is an empty string; what is len(s)?
8.7 How do you determine whether a character is in lowercase or uppercase?
8.8 How do you determine whether a character is alphanumeric?
8.3 Case Study: Checking Palindromes
This section presents a program that checks whether a string is a palindrome.
A string is a palindrome if it reads the same forward and backward. The words “mom,” “dad,”
and “noon,” for instance, are all palindromes.
The problem is to write a program that prompts the user to enter a string and reports
whether the string is a palindrome. One solution is to have the program check whether the first
character in the string is the same as the last character. If so, then the program can check
whether the second character is the same as the second-to-last character. This process contin-
ues until a mismatch is found or all the characters in the string are checked, except for the
middle character if the string has an odd number of characters.
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254 Chapter 8 More on Strings and Special Methods
To implement this idea, use two variables, say low and high, to denote the position of two
characters at the beginning and the end in a string s, as shown in Listing 8.1 (lines 13 and 16).
Initially, low is 0 and high is len(s) – 1. If the two characters at these positions match,
increment low by 1 and decrement high by 1 (lines 22–23). This process continues until
(low >= high) or a mismatch is found.
LISTING 8.1 CheckPalindrome.py
1 def main():
2 # Prompt the user to enter a string
3 .strip()
4
5 if :
6 print(s, “is a palindrome”)
7 else:
8 print(s, ” is not a palindrome”)
9
10 # Check if a string is a palindrome
11 def isPalindrome( ):
12 # The index of the first character in the string
13 low = 0
14
15 # The index of the last character in the string
16 high = – 1
17
18 while low < high: 19 if : 20 return False # Not a palindrome 21 22 low += 1 23 high -= 1 24 25 return True # The string is a palindrome 26 27 main() # Call the main function s[low] != s[high] len(s) s isPalindrome(s) s = input("Enter a string: ")input string low index high index update indexes Enter a string: noon is a palindrome noon Enter a string: moon is not a palindrome moon The program prompts the user to enter a string into s (line 3), which uses the strip() method to remove any starting and ending whitespace characters, and then invokes isPalindrome(s) to determine whether s is a palindrome (line 5). 8.4 Case Study: Converting Hexadecimals to Decimals This section presents a program that converts a hexadecimal number into a decimal number. Section 6.8 illustrates a program that converts a decimal number to hexadecimal format. How do you convert a hex number into a decimal? Key Point 8.4 Case Study: Converting Hexadecimals to Decimals 255 Given a hexadecimal number the equivalent decimal value is For example, the hex number AB8C is Our program will prompt the user to enter a hex number as a string and convert it into a decimal by using the following function: def hexToDecimal(hex): A brute-force approach is to convert each hex character into a decimal number, multiply it by for a hex digit at the i’s position, and add all the items together to obtain the equivalent decimal value for the hex number. Note that: This observation, known as Honer’s algorithm, leads to the following code for converting a hex string to a decimal number: decimalValue = 0 for i in range(len(hex)): hexChar = hex[i] decimalValue = decimalValue * 16 + hexCharToDecimal(hexChar) The following is a trace of the algorithm for hex number AB8C. = (c ((hn * 16 + hn-1) * 16 + hn-2) * 16 + c + h1) * 16 + h0 hn * 16n + hn-1 * 16n-1 + hn-2 * 16n-2 + c+ h1 * 161 + h0 * 160 16i 10 * 163 + 11 * 162 + 8 * 161 + 12 * 160 = 43916 hn * 16n + hn-1 * 16n-1 + hn-2 * 16n-2 + c + h2 * 162 + h1 * 161 + h0 * 160 hnhn-1hn-2 c h2h1h0, i hexChar hexCharToDecimal (hexChar) DecimalValue before the loop 0 after the 1st iteration 0 A 10 10 after the 2nd iteration 1 B 11 10 * 16 + 11 after the 3rd iteration 2 8 8 (10 * 16 + 11) * 16 + 8 after the 4th iteration 3 C 12 ((10 * 16 + 11) * 16 + 8) * 16 + 12 Listing 8.2 shows the complete program. LISTING 8.2 HexToDecimalConversion.py 1 def main(): 2 # Prompt the user to enter a hex number 3 hex = input("Enter a hex number: ").strip() 4 5 6 if decimal == None: 7 print("Incorrect hex number") 8 else: decimal = hexToDecimal(hex.upper()) input string hex to decimal 256 Chapter 8 More on Strings and Special Methods cannot convert hex char to decimal Enter a hex number: The decimal value for hex number AB8C is 43916 AB8C Enter a hex number: The decimal value for hex number af71 is 44913 af71 Enter a hex number: Incorrect hex number ax71 The program reads a string from the console (line 3) and invokes the hexToDecimal func- tion to convert a hex string to a decimal number (line 5). The characters can be entered in either lowercase or uppercase, and the program converts them to uppercase before invoking the hexToDecimal function. The hexToDecimal function is defined in lines 12–22 to return an integer. The length of the string is determined by invoking len(hex) in line 14. This function returns None for an incorrect hex number (line 20). The hexCharToDecimal function is defined in lines 24–28 to return a decimal value for a hex character. The character can be in either lowercase or uppercase. Invoking hex.upper() converts the characters to uppercase. When invoking hexCharToDecimal(ch), the character ch is already in uppercase. If ch is a letter between A and F, the program returns a decimal value 10 + ord(ch) – ord('A') (line 26). If ch is a digit, the program returns a decimal value ord(ch) – ord('0') (line 28). None 9 print("The decimal value for hex number", 10 hex, "is", decimal) 11 12 13 decimalValue = 0 14 for i in range(len(hex)): 15 ch = hex[i] 16 if 'A' <= ch <= 'F' or '0' <= ch <= '9': 17 decimalValue = decimalValue * 16 + \ 18 hexCharToDecimal(ch) 19 else: 20 return None 21 22 return decimalValue 23 24 25 if 'A' <= ch <= 'F': 26 return 10 + ord(ch) - ord('A') 27 else: 28 return ord(ch) - ord('0') 29 30 main() # Call the main function def hexCharToDecimal(ch): def hexToDecimal(hex): 8.5 Operator Overloading and Special Methods 257 [] operator + operator < operator operator overloading 8.5 Operator Overloading and Special Methods Python allows you to define special methods for operators and functions to perform common operations. These methods are named in a specific way for Python to recognize the association. In the preceding sections, you learned how to use operators for string operations. You can use the + operator to concatenate two strings, the * operator to concatenate the same string multi- ple times, the relational operators (==, !=, <, <=, >, and >=) to compare two strings, and the
index operator [] to access a character. For example,
1 s1 = “Washington”
2 s2 = “California”
3 print(“The first character in s1 is”, )
4 print(“s1 + s2 is”, )
5 print(“s1 < s2?", ) The operators are actually methods defined in the str class. Defining methods for opera- tors is called operator overloading. Operator overloading allows the programmer to use the built-in operators for user-defined methods. Table 8.1 lists the mapping between the operators and methods. You name these methods with two starting and ending underscores so Python will recognize the association. For example, to use the + operator as a method, you would define a method named __add__. Note that these methods are not private, because they have two ending underscores in addition to the two starting underscores. Recall that the initializer in a class is named __init__, which is a special method for initializing an object. For example, you can rewrite the preceding code using the methods as follows: 1 s1 = "Washington" 2 s2 = "California" 3 print("The first character in s1 is", )s1.__getitem__(0) s1 < s2 s1 + s2 s1[0] TABLE 8.1 Operator Overloading: Operators and Special Methods Operator/Function Method Description + __add__(self, other) Addition * __mul__(self, other) Multiplication - __sub__(self, other) Subtraction / __truediv__(self, other) Division % __mod__(self, other) Remainder < __lt__(self, other) Less than <= __le__(self, other) Less than or equal to == __eq__(self, other) Equal to != __ne__(self, other) Not equal to > __gt__(self, other) Greater than
>= __ge__(self, other) Greater than or equal to
[index] __getitem__(self, index) Index operator
in __contains__(self, value) Check membership
len __len__(self) The number of elements
str __str__(self) The string representation
__getitem__ method
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258 Chapter 8 More on Strings and Special Methods
4 print(“s1 + s2 is”, )
5 print(“s1 < s2?", ) s1.__getitem__(0) is the same as s1[0], s1.__add__(s2) is the same as s1 + s2, and s1.__lt__(s2) is the same as s1 < s2. Now you can see the advantages of oper- ator overloading. Using operators greatly simplifies programs, making them easier to read and maintain. Python supports the in operator, which can be used to determine whether a character is in a string or an element is a member of a container. The corresponding method is named __contains__(self, e). You can use the method __contains__ or the in operator to see if a character is in a string, as shown in the following code: 1 s1 = "Washington" 2 print("Is W in s1?", ) 3 print("Is W in s1?", ) W in s1 is the same as s1.__contains__('W'). If a class defines the __len__(self) method, Python allows you to invoke the method using a convenient syntax as a function call. For example, the __len__ method is defined in the str class, which returns the number of characters in a string. You can use the method __len__ or the function len to get the number of characters in a string, as shown in the fol- lowing code: 1 s1 = "Washington" 2 print("The length of s1 is", ) 3 print("The length of s1 is", ) len(s1) is the same as s1.__len__(). Many of the special operators are defined in Python built-in types such as int and float. For example, suppose i is 3 and j is 4. i.__add__(j) is the same as i + j and i.__sub__(j) is the same as i – j. Note You can pass an object to invoke print(x). This is equivalent to invoking print(x.__str__()) or print(str(x)). Note The comparison operators <, <=, ==, !=, >, and >= can also be implemented using the
__cmp__ (self, other) method. This method returns a negative integer if self
< other, zero if self == other, and a positive integer if self > other. For two
objects a and b, a < b calls a.__lt__(b) if the __lt__ is available. If not, the __cmp__ method is called to determine the order. 8.9 What is operator overloading? 8.10 What are the special methods for the operators +, -, *, /, %, ==, !=, <, <=, >,
and >=?
8.6 Case Study: The Rational Class
This section shows how to design the Rational class for representing and processing
rational numbers.
A rational number has a numerator and a denominator in the form a/b, where a is the numera-
tor and b is the denominator. For example, 1/3, 3/4, and 10/4 are rational numbers.
s1.__len__()
len(s1)
s1.__contains__(‘W’)
‘W’ in s1
s1.__lt__(s2)
s1.__add__(s2)__add__ method
__lt__ method
__contains__ method
in operator
in operator
__contains__ method
__len__ method
len method
len function
__len__ method
print object
Key
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VideoNote
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Define classes

A rational number cannot have a denominator of 0, but a numerator of 0 is fine. Every inte-
ger i is equivalent to a rational number i/1. Rational numbers are used in exact computations
involving fractions—for example, 1/3 0.33333…. This number cannot be precisely
represented in floating-point format using data type float. To obtain the exact result, we
must use rational numbers.
Python provides data types for integers and floating-point numbers but not for rational
numbers. This section shows how to design a class for rational numbers.
A rational number can be represented using two data fields: numerator and
denominator. You can create a rational number with a specified numerator and denominator
or create a default rational number with the numerator 0 and denominator 1. You can add,
subtract, multiply, divide, and compare rational numbers. You can also convert a rational
number into an integer, floating-point value, or string. The UML class diagram for the
Rational class is given in Figure 8.9.
=
Rational
-numerator: int
-denominator: int
Rational(numerator = 0: int,
denominator = 1: int)
_ _add_ _(secondRational:
Rational): Rational
_ _sub_ _(secondRational:
Rational): Rational
_ _mul_ _(secondRational:
Rational): Rational
_ _truediv_ _(secondRational:
Rational): Rational
_ _lt_ _(secondRational:
Rational): bool
_ _int_ _(): int
_ _float_ _(): float
_ _str_ _(): str
_ _getitem_ _(i)
Also _ _le_ _, _ _eq_ _, _ _ne_ _,
_ _gt_ _, _ _ge_ _ are supported
The numerator of this rational number.
The denominator of this rational number.
Creates a rational number with a specified numerator (default 0)
and denominator (default 1).
Compares this rational number with another.
Returns the addition of this rational number with another.
Returns the subtraction of this rational number with another.
Returns the multiplication of this rational number with another.
Returns the division of this rational number with another.
Returns the numerator divided by denominator as an integer.
Returns the numerator divided by denominator as a float.
Returns numerator using [0] and denominator using [1].
Returns a string in the form “numerator/denominator.” Returns
the numerator if the denominator is 1.
FIGURE 8.9 The UML diagram for the properties, initializer, and methods of the Rational class.
There are many equivalent rational numbers; for example, 1/3 2/6 3/9
4/12. For convenience, 1/3 is used to represent all rational numbers that are equivalent to
1/3. The numerator and the denominator of 1/3 have no common divisor except 1, so 1/3 is
said to be in lowest terms.
To reduce a rational number to its lowest terms, you need to find the greatest common divi-
sor (GCD) of the absolute values of its numerator and denominator and then divide both
numerator and denominator by this value. You can use the function for computing the GCD of
two integers n and d, as suggested in Listing 5.8, GreatestCommonDivisor.py. The numerator
and denominator in a Rational object are reduced to their lowest terms.
===
8.6 Case Study: The Rational Class 259

260 Chapter 8 More on Strings and Special Methods
As usual, we first write a test program to create Rational objects and test the functions in
the Rational class. Listing 8.3 is a test program.
LISTING 8.3 TestRationalClass.py
1 import Rational
2
3 # Create and initialize two rational numbers r1 and r2.
4 r1 =
5 r2 = Rational.Rational(2, 3)
6
7 # Display results
8 print(r1, “+”, r2, “=”, )
9 print(r1, “-“, r2, “=”, )
10 print(r1, “*”, r2, “=”, )
11 print(r1, “/”, r2, “=”, )
12
13 print(r1, “>”, r2, “is”, )
14 print(r1, “>=”, r2, “is”, )
15 print(r1, “<", r2, "is", ) 16 print(r1, "<=", r2, "is", ) 17 print(r1, "==", r2, "is", ) 18 print(r1, "!=", r2, ”is", ) 19 20 print("int(r2) is", ) 21 print("float(r2) is", ) 22 23 print("r2[0] is", ) 24 print("r2[1] is", )r2[1] r2[0] float(r2) int(r2) r1 != r2 r1 == r2 r1 <= r2 r1 < r2 r1 >= r2
r1 > r2
r1 / r2
r1 * r2
r1 – r2
r1 + r2
Rational.Rational(4, 2)
import Rational
create Rational
invoke add
invoke subtract
invoke multiply
invoke divide
compare two numbers
get int value
index operator
2 + 2/3 = 8/3
2 – 2/3 = 4/3
2 * 2/3 = 4/3
2 / 2/3 = 3
2 > 2/3 is True
2 >= 2/3 is True
2 < 2/3 is False 2 <= 2/3 is False 2 == 2/3 is False 2 != 2/3 is True int(r2) is 0 float(r2) is 0.6666666666666666 r2[0] is 2 r2[1] is 3 The program creates two rational numbers, r1 and r2 (lines 4 and 5), and displays the results of r1 + r2, r1 - r2, r1 * r2, and r1 / r2 (lines 8–11). r1 + r2 is equivalent to r1._ _add__(r2). The print(r1) function prints the string returned from str(r1). Invoking str(r1) returns a string representation for the rational number r1, which is the same as invoking r1.__str__(). Invoking int(r2) (line 20) returns an integer for the rational number r2, which is the same as invoking r2.__int__(). Invoking float(r2) (line 21) returns a float for the rational number r2, which is the same as invoking r2.__float__(). 8.6 Case Study: The Rational Class 261 gcd initialize numerator initialize denominator initializer add a b + c d = ad + bc bd subtract a b - c d = ad - bc bd multiply a b * c d = ac bd divide a b � c d = ad bc Invoking r2[0] (line 23) is the same as invoking r2._ _getitem__(0), which returns the numerator from r2. The Rational class is implemented in Listing 8.4. LISTING 8.4 Rational.py 1 class Rational: 2 3 divisor = gcd(numerator, denominator) 4 self.__numerator = (1 if denominator > 0 else -1) \
5 * int(numerator / divisor)
6 self.__denominator = int(abs(denominator) / divisor)
7
8 # Add a rational number to this rational number
9
10 n = self.__numerator * secondRational[1] + \
11 self.__denominator * secondRational[0]
12 d = self.__denominator * secondRational[1]
13 return Rational(n, d)
14
15 # Subtract a rational number from this rational number
16
17 n = self.__numerator * secondRational[1] – \
18 self.__denominator * secondRational[0]
19 d = self.__denominator * secondRational[1]
20 return Rational(n, d)
21
22 # Multiply a rational number by this rational number
23
24 n = self.__numerator * secondRational[0]
25 d = self.__denominator * secondRational[1]
26 return Rational(n, d)
27
28 # Divide a rational number by this rational number
29
30 n = self.__numerator * secondRational[1]
31 d = self.__denominator * secondRational[0]
32 return Rational(n, d)
33
34 # Return a float for the rational number
35
36 return self.__numerator / self.__denominator
37
38 # Return an integer for the rational number
39
40 return int(self.__float__())
41
42 # Return a string representation
43
44 if self.__denominator == 1:
45 return str(self.__numerator)
46 else:
47 return str(self.__numerator) + “/”, self.__denominator)
48
49
50 return self.__cmp__(secondRational) < 0 51 52 def __le__(self, secondRational): 53 return self.__cmp__(secondRational) <= 0 54 def __lt__(self, secondRational): def __str__(self): def __int__(self): def __float__(self): def __truediv__(self, secondRational): def __mul__(self, secondRational): def __sub__(self, secondRational): def __add__(self, secondRational): def __init__(self, numerator = 1, denominator = 0): float int str lt 262 Chapter 8 More on Strings and Special Methods 55 def __gt__(self, secondRational): 56 return self.__cmp__(secondRational) > 0
57
58 def __ge__(self, secondRational):
59 return self.__cmp__(secondRational) >= 0
60
61 # Compare two numbers
62
63 temp = self.__sub__(secondRational)
64 if temp[0] > 0:
65 return 1
66 elif temp[0] < 0: 67 return -1 68 else: 69 return 0 70 71 # Return numerator and denominator using an index operator 72 def __getitem__(self, index): 73 if index == 0: 74 return self.__numerator 75 else: 76 return self.__denominator 77 78 def gcd(n, d): 79 n1 = abs(n) 80 n2 = abs(d) 81 gcd = 1 82 83 k = 1 84 while k <= n1 and k <= n2: 85 if n1 % k == 0 and n2 % k == 0: 86 gcd = k 87 k += 1 88 89 return gcd The rational number is encapsulated in a Rational object. Internally, a rational number is represented in its lowest terms (lines 4–6), and the numerator determines its sign (line 4). The denominator is always positive (line 6). The data fields numerator and denominator are defined as private with two leading underscores. The gcd() is not a member method in the Rational class, but a function defined in the Rational module (Rational.py) (lines 78–89). Two Rational objects can interact with each other to perform addition, subtraction, mul- tiplication, and division operations. These methods return a new Rational object (lines 9–32). Note that secondRational[0] refers to the numerator of secondRational and secondRational[1] refers to the denominator of secondRational. The use of the index operator is supported by the __getitem(i)__ method (lines 72–76), which returns the numerator and denominator of the rational number based on the index. The __cmp__(secondRational) method (lines 62–69) compares this rational number to the other rational number. It first subtracts the second rational from this rational and saves the result in temp (line 63). The method returns -1, 0, or 1 if temp’s numerator is less than, equal to, or greater than 0. The comparison method __lt__, __le__, __gt__, and __ge__ are implemented using the __cmp__ method (lines 49–59). Note that the methods __ne__ and __eq__ are not implemented explicitly, but they are implicitly implemented by Python if the __cmp__ method is available. You have used the str, int, and float functions to convert an object to a str, int, or float. The methods __str__(), __int__(), and __float__() are implemented in the def __cmp__(self, secondRational):cmp getitem gcd Programming Exercises 263 Rational class (lines 35–47) to return a str object, int object, or float object from a Rationalobject. 8.11 Will the program work if you replace line 63 in Rational.py with the following code? temp = self – secondRational 8.12 Will the program work if you replace the __str__ method in lines 43–47 as follows? def __str__(self): if self.__denominator == 1: return str(self[0]) else: return str(self[0]) + "/" + str(self[1]) KEY TERMS concatenation operator 245 index operator 260 iterable 247 operator overloading 257 repetition operator 245 slicing operator 244 CHAPTER SUMMARY 1. A string object is immutable. Its contents cannot be changed. 2. You can use the Python functions len, min, and max to return the length of a string, and the minimum and maximum elements in a string. 3. You can use the index operator [] to reference an individual character in a string. 4. You can use the concatenate operator + to concatenate two strings, the repetition operator * to duplicate strings, the slicing operator [ : ] to get a substring, and the in and not in operators to check whether a character is in a string. 5. The comparison operators (==, !=, <, <=, >, and >=) can be used to compare two strings.
6. You can use a for loop to iterate all characters in a string.
7. You can use the methods such as endswith, startswith, isalpha, islower,
isupper, lower, upper, find, count, replace, and strip on a string object.
8. You can define special methods for overloading the operators.
TEST QUESTIONS
Do test questions for this chapter online at www.cs.armstrong.edu/liang/py/test.html.
PROGRAMMING EXERCISES
Sections 8.2–8.4
*8.1 (Check SSN) Write a program that prompts the user to enter a Social Security
number in the format ddd-dd-dddd, where d is a digit. The program displays
Valid SSN for a correct Social Security number or Invalid SSN otherwise.
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264 Chapter 8 More on Strings and Special Methods
**8.2 (Check substrings) You can check whether a string is a substring of another string
by using the find method in the str class. Write your own function to implement
find. Write a program that prompts the user to enter two strings and then checks
whether the first string is a substring of the second string.
**8.3 (Check password ) Some Web sites impose certain rules for passwords. Write a
function that checks whether a string is a valid password. Suppose the password
rules are as follows:
■ A password must have at least eight characters.
■ A password must consist of only letters and digits.
■ A password must contain at least two digits.
Write a program that prompts the user to enter a password and displays valid
password if the rules are followed or invalid password otherwise.
8.4 (Occurrences of a specified character) Write a function that finds the number of
occurrences of a specified character in a string using the following header:
def count(s, ch):
The str class has the count method. Implement your method without using the
count method. For example, count(“Welcome”, ‘e’) returns 2. Write a test
program that prompts the user to enter a string followed by a character and dis-
plays the number of occurrences of the character in the string.
**8.5 (Occurrences of a specified string) Write a function that counts the occurrences of a
specified non-overlapping string s2 in another string s1 using the following header:
def count(s1, s2):
For example, count(“system error, syntax error”, “error”) returns
2. Write a test program that prompts the user to enter two strings and displays the
number of occurrences of the second string in the first string.
*8.6 (Count the letters in a string) Write a function that counts the number of letters in
a string using the following header:
def countLetters(s):
Write a test program that prompts the user to enter a string and displays the num-
ber of letters in the string.
*8.7 (Phone keypads) The international standard letter/number mapping for telephones is:
Write a function that returns a number, given an uppercase letter, as follows:
def getNumber(uppercaseLetter):
Write a test program that prompts the user to enter a phone number as a string. The
input number may contain letters. The program translates a letter (uppercase or
lowercase) to a digit and leaves all other characters intact. Here is a sample run of
the program:

Programming Exercises 265
Enter a string:
1-800-3569377
1-800-Flowers
Enter a string:
18003569377
1800flowers
*8.8 (Binary to decimal ) Write a function that parses a binary number as a string into a
decimal integer. Use the function header:
def binaryToDecimal(binaryString):
For example, binary string 10001 is 17
So, binaryToDecimal(“10001”) returns 17.
Write a test program that prompts the user to enter a binary string and displays the
corresponding decimal integer value.
**8.9 (Binary to hex) Write a function that parses a binary number into a hex number.
The function header is:
def binaryToHex(binaryValue):
Write a test program that prompts the user to enter a binary number and displays
the corresponding hexadecimal value.
**8.10 (Decimal to binary) Write a function that parses a decimal number into a binary
number as a string. Use the function header:
def decimalToBinary(value):
Write a test program that prompts the user to enter a decimal integer value and dis-
plays the corresponding binary value.
Section 8.5
*8.11 (Reverse a string) Write a function that reverses a string. The header of the func-
tion is:
def reverse(s):
Write a test program that prompts the user to enter a string, invokes the reverse
function, and displays the reversed string.
*8.12 (Bioinformatics: find genes) Biologists use a sequence of letters A, C, T, and G to
model a genome. A gene is a substring of a genome that starts after a triplet ATG
and ends before a triplet TAG, TAA, or TGA. Furthermore, the length of a gene
string is a multiple of 3 and the gene does not contain any of the triplets ATG, TAG,
TAA, and TGA. Write a program that prompts the user to enter a genome and dis-
plays all genes in the genome. If no gene is found in the input sequence, the pro-
gram displays no gene is found. Here are the sample runs:
+ 1 = 17).
(1 * 24 + 0 * 23 + 0 * 22 + 0 * 2
Enter a genome string:
TTT
GGGCGT
TTATGTTTTAAGGATGGGGCGTTAGTT

266 Chapter 8 More on Strings and Special Methods
Enter a genome string:
no gene is found
TGTGTGTATAT
*8.13 (Longest common prefix) Write a method that returns the longest common prefix
of two strings. For example, the longest common prefix of distance and
disinfection is dis. The header of the method is:
def prefix(s1, s2)
If the two strings have no common prefix, the method returns an empty string.
Write a main method that prompts the user to enter two strings and displays their
common prefix.
**8.14 (Financial: credit card number validation) Rewrite Exercise 6.29 using a string
input for a credit card number.
**8.15 (Business: check ISBN-10) An ISBN-10 (International Standard Book Number)
consists of 10 digits: The last digit, is a checksum,
which is calculated from the other nine digits using the following formula:
If the checksum is 10, the last digit is denoted as X, according to the ISBN con-
vention. Write a program that prompts the user to enter the first 9 digits as a string
and displays the 10-digit ISBN (including leading zeros). Your program should
read the input as a string. Here are sample runs:
+ d6 * 6 + d7 * 7 + d8 * 8 + d9 * 9) % 11
(d1 * 1 + d2 * 2 + d3 * 3 + d4 * 4 + d5 * 5
d10,d1d2d3d4d5d6d7d8d9d10.
**8.16 (Business: check ISBN-13) ISBN-13 is a new standard for identifying books. It
uses 13 digits: The last digit, is a checksum,
which is calculated from the other digits using the following formula:
If the checksum is 10, replace it with 0. Your program should read the input as a
string. Here are sample runs:
10 – (d1 + 3d2 + d3 + 3d4 + d5 + 3d6 + d7 + 3d8 + d9 + 3d10 + d11 + 3d12) % 10
d13,d1d2d3d4d5d6d7d8d9d10d11d12d13.
Enter the first 9 digits of an ISBN-10 as a string:
The ISBN-10 number is 0136012671
013601267
Enter the first 9 digits of an ISBN-10 as a string:
The ISBN-10 number is 013031997X
013031997
Enter the first 12 digits of an ISBN-13 as a string:
The ISBN-13 number is 9780132130806
978013213080

Programming Exercises 267
Enter two points x1, y1, x2, y2:
The distance between the two points is 23.97
The two points are not near each other
2.1, 2.3, 19.1, 19.2
Enter two points x1, y1, x2, y2:
The distance between the two points is 1.91
The two points are near each other
2.1, 2.3, 2.3, 4.2
Enter the first 12 digits of an ISBN-13 as a string:
The ISBN-13 number is 9780132130790
978013213079
Section 8.6
**8.17 (The Point class) Design a class named Point to represent a point with x- and y-
coordinates. The class contains:
■ Two private data fields x and y that represent the coordinates with get methods.
■ A constructor that constructs a point with specified coordinates with default
point (0, 0).
■ A method named distance that returns the distance from this point to another
point of the Point type.
■ A method named isNearBy(p1) that returns true if point p1 is close to this
point. Two points are close if their distance is less than 5.
■ Implement the __str__ method to return a string in the form (x, y).
Draw the UML diagram for the class, and then implement the class. Write a test
program that prompts the user to enter two points, displays the distance between
them, and indicates whether they are near each other. Here are sample runs:
*8.18 (Geometry: The Circle2D class) Define the Circle2D class that contains:
■ Two private float data fields named x and y that specify the center of the circle
with get/set methods.
■ A private data field radius with get/set methods.
■ A constructor that creates a circle with the specified x, y, and radius. The
default values are all 0.
■ A method getArea() that returns the area of the circle.
■ A method getPerimeter() that returns the perimeter of the circle.
■ A method containsPoint(x, y) that returns True if the specified point (x,
y) is inside this circle (see Figure 8.10a).
■ A method contains(circle2D) that returns True if the specified circle is
inside this circle (see Figure 8.10b).
■ A method overlaps(circle2D) that returns True if the specified circle
overlaps with this circle (see Figure 8.10c).
■ Implement the __contains__(another) method that returns True if this
circle is contained in another circle.

268 Chapter 8 More on Strings and Special Methods
Draw the UML diagram for the class, and then implement the class. Write a test
program that prompts the user to enter two circles with x- and y-coordinates and the
radius, creates two Circle2D objects c1 and c2, displays their areas and perime-
ters, and displays the result of c1.containsPoint(c2.getX(), c2.getY()),
c1.contains(c2), and c1.overlaps(c2). Here is a sample run:
Enter x1, y1, radius1:
Enter x2, y2, radius2:
Area for c1 is 314.1592653589793
Perimeter for c1 is 62.83185307179586
Area for c2 is 314.1592653589793
Perimeter for c2 is 62.83185307179586
c1 contains the center of c2? True
c1 contains c2? False
c1 overlaps c2? True
9, 1.3, 10
5, 5.5, 10
(a) (b) (c)
p
FIGURE 8.10 (a) A point is inside the circle. (b) A circle is inside another circle. (c) A circle
overlaps another circle.
*8.19 (Geometry: The Rectangle2D class) Define the Rectangle2D class that
contains:
■ Two float data fields named x and y that specify the center of the rectangle
with get/set methods. (Assume that the rectangle sides are parallel to x- or y-
axes.)
■ The data fields width and height with get/set methods.
■ A constructor that creates a rectangle with the specified x, y, width, and
height with default values 0.
■ A method getArea() that returns the area of the rectangle.
■ A method getPerimeter() that returns the perimeter of the rectangle.
■ A method containsPoint(x, y) that returns True if the specified point (x,
y) is inside this rectangle (see Figure 8.11a).
■ A method contains(Rectangle2D) that returns True if the specified
rectangle is inside this rectangle (see Figure 8.11b).
■ A method overlaps(Rectangle2D) that returns True if the specified
rectangle overlaps with this rectangle (see Figure 8.11c).
■ Implement the __contains__(another) method that returns True if this
rectangle is contained in another rectangle.
■ Implement the __cmp__, __lt__, __le__, __eq__, __ne__, __gt__,
__ge__ methods that compare two circles based on their areas.
■ Implement the __cmp__, __lt__, __le__, __eq__, __ne__, __gt__,
__ge__ methods that compare two circles based on their radius.

Programming Exercises 269
Draw the UML diagram for the class, and then implement the class. Write a test pro-
gram that prompts the user to enter two rectangles with center x-, y-coordinates,
width, and height, creates two Rectangle2D objects r1 and r2, displays their areas
and perimeters, and displays the result of r1.containsPoint(r2.getX(),
r2.getY()), r1.contains(r2), and r1.overlaps(r2). Here is a sample run:
Enter x1, y1, width1, height1:
Enter x2, y2, width2, height2:
Area for r1 is 353.0
Perimeter for r1 is 90.6
Area for r2 is 21.2
Perimeter for r2 is 18.6
r1 contains the center of r2? False
r1 contains r2? False
r1 overlaps r2? False
1.3, 4.3, 4, 5.3
9, 1.3, 10, 35.3
8.20 (Use the Rational class) Write a program that computes the following summa-
tion series using the Rational class:
*8.21 (Math: The Complex class) Python has the complex class for performing com-
plex number arithmetic. In this exercise, you will design and implement your own
Complex class. Note that the complex class in Python is named in lowercase, but
our custom Complex class is named with C in uppercase.
A complex number is a number of the form where a and b are real numbers
and i is The numbers a and b are known as the real part and the imaginary
part of the complex number, respectively. You can perform addition, subtraction,
multiplication, and division for complex numbers using the following formulas:
You can also obtain the absolute value for a complex number using the following
formula:
(A complex number can be interpreted as a point on a plane by identifying the (a,b)
values as the coordinates of the point. The absolute value of the complex number
corresponds to the distance of the point to the origin, as shown in Figure 8.12.)
�a + bi � = 2a2 + b2
(a + bi)/(c + di ) = (ac + bd˛ ˛)/(c2 + d2 ) + (bc – ad )i/(c2 + d2 )
(a + bi) * (c + di ) = (ac – bd ) + (bc + ad )i
a + bi – (c + di) = (a – c) + (b – d )i
(a + bi) + (c + di) = (a + c) + (b + d )i
1-1. a + bi,
1
2
+
2
3
+
3
4
+ c +
8
9
+
9
10
(a) (b) (c)
p
FIGURE 8.11 (a) A point is inside the rectangle. (b) A rectangle is inside another rectangle.
(c) A rectangle overlaps another rectangle.

270 Chapter 8 More on Strings and Special Methods
Design a class named Complex for representing complex numbers and the meth-
ods __add__, __sub__, __mul__, __truediv__, and __abs__ for per-
forming complex-number operations, and override the __str__ method by
returning a string representation for a complex number. The __str__ method
returns (a + bi) as a string. If b is 0, it simply returns a.
Provide a constructor Complex(a, b) to create a complex number with
the default value of 0 for a and b. Also provide the getRealPart() and
getImaginaryPart() methods for returning the real and imaginary parts of the
complex number, respectively.
Write a test program that prompts the user to enter two complex numbers and dis-
plays the result of their addition, subtraction, multiplication, and division. Here is
a sample run:
a + bi
x-axis
y-axis
2 + 3i
3 – 2i
FIGURE 8.12 Point (2, 3) can be written as a complex number and as
(3 – 2i).
(3, -2)(2 + 3i)
Enter the first complex number:
Enter the second complex number:
(3.5 + 6.5i) + (-3.5 + 1i) = (0.0 + 7.5i)
(3.5 + 6.5i) – (-3.5 + 1i) = (7.0 + 5.5i)
(3.5 + 6.5i) * (-3.5 + 1i) = (-18.75 – 19.25i)
(3.5 + 6.5i) / (-3.5 + 1i) = (-0.43396226415 – 1.98113207547i)
|(3.5 + 6.5i)| = 4.47213595499958
-3.5, 1
3.5, 6.5

GUI PROGRAMMING
USING TKINTER
CHAPTER
9
Objectives
■ To create a simple GUI application with Tkinter (§9.2).
■ To process events by using callback functions that are bound to a widget’s
command option (§9.3).
■ To use labels, entries, buttons, check buttons, radio buttons, messages, and
text to create graphical user interfaces (§9.4).
■ To draw lines, rectangles, ovals, polygons, and arcs and display text strings
in a canvas (§9.5).
■ To use geometry managers to lay out widgets in a container (§9.6).
■ To lay out widgets in a grid by using the grid manager (§9.6.1).
■ To pack widgets side by side or on top of each other by using the pack
manager (§9.6.2).
■ To place widgets in absolute locations by using the place manager (§9.6.3).
■ To achieve a desired layout by using containers to group widgets (§9.7).
■ To use images in widgets (§9.8).
■ To create applications that contain menus (§9.9).
■ To create applications that contain popup menus (§9.10).
■ To bind a widget’s mouse and key events to a callback function for
processing events (§9.11).
■ To develop animations (§9.12).
■ To use scroll bars to scroll through the contents of a text widget (§9.13).
■ To use standard dialog boxes to display messages and accept user input
(§9.14).

272 Chapter 9 GUI Programming Using Tkinter
9.1 Introduction
Tkinter enables you to develop GUI programs and is an excellent pedagogical tool for
learning object-oriented programming.
There are many GUI modules available for developing GUI programs in Python. You have
used the turtle module for drawing geometric shapes. Turtle is easy to use and is an
effective pedagogical tool for introducing the fundamentals of programming to beginners.
However, you cannot use turtle to create graphical user interfaces. This chapter introduces
Tkinter, which will enable you to develop GUI projects. Tkinter is not only a useful tool for
developing GUI projects, but it is also a valuable pedagogical tool for learning object-
oriented programming.
Note
Tkinter (pronounced T-K-Inter) is short for “Tk interface.” Tk is a GUI library used by
many programming languages for developing GUI programs on Windows, Mac, and
UNIX. Tkinter provides an interface for Python programmers to use the Tk GUI library,
and it is the de-facto standard for developing GUI programs in Python.
9.2 Getting Started with Tkinter
The tkinter module contains the classes for creating GUIs. The Tk class creates a
window for holding GUI widgets (i.e., visual components).
Listing 9.1 introduces Tkinter with a simple example.
LISTING 9.1 SimpleGUI.py
1 from tkinter import * # Import all definitions from tkinter
2
3 window = Tk() # Create a window
4 label = Label(window, text = “Welcome to Python”) # Create a label
5 button = Button(window, text = “Click Me”) # Create a button
6 label.pack() # Place the label in the window
7 button.pack() # Place the button in the window
8
9 window.mainloop() # Create an event loop
When you run the program, a label and a button appear in the Tkinter window, as shown in
Figure 9.1.
what is Tkinter?
create a window
create a label
create a button
FIGURE 9.1 The label and button are created in Listing 9.1.
Whenever you create a GUI-based program in Tkinter, you need to import the tkinter
module (line 1) and create a window by using the Tk class (line 3). Recall that the asterisk (*) in
line 1 imports all definitions for classes, functions, and constants from the tkinter module to
the program.Tk() creates an instance of a window. Label and Button are Python Tkinter
place label
place button
event loop
Key
Point
Key
Point

9.3 Processing Events 273
Simple GUI
widget classes for creating labels and buttons. The first argument of a widget class is always the
parent container (i.e., the container in which the widget will be placed). The statement (line 4)
label = Label(window, text = “Welcome to Python”)
constructs a label with the text Welcome to Python that is contained in the window.
The statement (line 6)
label.pack()
places label in the container using a pack manager. In this example, the pack manager packs
the widget in the window row by row. More on the pack manager will be introduced in
Section 9.6.2. For now, you can use the pack manager without knowing its full details.
Tkinter GUI programming is event driven. After the user interface is displayed, the pro-
gram waits for user interactions such as mouse clicks and key presses. This is specified in the
following statement (line 9)
window.mainloop()
The statement creates an event loop. The event loop processes events continuously until
you close the main window, as shown in Figure 9.2.
widget class
parent container
Start event loop
Terminate
No
Yes
Close the
main window?
Detect and
process events
FIGURE 9.2 A Tkinter GUI program listens and processes events in a continuous loop.
9.1 What are turtle and Tkinter suitable for?
9.2 How do you create a window?
9.3 What is window.mainloop() for?
9.3 Processing Events
A Tkinter widget can be bound to a function, which is called when an event occurs.
The Button widget is a good way to demonstrate the basics of event-driven programming, so
we’ll use it in the following example.
When the user clicks a button, your program should process this event. You enable this
action by defining a processing function and binding the function to the button, as shown in
Listing 9.2.
VideoNote
✓Point✓Check
Key
Point

274 Chapter 9 GUI Programming Using Tkinter
LISTING 9.2 ProcessButtonEvent.py
1 # Import all definitions from tkinter
2
3
4 print(“OK button is clicked”)
5
6
7 print(“Cancel button is clicked”)
8
9 window = Tk() # Create a window
10 btOK = Button(window, text = “OK”, fg = “red”, command = processOK)
11 btCancel = Button(window, text = “Cancel”, bg = “yellow”,
12 command = processCancel)
13 btOK.pack() # Place the OK button in the window
14 btCancel.pack() # Place the Cancel button in the window
15
16 # Create an event loop
When you run the program, two buttons appear, as shown in Figure 9.3a. You can watch
the events being processed and see their associated messages in the command window in
Figure 9.3b.
window.mainloop()
def processCancel():
def processOK():
from tkinter import *
process OK
process Cancel
create a window
create a button
create a button
place button
place button
event loop
(a) (b)
FIGURE 9.3 (a) Listing 9.2 displays two buttons in a window. (b) Watching events being
processed in the command window.
callback functions
handlers
initialize GUI
create a button
create a button
The program defines the functions processOK and processCancel (lines 3–7). These
functions are bound to the buttons when the buttons are constructed. These functions are
known as callback functions, or handlers. The following statement (line 10)
btOK = Button(window, text = “OK”, fg = “red”, command = processOK)
binds the OK button to the processOK function, which will be called when the button is
clicked. The fg option specifies the button’s foreground color and the bg option specifies its
background color. By default, fg is black and bg is gray for all widgets.
You can also write this program by placing all the functions in one class, as shown in
Listing 9.3.
LISTING 9.3 ProcessButtonEventAlternativeCode.py
1 from tkinter import * # Import all definitions from tkinter
2
3 class ProcessButtonEvent:
4 def __init__(self):
5 window = Tk() # Create a window
6 btOK = Button(window, text = “OK”, fg = “red”,
7 command = )
8 btCancel = Button(window, text = “Cancel”, bg = “yellow”,
9 command = ) self.processCancel
self.processOK

9.4 The Widget Classes 275
10 btOK.pack() # Place the OK button in the window
11 btCancel.pack() # Place the Cancel button in the window
12
13 window.mainloop() # Create an event loop
14
15
16 print(“OK button is clicked”)
17
18
19 print(“Cancel button is clicked”)
20
21 ProcessButtonEvent() # Create an object to invoke __init__ method
The program defines a class for creating the GUI in the _ _init_ _ method (line 4). The
functions processOK and processCancel are now instance methods in the class, so they
are called by self.processOK (line 7) and self.processCancel (line 9).
There are two advantages of defining a class for creating a GUI and processing GUI
events. First, you can reuse the class in the future. Second, defining all the functions as meth-
ods enables them to access instance data fields in the class.
9.4 When you create a widget object from a widget class, what should be the first
argument?
9.5 What is a widget’s command option for?
9.4 The Widget Classes
Tkinter’s GUI classes define common GUI widgets such as buttons, labels, radio
buttons, check buttons, entries, canvases, and others.
Table 9.1 describes the core widget classes Tkinter provides.
def processCancel(self):
def processOK(self):
place button
place button
event loop
process OK
process Cancel
TABLE 9.1 Tkinter Widget Classes
Widget Class Description
Button A simple button, used to execute a command.
Canvas Structured graphics, used to draw graphs and plots, create graphics editors, and implement custom widgets.
Checkbutton Clicking a check button toggles between the values.
Entry A text entry field, also called a text field or a text box.
Frame A container widget for containing other widgets.
Label Displays text or an image.
Menu A menu pane, used to implement pull-down and popup menus.
Menubutton A menu button, used to implement pull-down menus.
Message Displays a text. Similar to the label widget, but can automatically wrap text to a given width or aspect ratio.
Radiobutton Clicking a radio button sets the variable to that value, and clears all other radio buttons associated with the same
variable.
Text Formatted text display. Allows you to display and edit text with various styles and attributes. Also supports
embedded images and windows.
There are many options for creating widgets from these classes. The first argument is
always the parent container. You can specify a foreground color, background color, font, and
cursor style when constructing a widget.
✓Point✓Check
Key
Point

276 Chapter 9 GUI Programming Using Tkinter
To specify a color, use either a color name (such as red, yellow, green, blue, white, black,
purple) or explicitly specify the red, green, and blue (RGB) color components by using a
string #RRGGBB, where RR, GG, and BB are hexadecimal representations of the red, green, and
blue values, respectively.
You can specify a font in a string that includes the font name, size, and style. Here are
some examples:
Times 10 bold
Helvetica 10 bold italic
CourierNew 20 bold italic
Courier 20 bold italic overstrike underline
By default, the text in a label or a button is centered. You can change its alignment by
using the justify option with the named constants LEFT, CENTER, or RIGHT. (Remember,
as discussed in Section 2.6, named constants are in all uppercase.) You can also display the
text in multiple lines by inserting the newline character \n to separate lines of text.
You can specify a particular style of mouse cursor by using the cursor option with string
values such as arrow (the default), circle, cross, plus, or some other shape.
When you construct a widget, you can specify its properties such as fg, bg, font,
cursor, text, and command in the constructor. Later in the program, you can change the
widget’s properties by using the following syntax:
widgetName[“propertyName”] = newPropertyValue
For example, the following code creates a button and its text property is changed to
Hide, bg property to red, and fg to #AB84F9. #AB84F9 is a color specified in the form of
RRGGBB.
btShowOrHide = Button(window, text = “Show”, bg = “white”)
btShowOrHide[“text”] = “Hide”
btShowOrHide[“bg”] = “red”
btShowOrHide[“fg”] = “#AB84F9” # Change fg color to #AB84F9
btShowOrHide[“cursor”] = “plus” # Change mouse cursor to plus
btShowOrHide[“justify”] = LEFT # Set justify to LEFT
Each class comes with a substantial number of methods. The complete information about
these classes is beyond the scope of this book. A good reference resource for Tkinter can be
found at www.pythonware.com/library/tkinter. This chapter provides examples that show you
how to use these widgets.
Listing 9.4 is an example of a program that uses the widgets Frame, Button,
Checkbutton, Radiobutton, Label, Entry (also known as a text field), Message, and
Text (also known as a text area).
LISTING 9.4 WidgetsDemo.py
1 from tkinter import * # Import all definitions from tkinter
2
3 class WidgetsDemo:
4
5 window = Tk() # Create a window
6 window.title(“Widgets Demo”) # Set a title
7
8 # Add a check button, and a radio button to frame1
9 frame1 = Frame(window) # Create and add a frame to window
10 frame1.pack()
11 self.v1 = IntVar()
def __init__(self):
font
text formatting
mouse cursor
change properties
create a window
window title
create frame
color

www.pythonware.com/library/tkinter

9.4 The Widget Classes 277
12 cbtBold = Checkbutton(frame1, text = “Bold”,
13 , command = )
14
15 rbRed = Radiobutton(frame1, text = “Red”, bg = “red”,
16 , value = 1,
17 command = )
18 rbYellow = Radiobutton(frame1, text = “Yellow”,
19 bg = “yellow”, variable = self.v2, value = 2,
20 command = )
21 cbtBold.grid(row = 1, column = 1)
22 rbRed.grid(row = 1, column = 2)
23 rbYellow.grid(row = 1, column = 3)
24
25 # Add a label, an entry, a button, and a message to frame1
26 frame2 = Frame(window) # Create and add a frame to window
27 frame2.pack()
28 label = Label(frame2, text = “Enter your name: “)
29
30 entryName = Entry(frame2, )
31 btGetName = Button(frame2, text = “Get Name”,
32 command = self.processButton)
33 message = Message(frame2, text = “It is a widgets demo”)
34 label.grid(row = 1, column = 1)
35 entryName.grid(row = 1, column = 2)
36 btGetName.grid(row = 1, column = 3)
37 message.grid(row = 1, column = 4)
38
39 # Add text
40 text = Text(window) # Create and add text to the window
41 text.pack()
42 text.insert(END,
43 “Tip\nThe best way to learn Tkinter is to read “)
44 text.insert(END,
45 “these carefully designed examples and use them “)
46 text.insert(END, “to create your applications.”)
47
48 window.mainloop() # Create an event loop
49
50
51 print(“check button is ”
52 + (“checked ” if self.v1.get() == 1 else “unchecked”))
53
54
55 print((“Red” if self.v2.get() == 1 else “Yellow”)
56 + ” is selected ” )
57
58
59 print(“Your name is ” + self.name.get())
60
61 WidgetsDemo() # Create GUI
When you run the program, the widgets are displayed as shown in Figure 9.4a. As you
click the Bold button, select the Yellow radio button, and type in “Johnson,” you can watch
the events being processed and see their associated messages in the command window in
Figure 9.4b.
The program creates the window (line 5) and invokes its title method to set a title (line
6). The Frame class is used to create a frame named frame1 and the parent container for the
frame is the window (line 9). This frame is used as the parent container for a check button and
two radio buttons, created in lines 12, 15, and 18.
def processButton(self):
def processRadiobutton(self):
def processCheckbutton(self):
textvariable = self.name
self.name = StringVar()
self.processRadiobutton
self.processRadiobutton
variable = self.v2
self.v2 = IntVar()
self.processCheckbuttonvariable = self.v1
create check button
create radio button
grid manager
create frame
create entry
create message
create text
insert text
event loop
check button status
radio button status
entry name
create GUI

278 Chapter 9 GUI Programming Using Tkinter
(a) (b)
FIGURE 9.4 (a) The widgets are displayed in the user interface. (b) Watching events being processed.
You use an entry (text field) for entering a value. The value must be an object of IntVar,
DoubleVar, or StringVar representing an integer, a float, or a string, respectively. IntVar,
DoubleVar, and StringVar are defined in the tkinter module.
The program creates a check button and associates it with the variable v1. v1 is an
instance of IntVar (line 11). v1 is set to 1 if the check button is checked, or 0 if it isn’t
checked. When the check button is clicked, Python invokes the processCheckbutton
method (line 13).
The program then creates a radio button and associates it with an IntVar variable, v2. v2
is set to 1 if the Red radio button is selected, or 2 if the Yellow radio button is checked. You
can define any integer or string values when constructing a radio button. When either of the
two buttons is clicked, the processRadiobutton method is invoked.
The grid geometry manager is used to place the check button and radio buttons into
frame1. These three widgets are placed in the same row and in columns 1, 2, and 3, respec-
tively (lines 21–23).
The program creates another frame, frame2 (line 26), for holding a label, an entry, a button,
and a message widget. Like frame1, frame2 is placed inside the window.
An entry is created and associated with the variable name of the StringVar type for stor-
ing the value in the entry (line 29). When you click the Get Name button, the processButton
method displays the value in the entry (line 59). The Message widget is like a label except that
it automatically wraps the words and displays them in multiple lines.
The grid geometry manager is used to place the widget in frame2. These widgets are
placed in the same row and in columns 1, 2, 3, and 4, respectively (lines 34–37).
The program creates a Text widget (line 40) for displaying and editing text. It is placed
inside the window (line 41). You can use the insert method to insert text into this widget.
The END option specifies that the text is inserted into the end of the current content.
Listing 9.5 is a program that lets the user change the color, font, and text of a label, as
shown in Figure 9.5.
LISTING 9.5 ChangeLabelDemo.py
1 from tkinter import * # Import all definitions from tkinter
2
3 class ChangeLabelDemo:
4
5 window = Tk() # Create a window
6 window.title(“Change Label Demo”) # Set a title
7
8 # Add a label to frame1
9 frame1 = Frame(window) # Create and add a frame to window
10 frame1.pack()
11 self.lbl = Label(frame1, text = “Programming is fun”)
12 self.lbl.pack()
13
def __init__(self):
IntVar
DoubleVar
StringVar
geometry manager
window title
create frame1
create label

9.4 The Widget Classes 279
14 # Add a label, entry, button, two radio buttons to frame2
15 frame2 = Frame(window) # Create and add a frame to window
16 frame2.pack()
17 label = Label(frame2, text = “Enter text: “)
18 self.msg = StringVar()
19 entry = Entry(frame2, textvariable = self.msg)
20 btChangeText = Button(frame2, text = “Change Text”,
21 command = self.processButton)
22 self.v1 = StringVar()
23 rbRed = Radiobutton(frame2, text = “Red”, bg = “red”,
24 variable = self.v1, value = ‘R’,
25 command = self.processRadiobutton)
26 rbYellow = Radiobutton(frame2, text = “Yellow”,
27 bg = “yellow”, variable = self.v1, value = ‘Y’,
28 command = self.processRadiobutton)
29
30 label.grid(row = 1, column = 1)
31 entry.grid(row = 1, column = 2)
32 btChangeText.grid(row = 1, column = 3)
33 rbRed.grid(row = 1, column = 4)
34 rbYellow.grid(row = 1, column = 5)
35
36 window.mainloop() # Create an event loop
37
38
39 if self.v1.get() == ‘R’:
40
41 elif self.v1.get() == ‘Y’:
42
43
44
45 # New text for the label
46
47 ChangeLabelDemo() # Create GUI
self.lbl[“text”] = self.msg.get()
def processButton(self):
self.lbl[“fg”] = “yellow”
self.lbl[“fg”] = “red”
def processRadiobutton(self):
When you select a radio button, the label’s foreground color changes. If you enter new text
in the entry field and click the Change Text button, the new text appears in the label.
The program creates the window (line 5) and invokes its title method to set a title
(line 6). The Frame class is used to create a frame named frame1 and the parent container for
the frame is the window (line 9). This frame is used as the parent container for a label created
in line 11. Because the label is a data field in the class, it can be referenced in a callback
function.
The program creates another frame, frame2 (line 15), for holding a label, an entry, a button,
and two radio buttons. Like frame1, frame2 is placed inside the window.
An entry is created and associated with the variable msg of the StringVar type for storing
the value in the entry (line 19). When you click the Change Text button, the processButton
method sets a new text entry for the label in frame1, using the text in the entry (line 45).
create frame2
create entry
button callback
radio button callback
radio button callback
event loop
set a new fg
set a new fg
FIGURE 9.5 The program changes the label’s text and fg properties dynamically.
set new text
create GUI

280 Chapter 9 GUI Programming Using Tkinter
Two radio buttons are created and associated with a StringVar variable, v2. v2 is set to
R if the Red radio button is selected, or to Y if the Yellow radio button is clicked. When the user
clicks either of the two buttons, Python invokes the processRadiobutton method to
change the label’s foreground color in frame1 (lines 38–42).
9.6 How do you create a label with the text Welcome, a white foreground, and a red back-
ground?
9.7 How do you create a button with the text OK, a white foreground, a red background,
and with the callback function processOK?
9.8 How do you create a check button with the text apple, a white foreground, a red
background, associated with the variable v1, and with the callback function
processApple?
9.9 How do you create a radio button with the text senior, a white foreground, a red
background, associated with the variable v1, and with the callback function
processSenior?
9.10 How do you create an entry with a white foreground, a red background, and associ-
ated with the variable v1?
9.11 How do you create a message with the text programming is fun, a white fore-
ground, and a red background?
9.12 LEFT, CENTER, and RIGHT are named constants defined in the tkinter module.
Use a print statement to display the values defined by LEFT, CENTER, and
RIGHT.
9.5 Canvas
You use the Canvas widget for displaying shapes.
You can use the methods create_rectangle, create_oval, create_arc,
create_polygon, or create_line to draw a rectangle, oval, arc, polygon, or line on a
canvas.
Listing 9.6 shows how to use the Canvas widget. The program displays a rectangle, an
oval, an arc, a polygon, a line, and a text string. The objects are all controlled by buttons, as
shown in Figure 9.6.
LISTING 9.6 CanvasDemo.py
1 from tkinter import * # Import all definitions from tkinter
2
3 class CanvasDemo:
4 def __init__(self):
5 window = Tk() # Create a window
6 window.title(“Canvas Demo”) # Set title
7
8 # Place canvas in the window
9
10
11 self.canvas.pack()
12
13 # Place buttons in frame
14 frame = Frame(window)
15 frame.pack()
16 btRectangle = Button(frame, text = “Rectangle”,
17 command = self.displayRect)
bg = “white”)
self.canvas = Canvas(window, width = 200, height = 100,
create a window
create a canvas
create a frame
create buttons
✓Point✓Check
Key
Point

9.5 Canvas 281
18 btOval = Button(frame, text = “Oval”,
19 command = self.displayOval)
20 btArc = Button(frame, text = “Arc”,
21 command = self.displayArc)
22 btPolygon = Button(frame, text = “Polygon”,
23 command = self.displayPolygon)
24 btLine = Button(frame, text = “Line”,
25 command = self.displayLine)
26 btString = Button(frame, text = “String”,
27 command = self.displayString)
28 btClear = Button(frame, text = “Clear”,
29 command = self.clearCanvas)
30 btRectangle.grid(row = 1, column = 1)
31 btOval.grid(row = 1, column = 2)
32 btArc.grid(row = 1, column = 3)
33 btPolygon.grid(row = 1, column = 4)
34 btLine.grid(row = 1, column = 5)
35 btString.grid(row = 1, column = 6)
36 btClear.grid(row = 1, column = 7)
37
38 window.mainloop() # Create an event loop
39
40 # Display a rectangle
41 def displayRect(self):
42
43
44 # Display an oval
45 def displayOval(self):
46
47
48
49 # Display an arc
50 def displayArc(self):
51
52
53
54 # Display a polygon
55 def displayPolygon(self):
56
57
58
59 # Display a line
60 def displayLine(self):
61
62
63 self.canvas.create_line(10, 90, 190, 10, width = 9,
64 arrow = “last”, activefill = “blue”, tags = “line”)
65
66 # Display a string
67 def displayString(self):
68
69
70
71 # Clear drawings
72 def clearCanvas(self):
73
74
75
76 CanvasDemo() # Create GUI
“line”, “string”)
self.canvas.delete(“rect”, “oval”, “arc”, “polygon”,
font = “Times 10 bold underline”, tags = “string”)
self.canvas.create_text(60, 40, text = “Hi, I am a string”,
tags = “line”)
self.canvas.create_line(10, 10, 190, 90, fill = “red”,
tags = “polygon”)
self.canvas.create_polygon(10, 10, 190, 90, 30, 50,
extent = 90, width = 8, fill = “red”, tags = “arc”)
self.canvas.create_arc(10, 10, 190, 90, start = 0,
tags = “oval”)
self.canvas.create_oval(10, 10, 190, 90, fill = “red”,
self.canvas.create_rectangle(10, 10, 190, 90, tags = “rect”)
place buttons
event loop
display rectangle
display oval
display arc
display polygon
display line
display string
clear canvas
create GUI

282 Chapter 9 GUI Programming Using Tkinter
The program creates a window (line 5) and sets its title (line 6). A Canvas widget is cre-
ated within the window with a width of 200 pixels, a height of 100 pixels, and a background
color of white (lines 9–10).
Seven buttons—labeled with the text Rectangle, Oval, Arc, Polygon, Line, String, and
Clear—are created (lines 16–29). The grid manager places the buttons in one row in a frame
(lines 30–36).
To draw graphics, you need to tell the widget where to draw. Each widget has its own
coordinate system with the origin (0, 0) at the upper-left corner. The x-coordinate increases to
the right, and the y-coordinate increases downward. Note that the Tkinter coordinate system
differs from the conventional coordinate system, as shown in Figure 9.7.
grid manager
coordinate system
The methods create_rectangle, create_oval, create_arc, create_polygon,
and create_line (lines 42, 46, 51, 56, and 61) are used to draw rectangles, ovals, arcs,
polygons, and lines, as illustrated in Figure 9.8.
The create_text method is used to draw a text string (line 68). Note that the horizontal
and vertical center of the text is displayed at (x, y) for create_text(x, y, text) as
shown in Figure 9.8.
All the drawing methods use the tags argument to identify the drawing. These tags are
used in the delete method for clearing the drawing from the canvas (lines 73–74).
create_text
tags
(0, 0) x-axis
y-axis
(x, y)
x
y
Tkinter
Coordinate
System
x-axis
Conventional
Coordinate
System
(0, 0)
y-axis
FIGURE 9.7 The Tkinter coordinate system is measured in pixels, with (0, 0) at its upper-
left corner.
FIGURE 9.6 The geometrical shapes and strings are drawn on the canvas.

9.6 The Geometry Managers 283
The width argument can be used to specify the pen size in pixels for drawing the shapes
(lines 52 and 63).
The arrow argument can be used with create_line to draw a line with an arrowhead
(line 64). The arrowhead can appear at the start, end, or both ends of the line with the argu-
ment value first, end, or both.
The activefill argument makes the shape change color when you move the mouse over
it (line 64).
9.13 Write the code to draw a line from (34, 50) to (50, 90).
9.14 Write the code to draw a rectangle centered at (70, 70) with a width of 100 and a
height of 100. Fill the rectangle with the color red.
9.15 Write the code to draw an oval centered at (70, 70) with a width of 200 and a height
of 100. Fill the rectangle with red.
9.16 Write the code to draw an arc with a starting angle of 30, with an extent angle of 45
in a bounding rectangle with its upper-left corner at (10, 10) and bottom-right corner
at (80, 80).
9.17 Write the code to draw a polygon with points at (10, 10), (15, 30), (140, 10), and
(10, 100). Fill the shape with red.
9.18 How do you draw a shape with a large pen size?
9.19 How do you draw a line with an arrowhead?
9.20 How do you make a shape change color when the mouse is moved over it?
9.6 The Geometry Managers
Tkinter uses a geometry manager to place widgets inside a container.
Tkinter supports three geometry managers: the grid manager, the pack manager, and the place
manager. You have already used the grid and pack managers. This section describes these
managers and introduces some additional features.
Tip
Since each manager has its own style of placing the widget, it is not a good practice to
mix the managers for the widgets in the same container. You can use a frame as a sub-
container to achieve the desired layout.
width
arrow
activefill
(x1, y1)
(x2, y2)
canvas.create_rectangle(x1, y1, x2, y2)
canvas.create_line(x1, y1, x2, y2)
(x1, y1)
(x2, y2)
canvas.create_polygon(x1, y1, x2, y2, x3, y3)
(x1, y1)
(x3, y3)
(x2, y2)
(x1, y1)
(x2, y2)
canvas.create_oval(x1, y1, x2, y2)
(x1, y1)
(x2, y2)
canvas.create_arc(x1, y1, x2, y2, start, extent)
canvas.create_text(x, y, text = “ABCDE”)
(x, y)
ABCDE
start
extent
FIGURE 9.8 The Canvas class contains the methods for drawing graphics.
✓Point✓Check
Key
Point

284 Chapter 9 GUI Programming Using Tkinter
9.6.1 The Grid Manager
The grid manager places widgets into the cells of an invisible grid in a container. You can
place a widget in a specified row and column. You can also use the rowspan and
columnspan parameters to place a widget in multiple rows and columns. Listing 9.7 uses the
grid manager to lay out a group of widgets, as shown in Figure 9.9.
LISTING 9.7 GridManagerDemo.py
1 from tkinter import * # Import all definitions from tkinter
2
3 class GridManagerDemo:
4 window = Tk() # Create a window
5 window.title(“Grid Manager Demo”) # Set title
6
7 message = Message(window, text =
8 “This Message widget occupies three rows and two columns”)
9 message.grid(row = 1, column = 1, , columnspan = 2)
10 Label(window, text = “First Name:”).grid(row = 1, column = 3)
11 Entry(window).grid(row = 1, column = 4, , pady = 5)
12 Label(window, text = “Last Name:”).grid(row = 2, column = 3)
13 Entry(window).grid(row = 2, column = 4)
14 Button(window, text = “Get Name”).grid(row = 3,
15 padx = 5, pady = 5, column = 4, )
16
17 window.mainloop() # Create an event loop
18
19 GridManagerDemo() # Create GUI
sticky = E
padx = 5
rowspan = 3
The Message widget is placed in row 1 and column 1 and it expands to three rows and two
columns (line 9). The Get Name button uses the sticky = E option (line 15) to stick to the
east in the cell so that it is right aligned with the Entry widgets in the same column. The
sticky option defines how to expand the widget if the resulting cell is larger than the widget
itself. The sticky option can be any combination of the named constants S, N, E, and W, or
NW, NE, SW, and SE.
The padx and pady options pad the optional horizontal and vertical space in a cell (lines
11 and 15). You can also use the ipadx and ipady options to pad the optional horizontal and
vertical space inside the widget borders.
9.6.2 The Pack Manager
The pack manager can place widgets on top of each other or place them side by side. You can
also use the fill option to make a widget fill its entire container.
Listing 9.8 displays three labels, as shown in Figure 9.10a. These three labels are packed
on top of each other. The red label uses the option fill with value BOTH and expand with
value 1. The fill option uses named constants X, Y, or BOTH to fill horizontally, vertically, or
both ways. The expand option tells the pack manager to assign additional space to the widget
rowspan
columnspan
rowspan
padx
FIGURE 9.9 The grid manager was used to place these widgets.
sticky
event loop
create GUI
sticky option
padx option
pady option
pack manager
side
fill
expand

9.6 The Geometry Managers 285
box. If the parent widget is larger than necessary to hold all the packed widgets, any extra
space is distributed among the widgets whose expand option is set to a nonzero value.
LISTING 9.8 PackManagerDemo.py
1 from tkinter import * # Import all definitions from tkinter
2
3 class PackManagerDemo:
4 def __init__(self):
5 window = Tk() # Create a window
6 window.title(“Pack Manager Demo 1”) # Set title
7
8 Label(window, text = “Blue”, bg = “blue”).pack()
9 Label(window, text = “Red”, bg = “red”).pack(
10 )
11 Label(window, text = “Green”, bg = “green”).pack(
12 )
13
14 window.mainloop() # Create an event loop
15
16 PackManagerDemo() # Create GUI
fill = BOTH
fill = BOTH, expand = 1
Listing 9.9 displays the three labels shown in Figure 9.10b. These three labels are packed
side by side using the side option. The side option can be LEFT, RIGHT, TOP, or BOTTOM.
By default, it is set to TOP.
LISTING 9.9 PackManagerDemoWithSide.py
1 from tkinter import * # Import all definitions from tkinter
2
3 class PackManagerDemoWithSide:
4 window = Tk() # Create a window
5 window.title(“Pack Manager Demo 2”) # Set title
6
7 Label(window, text = “Blue”, bg = “blue”).pack( )
8 Label(window, text = “Red”, bg = “red”).pack(
9 , fill = BOTH, expand = 1)
10 Label(window, text = “Green”, bg = “green”).pack(
11 , fill = BOTH)
12
13 window.mainloop() # Create an event loop
14
15 PackManagerDemoWithSide() # Create GUI
side = LEFT
side = LEFT
side = LEFT
expand
fill
create GUI
(a) (b)
FIGURE 9.10 (a) The pack manager uses the fill option to fill the container. (b) You can
place widgets side by side.
side
create GUI

286 Chapter 9 GUI Programming Using Tkinter
9.6.3 The Place Manager
The place manager places widgets in absolute positions. Listing 9.10 displays the three labels
shown in Figure 9.11.
LISTING 9.10 PlaceManagerDemo.py
1 from tkinter import * # Import all definitions from tkinter
2
3 class PlaceManagerDemo:
4 def __init__(self):
5 window = Tk() # Create a window
6 window.title(“Place Manager Demo”) # Set title
7
8 Label(window, text = “Blue”, bg = “blue”).
9
10 Label(window, text = “Red”, bg = “red”).place(
11 x = 50, y = 50)
12 Label(window, text = “Green”, bg = “green”).place(
13 x = 80, y = 80)
14
15 window.mainloop() # Create an event loop
16
17 PlaceManagerDemo() # Create GUI
x = 20, y = 20)
place(
The upper-left corner of the blue label is at (20, 20). All three labels are placed using the
place manager.
Note
The place manager is not compatible with all computers. If you run this program on Win-
dows with a screen monitor with resolution, the layout size is just right.
When the program is run on Windows with a monitor with a higher resolution, the com-
ponents appear very small and clump together. When it is run on Windows with a mon-
itor with a lower resolution, they cannot be shown in their entirety. Because of these
incompatibility issues, you should generally avoid using the place manager.
9.21 What is wrong if you write the following code using the pack manager for a
button?
button.pack(LEFT)
9.22 If you need to pad spaces between widgets, which geometry manager should you use?
9.23 Why should you avoid using the place manager?
9.24 X, Y, BOTH, S, N, E, and W, or NW, NE, SW, and SE are named constants defined in
the tkinter module. Use a print statement to display the values defined in these
constants.
1024 * 768
place manager
place
create GUI
FIGURE 9.11 The place manager places widgets in absolute positions.
✓Point✓Check

9.7 Case Study: Loan Calculator 287
9.7 Case Study: Loan Calculator
This section provides an example that uses GUI widgets, geometry layout managers,
and events.
Listing 2.8 developed a console-based program for computing loans. This section develops a
GUI application for computing loan payments, as shown in Figure 9.12a.
Developing a GUI application involves designing the user interface and writing the code to
process the events. Here are the major steps in writing the program:
1. Design the user interface (UI) by drawing a sketch, as shown in Figure 9.12b. The UI
consists of labels, text entry boxes, and a button. You can use the grid manager to posi-
tion them in the window.
2. Process the event. When the button is clicked, the program invokes a callback function
to obtain the user input for the interest rate, number of years, and loan amount from the
text entries, computes the monthly and total payments, and displays the values in the
labels.
Listing 9.11 shows the complete program.
LISTING 9.11 LoanCalculator.py
1 from tkinter import * # Import all definitions from tkinter
2
3 class LoanCalculator:
4
5 window = Tk() # Create a window
6 window.title(“Loan Calculator”) # Set title
7
8 Label(window, text = “Annual Interest Rate”).grid(row = 1,
9 column = 1, sticky = W)
10 Label(window, text = “Number of Years”).grid(row = 2,
11 column = 1, sticky = W)
12 Label(window, text = “Loan Amount”).grid(row = 3,
13 column = 1, sticky = W)
14 Label(window, text = “Monthly Payment”).grid(row = 4,
15 column = 1, sticky = W)
16 Label(window, text = “Total Payment”).grid(row = 5,
17 column = 1, sticky = W)
18
19
20 Entry(window, textvariable = self.annualInterestRateVar,
21 justify = RIGHT).grid(row = 1, column = 2)
22 self.numberOfYearsVar = StringVar()
self.annualInterestRateVar = StringVar()
def __init__(self):
label
label
label
label
entry
entry
entry
label
label
label
button
(a) (b)
FIGURE 9.12 The program computes loan payments and provides a graphical user interface.
create window
create labels
create entries
Key
Point
Create GUI application
VideoNote

288 Chapter 9 GUI Programming Using Tkinter
23 Entry(window, textvariable = self.numberOfYearsVar,
24 justify = RIGHT).grid(row = 2, column = 2)
25
26 Entry(window, textvariable = self.loanAmountVar,
27 justify = RIGHT).grid(row = 3, column = 2)
28
29
30 lblMonthlyPayment = Label(window, textvariable =
31 self.monthlyPaymentVar).grid(row = 4, column = 2,
32 sticky = E)
33 self.totalPaymentVar = StringVar()
34 lblTotalPayment = Label(window, textvariable =
35 self.totalPaymentVar).grid(row = 5,
36 column = 2, sticky = E)
37
38
39
40
41 window.mainloop() # Create an event loop
42
43
44 monthlyPayment = self.getMonthlyPayment(
45 float(self.loanAmountVar.get()),
46 float(self.annualInterestRateVar.get()) / 1200,
47 int(self.numberOfYearsVar.get()))
48 self.monthlyPaymentVar.set(format(monthlyPayment, “10.2f”))
49 totalPayment = float(self.monthlyPaymentVar.get()) * 12 \
50 * int(self.numberOfYearsVar.get())
51 self.totalPaymentVar.set(format(totalPayment, “10.2f”))
52
53
54
55 monthlyPayment = loanAmount * monthlyInterestRate / (1
56 – 1 / (1 + monthlyInterestRate) ** (numberOfYears * 12))
57 return monthlyPayment;
58
59 LoanCalculator() # Create GUI
The program creates the user interface with labels, entries, and a button placed in the win-
dow using the grid manager (lines 8–39). The command option for the button is set to the
computePayment method (line 38). When the Compute Payment button is clicked, its
method is invoked, which obtains the user input for the annual interest rate, years for the loan,
and loan amount to calculate the monthly payment and total payment (lines 43–51).
9.8 Displaying Images
You can add an image to a label, button, check button, or radio button.
To create an image, use the PhotoImage class as follows:
photo = PhotoImage(file = imagefilename)
The image file must be in GIF format. You can use a conversion utility to convert image
files in other formats into GIF format.
Listing 9.12 shows you how to add images to labels, buttons, check buttons, and radio but-
tons. You can also use the create_image method to display an image in a canvas, as shown
in Figure 9.13.
loanAmount, monthlyInterestRate, numberOfYears):
def getMonthlyPayment(self,
def computePayment(self):
row = 6, column = 2, sticky = E)
command = self.computePayment).grid(
btComputePayment = Button(window, text = “Compute Payment”,
self.monthlyPaymentVar = StringVar()
self.loanAmountVar = StringVar()
computePayment
set monthlyPayment
set totalPayment
getMonthlyPayment
create GUI
create button
callback
Key
Point

9.8 Displaying Images 289
LISTING 9.12 ImageDemo.py
1 from tkinter import * # Import all definitions from tkinter
2
3 class ImageDemo:
4 def __init__(self):
5 window = Tk() # Create a window
6 window.title(“Image Demo”) # Set title
7
8 # Create PhotoImage objects
9
10 chinaImage = PhotoImage(file = “image/china.gif”)
11 leftImage = PhotoImage(file = “image/left.gif”)
12 rightImage = PhotoImage(file = “image/right.gif”)
13 usImage = PhotoImage(file = “image/usIcon.gif”)
14 ukImage = PhotoImage(file = “image/ukIcon.gif”)
15 crossImage = PhotoImage(file = “image/x.gif”)
16 circleImage = PhotoImage(file = “image/o.gif”)
17
18 # frame1 to contain label and canvas
19 frame1 = Frame(window)
20 frame1.pack()
21 Label(frame1, ).pack(side = LEFT)
22 canvas = Canvas(frame1)
23
24 canvas[“width”] = 200
25 canvas[“height”] = 100
26 canvas.pack(side = LEFT)
27
28 # frame2 contains buttons, check buttons, and radio buttons
29 frame2 = Frame(window)
30 frame2.pack()
31
32 Button(frame2, image = rightImage).pack(side = LEFT)
33
34 Checkbutton(frame2, image = ukImage).pack(side = LEFT)
35
36 Radiobutton(frame2, image = circleImage).pack(side = LEFT)
37
38 window.mainloop() # Create an event loop
39
40 ImageDemo() # Create GUI
Radiobutton(frame2, image = crossImage).pack(side = LEFT)
Checkbutton(frame2, image = usImage).pack(side = LEFT)
Button(frame2, image = leftImage).pack(side = LEFT)
canvas.create_image(90, 50, image = chinaImage)
image = caImage
caImage = PhotoImage(file = “image/ca.gif”)
create window
create image
image in label
image in canvas
FIGURE 9.13 The program displays widgets with images.
image in button
image in check button
image in radio button
create GUI

290 Chapter 9 GUI Programming Using Tkinter
The program places image files in the image folder in the current program directory, then
creates PhotoImage objects for several images in lines 9–16. These objects are used in wid-
gets. The image is a property in Label, Button, Checkbutton, and RadioButton (lines 21
and 31–36). Image is not a property for Canvas, but you can use the create_image method
to display an image on the canvas (line 23). In fact, you can display multiple images in one
canvas.
9.25 What image format is supported in Python?
9.26 What is wrong with the following statement for creating a PhotoImage?
image = PhotoImage(“image/us.gif”)
9.27 How do you create a button that shows an image in c:\pybook\image\canada.gif?
9.9 Menus
You can use Tkinter to create menus, popup menus, and toolbars.
Tkinter provides a comprehensive solution for building graphical user interfaces. This section
introduces menus, popup menus, and toolbars.
Menus make selection easier and are widely used in windows. You can use the Menu class
to create a menu bar and a menu, and use the add_command method to add items to the menu.
Listing 9.13 shows you how to create the menus shown in Figure 9.14.
LISTING 9.13 MenuDemo.py
1 from tkinter import *
2
3 class MenuDemo:
4 def __init__(self):
5 window = Tk()
6 window.title(“Menu Demo”)
7
8 # Create a menu bar
9
10 # Display the menu bar
11
12 # Create a pull-down menu, and add it to the menu bar
13
14
15
16
17 operationMenu.add_command(label = “Subtract”,
18 command = self.subtract)
19 operationMenu.add_separator()
20 operationMenu.add_command(label = “Multiply”,
21 command = self.multiply)
22 operationMenu.add_command(label = “Divide”,
23 command = self.divide)
24
25 # Create more pull-down menus
26
27
28
29
30 # Add a tool bar frame
31 frame0 = Frame(window) # Create and add a frame to window
exitmenu.add_command(label = “Quit”, command = window.quit)
menubar.add_cascade(label = “Exit”, menu = exitmenu)
exitmenu = Menu(menubar, tearoff = 0)
command = self.add)
operationMenu.add_command(label = “Add”,
menubar.add_cascade(label = “Operation”, menu = operationMenu)
operationMenu = Menu(menubar, tearoff = 0)
window.config(menu = menubar)
menubar = Menu(window)create a menu bar
display menu bar
create a menu
display a menu
add menu item
create a menu
display a menu
add menu item
✓Point✓Check
Key
Point

9.9 Menus 291
32 frame0.grid(row = 1, column = 1, sticky = W)
33
34 # Create images
35
36 minusImage = PhotoImage(file = “image/minus.gif”)
37 timesImage = PhotoImage(file = “image/times.gif”)
38 divideImage = PhotoImage(file = “image/divide.gif”)
39
40 Button(frame0, image = plusImage, command =
41 self.add).grid(row = 1, column = 1, sticky = W)
42 Button(frame0, image = minusImage,
43 command = self.subtract).grid(row = 1, column = 2)
44 Button(frame0, image = timesImage,
45 command = self.multiply).grid(row = 1, column = 3)
46 Button(frame0, image = divideImage,
47 command = self.divide).grid(row = 1, column = 4)
48
49 # Add labels and entries to frame1
50 frame1 = Frame(window)
51 frame1.grid(row = 2, column = 1, pady = 10)
52 Label(frame1, text = “Number 1:”).pack(side = LEFT)
53 self.v1 = StringVar()
54 Entry(frame1, width = 5, textvariable = self.v1,
55 justify = RIGHT).pack(side = LEFT)
56 Label(frame1, text = “Number 2:”).pack(side = LEFT)
57 self.v2 = StringVar()
58 Entry(frame1, width = 5, textvariable = self.v2,
59 justify = RIGHT).pack(side = LEFT)
60 Label(frame1, text = “Result:”).pack(side = LEFT)
61 self.v3 = StringVar()
62 Entry(frame1, width = 5, textvariable = self.v3,
63 justify = RIGHT).pack(side = LEFT)
64
65 # Add buttons to frame2
66 frame2 = Frame(window) # Create and add a frame to window
67 frame2.grid(row = 3, column = 1, pady = 10, sticky = E)
68
69
70 Button(frame2, text = “Subtract”,
71 command = self.subtract).pack(side = LEFT)
72 Button(frame2, text = “Multiply”,
73 command = self.multiply).pack(side = LEFT)
74 Button(frame2, text = “Divide”,
75 command = self.divide).pack(side = LEFT)
76
77 mainloop()
78
79
80 self.v3.set(eval(self.v1.get()) + eval(self.v2.get()))
81
82 def subtract(self):
83 self.v3.set(eval(self.v1.get()) – eval(self.v2.get()))
84
85 def multiply(self):
86 self.v3.set(eval(self.v1.get()) * eval(self.v2.get()))
87
88 def divide(self):
89 self.v3.set(eval(self.v1.get()) / eval(self.v2.get()))
90
91 MenuDemo() # Create GUI
def add(self):
side = LEFT)
Button(frame2, text = “Add”, command = self.add).pack(
plusImage = PhotoImage(file = “image/plus.gif”) create an image
create a button
callback method
callback method
callback method
callback method
create GUI

292 Chapter 9 GUI Programming Using Tkinter
The program creates a menu bar in line 9, and the menu bar is added to the window. To dis-
play the menu, use the config method to add the menu bar to the container (line 10). To cre-
ate a menu inside a menu bar, use the menu bar as the parent container (line 13) and invoke
the menu bar’s add_cascade method to set the menu label (line 14). You can then use the
add_command method to add items to the menu (lines 15–23). Note that the tearoff is set
to 0, which specifies that the menu cannot be moved out of the window. If this option is not
set, the menu can be moved out of the window, as shown in Figure 9.14c.
The program creates another menu named Exit (lines 26–27) and adds the Quit menu
item to it (line 28).
The program creates a frame named frame0 (lines 31–32) and uses it to hold toolbar but-
tons. The toolbar buttons are buttons with images, which are created by using the
PhotoImage class (lines 35–38). The command for each button specifies a callback function
to be invoked when a toolbar button is clicked (lines 40–47).
The program creates a frame named frame1 (lines 50–51) and uses it to hold labels and
entries for numbers. Variables v1, v2, and v3 bind the entries (lines 53, 57, and 61).
The program creates a frame named frame2 (lines 66–67) and uses it to hold four buttons
for performing Add, Subtract, Multiply, and Divide. The Add button, Add menu item, and
Add tool bar button have the same callback function add (lines 79–80), which is invoked
when any one of them—the button, menu item, or tool bar button—is clicked.
9.10 Popup Menus
A popup menu, also known as a context menu, is like a regular menu, but it does not
have a menu bar and it can float anywhere on the screen.
Creating a popup menu is similar to creating a regular menu. First, you create an instance of
Menu, and then you can add items to it. Finally, you bind a widget with an event to pop up
the menu.
The example in Listing 9.14 uses popup menu commands to select a shape to be displayed
in a canvas, as shown in Figure 9.15.
LISTING 9.14 PopupMenuDemo.py
1 from tkinter import * # Import all definitions from tkinter
2
3 class PopupMenuDemo:
4 def __init__(self):
5 window = Tk() # Create a window
6 window.title(“Popup Menu Demo”) # Set title
7
(a) (b) (c)
FIGURE 9.14 The program performs arithmetic operations using menu commands, toolbar buttons, and buttons.
Key
Point

9.10 Popup Menus 293
8 # Create a popup menu
9 self.menu = Menu(window, tearoff = 0)
10 self.menu.add_command(label = “Draw a line”,
11 command = self.displayLine)
12 self.menu.add_command(label = “Draw an oval”,
13 command = self.displayOval)
14 self.menu.add_command(label = “Draw a rectangle”,
15 command = self.displayRect)
16 self.menu.add_command(label = “Clear”,
17 command = self.clearCanvas)
18
19 # Place canvas in window
20 self.canvas = Canvas(window, width = 200,
21 height = 100, bg = “white”)
22 self.canvas.pack()
23
24 # Bind popup to canvas
25 self.canvas.bind(““, self.popup)
26
27 window.mainloop() # Create an event loop
28
29 # Display a rectangle
30 def displayRect(self):
31 self.canvas.create_rectangle(10, 10, 190, 90, tags = “rect”)
32
33 # Display an oval
34 def displayOval(self):
35 self.canvas.create_oval(10, 10, 190, 90, tags = “oval”)
36
37 # Display two lines
38 def displayLine(self):
39 self.canvas.create_line(10, 10, 190, 90, tags = “line”)
40 self.canvas.create_line(10, 90, 190, 10, tags = “line”)
41
42 # Clear drawings
43 def clearCanvas(self):
44 self.canvas.delete(“rect”, “oval”, “line”)
45
46 def popup(self, event):
47 self.menu.post(event.x_root, event.y_root)
48
49 PopupMenuDemo() # Create GUI
create a menu
add menu item
create a canvas
bind popup menu
display rectangle
display oval
(a) (b) (c)
FIGURE 9.15 The program displays a popup menu when the canvas is clicked.
The program creates a menu to hold menu items (lines 9–17). A canvas is created to
display the shapes. The menu items use callback functions to instruct the canvas to draw
shapes.
display lines
clear canvas
create GUI

294 Chapter 9 GUI Programming Using Tkinter
Customarily, you display a popup menu by pointing to a widget and clicking the right
mouse button. The program binds the right mouse button click with the popup callback
function on the canvas (line 25). When you click the right mouse button, the popup call-
back function is invoked, which displays the menu at the location where the mouse is
clicked.
9.28 What method do you use to display a menu bar?
9.29 How do you display a popup menu?
9.11 Mouse, Key Events, and Bindings
You can use the bind method to bind mouse and key events to a widget.
The preceding example used the widget’s bind method to bind a mouse event with a callback
handler by using the syntax:
widget.bind(event, handler)
If a matching event occurs, the handler is invoked. In the preceding example, the event is
and the handler function is popup. The event is a standard Tkinter object,
which is automatically created when an event occurs. Every handler has an event as its argu-
ment. The following example defines the handler using the event as the argument:
menu.post(event.x_root, event.y_root)
The event object has a number of properties describing the event pertaining to the event.
For example, for a mouse event, the event object uses the x, y properties to capture the cur-
rent mouse location in pixels.
Table 9.2 lists some commonly used events and Table 9.3 lists some event properties.
The program in Listing 9.15 processes mouse and key events. It displays the window as
shown in Figure 9.16a. The mouse and key events are processed and the processing informa-
tion is displayed in the command window, as shown in Figure 9.16b.
def popup(event):
TABLE 9.2 Events
Event Description
An event occurs when a mouse button is moved while being held down on the widget.
Button-1, Button-2, and Button-3 identify the left, middle, and right buttons. When a mouse button
is pressed over the widget, Tkinter automatically grabs the mouse pointer’s location. ButtonPressed-i is
synonymous with Button-i.
An event occurs when a mouse button is released.
An event occurs when a mouse button is double-clicked.
An event occurs when a mouse pointer enters the widget.
An event occurs when a key is pressed.
An event occurs when a mouse pointer leaves the widget.
An event occurs when the Enter key is pressed. You can bind any key such as A, B, Up, Down, Left, Right
in the keyboard with an event.
An event occurs when the Shift+A keys are pressed. You can combine Alt, Shift, and Control with other keys.
An event occurs when a mouse button is triple-clicked.
✓Point✓Check
Key
Point

9.11 Mouse, Key Events, and Bindings 295
TABLE 9.3 Event Properties
Event Property Description
char The character entered from the keyboard for key events.
keycode The key code (i.e., Unicode) for the key entered from the keyboard for key events.
keysym The key symbol (i.e., character) for the key entered from the keyboard for key events.
num The button number (1, 2, 3) indicates which mouse button was clicked.
widget The widget object that fires this event.
x and y The current mouse location in the widget in pixels.
x__root and y_root The current mouse position relative to the upper-left corner of the screen, in pixels.
LISTING 9.15 MouseKeyEventDemo.py
1 from tkinter import * # Import all definitions from tkinter
2
3 class MouseKeyEventDemo:
4 def __init__(self):
5 window = Tk() # Create a window
6 window.title(“Event Demo”) # Set a title
7 canvas = Canvas(window, bg = “white”, width = 200, height = 100)
8 canvas.pack()
9
10 # Bind with event
11
12
13 # Bind with event
14
15
16
17 window.mainloop() # Create an event loop
18
19
20 print(“clicked at”, event.x, event.y)
21 print(“Position in the screen”, event.x_root, event.y_root)
22 print(“Which button is clicked? “, event.num)
23
24
25 print(“keysym? “, event.keysym)
26 print(“char? “, event.char)
27 print(“keycode? “, event.keycode)
28
29 MouseKeyEventDemo() # Create GUI
def processKeyEvent(self, event):
def processMouseEvent(self, event):
canvas.focus_set()
canvas.bind(““, self.processKeyEvent)
canvas.bind(““, self.processMouseEvent)
(a) (b)
FIGURE 9.16 The program processes mouse and key events.
create a canvas
bind a mouse event
bind a key event
set focus
process mouse event
process key event
create GUI

296 Chapter 9 GUI Programming Using Tkinter
The program creates a canvas (line 7) and binds a mouse event with the call-
back function processMouseEvent (line 11) on the canvas. Nothing is drawn on the canvas.
So it is blank as shown in Figure 9.16a. When the left mouse button is clicked on the canvas,
an event is created. The processMouseEvent is invoked to process an event that displays
the mouse pointer’s location on the canvas (line 20), on the screen (line 21), and which mouse
button is clicked (line 22).
The Canvas widget is also the source for the key event. The program binds a key event
with the callback function processKeyEvent on the canvas (line 14) and sets the focus on
the canvas so that the canvas will receive input from the keyboard (line 15).
Listing 9.16 displays a circle on the canvas. The circle radius is increased with a left mouse
click and decreased with a right mouse click, as shown in Figure 9.17.
LISTING 9.16 EnlargeShrinkCircle.py
1 from tkinter import * # Import all definitions from tkinter
2
3 class EnlargeShrinkCircle:
4 def __init__(self):
5
6
7 window = Tk() # Create a window
8 window.title(“Control Circle Demo”) # Set a title
9 self.canvas = Canvas(window, bg = “white”,
10 width = 200, height = 200)
11
12 self.canvas.create_oval(
13 100 – self.radius, 100 – self.radius,
14 100 + self.radius, 100 + self.radius, tags = “oval”)
15
16 # Bind canvas with mouse events
17
18
19
20 window.mainloop() # Create an event loop
21
22
23 self.canvas.delete(“oval”)
24 if self.radius < 100: 25 self.radius += 2 26 self.canvas.create_oval( 27 100 - self.radius, 100 - self.radius, 28 100 + self.radius, 100 + self.radius, tags = "oval") 29 30 31 self.canvas.delete("oval") 32 if self.radius > 2:
33 self.radius -= 2
34 self.canvas.create_oval(
35 100 – self.radius, 100 – self.radius,
36 100 + self.radius, 100 + self.radius, tags = “oval”)
37
38 EnlargeShrinkCircle() # Create GUI
The program creates a canvas (line 9) and displays a circle on the canvas with an initial
radius of 50 (lines 5 and 12–14). The canvas is bound to a mouse event with the
handler increaseCircle (line 17) and to a mouse event with the handler
decreaseCircle (line 18). When the left mouse button is pressed, the increaseCircle
def decreaseCircle(self, event):
def increaseCircle(self, event):
self.canvas.bind(““, self.decreaseCircle)
self.canvas.bind(““, self.increaseCircle)
self.canvas.pack()
self.radius = 50
initialize GUI
set radius property
create canvas
bind a mouse event
bind a mouse event
increase circle
decrease circle
create GUI

9.12 Animations 297
function is invoked to increase the radius (lines 24–25) and redisplay the circle (lines 26–28).
When the right mouse button is pressed, the decreaseCircle function is invoked to
decrease the radius (lines 32–33) and redisplay the circle (lines 34–36).
9.30 How do you bind a canvas with the left mouse click event and callback function p?
9.31 What is the event for moving the mouse while pressing the right mouse button?
9.32 What is the event for clicking the left mouse button twice?
9.33 What is the event for clicking the middle mouse button three times?
9.34 What argument is automatically passed to an event-handling function?
9.35 How do you get the current mouse location from the event object?
9.36 How do you get the key character from the event object?
9.12 Animations
Animations can be created by displaying a sequence of drawings.
The Canvas class can be used to develop animations. You can display graphics and text on
the canvas and use the move(tags, dx, dy) method to move the graphic with the specified
tags dx pixels to the right if dx is positive and dy pixels down if dy is positive. If dx or dy is
negative, the graphic is moved left or up.
The program in Listing 9.17 displays a moving message repeatedly from left to right, as
shown in Figure 9.18.
LISTING 9.17 AnimationDemo.py
1 from tkinter import * # Import all definitions from tkinter
2
3 class AnimationDemo:
4 def __init__(self):
5 window = Tk() # Create a window
6 window.title(“Animation Demo”) # Set a title
7
8 width = 250 # Width of the canvas
9
10
11 canvas.pack()
12
13 x = 0 # Starting x position
14
15 text = “Message moving?”, tags = “text”)
canvas.create_text(x, 30,
width = 250, height = 50)
canvas = Canvas(window, bg = “white”,
FIGURE 9.17 The program uses mouse events to control the circle’s size.
create a canvas
create a text string
✓Point✓Check
Key
Point

298 Chapter 9 GUI Programming Using Tkinter
16
17 dx = 3
18 while True:
19 # Move text dx unit
20 # Sleep for 100 milliseconds
21 # Update canvas
22 if x < width: 23 x += dx # Get the current position for string 24 else: 25 x = 0 # Reset string position to the beginning 26 canvas.delete("text") 27 # Redraw text at the beginning 28 canvas.create_text(x, 30, text = "Message moving?", 29 tags = "text") 30 31 window.mainloop() # Create an event loop 32 33 AnimationDemo() # Create GUI canvas.update() canvas.after(100) canvas.move("text", dx, 0) The program creates a canvas (line 9) and displays text on the canvas at the specified initial location (lines 13–15). The animation is done essentially in the following three statements in a loop (lines 19–21): canvas.move("text", dx, 0) # Move text dx unit canvas.after(100) # Sleep for 100 milliseconds canvas.update() # Update canvas The x-coordinate of the location is moved to the right dx units by invoking canvas.move (line 19). Invoking canvas.after(100) puts the program to sleep for 100 milliseconds (line 20). Invoking canvas.update() redisplays the canvas (line 21). You can add tools to control the animation’s speed, stop the animation, and resume the ani- mation. Listing 9.18 rewrites Listing 9.17 by adding four buttons to control the animation, as shown in Figure 9.19. LISTING 9.18 ControlAnimation.py 1 from tkinter import * # Import all definitions from tkinter 2 3 class ControlAnimation: 4 def __init__(self): 5 window = Tk() # Create a window 6 window.title("Control Animation Demo") # Set a title 7 8 self.width = 250 # Width of self.canvas 9 = Canvas(window, bg = "white", 10 width = self.width, height = 50) 11 self.canvas.pack() 12 13 frame = Frame(window) 14 frame.pack() 15 btStop = Button(frame, text = "Stop", command = self.stop) self.canvas move text FIGURE 9.18 The program animates a moving message. sleep update canvas restart from left delete text create a text string create GUI 9.12 Animations 299 16 btStop.pack(side = LEFT) 17 btResume = Button(frame, text = "Resume", 18 command = self.resume) 19 btResume.pack(side = LEFT) 20 btFaster = Button(frame, text = "Faster", 21 command = self.faster) 22 btFaster.pack(side = LEFT) 23 btSlower = Button(frame, text = "Slower", 24 command = self.slower) 25 btSlower.pack(side = LEFT) 26 27 # Starting x position 28 = 100 # Set a sleep time 29 self.canvas.create_text(self.x, 30, 30 text = "Message moving?", tags = "text") 31 32 33 34 self.animate() 35 36 window.mainloop() # Create an event loop 37 38 # Stop animation 39 self.isStopped = True 40 41 # Resume animation 42 self.isStopped = False 43 self.animate() 44 45 # Speed up the animation 46 if self.sleepTime > 5:
47 self.sleepTime -= 20
48
49 # Slow down the animation
50 self.sleepTime += 20
51
52 # Move the message
53 while not self.isStopped:
54 self.canvas.move(“text”, self.dx, 0) # Move text
55 self.canvas.after(self.sleepTime) # Sleep
56 self.canvas.update() # Update canvas
57 if self.x < self.width: 58 self.x += self.dx # Set new position 59 else: 60 self.x = 0 # Reset string position to beginning 61 self.canvas.delete("text") 62 # Redraw text at the beginning 63 self.canvas.create_text(self.x, 30, 64 text = "Message moving?", tags = "text") 65 66 ControlAnimation() # Create GUI def animate(self): def slower(self): def faster(self): def resume(self): def stop(self): self.isStopped = False self.dx = 3 self.sleepTime self.x = 0 FIGURE 9.19 The program uses buttons to control the animation. starting position initial sleep time stop resume faster slower animate update create GUI 300 Chapter 9 GUI Programming Using Tkinter The program starts the animation by invoking animate() (line 34). The isStopped variable determines whether the animation continues to move. It is set to False initially (line 33). When it is false, the loop in the animate method executes continuously (lines 53–64). Clicking the buttons Stop, Resume, Faster, or Slower stops, resumes, speeds up, or slows down the animation. When the Stop button is clicked, the stop function is invoked to set isStopped to True (line 39). This causes the animation loop to terminate (line 53). When the Resume button is clicked, the resume function is invoked to set isStopped to False (line 42) and resume animation (line 43). The speed of the animation is controlled by the variable sleepTime, which is set to 100 milliseconds initially (line 28). When the Faster button is clicked, the faster method is invoked to reduce sleepTime by 20 (line 47). When the Slower button is clicked, the slower function is invoked to increase sleepTime by 20 (line 50). 9.37 What method can you use to put the program to sleep? 9.38 What method can you use to update the drawing? 9.13 Scrollbars A Scrollbar widget can be used to scroll the contents in a Text, Canvas, or Listbox widget vertically or horizontally. Listing 9.19 gives an example of scrolling in a Text widget, as shown in Figure 9.20. LISTING 9.19 ScrollText.py 1 from tkinter import * # Import all definitions from tkinter 2 3 class ScrollText: 4 def __init__(self): 5 window = Tk() # Create a window 6 window.title("Scroll Text Demo") # Set title 7 8 frame1 = Frame(window) 9 frame1.pack() 10 scrollbar = Scrollbar(frame1) 11 scrollbar.pack(side = RIGHT, fill = Y) 12 text = Text(frame1, width = 40, height = 10, wrap = WORD, 13 ) 14 text.pack() 15 16 17 window.mainloop() # Create an event loop 18 19 ScrollText() # Create GUI scrollbar.config(command = text.yview) yscrollcommand = scrollbar.set create a Scrollbar create Text tie scrollbar with text create GUI FIGURE 9.20 You can use the scrollbar (on the far right) to scroll to see text not currently visible in the Text widget. ✓Point✓Check Key Point 9.14 Standard Dialog Boxes 301 The program creates a Scrollbar (line 10) and places it to the right of the text (line 11). The scrollbar is tied to the Text widget (line 15) so that the contents in the Text widget can be scrolled through. 9.39 What widgets can be used with a scrollbar? 9.40 How do you associate a scrollbar with a view? 9.14 Standard Dialog Boxes You can use standard dialog boxes to display message boxes or to prompt the user to enter numbers and strings. Finally, let’s look at Tkinter’s standard dialog boxes (often referred to simply as dialogs). Listing 9.20 gives an example of using these dialogs. A sample run of the program is shown in Figure 9.21. LISTING 9.20 DialogDemo.py 1 import tkinter.messagebox 2 import tkinter.simpledialog 3 import tkinter.colorchooser 4 5 6 7 tkinter.messagebox.showwarning("showwarning", "This is a warning") 8 9 tkinter.messagebox.showerror("showerror", "This is an error") 10 11 isYes = tkinter.messagebox.askyesno("askyesno", "Continue?") 12 print(isYes) 13 14 isOK = tkinter.messagebox.askokcancel("askokcancel", "OK?") 15 print(isOK) 16 17 isYesNoCancel = tkinter.messagebox.askyesnocancel( 18 "askyesnocancel", "Yes, No, Cancel?") 19 print(isYesNoCancel) 20 21 name = tkinter.simpledialog.askstring( 22 "askstring", "Enter your name") 23 print(name) 24 25 age = tkinter.simpledialog.askinteger( 26 "askinteger", "Enter your age") 27 print(age) 28 29 weight = tkinter.simpledialog.askfloat( 30 "askfloat", "Enter your weight") 31 print(weight) The program invokes the showinfo, showwarning, and showerror functions to display an information message (line 5), a warning (line 7), and an error (line 9). These functions are defined in the tkinter.messagebox module (line 1). The askyesno function displays the Yes and No buttons in the dialog box (line 11). The function returns True if the Yes button is clicked or False if the No button is clicked. tkinter.messagebox.showinfo("showinfo", "This is an info msg") showinfo showwarning showerror askyesno askokcancel askyesnocancel askstring askinteger askfloat ✓Point✓Check Key Point 302 Chapter 9 GUI Programming Using Tkinter The askokcancel function displays the OK and Cancel buttons in the dialog box (line 14). The function returns True if the OK button is clicked or False if the Cancel button is clicked. The askyesnocancel function displays the Yes, No, and Cancel buttons in the dialog box (line 17). The function returns True if the Yes button is clicked, False if the No button is clicked or None if the Cancel button is clicked. The askstring function (line 21) returns the string entered from the dialog box after the OK button is clicked or None if the Cancel button is clicked. The askinteger function (line 25) returns the integer entered from the dialog box after the OK button is clicked or None if the Cancel button is clicked. The askfloat function (line 29) returns the float entered from the dialog box after the OK button is clicked or None if the Cancel button is clicked. All the dialog boxes are modal windows, which means that the program cannot continue until a dialog box is dismissed. 9.41 Write a statement that displays “Welcome to Python” in a message dialog. 9.42 Write statements using a dialog box to prompt the user to enter an integer, a float, and a string. KEY TERMS FIGURE 9.21 You can use the standard dialogs to display message boxes and accept input. modal callback functions 274 geometry manager 278 grid manager 282 handlers 274 pack manager 284 parent container 273 place manager 286 widget class 273 ✓Point✓Check Programming Exercises 303 CHAPTER SUMMARY 1. To develop a GUI application in Tkinter, first use the Tk class to create a window, then create widgets and place them inside the window. The first argument of each widget class must be the parent container. 2. To place a widget in a container, you have to specify its geometry manager. 3. Tkinter supports three geometry managers: pack, grid, and place. The pack manager places widgets side by side or on top of each other. The grid manager places widgets in grids. The place manager places the widget in absolute locations. 4. Many widgets have the command option for binding an event with a callback func- tion. When an event occurs, the callback function is invoked. 5. The Canvas widget can be used to draw lines, rectangles, ovals, arcs, and polygons, and to display images and text strings. 6. Images can be used in many widgets such as labels, buttons, check buttons, radio but- tons, and canvases. 7. You can use the Menu class to create menu bars, menu items, and popup menus. 8. You can bind mouse and key events to a widget with a callback function. 9. You can use canvases to develop animations. 10. You can use standard dialog boxes to display messages and receive input. TEST QUESTIONS Do test questions for this chapter online at www.cs.armstrong.edu/liang/py/test.html. PROGRAMMING EXERCISES Note The image icons used in the exercises throughout the book can be obtained from www.cs.armstrong.edu/liang/py/book.zip under the image folder. Sections 9.2–9.8 *9.1 (Move the ball) Write a program that moves a ball in a panel. You should define a panel class for displaying the ball and provide the methods for moving the ball left, right, up, and down, as shown in Figure 9.22a. Check the boundaries to pre- vent the ball from moving out of sight completely. *9.2 (Create an investment-value calculator) Write a program that calculates the future value of an investment at a given interest rate for a specified number of years. The formula for the calculation is as follows: futureValue = investmentAmount * (1 + monthlyInterestRate)years * 12 download image files www.cs.armstrong.edu/liang/py/test.html www.cs.armstrong.edu/liang/py/book.zip 304 Chapter 9 GUI Programming Using Tkinter *9.3 (Select geometric figures) Write a program that draws a rectangle or an oval, as shown in Figure 9.23. The user selects a figure from a radio button and specifies whether it is filled by selecting a check button. 9.5 (Game: display a checkerboard ) Write a program that displays a checkerboard in which each white and black cell is a canvas with a background of black or white, as shown in Figure 9.25a. (a) (b) FIGURE 9.22 (a) You can click a button to move the ball. (b) You can obtain the future value by entering the investment amount, years, and annual interest rate. FIGURE 9.23 The program displays a rectangle or an oval when you select a shape type, and whether it is filled. FIGURE 9.24 The program displays 20 rectangles. Use text fields for users to enter the investment amount, years, and interest rate. Display the future amount in a text field when the user clicks the Calculate button, as shown in Figure 9.22b. *9.4 (Display rectangles) Write a program that displays 20 rectangles, as shown in Figure 9.24. Programming Exercises 305 9.6 (Game: display a tic-tac-toe board ) Write a program that displays nine labels. Each label may display an image icon for an X or an image icon for an O, as shown in Figure 9.25b. What to display is randomly decided. Use the random.randint(0, 1) function to generate an integer 0 or 1, which corre- sponds to displaying a cross image (X) icon or a not image (O) icon. The cross and not images are in the files x.gif and o.gif. 9.7 (Display an grid ) Write a program that displays an grid, as shown in Figure 9.25c. Use red for vertical lines and blue for horizontal lines. **9.8 (Display numbers in a triangular pattern) Write a program that displays numbers in a triangular pattern, as shown in Figure 9.25d. The number of lines in the dis- play changes to fit the window as the window resizes. 8 * 88 * 8 (a) (b) (c) (d) FIGURE 9.25 (a) The programs display a checkerboard, (b) a tic-tac-toe board, (c) a grid, and (d) numbers in a triangular formation. **9.9 (Display a bar chart) Write a program that uses a bar chart to display the percent- ages of the overall grade represented by the project, quizzes, the midterm exam, and the final exam, as shown in Figure 9.26a. Suppose that the project is 20 per- cent of the grade and its value is displayed in red, quizzes are 10 percent and are displayed in blue, the midterm exam is 30 percent and is displayed in green, and the final exam is 40 percent and is displayed in orange. FIGURE 9.26 (a) The programs display a bar chart and (b) a pie chart. 306 Chapter 9 GUI Programming Using Tkinter **9.10 (Display a pie chart) Write a program that uses a pie chart to display the percent- ages of the overall grade represented by the project, quizzes, the midterm exam, and the final exam, as shown in Figure 9.26b. Suppose that project is weighted as 20 percent of the grade and is displayed in red, quizzes are 10 percent and are dis- played in blue, the midterm exam is 30 percent and is displayed in green, and the final exam is 40 percent and is displayed in orange. **9.11 (Display a clock) Write a program that displays a clock to show the current time, as shown in Figure 9.27a. To obtain the current time, use the datetime class in Supplement II.B. Sections 9.9–9.14 **9.12 (Alternate two messages) Write a program to change, with a left mouse click, between two messages displayed on a canvas, “Programming is fun” and “It is fun to program,” as shown in Figure 9.27b–c. *9.13 (Display the mouse position) Write two programs: one that displays the mouse position when the mouse is clicked (see Figure 9.28a–b), and the other displays the mouse position when the mouse button is pressed and ceases to display it when the mouse button is released. *9.14 (Draw lines using the arrow keys) Write a program that draws line segments using the arrow keys. The line starts from the center of the frame and draws toward east, north, west, or south when the Right arrow key, Up arrow key, Left arrow key, or Down arrow key is clicked, as shown in Figure 9.28c. (b) (c)(a) FIGURE 9.27 (a) The program displays a clock for the current time. (b–c) The program alternates between the display of two messages. (a) (b) (c) FIGURE 9.28 (a–b) The program displays the location of the mouse pointer when the mouse is clicked. (c) The program draws a line when the Up, Down, Left, and Right arrow keys are pressed. Programming Exercises 307 **9.15 (Display a still fan) Write a program that displays a still fan, as shown in Figure 9.29a. **9.16 (Display a running fan) Write a program that displays a fan running, as shown in Figure 9.29a. **9.17 (Racing car) Write a program that simulates car racing, as shown in Figure 9.29b–d. The car moves from left to right. When it reaches the right end, it restarts from the left and continues the same process. Let the user increase and decrease the car’s speed by pressing the Up and Down arrow keys. *9.18 (Display flashing text) Write a program that displays the flashing text “Welcome,” as shown in Figure 9.30a–b. (Hint: To make the text flash, you need to repeatedly draw it on the canvas or alternately delete it. Use a Boolean variable to control the alternation.) *9.19 (Move a circle using keys) Write a program that moves a circle up, down, left, or right using the arrow keys, as shown in Figure 9.30c–d. **9.20 (Geometry: inside a circle?) Write a program that draws a fixed circle centered at (100, 60) with radius 50. Whenever the mouse is moved while the left button is pressed, display the message indicating whether the mouse pointer is inside the circle, as shown in Figure 9.31. **9.21 (Geometry: inside a rectangle?) Write a program that draws a fixed rectangle cen- tered at (100, 60) with width 100 and height 40. Whenever the mouse is moved, display the message indicating whether the mouse pointer is inside the rectangle, as shown in Figure 9.32. To detect whether the pointer is inside a rectangle, use the Rectangle2D class defined in Exercise 8.19. (a) (b) (c) (d) x x+20 x+40 y y–20 y–10 y–30 (x, y) FIGURE 9.29 (a) The programs display a fan and (b–c) a moving car. (d) You can redraw a car with a new base point. (a) (b) (c) (d) FIGURE 9.30 (a–b) The program displays a flashing label with text. (c–d) The circle is moved when the arrow keys are pressed. 308 Chapter 9 GUI Programming Using Tkinter **9.22 (Geometry: pendulum) Write a program that animates a pendulum swinging, as shown in Figure 9.33. Press the Up arrow key to increase the speed and the Down arrow key to decrease it. Press the S key to stop the animation and the R key to resume it. FIGURE 9.31 Detect whether the mouse pointer is inside a circle. FIGURE 9.32 Detect whether the mouse pointer is inside a rectangle. FIGURE 9.33 The program animates a pendulum swinging. FIGURE 9.34 The and buttons move the message on the panel, and you can also set the background color for the message. = 76= *9.23 (Buttons and radio buttons) Write a program that uses radio buttons to select back- ground colors for text, as shown in Figure 9.34. The available colors are red, yel- low, white, gray, and green. The program uses the buttons and to move the text left or right. = 76= Programming Exercises 309 9.24 (Display circles) Write a program that displays a new larger circle with a left mouse click and removes the largest circle with a right mouse click, as shown in Figure 9.35. **9.25 (Traffic lights) Write a program that simulates a traffic light. The program lets the user select one of three lights: red, yellow, or green. When a radio button is selected, the light is turned on, and only one light can be on at a time (see Figure 9.36a–b). No light is on when the program starts. *9.26 (Display balls with random colors) Write a program that displays ten balls with random colors and placed at random locations, at shown in Figure 9.36c. *9.27 (Compare loans with various interest rates) Rewrite Exercise 5.23 to create the user interface shown in Figure 9.37. Your program should let the user enter the loan amount and loan period in the number of years from a text field, and should display the monthly and total payments for each interest rate starting from 5 per- cent to 8 percent, with increments of one-eighth, in a text area. **9.28 (Geometry: display angles) Write a program that enables the user to drag the ver- tices of a triangle and displays the angles dynamically, as shown in Figure 9.38a. Change the mouse cursor to the cross-hair shape when the mouse is moved close to a vertex. The formula to compute angles A, B, and C (see Figure 9.38b) is given in Listing 3.2. Hint: Use the Point class to represent a point, as described in Exercise 8.17. Cre- ate three points at random locations initially. When the mouse is moved close to a point, change the cursor to a cross-hair pointer and reset the point to where the mouse is. Whenever a point is moved, redisplay the triangle and the angles. (+) FIGURE 9.35 The program adds/removes circles with left/right mouse clicks. (a) (b) (c) FIGURE 9.36 (a–b) The radio buttons let the user choose a traffic light color. (c) Ten balls with random colors are displayed at random locations. 310 Chapter 9 GUI Programming Using Tkinter **9.29 (Geometry: intersecting point) Write a program that displays two line segments with their end points and their intersecting point. Initially, the end points are at (20, 20) and (56, 130) for line 1 and at (100, 20) and (16, 130) for line 2. The user can use the mouse to drag a point and dynamically display the intersecting point, as shown in Figure 9.38c. (Hint: See Exercise 4.25 for finding the intersect- ing point of two unbounded lines. The hint for Exercise 9.28 applies to this exer- cise as well.) 9.30 (Display a rectanguloid ) Write a program that displays a rectanguloid, as shown in Figure 9.39a. 9.31 (Display five filled circles) Write a program that displays five filled circles, as shown in Figure 9.39b. Enable the user to drag the blue circle using the mouse, as shown in Figure 9.39c. (a) (b) (c) A B C a b c x1, y1 x2, y2 x3, y3 FIGURE 9.38 (a–b) The program enables the user to drag vertices and display the angles dynamically. (c) The program enables the user to drag vertices and display the lines and their intersecting point dynamically. (a) (b) (c) FIGURE 9.39 (a) The program displays a rectanguloid. (b–c) The blue circle is dragged with the mouse. FIGURE 9.37 The program displays a table for monthly payments and total payments on a given loan based on various interest rates. Programming Exercises 311 *9.32 (Two movable vertices and their distances) Write a program that displays two cir- cles with radius 20 at locations (20, 20) and (120, 50) with a line connecting the two circles, as shown in Figure 9.40a. The distance between the circles is dis- played along the line. The user can drag a circle. When that happens, the circle and its line are moved and the distance between the circles is updated. Your program should not allow the circles to get too close. Keep them at least 70 pixels apart between the two circles’ centers. **9.33 (Draw an arrow line) Write a program that randomly draws an arrow line when the Draw a Random Arrow Line button is clicked, as shown in Figure 9.40b. **9.34 (Address book) Write a program that creates a user interface for displaying an address, as shown in Figure 9.40c. (a) (b) (c) FIGURE 9.40 (a) The user can drag the circles and the program redisplays the distance. (b) The program draws an arrow line randomly. (c) The program creates a user interface for displaying addresses. This page intentionally left blank LISTS CHAPTER 10 Objectives ■ To describe why lists are useful in programming (§10.1). ■ To learn how to create lists (§10.2.1). ■ To explore common operations for sequences (§10.2.2). ■ To use the len, min, max, sum, and random.shuffle functions with a list (§10.2.3). ■ To access list elements by using indexed variables (§10.2.4). ■ To obtain a sublist from a larger list by using the slicing operator [start : end] (§10.2.5). ■ To use the + (concatenation), * (repetition), and in/not in operators on lists (§10.2.6). ■ To traverse elements in a list using a for loop (§10.2.7). ■ To compare the contents of two lists by using comparison operators (§10.2.8). ■ To create lists by using list comprehension (§10.2.9). ■ To invoke a list’s append, count, extend, index, insert, pop, remove, reverse, and sort methods (§10.2.10). ■ To split a string into a list using the str’s split method (§10.2.11). ■ To read data from the console into a list (§10.2.12). ■ To use lists in application development (§§10.3–10.5). ■ To copy the contents of one list to another (§10.6). ■ To develop and invoke functions that include list arguments and return lists (§§10.7–10.9). ■ To search elements using the linear (§10.10.1) or binary (§10.10.2) search algorithm. ■ To sort a list by using the selection sort (§10.11.1). ■ To sort a list by using the insertion sort (§10.11.2). ■ To develop a bouncing ball animation by using a list (§10.12). 314 Chapter 10 Lists 10.1 Introduction A list can store a collection of data of any size. Programs commonly need to store a large number of values. Suppose, for instance, that you need to read 100 numbers, compute their average, and then find out how many of the numbers are above the average. Your program first reads the numbers and computes their average, then compares each number with the average to determine whether it is above the average. In order to accomplish this task, the numbers must all be stored in variables. To do this, you would have to create 100 variables and repeatedly write almost identical code 100 times. Writing a program this way is impractical. So, how do you solve this problem? An efficient, organized approach is needed. Python provides a type called a list that stores a sequential collection of elements. In our example, you can store all 100 num- bers in a list and access them through a single list variable. The solution might look like Listing 10.1. LISTING 10.1 DataAnalysis.py 1 NUMBER_OF_ELEMENTS = 5 # For simplicity, use 5 instead of 100 2 # Create an empty list 3 sum = 0 4 5 for i in range(NUMBER_OF_ELEMENTS): 6 value = eval(input("Enter a new number: ")) 7 8 sum += value 9 10 average = sum / NUMBER_OF_ELEMENTS 11 12 count = 0 # The number of elements above average 13 for i in range(NUMBER_OF_ELEMENTS): 14 if numbers[i] > average:
15 count += 1
16
17 print(“Average is”, average)
18 print(“Number of elements above the average is”, count)
numbers.append(value)
numbers = []
why list?
create a list
store number in list
get average
above average?
Enter a new number:
Enter a new number:
Enter a new number:
Enter a new number:
Enter a new number:
Average is 3.0
Number of elements above the average is 2
5
4
3
2
1
The program creates an empty list (line 2). It repeatedly reads a number (line 6), appends
it to the list (line 7), and adds it to sum (line 8). It obtains average in line 10. It then com-
pares each number in the list with the average to count the number of values above the aver-
age (lines 12–15).
Note
In many other programming languages, you would use a type called an array to store a
sequence of data. An array has a fixed size. A Python list’s size is flexible. It can grow
and shrink on demand.
array
Key
Point

10.2 List Basics 315
index
10.2 List Basics
A list is a sequence defined by the list class. It contains the methods for creating,
manipulating, and processing lists. Elements in a list can be accessed through an index.
10.2.1 Creating Lists
The list class defines lists. To create a list, you can use list’s constructor, as follows:
list1 = list() # Create an empty list
list2 = list([2, 3, 4]) # Create a list with elements 2, 3, 4
list3 = list([“red”, “green”, “blue”]) # Create a list with strings
list4 = list(range(3, 6)) # Create a list with elements 3, 4, 5
list5 = list(“abcd”) # Create a list with characters a, b, c, d
You can also create a list by using the following syntax, which is a little simpler:
list1 = [] # Same as list()
list2 = [2, 3, 4] # Same as list([2, 3, 4])
list3 = [“red”, “green”] # Same as list([“red”, “green”])
The elements in a list are separated by commas and are enclosed by a pair of brackets ([]).
Note
A list can contain the elements of the same type or mixed types. For example, the fol-
lowing list is fine:
list4 = [2, “three”, 4]
10.2.2 List Is a Sequence Type
Strings and lists are sequence types in Python. A string is a sequence of characters, while a list
is a sequence of any elements. The common operations for sequences are summarized in
Table 10.1. These operations for strings were introduced in Chapter 8. The sequence opera-
tions for lists are the same as for strings. Sections 10.2.3–10.2.8 give examples of using these
operations for lists.
TABLE 10.1 Common Operations for Sequence s
Operation Description
x in s True if element x is in sequence s.
x not in s True if element x is not in sequence s.
s1 + s2 Concatenates two sequences s1 and s2.
s * n, n * s n copies of sequence s concatenated.
s[i] ith element in sequence s.
s[i : j] Slice of sequence s from index i to j 1.-
len(s) Length of sequence s, i.e., the number of elements in s.
min(s) Smallest element in sequence s.
max(s) Largest element in sequence s.
sum(s) Sum of all numbers in sequence s.
for loop Traverses elements from left to right in a for loop.
<, <=, >, >=, =, != Compares two sequences.
Key
Point
Use lists
VideoNote

316 Chapter 10 Lists
10.2.3 Functions for Lists
Several Python built-in functions can be used with lists. You can use the len function to
return the number of elements in the list, the max/min functions to return the elements with
the greatest and lowest values in the list, and the sum function to return the sum of all ele-
ments in the list. You can also use the shuffle function in the random module to shuffle the
elements randomly in the list. Here are some examples:
len
max
min
sum
random.shuffle
1 >>> list1 = [2, 3, 4, 1, 32]
2 >>> len(list1)
3 5
4 >>> max(list1)
5 32
6 >>> min(list1)
7 1
8 >>> sum(list1)
9 42
10 >>> import random
11 >>> random.shuffle(list1) # Shuffle the elements in list1
12 >>> list1
13 [4, 1, 2, 32, 3]
14 >>>
Invoking random.shuffle(list1) (line 11) randomly shuffles the elements in list1.
10.2.4 Index Operator []
An element in a list can be accessed through the index operator, using the following syntax:
myList[index]
List indexes are 0 based; that is, they range from 0 to len(myList)-1, as illustrated in
Figure 10.1.
myList = [5.6, 4.5, 3.3, 13.2, 4.0, 34.33, 34.0, 45.45, 99.993, 11123]
0 based
myList[index] can be used just like a variable, so it is also known as an indexed vari-
able. For example, the following code adds the values in myList[0] and myList[1] to
myList[2].
FIGURE 10.1 The list myList has 10 elements with indexes from 0 to 9.
myList reference
myList[0]
myList[1]
myList[2]
myList[3]
myList[4]
myList[6]
myList[5]
myList[7]
myList[8]
myList[9]
List reference
variable
List element at
index 5
5.6
4.5
3.3
13.2
4.0
34.33
34.0
45.45
99.993
11123
Element value

10.2 List Basics 317
myList[2] = myList[0] + myList[1]
The following loop assigns 0 to myList[0], 1 to myList[1], …, and 9 to
myList[9]:
for i in range(len(myList)):
myList[i] = i
Caution
Accessing a list out of bounds is a common programming error that results in a run-
time IndexError. To avoid this error, make sure that you do not use an index
beyond len(myList) – 1.
Programmers often mistakenly reference the first element in a list with index 1, but it
should be 0. This is called the off-by-one error. It is a common error in a loop to use <= where < should be used. For example, the following loop is wrong: i = 0 while i len(myList): print(myList[i]) i += 1 The <= should be replaced by <. Python also allows the use of negative numbers as indexes to reference positions relative to the end of the list. The actual position is obtained by adding the length of the list with the negative index. For example: <= IndexError off-by-one error negative index 1 >>> list1 = [2, 3, 5, 2, 33, 21]
2 >>> list1[-1]
3 21
4 >>> list1[-3]
5 2
6 >>>
In line 2, list1[-1] is same as list1[-1 + len(list1)], which gives the last ele-
ment in the list. In line 4, list1[-3] is same as list1[-3 + len(list1)], which gives
the third last element in the list.
10.2.5 List Slicing [start : end]
The index operator allows you to select an element at the specified index. The slicing opera-
tor returns a slice of the list using the syntax list[start : end]. The slice is a sublist
from index start to index end – 1. Here are some examples:
slicing operator
1 >>> list1 = [2, 3, 5, 7, 9, 1]
2 >>> list1[2 : 4]
3 [5, 7]
4 >>>
The starting index or ending index may be omitted. In this case, the starting index is 0 and
the ending index is the last index. For example:

318 Chapter 10 Lists
1 >>> list1 = [2, 3, 5, 2, 33, 21]
2 >>> list1[ : 2]
3 [2, 3]
4 >>> list1[3 : ]
5 [2, 33, 21]
6 >>>
Note that list1[ : 2] is the same as list1[0 : 2] (line 2), and that list1[3 : ] is
the same as list1[3 : len(list1)] (line 4).
You can use a negative index in slicing. For example:negative index
1 >>> list1 = [2, 3, 5, 2, 33, 21]
2 >>> list1[1 : -3]
3 [3, 5]
4 >>> list1[-4 : -2]
5 [3, 5]
6 >>>
In line 2, list1[1 : -3] is the same as list1[1 : -3 + len(list1)]. In line 4,
list1[-4 : -2] is the same as list1[-4 + len(list1) : -2 + len(list1)].
Note
If start >= end, list[start : end] returns an empty list. If end specifies a
position beyond the end of the list, Python will use the length of the list for end instead.
10.2.6 The +, *, and in/not in Operators
You can use the concatenation operator (+) to join two lists and the repetition operator (*) to
replicate elements in a list. Here are some examples:
concatenation operator +
repetition operator *
1 >>> list1 = [2, 3]
2 >>> list2 = [1, 9]
3 >>> list3 = list1 + list2
4 >>> list3
5 [2, 3, 1, 9]
6 >>>
7 >>> list4 = 3 * list1
8 >>> list4
9 [2, 3, 2, 3, 2, 3]
10 >>>
A new list is obtained by concatenating list1 with list2 (line 3). Line 7 duplicates
list1 three times to create a new list. Note that 3 * list1 is the same as list1 * 3.
You can determine whether an element is in a list by using the in or not in operator. For
example:
>>> list1 = [2, 3, 5, 2, 33, 21]
>>> 2 in list1
True

10.2 List Basics 319
10.2.7 Traversing Elements in a for Loop
The elements in a Python list are iterable. Python supports a convenient for loop, which
enables you to traverse the list sequentially without using an index variable. For example, the
following code displays all the elements in the list myList:
for u in myList:
print(u)
You can read the code as, “For each element u in myList, print it.”
You still have to use an index variable if you wish to traverse the list in a different order or
change the elements in the list. For example, the following code displays the elements at odd-
numbered positions.
for i in range(0, len(myList), 2):
print(myList[i])
10.2.8 Comparing Lists
You can compare lists using the comparison operators (>, >=, <, <=, ==, and !=). For this to work, the two lists must contain the same type of elements. The comparison uses lexicographical ordering: the first two elements are compared, and if they differ this deter- mines the outcome of the comparison; if they are equal, the next two elements are compared, and so on, until either list is exhausted. Here are some examples: >>> 2 not in list1
False
>>>
1 >>> list1 = [“green”, “red”, “blue”]
2 >>> list2 = [“red”, “blue”, “green”]
3 >>> list2 == list1
4 False
5 >>> list2 != list1
6 True
7 >>> list2 >= list1
8 False
9 >>> list2 > list1
10 False
11 >>> list2 < list1 12 True 13 >>> list2 <= list1 14 True 15 >>>
10.2.9 List Comprehensions
List comprehensions provide a concise way to create a sequential list of elements. A list com-
prehension consists of brackets containing an expression followed by a for clause, then zero
or more for or if clauses. The list comprehension produces a list with the results from eval-
uating the expression. Here are some examples:

320 Chapter 10 Lists
1 >>> list1 = [x for x in range(5)] # Returns a list of 0, 1, 2, 3, 4
2 >>> list1
3 [0, 1, 2, 3, 4]
4 >>>
5 >>> list2 = [0.5 * x for x in list1]
6 >>> list2
7 [0.0, 0.5, 1.0, 1.5, 2.0]
8 >>>
9 >>> list3 = [x for x in list2 if x < 1.5] 10 >>> list3
11 [0.0, 0.5, 1.0]
12 >>>
In line 1, list1 is created from an expression using a for clause. The numbers in list1
are 0, 1, 2, 3, and 4. Each number in list2 is half of the corresponding number in list1
(line 5). In line 9, list3 consists of the numbers whose value is less than 1.5 in list2.
10.2.10 List Methods
Once a list is created, you can use the list class’s methods (shown in Figure 10.2) to manip-
ulate the list.
1 >>> list1 = [2, 3, 4, 1, 32, 4]
2 >>> list1.append(19)
3 >>> list1
4 [2, 3, 4, 1, 32, 4, 19]
5 >>> list1.count(4) # Return the count for number 4
6 2
7 >>> list2 = [99, 54]
8 >>> list1.extend(list2)
9 >>> list1
10 [2, 3, 4, 1, 32, 4, 19, 99, 54]
11 >>> list1.index(4) # Return the index of number 4
12 2
FIGURE 10.2 The list class contains methods for manipulating a list.
list
Adds an element x to the end of the list.
Returns the number of times element x appears in the list.
Appends all the elements in l to the list.
Returns the index of the first occurrence of element x in the list.
Inserts an element x at a given index. Note that the first element in
the list has index 0.
Removes the element at the given position and returns it. The
parameter i is optional. If it is not specified, list.pop() removes
and returns the last element in the list.
Removes the first occurrence of element x from the list.
Reverses the elements in the list.
Sorts the elements in the list in ascending order.
append(x: object): None
count(x: object): int
extend(l: list): None
index(x: object): int
insert(index: int, x: object):
None
pop(i): object
remove(x: object): None
reverse(): None
sort(): None
Here are some examples that use the append, count, extend, index, and insert methods:

10.2 List Basics 321
Line 2 appends 19 to the list, and line 5 returns the count of the number of occurrences
of element 4 in the list. Invoking list1.extend() (line 8) appends list2 to list1.
Line 11 returns the index for element 4 in the list, and line 13 inserts 25 into the list at
index 1.
Here are some examples that use the insert, pop, remove, reverse, and sort
methods:
13 >>> list1.insert(1, 25) # Insert 25 at position index 1
14 >>> list1
15 [2, 25, 3, 4, 1, 32, 4, 19, 99, 54]
16 >>>
1 >>> list1 = [2, 25, 3, 4, 1, 32, 4, 19, 99, 54]
2 >>> list1.pop(2)
3 3
4 >>> list1
5 [2, 25, 4, 1, 32, 4, 19, 99, 54]
6 >>> list1.pop()
7 54
8 >>> list1
9 [2, 25, 4, 1, 32, 4, 19, 99]
10 >>> list1.remove(32) # Remove number 32
11 >>> list1
12 [2, 25, 4, 1, 4, 19, 99]
13 >>> list1.reverse() # Reverse the list
14 >>> list1
15 [99, 19, 4, 1, 4, 25, 2]
16 >>> list1.sort() # Sort the list
17 >>> list1
18 [1, 2, 4, 4, 19, 25, 99]
19 >>>
Line 2 removes the element at index 2 from the list. Invoking list1.pop() (line 6)
returns and removes the last element from list1. Line 10 removes element 32 from list1,
line 13 reverses the elements in the list, and line 15 sorts the elements in the list in ascending
order.
10.2.11 Splitting a String into a List
The str class contains the split method, which is useful for splitting items in a string into a
list. For example, the following statement:
items = “Jane John Peter Susan”.split()
splits the string Jane John Peter Susan into the list [‘Jane’, ‘John’, ‘Peter’,
‘Susan’]. In this case the items are delimited by spaces in the string. You can use a nonspace
delimiter. For example, the following statement:
items = “09/20/2012”.split(“/”)
splits the string 09/20/2012 into the list [’09’, ’20’, ‘2012’].

322 Chapter 10 Lists
Note
Python supports regular expressions, an extremely useful and powerful feature for
matching and splitting a string using a pattern. Regular expressions are complex for
beginning students. For this reason, we cover them in Supplement II.A, Regular
Expressions.
10.2.12 Inputting Lists
You may often need code that reads data from the console into a list. You can enter one data
item per line and append it to a list in a loop. For example, the following code reads ten num-
bers one per line into a list.
lst = [] # Create a list
print(“Enter 10 numbers: “)
for i in range(10):
lst.append(eval(input())
Sometimes it is more convenient to enter the data in one line separated by spaces. You can
use the string’s split method to extract data from a line of input. For example, the following
code reads ten numbers separated by spaces from one line into a list.
# Read numbers as a string from the console
s = input(“Enter 10 numbers separated by spaces from one line: “)
items = s.split() # Extract items from the string
lst = [eval(x) for x in items] # Convert items to numbers
Invoking input() reads a string. Using s.split() extracts the items delimited by
spaces from string s and returns items in a list. The last line creates a list of numbers by con-
verting the items into numbers.
10.2.13 Shifting Lists
Sometimes you need to shift the elements left or right. Python does not provide such
a method in the list class, but you can write the following function to perform a left
shift.
def shift(lst):
temp = lst[0] # Retain the first element
# Shift elements left
for i in range(1, len(lst)):
lst[i – 1] = lst[i]
# Move the first element to fill in the last position
lst[len(lst) – 1] = temp
10.2.14 Simplifying Coding
Lists can be used to greatly simplify coding for certain tasks. For example, suppose you
wish to obtain the English month name for a given month in number. If the month
names are stored in a list, the month name for a given month can be accessed simply
regular expressions
lst

10.2 List Basics 323
via index. The following code prompts the user to enter a month number and displays its
month name:
months = [“January”, “February”, “March”, …, “December”]
monthNumber = eval(input(“Enter a month number (1 to 12): “))
print(“The month is”, months[monthNumber – 1])
If the months list is not used, you would have to determine the month name using a lengthy
multi-way if-else statement as follows:
if monthNumber == 0:
print(“The month is January”)
elif monthNumber == 1:
print(“The month is February”)
…
else:
print(“The month is December”)
10.1 How do you create an empty list and a list with the three integers 1, 32, and 2?
10.2 Given lst = [30, 1, 12, 14, 10, 0], how many elements are in lst? What
is the index of the first element in lst? What is the index of the last element in lst?
What is lst[2]? What is lst[-2]?
10.3 Given lst = [30, 1, 2, 1, 0], what is the list after applying each of the fol-
lowing statements? Assume that each line of code is independent.
lst.append(40)
lst.insert(1, 43)
lst.extend([1, 43])
lst.remove(1)
lst.pop(1)
lst.pop()
lst.sort()
lst.reverse()
random.shuffle(lst)
10.4 Given lst = [30, 1, 2, 1, 0], what is the return value of each of the following
statements?
lst.index(1)
lst.count(1)
len(lst)
max(lst)
min(lst)
sum(lst)
10.5 Given list1 = [30, 1, 2, 1, 0] and list2 = [1, 21, 13], what is the
return value of each of the following statements?
list1 + list2
2 * list2
list2 * 2
list1[1 : 3]
list1[3]
✓Point✓Check

324 Chapter 10 Lists
10.6 Given list1 = [30, 1, 2, 1, 0], what is the return value of each of the fol-
lowing statements?
[x for x in list1 if x > 1]
[x for x in range(0, 10, 2)]
[x for x in range(10, 0, -2)]
10.7 Given list1 = [30, 1, 2, 1, 0] and list2 = [1, 21, 13], what is the
return value of each of the following statements?
list1 < list2 list1 <= list2 list1 == list2 list1 != list2 list1 > list2
list1 >= list2
10.8 Indicate true or false for the following statements:
(a) Every element in a list must have the same type.
(b) A list’s size is fixed after it is created.
(c) A list can have duplicate elements.
(d) The elements in a list can be accessed via an index operator.
10.9 What are list1 and list2 after the following lines of code?
list1 = [1, 43]
list2 = list1
list1[0] = 22
10.10 What are list1 and list2 after the following lines of code?
list1 = [1, 43]
list2 = [x for x in list1]
list1[0] = 22
10.11 How do you obtain a list from a string? Suppose s1 is welcome. What is
s1.split(‘o’)?
10.12 Write statements to do the following:
(a) Create a list with 100 Boolean False values.
(b) Assign the value 5.5 to the last element in the list.
(c) Display the sum of the first two elements.
(d) Compute the sum of the first five elements in the list.
(e) Find the minimum element in the list.
(f) Randomly generate an index and display the element of this index in the list.
10.13 What happens when your program attempts to access a list element with an invalid
index?
10.14 What is the output of the following code?
lst = [1, 2, 3, 4, 5, 6]

10.3 Case Study: Lotto Numbers 325
for i in range(1, 6):
lst[i] = lst[i – 1]
print(lst)
10.3 Case Study: Lotto Numbers
The problem is to write a program that determines whether all the input numbers
cover 1 to 99.
Each ticket for the Pick-10 lotto has 10 unique numbers ranging from 1 to 99. Suppose
you buy a lot of tickets and like to have them cover all the numbers from 1 to 99. Write a
program that reads the ticket numbers from a file and determines whether all numbers are
covered. Assume the last number in the file is 0. Suppose the file contains the following
numbers:
80 3 87 62 30 90 10 21 46 27
12 40 83 9 39 88 95 59 20 37
80 40 87 67 31 90 11 24 56 77
11 48 51 42 8 74 1 41 36 53
52 82 16 72 19 70 44 56 29 33
54 64 99 14 23 22 94 79 55 2
60 86 34 4 31 63 84 89 7 78
43 93 97 45 25 38 28 26 85 49
47 65 57 67 73 69 32 71 24 66
92 98 96 77 6 75 17 61 58 13
35 81 18 15 5 68 91 50 76
0
Your program should display
The tickets cover all numbers
Suppose the file contains the numbers
11 48 51 42 8 74 1 41 36 53
52 82 16 72 19 70 44 56 29 33
0
Your program should display
The tickets don’t cover all numbers
How do you mark a number as covered? You can create a list with 99 Boolean elements.
Each element in the list can be used to mark whether a number is covered. Let the list be
isCovered. Initially, each element is False, as shown in Figure 10.3a. Whenever a number
is read, its corresponding element is set to True. Suppose the numbers entered are 1, 2, 3, 99,
and 0. When number 1 is read, isCovered[0] is set to True (see Figure 10.3b). When num-
ber 2 is read, isCovered[2 – 1] is set to True (see Figure 10.3c). When number 3 is read,
isCovered[3 – 1] is set to True (see Figure 10.3d). When number 99 is read,
isCovered[98] is set to True (see Figure 10.3e).
The algorithm for the program can be described as follows:
for each number k read from the file,
mark number k as covered by setting isCovered[k – 1] true
Key
Point

326 Chapter 10 Lists
if every isCovered[i] is true:
The tickets cover all numbers
else:
The tickets don’t cover all numbers
The complete program is given in Listing 10.2.
LISTING 10.2 LottoNumbers.py
1 # Create a list of 99 Boolean elements with value False
2
3 endOfInput = False
4 while not endOfInput:
5 # Read numbers as a string from the console
6 s = input(“Enter a line of numbers separated by spaces: “)
7 items = s.split() # Extract items from the string
8 lst = [eval(x) for x in items] # Convert items to numbers
9
10 for number in lst:
11 if number == 0:
12 endOfInput = True
13 else:
14 # Mark its corresponding element covered
15 isCovered[number – 1] = True
16
17 # Check whether all numbers (1 to 99) are covered
18 allCovered = True # Assume all covered initially
19 for i in range(99):
20
21 allCovered = False # Find one number not covered
22 break
23
24 # Display result
25 if allCovered:
26 print(“The tickets cover all numbers”)
27 else:
28 print(“The tickets don’t cover all numbers”)
if not isCovered[i]:
isCovered = 99 * [False]
False
False
False
False
.
.
.
False
False
isCovered
[0]
[1]
[2]
[3]
(a)
[97]
[98]
False
False
False
.
.
.
False
False
isCovered
[0]
[1]
[2]
[3]
(b)
[97]
[98]
True True True
True
TrueFalse
False
.
.
.
False
False
isCovered
[0]
[1]
[2]
[3]
(c)
[97]
[98]
True
False
.
.
.
False
False
isCovered
[0]
[1]
[2]
[3]
(d)
[97]
[98]
False
.
.
.
False
isCovered
[0]
[1]
[2]
[3]
(e)
[97]
[98]
True
True
True
True
FIGURE 10.3 If number i appears in a Lotto ticket, isCovered[i – 1] is set to true.
create and initialize list
read input line
get input numbers
mark number covered
check allCovered?

10.4 Case Study: Deck of Cards 327
Enter a line of numbers separated by spaces:
Enter a line of numbers separated by spaces:
The tickets don’t cover all numbers
23 43 2 0
2 5 6 5 4 3
Enter a line of numbers separated by spaces:
Enter a line of numbers separated by spaces:
…
The tickets cover all numbers
7 8 9 10 11
1 2 3 4 5 6
Suppose you have created a text file named LottoNumbers.txt that contains the following
input data: 2 5 6 5 4 3 23 43 2 0
You can run the program by using the following command from the command window:
python LottoNumbers.py < LottoNumbers.txt The program creates a list of 99 Boolean values with the initial value False (line 2). It repeatedly reads a line of numbers (line 6), extracts the numbers from the line (lines 7–8). For each number, the program performs the following operations in a loop: ■ If the number is 0, set endOfInput True (line 12). ■ If the number is not zero, set its corresponding value for isCovered to True (line 15). When the number is 0, the input ends (line 4). The program determines whether all num- bers are covered in lines 18–22 and displays the result in lines 25–28. 10.4 Case Study: Deck of Cards The problem is to write a program that picks 4 cards randomly from a deck of 52 cards. All the cards can be represented using a list named deck, filled with initial values 0 to 51, as follows: deck = [x for x in range(52)] Or, you can use: deck = list(range(52)) Card numbers 0 to 12, 13 to 25, 26 to 38, and 39 to 51 represent 13 spades, 13 hearts, 13 diamonds, and 13 clubs, respectively, as shown in Figure 10.4. cardNumber // 13 deter- mines the suit of the card and cardNumber % 13 determines the rank of the card, as shown in Figure 10.5. After shuffling the deck, pick the first four cards from deck. The program dis- plays the cards from these four card numbers. Listing 10.3 gives the solution to the problem. LISTING 10.3 DeckOfCards.py 1 # Create a deck of cards 2 deck = [x for x in range(52)] create list deck Key Point 328 Chapter 10 Lists 3 4 # Create suits and ranks lists 5 suits = ["Spades", "Hearts", "Diamonds", "Clubs"] 6 ranks = ["Ace", "2", "3", "4", "5", "6", "7", "8", "9", 7 "10", "Jack", "Queen", "King"] 8 9 # Shuffle the cards 10 import random 11 random.shuffle(deck) 12 13 # Display the first four cards 14 for i in range(4): 15 suit = suits[deck[i] // 13] 16 rank = ranks[deck[i] % 13] 17 print("Card number", deck[i], "is the", rank, "of", suit) 0 . . . 12 13 . . . 25 26 . . . 38 39 . . . 51 13 Diamonds ( ) 13 Clubs ( ) 0 . . . 12 13 . . . 25 26 . . . 38 39 . . . 51 deck [0] . . . [12] [13] . . . [25] [26] . . . [38] [39] . . . [51] Random shuffle 6 48 11 24 . . . . . . . . . . . . . . . . deck [0] [1] [2] [3] [4] [5] . . . [25] [26] . . . [38] [39] . . . [51] Card number 6 is the 7 (6 % 13 = 6) of Spades (7 // 13 is 0) Card number 48 is the 10 (48 % 13 = 9) of Clubs (48 // 13 is 3) Card number 11 is the Queen (11 % 13 = 11) of Spades (11 // 13 is 0) Card number 24 is the Queen (24 % 13 = 11) of Hearts (24 // 13 is 1) 13 Hearts ( ) 13 Spades ( ) FIGURE 10.4 Fifty-two cards are stored in a list named deck. Card number 6 is the 7 of Spades Card number 48 is the 10 of Clubs Card number 11 is the Queen of Spades Card number 24 is the Queen of Hearts list of strings list of strings shuffle deck suit of a card rank of a card cardNumber // 13 = 0 3 2 1 Spades Hearts Diamonds Clubs cardNumber % 13 = 0 11 10 . Ace 1 2 . 12 Jack Queen King FIGURE 10.5 A card number identifies to a card. 10.5 Deck of Cards GUI 329 You can use Turtle or Tkinter to develop GUI programs in Python. Turtle is a good ped- agogical tool for introducing the fundamentals of programming, but its capability is lim- ited to drawing lines, shapes, and text strings. For developing comprehensive GUI projects, you should use Tkinter. From now on, we will use Tkinter in our GUI examples. Listing 10.4 gives the GUI program for creating the Shuffle button and displaying the four cards randomly. LISTING 10.4 DeckOfCardsGUI.py 1 from tkinter import * # Import all definitions from tkinter 2 import random 3 FIGURE 10.6 Clicking the Shuffle button displays four cards randomly. The program creates a deck of 52 cards (line 2), a list suits for the four suits (line 5), and a list ranks for the 13 cards in a suit (lines 6–7). The elements in suits and ranks are strings. The deck is initialized with the values 0 to 51. A deck value 0 represents the ace of spades, 1 represents the 2 of spades, 13 represents the ace of hearts, and 14 represents the 2 of hearts. Lines 10–11 randomly shuffle the deck. After the deck is shuffled, deck[i] contains an arbitrary value. deck[i] // 13 is 0, 1, 2, or 3, which determines the suit (line 15); deck[i] % 13 is a value between 0 and 12, which determines the rank (line 16). If the suits list is not defined, you would have to determine the suit using a lengthy if statement as follows: if deck[i] // 13 == 0: print("suit is Spades") elif deck[i] // 13 == 1: print("suit is Hearts") elif deck[i] // 13 == 2: print("suit is Diamonds") else: print("suit is Clubs") With suits = ["Spades", "Hearts", "Diamonds", "Clubs"] defined in a list, suits[deck // 13] gives the suit for the deck. Using lists greatly simplifies the solution for this program. 10.5 Deck of Cards GUI The program picks 4 cards randomly from a deck of 52 cards and displays the cards. This section presents a GUI program that lets the user click the Shuffle button to display four random cards graphically on the console, as shown in Figure 10.6. Key Point 330 Chapter 10 Lists set new images copy reference garbage collection Key Point 4 class DeckOfCardsGUI: 5 def __init__(self): 6 window = Tk() # Create a window 7 window.title("Pick Four Cards Randomly") # Set title 8 9 # Store images for cards 10 for i in range(1, 53): 11 self.imageList.append(PhotoImage(file = "image/card/" 12 + str(i) + ".gif")) 13 14 frame = Frame(window) # Hold four labels for cards 15 frame.pack() 16 17 self.labelList = [] # A list of four labels 18 for i in range(4): 19 self.labelList.append(Label(frame, 20 image = self.imageList[i])) 21 self.labelList[i].pack(side = LEFT) 22 23 Button(window, text = "Shuffle", 24 command = self.shuffle).pack() 25 26 window.mainloop() # Create an event loop 27 28 # Choose four random cards 29 def shuffle(self): 30 random.shuffle(self.imageList) 31 for i in range(4): 32 self.labelList[i]["image"] = self.imageList[i] 33 34 DeckOfCardsGUI() # Create GUI The program creates 52 images from the image files stored in the image/card folder in the current program directory (lines 9–12). The files are named 1.gif, 2.gif, ..., and 52.gif. The images are added to imageList. Each image is an instance of the PhotoImage class. The program creates a frame to hold four labels (lines 14–15). The labels are added to labelList (lines 17–21). The program creates a button (line 23). When the button is clicked, the shuffle function is invoked to randomly shuffle the image list (line 30) and set the first four images in the list as the labels (lines 31–32). 10.6 Copying Lists To copy the data in one list to another list, you have to copy individual elements from the source list to the target list. You often need to duplicate a list or part of a list in a program. In such cases you could attempt to use the assignment statement (=), as follows: list2 = list1 However, this statement does not copy the contents of the list referenced by list1 to list2; instead, it merely copies the reference value from list1 to list2. After this statement, list1 and list2 refer to the same list, as shown in Figure 10.7. The list previously referenced by list2 is no longer referenced; it becomes garbage. The memory space occupied by list2 will be automatically collected and reused by the Python interpreter. self.imageList = []image list add images to list label list create labels create a button random shuffle 10.6 Copying Lists 331 Two lists are created (lines 1–2) and each is an independent object with a different id (lines 4 and 6). After assigning list1 to list2, list2’s id is the same as list1’s (line 10). list1 and list2 now refer to the same object. To get a duplicate copy of list1 into list2, you can use: list2 = [x for x in list1] or simply: list2 = [] + list1 10.15 What is the output of the following code? list1 = list(range(1, 10, 2)) list2 = list1 list1[0] = 111 print(list1) print(list2) 10.16 What is the output of the following code? list1 = list(range(1, 10, 2)) list2 = [] + list1 list1[0] = 111 print(list1) print(list2) ✓Point✓Check Contents of list1 Contents of list1 Contents of list2 Contents of list2 list1 list2 Before the assignment list2 = list1 list1 list2 After the assignment list2 = list1 FIGURE 10.7 Before the assignment statement, list1 and list2 point to separate memory locations. After the assignment, the list1 reference value is passed to list2. 1 >>> list1 = [1, 2]
2 >>> list2 = [3, 4, 5]
3 >>> id(list1)
4 36207312
5 >>> id(list2)
6 36249848
7 >>>
8 >>> list2 = list1
9 >>> id(list2)
10 36207312
11 >>>
Here is an example to illustrate the concept:

332 Chapter 10 Lists
10.7 Passing Lists to Functions
When passing a list to a function, the contents of the list may change after the function
call, since a list is a mutable object.
Since list is an object, passing a list to a function is just like passing an object to a function.
For example, the following function displays the elements in a list:
def printList(lst):
for element in lst:
print(element)
You can invoke it by passing a list. For instance, the following statement invokes the
printList function to display 3, 1, 2, 6, 4, and 2.
printList([3, 1, 2, 6, 4, 2])
Note
The preceding statement creates a list and passes it to the function. There is no explicit
reference variable for the list. Such a list is called an anonymous list.
Since a list is a mutable object, the contents of a list may change in the function. Take the code
in Listing 10.5, for example:
LISTING 10.5 PassListArgument.py
1 def main():
2 x = 1 # x is an int variable
3 y = [1, 2, 3] # y is a list
4
5 # Invoke m with arguments x and y
6
7 print(“x is”, x)
8 print(“y[0] is”, y[0])
9
10 def :
11 number = 1001 # Assign a new value to number
12 numbers[0] = 5555 # Assign a new value to numbers[0]
13
14 main() # Call the main function
m(number, numbers)
m(x, y)
immutable object
mutable object
x is 1
y[0] is 5555
In this sample run, you see that after m is invoked (line 5, x remains 1, but y[0] is
changed to 5555. This is because y and numbers refer to the same list object. When m(x, y)
is invoked, the reference values of x and y are passed to number and numbers. Since y
contains the reference value to the list, numbers now contains the same reference value to
the same list. Since number is immutable, altering it inside a function creates a new
instance and the original instance outside the function is not changed. So, outside of the
function, x is still 1.
anonymous list
immutable vs. mutable
Key
Point

10.7 Passing Lists to Functions 333
The function add appends x to list lst if x is not in the list (lines 1–5). When the function
is executed for the first time (line 8), the default value [] for the argument lst is created.
This default value is created only once. add(1) adds 1 to lst.
When the function is called again (line 11), lst is now [1] not [], because lst is created
only once. After add(2) is executed, lst becomes [1, 2].
In line 14, the list argument [11, 12, 13, 14] is given, and this list is passed to lst.
In line 17, the default list argument is used. Since the default list now is [1, 2], after
invoking add(4), the default list becomes [1, 2, 4].
If you want the default list to be [] for every function call, you can revise the function as
shown in Listing 10.7.
LISTING 10.7 DefaultNoneListArgument.py
1 def add(x, ):
2 if lst == None:
3 lst = []
4 if x not in lst:
5 lst.append(x)
6
7 return lst
8
lst = None default argument
new empty list
[1]
[1, 2]
[11, 12, 13, 14, 3]
[1, 2, 4]
default argument
There is another issue we need to address regarding using a list as a default argument. Con-
sider the code in Listing 10.6.
LISTING 10.6 DefaultListArgument.py
1 def add(x, ):
2 if x not in lst:
3 lst.append(x)
4
5 return lst
6
7 def main():
8 list1 = add(1)
9 print(list1)
10
11 list2 = add(2)
12 print(list2)
13
14 list3 = add(3, [11, 12, 13, 14])
15 print(list3)
16
17 list4 = add(4)
18 print(list4)
19
20 main()
lst = []

334 Chapter 10 Lists
9 def main():
10 list1 = add(1)
11 print(list1)
12
13 list2 = add(2)
14 print(list2)
15
16 list3 = add(3, [11, 12, 13, 14])
17 print(list3)
18
19 list4 = add(4)
20 print(list4)
21
22 main()
return list
✓Point✓Check
[1]
[2]
[11, 12, 13, 14, 3]
[4]
Here a new empty list is created every time the add function is called without a list
argument (line 3). If the list argument is given when invoking the function, the default list
is not used.
10.8 Returning a List from a Function
When a function returns a list, the list’s reference value is returned.
You can pass list arguments when invoking a function. A function can also return a list. For
example, the following function returns a list that is the reversal of another list.
1 def reverse(lst):
2 result = []
3
4 for element in lst:
5 result.insert(0, element)
6
7 return result
Line 2 creates a new list result. Lines 4–5 copy elements from the list named lst to the
list named result. Line 7 returns the list. For example, the following statement returns a new
list list2 with the elements 6, 5, 4, 3, 2, and 1.
list1 = [1, 2, 3, 4, 5, 6]
list2 = reverse(list1)
Note that the list class has the method reverse() that can be invoked to reverse a list.
10.17 True or false? When a list is passed to a function, a new list is created and passed to
the function.
10.18 Show the output of the following two programs:
create a list
Key
Point
lst
result

10.9 Case Study: Counting the Occurrences of Each Letter 335
10.9 Case Study: Counting the Occurrences
of Each Letter
The program in this section counts the occurrence of each letter among 100 letters.
Listing 10.8 presents a program that counts the occurrences of each letter in a list of charac-
ters. The program does the following:
1. Generates 100 lowercase letters randomly and assigns them to a list of characters,
named chars, as shown in Figure 10.8a. You can obtain a random letter by using the
getRandomLowerCaseLetter() function in the RandomCharacter module in
Listing 6.11.
Key
Point
def main():
number = 0
numbers = [10]
m(number, numbers)
print(“number is”, number,
“and numbers[0] is”,
numbers[0])
def m(x, y):
x = 3
y[0] = 3
main()
def main():
lst = [1, 2, 3, 4, 5]
reverse(lst)
for value in lst:
print(value, end = ‘ ‘)
def reverse(lst):
newLst = len(lst) * [0]
for i in range(len(lst)):
newLst[i] = lst[len(lst) – 1 – i]
lst = newLst
main()
(a) (b)
10.19 Show the output of the following two programs:
def main():
list1 = m(1)
print(list1)
list2 = m(1)
print(list2)
def m(x, lst = [1, 1, 2, 3]):
if x in lst:
lst.remove(x)
return lst
main()
def main():
list1 = m(1)
print(list1)
list2 = m(1)
print(list2)
def m(x, lst = None):
if lst == None:
lst = [1, 1, 2, 3]
if x in lst:
lst.remove(x)
return lst
main()
(a) (b)

336 Chapter 10 Lists
…
…
chars[0]
chars[1]
…
…
chars[98]
chars[99]
…
…
counts[0]
counts[1]
…
…
counts[24]
counts[25]
(a) (b)
FIGURE 10.8 The chars list stores 100 characters, and the counts list stores 26 counts,
each of which counts the occurrences of a letter.
2. Counts the occurrences of each letter in the list. To do so, it creates a list named counts
that has 26 int values, each of which counts the occurrences of a letter, as shown in
Figure 10.8b. That is, counts[0] counts the number of times a appears in the list,
counts[1] counts the number of time b appears, and so on.
LISTING 10.8 CountLettersInList.py
1 import RandomCharacter # Defined in Listing 6.11
2
3 def main():
4 # Create a list of characters
5
6
7 # Display the list
8 print(“The lowercase letters are:”)
9
10
11 # Count the occurrences of each letter
12
13
14 # Display counts
15 print(“The occurrences of each letter are:”)
16
17
18 # Create a list of characters
19
20 # Create an empty list
21 chars = []
22
23 # Create lowercase letters randomly and add them to the list
24 for i in range(100):
25 chars.append(RandomCharacter.getRandomLowerCaseLetter())
26
27 # Return the list
28 return chars
29
30 # Display the list of characters
31
32 # Display the characters in the list with 20 on each line
33 for i in range(len(chars)):
34 if (i + 1) % 20 == 0:
35 print(chars[i])
def displayList(chars):
def createList():
displayCounts(counts)
counts = countLetters(chars)
displayList(chars)
chars = createList()create list
pass list chars
return list counts
pass list counts

10.9 Case Study: Counting the Occurrences of Each Letter 337
36 else:
37 print(chars[i], end = ‘ ‘)
38
39 # Count the occurrences of each letter
40
41 # Create a list of 26 integers with initial value 0
42 counts = 26 * [0]
43
44 # For each lowercase letter in the list, count it
45 for i in range(len(chars)):
46 counts[ord(chars[i]) – ord(‘a’)] += 1
47
48 return counts
49
50 # Display counts
51
52 for i in range(len(counts)):
53 if (i + 1) % 10 == 0:
54 print(counts[i], chr(i + ord(‘a’)))
55 else:
56 print(counts[i], chr(i + ord(‘a’)), end = ‘ ‘)
57
58 main() # Call the main function
def displayCounts(counts):
def countLetters(chars): counts
The lowercase letters are:
e y l s r i b k j v j h a b z n w b t v
s c c k r d w a m p w v u n q a m p l o
a z g d e g f i n d x m z o u l o z j v
h w i w n t g x w c d o t x h y v z y z
q e a m f w p g u q t r e n n w f c r f
The occurrences of each letter are:
5 a 3 b 4 c 4 d 4 e 4 f 4 g 3 h 3 i 3 j
2 k 3 l 4 m 6 n 4 o 3 p 3 q 4 r 2 s 4 t
3 u 5 v 8 w 3 x 3 y 6 z
The createList function (lines 19–28) generates a list of 100 random lowercase letters.
Line 5 invokes the function and assigns the list to chars. What would be wrong if you
rewrote the code as follows?
chars = 100 * [‘ ‘]
chars = createList()
You would be creating two lists. The first line would create a list by using 100 * [‘ ‘].
The second line would create a list by invoking createList() and assign the reference of
the list to chars. The list created in the first line would become garbage because it would no
longer be referenced. Python automatically collects garbage behind the scenes. Your program
would compile and run correctly, but it would create a list unnecessarily.
Invoking getRandomLowerCaseLetter() (line 25) returns a random lowercase letter.
This function is defined in the RandomCharacter class in Listing 6.11.
The countLetters function (lines 40–48) returns a list of 26 int values, each of which
stores the number of occurrences of a letter. The function processes each letter in the list and

increases its count by one. A brute-force approach to count the occurrences of each letter
might be as follows:
for i in range(len(chars)):
if chars[i] == ‘a’:
counts[0] += 1
elif chars[i] == ‘b’:
counts[1] += 1
…
But a better solution is given in lines 45–46.
for i in range(len(chars)):
counts[ord(chars[i]) – ord(‘a’)] += 1
If the letter (chars[i]) is a, the corresponding count is counts[ord(‘a’) –
ord(‘a’)] (i.e., counts[0]). If the letter is b, the corresponding count is
counts[ord(‘b’) – ord(‘a’)] (i.e., counts[1]), since the Unicode of b is one more
than that of a. If the letter is z, the corresponding count is counts[ord(‘z’) –
ord(‘a’)] (i.e., counts[25]), since the Unicode of z is 25 more than that of a.
10.10 Searching Lists
If a list is sorted, a binary search is more efficient than a linear search for finding an
element in the list.
Searching is the process of looking for a specific element in a list—for example, discover-
ing whether a certain score is included in a list of scores. The list class provides the
index method for searching and returning the index of a matching element from a list.
It also supports the in and not in operators for determining whether an element is in
a list.
Searching is a common task in computer programming. Many algorithms are devoted to
searching. This section discusses two commonly used approaches: linear searches and binary
searches.
10.10.1 The Linear Search Approach
The linear search approach compares the key element key sequentially with each element in
the list. It continues to do so until the key matches an element in the list or the list is exhausted
without a match being found. If a match is found, the linear search returns the matching ele-
ment’s index in the list. If no match is found, the search returns -1. The linearSearch func-
tion in Listing 10.9 illustrates this approach.
LISTING 10.9 LinearSearch.py
1 # The function for finding a key in the list
2 def linearSearch(lst, key):
3
4 if key == lst[i]:
5 return i
6
7 return -1
for i in range(len(lst)):
338 Chapter 10 Lists
Key
Point
Search a list
VideoNote
linear searches
binary searches
ith
[0] [1] [2]
key Compare key with lst[i] for i = 0, 1, …
…
linear search animation on
Companion Website

To better understand this function, trace it with the following statements:
lst = [1, 4, 4, 2, 5, -3, 6, 2]
i = linearSearch(lst, 4) # Returns 1
j = linearSearch(lst, -4) # Returns -1
k = linearSearch(lst, -3) # Returns 5
The linear search function compares the key with each element in the list. The elements can
be in any order. On average, the algorithm will have to examine half of the elements in a list
before finding the key, if it exists. Since the execution time of a linear search increases linearly
as the number of list elements increases, doing a linear search is inefficient for a large list.
10.10.2 The Binary Search Approach
A binary search is the other common search approach for a list of values. For a binary search
to work, the elements in the list must already be ordered. Assume that the list is in ascending
order. A binary search first compares the key with the element in the middle of the list. Consider
the following three cases:
■ If the key is less than the list’s middle element, you need to continue to search for the
key only in the first half of the list.
■ If the key is equal to the list’s middle element, the search ends with a match.
■ If the key is greater than the list’s middle element, you need to continue to search for
the key only in the second half of the list.
Note
Clearly, the binary search function eliminates half of the list after each comparison.
Sometimes you eliminate half of the elements, and sometimes you eliminate half plus
one. Suppose that the list has n elements. For convenience, let n be a power of 2. After
the first comparison, n/2 elements are left for further search; after the second compari-
son, (n/2)/2 elements are left. After the kth comparison, n/2k elements are left for further
search. When k = log2n, only one element is left in the list, and you need only one more
comparison. Therefore, in the worst-case scenario when using the binary search
approach, you need log2n+1 comparisons to find an element in the sorted list. In the
worst case for a list of 1024 elements, the binary search requires only 11 compar-
isons, whereas a linear search requires 1,023 comparisons in the worst case.
The portion of the list being searched shrinks by half after each comparison. Let low and
high denote, respectively, the first index and last index of the list that is currently being
searched. Initially, low is 0 and high is len(lst)–1. Let mid denote the index of the mid-
dle element, so mid is (low + high) // 2. Figure 10.9 shows how to find the key 11 in the
list [2, 4, 7, 10, 11, 45, 50, 59, 60, 66, 69, 70, 79] using a binary search.
You now know how a binary search works. The next task is to implement it in Python.
Don’t rush to create a complete implementation. Develop it incrementally, one step at a time.
You can start with the first iteration of the search, as shown in Figure 10.10a. It compares the
key with the middle element in the list, whose low index is 0 and high index is len(lst) –
1. If key < lst[mid], set the high index to mid - 1; if key == lst[mid], a match is found and the program returns mid; if key > lst[mid], set the low index to mid + 1.
Next, consider implementing the function to perform a search repeatedly by adding a loop,
as shown in Figure 10.10b. The search ends if the key is found, or if the key is not found when
low > high.
(210)
10.10 Searching Lists 339
binary search animation on
Companion Website

340 Chapter 10 Lists
When the key is not found, low is the insertion point where a key would be inserted to
maintain the order of the list. It is more useful to return the insertion point than -1. The func-
tion must return a negative value to indicate that the key is not in the list. Can it simply return
–low? No. If the key is less than lst[0], low would be 0. -0 is 0. This would indicate that
the key matches lst[0]. A good choice is to let the function return –low – 1 if the key is
not in the list. Returning –low – 1 indicates not only that the key is not in the list, but also
where the key would be inserted.
The complete program appears in Listing 10.10.
LISTING 10.10 BinarySearch.py
1 # Use binary search to find the key in the list
2 def binarySearch(lst, key):
3 low = 0
4 high = len(lst) – 1
5
6
7
8 if key < lst[mid]: mid = (low + high) // 2 while high >= low:
key is 11 low
key � 50
key � 7
[0] [1] [2] [3] [4] [5] [7] [8] [9] [10] [11]
2lst 4 7 10 11 45 50 59 60 66 69 70 79
mid
[6]
high
[12]
low
[0] [1] [2] [3] [4] [5]
2lst 4 7 10 11 45
mid high
key �� 11
[3] [4] [5]
lst 10 11 45
low mid high
FIGURE 10.9 A binary search eliminates half of the list from further consideration after each
comparison.
FIGURE 10.10
def binarySearch(lst, key):
low = 0
high = len(lst) – 1
if key < lst[mid]: high = mid - 1 elif key == lst[mid]: else: low = mid + 1 return mid mid = (low + high) // 2 def binarySearch(lst, key): low = 0 high = len(lst) - 1 mid = (low + high) // 2 if key < lst[mid]: high = mid – 1 elif key == lst[mid]: return mid else: low = mid + 1 # Not foundreturn -1 while high >= low:
(a) Version 1 (b) Version 2
why not -1?
A binary search is implemented incrementally.

10.11 Sorting Lists 341
9 high = mid – 1
10 elif key == lst[mid]:
11
12 else:
13 low = mid + 1
14
15 # Now high < low, key not found The binary search returns the index of the matching element if it is contained in the list (line 11). Otherwise, it returns –low – 1 (line 15). What would happen if we replaced (high >= low) in line 6 with (high > low)? The
search would miss a possible matching element. Consider a list with just one element: The
search would miss the element.
Does the function still work if there are duplicate elements in the list? Yes, as long as the
elements are sorted in increasing order, the function returns the index of one of the matching
elements if the element is in the list.
To better understand this function, trace it with the following statements and identify low
and high when the function returns.
lst = [2, 4, 7, 10, 11, 45, 50, 59, 60, 66, 69, 70, 79]
i = binarySearch(lst, 2) # Returns 0
j = binarySearch(lst, 11) # Returns 4
k = binarySearch(lst, 12) # Returns –6
l = binarySearch(lst, 1) # Returns –1
m = binarySearch(lst, 3) # Returns –2
The following table shows the low and high values when the function exits and also
shows the value returned from invoking the function.
return –low – 1
return mid
Note
Linear searches are useful for finding an element in a small list or an unsorted list, but
they are inefficient for large lists. Binary searches are more efficient, but they require that
the list be presorted.
10.11 Sorting Lists
There are many strategies for sorting elements in a list. Selection sorts and insertion
sorts are two common approaches.
Sorting, like searching, is a common task in computer programming. The list class provides
the sort method for sorting a list.
Many different algorithms have been developed for sorting. This section introduces two
simple, intuitive sorting algorithms: selection sort and insertion sort. By using these algo-
rithms, you will learn valuable techniques for developing and implementing other algorithms.
first half
matched
second half
Function Low High Value Returned
binarySearch(lst, 2) 0 1 0
binarySearch(lst, 11) 3 5 4
binarySearch(lst, 12) 5 4 -6
binarySearch(lst, 1) 0 -1 -1
binarySearch(lst, 3) 1 0 -2
binary search benefits
selection sort
insertion sort
Key
Point

342 Chapter 10 Lists
10.11.1 Selection Sort
Suppose that you want to sort a list in ascending order. A selection sort finds the smallest ele-
ment in the list and swaps it with the first element. It then finds the smallest element remaining
and swaps it with the first element in the remaining list, and so on, until only a single element
remains. Figure 10.11 shows how to sort the list [2, 9, 5, 4, 8, 1, 6] using a selection sort.
selection sort animation on
Companion Website
Select 1 (the smallest) and swap it
with 2 (the first) in the list.
The number 1 is now in the
correct position and thus no
longer needs to be considered.
The number 2 is now in the
correct position and thus no
longer needs to be considered.
The number 4 is now in the
correct position and thus no
longer needs to be considered.
The number 5 is now in the
correct position and thus no
longer needs to be considered.
The number 6 is now in the
correct position and thus no
longer needs to be considered.
2
1
1
1
1
1
1
9
9
2
2
2
2
2
5
swap
5
5
4
4
4
4
4
4
4
5
5
5
5
8
8
8
8
8
6
6
1
2
9
9
9
9
8
6
6
6
6
6
8
9
The number 8 is now in the
correct position and thus no
longer needs to be considered.
Select 2 (the smallest) and swap it
with 9 (the first) in the remaining
list.
Select 4 (the smallest) and swap it
with 5 (the first) in the remaining
list.
5 is the smallest and in the right
position. No swap is necessary.
Select 6 (the smallest) and swap it
with 8 (the first) in the remaining
list.
Select 8 (the smallest) and swap it
with 9 (the first) in the remaining
list.
Since there is only one element
remaining in the list, the sort is
completed.
swap
swap
swap
swap
FIGURE 10.11 A selection sort repeatedly selects the smallest element and swaps it with the first element in the remain-
ing list.
It can be difficult to develop a complete sorting solution on the first attempt. Start by writing
the code for the first iteration to find the smallest element in the list and swap it with the first ele-
ment, and then observe what would be different for the second iteration, the third, and so on. The
insight this gives you will enable you to write a loop that generalizes all the iterations.
The solution can be described as follows:
for i in range(len(lst)-1):
select the smallest element in lst[i : len(lst)]
swap the smallest with lst[i], if necessary
# lst[i] is in its correct position.
# The next iteration applies to lst[i+1 : len(lst)]
Listing 10.11 implements the solution.
LISTING 10.11 SelectionSort.py
1 # The function for sorting elements in ascending order
2 def selectionSort(lst):
3 for i in range(len(lst) – 1):

10.11 Sorting Lists 343
4 # Find the minimum in the lst[i : len(lst)]
5 currentMin = lst[i]
6 currentMinIndex = i
7
8 :
9 if currentMin > lst[j]:
10 currentMin = lst[j]
11 currentMinIndex = j
12
13 # Swap lst[i] with lst[currentMinIndex] if necessary
14 if currentMinIndex != i:
15 lst[currentMinIndex] = lst[i]
16 lst[i] = currentMin
The selectionSort(lst) function sorts any list of elements. The function is imple-
mented with a nested for loop. The outer loop (with the loop control variable i) (line 3) is
iterated in order to find the smallest element in the list, which ranges from lst[i] to
lst[len(lst)-1], and exchanges it with lst[i].
The variable i is initially 0. After each iteration of the outer loop, lst[i] is in the
right place. Eventually, all the elements are put in the right place; therefore, the whole list
is sorted.
To understand this function better, trace it with the following statements:
lst = [1, 9, 4.5, 10.6, 5.7, -4.5]
selectionSort(lst)
10.11.2 Insertion Sort
Suppose that you want to sort a list in ascending order. The insertion-sort algorithm sorts a list
of values by repeatedly inserting a new element into a sorted sublist until the whole list is
sorted. Figure 10.12 shows how to sort the list [2, 9, 5, 4, 8, 1, 6] using an insertion sort.
for j in range(i + 1, len(lst))
Step 1: Initially, the sorted sublist contains the
first element in the list. Insert 9 into the sublist.
Step 2: The sorted sublist is [2, 9]. Insert 5 into
the sublist.
Step 3: The sorted sublist is [2, 5, 9]. Insert 4 into
the sublist.
Step 4: The sorted sublist is [2, 4, 5, 9]. Insert 8
into the sublist.
Step 5: The sorted sublist is [2, 4, 5, 8, 9]. Insert
1 into the sublist.
Step 6: The sorted sublist is [1, 2, 4, 5, 8, 9].
Insert 6 into the sublist.
2
2
2
2
2
1
1
9
9
5
4
4
2
2
5
5
9
5
5
4
4
4
4
4
9
8
5
5
8
8
8
8
9
8
6
1
1
1
1
1
9
8
6
6
6
6
6
6
9Step 7: The entire list is now sorted.
FIGURE 10.12 An insertion sort repeatedly inserts a new element into a sorted sublist.
select
swap
insertion sort animation on
Companion Website

344 Chapter 10 Lists
The algorithm can be described as follows:
for i in range(1, len(lst)):
insert lst[i] into a sorted sublist lst[0 : i] so that
lst[0..i+1] is sorted.
To insert lst[i] into lst[0..i-1], save lst[i] into a temporary variable, say
currentElement. Move lst[i-1] to lst[i] if lst[i-1] > currentElement; move
lst[i-2] to lst[i-1] if lst[i-2] > currentElement; and so on, until lst[i-k] <= currentElement or k > i (we pass the first element of the sorted list). Assign
currentElement to lst[i-k+1]. For example, to insert 4 into [2, 5, 9] in Step 3 in
Figure 10.13, move lst[2] (9) to lst[3] since 9 > 4, and move lst[1] (5) to lst[2]
since 5 > 4. Finally, move currentElement (4) to lst[1].
The algorithm can be expanded and implemented as in Listing 10.12.
LISTING 10.12 InsertionSort.py
1 # The function for sorting elements in ascending order
2 def insertionSort(lst):
3 for i in range(1, len(lst)):
4 # insert lst[i] into a sorted sublist lst[0 : i] so that
5 # lst[0 : i+1] is sorted.
6 currentElement = lst[i]
7 k = i – 1
8
9 lst[k + 1] = lst[k]
10 k -= 1
11
12 # Insert the current element into lst[k + 1]
13
The insertionSort(lst) function sorts any list of elements. The function is imple-
mented with a nested for loop. The outer loop (with the loop control variable i) (line 3) is
iterated in order to obtain a sorted sublist, which ranges from lst[0] to lst[i]. The inner
loop (with the loop control variable k) inserts lst[i] into the sublist from lst[0] to
lst[i-1].
To better understand this function, trace it with the following statements:
lst = [1, 9, 4.5, 10.6, 5.7, -4.5]
insertionSort(lst)
lst[k + 1] = currentElement
while k >= 0 and lst[k] > currentElement:
[0][1][2][3][4][5][6]
2 5 9 4lst Step 1: Save 4 to the temporary variable currentElement.
currentElement: 4
[0][1][2][3][4][5][6]
2 5 9lst Step 2: Move lst[2] to lst[3].
[0][1][2][3][4][5][6]
2 5 9lst Step 3: Move lst[1] to lst[2].
[0][1][2][3][4][5][6]
2 4 5 9lst Step 4: Assign currentElement to lst[1].
FIGURE 10.13 A new element is inserted into a sorted sublist.
shift
insert

10.12 Case Study: Bouncing Balls 345
10.20 Use Figure 10.8 as an example to show how to apply the binary search approach to
a search for key 10 and key 12 in the list [2, 4, 7, 10, 11, 45, 50, 59, 60, 66, 69,
70, 79].
10.21 If the binary search function returns 4, is the key in the list? Where should the key
be inserted if you wish to insert the key into the list?
10.22 Use Figure 10.10 as an example to show how to apply the selection-sort approach to
sort [3.4, 5, 3, 3.5, 2.2, 1.9, 2].
10.23 Use Figure 10.11 as an example to show how to apply the insertion-sort approach to
sort [3.4, 5, 3, 3.5, 2.2, 1.9, 2].
10.24 How do you modify the selectionSort function in Listing 10.11 to sort elements
in decreasing order?
10.25 How do you modify the insertionSort function in Listing 10.12 to sort elements
in decreasing order?
10.12 Case Study: Bouncing Balls
The program in this section displays bouncing balls stored in a list.
Now let’s put things we have learned into developing an interesting project. The program
we’ll write in this section displays bouncing balls, as shown in Figure 10.14a.
–
Ball
The x-, y-coordinates for the center of the
ball. By default, it is (0, 0).
x: int
y: int
dx: int
dy: int
color: str
radius: int
dx and dy are the increments for (x, y).
The color of the ball.
The radius of the ball.
(a) (b)
FIGURE 10.14 (a) The program displays bouncing balls with control buttons. (b) The Ball class encapsulates informa-
tion about the ball.
The program enables the user to click the and buttons to add a ball or remove a ball
from the canvas, and click the Stop and Resume buttons to stop the ball movements or
resume them.
Each ball has its own center location (x, y), radius, color, and next increment for its
center position, dx and dy. You can define a class to encapsulate all this information, as
shown in Figure 10.14b. Initially, the ball is centered at (0, 0), and dx = 2 and dy = 2. In the
animation, the ball is moved to (x + dx, y + dy). When the ball reaches the right boundary,
change dx to -2. When the ball reaches the bottom boundary, change dy to -2. When the ball
reaches the left boundary, change dx to 2. When the ball reaches the top boundary, change dy
to 2. The program simulates a bouncing ball by changing the dx or dy values when the ball
touches the boundary of the canvas.
When the button is clicked, a new ball is created. How do you store the ball in the pro-
gram? You can store the balls in a list. When the button is clicked, the last ball in the list is
removed.
�
�
-+
the Ball class
✓Point✓Check
Key
Point

346 Chapter 10 Lists
The complete program is given in Listing 10.13.
LISTING 10.13 BounceBalls.py
1 from tkinter import * # Import all definitions from tkinter
2 from random import randint
3
4 # Return a random color string in the form #RRGGBB
5 def getRandomColor():
6 color = “#”
7 for j in range(6):
8 color += toHexChar(randint(0, 15)) # Add a random digit
9 return color
10
11 # Convert an integer to a single hex digit in a character
12 def toHexChar(hexValue):
13 if 0 <= hexValue <= 9: 14 return chr(hexValue + ord('0')) 15 else: # 10 <= hexValue <= 15 16 return chr(hexValue - 10 + ord('A')) 17 18 # Define a Ball class 19 20 def __init__(self): 21 self.x = 0 # Starting center position 22 self.y = 0 23 self.dx = 2 # Move right by default 24 self.dy = 2 # Move down by default 25 self.radius = 3 # The radius is fixed 26 self.color = getRandomColor() # Get random color 27 28 29 def __init__(self): 30 # Create a list for balls 31 32 window = Tk() # Create a window 33 window.title("Bouncing Balls") # Set a title 34 35 self.width = 350 # Width of the self.canvas 36 self.height = 150 # Height of the self.canvas 37 self.canvas = Canvas(window, bg = "white", 38 width = self.width, height = self.height) 39 self.canvas.pack() 40 41 frame = Frame(window) 42 frame.pack() 43 btStop = Button(frame, text = "Stop", command = self.stop) 44 btStop.pack(side = LEFT) 45 btResume = Button(frame, text = "Resume", 46 command = self.resume) 47 btResume.pack(side = LEFT) 48 btAdd = Button(frame, text = "+", command = self.add) 49 btAdd.pack(side = LEFT) 50 btRemove = Button(frame, text = "-", command = self.remove) 51 btRemove.pack(side = LEFT) 52 53 self.sleepTime = 100 # Set a sleep time 54 self.isStopped = False 55 self.animate() 56 self.ballList = [] class BounceBalls: class Ball: random color random hex number Ball class ball list create canvas create buttons sleep time isStopped? 10.12 Case Study: Bouncing Balls 347 57 window.mainloop() # Create an event loop 58 59 # Stop animation 60 self.isStopped = True 61 62 # Resume animation 63 self.isStopped = False 64 self.animate() 65 66 # Add a new ball 67 self.ballList.append(Ball()) 68 69 # Remove the last ball 70 self.ballList.pop() 71 72 # Animate ball movements 73 while not self.isStopped: 74 self.canvas.after(self.sleepTime) # Sleep 75 self.canvas.update() # Update self.canvas 76 self.canvas.delete("ball") 77 78 for ball in self.ballList: 79 self.redisplayBall(ball) 80 81 82 if ball.x > self.width or ball.x < 0: 83 ball.dx = -ball.dx 84 85 if ball.y > self.height or ball.y < 0: 86 ball.dy = -ball.dy 87 88 ball.x += ball.dx 89 ball.y += ball.dy 90 self.canvas.create_oval(ball.x - ball.radius, 91 ball.y - ball.radius, ball.x + ball.radius, 92 ball.y + ball.radius, fill = ball.color, tags = "ball") 93 94 BounceBalls() # Create GUI The program creates a canvas for displaying balls (lines 35–39), creates the buttons Stop, Resume, and (lines 43–51), and starts the animation (line 57). The animate method repaints the canvas every 100 milliseconds (lines 72–79). It redis- plays every ball in the ball list (lines 78–79). The redisplayBall method changes the direc- tion for dx and dy if the ball touches any boundaries of the canvas (lines 82–86), sets a new center position for the ball (lines 88–89), and redisplays the ball on the canvas (lines 90–92). When the Stop button is clicked, the stop method is invoked to set the isStopped vari- able to True (line 60) and the animation stops (line 73). When the Resume button is clicked, the resume method is invoked to set the isStopped variable to False (line 63) and the ani- mation resumes (line 73). When the + button is clicked, the add method is invoked to add a new ball to the ball list (line 67). When the - button is clicked, the remove method is invoked to remove the last ball from the ball list (line 70). When a ball is created (line 67), the Ball’s __init__ method is invoked to create and initialize the properties x, y, dx, dy, radius, and color. The color is a string #RRGGBB, where R, G, B is a hex digit. Each hex digit is randomly generated (line 26). The toHexChar(hexValue) method returns a hex character for the value between 0 and 15 (lines 12–16). -+ , def redisplayBall(self, ball): def animate(self): def remove(self): def add(self): def resume(self): def stop(self): stop resume add remove animate display ball create GUI 348 Chapter 10 Lists KEY TERMS anonymous list 332 binary searches 338 garbage collection 330 index 315 insertion sort 341 linear searches 338 selection sort 341 CHAPTER SUMMARY 1. You can use the Python built-in functions len, max, min, and sum to return the length of a list, the maximum and minimum elements in a list, and the sum of all the ele- ments in a list. 2. You can use the shuffle function in the randommodule to shuffle the elements in a list. 3. You can use the index operator [] to reference an individual element in a list. 4. Programmers often mistakenly reference the first element in a list with index 1, but it should be 0. This is called the index off-by-one error. 5. You can use the concatenation operator + to concatenate two lists, the repetition oper- ator * to duplicate elements, the slicing operator [:] to get a sublist, and the in and not in operators to check whether an element is in a list. 6. You can use a for loop to traverse all elements in a list. 7. You can use the comparison operators to compare the elements of two lists. 8. A list object is mutable. You can use the methods append, extend, insert, pop, and remove to add and remove elements to and from a list. 9. You can use the index method to get the index of an element in a list, and the count method to return the count of the element in the list. 10. You can use the sort and reverse methods to sort or reverse the elements in a list. 11. You can use the split method to split a string into a list. 12. When a function is invoked with a list argument, the reference of the list is passed to the function. 13. If a list is sorted, a binary search is more efficient than a linear search for finding an element in the list. 14. A selection sort finds the smallest number in the list and swaps it with the first ele- ment. It then finds the smallest number remaining and swaps it with the first element in the remaining list, and so on, until only a single number remains. 15. The insertion-sort algorithm sorts a list of values by repeatedly inserting a new ele- ment into a sorted sublist until the whole list is sorted. Programming Exercises 349 TEST QUESTIONS Do test questions for this chapter online at www.cs.armstrong.edu/liang/py/test.html. PROGRAMMING EXERCISES Note If the program prompts the user to enter a list of values, enter the values from one line separated by spaces. Sections 10.2–10.3 *10.1 (Assign grades) Write a program that reads a list of scores and then assigns grades based on the following scheme: The grade is A if score is best – 10. The grade is B if score is best – 20. The grade is C if score is best – 30. The grade is D if score is best – 40. The grade is F otherwise. Here is a sample run: 7= 7= 7= 7= Enter scores: Student 0 score is 40 and grade is C Student 1 score is 55 and grade is B Student 2 score is 70 and grade is A Student 3 score is 58 and grade is B 40 55 70 58 10.2 (Reverse the numbers entered) Write a program that reads a list of integers and displays them in the reverse order in which they were read. **10.3 (Count occurrence of numbers) Write a program that reads some integers between 1 and 100 and counts the occurrences of each. Here is a sample run of the program: Enter integers between 1 and 100: 2 occurs 2 times 3 occurs 1 time 4 occurs 1 time 5 occurs 2 times 6 occurs 1 time 23 occurs 1 time 43 occurs 1 time 2 5 6 5 4 3 23 43 2 Note that if a number occurs more than one time, the plural word “times” is used in the output. 10.4 (Analyze scores) Write a program that reads an unspecified number of scores and determines how many scores are above or equal to the average and how many scores are below the average. Assume the input numbers are separated by one space in one line. www.cs.armstrong.edu/liang/py/test.html 350 Chapter 10 Lists **10.5 (Print distinct numbers) Write a program that reads in numbers separated by a space in one line and displays distinct numbers (i.e., if a number appears mul- tiple times, it is displayed only once). (Hint: Read all the numbers and store them in list1. Create a new list list2. Add a number in list1 to list2. If the number is already in the list, ignore it.) Here is the sample run of the program: Enter ten numbers: The distinct numbers are: 1 2 3 6 4 5 1 2 3 2 1 6 3 4 5 2 *10.6 (Revise Listing 5.13, PrimeNumber.py) Listing 5.13 determines whether a number n is prime by checking whether 2, 3, 4, 5, 6, ..., n/2 is a divisor for n. If a divisor is found, n is not prime. A more efficient approach is to check whether any of the prime numbers less than or equal to can divide n evenly. If not, n is prime. Rewrite Listing 5.13 to display the first 50 prime numbers using this approach. You need to use a list to store the prime numbers and later use them to check whether they are possible divisors for n. *10.7 (Count single digits) Write a program that generates 1,000 random integers between 0 and 9 and displays the count for each number. (Hint: Use a list of ten integers, say counts, to store the counts for the number of 0s, 1s, ..., 9s.) Sections 10.4–10.7 10.8 (Find the index of the smallest element) Write a function that returns the index of the smallest element in a list of integers. If the number of such elements is greater than 1, return the smallest index. Use the following header: def indexOfSmallestElement(lst): Write a test program that prompts the user to enter a list of numbers, invokes this function to return the index of the smallest element, and displays the index. *10.9 (Statistics: compute deviation) Exercise 5.46 computes the standard deviation of numbers. This exercise uses a different but equivalent formula to compute the standard deviation of n numbers. To compute the standard deviation with this formula, you have to store the individual numbers using a list, so that they can be used after the mean is obtained. Your program should contain the following functions: # Compute the standard deviation of values def deviation(x): # Compute the mean of a list of values def mean(x): Write a test program that prompts the user to enter a list of numbers and displays the mean and standard deviation, as shown in the following sample run: mean = a n i=1 x i n = x1 + x2 + c + xn n deviation = Qa n i=1 (x i - mean)2 n - 1 2n Programming Exercises 351 Enter numbers: The mean is 3.11 The standard deviation is 1.55738 1.9 2.5 3.7 2 1 6 3 4 5 2 *10.10 (Reverse a list) The reverse function in Section 10.8 reverses a list by copying it to a new list. Rewrite the function that reverses the list passed in the argument and returns this list. Write a test program that prompts the user to enter a list of num- bers, invokes the function to reverse the numbers, and displays the numbers. Section 10.8 *10.11 (Random number chooser) You can shuffle a list using random.shuffle(lst). Write your own function without using random.shuffle(lst) to shuffle a list and return the list. Use the following function header: def shuffle(lst): Write a test program that prompts the user to enter a list of numbers, invokes the function to shuffle the numbers, and displays the numbers. 10.12 (Compute GCD) Write a function that returns the greatest common divisor (GCD) of integers in a list. Use the following function header: def gcd(numbers): Write a test program that prompts the user to enter five numbers, invokes the function to find the GCD of these numbers, and displays the GCD. Sections 10.9–10.12 10.13 (Eliminate duplicates) Write a function that returns a new list by eliminating the duplicate values in the list. Use the following function header: def eliminateDuplicates(lst): Write a test program that reads in a list of integers, invokes the function, and dis- plays the result. Here is the sample run of the program: Enter ten numbers: The distinct numbers are: 1 2 3 6 4 5 1 2 3 2 1 6 3 4 5 2 *10.14 (Revise selection sort) In Section 10.11.1, you used selection sort to sort a list. The selection-sort function repeatedly finds the smallest number in the current list and swaps it with the first one. Rewrite this program by finding the largest number and swapping it with the last one. Write a test program that reads in ten numbers, invokes the function, and displays the sorted numbers. **10.15 (Sorted?) Write the following function that returns true if the list is already sorted in increasing order: def isSorted(lst): Write a test program that prompts the user to enter a list and displays whether the list is sorted or not. Here is a sample run: 352 Chapter 10 Lists Enter list: The list is not sorted 1 1 3 4 4 5 7 9 10 30 11 Enter list: The list is already sorted 1 1 3 4 4 5 7 9 10 30 **10.16 (Bubble sort) Write a sort function that uses the bubble-sort algorithm. The bubble-sort algorithm makes several passes through the list. On each pass, successive neighboring pairs are compared. If a pair is in decreasing order, its values are swapped; otherwise, the values remain unchanged. The tech- nique is called a bubble sort or sinking sort because the smaller values grad- ually “bubble” their way to the top and the larger values “sink” to the bottom. Write a test program that reads in ten numbers, invokes the function, and dis- plays the sorted numbers. **10.17 (Anagrams) Write a function that checks whether two words are anagrams. Two words are anagrams if they contain the same letters. For example, silent and listen are anagrams. The header of the function is: def isAnagram(s1, s2): (Hint: Obtain two lists for the two strings. Sort the lists and check if two lists are identical.) Write a test program that prompts the user to enter two strings and, if they are anagrams, displays is an anagram; otherwise, it displays is not an anagram. ***10.18 (Game: Eight Queens) The classic Eight Queens puzzle is to place eight queens on a chessboard such that no two queens can attack each other (i.e., no two queens are in the same row, same column, or same diagonal). There are many possible solutions. Write a program that displays one such solution. A sample output is shown below: |Q| | | | | | | | | | | | |Q| | | | | | | | | | | |Q| | | | | | |Q| | | | | |Q| | | | | | | | | | | | |Q| | | |Q| | | | | | | | | | |Q| | | | | ***10.19 (Game: bean machine) The bean machine, also known as a quincunx or the Galton box, is a device for statistics experiments named after English scientist Sir Francis Galton. It consists of an upright board with evenly spaced nails (or pegs) in a triangular pattern, as shown in Figure 10.15. Balls are dropped from the opening of the board. Every time a ball hits a nail, it has a 50% chance of falling to the left or to the right. The piles of balls are accumulated in the slots at the bottom of the board. Programming Exercises 353 (a) (b) (c) FIGURE 10.15 Each ball takes a random path and falls into a slot. Write a program that simulates the bean machine. Your program should prompt the user to enter the number of the balls and the number of the slots in the machine. Simulate the falling of each ball by printing its path. For example, the path for the ball in Figure 10.15b is LLRRLLR and the path for the ball in Figure 10.15c is RLRRLRR. Display the final buildup of the balls in the slots in a histogram. Here is a sample run of the program: Enter the number of balls to drop: Enter the number of slots in the bean machine: LRLRLRR RRLLLRR LLRLLRR RRLLLLL LRLRRLR O O OOO 7 5 (Hint: Create a list named slots. Each element in slots stores the number of balls in a slot. Each ball falls into a slot via a path. The number of Rs in a path is the position of the slot where the ball falls. For example, for the path LRLRLRR, the ball falls into slots[4], and for the path is RRLLLLL, the ball falls into slots[2].) ***10.20 (Game: multiple Eight Queens solutions) Exercise 10.18 has you find one solution for the Eight Queens puzzle. Write a program to count all possible solutions for the Eight Queens problem and display all the solutions. **10.21 (Game: locker puzzle) A school has 100 lockers and 100 students. All lockers are closed on the first day of school. As the students enter, the first student, denoted S1, opens every locker. Then the second student, S2, begins with the second locker, denoted L2, and closes every other locker. Student S3 begins with the third locker and changes every third locker (closes it if it was open, and opens it if it was closed). Student S4 begins with locker L4 and changes every fourth locker. Student S5 starts with L5 and changes every fifth locker, and so on, until student S100 changes L100. 354 Chapter 10 Lists After all the students have passed through the building and changed the lockers, which lockers are open? Write a program to find your answer. (Hint: Use a list of 100 Boolean elements, each of which indicates whether a locker is open (True) or closed (False). Initially, all lockers are closed.) **10.22 (Simulation: coupon collector’s problem) Coupon Collector is a classic statistics problem with many practical applications. The problem is to pick objects from a set of objects repeatedly and find out how many picks are needed for all the objects to be picked at least once. A variation of the problem is to pick cards from a shuffled deck of 52 cards repeatedly and find out how many picks are needed before you see one of each suit. Assume a picked card is placed back in the deck before picking another. Write a program to simulate the number of picks needed to get four cards, one from each suit and display the four cards picked (it is possi- ble a card may be picked twice). Here is a sample run of the program: Queen of Spades 5 of Clubs Queen of Hearts 4 of Diamonds Number of picks: 12 10.23 (Algebra: solve quadratic equations) Write a function for solving a quadratic equation using the following header: def solveQuadratic(eqn, roots): The coefficients of a quadratic equation are passed to the list eqn and the noncomplex roots are stored in roots. The function returns the number of roots. See Programming Exercise 4.1 on how to solve a quadratic equation. Write a program that prompts the user to enter values for a, b, and c and displays the number of roots and all noncomplex roots. *10.24 (Math: combinations) Write a program that prompts the user to enter 10 integers and displays all the combinations of picking two numbers from the 10. *10.25 (Game: pick four cards) Write a program that picks four cards from a deck of 52 cards and computes their sum. An ace, king, queen, and jack represent 1, 13, 12, and 11, respectively. Your program should display the number of picks that yield the sum of 24. **10.26 (Merge two sorted lists) Write the following function that merges two sorted lists into a new sorted list: def merge(list1, list2): Implement the function in a way that takes len(list1) + len(list2) com- parisons. Write a test program that prompts the user to enter two sorted lists and displays the merged list. Here is a sample run: ax2 + bx + c = 0 Enter list1: Enter list2: The merged list is 1 2 4 5 5 6 16 61 111 2 4 5 6 1 5 16 61 111 Programming Exercises 355 *10.27 (Pattern recognition: four consecutive equal numbers) Write the following func- tion that tests whether the list has four consecutive numbers with the same value: def isConsecutiveFour(values): Write a test program that prompts the user to enter a series of integers and reports whether the series contains four consecutive numbers with the same value. **10.28 (Partition of a list) Write the following function that partitions the list using the first element, called a pivot: def partition(lst): After the partition, the elements in the list are rearranged so that all the ele- ments before the pivot are less than or equal to the pivot and the element after the pivot are greater than the pivot. The function also returns the index where the pivot is located in the new list. For example, suppose the list is [5, 2, 9, 3, 6, 8]. After the partition, the list becomes [3, 2, 5, 9, 6, 8]. Implement the function in a way that takes len(lst) comparisons. Write a test program that prompts the user to enter a list and displays the list after the partition. Here is a sample run: Enter a list: After the partition, the list is 9 1 5 1 10 61 11 16 10 1 5 16 61 9 11 1 ***10.29 (Game: hangman) Write a hangman game that randomly generates a word and prompts the user to guess one letter at a time, as shown in the sample run. Each letter in the word is displayed as an asterisk. When the user makes a correct guess, the actual letter is then displayed. When the user finishes a word, dis- play the number of misses and ask the user whether to continue playing. Create a list to store the words, as follows: # Use any words you wish words = ["write", "that", "program", ...] (Guess) Enter a letter in word ******* > p
(Guess) Enter a letter in word p****** > r
(Guess) Enter a letter in word pr**r** > p
p is already in the word
(Guess) Enter a letter in word pr**r** > o
(Guess) Enter a letter in word pro*r** > g
(Guess) Enter a letter in word progr** > n
n is not in the word
(Guess) Enter a letter in word progr** > m
(Guess) Enter a letter in word progr*m > a
The word is program. You missed 1 time
Do you want to guess another word? Enter y or n>
*10.30 (Culture: Chinese Zodiac) Simplify Listing 4.5, ChineseZodiac.py, using a list
of strings to store the animals’ names.

356 Chapter 10 Lists
10.34 (Turtle: draw histograms) Rewrite the preceding program using Turtle.
*10.35 (Tkinter: bouncing balls) Revise Listing 10.13 to add two buttons—Faster and
Slower, as shown in Figure 10.16b—to speed up or slow down the ball
movements.
10.31 (Occurrences of each digit in a string) Write a function that counts the occur-
rences of each digit in a string using the following header:
def count(s):
The function counts how many times a digit appears in the string. The return
value is a list of ten elements, each of which holds the count for a digit. For
example, after executing counts = count(“12203AB3”), counts[0] is 1,
counts[1] is 1, counts[2] is 2, and counts[3] is 2.
Write a test program that prompts the user to enter a string and displays the
number of occurrences of each digit in the string. Here is a sample run of the
program:
10.32 (Turtle: draw a line) Write the following function that draws a line from point
p1 ([x1, y1]) to point p2 ([x2, y2]).
# Draw a line
def drawLine(p1, p2):
10.33 (Tkinter: draw histograms) Write a program that generates 1,000 lowercase let-
ters randomly, counts the occurrence of each letter, and displays a histogram for
the occurrences, as shown in Figure 10.16a.
(a) (b)
FIGURE 10.16 (a) A histogram is drawn for the count of each letter. (b) Two buttons are
added to control the ball speed.
Enter a string:
1 occurs 1 time
2 occurs 3 times
3 occurs 3 times
4 occurs 1 time
5 occurs 1 time
232534312

Programming Exercises 357
(a) (b)
FIGURE 10.17 The program animates a linear search.
**10.37 (Tkinter: binary search animation) Write a program that animates the binary
search algorithm. Create a list with the numbers from 1 to 20 in this order. The
elements are displayed in a histogram, as shown in Figure 10.18. You need to
enter a search key in the text field. Clicking the Step button causes the program
to perform one comparison in the algorithm. Use a light-gray color to paint the
bars for the numbers in the current search range and use a red color to paint the
bar indicating the middle number in the search range. When the algorithm is
finished, display a dialog box to inform the user. Clicking the Reset button
enables a new search to start. This button also makes the text field editable.
(a) (b)
FIGURE 10.18 The program animates a binary search.
*10.38 (Tkinter: selection-sort animation) Write a program that animates the selection-sort
algorithm. Create a list that consists of 20 distinct numbers from 1 to 20 in a ran-
dom order. The elements are displayed in a histogram, as shown in Figure 10.19.
Clicking the Step button causes the program to perform an iteration of the outer
loop in the algorithm and repaints the histogram for the new list. Color the last bar
in the sorted sublist. When the algorithm is finished, display a dialog box to inform
the user. Clicking the Reset button creates a new random list for a new start.
**10.36 (Tkinter: linear search animation) Write a program that animates the linear
search algorithm. Create a list that consists of 20 distinct numbers from 1 to
20 in a random order. The elements are displayed in a histogram, as shown in
Figure 10.17. You need to enter a search key in the text field. Clicking the
Step button causes the program to perform one comparison in the algorithm
and repaints the histogram with a bar indicating the search position. When
the algorithm is finished, display a dialog box to inform the user. Clicking the
Reset button creates a new random list for a new start.

358 Chapter 10 Lists
*10.39 (Tkinter: the 24-point card game) The 24-point card game involves picking any four
cards from 52 cards, as shown in Figure 10.20. Note that the jokers are excluded. Each
card represents a number. An ace, king, queen, and jack represent 1, 13, 12, and 11,
respectively. Enter an expression that uses the four numbers from the four selected
cards. Each card number can be used only once in each expression, and each card
must be used. You can use the operators ( *, and /) and parentheses in the
expression. The expression must evaluate to 24. After entering the expression, click
the Verify button to check whether the numbers in the expression are currently selected
and whether the result of the expression is correct. Display the verification in a dialog
box. You can click the Refresh button to get another set of four cards. Assume that
images are stored in files named 1.gif, 2.gif, …, 52.gif, in the order of spades, hearts,
diamonds, and clubs. So, the first 13 images are for spades 1, 2, 3, …, and 13.
+ , – ,
(a) (b)
FIGURE 10.19 The program animates a selection sort.
FIGURE 10.20 The user enters an expression using the numbers in the cards.

Programming Exercises 359
*10.40 (Tkinter: insertion-sort animation) Write a program that animates the insertion-sort
algorithm. Create a list that consists of 20 distinct numbers from 1 to 20 in a ran-
dom order. The elements are displayed in a histogram, as shown in Figure 10.21.
Clicking the Step button causes the program to perform an iteration of the outer
loop in the algorithm and repaints the histogram for the new list. Color the last bar
in the sorted sublist. When the algorithm is finished, display a dialog box to inform
the user. Clicking the Reset button creates a new random list for a new start.
10.41 (Display five circles) Write a program that displays five circles, as shown in
Figure 10.22a. Enable the user to drag each circle using the mouse, as shown in
Figure 10.22b.
FIGURE 10.21 The program animates an insertion sort.
(a) (b)
FIGURE 10.22 Each circle can be dragged with the mouse.

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MULTIDIMENSIONAL
LISTS
Objectives
■ To learn how a two-dimensional list can represent two-dimensional data
(§11.1).
■ To access elements in a two-dimensional list by using row and column
indexes (§11.2).
■ To program common operations for two-dimensional lists (displaying lists,
summing all elements, finding min and max elements, random
shuffling, and sorting) (§11.2).
■ To pass two-dimensional lists to functions (§11.3).
■ To write a program for grading multiple-choice questions by using
two-dimensional lists (§11.4).
■ To solve the closest-pair problem by using two-dimensional lists
(§§11.5–11.6).
■ To check a Sudoku solution by using two-dimensional lists (§§11.7–11.8).
■ To use multidimensional lists (§11.9).
CHAPTER
11

362 Chapter 11 Multidimensional Lists
11.1 Introduction
Data in a table or a matrix can be stored in a two-dimensional list.
A two-dimensional list is a list that contains other lists as its elements. The preceding chapter
introduced how to use a list to store linear collections of elements. You can use a list to store
two-dimensional data, such as a matrix or a table, as well. For example, the following table,
which provides the distances between cities, can be stored in a list named distances.
distances = [
[0, 983, 787, 714, 1375, 967, 1087],
[983, 0, 214, 1102, 1505, 1723, 1842],
[787, 214, 0, 888, 1549, 1548, 1627],
[714, 1102, 888, 0, 661, 781, 810],
[1375, 1505, 1549, 661, 0, 1426, 1187],
[967, 1723, 1548, 781, 1426, 0, 239],
[1087, 1842, 1627, 810, 1187, 239, 0]
]
Each element in the distances list is another list, so distances is considered a nested
list. In this example, a two-dimensional list is used to store two-dimensional data.
11.2 Processing Two-Dimensional Lists
A value in a two-dimensional list can be accessed through a row and column index.
You can think of a two-dimensional list as a list that consists of rows. Each row is a list that
contains the values. The rows can be accessed using the index, conveniently called a row
index. The values in each row can be accessed through another index, called a column index.
A two-dimensional list named matrix is illustrated in Figure 11.1.
two-dimensional list
nested list
row index
Distance Table (in miles)
Chicago Boston New York Atlanta Miami Dallas Houston
Chicago 0 983 787 714 1,375 967 1,087
Boston 983 0 214 1,102 1,505 1,723 1,842
New York 787 214 0 888 1,549 1,548 1,627
Atlanta 714 1,102 888 0 661 781 810
Miami 1,375 1,505 1,549 661 0 1,426 1,187
Dallas 967 1,723 1,548 781 1,426 0 239
Houston 1,087 1,842 1,627 810 1,187 239 0
column index
FIGURE 11.1 The values in a two-dimensional list can be accessed through row and column
indexes.
1 2 3 4
00
0
0
5
[0] [1] [2] [3] [4]
6 7 0
0 0
0 9 3
0 0
1 0
1 8
0
[0]
[2]
[1]
[3]
[4] 0
matrix[0] is [1, 2, 3, 4, 5]
matrix[1] is [6, 7, 0, 0, 0]
matrix[2] is [0, 1, 0, 0, 0]
matrix[3] is [1, 0, 0, 0, 8]
matrix[4] is [0, 0, 9, 0, 3]
matrix[0][0] is 1
matrix[4][4] is 3
matrix = [
[1, 2, 3, 4, 5],
[6, 7, 0, 0, 0],
[0, 1, 0, 0, 0],
[1, 0, 0, 0, 8],
[0, 0, 9, 0, 3],
]
Key
Point
Key
Point
Process a matrix
VideoNote

11.2 Processing Two-Dimensional Lists 363
Each value in matrix can be accessed using matrix[i][j], where i and j are the row
and column indexes.
The following sections give some examples of using two-dimensional lists.
11.2.1 Initializing Lists with Input Values
The following loop initializes the matrix with user input values:
matrix = [] # Create an empty list
numberOfRows = eval(input(“Enter the number of rows: “))
numberOfColumns = eval(input(“Enter the number of columns: “))
for row in range(numberOfRows):
matrix.append([]) # Add an empty new row
for column in range(numberOfColumns):
value = eval(input(“Enter an element and press Enter: “))
matrix[row].append(value)
print(matrix)
11.2.2 Initializing Lists with Random Values
The following loop initializes a list that stores random values between 0 and 99:
import random
matrix = [] # Create an empty list
numberOfRows = eval(input(“Enter the number of rows: “))
numberOfColumns = eval(input(“Enter the number of columns: “))
for row in range(numberOfRows):
matrix.append([]) # Add an empty new row
for column in range(numberOfColumns):
matrix[row].append(random.randint(0, 99))
print(matrix)
11.2.3 Printing Lists
To print a two-dimensional list, you have to print each element in the list by using a loop like
the following:
matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] # Assume a list is given
for row in range(len(matrix)):
for column in range(len(matrix[row])):
print(matrix[row][column], end = ” “)
print() # Print a new line
Or you can write:
matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] # Assume a list is given
for row in matrix:
for value in row:
print(value, end = ” “)
print() # Print a new line

364 Chapter 11 Multidimensional Lists
11.2.4 Summing All Elements
Use a variable named total to store the sum. Initially, total is 0. Add each element in the
list to total by using a loop like this:
matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] # Assume a list is given
total = 0
for row in matrix:
for value in row:
total += value
print(“Total is”, total) # Print the total
11.2.5 Summing Elements by Column
For each column, use a variable named total to store its sum. Add each element in the col-
umn to total using a loop like this:
matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] # Assume a list is given
for column in range(len(matrix[0])):
total = 0
for row in range(len(matrix)):
total += matrix[row][column]
print(“Sum for column”, column, “is”, total)
11.2.6 Finding the Row with the Largest Sum
To find the row with the largest sum, you may use the variables maxRow and
indexOfMaxRow to track the largest sum and the index of the row. For each row, compute its
sum and update maxRow and indexOfMaxRow if the new sum is greater.
matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] # Assume a list is given
maxRow = sum(matrix[0]) # Get sum of the first row in maxRow
indexOfMaxRow = 0
for row in range(1, len(matrix)):
if sum(matrix[row]) > maxRow:
maxRow = sum(matrix[row])
indexOfMaxRow = row
print(“Row”, indexOfMaxRow, “has the maximum sum of”, maxRow)
11.2.7 Random Shuffling
You can shuffle the elements in a one-dimensional list by using the random.shuffle(list)
function, introduced in Section 10.2.3. How do you shuffle all the elements in a two-dimensional
list? To accomplish this, for each element matrix[row][column], randomly generate indexes
i and j and swap matrix[row][column] with matrix[i][j], as follows:
import random
matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] # Assume a list is given
for row in range(len(matrix)):
for column in range(len(matrix[row])):
i = random.randint(0, len(matrix) – 1)

11.3 Passing Two-Dimensional Lists to Functions 365
j = random.randint(0, len(matrix[row]) – 1)
# Swap matrix[row][column] with matrix[i][j]
matrix[row][column], matrix[i][j] = \
matrix[i][j], matrix[row][column]
print(matrix)
11.2.8 Sorting
You can apply the sort method to sort a two-dimensional list. It sorts the rows on their first
elements. For the rows with the same first element, they are sorted on the second elements. If
the first and second elements in the rows are the same, their third elements are sorted, and so
on. For example,
points = [[4, 2], [1, 7], [4, 5], [1, 2], [1, 1], [4, 1]]
points.sort()
print(points)
displays [[1, 1], [1, 2], [1, 7], [4, 1], [4, 2], [4, 5]].
11.1 How do you create a list for a two-dimensional set of data with three rows and four
columns with values 0?
11.2 Can you create a list for two-dimensional data with a different number of elements in
a row?
11.3 What is the output of the following code?
matrix = []
matrix.append(3 * [1])
matrix.append(3 * [1])
matrix.append(3 * [1])
matrix[0][0] = 2
print(matrix)
11.4 What is the output of the following code?
matrix = []
matrix.append([3 * [1]])
matrix.append([3 * [1]])
matrix.append([3 * [1]])
print(matrix)
matrix[0] = 3
print(matrix)
11.5 What is the output of the following code?
matrix = []
matrix.append([1, 2, 3])
matrix.append([4, 5])
matrix.append([6, 7, 8, 9])
print(matrix)
11.3 Passing Two-Dimensional Lists to Functions
When passing a two-dimensional list to a function, the list’s reference is passed to the
function.
You can pass a two-dimensional list to a function just as you pass a one-dimensional list. You
can also return a two-dimensional list from a function. Listing 11.1 gives an example with two
Key
Point
✓Point✓Check

366 Chapter 11 Multidimensional Lists
functions. The first function, getMatrix(), returns a two-dimensional list, and the second
function, accumulate(m), returns the sum of all the elements in a matrix.
LISTING 11.1 PassTwoDimensionalList.py
1 def getMatrix():
2 matrix = [] # Create an empty list
3
4 numberOfRows = eval(input(“Enter the number of rows: “))
5 numberOfColumns = eval(input(“Enter the number of columns: “))
6 for row in range(numberOfRows):
7 matrix.append([]) # Add an empty new row
8 for column in range(numberOfColumns):
9 value = eval(input(“Enter a value and press Enter: “))
10 matrix[row].append(value)
11
12 return matrix
13
14 def accumulate(m):
15 total = 0
16 for row in m:
17 total += sum(row)
18
19 return total
20
21 def main():
22 m = getMatrix() # Get a list
23 print(m)
24
25 # Display sum of elements
26 print(“\nSum of all elements is”, accumulate(m))
27
28 main() # Invoke main function
return matrix
accumulate function
get matrix
invoke accumulate function
Enter the number of rows:
Enter the number of columns:
Enter a value and press Enter:
Enter a value and press Enter:
Enter a value and press Enter:
Enter a value and press Enter:
[[1, 2], [3, 4]]
Sum of all elements is 10
4
3
2
1
2
2
The function getMatrix (lines 1–12) prompts the user to enter values for the matrix (line
9), and returns the list (line 12).
The function accumulate (lines 14–19) has a two-dimensional list argument. It returns
the sum of all elements in the list (line 26).
11.6 Show the output of the following code:
def f(m):
for i in range(len(m)):
for j in range(len(m[i])):
m[i][j] += 1
getMatrix function
✓Point✓Check

11.4 Problem: Grading a Multiple-Choice Test 367
def printM(m):
for i in range(len(m)):
for j in range(len(m[i])):
print(m[i][j], end = “”)
print()
m = [[0, 0], [0, 1]]
printM(m)
f(m)
printM(m)
11.4 Problem: Grading a Multiple-Choice Test
The problem is to write a program that grades multiple-choice tests.
Suppose there are eight students and ten questions, and the answers are stored in a two-
dimensional list. Each row records a student’s answers to the questions, as shown in the
following illustration.
The program grades the test and displays the result. To do this, the program compares each
student’s answers with the key, counts the number of correct answers, and displays it. Listing
11.2 shows the program.
LISTING 11.2 GradeExam.py
1 def main():
2 # Students’ answers to the questions
3
4
5
6
7
8
9
10
11
12
13 # Key to the questions
14 keys = [‘D’, ‘B’, ‘D’, ‘C’, ‘C’, ‘D’, ‘A’, ‘E’, ‘A’, ‘D’]
[‘E’, ‘B’, ‘E’, ‘C’, ‘C’, ‘D’, ‘E’, ‘E’, ‘A’, ‘D’]]
[‘B’, ‘B’, ‘A’, ‘C’, ‘C’, ‘D’, ‘E’, ‘E’, ‘A’, ‘D’],
[‘B’, ‘B’, ‘E’, ‘C’, ‘C’, ‘D’, ‘E’, ‘E’, ‘A’, ‘D’],
[‘A’, ‘B’, ‘D’, ‘C’, ‘C’, ‘D’, ‘E’, ‘E’, ‘A’, ‘D’],
[‘C’, ‘B’, ‘A’, ‘E’, ‘D’, ‘C’, ‘E’, ‘E’, ‘A’, ‘D’],
[‘E’, ‘D’, ‘D’, ‘A’, ‘C’, ‘B’, ‘E’, ‘E’, ‘A’, ‘D’],
[‘D’, ‘B’, ‘A’, ‘B’, ‘C’, ‘A’, ‘E’, ‘E’, ‘A’, ‘D’],
[‘A’, ‘B’, ‘A’, ‘C’, ‘C’, ‘D’, ‘E’, ‘E’, ‘A’, ‘D’],
answers = [ 2-D list
1-D list
0 1 2 3 4 5 6 7 8 9
Student 0 A B A C C D E E A D
Student 1 D B A B C A E E A D
Student 2 E D D A C B E E A D
Student 3 C B A E D C E E A D
Student 4 A B D C C D E E A D
Student 5 B B E C C D E E A D
Student 6 B B A C C D E E A D
Student 7 E B E C C D E E A D
Students’ Answers to the Questions:
Key to the Questions:
0 1 2 3 4 5 6 7 8 9
Key D B D C C D A E A D
The key is stored in a one-dimensional list:
Key
Point

368 Chapter 11 Multidimensional Lists
15
16 # Grade all answers
17 for i in range( ):
18 # Grade one student
19 correctCount = 0
20 for j in range( ):
21 if :
22 correctCount += 1
23
24 print(“Student”, i, “‘s correct count is”, correctCount)
25
26 main() # Call the main function
answers[i][j] == keys[j]
len(answers[i])
len(answers)
compare with key
Student 0’s correct count is 7
Student 1’s correct count is 6
Student 2’s correct count is 5
Student 3’s correct count is 4
Student 4’s correct count is 8
Student 5’s correct count is 7
Student 6’s correct count is 7
Student 7’s correct count is 7
The statement in lines 3–11 creates a two-dimensional list of characters and assigns the
reference to answers.
The statement in line 14 creates a list of keys and assigns the reference to keys.
Each row in the list answers stores a student’s answers, which are graded by comparing
them with the keys in the list keys. The result is displayed immediately after a student’s
answers are graded (lines 19–22).
11.5 Problem: Finding the Closest Pair
This section presents a geometric problem for finding the closest pair of points.
Given a set of points, the closest-pair problem is to find the two points that are nearest to each
other. In Figure 11.2, for example, points (1, 1) and (2, 0.5) are closest to each other.
There are several ways to solve this problem. An intuitive approach is to compute the dis-
tances between all pairs of points and find the one with the minimum distance, as imple-
mented in Listing 11.3.
(1, 1)
(–1, –1)
(–1, 3)
(2, 0.5)
(3, 3)
–1 3
x y
–1 –1
1 1
2 0.5
2 –1
3 3
4 2
4
0
1
2
3
4
5
6
7 –0.5
(4, 2)
(2, –1)
(4, –0.5)
FIGURE 11.2 Points can be represented in a nested list.
Key
Point

11.5 Problem: Finding the Closest Pair 369
LISTING 11.3 NearestPoints.py
1 # Compute the distance between two points (x1, y1) and (x2, y2)
2
3 return ((x2 – x1) * (x2 – x1) + (y2 – y1) * (y2 – y1)) ** 0.5
4
5
6 # p1 and p2 are the indexes in the points list
7 p1, p2 = 0, 1 # Initial two points
8
9 shortestDistance = distance(points[p1][0], points[p1][1],
10 points[p2][0], points[p2][1]) # Initialize shortestDistance
11
12 # Compute distance between every two points
13 for i in range(len(points)):
14 for j in range(i + 1, len(points)):
15 d = distance(points[i][0], points[i][1],
16 points[j][0], points[j][1]) # Find distance
17
18 if shortestDistance > d:
19 p1, p2 = i, j # Update p1, p2
20 shortestDistance = d # New shortestDistance
21
22 return p1, p2
This module defines the nearestPoints(points) function, which returns the indexes
of the two nearest points in the two-dimensional list points. The program uses the variable
shortestDistance (line 9) to store the distance between the two nearest points, and the
indexes of these two points in the points list are stored in p1 and p2 (line 19).
For each point at index i, the program computes the distance between points[i] and
points[j] for all j > i (lines 15–16). Whenever a shorter distance is found, the variable
shortestDistance and p1 and p2 are updated (lines 19–20).
The distance between two points (x1, y1) and (x2, y2) can be computed using the for-
mula (lines 2–3).
Note that there might be more than one closest pair of points with the same minimum dis-
tance. The program finds one such pair. You can modify the program to find all the closest
pairs in Programming Exercise 11.8.
The program in Listing 11.4 prompts the user to enter the points and then displays the
nearest two points.
LISTING 11.4 FindNearestPoints.py
1 import NearestPoints
2
3 def main():
4 numberOfPoints = eval(input(“Enter the number of points: “))
5
6 # Create a list to store points
7 points = []
8 print(“Enter”, numberOfPoints, “points:”, end = ”)
9 for i in range(numberOfPoints):
10 point = 2 * [0]
11 point[0], point[1] = \
12 eval(input(“Enter coordinates separated by a comma: “))
13 points.append(point)
14
15 # p1 and p2 are the indexes in the points list
2(x2 – x1)2 + (y2 – y1)2
def nearestPoints(points):
def distance(x1, y1, x2, y2): distance between two points
track two points
track shortestDistance
for each point i
for each point j
distance between i and j
update shortestDistance
import NearestPoints
multiple closest pairs
number of points
2-D list
read points
append a point

370 Chapter 11 Multidimensional Lists
16 p1, p2 = NearestPoints.nearestPoints(points)
17
18 # Display result
19 print(“The closest two points are (” +
20 str(points[p1][0]) + “, ” + str(points[p1][1]) + “) and (” +
21 str(points[p2][0]) + “, ” + str(points[p2][1]) + “)”)
22
23 main() # Call the main function
get nearest points
Enter the number of points:
Enter coordinates separated by a comma:
Enter coordinates separated by a comma:
Enter coordinates separated by a comma:
Enter coordinates separated by a comma:
Enter coordinates separated by a comma:
Enter coordinates separated by a comma:
Enter coordinates separated by a comma:
Enter coordinates separated by a comma:
The closest two points are (1, 1) and (2, 0.5)
4, -0.5
4, 2
3, 3
2, -1
2, 0.5
1, 1
-1, -1
-1, 3
8
The program prompts the user to enter the number of points (line 4). The points are read
from the console and stored in a two-dimensional list named points (line 11). The program
invokes the nearestPoints(points) function to return the indexes of the two nearest
points in the list (line 16).
The program assumes that the plane has at least two points. You can easily modify the pro-
gram in case the plane has zero or one point.
Tip
It is cumbersome to enter all points from the keyboard. You may store the input in a file,
with a name such as FindNearestPoints.txt, and run the program using the following
command from a command window:
python FindNearestPoints < FindNearestPoints.txt 11.6 GUI: Finding the Closest Pair This section displays the points in a canvas, finds the closest pair of points, and draws a line to connect these two points. The preceding section described a program that prompts the user to enter points and then finds the closest pair. This section presents a GUI program (Listing 11.5) that enables the user to create a point in the canvas with a left-mouse click, and it then dynamically finds the clos- est pair of points in the canvas and draws a line to connect these two points, as shown in Figure 11.3. LISTING 11.5 NearestPointsGUI.py 1 import NearestPoints 2 from tkinter import * # Import all definitions from tkinter 3 input file import NearestPoints Key Point 11.6 GUI: Finding the Closest Pair 371 FIGURE 11.3 You can add a point by clicking the left-mouse button. The two nearest points are connected with a line. 4 RADIUS = 2 # Radius of the point 5 6 class NearestPointsGUI: 7 def __init__(self): 8 self.points = [] # Store self.points 9 window = Tk() # Create a window 10 window.title("Find Nearest Points") # Set title 11 12 13 self.canvas.pack() 14 15 16 17 window.mainloop() # Create an event loop 18 19 20 if not self.isTooCloseToOtherPoints(event.x, event.y): 21 self.addThisPoint(event.x, event.y) 22 23 24 # Display this point 25 self.canvas.create_oval(x - RADIUS, y - RADIUS, 26 x + RADIUS, y + RADIUS) 27 # Add this point to self.points list 28 self.points.append([x, y]) 29 if len(self.points) > 2:
30 p1, p2 =
31 self.canvas.delete(“line”)
32 self.canvas.create_line(self.points[p1][0],
33 self.points[p1][1], self.points[p2][0],
34 self.points[p2][1], tags = “line”)
35
36
37 for i in range(len(self.points)):
38 if NearestPoints.distance(x, y,
39 self.points[i][0], self.points[i][1]) <= RADIUS + 2: 40 return True 41 42 return False 43 44 NearestPointsGUI() # Create GUI def isTooCloseToOtherPoints(self, x, y): NearestPoints.nearestPoints(self.points) def addThisPoint(self, x, y): def addPoint(self, event): self.canvas.bind("“, self.addPoint)
self.canvas = Canvas(window, width = 400, height = 200)
point radius
points list
create canvas
bind event handler
check mouse position
add a point
add to list
nearest points
draw a line
check mouse position
create GUI

372 Chapter 11 Multidimensional Lists
The program creates and displays a canvas (lines 12–13) and binds the left-mouse click event
to the callback function addPoint (line 15). When the user clicks the left mouse button on the
canvas, the addPoint handler is invoked (lines 19–21). The isTooCloseToOtherPoints(x,
y) method determines whether the mouse point is too close to any of the existing points on the
canvas (line 20). If not, the point is added to the canvas by invoking addThisPoint(x, y) (line
21).
The isTooCloseToOtherPoints(x, y) method (lines 36–42) determines whether the
point (x, y) is too close to other points in the canvas. If so, the program returns True (line
40); otherwise, it returns False (line 42).
The addThisPoint(x, y) method (lines 23–34) displays the point on the canvas (lines
25–26), adds the point to the points list (line 28), finds the new nearest points (line 30), and
draws a line to connect the points (lines 32–34).
Note that every time a new point is added, the nearestPoints function is invoked to find
a pair of nearest points. This function computes the distance between every pair of two points.
This will be very time-consuming as more points are added. For a more efficient approach,
see Programming Exercise 11.50.
11.7 Problem: Sudoku
The problem is to determine whether a given Sudoku solution is correct.
This section presents an interesting kind of problem that appears in the newspaper every day:
the number-placement puzzle commonly known as Sudoku. This is a very challenging pro-
gramming problem. To make it more accessible to novice programmers, this section presents
a solution to a simplified version of the Sudoku problem, which is to verify whether a solution
is correct. The complete solution for solving the Sudoku problem is presented in Supplement
III.A.
Sudoku is a grid divided into smaller boxes (also called regions or blocks), as
shown in Figure 11.4a. Some cells, called fixed cells, are populated with numbers from 1 to 9.
The objective is to fill the empty cells, also called free cells, with the numbers 1 to 9 so that
every row, column, and box contains the numbers 1 to 9, as shown in Figure 11.4b.3 * 3
3 * 39 * 9
fixed cells
free cells
5 3 7
6 1 9 5
9 8 6
8 6 3
4 8 3 1
7 2 6
6
4 1 9 5
8 7 9
(a) Puzzle
Solution
(b) Solution
5 3 4 6 7 8 9 1 2
6 7 2 1 9 5 3 4 8
1 9 8 3 4 2 5 6 7
8 5 9 7 6 1 4 2 3
4 2 6 8 5 3 7 9 1
7 1 3 9 2 4 8 5 6
9 6 1 5 3 7 2 8 4
2 8 7 4 1 9 6 3 5
3 4 5 2 8 6 1 7 9
FIGURE 11.4 The Sudoku puzzle in (a) is solved in (b).
For convenience, we use the value 0 to indicate a free cell, as shown in Figure 11.5a. The
grid can be naturally represented using a two-dimensional list, as shown in Figure 11.5b.
To find a solution for the puzzle, we must replace each 0 in the grid with an appropriate
number from 1 to 9. For the solution in Figure 11.4b, the list grid should be as shown in
Figure 11.6.
representing a grid
Key
Point

11.7 Problem: Sudoku 373
Suppose a solution to a Sudoku puzzle is entered. How do you determine whether the solu-
tion is correct? Here are two approaches:
■ One way to check the solution is to verify that every row, column, and box has the
numbers from 1 to 9.
■ The other way is to check each cell. Each cell must contain a number from 1 to 9,
and the cell must be unique in every row, column, and box.
The program in Listing 11.6 prompts the user to enter a solution and reports whether it is
valid. We use the second approach to determine whether the solution is correct. We place the
isValid function in the separate module in Listing 11.7 so that it can be used by other pro-
grams.
LISTING 11.6 TestCheckSudokuSolution.py
1 from CheckSudokuSolution import isValid
2
3 def main():
4 # Read a Sudoku solution
5 grid = readASolution()
6
7 if isValid(grid):
8 print(“Valid solution”)
9 else:
10 print(“Invalid solution”)
11
5 3 0 0 0 0 0 0
0 0
0 0
0 0
0 0
0 0
0 0
0
0
00
0
00 0
0 0
0 0
0
0 00
0 080 00
0 00
0 06
7
6 0 0
0 0
0 0
0 0 0
1 9 5
9 8 6
8 6 3
4 8 3 1
7 2 6
4 1 9 5
7 9
(a) (b)
grid =
[[5, 3, 0, 0, 7, 0, 0, 0, 0],
[6, 0, 0, 1, 9, 5, 0, 0, 0],
[0, 9, 8, 0, 0, 0, 0, 6, 0],
[8, 0, 0, 0, 6, 0, 0, 0, 3],
[4, 0, 0, 8, 0, 3, 0, 0, 1],
[7, 0, 0, 0, 2, 0, 0, 0, 6],
[0, 6, 0, 0, 0, 0, 2, 8, 0],
[0, 0, 0, 4, 1, 9, 0, 0, 5],
[0, 0, 0, 0, 8, 0, 0, 7, 9]
]
FIGURE 11.5 A grid can be represented using a two-dimensional list.
FIGURE 11.6 A solution is stored in grid.
A solution grid is
[[5, 3, 4, 6, 7, 8, 9, 1, 2],
[6, 7, 2, 1, 9, 5, 3, 4, 8],
[1, 9, 8, 3, 4, 2, 5, 6, 7],
[8, 5, 9, 7, 6, 1, 4, 2, 3],
[4, 2, 6, 8, 5, 3, 7, 9, 1],
[7, 1, 3, 9, 2, 4, 8, 5, 6],
[9, 6, 1, 5, 3, 7, 2, 8, 4],
[2, 8, 7, 4, 1, 9, 6, 3, 5],
[3, 4, 5, 2, 8, 6, 1, 7, 9]
]
read input
solution valid?

374 Chapter 11 Multidimensional Lists
12 # Read a Sudoku solution from the console
13 def readASolution():
14 print(“Enter a Sudoku puzzle solution:”)
15 grid = []
16 for i in range(9):
17 line = input().strip().split()
18 grid.append([eval(x) for x in line])
19
20 return grid
21
22 main() # Call the main function
Enter a Sudoku puzzle solution:
Valid solution
6 4 2 5 9 8 1 7 3
3 1 7 2 4 6 9 8 5
5 8 9 7 1 3 4 6 2
7 3 5 9 6 1 8 2 4
4 9 6 8 5 2 3 1 7
8 2 1 4 3 7 5 9 6
2 5 4 6 8 9 7 3 1
1 7 8 3 2 5 6 4 9
9 6 3 1 7 4 2 5 8
LISTING 11.7 CheckSudokuSolution.py
1 # Check whether a solution is valid
2 def isValid(grid):
3 for i in range(9):
4 for j in range(9):
5 if grid[i][j] < 1 or grid[i][j] > 9 \
6 or not isValidAt(i, j, grid):
7 return False
8 return True # The fixed cells are valid
9
10 # Check whether grid[i][j] is valid in the grid
11 def isValidAt(i, j, grid):
12 # Check whether grid[i][j] is valid in i’s row
13 for column in range(9):
14 if column != j and grid[i][column] == grid[i][j]:
15 return False
16
17 # Check whether grid[i][j] is valid in j’s column
18 for row in range(9):
19 if row != i and grid[row][j] == grid[i][j]:
20 return False
21
22 # Check whether grid[i][j] is valid in the 3-by-3 box
23 for row in range((i // 3) * 3, (i // 3) * 3 + 3):
24 for col in range((j // 3) * 3, (j // 3) * 3 + 3):
25 if row != i and col != j and \
26 grid[row][col] == grid[i][j]:
27 return False
28
29 return True # The current value at grid[i][j] is valid
read solution
solution valid?
check columns
check rows
check small boxes

11.8 Case Study: Sudoku GUI 375
In Listing 11.6, the program invokes the readASolution() function (line 5) to read a
Sudoku solution and return a two-dimensional list representing a Sudoku grid.
The isValid(grid) function determines whether the values in the grid are valid. It
checks whether each value is between 1 and 9 and whether each value is valid in the grid
(lines 7–10).
The isValidAt(i, j, grid) function in Listing 11.7 checks whether the value at
grid[i][j] is valid. It checks whether grid[i][j] appears more than once in row i (lines
18–20), in column j (lines 13–15), and in the box (lines 23–27).
How do you locate all the cells in the same box? For any grid[i][j], the starting cell of
the box that contains it is grid[(i // 3) * 3][(j // 3) * 3], as illustrated in
Figure 11.7.
3 * 3
3 * 3
isValid function
isValidAt function
For any grid[i][j] in this 3-by-3 box, its
starting cell is grid[3*(i//3)][3*(j//3)]
(i.e., grid[0][6]). For example, for
grid[2][8], i = 2 and j = 8, 3*(i//3) = 0 and
3*(j//3) = 6.
grid[0][6]
grid[6][3]
For any grid[i][j] in this 3-by-3 box, its
starting cell is grid[3*(i//3)][3*(j//3)]
(i.e., grid[6][3]). For example, for
grid[8][5], i = 8 and j = 5, 3*(i//3) = 6
and 3*(j//3) = 3.
grid[0][0]
FIGURE 11.7 The location of the first cell in a box determines the locations of the other cells in the box.3 * 3
With this insight, you can easily identify all the cells in the box. For example, if
grid[r][c] is the starting cell of a box, the cells in the box can be traversed in a
nested loop as follows:
# Get all cells in a 3-by-3 box starting at grid[r][c]
for row in range(r, r + 3):
for col in range(c, c + 3):
# grid[row][col] is in the box
It is cumbersome to enter 81 numbers from the console. When you test the program, you
may store the input in a file, say CheckSudokuSolution.txt (see www.cs.armstrong.edu/liang/
data/CheckSudokuSolution.txt), and run the program using the following command from a com-
mand window:
python TestCheckSudokuSolution.py < CheckSudokuSolution.txt 11.8 Case Study: Sudoku GUI This section shows how to create a GUI program that checks whether a given Sudoku solution is correct. The program in the preceding section reads a Sudoku solution from the console and checks whether the solution is correct. This section presents a GUI program that lets the user enter the solution from the Entry widget and click the Validate button to check if the solution is correct, as shown in Figure 11.8. 3 * 3 input file Key Point www.cs.armstrong.edu/liang/ 376 Chapter 11 Multidimensional Lists The complete program is given in Listing 11.8. LISTING 11.8 SudokuGUI.py 1 from tkinter import * # Import all definitions from tkinter 2 import tkinter.messagebox # Import tkinter.messagebox 3 from CheckSudokuSolution import isValid # Defined in Listing 11.7 4 5 class SudokuGUI: 6 def __init__(self): 7 window = Tk() # Create a window 8 window.title("Check Sudoku Solution") # Set title 9 10 frame = Frame(window) # Hold entries 11 frame.pack() 12 13 # A list of variables tied to entries 14 for i in range(9): 15 self.cells.append([]) 16 for j in range(9): 17 18 19 for i in range(9): 20 for j in range(9): 21 22 23 24 row = i, column = j) textvariable = self.cells[i][j]).grid( Entry(frame, width = 2, justify = RIGHT, self.cells[i].append(StringVar()) self.cells = [] FIGURE 11.8 You can enter the numbers in the Entry widget and click the Validate button to see if the solution is correct. import isValid entries 2-D list create entries 11.9 Multidimensional Lists 377 25 Button(window, text = "Validate", 26 command = ).pack() 27 28 window.mainloop() # Create an event loop 29 30 # Check if the numbers entered are a valid solution 31 32 # Get the numbers from the entries 33 values = [[eval(x.get()) 34 for x in self.cells[i]] for i in range(9)] 35 36 if isValid(values): 37 tkinter.messagebox.showinfo("Check Sudoku Solution", 38 "The solution is valid") 39 else: 40 tkinter.messagebox.showwarning("Check Sudoku Solution", 41 "The solution is invalid") 42 43 SudokuGUI() # Create GUI The program creates a two-dimensional list cells (lines 13–17). Each element in cells corresponds to a value in the entry (lines 19–23). The entries are created and placed using a grid manager in a frame. A button is created to be placed below the frame (lines 25–26). When the button is clicked, the callback handler validate is invoked (lines 31–41). The function obtains the values from the entries and puts them into the two-dimensional list values (lines 33–34), and then invokes the isValid function (defined in Listing 11.7) to check whether the numbers entered from the entries form a valid solution (line 36). The Tkin- ter’s standard dialog boxes are used to display whether a solution is valid (lines 36–41). 11.9 Multidimensional Lists A two-dimensional list consists of a list of one-dimensional lists and a three-dimensional list consists of a list of two-dimensional lists. In the preceding sections, you used two-dimensional lists to represent a matrix or a table. Occasionally, you need to represent n-dimensional data. You can create n-dimensional lists for any integer n. For example, you can use a three-dimensional list to store exam scores for a class of six students with five exams, and each exam has two parts (multiple-choice and essay). The following syntax creates a three-dimensional list named scores. scores = [ [[11.5, 20.5], [11.0, 22.5], [15, 33.5], [13, 21.5], [15, 2.5]], [[4.5, 21.5], [11.0, 22.5], [15, 34.5], [12, 20.5], [14, 11.5]], [[6.5, 30.5], [11.4, 11.5], [11, 33.5], [11, 23.5], [10, 2.5]], [[6.5, 23.5], [11.4, 32.5], [13, 34.5], [11, 20.5], [16, 11.5]], [[8.5, 26.5], [11.4, 52.5], [13, 36.5], [13, 24.5], [16, 2.5]], [[11.5, 20.5], [11.4, 42.5], [13, 31.5], [12, 20.5], [16, 6.5]]] scores[0][1][0] refers to the multiple-choice score for the first student’s second exam, which is 11.0. scores[0][1][1] refers to the essay score for the first student’s second exam, which is 22.5. The following figure depicts the meaning of the values in the list. def validate(self): self.validate create a button callback handler validate method Which student Which exam Multiple-choice or essay scores[ i ] [ j ] [ k ] Key Point 378 Chapter 11 Multidimensional Lists A multidimensional list is a list in which each element is another list. More specifically, a three-dimensional list consists of a list of two-dimensional lists, and a two-dimensional list consists of a list of one-dimensional lists. For example, scores[0] and scores[1] are two- dimensional lists, while scores[0][0], scores[0][1], scores[1][0], and scores[1][1] are one-dimensional lists and each contains two elements. len(scores) is 6, len(scores[0]) is 5, and len(scores[0][0]) is 2. 11.9.1 Problem: Daily Temperature and Humidity Suppose a meteorological station records the temperature and humidity at each hour of every day and stores the data for the past ten days in a text file named weather.txt (see www.cs.armstrong.edu/liang/data/weather.txt). Each line of the file consists of four numbers that indicate the day, hour, temperature, and humidity. The contents of the file may look like the one in (a): multidimensional list 1 1 76.4 0.92 1 2 77.7 0.93 ... 10 23 97.7 0.71 10 24 98.7 0.74 10 24 98.7 0.74 1 2 77.7 0.93 ... 10 23 97.7 0.71 1 1 76.4 0.92 (a) (b) Note that the lines in the file are not necessarily in order. For example, the file may appear as shown in (b). Your task is to write a program that calculates the average daily temperature and humidity for the 10 days. You can use input redirection to read the data from the file and store the data in a three-dimensional list named data. The first index of data ranges from 0 to 9 and rep- resents the 10 days; the second index ranges from 0 to 23 and represents the 24-hour periods; and the third index ranges from 0 to 1 and represents temperature and humidity, respectively. Note that the days are numbered from 1 to 10 and hours from 1 to 24 in the file. Since the list index starts from 0, data[0][0][0] stores the temperature in day 1 at hour 1 and data[9][23][1] stores the humidity in day 10 at hour 24. The program is given in Listing 11.9. LISTING 11.9 Weather.py 1 def main(): 2 NUMBER_OF_DAYS = 10 3 NUMBER_OF_HOURS = 24 4 5 # Initialize data 6 7 for i in range(NUMBER_OF_DAYS): 8 data.append([]) 9 for j in range(NUMBER_OF_HOURS): 10 data[i].append([]) 11 data[i][j].append(0) # Temperature value 12 data[i][j].append(0) # Humidity value 13 14 # Read input using input redirection from a file 15 for k in range(NUMBER_OF_DAYS * NUMBER_OF_HOURS): 16 line = input().strip().split() 17 day = eval(line[0]) 18 hour = eval(line[1]) 19 temperature = eval(line[2]) 20 humidity = eval(line[3]) data = []three-dimensional list www.cs.armstrong.edu/liang/data/weather.txt 11.9 Multidimensional Lists 379 21 data[day - 1][hour - 1][0] = temperature 22 data[day - 1][hour - 1][1] = humidity 23 24 # Find the average daily temperature and humidity 25 for i in range(NUMBER_OF_DAYS): 26 dailyTemperatureTotal = 0 27 dailyHumidityTotal = 0 28 for j in range(NUMBER_OF_HOURS): 29 dailyTemperatureTotal += data[i][j][0] 30 dailyHumidityTotal += data[i][j][1] 31 32 # Display result 33 print("Day " + str(i) + "'s average temperature is " 34 + str(dailyTemperatureTotal / NUMBER_OF_HOURS)) 35 print("Day " + str(i) + "'s average humidity is " 36 + str(dailyHumidityTotal / NUMBER_OF_HOURS)) 37 38 main() # Call the main function Day 0's average temperature is 77.7708 Day 0's average humidity is 0.929583 Day 1's average temperature is 77.3125 Day 1's average humidity is 0.929583 ... Day 9's average temperature is 79.3542 Day 9's average humidity is 0.9125 You can use the following command to run the program: python Weather.py < Weather.txt A three-dimensional list for storing the temperature and humidity is created in lines 6–12 with initial values 0. The loop in lines 15–22 reads the input to the list. You can enter the input from the keyboard, but doing so will be awkward. For convenience, we store the data in a file and use input redirection to read the data from the file. The program reads one line of input as a string and splits it into a list (line 16) to obtain the day, hour, temperature, and humidity (lines 17–20). The loop in lines 25–30 adds all temperatures for each hour in a day to dailyTemperatureTotal and all humidity for each hour to dailyHumidityTotal. The average daily temperature and humidity are displayed in lines 33–36. 11.9.2 Problem: Guessing Birthdays Listing 4.3, GuessBirthday.py, is a program that guesses a birthday. The program can be sim- plified by storing the numbers in a three-dimensional list and prompting the user for the answers using a loop, as shown in Listing 11.10. The sample run of the program can be the same as shown in Listing 4.3. LISTING 11.10 GuessBirthdayUsingList.py 1 def main(): 2 day = 0 # Day to be determined 3 4 5 [[ 1, 3, 5, 7], 6 [ 9, 11, 13, 15], 7 [17, 19, 21, 23], dates = [ three-dimensional list 380 Chapter 11 Multidimensional Lists 8 [25, 27, 29, 31]], 9 [[ 2, 3, 6, 7], 10 [10, 11, 14, 15], 11 [18, 19, 22, 23], 12 [26, 27, 30, 31]], 13 [[ 4, 5, 6, 7], 14 [12, 13, 14, 15], 15 [20, 21, 22, 23], 16 [28, 29, 30, 31]], 17 [[ 8, 9, 10, 11], 18 [12, 13, 14, 15], 19 [24, 25, 26, 27], 20 [28, 29, 30, 31]], 21 [[16, 17, 18, 19], 22 [20, 21, 22, 23], 23 [24, 25, 26, 27], 24 [28, 29, 30, 31]]] 25 26 for i in range(5): 27 print("Is your birthday in Set" + str(i + 1) + "?") 28 for j in range(4): 29 for k in range(4): 30 print(format( , "4d"), end = " ") 31 print() 32 33 answer = eval(input("Enter 0 for No and 1 for Yes: ")) 34 35 if answer == 1: 36 day += 37 38 print("Your birthday is " + str(day)) 39 40 main() # Call the main function A three-dimensional list dates is created in Lines 4–24. This list stores five two-dimensional lists of numbers, each of which is a four-by-four, two-dimensional list. The loop starting from line 26 displays the numbers in each two-dimensional list and prompts the user to answer whether the birthday is in the list (line 33). If the day is in the set, the first number (dates[i][0][0]) in the set is added to variable day (line 36). This pro- gram is identical to the one in Listing 4.3, except that this program places the five data sets in a list. This is a preferred way to organize data, because data can be reused and processed in loops. 11.7 Show the output of the following code: def f(m): for i in range(len(m)): for j in range(len(m[i])): for k in range(len(m[j])): m[i][j][k] += 1 def printM(m): for i in range(len(m)): for j in range(len(m[i])): for k in range(len(m[j])): print(m[i][j][k], end = "") print() m = [[[0, 0], [0, 1]], [[0, 0], [0, 1]]] dates[i][0][0] dates[i][j][k] display a question ✓Point✓Check Programming Exercises 381 printM(m) f(m) printM(m) KEY TERMS column index 362 multidimensional list 378 nested list 362 row index 362 two-dimensional list 362 CHAPTER SUMMARY 1. A two-dimensional list can be used to store two-dimensional data such as a table and a matrix. 2. A two-dimensional list is a list. Each of its elements is a list. 3. An element in a two-dimensional list can be accessed using the following syntax: listName[rowIndex][columnIndex]. 4. You can use lists of lists to form multidimensional lists for storing multidimensional data. TEST QUESTIONS Do test questions for this chapter online at www.cs.armstrong.edu/liang/py/test.html. PROGRAMMING EXERCISES Sections 11.2–11.3 *11.1 (Sum elements column by column) Write a function that returns the sum of all the elements in a specified column in a matrix using the following header: def sumColumn(m, columnIndex): Write a test program that reads a matrix and displays the sum of each col- umn. Here is a sample run: 3 * 4 Enter a 3-by-4 matrix row for row 0: Enter a 3-by-4 matrix row for row 1: Enter a 3-by-4 matrix row for row 2: Sum of the elements for column 0 is 16.5 9.5 1 3 1 5.5 6 7 8 1.5 2 3 4 www.cs.armstrong.edu/liang/py/test.html 382 Chapter 11 Multidimensional Lists Sum of the elements for column 1 is 9.0 Sum of the elements for column 2 is 13.0 Sum of the elements for column 3 is 13.0 *11.2 (Sum the major diagonal in a matrix) Write a function that sums all the numbers of the major diagonal in an matrix of integers using the following header: def sumMajorDiagonal(m): The major diagonal is the diagonal that runs from the top left corner to the bottom right corner in the square matrix. Write a test program that reads a matrix and displays the sum of all its elements on the major diagonal. Here is a sample run: 4 * 4 n * n Enter a 4-by-4 matrix row for row 1: Enter a 4-by-4 matrix row for row 2: Enter a 4-by-4 matrix row for row 3: Enter a 4-by-4 matrix row for row 4: Sum of the elements in the major diagonal is 34.5 13 14 15 16 9 10 11 12 5 6.5 7 8 1 2 3 4 *11.3 (Sort students by grades) Rewrite Listing 11.2, GradeExam.py, to display the stu- dents in increasing order of the number of correct answers. **11.4 (Compute the weekly hours for each employee) Suppose the weekly hours for all employees are stored in a table. Each row records an employee’s seven-day work hours with seven columns. For example, the following table stores the work hours for eight employees. Write a program that displays employees and their total hours in decreasing order of the total hours. Su M T W Th F Sa Employee 0 2 4 3 4 5 8 8 Employee 1 7 3 4 3 3 4 4 Employee 2 3 3 4 3 3 2 2 Employee 3 9 3 4 7 3 4 1 Employee 4 3 5 4 3 6 3 8 Employee 5 3 4 4 6 3 4 4 Employee 6 3 7 4 8 3 8 4 Employee 7 6 3 5 9 2 7 9 11.5 (Algebra: add two matrices) Write a function to add two matrices. The header of the function is: def addMatrix(a, b): In order to be added, the two matrices must have the same dimensions and the same or compatible types of elements. Let c be the resulting matrix. Each element is For example, for two matrices a and b, c is3 * 3aij + bij.cij Programming Exercises 383 Write a test program that prompts the user to enter two matrices and dis- plays their sum. Here is a sample run: 3 * 3 £a11 a12 a13a21 a22 a23 a31 a32 a33 ≥ + £b11 b12 b13b21 b22 b23 b31 b32 b33 ≥ = £a11 + b11 a12 + b12 a13 + b13a21 + b21 a22 + b22 a23 + b23 a31 + b31 a32 + b32 a33 + b33 ≥ Enter matrix1: Enter matrix2: The matrices are added as follows: 1.0 2.0 3.0 0.0 2.0 4.0 1.0 4.0 11.0 4.0 5.0 6.0 + 1.0 4.5 2.2 = 5.0 11.5 8.2 11.0 8.0 11.0 1.1 4.3 5.2 8.1 12.3 14.2 0 2 4 1 4.5 2.2 1.1 4.3 5.2 1 2 3 4 5 6 7 8 9 **11.6 (Algebra: multiply two matrices) Write a function to multiply two matrices. The header of the function is: def multiplyMatrix(a, b) To multiply matrix a by matrix b, the number of columns in a must be the same as the number of rows in b, and the two matrices must have elements of the same or compatible types. Let c be the result of the multiplication. Assume the column size of matrix a is n. Each element is For example, for two matrices a and b, c is where Write a test program that prompts the user to enter two matrices and dis- plays their product. Here is a sample run: 3 * 3 cij = ai1 * b1j + ai2 * b2j + ai3 * b3j. = £c11 c12 c13c21 c22 c23 c31 c32 c33 ≥£a11 a12 a13a21 a22 a23 a31 a32 a33 ≥ * £b11 b12 b13b21 b22 b23 b31 b32 b33 ≥ 3 * 3 ai1 * b1j + ai2 * b2j + c + ain * bnj.cij Enter matrix1: Enter matrix2: The multiplication of the matrices is 1 2 3 0 2.0 4.0 5.3 23.9 24 4 5 6 * 1 4.5 2.2 = 11.6 56.3 58.2 7 8 9 1.1 4.3 5.2 111.9 88.7 92.4 0 2 4 1 4.5 2.2 1.1 4.3 5.2 1 2 3 4 5 6 7 8 9 *11.7 (Points nearest to each other) The program in Listing 11.3 finds the two points in a two-dimensional space nearest to each other. Revise the program so that it finds the two points in a three-dimensional space nearest to each other. Use a two-dimensional list to represent the points. Test the program using the following points: points = [[-1, 0, 3], [-1, -1, -1], [4, 1, 1], [2, 0.5, 9], [3.5, 2, -1], [3, 1.5, 3], [-1.5, 4, 2], [5.5, 4, -0.5]] 384 Chapter 11 Multidimensional Lists The formula for computing the distance between two points (x1, y1, z1) and (x2, y2, z2) in a three-dimensional space is **11.8 (All closest pairs of points) Revise Listing 11.4, FindNearestPoints.py, to find all the nearest pairs of points that have the same minimum distance. ***11.9 (Game: play a tic-tac-toe game) In a game of tic-tac-toe, two players take turns marking an available cell in a grid with their respective tokens (either X or O). When one player has placed three tokens in a horizontal, vertical, or diagonal row on the grid, the game is over and that player has won. A draw (no winner) occurs when all the cells in the grid have been filled with tokens and neither player has achieved a win. Create a program for playing tic-tac-toe. The program prompts two players to alternately enter an X token and an O token. Whenever a token is entered, the program redisplays the board on the console and determines the status of the game (win, draw, or continue). Here is a sample run: 3 * 3 2(x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2. ————————————- | | | | ————————————- | | | | ————————————- | | | | ————————————- Enter a row (0, 1, or 2) for player X: Enter a column (0, 1, or 2) for player X: ————————————- | | | | ————————————- | | X | | ————————————- | | | | ————————————- Enter a row (0, 1, or 2) for player O: Enter a column (0, 1, or 2) for player O: ————————————- | | | | ————————————- | | X | O | ————————————- | | | | ————————————- Enter a row (0, 1, or 2) for player X: ... ————————————- | X | | | ————————————- | O | X | O | ————————————- | | | X | ————————————- X player won 2 1 1 1 Programming Exercises 385 *11.10 (Largest rows and columns) Write a program that randomly fills in 0s and 1s into a matrix, prints the matrix, and finds the rows and columns with the most 1s. Here is a sample run of the program: 0011 0011 1101 1010 The largest row index: 2 The largest column index: 2, 3 **11.11 (Game: nine heads and tails) Nine coins are placed in a matrix with some face up and some face down. You can represent the state of the coins with the val- ues 0 (heads) and 1 (tails). Here are some examples: 0 0 0 1 0 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 Each state can also be represented using a binary number. For example, the pre- ceding matrices correspond to the numbers: 000010000 101001100 110100001 101110100 100111110 There are a total of 512 possibilities. So, you can use the decimal numbers 0, 1, 2, 3, ..., and 511 to represent all states of the matrix. Write a program that prompts the user to enter a number between 0 and 511 and displays the corresponding matrix with the characters H and T. Here is a sample run:3 * 3 3 * 3 4 * 4 Enter a number between 0 and 511: H H H H H H T T T 7 The user entered 7, which corresponds to 000000111. Since 0 stands for H and 1 for T, the output is correct. **11.12 (Financial application: compute tax) Rewrite Listing 4.7, ComputeTax.py, using lists. For each filing status, there are six tax rates. Each rate is applied to a certain amount of taxable income. For example, from the taxable income of $400,000 for a single filer, $8,350 is taxed at 10%, (33,950 – 8,350) at 15%, (82,250 – 33,950) at 25%, (171,550 – 82,250) at 28%, (372,950 – 171,550) at 33%, and (400,000 – 372,950) at 35%. The six rates are the same for all filing statuses, which can be represented in the following list: rates = [0.10, 0.15, 0.25, 0.28, 0.33, 0.35] The brackets for each rate for all the filing statuses can be represented in a two- dimensional list as follows: brackets = [ [8350, 33950, 82250, 171550, 372950], # Single filer [16700, 67900, 137050, 208850, 372950], # Married jointly [8350, 33950, 68525, 104425, 186475], # Married separately [11950, 45500, 117450, 190200, 372950] # Head of household ] 386 Chapter 11 Multidimensional Lists Suppose the taxable income is $400,000 for single filers. The tax can be computed as follows: tax = brackets[0][0] * rates[0] + (brackets[0][1] – brackets[0][0]) * rates[1] + (brackets[0][2] – brackets[0][1]) * rates[2] + (brackets[0][3] – brackets[0][2]) * rates[3] + (brackets[0][4] – brackets[0][3]) * rates[4] + (400000 – brackets[0][4]) * rates[5] *11.13 (Locate the largest element) Write the following function that returns the location of the largest element in a two-dimensional list: def locateLargest(a): The return value is a one-dimensional list that contains two elements. These two elements indicate the row and column indexes of the largest element in the two-dimensional list. Write a test program that prompts the user to enter a two- dimensional list and displays the location of the largest element in the list. Here is a sample run: Enter the number of rows in the list: Enter a row: Enter a row: Enter a row: The location of the largest element is at (1, 2) 35 44 5.5 11.6 4.5 3 45 3.5 23.5 35 2 10 3 **11.14 (Explore matrix) Write a program that prompts the user to enter the length of a square matrix, randomly fills in 0s and 1s into the matrix, prints the matrix, and finds the rows, columns, and major diagonal with all 0s or all 1s. Here is a sample run of the program: Enter the size for the matrix: 0111 0000 0100 1111 All 0s on row 1 All 1s on row 3 No same numbers in a column No same numbers in the major diagonal 4 Sections 11.4–11.9 *11.15 (Geometry: same line?) Exercise 6.19 gives a function for testing whether three points are on the same line. Write the following function to test whether all the points in the points list are on the same line: def sameLine(points): Write a program that prompts the user to enter five points and displays whether they are on the same line. Here are sample runs: Programming Exercises 387 Enter five points: The five points are not on the same line 3.4 2 6.5 11.5 2.3 2.3 5.5 5 -5 4 Enter five points: The five points are on the same line 1 1 2 2 3 3 4 4 5 5 *11.16 (Sort a list of points on y-coordinates) Write the following function to sort a list of points on their y-coordinates. Each point is a list of two values for x- and y- coordinates. # Returns a new list of points sorted on the y-coordinates def sort(points): For example, the points [[4, 2], [1, 7], [4, 5], [1, 2], [1, 1], [4, 1]] will be sorted to [[1, 1], [4, 1], [1, 2], [4, 2], [4, 5], [1, 7]]. Write a test program that displays the sorted result for points [[4, 34], [1, 7.5], [4, 8.5], [1, -4.5], [1, 4.5], [4, 6.6]] using print(list). ***11.17 (Financial tsunami) Banks lend money to each other. In tough economic times, if a bank goes bankrupt, it may not be able to pay back the loan. A bank’s total assets are its current balance plus its loans to other banks. The diagram in Figure 11.9 shows five banks. The banks’ current balances are 25, 125, 175, 75, and 181 million dollars, respectively. The directed edge from node 1 to node 2 indicates that bank 1 lends 40 million dollars to bank 2. 1 2 3 4 0 100.5 125 85 40 75 175125 125 125 320.5 181 25 75 FIGURE 11.9 Banks lend money to each other. If a bank’s total assets are under a certain limit, the bank is unsafe. The money it borrowed cannot be returned to the lender, and the lender cannot count the loan in its total assets. Consequently, the lender may also be unsafe if its total assets are under the limit. Write a program to find all unsafe banks. Your pro- gram should read the input as follows. It first reads two integers n and limit, where n indicates the number of banks and limit is the minimum total assets for keeping a bank safe. It then reads n lines that describe the information for n banks with ids from 0 to n - 1. The first number in the line is the bank’s balance, the second number indicates the number of banks that borrowed money from the bank, and the rest are pairs of two numbers. Each pair describes a borrower. The first number in the pair is the borrower’s id and the second is the amount borrowed. For example, the input for the five banks in Figure 11.9 is as follows (note that the limit is 201): 5 201 25 2 1 100.5 4 320.5 388 Chapter 11 Multidimensional Lists 125 2 2 40 3 85 175 2 0 125 3 75 75 1 0 125 181 1 2 125 The total assets of bank 3 are (75 + 125), which is under 201, so bank 3 is unsafe. After bank 3 becomes unsafe, the total assets of bank 1 fall below the limit (125 + 40), so bank 1 also becomes unsafe. The output of the program should be: Unsafe banks are 3 1 (Hint: Use a two-dimensional list borrowers to represent loans. borrowers[i][j] indicates the loan that bank i loans to bank j. Once bank j becomes unsafe, borrowers[i][j] should be set to 0.) *11.18 (Shuffle rows) Write a function that shuffles the rows in a two-dimensional list using the following header: def shuffle(m): Write a test program that shuffles the following matrix: m = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]] **11.19 (Pattern recognition: four consecutive equal numbers) Write the following function that tests whether a two-dimensional list has four consecutive numbers of the same value, either horizontally, vertically, or diagonally: def isConsecutiveFour(values): Write a test program that prompts the user to enter the number of rows and columns of a two-dimensional list and then the values in the list. The pro- gram displays True if the list contains four consecutive numbers with the same value; otherwise, it displays False. Here are some examples of the True cases: 0 1 0 3 1 6 1 0 1 6 8 6 0 1 5 6 2 1 8 2 9 6 5 6 1 1 9 1 1 3 6 1 4 0 7 3 3 3 3 4 0 7 0 1 0 3 1 6 1 0 1 6 8 6 0 1 5 5 2 1 8 2 9 6 5 6 1 1 9 1 1 5 6 1 4 0 7 3 5 3 3 4 0 7 0 1 0 3 1 6 1 0 1 6 8 6 0 1 5 6 2 1 6 2 9 6 5 6 6 1 9 1 1 3 6 1 4 0 7 3 6 3 3 4 0 7 0 1 0 3 1 6 1 0 1 6 8 6 0 1 9 6 2 1 8 2 9 6 9 6 1 1 9 1 1 3 9 1 4 0 7 3 3 3 9 4 0 7 ***11.20 (Game: Connect Four) Connect Four is a two-player board game in which the players alternately drop colored disks into a seven-column, six-row vertically suspended grid, as shown at cs.armstrong.edu/liang/ConnectFour/ConnectFour.html. The objective of the game is to connect four same-colored disks in a row, col- umn, or diagonal before your opponent does. The program prompts two players to drop a red or yellow disk alternately. Whenever a disk is dropped, the pro- gram redisplays the board on the console and determines the status of the game (win, draw, or continue). Here is a sample run: Programming Exercises 389 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ——————————————— Drop a red disk at column (0–6): | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |R| | | | | | | ——————————————— Drop a yellow disk at column (0–6): | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |R| | |Y| | | | ... ... ... Drop a yellow disk at column (0–6): | | | | | | | | | | | | | | | | | | | |R| | | | | | | |Y|R|Y| | | | |R|Y|Y|Y|Y| |R|Y|R|Y|R|R|R| ——————————————— The yellow player won 6 3 0 ***11.21 (Game: multiple Sudoku solutions) The complete solution for the Sudoku problem is given in Supplement III.A. A Sudoku problem may have multiple solutions. Modify Sudoku.py in Supplement III.A to display the total number of the solutions. Display two solutions if multiple solutions exist. **11.22 (Even number of 1s) Write a program that generates a two-dimensional matrix filled with 0s and 1s, displays the matrix, and checks to see if every row and every column has an even number of 1s. *11.23 (Game: find the flipped cell) Suppose you are given a matrix filled with 0s and 1s. All rows and all columns have the even number of 1s. Let the user flip one cell (i.e., flip from 1 to 0 or from 0 to 1) and write a program to find which cell was flipped. Your program should prompt the user to enter a two-dimensional list with 0s and 1s and find the first row r and first column c where the even number of 1s property is violated. The flipped cell is at (r, c). 6 * 6 6 * 6 6 * 6 390 Chapter 11 Multidimensional Lists *11.24 (Check Sudoku solution) Listing 11.7 checks whether a solution is valid by check- ing whether every number is valid in the grid. Rewrite the program by checking whether every row, column, and box has the numbers 1 to 9. *11.25 (Markov matrix) An matrix is called a positive Markov matrix if each ele- ment is positive and the sum of the elements in each column is 1. Write the fol- lowing function to check whether a matrix is a Markov matrix: def isMarkovMatrix(m): Write a test program that prompts the user to enter a matrix of numbers and tests whether it is a Markov matrix. Here are sample runs: 3 * 3 n * n Enter a 3-by-3 matrix row by row: It is a Markov matrix 0.30 0.12 0.4 0.55 0.005 0.225 0.15 0.875 0.375 Enter a 3-by-3 matrix row by row: It is not a Markov matrix 0.30 0.22 -0.4 0.65 0.005 0.225 0.95 -0.875 0.375 *11.26 (Row sorting) Implement the following function to sort the rows in a two- dimensional list. A new list is returned and the original list is intact. def sortRows(m): Write a test program that prompts the user to enter a matrix of numbers and displays a new row-sorted matrix. Here is a sample run: 3 * 3 Enter a 3-by-3 matrix row by row: The row-sorted list is 0.15 0.375 0.875 0.005 0.225 0.55 0.12 0.30 0.4 0.30 0.12 0.4 0.55 0.005 0.225 0.15 0.875 0.375 *11.27 (Column sorting) Implement the following function to sort the columns in a two- dimensional list. A new list is returned and the original list is intact. def sortColumns(m): Programming Exercises 391 Write a test program that prompts the user to enter a matrix of numbers and displays a new column-sorted matrix. Here is a sample run: 3 * 3 Enter a 3-by-3 matrix row by row: The column-sorted list is 0.15 0.005 0.225 0.3 0.12 0.375 0.55 0.875 0.4 0.30 0.12 0.4 0.55 0.005 0.225 0.15 0.875 0.375 11.28 (Strictly identical lists) The two-dimensional lists m1 and m2 are strictly identical if their corresponding elements are equal. Write a function that returns True if m1 and m2 are strictly identical, using the following header: def equals(m1, m2): Write a test program that prompts the user to enter two lists of integers and displays whether the two are strictly identical. Here are the sample runs: 3 * 3 Enter m1: Enter m2: The two lists are strictly identical 51 22 25 6 1 4 24 54 6 51 22 25 6 1 4 24 54 6 Enter m1: Enter m2: The two lists are not strictly identical 51 22 25 6 1 4 24 54 6 51 25 22 6 1 4 24 54 6 11.29 (Identical lists) The two-dimensional lists m1 and m2 are identical if they have the same contents. Write a function that returns True if m1 and m2 are identical, using the following header: def equals(m1, m2): Write a test program that prompts the user to enter two lists of integers and dis- plays whether the two are identical. Here are the sample runs: Enter m1: Enter m2: The two lists are identical 51 22 25 6 1 4 24 54 6 51 25 22 6 1 4 24 54 6 Enter m1: Enter m2: The two lists are not identical 51 22 25 6 1 4 24 54 6 51 5 22 6 1 4 24 54 6 392 Chapter 11 Multidimensional Lists *11.30 (Algebra: solve linear equations) Write a function that solves the following system of linear equations: The function header is: def linearEquation(a, b): The function returns None if is 0; otherwise, it returns the solution for x and y in a list. Write a test program that prompts the user to enter and and displays the result. If is 0, report that The equation has no solution. Here are the sample runs: a00a11 - a01a10b1a00, a01, a10, a11, b0, a00a11 - a01a10 a00x + a01y = b0 a10x + a11y = b1 x = b0a11 - b1a01 a00a11 - a01a10 y = b1a00 - b0a10 a00a11 - a01a10 2 * 2 Enter a00, a01, a10, a11, b0, b1: x is -2.0 and y is 3.0 9, 4, 3, -5, -6, -21 Enter a00, a01, a10, a11, b0, b1: The equation has no solution 1, 2, 2, 4, 40, 5 *11.31 (Geometry: intersecting point) Write a function that returns the intersecting point of two lines. The intersecting point of the two lines can be found by using the formula shown in Exercise 4.25. Assume that (x1, y1) and (x2, y2) are the two points on line 1 and (x3, y3) and (x4, y4) are the two points on line 2. The function header is: def getIntersectingPoint(points): The points are stored in the two-dimensional list points, with (points[0][0], points[0][1]) for (x1, y1). The function returns the inter- secting point (x, y) in a list, and None if the two lines are parallel. Write a program that prompts the user to enter four points and displays the intersecting point. See Exercise 4.25 for a sample run. *11.32 (Geometry: area of a triangle) Write a function that returns the area of a triangle using the following header: def getTriangleArea(points): The points are stored in the two-dimensional list points, with (points[0][0], points[0][1]) for (x1, y1). The triangle area can be com- puted using the formula in Exercise 2.14. The function returns None if the three points are on the same line. Write a program that prompts the user to enter three points and displays the area of the triangle. Here is a sample run: 3 * 2 4 * 2 Enter x1, y1, x2, y2, x3, y3: The area of the triangle is 2.25 2.5 2 5 -1.0 4.0 2.0 Enter x1, y1, x2, y2, x3, y3: The three points are on the same line 2 2 4.5 4.5 6 6 Programming Exercises 393 *11.33 (Geometry: polygon subareas) A convex four-vertex polygon is divided into four triangles, as shown in Figure 11.10. Write a program that prompts the user to enter the coordinates of four vertices and displays the areas of the four triangles in increasing order. Here is a sample run: Enter x1, y1, x2, y2, x3, y3, x4, y4: The areas are 6.17 7.96 8.08 10.42 -2.5 2 4 4 3 -2 -2 -3.5 v2 (x2, y2) v3 (x3, y3) v4 (x4, y4) v1 (x1, y1) FIGURE 11.10 A four-vertex polygon is defined by four vertices. *11.34 (Geometry: rightmost lowest point) In computational geometry, often you need to find the rightmost lowest point in a set of points. Write the following function that returns the rightmost lowest point in a set of points: # Return a list of two values for a point def getRightmostLowestPoint(points): Write a test program that prompts the user to enter the coordinates of six points and displays the rightmost lowest point. Here is a sample run: Enter 6 points: The rightmost lowest point is (6.5, -7) 1.5 2.5 -3 4.5 5.6 -7 6.5 -7 8 1 10 2.5 *11.35 (Central city) Given a set of cities, the central point is the city that has the shortest total distance to all other cities. Write a program that prompts the user to enter the number of the cities and the locations of the cities (that is, their coordinates), and finds the central city. Enter the number of cities: Enter the coordinates of the cities: The central city is at (2.5, 5) 2.5 5 5.1 3 1 9 5.4 54 5.5 2.1 5 **11.36 (Simulation using Turtle: self-avoiding random walk) A self-avoiding walk in a lattice is a path from one point to another that does not visit the same point twice. Self-avoiding walks have applications in physics, chemistry, and mathematics. They can be used to model chainlike entities such as solvents and polymers. Write a Turtle program that displays a random path that starts from the center and ends at a point on the boundary, as shown in Figure 11.11a, or ends at a dead-end point (i.e., surrounded by four points that have already been visited), as shown in Figure 11.11b. Assume the size of the lattice is 16 * 16. 394 Chapter 11 Multidimensional Lists **11.37 (Simulation: self-avoiding random walk) Write a simulation program to show that the chance of getting dead-end paths increases as the grid size increases. Your pro- gram simulates lattices with sizes from 10 to 80. For each lattice size, simulate a self-avoiding random walk 10,000 times and display the probability of the dead- end paths, as shown in the following sample output: (a) (b) FIGURE 11.11 (a) A path ends at a boundary point. (b) A path ends at dead-end point. For a lattice of size 10, the probability of dead-end paths is 11.6% For a lattice of size 11, the probability of dead-end paths is 14.0% ... For a lattice of size 80, the probability of dead-end paths is 99.5% **11.38 (Turtle: draw a polygon/polyline) Write the following functions that draw a polygon/polyline to connect all points in the list. Each element in the list is a list of two coordinates. # Draw a polyline to connect all the points in the list def drawPolyline(points): # Draw a polygon to connect all the points in the list and # close the polygon by connecting the first point with the last point def drawPolygon(points): # Fill a polygon by connecting all the points in the list def fillPolygon(points): FIGURE 11.12 Clicking the Solve button highlights the four consecutive numbers in a diagonal, a row, or a column. **11.39 (Tkinter: four consecutive equal numbers) Write a GUI program for Exercise 11.19, as shown in Figure 11.12. Let the user enter the numbers in the text fields in a grid of six rows and seven columns. The user can click the Solve button to high- light a sequence of four equal numbers, if it exists. Chessboard VideoNote Programming Exercises 395 **11.40 (Guess the capitals) Write a program that repeatedly prompts the user to enter a capital for a state. Upon receiving the user input, the program reports whether the answer is correct. Assume that 50 states and their capitals are stored in a two- dimensional list, as shown in Figure 11.13. The program prompts the user to answer all the states’ capitals and displays the total correct count. The user’s answer is not case sensitive. Implement the program using a list to represent the data in the following table. Alabama Montgomery Alaska Juneau Arizona Phoenix ... ... ... ... What is the capital of Alabama? The correct answer should be Montgomery What is the capital of Alaska? Your answer is correct What is the capital of Arizona? ... ... The correct count is 35 Juneau Montogomery FIGURE 11.13 A two-dimensional list stores states and their capitals. Here is a sample run: ***11.41 (Tkinter: Sudoku solutions) The complete solution for the Sudoku problem is given in Supplement III.A. Write a GUI program that enables the user to enter a Sudoku puzzle and click the Solve button to display a solution, as shown in Figure 11.14. (a) (b) FIGURE 11.14 The user can enter a Sudoku puzzle in (a) and click the Solve button to display the solution in (b). 396 Chapter 11 Multidimensional Lists *11.42 (Tkinter: plot the sine function) Exercise 5.52 draws a sine function using Turtle. Rewrite the program to draw a sine function using Tkinter, as shown in Figure 11.15a. Hint The Unicode for p is \u03c0. To display –2p use turtle.write("-2\u03c0"). For a trigonometric function like sin(x), x is in radians. Use the following loop to add the points to a polygon p: p = [] for x in range(-175, 176): p.append([x, -50 * math.sin((x / 100.0) * 2 * math.pi)]) –2p is displayed at (-100, -15), the center of the axis is at (0, 0), and 2p is displayed at (100, -15). *11.43 (Tkinter: plot the sine and cosine functions) Exercise 5.53 draws sine and cosine functions using Turtle. Rewrite the program to draw the sine and cosine functions using Tkinter, as shown in Figure 11.15b. 11.44 (Tkinter: draw a polygon) Write a program that prompts the user to enter the coordinates of six points and fills the polygon that connects the points, as shown in Figure 11.16a. Note that you can draw a polygon using canvas.create_polygon(points), where points is a two-dimensional list that stores the x- and y-coordinates of the points. *11.45 (Tkinter: plot the square function) Exercise 5.54 draws a square function. Rewrite the program to draw the square function using Tkinter, as shown in Figure 11.16b. (a) (b) FIGURE 11.15 (a) The program plots a sine function. (b) The program plots a sine function in blue and a cosine function in red. (a) (b) FIGURE 11.16 (a) A polygon is drawn from a list of values. (b) The program plots a diagram for function f(x) = x2. Programming Exercises 397 *11.46 (Tkinter: display a STOP sign) Write a program that displays a STOP sign, as shown in Figure 11.17a. The hexagon is in red and the text is in black. *11.47 (Tkinter: largest block) Write a program that displays a square matrix, as shown in Figure 11.17b. Each element in the matrix is a 0 or 1, randomly generated with a click of the Refresh button. Display each number centered in a text box. Allow the user to change the entry value. Click the Find Largest Block button to find a largest square submatrix that consists of 1s. Highlight the numbers in the block, as shown in Figure 11.17c. **11.48 (Geometry: find the bounding rectangle) Write a program that enables the user to add and remove points in a two-dimensional plane dynamically, as shown in Figure 11.18. A minimum bounding rectangle is updated as the points are added and removed. Assume the radius of each point is 10 pixels. 10 * 10 (a) (b) (c) FIGURE 11.17 (a) The program displays a STOP sign. (b–c) The program displays 0s and 1s randomly with a click of the Refresh button. FIGURE 11.18 The program enables the user to add and remove points dynamically and display the bounding rectangle. FIGURE 11.19 The program displays a new tic-tac-toe board upon clicking the Refresh button. 11.49 (Game: display a tic-tac-toe board) Revise Exercise 9.6 to display a new tic-tac-toe board with a click of the Refresh button, as shown in Figure 11.19. 398 Chapter 11 Multidimensional Lists 11.50 (Geometry: find nearest points) When a new point is added to the plane, Listing 11.5 finds the pair of two nearest points by examining the distance between every pair of two points. This approach is correct, but not efficient. A more efficient algo- rithm can be described as follows: Let d be the current shortest distance between two nearest points p1 and p2 Let p be the new point added to the plane For each existing point t: if distance(p, t) < d: d = distance(p, t) p1, p2 = p, t Rewrite Listing 11.5 using this new approach. **11.51 (Sort students) Write a program that prompts the user to enter the students’ names and their scores on one line, and prints student names in increasing order of their scores. (Hint: Create a list. Each element in the list is a sublist with two elements: score and name. Apply the sort method to sort the list. This will sort the list on scores.) Enter students’ names and scores: John 34 Jim 45 Tim 45 Peter 59 Tim 45 John 34 Jim 45 Peter 59 Enter number n: Enter 4 rows of letters separated by spaces: The input list is a Latin square D C A B C D B A B A D C A B C D 4 Enter number n: Enter 3 rows of letters separated by spaces: Wrong input. The letters must be from A to C. A F D 3 **11.52 (Latin square) A Latin square is an n by n list filled with n different Latin letters, each occurring exactly once in each row and once in each column. Write a pro- gram that prompts the user to enter the number n and the list of characters, as shown in the sample output and check if the input list is a Latin square. The char- acters are the first n characters starting from A. INHERITANCE AND POLYMORPHISM CHAPTER 12 Objectives ■ To define a subclass from a superclass through inheritance (§12.2). ■ To override methods in a subclass (§12.3). ■ To explore the object class and its methods (§12.4). ■ To understand polymorphism and dynamic binding (§12.5). ■ To determine whether an object is an instance of a class by using the isinstance function (§12.6). ■ To design a GUI class for displaying a reusable clock (§12.7). ■ To discover relationships among classes (§12.8). ■ To design classes by using composition and inheritance relationships (§§12.9–12.11). 400 Chapter 12 Inheritance and Polymorphism 12.1 Introduction Object-oriented programming (OOP) allows you to define new classes from existing classes. This is called inheritance. As discussed earlier in the book, the procedural paradigm focuses on designing functions and the object-oriented paradigm couples data and methods together into objects. Software design using the object-oriented paradigm focuses on objects and operations on objects. The object- oriented approach combines the power of the procedural paradigm with an added dimension that integrates data with operations into objects. Inheritance extends the power of the object-oriented paradigm by adding an important and powerful feature for reusing software. Suppose that you want to define classes to model cir- cles, rectangles, and triangles. These classes have many common features. What is the best way to design these classes to avoid redundancy and make the system easy to comprehend and maintain? The answer is to use inheritance. 12.2 Superclasses and Subclasses Inheritance enables you to define a general class (a superclass) and later extend it to more specialized classes (subclasses). You use a class to model objects of the same type. Different classes may have some common properties and behaviors that you can generalize in a class, which can then be shared by other classes. Inheritance enables you to define a general class and later extend it to define more spe- cialized classes. The specialized classes inherit the properties and methods from the general class. Consider geometric objects. Suppose you want to design classes to model geometric objects such as circles and rectangles. Geometric objects have many common properties and behaviors; for example, they can be drawn in a certain color, and they can be either filled or unfilled. Thus, a general class GeometricObject can be used to model all geometric objects. This class contains the properties color and filled and their appropriate get and set methods. Assume that this class also contains the dateCreated property and the getDateCreated() and _ _str_ _() methods. The _ _str_ _() method returns a string description for the object. Because a circle is a special type of geometric object, it shares common properties and methods with other geometric objects. For this reason, it makes sense to define a Circle class that extends the GeometricObject class. Similarly, you can define Rectangle as a subclass of GeometricObject. Figure 12.1 shows the relationship among these classes. A triangular arrow pointing to the superclass is used to denote the inheritance relationship between the two classes involved. Note In OOP terminology, a class C1 extended from another class C2 is called a derived class, child class, or subclass, and C2 is called a base class, parent class, or superclass. For consistency, this book uses the terms “subclass” and “superclass.” A subclass inherits accessible data fields and methods from its superclass, but it can also have other data fields and methods. In our example: ■ The Circle class inherits all accessible data fields and methods from the GeometricObject class. In addition, it has a new data field, radius, and its asso- ciated get and set methods. It also contains the getArea(), getPerimeter(), and getDiameter() methods for returning the area, perimeter, and diameter of a circle. The printCircle() method is defined to print the information about the circle. inheritance why inheritance? Inheritance and polymorphism triangular arrow VideoNote subclass superclass Key Point Key Point 12.2 Superclasses and Subclasses 401 ■ The Rectangle class inherits all accessible data fields and methods from the GeometricObject class. In addition, it has the data fields width and height and the associated get and set methods. It also contains the getArea() and getPerimeter() methods for returning the area and perimeter of the rectangle. The GeometricObject, Circle, and Rectangle classes are shown in Listings 12.1, 12.2, and 12.3. LISTING 12.1 GeometricObject.py 1 2 3 self.__color = color 4 self.__filled = filled 5 6 def getColor(self): 7 return self.__color 8 9 def setColor(self, color): 10 self.__color = color 11 12 def isFilled(self): 13 return self.__filled def __init__(self, color = "green", filled = True): class GeometricObject: FIGURE 12.1 The GeometricObject class is the superclass for Circle and Rectangle. The color of the object (default : green). Indicates whether the object is filled with a color (default: True). Returns the color. Sets a new color. Returns the filled property. Sets a new filled property. Returns a string representation of this object. GeometricObject -color: str -filled: bool Creates a GeometricObject with the specified color and filled values. GeometricObject(color: str, filled: bool) getColor(): str setColor(color: str): None isFilled(): bool setFilled(filled: bool): None _ _str_ _(): str Circle -radius: float Circle(radius: float, color: str, filled: bool) getRadius(): float getArea(): float setRadius(radius: float): None printCircle(): None getPerimeter(): float getDiameter(): float Rectangle -height: float Rectangle(width: float, height: float, color: string, filled: bool) getWidth(): float getHeight(): float setHeight(height: float): None setWidth(width: float): None getArea(): float getPerimeter(): float -width: float GeometricObject class initializer data fields getColor setColor isFilled 402 Chapter 12 Inheritance and Polymorphism 14 15 def setFilled(self, filled): 16 self.__filled = filled 17 18 def __str__(self): 19 return "color: " + self.__color + \ 20 " and filled: " + str(self.__filled) LISTING 12.2 CircleFromGeometricObject.py 1 from GeometricObject import GeometricObject 2 import math # math.pi is used in the class 3 4 5 def __init__(self, radius): 6 7 self.__radius = radius 8 9 def getRadius(self): 10 return self.__radius 11 12 def setRadius(self, radius): 13 self.__radius = radius 14 15 def getArea(self): 16 return self.__radius * self.__radius * math.pi 17 18 def getDiameter(self): 19 return 2 * self.__radius 20 21 def getPerimeter(self): 22 return 2 * self.__radius * math.pi 23 24 def printCircle(self): 25 print(self.__str__() + " radius: " + str(self.__radius)) The Circle class is derived from the GeometricObject class (Listing 12.1), based on the following syntax: super().__init__() class Circle(GeometricObject): setFilled __str__ import GeometricObject extend GeometricObject initializer superclass initializer subclass superclass class Circle(GeometricObject): This tells Python that the Circle class inherits the GeometricObject class, thus inher- iting the methods getColor, setColor, isFilled, setFilled, and __str__. The printCircle method invokes the __str__() method defined to obtain properties defined in the superclass (line 25). super().__init__() calls the superclass’s __init__ method (line 6). This is neces- sary to create data fields defined in the superclass. Note Alternatively, you can invoke the superclass’s __init__ method by using: GeometricObject.__init__(self) 12.2 Superclasses and Subclasses 403 This is an old style of syntax that is still supported in Python, but it isn’t the preferred style. super() refers to the superclass. Using super() lets you avoid referring the superclass explicitly. When invoking a method using super(), don’t pass self in the argument. For example, you should use super().__init__() rather than super().__init__(self) The Rectangle class, derived from the GeometricObject class (Listing 12.1), is defined similarly in Listing 12.3. extend superclass subclass superclass class Rectangle(GeometricObject): LISTING 12.3 RectangleFromGeometricObject.py 1 from GeometricObject import GeometricObject 2 3 class Rectangle(GeometricObject): 4 def __init__(self, width = 1, height = 1): 5 6 self.__width = width 7 self.__height = height 8 9 def getWidth(self): 10 return self.__width 11 12 def setWidth(self, width): 13 self.__width = width 14 15 def getHeight(self): 16 return self.__height 17 18 def setHeight(self, height): 19 self.__height = self.__height 20 21 def getArea(self): 22 return self.__width * self.__height 23 24 def getPerimeter(self): 25 return 2 * (self.__width + self.__height) The code in Listing 12.4 creates Circle and Rectangle objects and invokes the getArea() and getPerimeter() methods on these objects. The __str__() method is inherited from the GeometricObject class and is invoked from a Circle object (line 5) and a Rectangle object (line 11). LISTING 12.4 TestCircleRectangle.py 1 from CircleFromGeometricObject import Circle 2 from RectangleFromGeometricObject import Rectangle 3 super().__init__() initializer superclass initializer methods 404 Chapter 12 Inheritance and Polymorphism 4 def main(): 5 6 print("A circle", ) 7 print("The radius is", ) 8 print("The area is", ) 9 print("The diameter is", ) 10 11 12 print("\nA rectangle", ) 13 print("The area is", ) 14 print("The perimeter is", ) 15 16 main() # Call the main function rectangle.getPerimeter() rectangle.getArea() rectangle rectangle = Rectangle(2, 4) circle.getDiameter() circle.getArea() circle.getRadius() circle circle = Circle(1.5)Circle object invoke __str__ Rectangle object invoke __str__ A circle color: green and filled: True The radius is 1.5 The area is 7.06858347058 The diameter is 3.0 A rectangle color: green and filled: True The area is 8 The perimeter is 12 Line 6 invokes the print function to print a circle. Recall from Section 8.5, this is the same as print("A circle", ) The __str__() method is not defined in the Circle class, but is defined in the GeometricObject class. Since Circle is a subclass of GeometricObject, __str__() can be invoked from a Circle object. The __str__()method displays the color and filled properties of a GeometricObject (lines 18–20 in Listing 12.1). The default color for a GeometricObject object is green and filled is True (line 2 Listing 12.1). Since a Circle inherits from GeometricObject, the default color for a Circle object is green and the default value for filled is True. The following points regarding inheritance are worthwhile to note: ■ Contrary to the conventional interpretation, a subclass is not a subset of its superclass. In fact, a subclass usually contains more information and methods than its superclass. ■ Inheritance models the is-a relationships, but not all is-a relationships should be modeled using inheritance. For example, a square is a rectangle, but you should not extend a Square class from a Rectangle class, because the width and height properties are not appropriate for a square. Instead, you should define a Square class to extend the GeometricObject class and define the side property for the side of a square. ■ Do not blindly extend a class just for the sake of reusing methods. For example, it makes no sense for a Tree class to extend a Person class, even though they share common properties such as height and weight. A subclass and its superclass must have the is-a relationship. ■ Python allows you to derive a subclass from several classes. This capability is known as multiple inheritance. To define a class derived from multiple classes, use the following syntax: class Subclass(SuperClass1, SuperClass2, ...): initializer methods circle.__str__() more in subclass nonextensible is-a is-a relationships no blind extension multiple inheritance 12.3 Overriding Methods 405 12.1 How do you define a class that extends a superclass? What is super()? How do you invoke the superclass’s initializer? 12.2 What problem arises in running the following program? How do you fix it? class A: def __init__(self, i = 0): self.i = i class B(A): def __init__(self, j = 0): self.j = j def main(): b = B() print(b.i) print(b.j) main() # Call the main function 12.3 True or false? A subclass is a subset of a superclass. 12.4 Does Python support multiple inheritance? How do you define a class that extends multiple classes? 12.3 Overriding Methods To override a method, the method must be defined in the subclass using the same header as in its superclass. A subclass inherits methods from a superclass. Sometimes it is necessary for the subclass to modify the implementation of a method defined in the superclass. This is referred to as method overriding. The __str__ method in the GeometricObject class returns the string describing a geo- metric object. This method can be overridden to return the string describing a circle. To over- ride it, add the following new method in Listing 12.2, CircleFromGeometricObject.py: 1 class Circle(GeometricObject): 2 # Other methods are omitted 3 4 # Override the __str__ method defined in GeometricObject 5 def __str__(self): 6 return + " radius: " + str(radius) The __str__() method is defined in the GeometricObject class and modified in the Circle class. Both methods can be used in the Circle class. To invoke the __str__ method defined in the GeometricObject class from the Circle class, use super().__str__() (line 6). Similarly, you can override the __str__ method in the Rectangle class as follows: def __str__(self): return + " width: " + \ str(self.__width) + " height: " + str(self.__height) For the rest of the book, we assume that the __str__() method in GeometricObject class has been overridden in the Circle and Rectangle classes. super().__str__() super().__str__() override __str__ in superclass ✓Point✓Check Key Point 406 Chapter 12 Inheritance and Polymorphism The Circle class is derived from GeometricObject and the Rectangle class is derived from GeometricObject. The GeometricObject class is actually derived from object. It is important to be familiar with the methods provided by the object class so that you can use them in your classes. All methods defined in the object class are special methods with two leading underscores and two trailing underscores. We discuss four methods—__new__(), __init__(), __str__(), and __eq__(other)—in this section. class ClassName: ... class ClassName(object): ...Equivalent Note Recall that you can define a private method in Python by adding two underscores in front of a method name (see Chapter 7). A private method cannot be overridden. If a method defined in a subclass is private in its superclass, the two methods are completely unrelated, even though they have the same name. 12.5 True or false? (a) You can override a nonprivate method defined in a superclass. (b) You can override a private method defined in a superclass. (c) You can override the initializer defined in a superclass. (d) When constructing an object from a subclass, its superclass’s initializer is auto- matically invoked. 12.6 Show the printout of the following program: class A: def __init__(self, i = 0): self.i = i def m1(self): self.i += 1 class B(A): def __init__(self, j = 0): super().__init__(3) self.j = j def m1(self): self.i += 1 def main(): b = B() b.m1() print(b.i) print(b.j) main() # Call the main function 12.4 The object Class Every class in Python is descended from the object class. The object class is defined in the Python library. If no inheritance is specified when a class is defined, its superclass is object by default. For example, the following two class definitions are the same: Key Point ✓Point✓Check 12.4 The object Class 407 The __new__() method is automatically invoked when an object is constructed. This method then invokes the __init__() method to initialize the object. Normally you should only override the __init__() method to initialize the data fields defined in the new class. The __str__() method returns a string description for the object. By default, it returns a string consisting of a class name of which the object is an instance and the object’s memory address in hexadecimal format. For example, consider the following code for the Loan class, which was defined in Listing 7.8: loan = Loan(1, 1, 1, "Smith") print(loan) # Same as print(loan.__str__()) The code displays something like . This mes-
sage is not very helpful or informative. Usually you should override the __str__() method
so that it returns an informative description for the object. For example, the __str__()
method in the object class was overridden in the GeometricObject class in lines 18–20 in
Listing 12.1 as follows:
def __str__(self):
return “color: ” + self.__color + \
” and filled: ” + str(self.__filled)
The __eq__(other) method returns True if two objects are the same. So,
x.__eq__(x) is True, but x.__eq__(y) returns False, because x and y are two different
objects even though they may have the same contents. Recall that x.__eq__(y) is same as
x == y (see Section 8.5).
You can override this method to return True if two objects have the same contents. The
__eq__ method is overridden in many Python built-in classes such as int, float, bool,
string, and list to return True if two objects have the same contents.
12.7 True or false?
(a) Every object is an instance of the object class.
(b) If a class does not extend a superclass explicitly, it extends object by default.
12.8 Show the printout of the following code:
class A:
def __init__(self, i = 0):
self.i = i
def m1(self):
self.i += 1
def __str__(self):
return str(self.i)
x = A(8)
print(x)
12.9 Show the printout of the following program:
class A:
def __new__(self):
print(“A’s __new__() invoked”)
def __init__(self):
print(“A’s __init__() invoked”)
__new__()
__init__()
__str__()
__eq__(other)
✓Point✓Check

408 Chapter 12 Inheritance and Polymorphism
class B(A):
def __new__(self):
print(“B’s __new__() invoked”)
def __init__(self):
print(“B’s __init__() invoked”)
def main():
b = B()
a = A()
main() # Call the main function
12.10 Show the printout of the following program:
class A:
def __new__(self):
self.__init__(self)
print(“A’s __new__() invoked”)
def __init__(self):
print(“A’s __init__() invoked”)
class B(A):
def __new__(self):
self.__init__(self)
print(“B’s __new__() invoked”)
def __init__(self):
print(“B’s __init__() invoked”)
def main():
b = B()
a = A()
main() # Call the main function
12.11 Show the printout of the following program:
class A:
def __init__(self):
print(“A’s __init__() invoked”)
class B(A):
def __init__(self):
print(“B’s __init__() invoked”)
def main():
b = B()
a = A()
main() # Call the main function
12.12 Show the printout of the following program:
class A:
def __init__(self, i):
self.i = i

12.5 Polymorphism and Dynamic Binding 409
def __str__(self):
return “A”
class B(A):
def __init__(self, i, j):
super().__init__(i)
self.j = j
def main():
b = B(1, 2)
a = A(1)
print(a)
print(b)
main() # Call the main function
12.13 Show the printout of the following program:
class A:
def __init__(self, i):
self.i = i
def __str__(self):
return “A”
def __eq__(self, other):
return self.i == other.i
def main():
x = A(1)
y = A(1)
print(x == y)
main() # Call the main function
12.5 Polymorphism and Dynamic Binding
Polymorphism means that an object of a subclass can be passed to a parameter of a
superclass type. A method may be implemented in several classes along the
inheritance chain. Python decides which method is invoked at runtime. This is known
as dynamic binding.
The three pillars of object-oriented programming are encapsulation, inheritance, and
polymorphism. You have already learned the first two. This section introduces polymorphism.
The inheritance relationship enables a subclass to inherit features from its superclass with
additional new features. A subclass is a specialization of its superclass; every instance of a
subclass is also an instance of its superclass, but not vice versa. For example, every circle is a
geometric object, but not every geometric object is a circle. Therefore, you can always pass an
instance of a subclass to a parameter of its superclass type. Consider the code in Listing 12.5.
LISTING 12.5 PolymorphismDemo.py
1 from CircleFromGeometricObject import Circle
2 from RectangleFromGeometricObject import Rectangle
3
4 def main():
5 # Display circle and rectangle properties
polymorphism
Dynamic binding
VideoNote
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410 Chapter 12 Inheritance and Polymorphism
6 c =
7 r =
8
9
10 print(“Are the circle and rectangle the same size?”,
11 isSameArea(c, r))
12
13 # Display geometric object properties
14 def :
15 print(g.__str__())
16
17 # Compare the areas of two geometric objects
18 def :
19 return g1.getArea() == g2.getArea()
20
21 main() # Call the main function
isSameArea(g1, g2)
displayObject(g)
displayObject(r)
displayObject(c)
Rectangle(1, 3)
Circle(4)
polymorphic call
polymorphic call
polymorphic call
color: green and filled: True radius: 4
color: green and filled: True width: 1 height: 3
Are the circle and rectangle the same size? False
The displayObject method (line 14) takes a parameter of the GeometricObject type.
You can invoke displayObject by passing any instance of GeometricObject (for exam-
ple, Circle(4) and Rectangle(1, 3) in lines 8–9). An object of a subclass can be used
wherever its superclass object is used. This is commonly known as polymorphism (from a
Greek word meaning “many forms”).
As seen in this example, c is an object of the Circle class. Circle is a subclass of
GeometricObject. The __str__() method is defined in both classes. So, which
__str__() method is invoked by g in the displayObject method (line 15)? The
__str__() method invoked by g is determined using dynamic binding.
Dynamic binding works as follows: Suppose an object o is an instance of classes C1, C2, …,
Cn-1, and Cn, where C1 is a subclass of C2, C2 is a subclass of C3, …, and Cn-1 is a subclass of
Cn, as shown in Figure 12.2. That is, Cn is the most general class, and C1 is the most specific
class. In Python, Cn is the object class. If o invokes a method p, Python searches the imple-
mentation for the method p in C1, C2, …, Cn-1, and Cn, in this order, until it is found. Once an
implementation is found, the search stops and the first-found implementation is invoked.
Listing 12.6 provides an example that demonstrates dynamic binding.
what is polymorphism?
dynamic binding
override __str__()
. . . . .
object
If o is an instance of C1, o is also an
instance of C2, C3, …, Cn-1, and Cn.
Cn Cn-1 C2 C1
FIGURE 12.2 The method to be invoked is dynamically bound at runtime.
LISTING 12.6 DynamicBindingDemo.py
1 class Student:
2 def __str__(self):
3 return “Student”

12.6 The isinstance Function 411
4
5 def printStudent(self):
6 print(self.__str__())
7
8 class GraduateStudent(Student):
9 def __str__(self):
10 return “Graduate Student”
11
12 a = Student()
13 b = GraduateStudent()
14 a.printStudent()
15 b.printStudent()
override __str__()
Student
Graduate Student
Since a is an instance of Student, the printStudent method in the Student class is
invoked for a.printStudent() (line 14), which invokes the Student class’s __str__()
method to return Student.
No printStudent method is defined in GraduateStudent. However, since it is defined
in the Student class and GraduateStudent is a subclass of Student, the printStudent
method in the Student class is invoked for b.printStudent() (line 15). The
printStudent method invokes GraduateStudent’s __str__() method to display
Graduate Student, since the object b that invokes printStudent is GraduateStudent
(lines 6 and 10).
12.6 The isinstance Function
The isinstance function can be used to determine whether an object is an instance
of a class.
Suppose you want to modify the displayObject function in Listing 12.5 to perform the fol-
lowing tasks:
■ Display the area and perimeter of a GeometricObject instance.
■ Display the diameter if the instance is a Circle, and the width and height if the
instance is a Rectangle.
How can this be done? You might be tempted to write the function as:
def displayObject(g):
print(“Area is”, g.getArea())
print(“Perimeter is”, g.getPerimeter())
print(“Diameter is”, g.getDiameter())
print(“Width is”, g.getWidth())
print(“Height is”, g.getHeight())
This won’t work, however, because not all GeometricObject instances have the
getDiameter(), getWidth(), or getHeight() methods. For example, invoking
display(Circle(5)) will cause a runtime error because Circle does not have the
getWidth() and getHeight() methods, and invoking display(Rectangle(2, 3))
will cause a runtime error because Rectangle does not have the getDiameter() method.
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412 Chapter 12 Inheritance and Polymorphism
You can fix this problem by using Python’s built-in isinstance function. This function
determines whether an object is an instance of a class by using the following syntax:
isinstance(object, ClassName)
For example, isinstance(“abc”, str) returns True because “abc” is an instance of
the str class, but isinstance(12, str) returns False because 12 is not an instance of
the str class.
Using the isinstance function, you can implement the displayObject function as
shown in Listing 12.7.
LISTING 12.7 IsinstanceDemo.py
1 from CircleFromGeometricObject import Circle
2 from RectangleFromGeometricObject import Rectangle
3
4 def main():
5 # Display circle and rectangle properties
6 c = Circle(4)
7 r = Rectangle(1, 3)
8 print(“Circle…”)
9 displayObject(c)
10 print(“Rectangle…”)
11 displayObject(r)
12
13 # Display geometric object properties
14 def displayObject(g):
15 print(“Area is”, g.getArea())
16 print(“Perimeter is”, g.getPerimeter())
17
18 if :
19 print(“Diameter is”, g.getDiameter())
20 elif :
21 print(“Width is”, g.getWidth())
22 print(“Height is”, g.getHeight())
23
24 main() # Call the main function
isinstance(g, Rectangle)
isinstance(g, Circle)
polymorphic call
polymorphic call
isinstance?
isinstance?
Circle…
Area is 50.26548245743669
Perimeter is 25.132741228718345
Diameter is 8
Rectangle…
Area is 3
Perimeter is 8
Width is 1
Height is 3
Invoking displayObject(c) passes c to g (line 9). g is now an instance of Circle (line
18). The program displays the circle’s diameter (line 19).
Invoking displayObject(r) passes r to g (line 11). g is now an instance of Rectangle
(line 20). The program displays the rectangle’s width and height (lines 21–22).

12.6 The isinstance Function 413
class Person:
def getInfo(self):
return “Person”
def printPerson(self):
print(self.getInfo())
class Student(Person):
def getInfo(self):
return “Student”
Person().printPerson()
Student().printPerson()
(a)
12.14 Explain encapsulation, inheritance, and polymorphism.
12.15 Show the output of the following code:
12.16 Suppose that Fruit, Apple, Orange, GoldenDelicious, and McIntosh are
defined in the inheritance hierarchy as follows:
Fruit
Apple
McIntosh
Orange
GoldenDelicious
Assume that the following statements are given:
goldenDelicious = GoldenDelicious()
orange = Orange()
Answer the following questions:
(a) Is goldenDelicious an instance of Fruit?
(b) Is goldenDelicious an instance of Orange?
(c) Is goldenDelicious an instance of Apple?
(d) Is goldenDelicious an instance of GoldenDelicious?
(e) Is goldenDelicious an instance of McIntosh?
(f) Is orange an instance of Orange?
(g) Is orange an instance of Fruit?
class Person:
def __getInfo(self):
return “Person”
def printPerson(self):
print(self.__getInfo())
class Student(Person):
def __getInfo(self):
return “Student”
Person().printPerson()
Student().printPerson()
(b)
✓Point✓Check

414 Chapter 12 Inheritance and Polymorphism
(h) Is orange an instance of Apple?
(i) Suppose the method makeAppleCider is defined in the Apple class. Can
goldenDelicious invoke this method? Can orange invoke this method?
( j) Suppose the method makeOrangeJuice is defined in the Orange class. Can
orange invoke this method? Can goldenDelicious invoke this method?
12.7 Case Study: A Reusable Clock
This section designs a GUI class for displaying a clock.
Suppose you want to display a clock on a canvas and later reuse the clock in other programs.
You need to define a clock class to make the clock reusable. Furthermore, in order to display
the clock graphically, you should define it as a widget. Your best option is to define a clock
class that extends Canvas so that a clock object can be used in the same way as a Canvas
object.
The contract of the class is shown in Figure 12.3.
-hour: int
-minute: int
-second: int
tkinter.Canvas
StillClock
The hour in the clock.
The minute in the clock.
The second in the clock.
Constructs a default clock for the current time,
placed inside a container.
Sets hour, minute, and second to current time.
StillClock(container)
setCurrentTime(): None
The get and set methods for these
data fields are provided in the class, but
omitted from the UML diagram for brevity.
FIGURE 12.3 StillClock displays an analog clock.
Listing 12.8 is a test program that uses the StillClock class to display an analog clock.
The program enables the user to enter a new hour, minute, and second from the Entry fields,
as shown in Figure 12.4a.
LISTING 12.8 DisplayClock.py
1 from tkinter import * # Import all definitions from tkinter
2
3
4 class DisplayClock:
5 def __init__(self):
6 window = Tk() # Create a window
7 window.title(“Change Clock Time”) # Set title
8
9 # Create a clock
10 self.clock.pack()
11
12 frame = Frame(window)
13 frame.pack()
self.clock = StillClock(window)
from StillClock import StillClockimport StillClock
create a clock
Key
Point

12.7 Case Study: A Reusable Clock 415
14 Label(frame, text = “Hour: “).pack(side = LEFT)
15
16
17
18
19 Label(frame, text = “Minute: “).pack(side = LEFT)
20 self.minute = IntVar()
21 self.minute.set(self.clock.getMinute())
22 Entry(frame, textvariable = self.minute,
23 width = 2).pack(side = LEFT)
24 Label(frame, text = “Second: “).pack(side = LEFT)
25 self.second = IntVar()
26 self.second.set(self.clock.getMinute())
27 Entry(frame, textvariable = self.second,
28 width = 2).pack(side = LEFT)
29
30
31
32 window.mainloop() # Create an event loop
33
34
35 self.clock.setHour(self.hour.get())
36 self.clock.setMinute(self.minute.get())
37 self.clock.setSecond(self.second.get())
38
39 DisplayClock() # Create GUI
def setNewTime(self):
command = self.setNewTime).pack(side = LEFT)
Button(frame, text = “Set New Time”,
width = 2).pack(side = LEFT)
Entry(frame, textvariable = self.hour,
self.hour.set(self.clock.getHour())
self.hour = IntVar()
The rest of this section explains how to implement the StillClock class. Since you can
use the class without knowing how it is implemented, you may skip the implementation if you
wish.
How do you obtain the current time? Python provides the datetime class, which can be
used to obtain the current computer time. You can use the now() function to return an
instance of datetime for the current time, and use the data fields year, month, day, hour,
(a) (b)
12
6
3
(xEnd, yEnd)
(0,0)
(xCenter, yCenter)
handLength
9

FIGURE 12.4 (a) The DisplayClock program displays a clock and enables the user to change the time. (b) The
endpoint of a clock hand can be determined, given the spanning angle, the hand length, and the center point.
create entries
create button
callback handler
setNewTime
create GUI
skip implementation?
obtain current time

416 Chapter 12 Inheritance and Polymorphism
minute, and second to extract date and time information from the object, as shown in the
following code:
from datetime import datetime
d = datetime.now()
print(“Current year is”, d.year)
print(“Current month is”, d.month)
print(“Current day of month is”, d.day)
print(“Current hour is”, d.hour)
print(“Current minute is”, d.minute)
print(“Current second is”, d.second)
To draw a clock, you need to draw a circle and three hands for the second, minute, and
hour. To draw a hand, you need to specify the two ends of the line. As shown in Figure 12.4b,
one end is at the center of the clock at (xCenter, yCenter); the other end, at (xEnd,
yEnd), is determined by the following formula:
xEnd = xCenter + handLength × sin(θ)
yEnd = yCenter – handLength × cos(θ)
Since there are 60 seconds in one minute, the angle θ (see Figure 12.4b) for the second
hand is:
θ = second × (2π/60)
The position of the minute hand is determined by the minute and second. The exact minute
value combined with seconds is minute + second/60. For example, if the time is 3 min-
utes and 30 seconds, the total minutes are 3.5. Since there are 60 minutes in one hour, the
angle for the minute hand is:
θ = (minute + second/60) × (2π/60)
Since one circle is divided into 12 hours, the angle for the hour hand is:
θ = (hour + minute/60 + second/(60 × 60)) × (2π/12)
For simplicity in computing the angles of the minute hand and hour hand, you can omit the
seconds, because they are negligibly small. Therefore, the endpoints for the second hand,
minute hand, and hour hand can be computed as:
xSecond = xCenter + secondHandLength × sin(second × (2π/60))
ySecond = yCenter – secondHandLength × cos(second × (2π/60))
xMinute = xCenter + minuteHandLength × sin(minute × (2π/60))
yMinute = yCenter – minuteHandLength × cos(minute × (2π/60))
xHour = xCenter + hourHandLength × sin((hour + minute/60) × (2π/12))
yHour = yCenter – hourHandLength × cos((hour + minute/60) × (2π/12))
The StillClock class is implemented in Listing 12.9.
LISTING 12.9 StillClock.py
1 from tkinter import * # Import all definitions from tkinter
2 import math
3 from datetime import datetime
4
5
6 def __init__(self, container):
7 super().__init__(container)
class StillClock(Canvas):
draw a clock
extend Canvas
initializer

12.7 Case Study: A Reusable Clock 417
8
9
10
11 return self.__hour
12
13
14 self.__hour = hour
15 self.delete(“clock”)
16 self.drawClock()
17
18 def getMinute(self):
19 return self.__minute
20
21 def setMinute(self, minute):
22 self.__minute = minute
23 self.delete(“clock”)
24 self.drawClock()
25
26 def getSecond(self):
27 return self.__second
28
29 def setSecond(self, second):
30 self.__second = second
31 self.delete(“clock”)
32 self.drawClock()
33
34 def setCurrentTime(self):
35 d = datetime.now()
36 self.__hour = d.hour
37 self.__minute = d.minute
38 self.__second = d.second
39 self.delete(“clock”)
40 self.drawClock()
41
42 def drawClock(self):
43 width = float(self[“width”])
44 height = float(self[“height”])
45 radius = min(width, height) / 2.4
46 secondHandLength = radius * 0.8
47 minuteHandLength = radius * 0.65
48 hourHandLength = radius * 0.5
49
50 self.create_oval(width / 2 – radius, height / 2 – radius,
51 width / 2 + radius, height / 2 + radius, tags = “clock”)
52 self.create_text(width / 2 – radius + 5, height / 2,
53 text = “9”, tags = “clock”)
54 self.create_text(width / 2 + radius – 5, height / 2,
55 text = “3”, tags = “clock”)
56 self.create_text(width / 2, height / 2 – radius + 5,
57 text = “12”, tags = “clock”)
58 self.create_text(width / 2, height / 2 + radius – 5,
59 text = “6”, tags = “clock”)
60
61 xCenter = width / 2
62 yCenter = height / 2
63 second = self.__second
64 xSecond = xCenter + secondHandLength \
65 * math.sin(second * (2 * math.pi / 60))
66 ySecond = yCenter – secondHandLength \
67 * math.cos(second * (2 * math.pi / 60))
def setHour(self, hour):
def getHour(self):
self.setCurrentTime()
getHour
setHour
set current time
draw clock

418 Chapter 12 Inheritance and Polymorphism
68 self.create_line(xCenter, yCenter, xSecond, ySecond,
69 fill = “red”, tags = “clock”)
70
71 minute = self.__minute
72 xMinute = xCenter + \
73 minuteHandLength * math.sin(minute * (2 * math.pi / 60))
74 yMinute = yCenter – \
75 minuteHandLength * math.cos(minute * (2 * math.pi / 60))
76 self.create_line(xCenter, yCenter, xMinute, yMinute,
77 fill = “blue”, tags = “clock”)
78
79 hour = self.__hour % 12
80 xHour = xCenter + hourHandLength * \
81 math.sin((hour + minute / 60) * (2 * math.pi / 12))
82 yHour = yCenter – hourHandLength * \
83 math.cos((hour + minute / 60) * (2 * math.pi / 12))
84 self.create_line(xCenter, yCenter, xHour, yHour,
85 fill = “green”, tags = “clock”)
86
87 timestr = str(hour) + “:” + str(minute) + “:” + str(second)
88 self.create_text(width / 2, height / 2 + radius + 10,
89 text = timestr, tags = “clock”)
The StillClock class extends the Canvas widget (line 5), so a StillClock is a
Canvas. You can use StillClock just like a canvas.
The StillClock class’s initializer invokes the Canvas initializer (line 7), then sets the
data fields hour, minute, and second using the current time by invoking the
setCurrentTime method (line 8).
The data fields hour, minute, and second are accompanied by the get and set methods to
retrieve and set these data fields (lines 10–32). When a new value is set for the hour, minute,
or second, the drawClock method is invoked to redraw the clock (lines 16, 24, and 32).
The setCurrentTime method gets the current time by invoking datetime.now() (line
35) to obtain the current hour, minute, and second (lines 36–38), and invokes the drawClock
method to redraw the clock (line 40).
The drawClock method obtains the width and height of the canvas (lines 43–44) and sets
the appropriate size for the hour hand, minute hand, and second hand (lines 45–48). It then
uses Canvas’s drawing methods to draw a circle, lines, and text strings for displaying a clock
(lines 50–89).
12.8 Class Relationships
To design classes, you need to explore the relationships among classes. The common
relationships among classes are association, aggregation , composition, and
inheritance.
You have already used inheritance to model the is-a relationship. We now explore other
relationships.
12.8.1 Association
Association is a general binary relationship that describes an activity between two classes. For
example, a student taking a course is an association between the Student class and the
Course class, and a faculty member teaching a course is an association between the Faculty
class and the Course class. These associations can be represented in UML graphical nota-
tion, as shown in Figure 12.5.
association
Key
Point

12.8 Class Relationships 419
An association is illustrated by a solid line between two classes with an optional label that
describes the relationship. In Figure 12.5, the labels are Take and Teach. Each relationship
may have an optional small black triangle that indicates the direction of the relationship. In
this figure, the direction indicates that a student takes a course (as opposed to a course taking
a student).
Each class involved in the relationship may have a role name that describes the role it plays
in the relationship. In Figure 12.5, teacher is the role name for Faculty.
Each class involved in an association may specify a multiplicity. A multiplicity could be a
number or an interval that specifies how many of the class’s objects are involved in the rela-
tionship. The character * means an unlimited number of objects, and the interval m..n indi-
cates that the number of objects is between m and n, inclusively. In Figure 12.5, each student
may take any number of courses, and each course must have at least five and at most sixty stu-
dents. Each course is taught by only one faculty member, and a faculty member may teach
from zero to three courses per semester.
In Python code, you can implement associations by using data fields and methods. For
example, the relationships in Figure 12.5 may be implemented using the classes in Figure
12.6. The relation “a student takes a course” is implemented using the addCourse method in
the Student class and the addStudent method in the Course class. The relation “a faculty
teaches a course” is implemented using the addCourse method in the Faculty class and the
setFaculty method in the Course class. The Student class may use a list to store the
courses that the student is taking, the Faculty class may use a list to store the courses that
the faculty is teaching, and the Course class may use a list to store students enrolled in the
course and a data field to store the instructor who teaches the course.
Student
Teacher
10..35..6 * Course Faculty
Take Teach
FIGURE 12.5 This UML diagram shows that a student may take any number of courses, a
faculty member may teach at most three courses, a course may have from five to sixty stu-
dents, and a course is taught by only one faculty member.
multiplicity
12.8.2 Aggregation and Composition
Aggregation is a special form of association that represents an ownership relationship
between two objects. Aggregation models has-a relationships. The owner object is called an
aggregating object, and its class is called an aggregating class. The subject object is called an
aggregated object, and its class is called an aggregated class.
An object can be owned by several other aggregating objects. If an object is exclusively
owned by an aggregating object, the relationship between the object and its aggregating
object is referred to as a composition. For example, “a student has a name” is a composition
relationship between the Student class and the Name class, whereas “a student has an
address” is an aggregation relationship between the Student class and the Address class,
aggregation
aggregating object
aggregating class
aggregated object
aggregated class
composition
FIGURE 12.6
class Student:
# Add course to a list
def addCourse(self,
course):
class Course:
# Add student to a list
def addStudent(self,
student):
def setFaculty(self, faculty):
class Faculty:
# Add course to a list
def addCourse(self,
course):
The association relations are implemented using data fields and methods in classes.

420 Chapter 12 Inheritance and Polymorphism
since an address can be shared by several students. In UML, a filled diamond is attached to an
aggregating class (in this case, Student) to denote the composition relationship with an
aggregated class (Name), and an empty diamond is attached to an aggregating class
(Student) to denote the aggregation relationship with an aggregated class (Address), as
shown in Figure 12.7.
Aggregation
AddressName
Composition
1 1 1 1..3
Student
FIGURE 12.7 Each student has a name and an address.
In Figure 12.7, each student has only one multiplicity—address—and each address can be
shared by up to 3 students. Each student has one name, and a name is unique for each student.
An aggregation relationship is usually represented as a data field in the aggregating class.
For example, the relationships in Figure 12.7 may be implemented using the classes in Figure
12.8. The relation “a student has a name” and “a student has an address” are implemented in
the data field name and address in the Student class.
Person
Supervisor
1
(a) (b)
1
Person
Supervisor
1
m
FIGURE 12.9 (a) A person can have a supervisor. (b) A person can have several supervisors.
FIGURE 12.8
class Name:
…
class Address:
…
The composition relations are implemented using data fields in classes.
class Student:
def _init_(self, name, addresses)
self.name = name
self.address = address
…
Aggregated class Aggregating class Aggregated class
Aggregation can exist between objects of the same class. For example, Figure 12.9a illus-
trates that a person can have a supervisor.
The relationship “a person has a supervisor” can be represented as a data field in the
Person class, as follows:
# The type for the data is the class itself
self.supervisor = supervisor
…
def __init__(self, supervisor)
class Person:

12.9 Case Study: Designing the Course Class 421
If a person has several supervisors, as shown in Figure 12.9b, you can use a list to store
supervisors.
Note
Because aggregation and composition relationships are both implemented in classes in
similar ways, for simplicity, we refer to both as compositions.
12.17 What are the common types of relationships among classes? Describe the UML
graphical notation for modeling the relationships among classes.
12.18 What relationship is appropriate for the following classes? Draw the relationships
using UML diagrams.
■ Company and Employee
■ Course and Faculty
■ Student and Person
■ House and Window
■ Account and Savings Account
12.9 Case Study: Designing the Course Class
This section designs a class for modeling courses.
Suppose you need to process course information. Each course has a name and has students
enrolled. You want to be able to add/drop a student to/from the course. You can use a class to
model the courses, as shown in Figure 12.10.
Course
-courseName: str
-students: list
Course(courseName: str)
getCourseName(): str
addStudent(student: str): None
dropStudent(student: str): None
getStudents(): list
getNumberOfStudents(): int
The name of the course.
A list to store the students in the course.
Creates a course with the specified name.
Returns the course name.
Adds a new student to the course.
Drops a student from the course.
Returns the students in the course.
Returns the number of students in the course.
FIGURE 12.10 The Course class models the courses.
A Course object can be created using the constructor Course(name) by passing a course
name. You can add students to the course using the addStudent(student) method, drop a
student from the course using the dropStudent(student) method, and return the names of
all the students in the course using the getStudents() method. Suppose the Course class is
available. Listing 12.10 gives a test program that creates two courses and adds students to them.
LISTING 12.10 TestCourse.py
1 from Course import Course
2
3 def main():
aggregation or composition
Key
Point
✓Point✓Check

422 Chapter 12 Inheritance and Polymorphism
4
5
6
7
8 course1.addStudent(“Brian Smith”)
9 course1.addStudent(“Anne Kennedy”)
10
11
12 course2.addStudent(“Steve Smith”)
13
14 print(“Number of students in course1:”,
15 )
16 students =
17 for student in students:
18 print(student, end = “, “)
19
20 print(“\nNumber of students in course2:”,
21 course2.getNumberOfStudents())
22
23 main() # Call the main function
course1.getStudents()
course1.getNumberOfStudents()
course2.addStudent(“Peter Jones”)
course1.addStudent(“Peter Jones”)
course2 = Course(“Database Systems”)
course1 = Course(“Data Structures”)create a course
add a student
number of students
return students
Number of students in course1: 3
Peter Jones, Brian Smith, Anne Kennedy,
Number of students in course2: 2
The Course class is implemented in Listing 12.11. It uses a list to store the students for the
course in line 4. The addStudent method (line 6) adds a student to the list. The
getStudents method returns the list (line 9). The dropStudent method (line 18) is left as
an exercise.
LISTING 12.11 Course.py
1 class Course:
2 def __init__(self, courseName):
3 self.__courseName = courseName
4 self.__students = []
5
6
7 self.__students.append(student)
8
9
10 return self.__students
11
12
13 return len(self.__students)
14
15
16 return self.__courseName
17
18
19 print(“Left as an exercise”)
When you create a Course object, a list object is created. A Course object contains a ref-
erence to the list. For simplicity, you can say that the Course object contains the list.
The user can create a Course and manipulate it through the public methods addStudent,
dropStudent, getNumberOfStudents, and getStudents. However, the user doesn’t
def dropStudent(student):
def getCourseName(self):
def getNumberOfStudents(self):
def getStudents(self):
def addStudent(self, student):
students list
add a student
return students
number of students

12.10 Designing a Class for Stacks 423
need to know how these methods are implemented. The Course class encapsulates the inter-
nal implementation. This example uses a list to store the names of students. You may use a
different data type to store student names. The program that uses Course does not need to
change as long as the contract of the public methods remains unchanged.
12.10 Designing a Class for Stacks
This section designs a class for modeling stacks.
Recall that a stack (see Chapter 6) holds data in a last-in, first-out fashion, as shown in
Figure 12.11.
Data1
Data2
Data1
Data3
Data3
Data2
Data1
Data1
Data1
Data2
Data1
Data2
Data2
Data1
Data3
FIGURE 12.11 Data1, Data2, and Data3 are pushed onto the stack in this order and popped
out in the reversed order.
list Stack list Stack
(a) Using inheritance (b) Using composition
FIGURE 12.12 Stack may be implemented using inheritance or composition.
Stacks have many applications. For example, a computer uses a stack to process function
invocations. When a function is invoked, an activation record that stores its parameters and
local variables is pushed onto a stack. When a function calls another function, the new func-
tion’s activation record is pushed onto the stack. When a function finishes its work and returns
to its caller, its activation record is removed from the stack.
You can define a class to model stacks and use a list to store the elements in a stack. There
are two ways to design a stack class:
■ Using inheritance, you can define a stack class by extending list, as shown in
Figure 12.12a.
■ Using composition, you can create a list as a data field in the Stack class, as shown
in Figure 12.12b.
stack
inheritance
composition
Both designs are fine, but using composition is better because it enables you to define a
completely new stack class without inheriting the unnecessary and inappropriate methods
from the list class. We use the composition approach in this section and leave you to imple-
ment the inheritance approach in Exercise 12.16. The UML diagram for the Stack class is
shown in Figure 12.13.
Suppose that the Stack class is available. The test program in Listing 12.12 uses the class
to create a stack (line 3), store ten integers 0, 1, 2, …, and 9 (lines 5–6), and display them in
reverse order (line 9).
composition
inheritance
Key
Point

424 Chapter 12 Inheritance and Polymorphism
LISTING 12.12 TestStack.py
1 from Stack import Stack
2
3 stack = Stack()
4
5 for i in range(10):
6 stack.push(i)
7
8 while not stack.isEmpty():
9 print(stack.pop(), end = ” “)
Stack
-elements: list
Stack()
isEmpty(): bool
peek(): object
push(value: object): None
pop(): object
getSize(): int
A list to store the elements in the stack.
Constructs an empty stack.
Returns True if the stack is empty.
Returns the element at the top of the stack without
removing it from the stack.
Stores an element at the top of the stack.
Removes the element at the top of the stack and returns it.
Returns the number of elements in the stack.
FIGURE 12.13 The Stack class encapsulates the stack storage and provides the operations
for manipulating the stack.
create a stack
push onto stack
pop from stack
9 8 7 6 5 4 3 2 1 0
How do you implement the Stack class? You can use a list to store the elements in a stack,
as shown in Listing 12.13.
LISTING 12.13 Stack.py
1 class Stack:
2 def __init__(self):
3 self.__elements = []
4
5 # Return True if the stack is empty
6 def isEmpty(self):
7 return len(self.__elements) == 0
8
9 # Return the element at the top of the stack
10 # without removing it from the stack.
11 def peek(self):
12 if self.isEmpty():
13 return None
14 else:
15 return self.__elements[len(elements) – 1]
16
17 # Store an element at the top of the stack
18 def push(self, value):
19 self.__elements.append(value)
list to store elements
isEmpty
peek
push

12.11 Case Study: The FigureCanvas Class 425
pop
getSize
20
21 # Remove the element at the top of the stack and return it
22 def pop(self):
23 if self.isEmpty():
24 return None
25 else:
26 return self.__elements.pop()
27
28 # Return the size of the stack
29 def getSize(self):
30 return len(self.__elements)
In line 3, the data field elements is defined as private with two leading underscores.
elements is a list, but the client is not aware that the elements in the stack are stored in a list.
The client accesses the stack through the methods isEmpty(), peek(), push(element),
pop(), and getSize().
12.11 Case Study: The FigureCanvas Class
This case study develops the FigureCanvas class for displaying various figures.
The FigureCanvas class enables the user to set the figure type, specify whether the figure is
filled, and display the figure on a canvas. The UML diagram for the class, which can display
lines, rectangles, ovals, and arcs, is shown in Figure 12.14. The figureType property
decides which figure to display. If the filled property is True, the rectangle, oval, or arc is
filled with a color.
-figureType: str
-filled: bool
FigureCanvas(container, figureType,
filled, width, height)
Specifies the figure type (line, rectangle, oval, or arc).
Specifies whether the figure is filled (default: False).
Creates a figure canvas inside a container with the specified figure
type, filled, width (default 200), and height (default 200).
FigureCanvas
tkinter.Canvas
The get and set methods for these data fields
are provided in the class, but they are
omitted from the UML diagram for brevity.
FIGURE 12.14 The FigureCanvas class displays various types of figures on the panel.
The UML diagram serves as the contract for the FigureCanvas class. The user can use
the class without knowing how the class is implemented. We will begin by writing the pro-
gram in Listing 12.14 that uses the class to display seven figures in a panel, as shown in
Figure 12.15.
LISTING 12.14 DisplayFigures.py
1 from tkinter import * # Import all definitions from tkinter
2
3
4 class DisplayFigures:
5 def __init__(self):
6 window = Tk() # Create a window
7 window.title(“Display Figures”) # Set title
from FigureCanvas import FigureCanvas import FigureCanvas
Key
Point

426 Chapter 12 Inheritance and Polymorphism
8
9
10
11 figure2 = FigureCanvas(window, “rectangle”, False, 100, 100)
12 figure2.grid(row = 1, column = 2)
13 figure3 = FigureCanvas(window, “oval”, False, 100, 100)
14 figure3.grid(row = 1, column = 3)
15 figure4 = FigureCanvas(window, “arc”, False, 100, 100)
16 figure4.grid(row = 1, column = 4)
17 figure5 = FigureCanvas(window, “rectangle”, True, 100, 100)
18 figure5.grid(row = 1, column = 5)
19 figure6 = FigureCanvas(window, “oval”, True, 100, 100)
20 figure6.grid(row = 1, column = 6)
21 figure7 = FigureCanvas(window, “arc”, True, 100, 100)
22 figure7.grid(row = 1, column = 7)
23
24 window.mainloop() # Create an event loop
25
26 DisplayFigures() # Create GUI
figure1.grid(row = 1, column = 1)
figure1 = FigureCanvas(window, “line”, width = 100, height = 100)
The FigureCanvas class is implemented in Listing 12.15. Four types of figures are
drawn according to the figureType property (lines 26–34).
LISTING 12.15 FigureCanvas.py
1 from tkinter import * # Import all definitions from tkinter
2
3 class FigureCanvas(Canvas):
4 def __init__(self, container, figureType, filled = False,
5 width = 100, height = 100):
6 super().__init__(container,
7 width = width, height = height)
8 self.__figureType = figureType
9 self.__filled = filled
10 self.drawFigure()
11
12 def getFigureType(self):
13 return self.__figureType
14
15 def getFilled(self):
16 return self.__filled
17
18
19 self.__figureType = figureType
20 self.drawFigure()
21
22 def setFilled(self, filled):
def setFigureType(self, figureType):
FIGURE 12.15 Seven FigureCanvas objects are created to display seven figures.
create figure
place figure
create GUI
extend Canvas
superclass initializer
draw figure
set figure type
set fill

12.11 Case Study: The FigureCanvas Class 427
23 self.__filled = filled
24 self.drawFigure()
25
26
27 if self.__figureType == “line”:
28 self.line()
29 elif self.__figureType == “rectangle”:
30 self.rectangle()
31 elif self.__figureType == “oval”:
32 self.oval()
33 elif self.__figureType == “arc”:
34 self.arc()
35
36
37 width = int(self[“width”])
38 height = int(self[“height”])
39 self.create_line(10, 10, width – 10, height – 10)
40 self.create_line(width – 10, 10, 10, height – 10)
41
42
43 width = int(self[“width”])
44 height = int(self[“height”])
45 if self.__filled:
46 self.create_rectangle(10, 10, width – 10, height – 10,
47 fill = “red”)
48 else:
49 self.create_rectangle(10, 10, width – 10, height – 10)
50
51
52 width = int(self[“width”])
53 height = int(self[“height”])
54 if self.__filled:
55 self.create_oval(10, 10, width – 10, height – 10,
56 fill = “red”)
57 else:
58 self.create_oval(10, 10, width – 10, height – 10)
59
60
61 width = int(self[“width”])
62 height = int(self[“height”])
63 if self.__filled:
64 self.create_arc(10, 10, width – 10, height – 10,
65 start = 0, extent = 145, fill = “red”)
66 else:
67 self.create_arc(10, 10, width – 10, height – 10,
68 start = 0, extent = 145)
The FigureCanvas class extends the Canvas widget (line 3). Thus, a FigureCanvas is
a canvas, and you can use FigureCanvas just like a canvas. You can construct a
FigureCanvas by specifying the container, figure type, whether the figure is filled, and the
canvas width and height (lines 4–5).
The FigureCanvas class’s initializer invokes the Canvas initializer (lines 6–7), sets the
data field’s figureType and filled properties (lines 8–9), and invokes the drawFigure
method (line 10) to draw a figure.
The drawFigure method draws a figure based on the figureType and filled proper-
ties (lines 26–34).
The methods line, rectangle, oval, and arc draw lines, rectangles, ovals, and arcs
(lines 36–68).
def arc(self):
def oval(self):
def rectangle(self):
def line(self):
def drawFigure(self): draw figure
fill a rectangle
draw a rectangle
fill an oval
draw an oval
fill an arc
draw an arc
draw lines

428 Chapter 12 Inheritance and Polymorphism
KEY TERMS
aggregation 419
association 418
composition 419
dynamic binding 410
inheritance 400
is-a relationships 404
multiple inheritance 404
override 405
polymorphism 409
CHAPTER SUMMARY
1. You can derive a new class from an existing class. This is known as class inheritance.
The new class is called a subclass, child class or extended class. The existing class is
called a superclass, parent class, or base class.
2. To override a method, the method must be defined in the subclass using the same
header as in its superclass.
3. The object class is the root class for all Python classes. The methods __str__()
and __eq__(other) are defined in the object class.
4. Polymorphism means that an object of a subclass can be passed to a parameter of a
superclass type. A method may be implemented in several classes along the inheri-
tance chain. Python decides which method is invoked at runtime. This is known as
dynamic binding.
5. The isinstance function can be used to determine whether an object is an instance
of a class.
6. The common relationships among classes are association, aggregation, composition,
and inheritance.
TEST QUESTIONS
Do test questions for this chapter online at www.cs.armstrong.edu/liang/py/test.html.
PROGRAMMING EXERCISES
Sections 12.2–12.6
12.1 (The Triangle class) Design a class named Triangle that extends the
GeometricObject class. The Triangle class contains:
■ Three float data fields named side1, side2, and side3 to denote the three
sides of the triangle.
■ A constructor that creates a triangle with the specified side1, side2, and
side3 with default values 1.0.
■ The accessor methods for all three data fields.
■ A method named getArea() that returns the area of this triangle.
■ A method named getPerimeter() that returns the perimeter of this triangle.
■ A method named __str__() that returns a string description for the triangle.

www.cs.armstrong.edu/liang/py/test.html

Programming Exercises 429
For the formula to compute the area of a triangle, see Exercise 2.14. The
__str__() method is implemented as follows:
return “Triangle: side1 = ” + str(side1) + ” side2 = ” +
str(side2) + ” side3 = ” + str(side3)
Draw the UML diagrams for the classes Triangle and GeometricObject.
Implement the Triangle class. Write a test program that prompts the user to
enter the three sides of the triangle, a color, and 1 or 0 to indicate whether the tri-
angle is filled. The program should create a Triangle object with these sides and
set the color and filled properties using the input. The program should display the
triangle’s area, perimeter, color, and True or False to indicate whether the trian-
gle is filled or not.
**12.2 (The Location class) Design a class named Location for locating a maximal
value and its location in a two-dimensional list. The class contains the public data
fields row, column, and maxValue that store the maximal value and its indexes in
a two-dimensional list, with row and column as int types and maxValue as a
float type.
Write the following method that returns the location of the largest element in a
two-dimensional list.
def Location locateLargest(a):
The return value is an instance of Location. Write a test program that prompts
the user to enter a two-dimensional list and displays the location of the largest ele-
ment in the list. Here is a sample run:
Enter the number of rows and columns in the list:
Enter row 0:
Enter row 1:
Enter row 2:
The location of the largest element is 45 at (1, 2)
35 44 5.5 12.6
4.5 3 45 3.5
23.5 35 2 10
3, 4
**12.3 (Game: ATM machine) Use the Account class created in Exercise 7.3 to simulate
an ATM machine. Create ten accounts in a list with the ids 0, 1, …, 9, and an ini-
tial balance of $100. The system prompts the user to enter an id. If the id is entered
incorrectly, ask the user to enter a correct id. Once an id is accepted, the main
menu is displayed as shown in the sample run. You can enter a choice of 1 for
viewing the current balance, 2 for withdrawing money, 3 for depositing money,
and 4 for exiting the main menu. Once you exit, the system will prompt for an id
again. So, once the system starts, it won’t stop.
Enter an account id:
Main menu
1: check balance
2: withdraw
3: deposit
4: exit
4

430 Chapter 12 Inheritance and Polymorphism
*12.4 (Geometry: find the bounding rectangle) A bounding rectangle is the minimum
rectangle that encloses a set of points in a two-dimensional plane, as shown in
Figure 12.16. Write a method that returns a bounding rectangle for a set of points
in a two-dimensional plane, as follows:
def getRectangle(points):
You defined the Rectangle2D class in Exercise 8.19. Write a test program that
prompts the user to enter the points as x1 y1 x2 y2 x3 y3 … in one line, and dis-
plays the bounding rectangle’s center, width, and height. Here is a sample run:
Enter a choice:
The balance is 100.00
Main menu
1: check balance
2: withdraw
3: deposit
4: exit
Enter a choice:
Enter an amount to withdraw:
Main menu
1: check balance
2: withdraw
3: deposit
4: exit
Enter a choice:
The balance is 97.00
Main menu
1: check balance
2: withdraw
3: deposit
4: exit
Enter a choice:
Enter an amount to deposit:
Main menu
1: check balance
2: withdraw
3: deposit
4: exit
Enter a choice:
The balance is 107.00
Main menu
1: check balance
2: withdraw
3: deposit
4: exit
Enter a choice:
Enter an account id:
4
1
10
3
1
3
2
1

Programming Exercises 431
Enter the points:
The bounding rectangle is centered at (5.0, 6.25) with width
8.0 and height 7.5
1.0 2.5 3 4 5 6 7 8 9 10
Sections 12.7–12.11
**12.5 (Game: Tic-tac-toe) Write a program that plays the tic-tac-toe game. Two players
take turns clicking an available cell in a grid with their respective tokens
(either X or O). When one player has placed three tokens in a horizontal, vertical,
or diagonal row on the grid, the game is over and that player has won. A draw (no
winner) occurs when all the cells in the grid have been filled with tokens and nei-
ther player has achieved a win. Figure 12.17 shows the representative sample runs
of the example.
3 * 3
FIGURE 12.16 Points are enclosed inside a rectangle.
(a) The X player won the game (b) Draw—no winners (c) The O player won the game
FIGURE 12.17 Two players play a tic-tac-toe game.
Assume that all the cells are initially empty, and that the first player takes the X
token and the second player the O token. To mark a cell, the player points the
mouse to the cell and clicks it. If the cell is empty, the token (X or O) is displayed.
If the cell is already filled, the player’s action is ignored.
Define a custom class named Cell that extends Label for displaying a token and
for responding to the button-click event. The class contains a data field token with
three possible values—’ ‘, X, and O—that denote whether the cell has been occu-
pied and which token is used in the cell if it is occupied.
The three image files x.gif, o.gif, and empty.gif can be obtained from
cs.armstrong.edu/liang/py/book.zip in the image folder. Use these three images
to display the X, O, and empty cells.
**12.6 (Tkinter: two circles intersect?) Using the Circle2D class you defined in Exer-
cise 8.18, write a program that enables the user to point the mouse inside a circle
and drag it. As the circle is being dragged, the label displays whether two circles
overlap, as shown in Figure 12.18.

432 Chapter 12 Inheritance and Polymorphism
**12.7 (Tkinter: two rectangles intersect?) Using the Rectangle2D class you defined in
Exercise 8.19, write a program that enables the user to point the mouse inside a
rectangle and drag it. As the rectangle is being dragged, the label displays whether
two rectangles overlap, as shown in Figure 12.19.
**12.8 (Tkinter: two circles intersect?) Using the Circle2D class you defined in Exer-
cise 8.18, write a program that enables the user to specify the location and size of
two circles and displays whether the circles intersect, as shown in Figure 12.20.
Enable the user to point the mouse inside a circle and drag it. As a circle is being
dragged, the program updates the circle’s center coordinates and its radius in the
text fields.
**12.9 (Tkinter: two rectangles intersect?) Using the Rectangle2D class you defined in
Exercise 8.19, write a program that enables the user to specify the location and
size of the rectangles and displays whether the two rectangles intersect, as shown
(a) (b)
FIGURE 12.19 Check whether two rectangles are overlapping.
FIGURE 12.20 Check whether two circles are overlapping.
(a) (b)
FIGURE 12.18 Check whether two circles are overlapping.

Programming Exercises 433
**12.11 (Tkinter: guess birthday) Listing 4.3, GuessBirthday.py, gives a program for
guessing a birthday. Create a program for guessing birthdays as shown in Figure
12.23. The program prompts the user to check whether the date is in any of the
five sets. The date is displayed in a message box upon clicking the Guess Birth-
day button.
*12.12 (Tkinter: a group of clocks) Write a program that displays four clocks, as shown in
Figure 12.24.
FIGURE 12.21 Check whether two rectangles are overlapping.
FIGURE 12.22 The program simulates four cars racing.
FIGURE 12.23 This program guesses the birthdays.
in Figure 12.21. Enable the user to point the mouse inside a rectangle and drag it.
As a rectangle is being dragged, the program updates the rectangle’s center coor-
dinates, width, and height in the text fields.
**12.10 (Tkinter: four cars) Write a program that simulates four cars racing, as shown in
Figure 12.22. You should define a subclass of Canvas to display a car.

434 Chapter 12 Inheritance and Polymorphism
**12.14 (Tkinter: Mandelbrot fractal ) The Mandelbrot fractal is a well-known image
created from a Mandelbrot set (see Figure 12.26a). A Mandelbrot set is defined
using the following iteration:
c is a complex number, and the starting point of the iteration is (For
information on complex numbers, see Exercise 8.21.) For a given c, the iteration
will produce a sequence of complex numbers: It can be
shown that the sequence either tends to infinity or stays bounded, depending on
the value of c. For example, if c is 0, the sequence is which is
bounded. If c is i, the sequence is which
is bounded. If c is the sequence is which is
unbounded. It is known that if the absolute value of a complex value in the
sequence is greater than 2, then the sequence is unbounded. The Mandelbrot set
consists of the c value such that the sequence is bounded. For example, 0 and i
are in the Mandelbrot set. A Mandelbrot image can be created using the follow-
ing code:
1 COUNT_LIMIT = 60
2
3 # Paint a Mandelbrot image in the canvas
zi
[0, 1 + i, 1 + 3i, c ],1 + i,
[0, i, -1 + i, – i, -1 + i, i, c ],
[0, 0, c ],
[z0, z1, c , zn, c ].
z0 = 0.
zn+1 = z2n + c
FIGURE 12.25 The program enables two players to play the Connect Four game.
FIGURE 12.24 The program displays four clocks.
***12.13 (Tkinter: Connect Four game) In Exercise 11.20, you created a Connect Four
game that enables two players to play the game on the console. Rewrite the pro-
gram using a GUI program, as shown in Figure 12.25. The program enables
two players to place red and yellow disks in turn. To place a disk, the player
needs to click on an available cell. An available cell is unoccupied and its
downward neighbor is occupied. The program flashes the four winning cells if
a player wins, and reports no winners if all cells are occupied with no winners.

Programming Exercises 435
4 def paint():
5 x = -2.0
6 while x < 2.0: 7 y = -2.0 8 while y < 2.0: 9 c = count(complex(x, y)) 10 if c == COUNT_LIMIT: 11 color = "red" # c is in a Mandelbrot set 12 else: 13 # get hex value RRGGBB that is dependent on c 14 color = "#RRGGBB" 15 16 # Fill a tiny rectangle with the specified color 17 canvas.create_rectangle(x * 100 + 200, y * 100 + 200, 18 x * 100 + 200 + 5, y * 100 + 200 + 5, fill = color) 19 y += 0.05 20 x += 0.05 21 22 # Return the iteration count 23 def count(c): 24 z = complex(0, 0) # z0 25 26 for i in range(COUNT_LIMIT): 27 z = z * z + c # Get z1, z2, ... 28 if abs(z) > 2: return i # The sequence is unbounded
29
30 return COUNT_LIMIT # Indicate a bounded sequence
(a) (b)
FIGURE 12.26 A Mandelbrot image is shown in (a) and a Julia set image is shown in (b).
The count(c) function (lines 23–28) computes If none of their
absolute values exceeds 2, we assume c is in the Mandelbrot set. Of course,
there could always be an error, but 60 (COUNT_LIMIT) iterations usually are
enough. Once we find that the sequence is unbounded, the method returns the
z1, z2, c , z60.

436 Chapter 12 Inheritance and Polymorphism
**12.18 (Tkinter: the BarChart class) Develop a class named BarChart that extends
Canvas for displaying a bar chart:
BarChart(parent, data, width = 400, height = 300)
Where data is a list, each element in the list is a nested list that consists of a
value, a title for the value, and a color for the bar in the bar chart. For example,
for data = [[40, “CS”, “red”], [30, “IS”, “blue”], [50, “IT”,
“yellow”]], the bar chart is as shown in the left part of Figure 12.28. For data
= [[140, “Freshman”, “red”], [130, “Sophomore”, “blue”],
[150, “Junior”, “yellow”], [80, “Senior”, “green”]], the bar
chart is as shown in the right part of Figure 12.28. Write a test program that dis-
plays two bar charts, as shown in Figure 12.28.
**12.19 (Tkinter: the PieChart class) Develop a class named PieChart that extends
Canvas for displaying a pie chart using the following constructor:
PieChart(parent, data, width = 400, height = 300)
FIGURE 12.27 The program can automatically find a solution if one exists.
iteration count (line 28). The method returns COUNT_LIMIT if the sequence is
bounded (line 30).
The loop in lines 6–20 examines each point (x, y) for and
with interval 0.01 to see if its corresponding complex number
is in the Mandelbrot set (line 9). If so, paint the point red (line 11).
If not, set a color that is dependent on its iteration count (line 14). Note that the
point is painted in a square with width 5 and height 5. All the points are scaled
and mapped to a grid of pixels (lines 17–18).
Complete the program to draw a Mandelbrot image, as shown in Figure 12.26a.
**12.15 (Tkinter: Julia set) The preceding exercise describes Mandelbrot sets. The Man-
delbrot set consists of the complex c value such that the sequence
is bounded with fixed and c varying. If we fix c and vary the
point (x, y) is said to be in a Julia set for a fixed complex value c if the function
stays bounded. Write a program that draws a Julia set as shown
in Figure 12.26b. Note that you only need to revise the count method in Exer-
cise 12.14 by using a fixed c value
*12.16 (Implement Stack using inheritance) In Listing 12.13, the Stack class is
implemented using composition. Define a new Stack class using inheritance
that extends list.
Draw UML diagrams of the new class. Implement it. Write a test program that
prompts the user to enter five strings and displays them in reverse order.
***12.17 (Tkinter: the 24-point card game) Enhance Exercise 10.37 to enable the com-
puter to display the expression for a 24-point game solution if one exists, as
shown in Figure 12.27. Otherwise, report that the solution does not exist.
(-0.3 + 0.6i).
zn+1 = z2n + c
z0 (= x + yi),z0
zn+1 = z2n + c
400 * 400
c = x + yi
-2 6 y 6 2
-2 6 x 6 2

Programming Exercises 437
**12.20 (Tkinter: The RegularPolygonCanvas Class) Define a subclass of Canvas,
named RegularPolygonCanvas, to paint an n-sided regular polygon. The class
contains a property named numberOfSides, which specifies the number of sides
in the polygon. The polygon is centered in the canvas, and the polygon’s size is
proportional to the size of the canvas. Create a triangle, square, pentagon, hexa-
gon, heptagon, and octagon from RegularPolygonCanvas and display them, as
shown in Figure 12.30.
FIGURE 12.28 The program uses the BarChart class to display bar charts.
Where data is a list, each element in the list is a nested list that consists of a
value, a title for the value, and a color for the wedge in the pie chart. For exam-
ple, for data = [[40, “CS”, “red”], [30, “IS”, “blue”], [50,
“IT”, “yellow”]], the pie chart is as shown in the left part of Figure 12.29.
For data = [[140, “Freshman”, “red”], [130, “Sophomore”,
“blue”], [150, “Junior”, “yellow”], [80, “Senior”,
“green”]], the pie chart is as shown in the right part of Figure 12.29. Write a
test program that displays two pie charts, as shown in Figure 12.29.
FIGURE 12.29 The program uses the PieChart class to display pie charts.
FIGURE 12.30 The program displays several n-sided polygons.

438 Chapter 12 Inheritance and Polymorphism
*12.22 (Flip coins) Write a program that displays heads (H) or tails (T) for each of nine
coins, as shown in Figure 12.31c–d. When a cell is clicked, the coin is flipped.
Write a custom cell class that extends Label. In the initializer of the class, bind
the event with the method for flipping the coin. When the program
starts, all cells initially display H.
(a) (b) (c) (d)
FIGURE 12.31 (a–b) Clicking the or button increases or decreases the number of sides of a regular polygon.
(c–d) The program enables the user to click a cell to flip a coin.
-1+1
*12.21 (Tkinter: display an n-sided regular polygon) In Exercise 12.20 you created the
RegularPolygonCanvas subclass for displaying an n-sided regular polygon.
Write a program that displays a regular polygon and uses two buttons named
and to increase or decrease the size of the polygon, as shown in Figure
12.31a–b. Also enable the user to increase or decrease the size by clicking the
right or left mouse button and by pressing the UP and DOWN arrow keys.
-1
+1

FILES AND EXCEPTION
HANDLING
Objectives
■ To open a file using the open function for reading and writing data
(§13.2.1).
■ To write data to a file using the write method in a file object (§13.2.2).
■ To test the existence of a file using the os.path.isfile function (§13.2.3).
■ To read data from a file using the read, readline, and readlines meth-
ods in a file object (§§13.2.4–13.2.5).
■ To append data to a file by opening the file in the append mode (§13.2.6).
■ To read and write numeric data (§13.2.7).
■ To display open and save file dialogs for getting file names for reading and
writing data (§13.3).
■ To develop applications with files (§13.4).
■ To read data from a Web resource (§13.5).
■ To handle exceptions by using the try, except, and finally clauses
(§13.6).
■ To raise exceptions by using the raise statements (§13.7).
■ To become familiar with Python’s built-in exception classes (§13.8).
■ To access an exception object in the handler (§13.8).
■ To define custom exception classes (§13.9).
■ To perform binary IO using the load and dump functions in the pickle
module (§13.10).
■ To create an address book using binary IO (§13.11).
CHAPTER
13

440 Chapter 13 Files and Exception Handling
13.1 Introduction
You can use a file to store data permanently; you can use exception handling to make
your programs reliable and robust.
Data used in a program is temporary; unless the data is specifically saved, it is lost when the pro-
gram terminates. To permanently store the data created in a program, you need to save it in a file
on a disk or some other permanent storage device. The file can be transported and can be read
later by other programs. In this chapter, you learn how to read and write data from and to a file.
What happens if your program tries to read data from a file but the file does not exist? Your
program will be abruptly terminated. In this chapter you will learn how to write the program
to handle this exception so the program can continue to execute.
13.2 Text Input and Output
To read and write data from or to a file, use the open function to create a file object
and use the object’s read and write methods to read and write data.
A file is placed in a directory in the file system. An absolute filename contains a filename with
its complete path and drive letter. For example, c:\pybook\Scores.txt is the absolute filename
for the file Scores.txt on the Windows operating system. Here, c:\pybook is referred to as the
directory path to the file. Absolute filenames are machine dependent. On the UNIX platform,
the absolute filename may be /home/liang/pybook/Scores.txt, where /home/liang/pybook is
the directory path to the file Scores.txt.
A relative filename is relative to its current working directory. The complete directory path
for a relative file name is omitted. For example, Scores.py is a relative filename. If its current
working directory is c:\pybook, the absolute filename would be c:\pybook\Scores.py.
Files can be classified into text or binary files. A file that can be processed (that is, read,
created, or modified) using a text editor such as Notepad on Windows or vi on UNIX is called
a text file. All the other files are called binary files. For example, Python source programs are
stored in text files and can be processed by a text editor, but Microsoft Word files are stored in
binary files and are processed by the Microsoft Word program.
Although it is not technically precise and correct, you can envision a text file as consisting
of a sequence of characters and a binary file as consisting of a sequence of bits. Characters in
a text file are encoded using a character encoding scheme such as ASCII and Unicode. For
example, the decimal integer 199 is stored as the sequence of the three characters 1, 9, and 9,
in a text file, and the same integer is stored as a byte-type value C7 in a binary file, because
decimal 199 equals hex C7 The advantage of binary files is that they
are more efficient to process than text files.
Note
Computers do not differentiate between binary files and text files. All files are stored in
binary format, and thus all files are essentially binary files. Text IO (input and output) is
built upon binary IO to provide a level of abstraction for character encoding and decoding.
This section shows you how to read and write strings from and to a text file. Binary files
are introduced in Section 13.10.
13.2.1 Opening a File
How do you write data to a file and read the data back from a file? You need to first create a
file object that is associated with a physical file. This is called opening a file. The syntax for
opening a file is:
fileVariable = open(filename, mode)
The open function returns a file object for filename. The mode parameter is a string that
specifies how the file will be used (for reading or writing), as shown in Table 13.1.
(199 = 12 * 161 + 7).
why files?
why exception handling?
absolute filename
directory path
text file
binary file
why binary file?
Key
Point
Key
Point
relative filename

13.2 Text Input and Output 441
TABLE 13.1 File Modes
Mode Description
“r” Opens a file for reading.
“w” Opens a new file for writing. If the file already exists, its
old contents are destroyed.
“a” Opens a file for appending data from the end of the file.
“rb” Opens a file for reading binary data.
“wb” Opens a file for writing binary data.
For example, the following statement opens a file named Scores.txt in the current direc-
tory for reading:
input = open(“Scores.txt”, “r”)
You can also use the absolute filename to open the file in Windows, as follows:
input = open(r”c:\pybook\Scores.txt”, “r”)
The statement opens the file Scores.txt that is in the c:\pybook directory for reading. The
r prefix before the absolute filename specifies that the string is a raw string, which causes the
Python interpreter to treat backslash characters as literal backslashes. Without the r prefix,
you would have to write the statement using an escape sequence as:
input = open(“c:\\pybook\\Scores.txt”, “r”)
13.2.2 Writing Data
The open function creates a file object, which is an instance of the _io.TextIOWrapper
class. This class contains the methods for reading and writing data and for closing the file, as
shown in Figure 13.1.
After a file is opened for writing data, you can use the write method to write a string to
the file. In Listing 13.1, the program writes three strings to the file Presidents.txt.
LISTING 13.1 WriteDemo.py
1 def main():
2 # Open file for output
3 outfile = open(“Presidents.txt”, “w”)
raw string
_io.TextIOWrapper
read([number.int): str Returns the specified number of characters from the file. If the
argument is omitted, the entire remaining contents in the file
are read.
readline(): str
readlines(): list
write(s: str): None
close(): None
Returns the next line of the file as a string.
Returns a list of the remaining lines in the file.
Writes the string to the file.
Closes the file.
FIGURE 13.1 A file object contains the methods for reading and writing data.
open file for writing

442 Chapter 13 Files and Exception Handling
4
5 # Write data to the file
6
7 outfile.write(“George Bush\n”)
8 outfile.write(“Barack Obama”)
9
10 # Close the output file
11
12 main() # Call the main function
The program opens a file named Presidents.txt using the w mode for writing data (line 3).
If the file does not exist, the open function creates a new file. If the file already exists, the
contents of the file will be overwritten with new data. You can now write data to the file.
When a file is opened for writing or reading, a special marker called a file pointer is posi-
tioned internally in the file. A read or write operation takes place at the pointer’s location.
When a file is opened, the file pointer is set at the beginning of the file. When you read or
write data to the file, the file pointer moves forward.
The program invokes the write method on the file object to write three strings (lines 6–8).
Figure 13.2 shows the position of the file pointer after each write.
outfile.close()
outfile.write(“Bill Clinton\n”)write data
close file
file pointer
The program closes the file to ensure that data is written to the file (line 10). After this pro-
gram is executed, three names are written to the file. You can view the file in a text editor, as
shown in Figure 13.3.
Bill Clinton\n
Bill Clinton\nGeorge Bush\n
Bill Clinton\nGeorge Bush\nBarack Obama
After outfile.write(“Bill Clinton\n”)
After outfile.write(“George Bush\n”)
After outfile.write(“Barack Obama”)
Initial file pointer position
file pointer
file pointer
file pointer
file pointer
FIGURE 13.2 Three strings are written to the file.
FIGURE 13.3 A file named Presidents.txt contains three names.

13.2 Text Input and Output 443
Note
When you invoke print(str), the function automatically inserts the newline charac-
ter \n after displaying the string. However, the write function does not automatically
insert the newline character. You have to explicitly write the newline character to the file.
Warning
If you open an existing file for writing, the original contents of the file will be
destroyed/overwritten with the new text.
13.2.3 Testing a File’s Existence
To prevent the data in an existing file from being erased by accident, you should test to see if
the file exists before opening it for writing. The isfile function in the os.path module can
be used to determine whether a file exists. For example:
import os.path
if os.path.isfile(“Presidents.txt”):
print(“Presidents.txt exists”)
Here isfile(“Presidents.txt”) returns True if the file Presidents.txt exists in the
current directory.
13.2.4 Reading Data
After a file is opened for reading data, you can use the read method to read a specified number
of characters or all characters from the file and return them as a string, the readline() method
to read the next line, and the readlines() method to read all the lines into a list of strings.
Suppose the file Presidents.txt contains the three lines shown in Figure 13.3. The program
in Listing 13.2 reads the data from the file.
LISTING 13.2 ReadDemo.py
1 def main():
2 # Open file for input
3
4 print(“(1) Using read(): “)
5 print( )
6 infile.close() # Close the input file
7
8 # Open file for input
9 infile = open(“Presidents.txt”, “r”)
10 print(“\n(2) Using read(number): “)
11 s1 =
12 print(s1)
13 s2 =
14 print( )
15 infile.close() # Close the input file
16
17 # Open file for input
18 infile = open(“Presidents.txt”, “r”)
19 print(“\n(3) Using readline(): “)
20 line1 =
21 line2 = infile.readline()
22 line3 = infile.readline()
23 line4 = infile.readline()
24 print(repr(line1))
25 print(repr(line2))
26 print(repr(line3))
27 print(repr(line4))
28 infile.close() # Close the input file
infile.readline()
repr(s2)
infile.read(10)
infile.read(4)
infile.read()
infile = open(“Presidents.txt”, “r”)
open file for reading
read all data
close file
open file for reading
read characters
read characters
raw string
read a line
Process text file
VideoNote

444 Chapter 13 Files and Exception Handling
29
30 # Open file for input
31 infile = open(“Presidents.txt”, “r”)
32 print(“\n(4) Using readlines(): “)
33 print( )
34 infile.close() # Close the input file
35
36 main() # Call the main function
infile.readlines()read all lines
(1) Using read():
Bill Clinton
George Bush
Barack Obama
(2) Using read(number):
Bill
‘ Clinton\nG’
(3) Using readline():
‘Bill Clinton\n’
‘George Bush\n’
‘Barack Obama’
”
(4) Using readlines():
[‘Bill Clinton\n’, ‘George Bush\n’, ‘Barack Obama’]
The program first opens the file Presidents.txt using the r mode for reading through the file
object infile (line 3). Invoking the infile.read() method reads all characters from the
file and returns them as a string (line 5). The file is closed (line 6).
The file is reopened for reading (line 9). The program uses the read(number) method to
read the specified number of characters from the file. Invoking infile.read(4) reads 4
characters (line 11) and infile.read(10) reads 10 characters (line 13). The repr(s)
function returns a raw string for s, which causes the escape sequence to be displayed as liter-
als, as shown in the output.
Figure 13.4 shows the file pointer’s position after each read.
The file is closed (line 15) and reopened for reading (line 18). The program uses the
readline() method to read a line (line 20). Invoking infile.readline() reads a line
using read()
using read(number)
repr function
using readline()
Bill Clinton\nGeorge Bush\nBarack Obama
Bill Clinton\nGeorge Bush\nBarack Obama
Bill Clinton\nGeorge Bush\nBarack Obama
Initial file pointer position
After s1 = infile.read(4)
s1 is ‘Bill’
After s2 = infile.read(10)
s2 is ‘Clinton\nG’
file pointer
file pointer
file pointer
FIGURE 13.4 The file pointer moves forward as characters are read from the file.

13.2 Text Input and Output 445
that ends with \n. All characters in a line are read including the \n. When the file pointer is
positioned at the end of the file, invoking readline() or read() returns an empty string ”.
Figure 13.5 shows the file pointer’s position after each readline method is called.
The file is closed (line 28) and reopened for reading (line 31). The program uses the
readlines() method to read all lines and return a list of strings. Each string corresponds to
a line in the file.
13.2.5 Reading All Data from a File
Programs often need to read all data from a file. Here are two common approaches to accom-
plishing this task:
1. Use the read() method to read all data from the file and return it as one string.
2. Use the readlines() method to read all data and return it as a list of strings.
These two approaches are simple and appropriate for small files, but what happens if the
file is so large that its contents cannot be stored in the memory? You can write the following
loop to read one line at a time, process it, and continue reading the next line until it reaches the
end of the file:
line = infile.readline() # Read a line
while line != ”:
# Process the line here …
# Read next line
line = infile.readline()
Note that when the program reaches the end of the file, readline() returns ”.
using readlines()
Bill Clinton\nGeorge Bush\nBarack Obama
Bill Clinton\nGeorge Bush\nBarack Obama
Bill Clinton\nGeorge Bush\nBarack Obama
Initial file pointer position
After line1 = infile.readline()
line1 is ‘Bill Clinton\n’
After line2 = infile.readline()
line2 is ‘George Bush\n’
After line3 = infile.readline()
line3 is ‘Barack Obama’
After line4 = infile.readline()
line4 is ”
file pointer
file pointer
file pointer
Bill Clinton\nGeorge Bush\nBarack Obama
file pointer
Bill Clinton\nGeorge Bush\nBarack Obama
file pointer
FIGURE 13.5 The readline() method reads a line.

446 Chapter 13 Files and Exception Handling
Python also lets you read all lines by using a for loop, as follows:
for line in infile:
# Process the line here …
This is much simpler than using a while loop.
Listing 13.3 illustrates a program that copies data from a source file to a target file and
counts the number of lines and characters in the file.
LISTING 13.3 CopyFile.py
1 import os.path
2 import sys
3
4 def main():
5 # Prompt the user to enter filenames
6 f1 = input(“Enter a source file: “).strip()
7 f2 = input(“Enter a target file: “).strip()
8
9 # Check if target file exists
10 if :
11 print(f2 + ” already exists”)
12 sys.exit()
13
14 # Open files for input and output
15 infile = open(f1, “r”)
16 outfile = open(f2, “w”)
17
18 # Copy from input file to output file
19 countLines = countChars = 0
20 for line in infile:
21 countLines += 1
22 countChars += len(line)
23 outfile.write(line)
24 print(countLines, “lines and”, countChars, “chars copied”)
25
26 infile.close() # Close the input file
27 outfile.close() # Close the output file
28
29 main() # Call the main function
os.path.isfile(f2)
input file
output file
check file existence
open file for input
open file for output
initialize countLines and
countChars
read a line
increase countLines
increase countChars
write a line
close input file
close output file
Enter a source file:
Enter a target file:
output1.txt already exists
output1.txt
input.txt
Enter a source file:
Enter a target file:
3 lines and 73 characters copied
output2.txt
input.txt
The program prompts the user to enter a source file f1 and a target file f2 (lines 6–7) and
determines whether f2 already exists (lines 10–12). If so, the program displays a message that
the file already exists (line 11) and exits (line 12). If the file doesn’t already exist, the program
opens file f1 for input and f2 for output (lines 15–16). It then uses a for loop to read each
line from file f1 and write each line into file f2 (lines 20–23). The program tracks the number

13.2 Text Input and Output 447
open file for appending
write data
close file
Programming is fun
Programming is fun\nPython is interpreted\n
Initial file pointer position when file
is opened with mode “a”
File pointer position after
outfile.write(“\nPython is interpreted\n”)
file pointer
file pointer
FIGURE 13.6 The data is appended to the file.
of lines and characters read from the file (lines 21–22). To ensure that the files are processed
properly, you need to close the files after they are processed (lines 26–27).
13.2.6 Appending Data
You can use the a mode to open a file for appending data to the end of an existing file. Listing
13.4 gives an example of appending two new lines into a file named Info.txt.
LISTING 13.4 AppendDemo.py
1 def main():
2 # Open file for appending data
3
4
5 # Close the file
6
7 main() # Call the main function
The program opens a file named Info.txt using the a mode for appending data to the file
through the file object outfile (line 3). Assume the existing file contains the text “Program-
ming is fun.” Figure 13.6 shows the position of the file pointer after the file is opened and after
each write. When the file is opened, the file pointer is positioned at the end of the file.
outfile.close()
outfile.write(“\nPython is interpreted\n”)
outfile = open(“Info.txt”, “a”)
The program closes the file to ensure that the data is properly written to the file (line 5).
13.2.7 Writing and Reading Numeric Data
To write numbers to a file, you must first convert them into strings and then use the write
method to write them to the file. In order to read the numbers back correctly, separate them
with whitespace characters, such as ” ” or \n.
In Listing 13.5, the program writes ten random single digits to a file and reads them back
from the file.
LISTING 13.5 WriteReadNumbers.py
1 from random import randint
2
3 def main():
4 # Open file for writing data
5
6 for i in range(10):
7 outfile.write(str(randint(0, 9)) + ” “)
outfile = open(“Numbers.txt”, “w”) open file for writing
write data

448 Chapter 13 Files and Exception Handling
8 # Close the file
9
10 # Open file for reading data
11
12
13 numbers = [eval(x) for x in ]
14 for number in numbers:
15 print(number, end = ” “)
16 infile.close() # Close the file
17
18 main() # Call the main function
s.split()
s = infile.read()
infile = open(“Numbers.txt”, “r”)
outfile.close()close file
open file for reading
convert to numbers
close file
8 1 4 1 2 5 5 1 3 2
The program opens a file named Numbers.txt using the w mode for writing data to that
file using the file object outfile (line 5). The for loop writes ten numbers into the file,
separated by spaces (lines 6–7). Note that the numbers are converted to strings before being
written to the file.
The program closes the output file (line 8) and reopens it using the r mode for reading data
through the file object infile (line 11). The read() method reads all data as a string (line
12). Since the numbers are separated by spaces, the string’s split method splits the string
into a list (line 13). The numbers are obtained from the list and displayed (lines 14–15).
13.1 How do you open a file for reading, for writing, and for appending, respectively?
13.2 What is wrong about creating a file object using the following statement?
infile = open(“c:\book\test.txt”, “r”)
13.3 When you open a file for reading, what happens if the file does not exist? When you
open a file for writing, what happens if the file already exists?
13.4 How do you determine whether a file exists?
13.5 What method do you use to read 30 characters from a file?
13.6 What method do you use to read all data into a string?
13.7 What method do you use to read a line?
13.8 What method do you use to read all lines into a list?
13.9 Will your program have a runtime error if you invoke read() or readline() at the
end of the file?
13.10 When reading data, how do you know if it is the end of the file?
13.11 What function do you use to write data to a file?
13.12 How do you denote a raw string literal in the program?
13.13 How do you write and read numeric data?
13.3 File Dialogs
The tkinter.filedialog module contains the functions askopenfilename and
asksaveasfilename for displaying the file Open and Save As dialog boxes.
Tkinter provides the tkinter.filedialog module with the following two functions:
# Display a file dialog box for opening an existing file
filename = askopenfilename()
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13.3 File Dialogs 449
# Display a file dialog box for specifying a file for saving data
filename = asksaveasfilename()
Both functions return a filename. If the dialog is cancelled by the user, the function returns
None. Here is an example of using these two functions:
1 from tkinter.filedialog import askopenfilename
2 from tkinter.filedialog import asksaveasfilename
3
4 filenameforReading = askopenfilename()
5 print(“You can read from ” + filenameforReading)
6
7 filenameforWriting = asksaveasfilename()
8 print(“You can write data to ” + filenameforWriting)
When you run this code, the askopenfilename() function displays the Open dialog box
for specifying a file to open, as shown in Figure 13.7a. The asksaveasfilename() func-
tion displays the Save As dialog for specifying the name of the file to save, as shown in
Figure 13.7b.
file dialog for opening
file dialog for saving
(a) (b)
FIGURE 13.7 The askopenfilename() function displays the Open dialog (a) and the asksaveasfilename() function
displays the Save As dialog (b).
Now let’s create a simple text editor that uses menus, toolbar buttons, and file dialogs, as
shown in Figure 13.8. The editor enables the user to open and save text files. Listing 13.6
shows the program.
LISTING 13.6 FileEditor.py
1 from tkinter import *
2
3
4
5 class FileEditor:
6 def __init__(self):
7 window = Tk()
8 window.title(“Simple Text Editor”)
from tkinter.filedialog import asksaveasfilename
from tkinter.filedialog import askopenfilename import file dialogs

450 Chapter 13 Files and Exception Handling
9
10 # Create a menu bar
11
12 window.config(menu = menubar) # Display the menu bar
13
14 # Create a pull-down menu and add it to the menu bar
15 operationMenu = Menu(menubar, tearoff = 0)
16 menubar.add_cascade(label = “File”, menu = operationMenu)
17 operationMenu.add_command(label = “Open”,
18 command = )
19 operationMenu.add_command(label = “Save”,
20 command = )
21
22 # Add a tool bar frame
23 frame0 = Frame(window) # Create and add a frame to window
24 frame0.grid(row = 1, column = 1, sticky = W)
25
26 # Create images
27 openImage = PhotoImage(file = “image/open.gif”)
28 saveImage = PhotoImage(file = “image/save.gif”)
29
30 Button(frame0, image = openImage, command =
31 self.openFile).grid(row = 1, column = 1, sticky = W)
32 Button(frame0, image = saveImage,
33 command = self.saveFile).grid(row = 1, column = 2)
34
35 frame1 = Frame(window) # Hold editor pane
36 frame1.grid(row = 2, column = 1)
37
38 scrollbar = Scrollbar(frame1)
39 scrollbar.pack(side = RIGHT, fill = Y)
40 self.text = Text(frame1, width = 40, height = 20,
41 wrap = WORD, yscrollcommand = scrollbar.set)
42 self.text.pack()
43 scrollbar.config(command = self.text.yview)
44
self.saveFile
self.openFile
menubar = Menu(window)
FIGURE 13.8 The editor enables you to open and save files from the File menu or from the toolbar.
menu bar
add menu
open file handler
save file handler
toolbar buttons
scrollbar
text
handle scrolling

13.4 Case Study: Counting Each Letter in a File 451
45 window.mainloop() # Create an event loop
46
47
48 filenameforReading = askopenfilename()
49 infile = open(filenameforReading, “r”)
50 self.text.insert(END, infile.read()) # Read all from the file
51 infile.close() # Close the input file
52
53
54 filenameforWriting = asksaveasfilename()
55 outfile = open(filenameforWriting, “w”)
56 # Write to the file
57 outfile.write(self.text.get(1.0, END))
58 outfile.close() # Close the output file
59
60 FileEditor() # Create GUI
The program creates the File menu (lines 15–20). The File menu contains the menu com-
mands Open for loading a file (line 18) and Save for saving a file (line 20). When the Open
menu is clicked, the openFile method (lines 47–51) is invoked to display the Open dialog to
open a file using the askopenfilename function (line 48). After the user selects a file, the
filename is returned and used to open the file for reading (line 49). The program reads the data
from the file and inserts it into the Text widget (line 50).
When the Save menu is clicked, the saveFile method (lines 53–58) is invoked to display
the Save As dialog to save a file using the asksaveasfilename function (line 54). After the
user enters or selects a file, the filename is returned and used to open the file for writing (line
55). The program reads the data from the Text widget and writes it to the file (line 57).
The program also creates toolbar buttons (lines 30–33) and places them in a frame. The
toolbar buttons are the buttons with image icons. When the Open toolbar button is clicked,
the callback method openFile is invoked (line 31). When the Save toolbar button is
clicked, the callback method saveFile is invoked (line 33).
The program creates a text area using the Text widget tied with a scroll bar (lines 38–43).
The Text widget and scrollbar are placed inside frame1.
13.14 How do you display a file dialog for opening a file?
13.15 How do you display a file dialog for saving a file?
13.4 Case Study: Counting Each Letter in a File
The problem in this case study is to write a program that prompts the user to enter a
filename and counts the number of occurrences of each letter in the file regardless of case.
Here are the steps to solve this problem:
1. Read each line from the file as a string.
2. Use the string’s lower() method to convert all the uppercase letters in the string to
lowercase.
3. Create a list named counts that has 26 int values, each of which counts the occur-
rences of a letter. That is, counts[0] counts the number of times a appears,
counts[1] counts the number of bs, and so on.
4. For each character in the string, determine whether it is a lowercase letter. If so, incre-
ment the corresponding count in the list.
5. Finally, display the count.
Listing 13.7 shows the complete program.
def saveFile(self):
def openFile(self): open file
save file
create GUI
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452 Chapter 13 Files and Exception Handling
LISTING 13.7 CountEachLetter.py
1 def main():
2 filename = input(“Enter a filename: “).strip()
3 infile = open(filename, “r”) # Open the file
4
5 counts = 26 * [0] # Create and initialize counts
6 for line in infile:
7 # Invoke the countLetters function to count each letter
8
9
10 # Display results
11 for i in range(len(counts)):
12 if counts[i] != 0:
13 print(chr(ord(‘a’) + i) + ” appears ” + str(counts[i])
14 + (” time” if counts[i] == 1 else ” times”))
15
16 infile.close() # Close file
17
18 # Count each letter in the string
19 def countLetters(line, counts):
20 for ch in line:
21 if :
22 counts[ord(ch) – ord(‘a’)] += 1
23
24 main() # Call the main function
ch.isalpha()
countLetters(line.lower(), counts)
enter a filename
open file
create a list
read a line
count letters in line
display results
count letters
count a letter
Enter a filename:
a appears 3 times
b appears 3 times
x appears 1 time
input.txt
The main function prompts the user to enter a filename (line 2) and opens the file (line 3).
It creates a list with 26 elements initialized to 0 (line 5). The for loop (lines 6–8) reads each
line from the file, converts the letters to lowercase, and passes them to invoke
countLetters.
The countLetters(line, counts) function examines each character in line. If it is
a lowercase letter, the program adds 1 to its corresponding counts (lines 21–22).
After all the lines are processed, the program displays each letter contained in the file and
its count, if the count is greater than 0 (lines 11–14).
13.5 Retrieving Data from the Web
You can use the urlopen function to open a Uniform Resource Locator (URL) and
read data from the Web.
Using Python, you can write simple code to read data from a Web site. All you need to do is
to open a URL by using the urlopen function, as follows:
infile = urllib.request.urlopen(“http://www.yahoo.com”)
The urlopen function (defined in the urllib.request module) opens a URL resource
like a file. Here is an example that reads and displays the Web content for a given URL:
import urllib.request
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13.5 Retrieving Data from the Web 453
enter a URL
open a URL
read data from URL
count letters in line
infile = urllib.request.urlopen(“http://www.yahoo.com/index.html”)
print(infile.read().decode())
The data read from the URL using infile.read() is raw data in bytes. Invoking the
decode() method converts the raw data to a string.
Let’s rewrite the program in Listing 13.7 to prompt the user to enter a file from a URL on
the Internet rather than from a local system. The program is given in Listing 13.8.
LISTING 13.8 CountEachLetterURL.py
1 import urllib.request
2
3 def main():
4
5
6 s = # Read the content as string
7
8
9
10 # Display results
11 for i in range(len(counts)):
12 if counts[i] != 0:
13 print(chr(ord(‘a’) + i) + ” appears ” + str(counts[i])
14 + (” time” if counts[i] == 1 else ” times”))
15
16 # Count each letter in the string
17
18 counts = 26 * [0] # Create and initialize counts
19 for ch in s:
20 if ch.isalpha():
21
22 return counts
23
24 main() # Call the main function
counts[ord(ch) – ord(‘a’)] += 1
def countLetters(s):
counts = countLetters(s.lower())
infile.read().decode()
infile = urllib.request.urlopen(url)
url = input(“Enter a URL for a file: “).strip()
Enter a filename:
a appears 102 times
b appears 14 times
c appears 31 times
d appears 58 times
e appears 165 times
f appears 27 times
g appears 28 times
h appears 80 times
i appears 68 times
k appears 3 times
l appears 42 times
m appears 13 times
n appears 77 times
o appears 92 times
p appears 15 times
q appears 1 time
r appears 79 times
s appears 43 times
t appears 126 times
u appears 21 times
v appears 24 times
w appears 28 times
y appears 10 times
http://cs.armstrong.edu/liang/data/Lincoln.txt
display results
count letters
count a letter

454 Chapter 13 Files and Exception Handling
The main function prompts the user to enter a URL (line 4), opens the URL (line 5), and
reads data from the URL into a string (line 6). The program converts the string to lowercase
and invokes the countLetters function to count the occurrences of each letter in the string
(line 8). The function returns a list showing how many times each letter occurs.
The countLetters(s) function creates a list of 26 elements with an initial value of 0
(line 18). The function examines each character in s. If it is a lowercase letter, the program
adds 1 to its corresponding counts (lines 20–21).
Note
The http:// prefix is required in the URL for the urlopen function to recognize a
valid URL. It would be wrong if you enter a URL like this:
cs.armstrong.edu/liang/data/Lincoln.txt
13.16 How do you open a Web page from a Python program?
13.17 What function can be used to return a raw string from a normal string?
13.6 Exception Handling
Exception handling enables a program to deal with exceptions and continue its
normal execution.
When running the programs in the preceding sections, what happens if the user enters a file or a
URL that does not exist? The program would be aborted and raise an error. For example, if you try
to run Listing 13.7 by entering a nonexistent filename, the program would report this IOError:
Handle exceptions
why exception handling?
c:\pybook\python CountEachLetter.py
Enter a filename:
Traceback (most recent call last):
File “C:\pybook\CountEachLetter.py”, line 23, in
main()
File “C:\pybook\CountEachLetter.py”, line 4, in main
infile = open(filename, “r”) # Open the file
IOError: [Errno 22] Invalid argument: ‘NonexistentOrIncorrectFile.txt\r’
NonexistentOrIncorrectFile.txt
The lengthy error message is called a stack traceback or traceback. The traceback gives
information on the statement that caused the error by tracing back to the function calls that led
to this statement. The line numbers of the function calls are displayed in the error message for
tracing the errors.
An error that occurs at runtime is also called an exception. How can you deal with an
exception so that the program can catch the error and prompt the user to enter a correct file-
name? This can be done using Python’s exception handling syntax.
The syntax for exception handling is to wrap the code that might raise (or throw) an excep-
tion in a try clause, as follows:
try:

except :

Here, contains the code that may raise an exception. When an exception occurs,
the rest of the code in is skipped. If the exception matches an exception type, the cor-
responding handler is executed. is the code that processes the exception. Now
you can insert new code for exception handling into lines 2 and 3 in Listing 13.7 to let the user
enter a new filename if the input is incorrect, as shown in Listing 13.9.
traceback
try … except
VideoNote
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13.6 Exception Handling 455
try clause
enter a filename
open file
create a list
read a line
count letters in line
LISTING 13.9 CountEachLetterWithExceptionHandling.py
1 def main():
2 while True:
3
4 filename = input(“Enter a filename: “).strip()
try:
Enter a filename:
File NonexistentOrIncorrectFile does not exist. Try again
Enter a filename:
File Lincoln.dat does not exist. Try again
Enter a filename:
a appears 102 times
b appears 14 times
…
…
w appears 28 times
y appears 10 times
Lincoln.txt
Lincoln.dat
NonexistentOrIncorrectFile
The program uses a while loop to repeatedly prompt the user to enter a filename (lines
2–8). If the name is correct, the program exits the loop (line 6). If an IOError exception is
raised by invoking the open function (line 5), the except clause is executed to process the
exception (lines 7–8) and the loop continues.
The try/except block works as follows:
■ First, the statements in the body between try and except are executed.
■ If no exception occurs, the except clause is skipped. In this case, the break state-
ment is executed to exit the while loop.
display results
count letters
count a letter
try … except
if an exception occurs
5 infile = open(filename, “r”) # Open the file
6 break
7
8 print(“File ” + filename + ” does not exist. Try again”)
9
10 counts = 26 * [0] # Create and initialize counts
11 for line in infile:
12 # Invoke the countLetters function to count each letter
13 countLetters(line.lower(), counts)
14
15 # Display results
16 for i in range(len(counts)):
17 if counts[i] != 0:
18 print(chr(ord(‘a’) + i) + ” appears ” + str(counts[i])
19 + (” time” if counts[i] == 1 else ” times”))
20
21 infile.close() # Close file
22
23 # Count each letter in the string
24 def countLetters(line, counts):
25 for ch in line:
26 if ch.isalpha():
27 counts[ord(ch) – ord(‘a’)] += 1
28
29 main()
except IOError:

456 Chapter 13 Files and Exception Handling
multiple excepts
else
finally clause
enter two numbers
except ZeroDivisionError
except SyntaxError
except
else
finally
■ If an exception occurs during execution of the try clause, the rest of the clause is
skipped. In this case, if the file does not exist, the open function raises an exception
and the break statement is skipped.
■ When an exception occurs, if the exception type matches the exception name after
the except keyword, the except clause is executed, and then the execution contin-
ues after the try statement.
■ If an exception occurs and it does not match the exception name in the except
clause, the exception is passed on to the caller of this function; if no handler is found,
it is an unhandled exception and execution stops with an error message displayed.
A try statement can have more than one except clause to handle different exceptions.
The statement can also have an optional else and/or finally statement, in a syntax like this:
1 try:
2
3 except :
4
5 …
6 except :
7
8 except:
9
10 else:
11 12 finally:
13 The multiple excepts are similar to elifs. When an exception occurs, it is checked to
match an exception in an except clause after the try clause sequentially. If a match is found,
the handler for the matching case is executed and the rest of the except clauses are skipped.
Note that the in the last except clause may be omitted. If the exception
does not match any of the exception types before the last except clause (line 8), the
(line 9) for the last except clause is executed.
A try statement may have an optional else clause, which is executed if no exception is
raised in the try body.
A try statement may have an optional finally clause, which is intended to define clean-
up actions that must be performed under all circumstances. Listing 13.10 gives an example of
using exception handling.
LISTING 13.10 TestException.py
1 def main():
2
3 number1, number2 = eval(
4 input(“Enter two numbers, separated by a comma: “))
5 result = number1 / number2
6 print(“Result is”, result)
7
8 print(“Division by zero!”)
9
10 print(“A comma may be missing in the input”)
11
12 print(“Something wrong in the input”)
13
14 print(“No exceptions”)
15 finally:
else:
except:
except SyntaxError:
except ZeroDivisionError:
try:

13.7 Raising Exceptions 457
16 print(“The finally clause is executed”)
17
18 main() # Call the main function
Enter two numbers, separated by a comma:
Result is 0.75
No exceptions
The finally clause is executed
3, 4
Enter two numbers, separated by a comma:
Division by zero!
The finally clause is executed
2, 0
Enter two numbers, separated by a comma:
A comma may be missing in the input
The finally clause is executed
2 3
Enter two numbers, separated by a comma:
Something wrong in the input
The finally clause is executed
a, v
When you enter 3, 4, the program computes the division and displays the result, then the
else clause is executed, and finally the finally clause is executed.
When you enter 2, 0, a ZeroDivisionError is raised when executing the division (line
5). The except clause in line 7 caught this exception and processed it, and the finally
clause is then executed.
When you enter 2 3, a SyntaxError is raised. The except clause in line 9 caught this
exception and processed it, and the finally clause is then executed.
When you enter a, v, an exception is raised. This exception is processed by the except
clause in line 11, and the finally clause is then executed.
13.7 Raising Exceptions
Exceptions are wrapped in objects, and objects are created from classes. An exception
is raised from a function.
You learned how to write the code to handle exceptions in the preceding section. Where does
an exception come from? How is an exception created? The information pertaining to an
exception is wrapped in an object. An exception is raised from a function. When a function
detects an error, it creates an object from an appropriate exception class and throws the excep-
tion to the caller of the function, using the following syntax:
raise ExceptionClass(“Something is wrong”)
Here’s how this works. Suppose the program detects that an argument passed to a function
violates the function’s contract; for example, the argument must be nonnegative, but a nega-
tive argument is passed. The program can create an instance of RuntimeError and raise the
exception, as follows:
ex = RuntimeError(“Wrong argument”)
raise ex
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458 Chapter 13 Files and Exception Handling
import GeometricObject
extend GeometricObject
initialize radius
raise exception
set radius
create a circle
handle exception
c1’s area is 78.53981633974483
Invalid radius
Or, if you prefer, you can combine the preceding two statements in one like this:
raise RuntimeError(“Wrong argument”)
You can now modify the setRadius method in the Circle class in Listing 12.2 to raise a
RuntimeError exception if the radius is negative. The revised Circle class is given in
Listing 13.11.
LISTING 13.11 CircleWithException.py
1 from GeometricObject import GeometricObject
2 import math
3
4 class Circle(GeometricObject):
5 def __init__(self, radius):
6 super().__init__()
7 self.setRadius(radius)
8
9 def getRadius(self):
10 return self.__radius
11
12
13 if radius < 0: 14 15 else: 16 self.__radius = radius 17 18 def getArea(self): 19 return self.__radius * self.__radius * math.pi 20 21 def getDiameter(self): 22 return 2 * self.__radius 23 24 def getPerimeter(self): 25 return 2 * self.__radius * math.pi 26 27 def printCircle(self): 28 print(self.__str__() + " radius: " + str(self.__radius)) The test program in Listing 13.12 creates circle objects using the new Circle class in Listing 13.11. LISTING 13.12 TestCircleWithException.py 1 from CircleWithException import Circle 2 3 try: 4 c1 = Circle(5) 5 print("c1's area is", c1.getArea()) 6 c2 = Circle(-5) 7 print("c2's area is", c2.getArea()) 8 c3 = Circle(0) 9 print("c3's area is", c3.getArea()) 10 except RuntimeException: 11 print("Invalid radius") raise RuntimeError("Negative radius") def setRadius(self, radius): 13.7 Raising Exceptions 459 When attempting to create a Circle object with a negative radius (line 6), a RuntimeError is raised. The exception is caught in the except clause in lines 10–11. Now you know how to raise exceptions and how to handle exceptions. So what are the benefits of using exception handling? It enables a function to throw an exception to its caller. The caller can handle this exception. Without this capability, the called function itself must handle the exception or terminate the program. Often the called function does not know what to do in case of an error. This is typically the case for library functions. The library function can detect the error, but only the caller knows what needs to be done when an error occurs. The essential benefit of exception handling is to separate the detection of an error (done in a called function) from the handling of an error (done in the calling method). Many library functions raise exceptions, such as ZeroDivisionError, TypeError, and IndexError. You can use the try-except syntax to catch and process the exceptions. Functions may invoke other functions in a chain of function calls. Consider an example involving multiple function calls. Suppose the main function invokes function1, function1 invokes function2, function2 invokes function3, and function3 raises an exception, as shown in Figure 13.9. Consider the following scenario: ■ If the exception type is Exception3, it is caught by the except block for handling this exception in function2. statement5 is skipped, and statement6 is executed. ■ If the exception type is Exception2, function2 is aborted, the control is returned to function1, and the exception is caught by the except block for handling Exception2 in function1. statement3 is skipped, and statement4 is executed. ■ If the exception type is Exception1, function1 is aborted, the control is returned to the main function, and the exception is caught by the except block for handling Exception1 in the main function. statement1 is skipped, and statement2 is executed. ■ If the exception is not caught in function2, function1, or main, the program terminates, and statement1 and statement2 are not executed. exception handling benefits def main(): ... try: ... invoke function1 statement1 except Exception1: Handle Exception1 statement2; def function1(): ... try: ... invoke function2 statement3 except Exception2: Handle Exception2 statement4 def function2(): ... try: ... invoke function3 statement5 except Exception3: Handle Exception3 statement6 An exception is thrown in function3 Call Stack main function main function function1 main function function1 main function function1 function2 function2 function3 FIGURE 13.9 If an exception is not caught in the current function, it is passed to its caller. The process is repeated until the exception is caught or passed to the main function. 460 Chapter 13 Files and Exception Handling read a number catch exception Enter a number: The number entered is 34 34 Enter a number: Exception: name 'one' is not defined one When you enter a nonnumeric value, an object of NameError is thrown from line 2. This object is assigned to variable ex. So, you can access it to handle the exception. The __str__() method in ex is invoked to return a string that describes the exception. In this case the string is name 'one' is not defined. 13.9 Defining Custom Exception Classes You can define a custom exception class by extending BaseException or a subclass of BaseException. So far we have used Python’s built-in exception classes such as ZeroDivisionError, SyntaxError, RuntimeError, and NameError in this chapter. Are there any other types of exceptions you can use? Yes, Python has many more built-in exceptions. Figure 13.10 shows some of them. Note The class names Exception, StandardError, and RuntimeError are somewhat confusing. All three of these classes are exceptions, and all of the errors occur at runtime. The BaseException class is the root of exception classes. All Python exception classes inherit directly or indirectly from BaseException. As you can see, Python provides quite a 13.8 Processing Exceptions Using Exception Objects You can access an exception object in the except clause. As stated earlier, an exception is wrapped in an object. To throw an exception, you first create an exception object and then use the raise keyword to throw it. Can this exception object be accessed from the except clause? Yes. You can use the following syntax to assign the excep- tion object to a variable: try

With this syntax, when the except clause catches the exception, the exception object is
assigned to a variable named ex. You can now use the object in the handler.
Listing 13.13 gives an example that prompts the user to enter a number and displays the
number if the input is correct. Otherwise, the program displays an error message.
LISTING 13.13 ProcessExceptionObject.py
1 try:
2 number = eval(input(“Enter a number: “))
3 print(“The number entered is”, number)
4 except NameError as :
5 print(“Exception:”, )ex
ex
except ExceptionType as ex:
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Key
Point

13.9 Defining Custom Exception Classes 461
few exception classes. You can also define your own exception classes, derived from
BaseException or from a subclass of BaseException, such as RuntimeError.
The setRadius method in the Circle class in Listing 13.11 throws a RuntimeError
exception if the radius is negative. The caller can catch this exception, but the caller does not
know what radius caused this exception. To fix this problem, you can define a custom excep-
tion class to store the radius, as shown in Listing 13.14.
LISTING 13.14 InvalidRadiusException.py
1 class :
2 def __init__(self, radius):
3 super().__init__()
4 self.radius = radius
This custom exception class extends RuntimeError (line 1). The initializer simply
invokes the superclass’s initializer (line 3) and sets the radius in the data field (line 4).
Now let’s modify the setRadius(radius) method in the Circle class to raise an
InvalidRadiusException if the radius is negative, as shown in Listing 13.15.
LISTING 13.15 CircleWithCustomException.py
1 from GeometricObject import GeometricObject
2 from InvalidRadiusException import InvalidRadiusException
3 import math
4
5
6 def __init__(self, radius):
7
8
9
10 def getRadius(self):
11 return self.__radius
12
13 def setRadius(self, radius):
self.setRadius(radius)
super().__init__()
class Circle(GeometricObject):
InvalidRadiusException(RuntimeError)
BaseException
Exception
ZeroDivisionError IndentationError
StandardError
RuntimeError LookupError SyntaxErrorArithmeticError EnvironmentError
IOError OSError IndexError KeyError
FIGURE 13.10 Exceptions raised are instances of the classes shown in this diagram, or of subclasses of one of these
classes.
extend RuntimeError
import GeometricObject
import
InvalidRadiusException
extend GeometricObject
initialize radius
setRadius

462 Chapter 13 Files and Exception Handling
14
15 self.__radius = radius
16 else:
17
18
19 def getArea(self):
20 return self.__radius * self.__radius * math.pi
21
22 def getDiameter(self):
23 return 2 * self.__radius
24
25 def getPerimeter(self):
26 return 2 * self.__radius * math.pi
27
28 def printCircle(self):
29 print(self.__str__(), “radius:”, self.__radius)
The setRadius method raises an InvalidRadiusException if the radius is negative
(line 17). Listing 13.16 gives a test program that creates circle objects using the new Circle
class in Listing 13.15.
LISTING 13.16 TestCircleWithCustomException.py
1 from CircleWithCustomException import Circle
2 from InvalidRadiusException import InvalidRadiusException
3
4 try:
5 c1 = Circle(5)
6 print(“c1’s area is”, c1.getArea())
7 c2 = Circle(-5)
8 print(“c2’s area is”, c2.getArea())
9 c3 = Circle(0)
10 print(“c3’s area is”, c3.getArea())
11 except InvalidRadiusException as ex:
12 print(“The radius”, , “is invalid”)
13 except Exception:
14 print(“Something is wrong”)
ex.radius
raise InvalidRadiusException(radius)
if radius >= 0:
get radius
c1’s area is 78.53981633974483
The radius -5 is invalid
When creating a Circle object with a negative radius (line 7), an
InvalidRadiusException is raised. The exception is caught in the except clause in
lines 11–12.
The order in which exceptions are specified in except blocks is important, because
Python finds a handler in this order. If an except block for a superclass type appears before
an except block for a subclass type, the except block for the subclass type will never be
executed. Thus, it would be wrong to write the code as follows:
try:
….
print(“Something is wrong”)
print(“Invalid radius”)
except InvalidRadiusException:
except Exception:
order of exception handlers

13.9 Defining Custom Exception Classes 463
13.18 Suppose that statement2 causes an exception in the following try-except
block:
try:
statement1
statement3
except Exception1:
# Handle exception 1
except Exception2:
# Handle exception 2
statement4
Answer the following questions:
■ Will statement3 be executed?
■ If the exception is not caught, will statement4 be executed?
■ If the exception is caught in the except block, will statement4 be executed?
13.19 What is displayed when the following program is run?
try:
list = 10 * [0]
x = list[10]
print(“Done “)
except IndexError:
print(“Index out of bound”)
13.20 What is displayed when the following program is run?
def main():
try:
f()
print(“After the function call”)
except ZeroDivisionError:
print(“Divided by zero!”)
except:
print(“Exception”)
def f():
print(1 / 0)
main() # Call the main function
13.21 What is displayed when the following program is run?
def main():
try:
f()
print(“After the function call”)
except IndexError:
print(“Index out of bound”)
except:
print(“Exception in main”)
def f():
try:
s =”abc”
print(s[3])
statement2
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464 Chapter 13 Files and Exception Handling
except ZeroDivisionError:
print(“Divided by zero!”)
main() # Call the main function
13.22 Suppose that statement2 causes an exception in the following statement:
try:
statement1
statement3
except Exception1:
# Handle exception
except Exception2:
# Handle exception
except Exception3:
# Handle exception
finally:
statement4
statement5
Answer the following questions:
■ Will statement5 be executed if the exception is not caught?
■ If the exception is of type Exception3, will statement4 be executed, and will
statement5 be executed?
13.23 How do you raise an exception in a function?
13.24 What are the benefits of using exception handling?
13.25 What is displayed when the following program is run?
try:
lst = 10 * [0]
x = lst[9]
print(“Done”)
except IndexError:
print(“Index out of bound”)
else:
print(“Nothing is wrong”)
finally:
print(“Finally we are here”)
print(“Continue”)
13.26 What is displayed when the following program is run?
try:
lst = 10 * [0]
x = lst[10]
print(“Done “)
except IndexError:
print(“Index out of bound”)
else:
print(“Nothing is wrong”)
finally:
print(“Finally we are here”)
print(“Continue”)
statement2

13.10 Binary IO Using Pickling 465
13.27 What is wrong in the following code?
try:
# Some code here
…
except ArithmeticError:
print(“ArithmeticError”)
except ZeroDivisionError:
print(“ZeroDivisionError”)
print(“Continue”)
13.28 How do you define a custom exception class?
13.10 Binary IO Using Pickling
To perform binary IO using pickling, open a file using the mode rb or wb for reading
binary or writing binary and invoke the pickle module’s dump and load functions to
write and read data.
You can write strings and numbers to a file. Can you write any object such as a list directly to
a file? Yes. This would require binary IO. There are many ways to perform binary IO in
Python. This section introduces binary IO using the dump and load functions in the pickle
module.
The Python pickle module implements the powerful and efficient algorithms for serializ-
ing and deserializing objects. Serializing is the process of converting an object into a stream
of bytes that can be saved to a file or transmitted on a network. Deserializing is the opposite
process that extracts an object from a stream of bytes. Serializing/deserializing is also known
as pickling/unpickling or dumping/loading objects in Python.
13.10.1 Dumping and Loading Objects
As you know, all data in Python are objects. The pickle module enables you to write and
read any data using the dump and load functions. Listing 13.17 demonstrates these functions.
LISTING 13.17 BinaryIODemo.py
1 import pickle
2
3 def main():
4 # Open file for writing binary
5 outfile = open(“pickle.dat”, “wb”)
6 pickle.dump(45, outfile)
7 pickle.dump(56.6, outfile)
8 pickle.dump(“Programming is fun”, outfile)
9 pickle.dump([1, 2, 3, 4], outfile)
10 outfile.close() # Close the output file
11
12 # Open file for reading binary
13 infile = open(“pickle.dat”, “rb”)
14 print(pickle.load(infile))
15 print(pickle.load(infile))
16 print(pickle.load(infile))
17 print(pickle.load(infile))
18 infile.close() # Close the input file
19
20 main() # Call the main function
serializing
deserializing
pickle module
open for binary write
dump an int
dump a float
dump a string
dump a list
close file
open for binary read
load an object
close file
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466 Chapter 13 Files and Exception Handling
45
56.6
Programming is fun
[1, 2, 3, 4]
To use pickle, you need to import the pickle module (line 1). To write objects to a file,
open the file using the mode wb for writing binary (line 5) and use the dump(object)
method to write the object into the file (lines 6–9). This method serializes the object into a
stream of bytes and stores them in the file.
The program closes the file (line 10) and opens it for reading binary (line 13). The load
method is used to read the objects (lines 14–17). This method reads a stream of bytes and
deserializes them into an object.
13.10.2 Detecting the End of File
If you don’t know how many objects are in the file, how do you read all the objects? You can
repeatedly read an object using the load function until it throws an EOFError (end of file)
exception. When this exception is raised, catch it and process it to end the file-reading process.
The program in Listing 13.18 stores an unspecified number of integers in a file by using
object IO, and then it reads all the numbers back from the file.
LISTING 13.18 DetectEndOfFile.py
1 import pickle
2
3 def main():
4 # Open file for writing binary
5
6
7 data = eval(input(“Enter an integer (the input exits ” +
8 “if the input is 0): “))
9 while data != 0:
10
11 data = eval(input(“Enter an integer (the input exits ” +
12 “if the input is 0): “))
13
14 outfile.close() # Close the output file
15
16 # Open file for reading binary
17
18
19 end_of_file = False
20
21 try:
22 print( , end = ” “)
23 except EOFError:
24
25
26 infile.close() # Close the input file
27
28 print(“\nAll objects are read”)
29
30 main() # Call the main function
end_of_file = True
pickle.load(infile)
while not end_of_file:
infile = open(“numbers.dat”, “rb”)
pickle.dump(data, outfile)
outfile = open(“numbers.dat”, “wb”)open for binary write
dump an int
close file
open for binary read
load an object
handle exception
set end_of_file

13.11 Case Study: Address Book 467
Enter an integer (the input exits if the input is 0):
Enter an integer (the input exits if the input is 0):
Enter an integer (the input exits if the input is 0):
Enter an integer (the input exits if the input is 0):
Enter an integer (the input exits if the input is 0):
4 5 7 9
All objects are read
0
9
7
5
4
The program opens the file for writing binary (line 5) and repeatedly prompts the
user to enter an integer and saves it to the file using the dump function (line 10) until the
integer is 0.
The program closes the file (line 14) and reopens it for reading binary (line 17). It repeat-
edly reads an object using the load function (line 22) in a while loop until an EOFError
exception occurs. When an EOFError exception occurs, end_of_file is to set to True,
which terminates the while loop (line 20).
As shown in the sample output, the user entered four integers and they are saved and then
read back and displayed on the console.
13.29 How do you open a file for writing objects and reading objects?
13.30 How do you invoke the function to write an object and to read an object?
13.31 What is wrong if the code in lines 20–24 in Listing 13.18 is replaced by the fol-
lowing code?
while not end_of_file:
try:
print(pickle.load(infile), end = ” “)
except EOFError:
end_of_file = True
finally:
infile.close() # Close the input file
13.32 Can you replace the code in lines 20–24 in Listing 13.18 with the following code?
try:
while not end_of_file:
print(pickle.load(infile), end = ” “)
except EOFError:
print(“\nAll objects are read”)
finally:
infile.close() # Close the input file
13.11 Case Study: Address Book
The problem in this case study is to create an address book using binary IO.
Now we will use object IO to create a useful project for storing and viewing an address book.
The user interface of the program is shown in Figure 13.11. The Add button stores a new
FIGURE 13.11 AddressBook stores and retrieves addresses from a file.
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468 Chapter 13 Files and Exception Handling
address at the end of the file. The First, Next, Previous, and Last buttons retrieve the first,
next, previous, and last addresses from the file, respectively.
We will define a class named Address to represent an address and use a list to store all the
addresses. When the Add button is clicked, the program creates an Address object with
the name, street, city, state, and ZIP code collected from the user input, appends the object to
the list, and stores the list to a file using binary IO. Assume that the file is named address.dat.
When the program is launched, it first reads the list from the file and displays the first
address from the list in the user interface. If the file is empty, it displays empty entries. The
program is given in Listing 13.19.
LISTING 13.19 AddressBook.py
1 import pickle
2 import os.path
3 from tkinter import * # Import all definitions from tkinter
4 import tkinter.messagebox
5
6
7 def __init__(self, name, street, city, state, zip):
8 self.name = name
9 self.street = street
10 self.city = city
11 self.state = state
12 self.zip = zip
13
14
15
16 window = Tk() # Create a window
17 window.title(“AddressBook”) # Set title
18
19
20 self.streetVar = StringVar()
21 self.cityVar = StringVar()
22 self.stateVar = StringVar()
23 self.zipVar = StringVar()
24
25 frame1 = Frame(window)
26 frame1.pack()
27 Label(frame1, text = “Name”).grid(row = 1,
28 column = 1, sticky = W)
29 Entry(frame1, textvariable = self.nameVar,
30 width = 40).grid(row = 1, column = 2)
31
32 frame2 = Frame(window)
33 frame2.pack()
34 Label(frame2, text = “Street”).grid(row = 1,
35 column = 1, sticky = W)
36 Entry(frame2, textvariable = self.streetVar,
37 width = 40).grid(row = 1, column = 2)
38
39 frame3 = Frame(window)
40 frame3.pack()
41 Label(frame3, text = “City”, width = 5).grid(row = 1,
42 column = 1, sticky = W)
43 Entry(frame3,
44 textvariable = self.cityVar).grid(row = 1, column = 2)
45 Label(frame3, text = “State”).grid(row = 1,
46 column = 3, sticky = W)
47 Entry(frame3, textvariable = self.stateVar,
self.nameVar = StringVar()
def __init__(self):
class AddressBook:
class Address:Address class
entry variables
create UI

13.11 Case Study: Address Book 469
48 width = 5).grid(row = 1, column = 4)
49 Label(frame3, text = “ZIP”).grid(row = 1,
50 column = 5, sticky = W)
51 Entry(frame3, textvariable = self.zipVar,
52 width = 5).grid(row = 1, column = 6)
53
54 frame4 = Frame(window)
55 frame4.pack()
56 Button(frame4, text = “Add”,
57 command = self.processAdd).grid(row = 1, column = 1)
58 btFirst = Button(frame4, text = “First”,
59 command = self.processFirst).grid(row = 1, column = 2)
60 btNext = Button(frame4, text = “Next”,
61 command = self.processNext).grid(row = 1, column = 3)
62 btPrevious = Button(frame4, text = “Previous”, command =
63 self.processPrevious).grid(row = 1, column = 4)
64 btLast = Button(frame4, text = “Last”,
65 command = self.processLast).grid(row = 1, column = 5)
66
67
68
69
70 if len(self.addressList) > 0:
71 self.setAddress()
72
73 window.mainloop() # Create an event loop
74
75
76 outfile = open(“address.dat”, “wb”)
77 pickle.dump(self.addressList, outfile)
78 tkinter.messagebox.showinfo(
79 “Address saved”, “A new address is saved”)
80 outfile.close()
81
82
83 if not os.path.isfile(“address.dat”):
84 return [] # Return an empty list
85
86 try:
87 infile = open(“address.dat”, “rb”)
88 addressList = pickle.load(infile)
89 except EOFError:
90 addressList = []
91
92 infile.close()
93 return addressList
94
95
96 address = Address(self.nameVar.get(),
97 self.streetVar.get(), self.cityVar.get(),
98 self.stateVar.get(), self.zipVar.get())
99 self.addressList.append(address)
100 self.saveAddress()
101
102
103 self.current = 0
104 self.setAddress()
105
106
107 if self.current < len(self.addressList) - 1: def processNext(self): def processFirst(self): def processAdd(self): def loadAddress(self): def saveAddress(self): self.current = 0 self.addressList = self.loadAddress() create buttons load addresses initialize current setAddress saveAddress store list loadAddress return empty list read list return list processAdd create address append address store address list processFirst initialize current set address processNext 470 Chapter 13 Files and Exception Handling 108 self.current += 1 109 self.setAddress() 110 111 112 print("Left as exercise") 113 114 115 print("Left as exercise") 116 117 118 self.nameVar.set(self.addressList[self.current].name) 119 self.streetVar.set(self.addressList[self.current].street) 120 self.cityVar.set(self.addressList[self.current].city) 121 self.stateVar.set(self.addressList[self.current].state) 122 self.zipVar.set(self.addressList[self.current].zip) 123 124 AddressBook() # Create GUI The Address class is defined with the __init__ method that creates an Address object with a name, street, city, state, and ZIP code (lines 6–12). The __init__ method in AddressBook creates the user interface for displaying and processing addresses (lines 25–65). It reads the address list from the file (line 67) and sets the current index for the address in the list to 0 (line 68). If the address list is not empty, the pro- gram displays the first address (lines 70–71). The saveAddress method writes the address list to the file (line 77) and displays a mes- sage dialog to alert the user that a new address has been added (lines 78–79). The loadAddress method reads the address list to the file (line 88). If the file does not exist, the program returns an empty list (lines 83–84). The processAdd method creates an Address object using the values from the entries. It appends the object to the list (line 99) and invokes the saveAddress method to store the newly updated list to the file (line 100). The processFirst method resets current to 0, which points to the first address in the address list (line 103). It then sets the address in the entries by invoking the setAddress method (line 104). The processNext method moves current to point to the next address in the list (line 108) if current is not pointing to the last address in the list (line 107) and resets the address in the entries (line 109). The setAddress method sets the address fields for the entries (lines 117–122). The meth- ods processPrevious and processLast are left as an exercise. KEY TERMS def setAddress(self): def processLast(self): def processPrevious(self):processPrevious processLast setAddress create GUI absolute filename 440 binary file 440 deserializing 465 directory path 440 file pointer 442 raw string 441 relative filename 440 serializing 465 text file 440 traceback 454 CHAPTER SUMMARY 1. You can use file objects to read/write data from/to files. You can open a file to create a file object with mode r for reading, w for writing, and a for appending. 2. You can use the os.path.isfile(f) function to check if a file exists. Programming Exercises 471 3. Python has a file class that contains the methods for reading and writing data, and for closing a file. 4. You can use the read(), readline(), and readlines() methods to read data from a file. 5. You can use the write(s) method to write a string to a file. 6. You should close the file after the file is processed to ensure that the data is saved properly. 7. You can read a Web resource just like reading data from a file. 8. You can use exception handling to catch and handle runtime errors. You place the code that may raise an exception in the try clause, list the exceptions in the except clauses, and process the exception in the except clause. 9. Python provides built-in exception classes such as ZeroDivisionError, SyntaxError, and RuntimeError. All Python exception classes inherit directly or indirectly from BaseException. You can also define your own exception class derived from BaseException or from a subclass of BaseException, such as RuntimeError. 10. You can use the Python pickle module to store objects in a file. The dump function writes an object to the file and the load function reads an object from the file. TEST QUESTIONS Do test questions for this chapter online at www.cs.armstrong.edu/liang/py/test.html. PROGRAMMING EXERCISES Sections 13.2–13.5 **13.1 (Remove text) Write a program that removes all the occurrences of a specified string from a text file. Your program should prompt the user to enter a filename and a string to be removed. Here is a sample run: Enter a filename: Enter the string to be removed: Done morning test.txt *13.2 (Count characters, words, and lines in a file) Write a program that will count the number of characters, words, and lines in a file. Words are separated by a white- space character. Your program should prompt the user to enter a filename. Here is a sample run: Enter a filename: 1777 characters 210 words 71 lines test.txt www.cs.armstrong.edu/liang/py/test.html 472 Chapter 13 Files and Exception Handling *13.3 (Process scores in a text file) Suppose that a text file contains an unspecified num- ber of scores. Write a program that reads the scores from the file and displays their total and average. Scores are separated by blanks. Your program should prompt the user to enter a filename. Here is a sample run: Enter a filename: There are 70 scores The total is 800 The average is 33.33 scores.txt *13.4 (Write/read data) Write a program that writes 100 integers created randomly into a file. Integers are separated by a space in the file. Read the data back from the file and display the sorted data. Your program should prompt the user to enter a file- name. If the file already exists, do not override it. Here is a sample run: Enter a filename: The file already exists test.txt Enter a filename: 20 34 43 ... 50 test1.txt **13.5 (Replace text) Write a program that replaces text in a file. Your program should prompt the user to enter a filename, an old string, and a new string. Here is a sample run: Enter a filename: Enter the old string to be replaced: Enter the new string to replace the old string: Done afternoon morning test.txt *13.6 (Count words) Write a program that counts the number of words in President Abraham Lincoln’s Gettysburg Address from http://cs.armstrong.edu/liang/data/ Lincoln.txt. **13.7 (Game: hangman) Rewrite Exercise 10.29. The program reads the words stored in a text file named hangman.txt. Words are delimited by spaces. 13.8 (Encrypt files) Encode the file by adding 5 to every byte in the file. Write a pro- gram that prompts the user to enter an input filename and an output filename and saves the encrypted version of the input file to the output file. 13.9 (Decrypt files) Suppose a file is encrypted using the scheme in Exercise 13.8. Write a program to decode an encrypted file. Your program should prompt the user to enter an input filename and an output filename and should save the unen- crypted version of the input file to the output file. http://cs.armstrong.edu/liang/data/Lincoln.txt http://cs.armstrong.edu/liang/data/Lincoln.txt Programming Exercises 473 File 6 0 30 30 1 2 1 90 30 0 3 2 30 90 0 3 4 3 90 90 1 2 4 5 4 30 150 2 3 5 5 90 150 3 4 (a) (b) 0 2 3 1 4 5 FIGURE 13.12 The program reads the information about the graph and displays it visually. Sections 13.6–13.9 13.10 (The Rational class) Modify the Rational class in Listing 8.4, Rational.py, to throw a RuntimeError exception if the denominator is 0. 13.11 (The Triangle class) Modify the Triangle class in Programming Exercise 12.1 to throw a RuntimeError exception if the three given sides cannot form a triangle. 13.12 (The TriangleError class) Define an exception class named TriangleError that extends RuntimeError. The TriangleError class contains the private data fields side1, side2, and side3 with accessor methods for the three sides of a triangle. Modify the Triangle class in Exercise 12.1 to throw a TriangleError exception if the three given sides cannot form a triangle. Sections 13.10–13.11 **13.13 (Tkinter: display a graph) A graph consists of vertices and edges that connect vertices. Write a program that reads a graph from a file and displays it on a panel. The first line in the file contains a number that indicates the number of vertices (n). The vertices are labeled as 0, 1, ..., n-1. Each subsequent line, with the format u x y v1, v2, ..., describes that the vertex u is located at position (x, y) with the edges (u, v1), (u, v2), and so on. Figure 13.12a gives an example of the file for a graph. Your program prompts the user to enter the name of the file, reads data from the file, and displays the graph on a panel, as shown in Figure 13.12b. **13.14 (Tkinter: display a graph) Rewrite Exercise 13.13 to read data from a Web URL such as http://cs.armstrong.edu/liang/data/graph.txt. The program should prompt the user to enter the URL for the file. **13.15 (Tkinter: address book) Rewrite the address book case study in Section 13.11 with the following improvements, as shown in Figure 13.13: (a) Add a new button named Update. Clicking it enables the user to update the address that is currently displayed. (b) Add a label below the buttons to display the current address location and the total number of addresses in the list. (c) Implement the unfinished processPrevious and processLast methods in Listing 13.19. http://cs.armstrong.edu/liang/data/graph.txt 474 Chapter 13 Files and Exception Handling FIGURE 13.13 The new Update button and status label are added in the AddressBook UI. **13.16 (Create large dataset) Create a data file with 1000 lines. Each line in the file con- sists of a faculty first name, last name, rank, and salary. Faculty’s first name and last name for the ith line are FirstNamei and LastNamei. The rank is randomly generated as assistant, associate, and full. The salary is randomly generated as a number with two digits after the decimal point. The salary for assistant professor should be in the range from 50,000 to 80,000, for associate professor from 60,000 to 110,000, and for full professor from 75,000 to 130,000. Save the file in Salary.txt. Here are some sample data:. FirstName1 LastName1 assistant 60055.95 FirstName2 LastName2 associate 81112.45 . . . FirstName1000 LastName1000 full 92255.21 *13.17 (Process large dataset) A university posts its employee salary at http://cs .armstrong.edu/liang/data/Salary.txt. Each line in the file consists of faculty first name, last name, rank, and salary (see Exercise 13.16). Write a program to display the total salary for assistant professors, associate professors, full professors, and all faculty, respectively, and display the average salary for assistant professors, associate professors, full professors, and all faculty, respectively. http://cs.armstrong.edu/liang/data/Salary.txt http://cs.armstrong.edu/liang/data/Salary.txt TUPLES, SETS, AND DICTIONARIES Objectives ■ To create tuples (§14.2). ■ To use tuples as fixed lists to prevent elements from being added, deleted, or replaced (§14.2). ■ To apply common sequence operations for tuples (§14.2). ■ To create sets (§14.3.1). ■ To add and remove elements in a set using the add and remove methods (§14.3.2). ■ To use the len, min, max, and sum functions for a set of elements (§14.3.2). ■ To use the in and not in operators to determine whether an element is in a set (§14.3.2). ■ To traverse the elements in a set using a for loop (§14.3.2). ■ To test whether a set is a subset or a superset of another set using the issubset or issuperset method (§14.3.3). ■ To test whether two sets have the same contents using the == operator (§14.3.4). ■ To perform set union, intersection, difference, and symmetric difference using the operators |, &, -, and ^ (§14.3.5). ■ To compare the performance differences between sets and lists (§14.4). ■ To use sets to develop a program that counts the keywords in a Python source file (§14.5). ■ To create dictionaries (§14.6.1). ■ To add, modify, and retrieve elements in a dictionary using the syntax dictionaryName[key] (§14.6.2). ■ To delete items in a dictionary using the del keyword (§14.6.3). ■ To traverse keys in a dictionary using a for loop (§14.6.4). ■ To obtain the size of a dictionary using the len function (§14.6.5). ■ To test whether a key is in a dictionary using the in or not in operator (§14.6.6). ■ To test whether two dictionaries have the same content using the == operator (§14.6.7). ■ To use the keys, values, items, clean, get, pop, and popitem methods on a dictionary (§14.6.8). ■ To use dictionaries to develop applications (§14.7). CHAPTER 14 476 Chapter 14 Tuples, Sets, and Dictionaries 14.1 Introduction You can use a tuple for storing a fixed list of elements, a set for storing and quickly accessing nonduplicate elements, and a dictionary for storing key/value pairs and for accessing elements quickly using the keys. The “No-Fly” list is a list, created and maintained by the U.S. government’s Terrorist Screening Center, of people who are not permitted to board a commercial aircraft for travel in or out of the United States. Suppose we need to write a program that checks whether a person is on the No-Fly list. You can use a Python list to store names in the No-Fly list. However, a more efficient data structure for this application is a set. In computer science, a data structure is a particular way of storing and organizing data in a computer so that it can be used efficiently for certain applications. This chapter introduces sets along with two additional useful data structures—tuples and dictionaries. 14.2 Tuples Tuples are like lists, but their elements are fixed; that is, once a tuple is created, you cannot add new elements, delete elements, replace elements, or reorder the elements in the tuple. If the contents of a list in your application shouldn’t change, you can use a tuple to prevent elements from being added, deleted, or replaced accidentally. A tuple is very much like a list, except that its elements are fixed. Furthermore, tuples are more efficient than lists due to Python’s implementations. You create a tuple by enclosing its elements inside a pair of parentheses. The elements are separated by commas. You can create an empty tuple and create a tuple from a list, as shown in the following example: t1 = () # Create an empty tuple t2 = (1, 3, 5) # Create a tuple with three elements # Create a tuple from a list t3 = tuple([2 * x for x in range(1, 5)]) You can also create a tuple from a string. Each character in the string becomes an element in the tuple. For example: # Create a tuple from a string t4 = tuple("abac") # t4 is ['a', 'b', 'a', 'c'] Tuples are sequences. The common operations for sequences in Table 10.1 can be used for tuples. You can use the functions len, min, max, and sum on a tuple. You can use a for loop to traverse all elements in a tuple, and can access the elements or slices of the elements using an index operator. You can use the in and not in operators to determine whether an element is in a tuple, and can also compare the elements in tuples using the comparison operators. Listing 14.1 gives an example of using tuples. LISTING 14.1 TupleDemo.py 1 tuple1 = ("green", "red", "blue") # Create a tuple 2 print(tuple1) 3 4 tuple2 = tuple([7, 1, 2, 23, 4, 5]) # Create a tuple from a list 5 print(tuple2) 6 problem tuple creating tuples tuple operations create a tuple Key Point Key Point data structure 14.2 Tuples 477 use functions7 print("length is", len(tuple2)) # Use function len 8 print("max is", max(tuple2)) # Use max 9 print("min is", min(tuple2)) # Use min 10 print("sum is", sum(tuple2)) # Use sum 11 12 print("The first element is", tuple2[0]) # Use index operator 13 14 tuple3 = tuple1 + tuple2 # Combine two tuples 15 print(tuple3) 16 17 tuple3 = 2 * tuple1 # Duplicate a tuple 18 print(tuple3) 19 20 print(tuple2[2 : 4]) # Slicing operator 21 print(tuple1[-1]) 22 23 print(2 in tuple2) # in operator 24 25 for v in tuple1: 26 print(v, end = ' ') 27 print() 28 29 list1 = list(tuple2) # Obtain a list from a tuple 30 list1.sort() 31 tuple4 = tuple(list1) 32 tuple5 = tuple(list1) 33 print(tuple4) 34 print(tuple4 == tuple5) # Compare two tuples index operator + * slicing in operator for loop create a list from tuple compare ('green', 'red', 'blue') (7, 1, 2, 23, 4, 5) length is 6 max is 23 min is 1 sum is 42 The first element is 7 ('green', 'red', 'blue', 7, 1, 2, 23, 4, 5) ('green', 'red', 'blue', 'green', 'red', 'blue') (2, 23) blue True green red blue (1, 2, 4, 5, 7, 23) True False The program creates tuple tuple1 with some strings (line 1) and tuple tuple2 from a list (line 4). It applies the len, max, min, and sum functions on tuple2 (lines 7–10). You can use the index operator to access elements in a tuple (line 12), the + operator to combine two tuples (line 14), the * operator to duplicate a tuple (line 17), and the slicing operator to get a portion of the tuple (lines 20–21). You can use the in operator to determine whether a specific element is in a tuple (line 23). The elements in a tuple can be traversed using a for loop (lines 25–26). The program creates a list (line 29), sorts the list (line 30), and then creates two tuples from this list (lines 31–32). The comparison operator == is used to compare tuples (line 34). Tuples have fixed elements. So wouldn’t the statement in line 17 throw an error since tuple3 has already been defined in line 14? Line 17 is fine, though, because it assigns a new tuple to variable tuple3. Now tuple3 points to the new tuple. “Tuples have fixed elements” 478 Chapter 14 Tuples, Sets, and Dictionaries means that you cannot add new elements, delete elements, replace the elements, or shuffle the elements in a tuple. Note A tuple contains a fixed list of elements. An individual element in a tuple may be muta- ble. For example, the following code creates a tuple of circles (line 2), and changes the first circle’s radius to 30 (line 3). 1 >>> from CircleFromGeometricObject import Circle
2 >>> circles = (Circle(2), Circle(4), Circle(7))
3 >>> circles[0].setRadius(30)
4 >>> circles[0].getRadius()
5 >>> 30
6 >>>
In this example, each element in the tuple is a circle object. Even though you cannot
add, delete, or replace circle objects in the tuple, you can change a circle’s radius, since
a circle object is mutable. If a tuple contains immutable objects, the tuple is said to be
immutable. For example, a tuple of numbers or a tuple of strings is immutable.
14.1 What are the differences between a list and a tuple? How do you create a tuple from a
list? How do you create a list from a tuple?
14.2 What is wrong in the following code?
t = (1, 2, 3)
t.append(4)
t.remove(0)
t[0] = 1
14.3 Is the following code correct?
t1 = (1, 2, 3, 7, 9, 0, 5)
t2 = (1, 2, 5)
t1 = t2
14.4 Show the printout of the following code:
t = (1, 2, 3, 7, 9, 0, 5)
print(t)
print(t[0])
print(t[1: 3])
print(t[-1])
print(t[ : -1])
print(t[1 : -1])
14.5 Show the printout of the following code:
t = (1, 2, 3, 7, 9, 0, 5)
print(max(t))
print(min(t))
print(sum(t))
print(len(t))
14.6 Show the printout of the following code:
t1 = (1, 2, 3, 7, 9, 0, 5)
t2 = (1, 3, 22, 7, 9, 0, 5)
print(t1 == t2)
print(t1 != t2)
print(t1 > t2)
print(t1 < t2) immutable tuple ✓Point✓Check 14.3 Sets 479 14.3 Sets Sets are like lists in that you use them for storing a collection of elements. Unlike lists, however, the elements in a set are nonduplicates and are not placed in any particular order. If your application does not care about the order of the elements, using a set to store elements is more efficient than using lists due to Python’s implementations. This section introduces how to use sets. 14.3.1 Creating Sets You can create a set of elements by enclosing the elements inside a pair of curly braces ({}). The elements are separated by commas. You can create an empty set, or you can create a set from a list or a tuple, as shown in the following examples: s1 = set() # Create an empty set s2 = {1, 3, 5} # Create a set with three elements s3 = set([1, 3, 5]) # Create a set from a tuple # Create a set from a list s4 = set([x * 2 for x in range(1, 10)]) Likewise, you can create a list or a tuple from a set by using the syntax list(set) or tuple(set). You can also create a set from a string. Each character in the string becomes an element in the set. For example: # Create a set from a string s5 = set("abac") # s5 is {'a', 'b', 'c'} Note that although the character a appears twice in the string, it appears only once in the set because a set does not store duplicate elements. A set can contain the elements of the same type or mixed types. For example, s {1, 2, 3, "one", "two", "three"} is a set that contains numbers and strings. Each element in a set must be hashable. Each object in Python has a hash value and an object is hashable if its hash value never changes during its lifetime. All types of objects introduced so far except lists are hashable. Why set elements must be hashable is explained in bonus Web Chapter 21, Hashing: Implementing Sets and Dictionaries. 14.3.2 Manipulating and Accessing Sets You can add an element to a set or remove an element by using the add(e) or remove(e) method. You can use the len, min, max, and sum functions on a set, and a for loop to tra- verse all elements in a set. You can use the in or not in operator to determine whether an element is in the set. For example: = Use sets set hashable >>> s1 = {1, 2, 4}
>>> s1.add(6)
>>> s1
{1, 2, 4, 6}
>>> len(s1)
4
>>> max(s1)
6
VideoNote
Key
Point

480 Chapter 14 Tuples, Sets, and Dictionaries
Note
The remove(e) method will throw a KeyError exception if the element to be
removed is not in the set.
14.3.3 Subset and Superset
A set s1 is a subset of s2 if every element in s1 is also in s2. You can use the
s1.issubset(s2) method to determine whether s1 is a subset of s2, as shown in the
following code:
issubset
>>> s1 = {1, 2, 4}
>>> s2 = {1, 4, 5, 2, 6}
>>> s1.issubset(s2) # s1 is a subset of s2
True
>>>
A set s1 is a superset of set s2 if every element in s2 is also in s1. You can use the
s1. issuperset(s2) method to determine whether s1 is a superset of s2, as shown in the
following code:
issuperrset
>>> s1 = {1, 2, 4}
>>> s2 = {1, 4, 5, 2, 6}
>>> s2.issuperset(s1) # s2 is a superset of s1
True
>>>
14.3.4 Equality Test
You can use the == and != operators to test if two sets contain the same elements. For
example:
>>> s1 = {1, 2, 4}
>>> s2 = {1, 4, 2}
>>> s1 == s2
True
>>> s1 != s2
False
>>>
>>> min(s1)
1
>>> sum(s1)
13
>>> 3 in s1
False
>>> s1.remove(4)
>>> s1
{1, 2, 6}
>>>

14.3 Sets 481
In this example, s1 and s2 contain the same elements regardless of the order of the ele-
ments in the sets.
Note that it makes no sense to compare the sets using the conventional comparison opera-
tors (>, >=, <=, and <), because the elements in a set are not ordered. However, these operators have special meanings when used for sets: ■ s1 < s2 returns True if s1 is a proper subset of s2. ■ s1 <= s2 returns True if s1 is a subset of s2. ■ s1 > s2 returns True if s1 is a proper superset of s2.
■ s1 >= s2 returns True if s1 is a superset of s2.
Note
If s1 is a proper subset of s2, every element in s1 is also in s2, and at least one element
in s2 is not in s1. If s1 is a proper subset of s2, s2 is a proper superset of s1.
14.3.5 Set Operations
Python provides the methods for performing set union, intersection, difference, and symmet-
ric difference operations.
The union of two sets is a set that contains all the elements from both sets. You can use the
union method or the | operator to perform this operation. For example: union |
>>> s1 = {1, 2, 4}
>>> s2 = {1, 3, 5}
>>> s1.union(s2)
{1, 2, 3, 4, 5}
>>>
>>> s1 | s2
{1, 2, 3, 4, 5}
>>>
The intersection of two sets is a set that contains the elements that appear in both sets. You can
use the intersection method or the & operator to perform this operation. For example: intersection &
>>> s1 = {1, 2, 4}
>>> s2 = {1, 3, 5}
>>> s1.intersection(s2)
{1}
>>>
>>> s1 & s2
{1}
>>>
The difference between set1 and set2 is a set that contains the elements in set1 but not
in set2. You can use the difference method or the – operator to perform this operation.
For example:
>>> s1 = {1, 2, 4}
>>> s2 = {1, 3, 5}
>>> s1.difference(s2)
difference –
set union
set intersection
set difference

482 Chapter 14 Tuples, Sets, and Dictionaries
The symmetric difference (or exclusive or) of two sets is a set that contains the elements in
either set, but not in both sets. You can use the symmetric_difference method or the ^
operator to perform this operation. For example:
symmetric_difference ^
>>> s1 = {1, 2, 4}
>>> s2 = {1, 3, 5}
>>> s1.symmetric_difference(s2)
{2, 3, 4, 5}
>>>
>>> s1 ^ s2
{2, 3, 4, 5}
>>>
Note that these set methods return a resulting set, but they do not change the elements in
the sets.
Listing 14.2 illustrates a program that uses sets.
LISTING 14.2 SetDemo.py
1 set1 = {“green”, “red”, “blue”, “red”} # Create a set
2 print(set1)
3
4 set2 = set([7, 1, 2, 23, 2, 4, 5]) # Create a set from a list
5 print(set2)
6
7 print(“Is red in set1?”, “red” in set1)
8
9 print(“length is”, len(set2)) # Use function len
10 print(“max is”, max(set2)) # Use max
11 print(“min is”, min(set2)) # Use min
12 print(“sum is”, sum(set2)) # Use sum
13
14 set3 = set1 {“green”, “yellow”} # Set union
15 print(set3)
16
17 set3 = set1 {“green”, “yellow”} # Set difference
18 print(set3)
19
20 set3 = set1 {“green”, “yellow”} # Set intersection
21 print(set3)
22
23 set3 = set1 {“green”, “yellow”} # Set exclusive or
24 print(set3)
25
26 list1 = list(set2) # Obtain a list from a set
27 print(set1 == {“green”, “red”, “blue”}) # Compare two sets
28
29 set1.add(“yellow”)
^
&
–
|
create a set
create a set from list
is in set?
union |
difference –
intersection &
exclusive or ^
create a list from set
compare
{2, 4}
>>>
>>> s1 – s2
{2, 4}
>>>
set symmetric_difference

14.3 Sets 483
30 print(set1)
31
32
33 print(set1)
set1.remove(“yellow”)
{‘blue’, ‘green’, ‘red’}
{1, 2, 4, 5, 7, 23}
Is red in set1? True
length is 6
max is 23
min is 1
sum is 42
{‘blue’, ‘green’, ‘yellow’, ‘red’}
{‘blue’, ‘red’}
{‘green’}
{‘blue’, ‘red’, ‘yellow’}
True
{‘blue’, ‘green’, ‘yellow’, ‘red’}
{‘blue’, ‘green’, ‘red’}
The program creates set1 as {“green”, “red”, “blue”, “red”} (line 1). Because
a set does not contain any duplicates, only one element red is stored in set1. The program
creates set2 from a list using the set function (line 4).
The program applies the len, max, min, and sum functions on the sets (lines 9–12). Note
that you cannot use the index operator to access elements in a set, because the elements are
not in any particular order.
The program performs the set union, difference, intersection, and symmetric difference
operations in lines 14–24.
Set union: {“green”, “red”, “blue”} | {“green”, “yellow”})
=> {“green”, “red”, “blue”, “yellow”} (line 14)
Set difference: {“green”, “red”, “blue”} – {“green”, “yellow”})
=> {“red”, “blue”} (line 17)
Set intersection: {“green”, “red”, “blue”} & {“green”, “yellow”})
=> {“green”} (line 20)
Set symmetric_difference: {“green”, “red”, “blue”} ^ {“green”, “yellow”})
=> {“red”, “blue”, “yellow”} (line 23)
The program uses == to determine whether the two sets have the same elements (line 27).
The program uses the add and remove methods to add and remove an element in the set
(lines 29 and 32).
14.7 How do you create an empty set?
14.8 Can a list, set, or tuple have elements of different types?
14.9 Which of the following sets are created correctly?
s = {1, 3, 4}
s = {{1, 2}, {4, 5}}
s = {[1, 2], [4, 5]}
s = {(1, 2), (4, 5)}
14.10 What are the differences between a list and a set? How do you create a set from a list?
How do you create a list from a set? How do you create a tuple from a set?
len, max, min, sum
|, -, &, ^
comparisons
add
remove
✓Point✓Check

484 Chapter 14 Tuples, Sets, and Dictionaries
14.11 Show the printout of the following code:
students = {“peter”, “john”}
print(students)
students.add(“john”)
print(students)
students.add(“peterson”)
print(students)
students.remove(“peter”)
print(students)
14.12 Will the following code have a runtime error?
students = {“peter”, “john”}
students.remove(“johnson”)
print(students)
14.13 Show the printout of the following code:
student1 = {“peter”, “john”, “tim”}
student2 = {“peter”, “johnson”, “tim”}
print(student1.issuperset({“john”}))
print(student1.issubset(student2))
print({1, 2, 3} > {1, 2, 4})
print({1, 2, 3} < {1, 2, 4}) print({1, 2} < {1, 2, 4}) print({1, 2} <= {1, 2, 4}) 14.14 Show the printout of the following code: numbers = {1, 4, 5, 6} print(len(numbers)) print(max(numbers)) print(min(numbers)) print(sum(numbers)) 14.15 Show the printout of the following code: s1 = {1, 4, 5, 6} s2 = {1, 3, 6, 7} print(s1.union(s2)) print(s1 | s2) print(s1.intersection(s2)) print(s1 & s2) print(s1.difference(s2)) print(s1 - s2) print(s1.symmetric_difference(s2)) print(s1 ^ s2) 14.16 Show the printout of the following code: set1 = {2, 3, 7, 11} print(4 in set1) print(3 in set1) print(len(set1)) print(max(set1)) print(min(set1)) print(sum(set1)) print(set1.issubset({2, 3, 6, 7, 11})) print(set1.issuperset({2,3, 7, 11})) 14.17 Show the output of the following code: set1 = {1, 2, 3} set2 = {3, 4, 5} set3 = set1 | set2 14.4 Comparing the Performance of Sets and Lists 485 print(set1, set2, set3) set3 = set1 – set2 print(set1, set2, set3) set3 = set1 & set2 print(set1, set2, set3) set3 = set1 ^ set2 print(set1, set2, set3) 14.4 Comparing the Performance of Sets and Lists Sets are more efficient than lists for the in and not in operator and for the remove method. The elements in a list can be accessed using the index operator. However, sets do not support the index operator, because the elements in a set are unordered. To traverse all elements in a set, use a for loop. We now conduct an interesting experiment to test the performance of sets and lists. The program in Listing 14.3 shows the execution time of (1) testing whether an element is in a set and a list, and (2) removing elements from a set and a list. LISTING 14.3 SetListPerformanceTest.py 1 import random 2 import time 3 4 NUMBER_OF_ELEMENTS = 10000 5 6 # Create a list 7 lst = list(range(NUMBER_OF_ELEMENTS)) 8 random.shuffle(lst) 9 10 # Create a set from the list 11 s = set(lst) 12 13 # Test if an element is in the set 14 startTime = time.time() # Get start time 15 for i in range(NUMBER_OF_ELEMENTS): 16 i in s 17 endTime = time.time() # Get end time 18 runTime = int((endTime - startTime) * 1000) # Get test time 19 print("To test if", NUMBER_OF_ELEMENTS, 20 "elements are in the set\n", 21 "The runtime is", runTime, "milliseconds") 22 23 # Test if an element is in the list 24 startTime = time.time() # Get start time 25 for i in range(NUMBER_OF_ELEMENTS): 26 i in lst 27 endTime = time.time() # Get end time 28 runTime = int((endTime - startTime) * 1000) # Get test time 29 print("\nTo test if", NUMBER_OF_ELEMENTS, 30 "elements are in the list\n", 31 "The runtime is", runTime, "milliseconds") 32 33 # Remove elements from a set one at a time 34 startTime = time.time() # Get start time create a list create a set number in set? get run time number in list? Key Point 486 Chapter 14 Tuples, Sets, and Dictionaries 35 for i in range(NUMBER_OF_ELEMENTS): 36 s.remove(i) 37 endTime = time.time() # Get end time 38 runTime = int((endTime - startTime) * 1000) # Get test time 39 print("\nTo remove", NUMBER_OF_ELEMENTS, 40 "elements from the set\n", 41 "The runtime is", runTime, "milliseconds") 42 43 # Remove elements from a list one at a time 44 startTime = time.time() # Get start time 45 for i in range(NUMBER_OF_ELEMENTS): 46 lst.remove(i) 47 endTime = time.time() # Get end time 48 runTime = int((endTime - startTime) * 1000) # Get test time 49 print("\nTo remove", NUMBER_OF_ELEMENTS, 50 "elements from the list\n", 51 "The runtime is", runTime, "milliseconds") remove from list To test if 10000 elements are in the set The runtime is 5 milliseconds To test if 10000 elements are in the list The runtime is 4274 milliseconds To remove 10000 elements from the set The runtime is 7 milliseconds To remove 10000 elements from the list The runtime is 1853 milliseconds In line 7, the range(NUMBER_OF_ELEMENTS) function returns a sequence of numbers from 0 to NUMBER_OF_ELEMENTS – 1. So list(range(NUMBER_OF_ELEMENTS)) returns a list of integers from 0 to NUMBER_OF_ELEMENTS – 1 (line 7). The program shuffles the list (line 8), and creates a set from the list (line 11). Now the set and the list contain the same elements. The program obtains the runtime for testing whether the elements 0 to NUMBER_OF_ELEMENTS – 1 are in the set (lines 14–21) and in the list (lines 24–31). As you can see in the output, it takes 5 milliseconds to test this for the set and 4,274 milliseconds for the list. The program obtains the runtime for removing the elements 0 to NUMBER_OF_ELEMENTS – 1 from the set (lines 34–41) and in the list (lines 44–51). Again, you can see in the output that it takes 7 milliseconds for the set and 1,853 milliseconds for the list. As these runtimes illustrate, sets are much more efficient than lists for testing whether an element is in a set or a list. So, the “No-Fly” list mentioned at the beginning of this chapter should be implemented using a set instead of a list, because it is much faster to test whether an element is in a set than in a list. You may wonder why sets are more efficient than lists. To get the answers, read the online bonus chapters on developing efficient algorithms, linked lists, and hashing. 14.5 Case Study: Counting Keywords This section presents an application that counts the number of the keywords in a Python source file. For each word in a Python source file, we need to determine whether the word is a keyword. To handle this efficiently, store all the keywords in a set and use the in operator to test if a word is in the keyword set. Listing 14.4 gives this program. sets are better bonus chapters remove from set Key Point 14.6 Dictionaries 487 dictionary what is a dictionary? Enter a Python source code filename: The number of keywords in GuessNumber.py is 7 GuessNumber.py Enter a Python source file: File TTT.py does not exist TTT.py keyword set enter a filename file exists? open file read and split words is a keyword? count keyword Key Point LISTING 14.4 CountKeywords.py 1 import os.path 2 import sys 3 4 def main(): 5 keyWords = {"and", "as", "assert", "break", "class", 6 "continue", "def", "del", "elif", "else", 7 "except", "False", "finally", "for", "from", 8 "global", "if", "import", "in", "is", "lambda", 9 "None", "nonlocal", "not", "or", "pass", "raise", 10 "return", "True", "try", "while", "with", "yield"} 11 12 filename = input("Enter a Python source code filename: ").strip() 13 14 if not os.path.isfile(filename): # Check if file exists 15 print("File", filename, "does not exist") 16 sys.exit() 17 18 infile = open(filename, "r") # Open files for input 19 20 text = infile.read().split() # Read and split words from the file 21 22 count = 0 23 for word in text: 24 if : 25 count += 1 26 27 print("The number of keywords in", filename, "is", count) 28 29 main() word in keyWords The program creates a set for keywords (lines 5–10) and prompts the user to enter a Python source filename (line 12). It checks if the file exists (line 14). If not, exit the program (line 16). The program opens the file and splits the words from the text (line 20). For each word, the program checks if the word is a keyword (line 24). If so, increase the count by 1 (line 25). 14.6 Dictionaries A dictionary is a container object that stores a collection of key/value pairs. It enables fast retrieval, deletion, and updating of the value by using the key. Suppose your program needs to store the detailed information on terrorists in the “No-Fly” list. A dictionary is an efficient data structure for such a task. A dictionary is a collection that 488 Chapter 14 Tuples, Sets, and Dictionaries stores the values along with the keys. The keys are like an index operator. In a list, the indexes are integers. In a dictionary, the key must be a hashable object. A dictionary cannot contain duplicate keys. Each key maps to one value. A key and its corresponding value form an item (or entry) stored in a dictionary, as shown in Figure 14.1a. The data structure is a called a “dic- tionary” because it resembles a word dictionary, where the words are the keys and the words’ definitions are the values. A dictionary is also known as a map, which maps each key to a value. 14.6.1 Creating a Dictionary You can create a dictionary by enclosing the items inside a pair of curly braces ({}). Each item consists of a key, followed by a colon, followed by a value. The items are separated by commas. For example, the following statement: students = {"111-34-3434":"John", "132-56-6290":"Peter"} creates a dictionary with two items, as shown in Figure 14.1b. The item is in the form key:value. The key in the first item is 111-34-3434, and its corresponding value is John. The key must be of a hashable type such as numbers and strings. The value can be of any type. You can create an empty dictionary by using the following syntax: students = {} # Create an empty dictionary Note Python uses curly braces for sets and dictionaries. The syntax {} denotes an empty dic- tionary. To create an empty set, use set(). 14.6.2 Adding, Modifying, and Retrieving Values To add an item to a dictionary, use the syntax: dictionaryName[key] = value For example: students["234-56-9010"] = "Susan" If the key is already in the dictionary, the preceding statement replaces the value for the key. key/value pair dictionary item dictionary entry map Item (a) (b) Corresponding value Item Search key A dictionary Search key Corresponding value 111-34-3434 John Peter132-56-6290 FIGURE 14.1 A dictionary’s item is a key/value pair. Use dictionaries VideoNote 14.6 Dictionaries 489 To retrieve a value, simply write an expression using dictionaryName[key]. If the key is in the dictionary, the value for the key is returned. Otherwise, a KeyError exception is raised. For example: 1 >>> students = {“111-34-3434″:”John”, “132-56-6290″:”Peter”}
2 >>> students[“234-56-9010”] = “Susan” # Add a new item
3 >>> students[“234-56-9010”]
4 “Susan”
5 >>> students[“111-34-3434”] = “John Smith”
6 >>> students[“111-34-3434”]
7 “John Smith”
8 >>> student[“343-45-5455”]
9 Traceback (most recent call last):
10 File ““, line 1, in
11 KeyError: ‘343-45-5455’
12 >>>
Line 1 creates a dictionary with two items. Line 2 adds a new item with the key 234-56-
9010 and the value Susan. The value associated with the key 234-56-9010 is returned in
line 3. Line 5 modifies the item for the key 111-34-3434 with the new value John Smith,
and line 8 retrieves the value for a nonexistent key 343-45-5455, which raises a KeyError
exception.
14.6.3 Deleting Items
To delete an item from a dictionary, use the syntax:
del dictionaryName[key]
For example:
del students[“234-56-9010”]
This statement deletes an item with the key 234-56-9010 from the dictionary. If the key
is not in the dictionary, a KeyError exception is raised.
14.6.4 Looping Items
You can use a for loop to traverse all keys in the dictionary. For example:
1 >>> students = {“111-34-3434″:”John”, “132-56-6290″:”Peter”}
2 >>> for key in students:
3 … print(key + “:” + str(students[key]))
4 …
5 “111-34-3434″:”John”
6 “132-56-6290″:”Peter”
7 >>>
The for loop iterates on keys in dictionary students (line 2). students[key] returns the
value for the key (line 3).

490 Chapter 14 Tuples, Sets, and Dictionaries
len(dictionary)
1 >>> students = {“111-34-3434″:”John”, “132-56-6290″:”Peter”}
2 >>> len(students)
3 2
4 >>>
In line 2, len(students) returns the number of items in dictionary students.
14.6.6 Testing Whether a Key Is in a Dictionary
You can use the in or not in operator to determine whether a key is in the dictionary. For
example:
in operator
1 >>> students = {“111-34-3434″:”John”, “132-56-6290″:”Peter”}
2 >>> “111-34-3434” in students
3 True
4 >>> “999-34-3434” in students
5 False
6 >>>
14.6.5 The len Function
You can find the number of the items in a dictionary by using len(dictionary). For
example:
In line 2, “111-34-3434” in students checks whether the key 111-34-3434 is in
dictionary students.
14.6.7 Equality Test
You can use the == and != operators to test whether two dictionaries contain the same items.
For example:
>>> d1 = {“red”:41, “blue”:3}
>>> d2 = {“blue”:3, “red”:41}
>>> d1 == d2
True
>>> d1 != d2
False
>>>
In this example, d1 and d2 contain the same items regardless of the order of the items in a
dictionary.
Note
You cannot use the comparison operators (>, >=, <=, and <) to compare dictionaries because the items are not ordered. 14.6 Dictionaries 491 14.6.8 The Dictionary Methods The Python class for dictionaries is dict. Figure 14.2 lists the methods that can be invoked from a dictionary object. dict keys(): tuple values(): tuple items(): tuple Returns a sequence of keys. Returns a sequence of values. Returns a sequence of tuples. Each tuple is (key, value) for an item. clear(): None get(key): value pop(key): value popitem(): tuple Deletes all entries. Returns the value for the key. Removes the item for the key and returns its value. Returns a randomly selected key/value pair as a tuple and removes the selected item. FIGURE 14.2 The dict class provides methods for manipulating a dictionary object. 1 >>> students = {“111-34-3434″:”John”, “132-56-6290″:”Peter”}
2 >>> tuple(students.keys())
3 (“111-34-3434”, “132-56-6290”)
4 >>> tuple(students.values())
5 (“John”, “Peter”)
6 >>> tuple(students.items())
7 ((“111-34-3434”, “John”), (“132-56-6290”, “Peter”))
8 >>> students.get(“111-34-3434”)
9 “John”
10 >>> print(students.get(“999-34-3434”))
11 None
12 >>> students.pop(“111-34-3434”)
13 “John”
14 >>> students
15 {“132-56-6290″:”Peter”}
16 >>> students.clear()
17 >>> students
18 {}
19 >>>
The dictionary students is created in line 1, and students.keys() in line 2 returns the
keys in the dictionary. In line 4, students.values() returns the values in the dictionary,
and students.items() in line 6 returns items as tuples in the dictionary. In line 10, invok-
ing students.get(“999-34-3434”) returns the student name for the key 999-34-3434.
Invoking students.pop(“111-34-3434″) in line 12 removes the item in the dictionary
with the key 111-34-3434. In line 16, invoking students.clear() removes all items
from the dictionary.
The get(key) method is similar to dictionaryName[key] except that the get method
returns None if the key is not in the dictionary rather than raising an exception. The
pop(key) method is the same as del dictionaryName[key].
Here are some examples that show these methods in use:

492 Chapter 14 Tuples, Sets, and Dictionaries
14.18 How do you create an empty dictionary?
14.19 Which of the following dictionaries are created correctly?
d = {1:[1, 2], 3:[3, 4]}
d = {[1, 2]:1, [3, 4]:3}
d = {(1, 2):1, (3, 4):3}
d = {1:”john”, 3:”peter”}
d = {“john”:1, “peter”:3}
14.20 Each item in a dictionary has two parts. What are they called?
14.21 Suppose a dictionary named students is {“john”:3, “peter”:2}. What do the
following statements do?
(a) students[“susan”] = 5
(b) students[“peter”] = 5
(c) students[“peter”] += 5
(d) del students[“peter”]
14.22 Suppose a dictionary named students is {“john”:3, “peter”:2}. What do the
following statements do?
(a) print(len(students))
(b) print(students.keys())
(c) print(students.values())
(d) print(students.items())
14.23 Show the output of the following code:
def main():
d = {“red”:4, “blue”:1, “green”:14, “yellow”:2}
print(d[“red”])
print(list(d.keys()))
print(list(d.values()))
print(“blue” in d)
print(“purple” in d)
d[“blue”] += 10
print(d[“blue”])
main() # Call the main function
14.24 Show the output of the following code:
def main():
d = {}
d[“susan”] = 50
d[“jim”] = 45
d[“joan”] = 54
d[“susan”] = 51
d[“john”] = 53
print(len(d))
main() # Call the main function
14.25 For a dictionary d, you can use d[key] or d.get(key) to return the value for the
key. What are the differences between them?
14.7 Case Study: Occurrences of Words
This case study writes a program that counts the occurrences of words in a text file
and displays ten most frequently used words in decreasing order of their occurrence
counts.
✓Point✓Check
Key
Point

14.7 Case Study: Occurrences of Words 493
enter a file
open file
create a dictionary
process each line
get pairs to list
The program in this case study uses a dictionary to store an item consisting of a word and its
count. The program determines whether each word is already a key in the dictionary. If not,
the program adds a dictionary item with the word as the key and the value 1. Otherwise, the
program increases the value for the word (key) by 1 in the dictionary. Assume the words are
case-insensitive (for example, Good is treated the same as good). The program displays the
ten most frequently used words in the file in decreasing order of their count.
Listing 14.5 shows the solution to the problem.
LISTING 14.5 CountOccurrenceOfWords.py
1 def main():
2 # Prompt the user to enter a file
3 filename = input(“Enter a filename: “).strip()
4 infile = open(filename, “r”) # Open the file
5
6 # Create an empty dictionary to count words
7 for line in infile:
8
9
10 # Get pairs from the dictionary
11
12 # Reverse pairs in the list
13
14 # Sort pairs in items
15
16 for i in range(len(items) – 1, len(items) – 11, -1):
17 print(items[i][1] + “\t” + str(items[i][0]))
18
19 # Count each word in the line
20 def processLine(line, wordCounts):
21 line = replacePunctuations(line) # Replace punctuation with space
22 # Get words from each line
23 for word in words:
24 if word in wordCounts:
25
26 else:
27
28
29 # Replace punctuation in the line with a space
30 def replacePunctuations(line):
31 for ch in line:
32 if ch in “~@#$%^&*()_-+=~<>?/,.;:!{}[]|’\””:
33
34
35 return line
36
37 main() # Call the main function
line = line.replace(ch, ” “)
wordCounts[word] = 1
wordCounts[word] += 1
words = line.split()
items.sort()
items = [[x, y] for (y, x) in pairs]
pairs = list(wordCounts.items())
processLine(line.lower(), wordCounts)
wordCounts = {}
reverse pair
display item
replace punctuation
extract words
increase word count
new word
replace punctuation
Enter a filename:
that 13
the 11
we 10
to 8
here 8
a 7
and 6
Lincoln.txt

494 Chapter 14 Tuples, Sets, and Dictionaries
The program prompts the user to enter a filename (line 3) and opens the file (line 4). It cre-
ates a dictionary wordCounts (line 6) to store pairs of words and their occurrence counts.
The words serve as the keys.
The program reads each line from the file and invokes processLine(line, wordCounts)
to count the occurrence of each word in the line (lines 7–8). Suppose the wordCounts dictionary
is {“red”:7, “blue”:5, “green”:2}. How do you sort it? The dictionary object does not
have the sortmethod. But the list object has it, so you can get the pairs into a list and then sort
that list. The program obtains the list of pairs in line 10. If you apply the sort method to the list,
the pairs will be sorted on their first element, but we need to sort each pair on their count (the
second element). How can we do this? The trick is to reverse the pair. The program creates a new
list with all the pairs reversed (line 12), and then applies the sort method (line 14). Now the list
is sorted like this: [[2, “green”], [5, “blue”], [7, “red”]].
The program displays the last ten pairs from the list to show the words with the highest
count (lines 16–17).
The processLine(line, wordCounts) function invokes replacePunctuations(line)
to replace all punctuation marks by spaces (line 21), then extracts words by using the split
method (line 22). If a word is already in the dictionary, the program increases its count (line
25); otherwise, the program adds a new pair to the dictionary (line 27).
The replacePunctuations(line) method checks each character in each line. If it is a
punctuation mark, the program replaces it with a space (lines 32–33).
Now sit back and think how you would write this program without using a dictionary. You
could use a nested list such as [[key1, value1], [key2, value2], … ], but your
new program would be longer and more complex. You will find that a dictionary is a very
efficient and powerful data structure for solving problems such as this.
KEY TERMS
sort pairs
of 5
nation 5
it 5
data structure 476
dictionary 487
dictionary entry 488
dictionary item 488
hashable 479
immutable tuple 478
key/value pair 488
map 488
set 479
set difference 481
set intersection 481
set union 481
set symmetric difference 482
tuple 476
CHAPTER SUMMARY
1. A tuple is a fixed list. You cannot add, delete, or replace elements in a tuple.
2. Since a tuple is a sequence, the common operations for sequences can be used for
tuples.
3. Though you cannot add, delete, or replace elements in a tuple, you can change the
content of individual elements if the elements are mutable.
4. A tuple is immutable if all its elements are immutable.
processLine
replacePunctuations (line)

Programming Exercises 495
5. Sets are like lists in that you use them for storing a collection of elements. Unlike
lists, however, the elements in a set are nonduplicates and are not placed in any par-
ticular order.
6. You can add an element to a set using the add method and remove an element from
the list using the remove method.
7. The len, min, max, and sum functions can be applied to a set.
8. You can use a for loop to traverse the elements in a set.
9. You can use the issubset or issuperset method to test whether a set is a subset
or a superset of another set, and use the |, &, —, and ^ operators to perform set union,
intersection, difference, and symmetric difference.
10. Sets are more efficient than lists for testing whether an element is in a set or a list as
well as for removing elements from a set or a list.
11. A dictionary can be used to store key/value pairs. You can retrieve a value using a key.
The keys are like an index operator. In a list, the indexes are integers. In a dictionary,
the keys can be any hashable objects such as numbers and strings.
12. You can use dictionaryName[key] to retrieve a value in the dictionary for the
given key and use dictionaryName[key] = value to add or modify an item in a
dictionary.
13. You can use del dictionaryName[key] to delete an item for the given key.
14. You can use a for loop to traverse all keys in a dictionary.
15. You can use the len function to return the number of items in a dictionary.
16. You can use the in and not in operators to test if a key is in a dictionary and use the
== and != operator to test if two dictionaries are the same.
17. You can use the methods keys(), values(), items(), clear(), get(key),
pop(key), and popitem() on a dictionary.
TEST QUESTIONS
Do test questions for this chapter online at www.cs.armstrong.edu/liang/py/test.html.
PROGRAMMING EXERCISES
Sections 14.2–14.6
*14.1 (Display keywords) Revise Listing 14.4 CountKeywords.py to display the key-
words in a Python source file as well as to count the number of the keywords.
*14.2 (Count occurrences of numbers) Write a program that reads an unspecified num-
ber of integers and finds the ones that have the most occurrences. For example, if
you enter 2 3 40 3 5 4 –3 3 3 2 0, the number 3 occurs most often. Enter all num-
bers in one line. If not one but several numbers have the most occurrences, all of
them should be reported. For example, since 9 and 3 appear twice in the list 9 30
3 9 3 2 4, both occurrences should be reported.

www.cs.armstrong.edu/liang/py/test.html

496 Chapter 14 Tuples, Sets, and Dictionaries
(b)(a)
FIGURE 14.3 The program lets the user select a file and displays the occurrence counts of the letters in the file.
*14.3 (Count the occurrences of each keyword) Write a program that reads in a Python
source code file and counts the occurrence of each keyword in the file. Your pro-
gram should prompt the user to enter the Python source code filename.
*14.4 (Tkinter: Count the occurrences of each letter) Rewrite Listing 14.5 using a GUI
program to let the user enter the file from an entry field, as shown in Figure 14.3a.
You can also select a file by clicking the Browse button to display an Open file dia-
log box, as shown in Figure 14.3b. The file selected is then displayed in the entry
field. Clicking the Show Result button displays the result in a text widget. You
need to display a message in a message box if the file does not exist.
*14.5 (Tkinter: Count the occurrences of each letter) Revise the preceding exercise to
display a histogram for the result, as shown in Figure 14.4. You need to display a
message in a message box if the file does not exist.
FIGURE 14.4 The program lets the user select a file and displays the occurrence counts in a
histogram.
*14.6 (Tkinter: Count the occurrences of each letter) Rewrite Listing 14.5 using a GUI
program to let the user enter the URL from an entry field, as shown in Figure 14.5.
Clicking the Show Result button displays the result in a text widget. You need to
display a message in a message box if the URL does not exist.

Programming Exercises 497
*14.7 (Tkinter: Count the occurrences of each letter) Revise the preceding exercise to
display a histogram for the result, as shown in Figure 14.6. You need to display a
message in a message box if the URL does not exist.
FIGURE 14.6 The program lets the user enter a URL for a file and displays the occurrence
counts of the letters in a histogram.
14.8 (Display nonduplicate words in ascending order) Write a program that prompts
the user to enter a text file, reads words from the file, and displays all the nondu-
plicate words in ascending order.
***14.9 (Game: hangman) Write the hangman game with a graphics display, as shown in
Figure 14.7. After seven misses, the program displays the word. The user can
press the Enter key to continue to guess another word.
*14.10 (Guess the capitals) Rewrite Exercise 11.40 using a dictionary to store the pairs
of states and capitals so that the questions are randomly displayed.
*14.11 (Count consonants and vowels) Write a program that prompts the user to enter a
text filename and displays the number of vowels and consonants in the file. Use
a set to store the vowels A, E, I, O, and U.
FIGURE 14.5 The program lets the user enter a URL for a file and displays the occurrence
counts of the letters in the file.

FIGURE 14.7 The hangman game lets the user enter letters to guess a word.
498 Chapter 14 Tuples, Sets, and Dictionaries

RECURSION
CHAPTER
15
Objectives
■ To explain what a recursive function is and describe the benefits of using
recursion (§15.1).
■ To develop recursive programs for recursive mathematical functions
(§§15.2–15.3).
■ To explain how recursive function calls are handled in a call stack
(§§15.2–15.3).
■ To solve problems using recursion (§15.4).
■ To use a helper function to design a recursive function (§15.5).
■ To implement a selection sort using recursion (§15.5.1).
■ To implement a binary search using recursion (§15.5.2).
■ To get a directory’s size using recursion (§15.6).
■ To solve the Towers of Hanoi problem using recursion (§15.7).
■ To draw fractals using recursion (§15.8).
■ To solve the Eight Queens problem using recursion (§15.9).
■ To explain the relationship and differences between recursion and iteration
(§15.10).
■ To understand tail-recursive functions and explain why
they are desirable (§15.11).

500 Chapter 15 Recursion
15.1 Introduction
Recursion is a technique that leads to elegant solutions to problems that are difficult to
program using simple loops.
Suppose you want to find all the files in a directory that contain a particular word. How do
you solve this problem? There are several ways to do so. An intuitive and effective solution is
to use recursion by searching the files in each subdirectory recursively.
The H-tree shown in Figure 15.1 is used in a very large-scale integration (VLSI) design as
a clock distribution network for routing timing signals to all parts of a chip with equal propa-
gation delays. How do you write a program to display the H-tree? A good approach is to use
recursion by exploring the recursive pattern.
search word problem
H-tree problem
To use recursion is to program by using recursive functions—functions that invoke them-
selves. Recursion is a useful programming technique. In some cases, it enables you to develop
a natural, straightforward, simple solution to an otherwise difficult problem. This chapter
introduces the concepts and techniques of recursive programming and presents examples that
show you how to “think recursively.”
15.2 Case Study: Computing Factorials
A recursive function is one that invokes itself.
Many mathematical functions are defined using recursion. Let’s begin with a simple example.
The factorial of a number n can be recursively defined as follows:
0! = 1;
n! = n × (n – 1)!; n > 0
How do you find n! for a given n? To find 1! is easy, because you know that 0! is 1, and
1! is 1 × 0!. Assuming that you know (n – 1)!, you can obtain n! immediately by using
n × (n – 1)!. Thus, the problem of computing n! is reduced to computing (n – 1)!.
When computing (n – 1)!, you can apply the same idea recursively until n is reduced to 0.
Let factorial(n) be the function for computing n!. If you call the function with n = 0,
it immediately returns the result. The function knows how to solve the simplest case, which is
referred to as the base case or the stopping condition. If you call the function with n > 0, it
reduces the problem into a subproblem for computing the factorial of n – 1. The subproblem
is essentially the same as the original problem, but it is simpler or smaller. Because the sub-
problem has the same property as the original problem, you can call the function with a
different argument, which is referred to as a recursive call.
recursive function
base case or stopping
condition
recursive call
(a) (b) (c) (d)
FIGURE 15.1 An H-tree can be displayed using recursion.
Key
Point
Key
Point
Function sum
VideoNote

15.2 Case Study: Computing Factorials 501
The recursive algorithm for computing factorial(n) can be simply described as
follows:
if n == 0:
return 1
else:
return n * factorial(n – 1)
A recursive call can result in many more recursive calls, because the function keeps on
dividing a subproblem into new subproblems. For a recursive function to terminate, the
problem must eventually be reduced to a stopping case, at which point the function returns a
result to its caller. The caller then performs a computation and returns the result to its own
caller. This process continues until the result is passed back to the original caller. The origi-
nal problem can now be solved by multiplying n by the result of factorial(n – 1).
Listing 15.1 is a complete program that prompts the user to enter a nonnegative integer and
displays the factorial for the number.
LISTING 15.1 ComputeFactorial.py
1 def main():
2 n = eval(input(“Enter a nonnegative integer: “))
3 print(“Factorial of”, n, “is”, )
4
5 # Return the factorial for the specified number
6
7 if n == 0: # Base case
8 return 1
9 else:
10 return n * # Recursive call
11
12 main() # Call the main function
factorial(n – 1)
def factorial(n):
factorial(n)
base case
recursion
Enter a nonnegative integer:
Factorial of 4 is 24
4
Enter a nonnegative integer:
Factorial of 10 is 3628800
10
The factorial function (lines 6–10) is essentially a direct translation of the recursive
mathematical definition for the factorial into Python code. The call to factorial is recursive
because it calls itself. The parameter passed to factorial is decremented until it reaches the
base case of 0.
Now that you have seen how to write a recursive function, let’s see how recursion works.
Figure 15.2 illustrates the execution of the recursive calls, starting with n = 4. The use of
stack for recursive calls is shown in Figure 15.3.
Pedagogical Note
It is simpler and more efficient to implement the factorial function by using a loop.
However, we use the recursive factorial function here to demonstrate the concept of
recursion. Later in this chapter, we will present some problems that are inherently recur-
sive and are difficult to solve without using recursion.
how does it work?

502 Chapter 15 Recursion
return 1
return 2 * factorial(1)
return 1 * factorial(0)
Step 9: return 24
Step 0: execute factorial(4)
Step 1: execute factorial(3)
Step 2: execute factorial(2)
Step 3: execute factorial(1)
Step 5: return 1
Step 6: return 1
Step 7: return 2
Step 8: return 6
Step 4: execute factorial(0)
factorial(4)
return 3 * factorial(2)
return 4 * factorial(3)
FIGURE 15.2 Invoking factorial(4) spawns recursive calls to factorial.
Space required
for factorial(4)
n: 4
1 Space required
for factorial(4)
n: 4
2 Space required
for factorial(3)
n: 3
Space required
for factorial(4)
n: 4
3
Space required
for factorial(3)
n: 3
Space required
for factorial(2)
n: 2
Space required
for factorial(4)
n: 4
4
Space required
for factorial(3)
n: 3
Space required
for factorial(2)
n: 2
Space required
for factorial(1)
n: 1
Space required
for factorial(4)
n: 4
5
Space required
for factorial(3)
n: 3
Space required
for factorial(2)
n: 2
Space required
for factorial(1)
n: 1
Space required
for factorial(0)
n: 0
Space required
for factorial(4)
n: 4
6
Space required
for factorial(3)
n: 3
Space required
for factorial(2)
n: 2
Space required
for factorial(1)
n: 1
Space required
for factorial(4)
n: 4
7
Space required
for factorial(3)
n: 3
Space required
for factorial(2)
n: 2
Space required
for factorial(4)
n: 4
8 Space required
for factorial(3)
n: 3
Space required
for factorial(4)
n: 4
9
FIGURE 15.3 When factorial(4) is being executed, the factorial function is called recursively, causing stack
space to dynamically change.

15.3 Case Study: Computing Fibonacci Numbers 503
If recursion does not reduce the problem in a manner that allows it to eventually converge
into the base case, infinite recursion can occur. For example, suppose you mistakenly write
the factorial function as follows:
def :
return n *
The function runs infinitely and causes a RuntimeError.
The example discussed so far shows a recursive function that invokes itself. This is known
as direct recursion. It is also possible to create indirect recursion. This occurs when function
A invokes function B, which in turn invokes function A. There can even be several more func-
tions involved in the recursion. For example, function A invokes function B, which invokes
function C, which invokes function A.
15.1 What is a recursive function?
15.2 How many times would the factorial function in Listing 15.1 be invoked for
factorial(6)?
15.3 Write a recursive mathematical definition for computing for a positive integer n.
15.4 Write a recursive mathematical definition for computing for a positive integer n
and a real number x.
15.5 Write a recursive mathematical definition for computing for
a positive integer.
15.6 What is an infinite recursion? What is a direct recursion? What is an indirect recursion?
15.3 Case Study: Computing Fibonacci Numbers
In some cases, recursion enables you to create an intuitive, straightforward, simple
solution to a problem.
The factorial function in the preceding section could easily be rewritten without using
recursion. In this section, we show an example for creating an intuitive, straightforward, sim-
ple solution to a problem using recursion that would otherwise be difficult to solve. Consider
the well-known Fibonacci-series problem:
The series: 0 1 1 2 3 5 8 13 21 34 55 89 . . .
indexes: 0 1 2 3 4 5 6 7 8 9 10 11
The Fibonacci series begins with 0 and 1, and each subsequent number is the sum of the
preceding two. The series can be recursively defined as follows:
fib(0) = 0
fib(1) = 1
fib(index) = fib(index – 2) + fib(index – 1); index >= 2
Note
The Fibonacci series was named for Leonardo Fibonacci, a medieval mathematician who
originated it to model the growth of the rabbit population. It can be applied in numeric
optimization and in various other areas.
How do you find fib(index) for a given index? It is easy to find fib(2), because you
know fib(0) and fib(1). Assuming that you know fib(index – 2) and fib(index –
1), you can obtain fib(index) immediately. Thus, the problem of computing fib(index)
is reduced to computing fib(index – 2) and fib(index – 1). When doing so, you
apply the idea recursively until index is reduced to 0 or 1.
1 + 2 + 3 + c + n
xn
2n
factorial(n – 1)
factorial(n)
infinite recursion
direct recursion
indirect recursion
✓Point✓Check
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Point

504 Chapter 15 Recursion
The base case is index = 0 or index = 1. If you call the function with index = 0 or
index = 1, it immediately returns the result. If you call the function with index >= 2, it
divides the problem into two subproblems for computing fib(index – 1) and fib(index
– 2) using recursive calls. The recursive algorithm for computing fib(index) can be sim-
ply described as follows:
if index == 0:
return 0
elif index == 1:
return 1
else:
return fib(index – 1) + fib(index – 2)
Listing 15.2 is a complete program that prompts the user to enter an index and computes
the Fibonacci number for that index.
LISTING 15.2 ComputeFibonacci.py
1 def main():
2 index = eval(input(“Enter an index for a Fibonacci number: “))
3 # Find and display the Fibonacci number
4 print(“The Fibonacci number at index”, index, “is”, )
5
6 # The function for finding the Fibonacci number
7 def :
8 if index == 0: # Base case
9 return 0
10 elif index == 1: # Base case
11 return 1
12 else: # Reduction and recursive calls
13 return
14
15 main() # Call the main function
fib(index – 1) + fib(index – 2)
fib(index)
fib(index)
base case
base case
recursion
Enter an index for a Fibonacci number:
The Fibonacci number at index 1 is 1
1
Enter an index for a Fibonacci number:
The Fibonacci number at index 6 is 8
6
Enter an index for a Fibonacci number:
The Fibonacci number at index 7 is 13
7
The program does not show the considerable amount of work done behind the scenes by
the computer. Figure 15.4, however, shows the successive recursive calls for evaluating
fib(4). The original function, fib(4), makes two recursive calls, fib(3) and fib(2),
and then returns fib(3) + fib(2). But in what order are these functions called? In
Python, operands are evaluated from left to right, so fib(2) is called after fib(3) is
completely evaluated. The labels in Figure 15.4 show the order in which the functions
are called.

15.4 Problem Solving Using Recursion 505
return fib(3) + fib(2)
10: return fib(3)
fib(4)
0: call fib(4)17: return fib(4)
return fib(2) + fib(1) return fib(1) + fib(0)
1: call fib(3)
11: call fib(2)
16: return fib(2)
return 1 return 0
12: call fib(1)
13: return fib(1) 14: call fib(0)
15: return fib(0)
return fib(1) + fib(0) return 1
2: call fib(2)
7: return fib(2)
8: call fib(1)
9: return fib(1)
return 1 return 0
3: call fib(1)
4: return fib(1) 5: call fib(0)
6: return fib(0)
FIGURE 15.4 Invoking fib(4) spawns recursive calls to fib.
As shown in Figure 15.4, there are many duplicated recursive calls. For instance, fib(2)
is called twice, fib(1) three times, and fib(0) twice. In general, computing fib(index)
requires roughly twice as many recursive calls as does computing fib(index – 1). As you
try larger index values, the number of calls substantially increases, as shown in Table 15.1.
def f(n):
if n == 1:
return 1
else:
return n + f(n – 1)
print(“Sum is”, f(5))
def f(n):
if n > 0:
print(n % 10)
f(n // 10)
f(1234567)
15.4 Problem Solving Using Recursion
If you think recursively, many problems can be solved using recursion.
The preceding sections presented two classic recursion examples. All recursive functions
have the following characteristics:
■ The function is implemented using an if-else or a switch statement that leads to
different cases.
■ One or more base cases (the simplest case) are used to stop recursion.
recursion characteristics
if-else
base cases
Key
Point
✓Point✓Check
TABLE 15.1 Number of Recursive Calls in fib(n)
n 2 3 4 10 20 30 40 50
# of calls 3 5 9 177 21891 2692537 331160281 2075316483
Pedagogical Note
The recursive implementation of the fib function is very simple and straightforward, but it
isn’t efficient. See Programming Exercise 15.2 for an efficient solution using loops. Though it is
not practical, the recursive fib function is a good example of how to write recursive functions.
15.7 How many times would the fib function in Listing 15.2 be invoked for fib(6)?
15.8 Show the output of the following programs and identify their base cases and recursive
calls.

506 Chapter 15 Recursion
■ Every recursive call reduces the original problem, bringing it increasingly closer to a
base case until it becomes that case.
In general, to solve a problem through recursion, you break it into subproblems. Each sub-
problem is almost the same as the original problem, but it is smaller in size. You can apply the
same approach to each subproblem to solve it recursively.
Recursion is everywhere. It is fun to think recursively. Consider drinking coffee. You can
describe the procedure recursively, as follows:
def drinkCoffee(cup):
if cup is not empty:
cup.takeOneSip() # Take one sip
drinkCoffee(cup)
Assume cup is an object for a cup of coffee with the instance functions isEmpty() and
takeOneSip(). You can break the problem into two subproblems: one is to drink one sip of
coffee, and the other is to drink the rest of the coffee in the cup. The second problem is the
same as the original problem but smaller in size. The base case for the problem is when the
cup is empty.
Consider the problem of printing a message n times. You can break the problem into two
subproblems: one is to print the message one time, and the other is to print it n – 1 times. The
second problem is the same as the original problem but it is smaller in size. The base case for
the problem is n == 0. You can solve this problem using recursion as follows:
def nPrintln(message, n):
if n >= 1:
print(message)
nPrintln(message, n – 1)
# The base case is n == 0
Note that the fib function in the preceding section returns a value to its caller, but the
nPrintln function is void and does not.
If you think recursively, you can use recursion to solve many of the problems presented in
earlier chapters of this book. Consider the palindrome problem in Listing 8.1. Recall that a
string is a palindrome if it reads the same from the left and from the right. For example,
“mom” and “dad” are palindromes, but “uncle” and “aunt” are not. The problem of determin-
ing whether a string is a palindrome can be divided into two subproblems:
■ Determine whether the first character and the last character of the string are equal.
■ Ignore the two end characters and see if the rest of the substring is a palindrome.
The second subproblem is the same as the original problem but smaller in size. There are
two base cases: (1) the two end characters are not the same, and (2) the string size is 0 or 1. In
case 1, the string is not a palindrome; in case 2, the string is a palindrome. The recursive func-
tion for this problem can be implemented as shown in Listing 15.3.
LISTING 15.3 RecursivePalindromeUsingSubstring.py
1
2 if len(s) <= 1: # Base case 3 return True 4 elif s[0] != s[len(s) - 1]: # Base case 5 return False 6 else: 7 return 8 isPalindrome(s[1 : len(s) – 1]) def isPalindrome(s): reduction think recursively recursive call think recursively function header base case base case recursive call Function print numbers VideoNote 15.5 Recursive Helper Functions 507 9 def main(): 10 print("Is moon a palindrome?", isPalindrome("moon")) 11 print("Is noon a palindrome?", isPalindrome("noon")) 12 print("Is a a palindrome?", isPalindrome("a")) 13 print("Is aba a palindrome?", isPalindrome("aba")) 14 print("Is ab a palindrome?", isPalindrome("ab")) 15 16 main() # Call the main function Is moon a palindrome? False Is noon a palindrome? True Is a a palindrome? True Is aba a palindrome? True Is ab a palindrome? False The string slicing operator in line 7 creates a new string that is the same as the original string except without the first and last characters. Checking whether a string is a palindrome is equivalent to checking whether the substring is a palindrome if the two end characters in the original string are the same. 15.9 Describe the characteristics of recursive functions. 15.10 Show the call stacks for isPalindrome("abcba") using the functions defined in Listing 15.3. 15.11 Show the output of the following two programs: def f(n): if n > 0:
print(n, end = ‘ ‘)
f(5)
f(n – 1)
def f(n):
if n > 0:
print(n, end = ‘ ‘)
f(5)
f(n – 1)
15.12 What is wrong in the following function?
def f(n):
if :
print(n, end = ‘ ‘)
f(n / 10)
f(1234567)
n != 0
15.5 Recursive Helper Functions
Sometimes you can find a recursive solution by slightly changing the original problem.
This new function is called a recursive helper function. The original problem can be
solved by invoking the recursive helper function.
The preceding recursive isPalindrome function is not efficient, because it creates a new string
for every recursive call. To avoid creating new strings, you can use the low and high indexes to
indicate the range of the substring. These two indexes must be passed to the recursive function.
✓Point✓Check
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508 Chapter 15 Recursion
helper function
base case
Since the original function is isPalindrome(s), you have to create the new function
isPalindromeHelper(s, low, high) to accept additional information on the string, as
shown in Listing 15.4.
LISTING 15.4 RecursivePalindrome.py
1
2 return isPalindromeHelper(s, 0, len(s) – 1)
3
4 :
5 if : # Base case
6 return True
7 elif : # Base case
8 return False
9 else:
10 return
11
12 def main():
13 print(“Is moon a palindrome?”, isPalindrome(“moon”))
14 print(“Is noon a palindrome?”, isPalindrome(“noon”))
15 print(“Is a a palindrome?”, isPalindrome(“a”))
16 print(“Is aba a palindrome?”, isPalindrome(“aba”))
17 print(“Is ab a palindrome?”, isPalindrome(“ab”))
18
19 main() # Call the main function
The isPalindrome(s) function checks whether a string s is a palindrome, and the
isPalindromeHelper(s, low, high) function checks whether a substring s[low :
high + 1] is a palindrome. The isPalindrome(s) function passes the string s with low
= 0 and high = len(s) – 1 to the isPalindromeHelper function, which can be
invoked recursively to check a palindrome in an ever-shrinking substring. It is a common
design technique in recursive programming to define a second function that receives addi-
tional parameters. Such a function is known as a recursive helper function.
Helper functions are very useful in designing recursive solutions for problems involving
strings and lists. The sections that follow give two more examples.
15.5.1 Selection Sort
Selection sort was introduced in Section 10.11.1. Recall that it finds the smallest element in a
list and swaps it with the first element. It then finds the smallest element remaining and swaps
it with the first element in the remaining list, and so on until the remaining list contains only a
single element. The problem can be divided into two subproblems:
■ Find the smallest element in the list and swap it with the first element.
■ Ignore the first element and sort the remaining smaller list recursively.
The base case is that the list contains only one element. Listing 15.5 gives the recursive
sort function.
LISTING 15.5 RecursiveSelectionSort.py
1 def sort(lst):
2 # Sort the entire list
3
4
5 if low < high: 6 # Find the smallest element and its index in lst[low .. high] 7 indexOfMin = low def sortHelper(lst, low, high): sortHelper(lst, 0, len(lst) - 1) isPalindromeHelper(s, low + 1, high - 1) s[low] != s[high] high <= low def isPalindromeHelper(s, low, high) def isPalindrome(s): base case recursive helper function helper function base case 15.5 Recursive Helper Functions 509 8 min = lst[low] 9 for i in range(low + 1, high + 1): 10 if lst[i] < min: 11 min = lst[i] 12 indexOfMin = i 13 14 # Swap the smallest in lst[low .. high] with lst[low] 15 lst[indexOfMin] = lst[low] 16 lst[low] = min 17 18 # Sort the remaining lst[low+1 .. high] 19 20 21 def main(): 22 lst = [3, 2, 1, 5, 9, 0] 23 sort(lst) 24 print(lst) 25 26 main() # Call the main function The sort(lst) function sorts a list in lst[0..len(lst) - 1] and the sortHelper(lst, low, high) function sorts a sublist in lst[low..high]. The second function can be invoked recursively to sort an ever-shrinking sublist. 15.5.2 Binary Search Binary search was introduced in Section 10.10.2. For a binary search to work, the elements in the list must already be ordered. The binary search first compares the key with the element in the middle of the list. Consider the following three cases: ■ Case 1: If the key is less than the middle element, the program recursively searches for the key in the first half of the list. ■ Case 2: If the key is equal to the middle element, the search ends with a match. ■ Case 3: If the key is greater than the middle element, the program recursively searches for the key in the second half of the list. Case 1 and Case 3 reduce the search to a smaller list. Case 2 is a base case when there is a match. Another base case is that the search is exhausted without a match. Listing 15.6 gives a simple solution for the binary search problem using recursion. LISTING 15.6 RecursiveBinarySearch.py 1 2 low = 0 3 high = len(lst) - 1 4 return recursiveBinarySearchHelper(lst, key, low, high) 5 6 7 if : # The list has been exhausted without a match 8 return –low - 1 9 10 mid = (low + high) // 2 11 if key < lst[mid]: 12 13 elif key == lst[mid]: 14 return mid 15 else: 16 return recursiveBinarySearchHelper(lst, key, mid + 1, high) return recursiveBinarySearchHelper(lst, key, low, mid - 1) low > high
def recursiveBinarySearchHelper(lst, key, low, high):
def recursiveBinarySearch(lst, key):
sortHelper(lst, low + 1, high) recursive call
helper function
base case
recursive call
base case
recursive call

510 Chapter 15 Recursion
17
18 def main():
19 lst = [3, 5, 6, 8, 9, 12, 34, 36]
20 print(recursiveBinarySearch(lst, 3))
21 print(recursiveBinarySearch(lst, 4))
22
23 main() # Call the main function
The recursiveBinarySearch function finds a key in the whole list (lines 1–4). The
recursiveBinarySearchHelper function finds a key in the list with the index from low
to high (lines 6–16).
The recursiveBinarySearch function passes the initial list with low = 0 (line 2) and
high = len(lst) – 1 (line 3) to the recursiveBinarySearchHelper function, which
is invoked recursively to find the key in an ever-shrinking sublist.
15.13 What is a recursive helper function?
15.14 Show the call stack for sort([2, 3, 5, 1]) using the function defined in
Listing 15.5.
15.6 Case Study: Finding the Directory Size
Recursive functions can efficiently solve problems with recursive structures.
The preceding examples can easily be solved without using recursion. This section presents a
problem that is difficult to solve without using recursion. The problem is to find the size of a
directory. The size of a directory is the sum of the sizes of all the files in the directory. A direc-
tory d may contain subdirectories. Suppose a directory contains files … and subdi-
rectories … as shown in Figure 15.5., dn,d1, d2,
, fmf1, f2,
directory
. . . d2d1
f1 f2 . . .fm dn
FIGURE 15.5 A directory contains files and subdirectories.
The size of the directory can be defined recursively as follows:
To implement the program, you need the following three functions from the os module:
■ os.path.isfile(s), which returns True if s is a filename. Recall that this func-
tion was introduced in §13.2.3 to check if a file exists.
■ os.path.getsize(filename), which returns the size of the file.
■ os.listdir(directory), which returns a list of the subdirectories and files
under the directory.
The program in Listing 15.7 prompts the user to enter a directory or a filename and dis-
plays its size.
size(d ) = size( f1) + size( f2) + c + size( fm) + size(d1) + size(d2) + c + size(dn)
✓Point✓Check
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Point

15.6 Case Study: Finding the Directory Size 511
LISTING 15.7 DirectorySize.py
1 import os
2
3 def main():
4 # Prompt the user to enter a directory or a file
5 path = input(“Enter a directory or a file: “).strip()
6
7 # Display the size
8 try:
9 print( , “bytes”)
10 except:
11 print(“Directory or file does not exist”)
12
13 :
14 size = 0 # Store the total size of all files
15
16 if not :
17 # All files and subdirectories
18 for subdirectory in lst:
19 size +=
20 else: # Base case, it is a file
21 size += os.path.getsize( ) # Accumulate file size
22
23 return size
24
25 main() # Call the main function
path
getSize(path + “\\” + subdirectory)
lst = os.listdir(path)
os.path.isfile(path)
def getSize(path)
getSize(path) invoke function
Enter a directory or a file:
619631 bytes
c:\pybook
Enter a directory or a file:
76 bytes
c:\pybook\Welcome.py
Enter a directory or a file:
Directory or file does not exist
c:\book\NonExistentFile
If the path is a directory (line 16), each subitem (file or subdirectory) in the directory is
recursively invoked to obtain its size (line 19). If the path is a file (line 20), the file size is
obtained (line 21).
If the user enters an incorrect or a nonexistent file or directory, the program throws an
exception (line 11).
Tip
To avoid mistakes, it is a good practice to test base cases. For example, you should test
the program for an input of a filename, an empty directory, a nonexistent directory, and
a nonexistent filename.
15.15 What function do you use to test if a filename exists? What function do you use to
return the size of a file? What function do you use to return all files and subdirectories
under a directory?
getSize function
is directory?
all subitems
recursive call
base case
testing base cases
✓Point✓Check

512 Chapter 15 Recursion
15.7 Case Study: Towers of Hanoi
The Towers of Hanoi problem is a classic problem that can be solved easily by using
recursion, but it is difficult to solve otherwise.
The Towers of Hanoi problem is a classic recursion problem that every computer scientist
knows. The problem involves moving a specified number of disks of distinct sizes from one
tower to another while observing the following rules:
■ There are n disks labeled 1, 2, 3, . . ., n, and three towers labeled A, B, and C.
■ No disk can be on top of a smaller disk at any time.
■ All the disks are initially placed on tower A.
■ Only one disk can be moved at a time, and it must be the top disk on a tower.
The objective of the problem is to move all the disks from tower A to tower B with the
assistance of tower C. For example, if you have three disks, the steps to move all of the disks
from tower A to B are shown in Figure 15.6.
A B C
A B C
A B C
A B C
A B CA C
B
Original position
Step 1: Move disk 1 from A to B
Step 2: Move disk 2 from A to C
Step 3: Move disk 1 from B to C
Step 4: Move disk 3 from A to B
Step 5: Move disk 1 from C to A
Step 7: Move disk 1 from A to B
Step 6: Move disk 2 from C to B
A A B C
B
C
0 4
1 5
2 6
3 7
1
2
3
2
3
3 1 2
23
1
3
2
31
1 3 2
2
1
1
1
23
FIGURE 15.6 The goal of the Towers of Hanoi problem is to move disks from tower A to
tower B without breaking the rules.
Note
The Towers of Hanoi is a classic computer-science problem, to which many Web sites
are devoted. One of them worth looking at is www.cut-the-knot.com/recurrence/hanoi.shtml.
Key
Point

www.cut-the-knot.com/recurrence/hanoi.shtml

15.7 Case Study: Towers of Hanoi 513
In the case of three disks, you can find the solution manually. For a larger number of disks,
however—even for four—the problem is quite complex. Fortunately, the problem has an
inherently recursive nature, which leads to a straightforward recursive solution.
The base case for the problem is n = 1. If n == 1, you could simply move the disk from
A to B. When n > 1, you could split the original problem into three subproblems and solve
them sequentially, as follows:
1. Move the first n – 1 disks from A to C with the assistance of tower B, as shown in Step 1
in Figure 15.7.
2. Move disk n from A to B, as shown in Step 2 in Figure 15.7.
3. Move n – 1 disks from C to B with the assistance of tower A, as shown in Step 3 in
Figure 15.7.
The following function moves n disks from the fromTower to the toTower with the assis-
tance of the auxTower:
def moveDisks(n, fromTower, toTower, auxTower):
The algorithm for the function can be described as follows:
if n == 1: # Stopping condition
Move disk 1 from the fromTower to the toTower
else:
moveDisks(n – 1, fromTower, auxTower, toTower)
Move disk n from the fromTower to the toTower
moveDisks(n – 1, auxTower, toTower, fromTower)
The program in Listing 15.8 prompts the user to enter the number of disks and invokes the
recursive function moveDisks to display the solution for moving the disks.
LISTING 15.8 TowersOfHanoi.py
1 def main():
2 n = eval(input(“Enter number of disks: “))
3
A B
Original position
C
A B
Step 1: Move the first n – 1 disks from
A to C recursively
C
A B
Step 2: Move disk n from A to B
C
A B
Step 3: Move n – 1 disks from
C to B recursively
C
.
.
.
n – 1 disks
.
.
.
n – 1 disks
.
.
.
n – 1 disks
.
.
.
n – 1 disks
20
31
FIGURE 15.7 The Towers of Hanoi problem can be decomposed into three subproblems.

514 Chapter 15 Recursion
4 # Find the solution recursively
5 print(“The moves are:”)
6
7
8 # The function for finding the solution to move n disks
9 # from fromTower to toTower with auxTower
10 def :
11 if n == 1: # Stopping condition
12 print(“Move disk”, n, “from”, fromTower, “to”, toTower)
13 else:
14
15 print(“Move disk”, n, “from”, fromTower, “to”, toTower)
16
17
18 main() # Call the main function
moveDisks(n – 1, auxTower, toTower, fromTower)
moveDisks(n – 1, fromTower, auxTower, toTower)
moveDisks(n, fromTower, toTower, auxTower)
moveDisks(n, ‘A’, ‘B’, ‘C’)
base case
recursion
recursion
Enter number of disks:
The moves are:
Move disk 1 from A to C
Move disk 2 from A to B
Move disk 1 from C to B
Move disk 3 from A to C
Move disk 1 from B to A
Move disk 2 from B to C
Move disk 1 from A to C
Move disk 4 from A to B
Move disk 1 from C to B
Move disk 2 from C to A
Move disk 1 from B to A
Move disk 3 from C to B
Move disk 1 from A to C
Move disk 2 from A to B
Move disk 1 from C to B
4
Consider tracing the program for n = 3. The successive recursive calls are shown in
Figure 15.8. As you can see, writing the program is easier than tracing the recursive calls. The
system uses stacks to trace the calls behind the scenes. To some extent, recursion provides a
level of abstraction that hides iterations and other details from the user.
moveDisks(2,’A’,’C’,’B’)
move disk 3 from A to B
moveDisks(2,’C’,’B’,’A’)
moveDisks(3,’A’,’B’,’C’)
moveDisks(1,’A’,’B’,’C’)
move disk 2 from A to C
moveDisks(1,’B’,’C’,’A’)
moveDisks(2,’A’,’C’,’B’)
moveDisks(1,’C’,’A’,’B’)
move disk 2 from C to B
moveDisks(1,’A’,’B’,’C’)
moveDisks(2,’C’,’B’,’A’)
moveDisks(1,’A’,’B’,’C’)
move disk 1 from A to B
moveDisks(1,’B’,’C’,’A’)
move disk 1 from B to C
moveDisks(1,’C’,’A’,’B’)
move disk 1 from C to A
moveDisks(1,’A’,’B’,’C’)
move disk 1 from A to B
FIGURE 15.8 Invoking moveDisks(3, ‘A’, ‘B’, ‘C’) spawns calls to moveDisks recursively.

15.8 Case Study: Fractals 515
15.16 How many times would the moveDisks function in Listing 15.8 be invoked for
moveDisks(5, ‘A’, ‘B’, ‘C’)?
15.8 Case Study: Fractals
Recursion is ideal for displaying fractals, because fractals are inherently recursive.
A fractal is a geometrical figure, but unlike triangles, circles, and rectangles, fractals can be
divided into parts, each of which is a reduced-size copy of the whole. There are many inter-
esting examples of fractals. This section introduces a simple fractal, the Sierpinski triangle,
named after a famous Polish mathematician.
A Sierpinski triangle is created as follows:
1. Begin with an equilateral triangle, which is considered to be a Sierpinski fractal of
order (or level) 0, as shown in Figure 15.9a.
2. Connect the midpoints of the sides of the triangle of order 0 to create a Sierpinski trian-
gle of order 1 (Figure 15.9b).
3. Leave the center triangle intact. Connect the midpoints of the sides of the three other tri-
angles to create a Sierpinski triangle of order 2 (Figure 15.9c).
4. You can repeat the same process recursively to create a Sierpinski triangle of order 3, 4,
and so on (Figure 15.9d).
(a) Order 0 (b) Order 1
(c) Order 2 (d) Order 3
FIGURE 15.9 A Sierpinski triangle is a pattern of recursive triangles.
✓Point✓Check
Key
Point

516 Chapter 15 Recursion
The problem is inherently recursive. How do you develop a recursive solution for it? Con-
sider the base case when the order is 0. It is easy to draw a Sierpinski triangle of order 0. How
do you draw a Sierpinski triangle of order 1? The problem can be reduced to drawing three Sier-
pinski triangles of order 0. How do you draw a Sierpinski triangle of order 2? The problem can
be reduced to drawing three Sierpinski triangles of order 1, so the problem of drawing a Sier-
pinski triangle of order n can be reduced to drawing three Sierpinski triangles of order n – 1.
Listing 15.9 is a program that displays a Sierpinski triangle of any order, as shown in Figure
15.9. You can enter an order in a text field to display a Sierpinski triangle of the specified order.
LISTING 15.9 SierpinskiTriangle.py
1 from tkinter import * # Import all definition from tkinter
2
3 class SierpinskiTriangle:
4 def __init__(self):
5 window = Tk() # Create a window
6 window.title(“Sierpinski Triangle”) # Set a title
7
8 self.width = 200
9 self.height = 200
10
11
12 self.canvas.pack()
13
14 # Add a label, an entry, and a button to frame1
15 frame1 = Frame(window) # Create and add a frame to window
16 frame1.pack()
17
18 Label(frame1,
19 text = “Enter an order: “).pack(side = LEFT)
20
21 entry = Entry(frame1, ,
22 justify = RIGHT).pack(side = LEFT)
23 Button(frame1, text = “Display Sierpinski Triangle”,
24 command = self.display).pack(side = LEFT)
25
26 window.mainloop() # Create an event loop
27
28
29 self.canvas.delete(“line”)
30 p1 = [self.width / 2, 10]
31 p2 = [10, self.height – 10]
32 p3 = [self.width – 10, self.height – 10]
33
34
35
36 # Base condition
37 # Draw a triangle to connect three points
38
39 self.drawLine(p2, p3)
40 self.drawLine(p3, p1)
41 else:
42 # Get the midpoint of each triangle’s edge
43 p12 = self.midpoint(p1, p2)
44 p23 = self.midpoint(p2, p3)
45 p31 = self.midpoint(p3, p1)
46
47 # Recursively display three triangles
48 self.displayTriangles(order – 1, p1, p12, p31)
self.drawLine(p1, p2)
if order == 0:
def displayTriangles(self, order, p1, p2, p3):
self.displayTriangles(int(self.order.get()), p1, p2, p3)
def display(self):
textvariable = self.order
self.order = StringVar()
width = self.width, height = self.height)
self.canvas = Canvas(window,create a canvas
create an entry
create a button
display triangle
recursive triangles
draw one triangle
get midpoints
top subtriangle

15.8 Case Study: Fractals 517
49 self.displayTriangles(order – 1, p12, p2, p23)
50 self.displayTriangles(order – 1, p31, p23, p3)
51
52 def drawLine(self, p1, p2):
53 self.canvas.create_line(
54 p1[0], p1[1], p2[0], p2[1], tags = “line”)
55
56 # Return the midpoint between two points
57 def midpoint(self, p1, p2):
58 p = 2 * [0]
59 p[0] = (p1[0] + p2[0]) / 2
60 p[1] = (p1[1] + p2[1]) / 2
61 return p
62
63 SierpinskiTriangle() # Create GUI
When you enter an order in the text field and then click the Display Sierpinski Triangle
button, the callback display function is invoked to create three points and display the trian-
gle (lines 30–33).
The three points of the triangle are passed to invoke displayTriangles (line 35). If
order == 0, the displayTriangles(order, p1, p2, p3) function displays a triangle
that connects three points p1, p2, and p3 in lines 38–40, as shown in Figure 15.10a. Other-
wise, it performs the following tasks:
1. Obtains a midpoint between p1 and p2 (line 43), a midpoint between p2 and p3 (line
44), and a midpoint between p3 and p1 (line 45), as shown in Figure 15.10b.
2. Recursively invokes displayTriangles with a reduced order to display three smaller
Sierpinski triangles (lines 48–50). Note that each small Sierpinski triangle is struc-
turally identical to the original big Sierpinski triangle except that the order of a small
triangle is one less, as shown in Figure 15.10b.
p1
p3p2
Draw the Sierpinski triangle
displayTriangles(order, p1, p2, p3)
p1
(a)
p3p2
p12 p31
p23
Recursively draw the small Sierpinski triangle
displayTriangles(
order – 1, p1, p12, p31)
Recursively draw the
small Sierpinski triangle
displayTriangles(
order – 1, p31, p23, p3)
Recursively draw the small
Sierpinski triangle
displayTriangles(
order – 1, p12, p2, p23)
(b)
FIGURE 15.10 Drawing a Sierpinski triangle spawns calls to draw three small Sierpinski triangles recursively.
left subtriangle
right subtriangle
draw a line
midpoint
create GUI
display function
displayTriangles
function

518 Chapter 15 Recursion
15.9 Case Study: Eight Queens
The Eight Queens problem is to find a solution to place a queen in each row on a
chessboard so that no two queens can attack each other.
This case study creates a program that arranges eight queens on a chessboard. There can only
be one queen in each row, and the queens must be positioned such that no two queens can take
the other. You need to use a two-dimensional list to represent the chessboard, but because
each row can have only one queen, it is sufficient to use a one-dimensional list to denote the
queen’s position in the row. So, create a list named queens as follows:
queens = 8 * [-1]
Assign j to queens[i] to denote that a queen is placed in row i and column j. Figure
15.11a shows the contents of the list queens for the chessboard in Figure 15.11b. Initially,
queens[i] = -1 indicates that row i is not occupied.
The program in Listing 15.10 displays a solution for the Eight Queens problem.
LISTING 15.10 EightQueens.py
1 from tkinter import * # Import all definitions from tkinter
2
3 SIZE = 8 # The size of the chessboard
4 class EightQueens:
5 def __init__(self):
6 self.queens = SIZE * [-1] # Queen positions
7 self.search(0) # Search for a solution from row 0
8
9 # Display solution in queens
10 window = Tk() # Create a window
11 window.title(“Eight Queens”) # Set a title
12
13
14 for i in range(SIZE):
15 for j in range(SIZE):
16 if self.queens[i] == j:
17 Label(window, ).grid(
18 row = i, column = j)
image = image
image = PhotoImage(file = “image/queen.gif”)
initialize queens
start search
create queen image
display chessboard
display queen
(a) (b)
0
4
7
5
2
6
1
3
queens[0]
queens[1]
queens[2]
queens[3]
queens[4]
queens[5]
queens[6]
queens[7]
FIGURE 15.11 queens[i] denotes the position of the queen in row i.
Key
Point

15.9 Case Study: Eight Queens 519
19 else:
20 Label(window, width = 5, height = 2,
21 bg = “red”).grid(row = i, column = j)
22
23 window.mainloop() # Create an event loop
24
25 # Search for a solution starting from a specified row
26
27 if row == SIZE: # Stopping condition
28 return True # A solution found to place 8 queens
29
30 for column in range(SIZE):
31 self.queens[row] = column # Place it at (row, column)
32 if self.isValid(row, column) and :
33 return True # Found and exit for loop
34
35 # No solution for a queen placed at any column of this row
36 return False
37
38 # Check if a queen can be placed at row i and column j
39
40 for i in range(1, row + 1):
41 if ( # Check column
42 or
43 or :
44 return False # There is a conflict
45 return True # No conflict
46
47 EightQueens() # Create GUI
The program initializes the list queens with eight values –1 to indicate that no queens
have been placed on the chessboard (line 6). The program invokes search(0) (line 7) to start
a search for a solution from row 0, which recursively invokes search(1), search(2), …,
and search(7) (line 32).
After a solution is found, the program displays 64 labels in the window (8 per row) and
places a queen image in the cell at queens[i] for each row i (line 17).
The recursive search(row) function returns True if all the rows are filled (lines
27–28). The function checks whether a queen can be placed in column 0, 1, 2, …, and 7 in
a for loop (line 30). The program places a queen in the column (line 31). If the placement
is valid, the program recursively searches for the next row by invoking search(row + 1)
(line 32). If this search is successful, the program returns True (line 33) to exit the for
loop. In this case, there is no need to look for the next column in the row. If there is no solu-
tion that allows a queen to be placed in any column in this row, the function returns False
(line 36).
Suppose you invoke search(row) for row 3, as shown in Figure 15.12a. The function
tries to fill in a queen in column 0, 1, 2, and so on in this order. For each trial, the
isValid(row, column) function (line 32) is called to check whether placing a queen at the
specified position causes a conflict with the queens placed earlier. It also ensures that no
queen is placed in the same column (line 41), upper left diagonal (line 42), or upper right
diagonal (line 43), as shown in Figure 15.12b. If isValid(row, column) returns False,
the program checks the next column, as shown in Figure 15.12c. If isValid(row, column)
returns True, the program recursively invokes search(row + 1), as shown in Figure
15.12d. If search(row + 1) returns False, the program checks the next column on the
preceding row, as shown Figure 15.12c.
self.queens[row – i] == column + i)
self.queens[row – i] == column – i
self.queens[row – i] == column
def isValid(self, row, column):
self.search(row + 1)
def search(self, row): search this row
search columns
place a queen
recursive call
found
not found
check validity
check column
check upleft diagonal
check upright diagonal

520 Chapter 15 Recursion
15.10 Recursion vs. Iteration
Recursion is an alternative form of program control. It is essentially repetition without
a loop.
When you use loops, you specify a loop body. The repetition of the loop body is controlled by
the loop control structure. In recursion, the function itself is called repeatedly. A selection
statement must be used to control whether to call the function recursively or not.
Recursion bears substantial overhead. Each time the program calls a function, the system must
allocate memory for all of the function’s local variables and parameters. This can consume
considerable computer memory and requires extra time to manage the additional memory.
Any problem that can be solved recursively can be solved nonrecursively with iterations.
Recursion has at least one negative aspect: that is, it uses up too much time and memory. Why,
then, should you use it? In some cases, using recursion enables you to specify a clear, simple
solution for an inherently recursive problem that would otherwise be difficult to achieve. For
example, the directory-size problem, the Towers of Hanoi problem, and the fractal problem
are rather cumbersome to solve without using recursion.
The decision whether to use recursion or iteration should be based on the nature of, and your
understanding of, the problem you are trying to solve. The rule of thumb is to use whichever
approach can best develop an intuitive solution that naturally mirrors the problem. If an iterative
solution is obvious, use it—it will generally be more efficient than the recursive option.
Caution
Recursive programs can run out of memory, causing a stack-overflow exception.
Tip
Avoid using recursion if you are concerned about your program’s performance, because
it takes more time and consumes more memory than iteration. In general, recursion can
be used to solve the inherent recursive problems such as Towers of Hanoi, Directory
size, and Sierpinski triangles.
recursion overhead
recursion advantages
recursion or iteration?
stack overflow
0 1 2 3 4 5 6 7
0
1
2
3
4
5
6
7
(a)
upright diagonal
search(row)
check
column
0 1 2 3 4 5 6 7
0
1
2
3
4
5
6
7
(b)
upright diagonal
check
column
upleft
0 1 2 3 4 5 6 7
0
1
2
3
4
5
6
7
(c)
upright diagonal
check
column
upleft
0 1 2 3 4 5 6 7
0
1
2
3
4
5
6
7
(d)
upright diagonal
search(row
1)
check
column
search(row)
search(row)
FIGURE 15.12 Invoking search(row) fills in a queen in a column in the row.
performance concern
Key
Point

15.11 Tail Recursion 521
15.17 Which of the following statements are true?
■ Any recursive function can be converted into a nonrecursive function.
■ Recursive functions take more time and memory to execute than nonrecursive
functions.
■ Recursive functions are always simpler than nonrecursive functions.
■ There is always a selection statement in a recursive function to check whether a
base case is reached.
15.18 What is a cause for a stack-overflow exception?
15.11 Tail Recursion
A tail recursive function is efficient for reducing stack size.
A recursive function is said to be tail recursive if there are no pending operations to be per-
formed on return from a recursive call, as illustrated in Figure 15.13a. However, function B in
Figure 15.13b is not tail recursive because there are pending operations after a function call is
returned.
For example, the recursive isPalindromeHelper function (lines 4–10) in Listing 15.4 is
tail recursive because there are no pending operations after recursively invoking
isPalindromeHelper in line 10. However, the recursive factorial function (lines 6–10)
in Listing 15.1 is not tail recursive, because there is a pending operation, namely multiplica-
tion, to be performed on return from each recursive call.
Tail recursion may be desirable: Because the function ends when the last recursive call
ends, there is no need to store the intermediate calls in the stack.
A nontail-recursive function can often be converted to a tail-recursive function by using
auxiliary parameters. These parameters are used to contain the result. The idea is to incorpo-
rate the pending operations into the auxiliary parameters in such a way that the recursive call
no longer has a pending operation. You may define a new auxiliary recursive function with the
auxiliary parameters. For example, the factorial function in Listing 15.1 can be written in
a tail-recursive way as follows:
1 # Return the factorial for a specified number
2 def factorial(n):
3 return factorialHelper(n, 1) # Call auxiliary function
4
5 # Auxiliary tail-recursive function for factorial
6 def factorialHelper(n, result):
FIGURE 15.13
Recursive function A
…
…
…
Invoke function A recursively
(a) Tail recursion
Recursive function B
…
…
Invoke function B recursively
…
…
(b) Nontail recursion
A tail-recursive function has no pending operations after a recursive call.
tail recursive
original function
invoke auxiliary function
auxiliary function
Key
Point
✓Point✓Check

522 Chapter 15 Recursion
7 if n == 0:
8 return result
9 else:
10 return factorialHelper(n – 1, n * result)
The first factorial function simply invokes the auxiliary function (line 3). In line 6, the
auxiliary function contains the auxiliary parameter result that stores the result for a factorial
of n. This function is invoked recursively in line 10. There is no pending operation after a call
is returned. The final result is returned in line 8, which is also the return value from invoking
factorialHelper(n, 1) in line 3.
15.19 What is tail recursion?
15.20 Why is tail recursion desirable?
15.21 Is the recursive selection function in Listing 15.5 tail recursive?
15.22 Rewrite the fib function in Listing 15.2 using tail recursion.
KEY TERMS
recursive call
base case 500
direct recursion 503
indirect recursion 503
infinite recursion 503
recursive function 500
recursive helper function 508
stopping condition 500
tail recursive 521
CHAPTER SUMMARY
1. A recursive function is one that directly or indirectly invokes itself. For a recursive
function to terminate, there must be one or more base cases.
2. Recursion is an alternative form of program control. It is essentially repetition with-
out a loop control. It can be used to specify simple, clear solutions for inherently
recursive problems that would otherwise be difficult to solve.
3. Sometimes the original function needs to be modified to receive additional parame-
ters in order to be invoked recursively. A recursive helper function can be defined for
this purpose.
4. Recursion bears substantial overhead. Each time the program calls a function, the
system must allocate memory for all of the function’s local variables and parameters.
This can consume considerable computer memory and requires extra time to manage
the additional memory.
5. A recursive function is said to be tail recursive if there are no pending operations to
be performed on return from a recursive call. Tail recursion is efficient.
TEST QUESTIONS
Do test questions for this chapter online at www.cs.armstrong.edu/liang/py/test.html.
✓Point✓Check

www.cs.armstrong.edu/liang/py/test.html

Programming Exercises 523
PROGRAMMING EXERCISES
Sections 15.2–15.3
*15.1 (Sum the digits in an integer using recursion) Write a recursive function that com-
putes the sum of the digits in an integer. Use the following function header:
def sumDigits(n):
For example, sumDigits(234) returns Write a test program
that prompts the user to enter an integer and displays its sum.
*15.2 (Fibonacci numbers) Rewrite the fib function in Listing 15.2 using iterations.
(Hint: To compute fib(n) without recursion, you need to obtain fib(n – 2)
and fib(n – 1) first.) Let f0 and f1 denote the two previous Fibonacci num-
bers. The current Fibonacci number would then be f0 + f1. The algorithm can be
described as follows:
f0 = 0 # For fibs(0)
f1 = 1 # For fib(1)
for i in range(2, n + 1):
currentFib = f0 + f1
f0 = f1
f1 = currentFib
# After the loop, currentFib is fib(n)
Write a test program that prompts the user to enter an index and displays its
Fibonacci number.
*15.3 (Compute greatest common divisor using recursion) The gcd(m, n) can also be
defined recursively as follows:
■ If m % n is 0, gcd(m, n) is n.
■ Otherwise, gcd(m, n) is gcd(n, m % n).
Write a recursive function to find the GCD. Write a test program that prompts the
user to enter two integers and displays their GCD.
15.4 (Sum series) Write a recursive function to compute the following series:
Write a test program that displays m(i) for i 1, 2, …, 10.
15.5 (Sum series) Write a recursive function to compute the following series:
Write a test program that displays m(i) for i 1, 2, …, 10.
*15.6 (Summing series) Write a recursive function to compute the following series:
Write a test program that prompts the user to enter an integer for i and displays m(i).
*15.7 (Fibonacci series) Modify Listing 15.2 so that the program finds the number of
times the fib function is called. (Hint: Use a global variable and increment it
every time the function is called.)
m(i) =
1
2
+
2
3
+ c +
i
i + 1
=
m(i) =
1
3
+
2
5
+
3
7
+
4
9
+
5
11
+
6
13
+ c +
i
2i + 1
=
m(i) = 1 +
1
2
+
1
3
+ c +
1
i
2 + 3 + 4 = 9.

524 Chapter 15 Recursion
Section 15.4
*15.8 (Print the digits in an integer reversely) Write a recursive function that displays
an integer value reversely on the console using the following header:
def reverseDisplay(value):
For example, invoking reverseDisplay(12345) displays 54321. Write a test
program that prompts the user to enter an integer and displays its reversal.
*15.9 (Print the characters in a string reversely) Write a recursive function that dis-
plays a string reversely on the console using the following header:
def reverseDisplay(value):
For example, reverseDisplay(“abcd”) displays dcba. Write a test program
that prompts the user to enter a string and displays its reversal.
*15.10 (Occurrences of a specified character in a string) Write a recursive function that
finds the number of occurrences of a specified letter in a string using the follow-
ing function header.
def count(s, a):
For example, count(“Welcome”, ‘e’) returns 2. Write a test program that
prompts the user to enter a string and a character, and displays the number of
occurrences for the character in the string.
Section 15.5
**15.11 (Print the characters in a string reversely) Rewrite Exercise 15.9 using a helper
function to pass the substring for the high index to the function. The helper
function header is:
def reverseDisplayHelper(s, high):
*15.12 (Find the largest number in a list) Write a recursive function that returns the
largest integer in a list. Write a test program that prompts the user to enter a list
of integers and displays the largest element.
*15.13 (Find the number of uppercase letters in a string) Write a recursive function to
return the number of uppercase letters in a string using the following function
headers:
def countUppercase(s):
def countUppercaseHelper(s, high):
Write a test program that prompts the user to enter a string and displays the num-
ber of uppercase letters in the string.
*15.14 (Occurrences of a specified character in a string) Rewrite Exercise 15.10 using a
helper function to pass the substring of the high index to the function. The
helper function header is:
def countHelper(s, a, high):
*15.15 (Find the number of uppercase letters in a list) Write a recursive function to
return the number of uppercase letters in a list of characters. You need to define
the following two functions. The second one is a recursive helper function.
def count(chars):
def countHelper(chars, high):
Write a test program that prompts the user to enter a list of characters in one line
and displays the number of uppercase letters in the list.

Programming Exercises 525
*15.16 (Occurrences of a specified character in a list) Write a recursive function that finds
the number of occurrences of a specified character in a list. You need to define the
following two functions. The second one is a recursive helper function.
def count(chars, ch):
def countHelper(chars, ch, high):
Write a test program that prompts the user to enter a list of characters in one line,
and a character, and displays the number of occurrences of the character in the list.
Sections 15.6–15.11
*15.17 (Tkinter: Sierpinski triangle) Revise Listing 15.9 to let the user use left-
mouse/right-mouse clicks to increase/decrease the current order by 1. The initial
order is 0.
*15.18 (Towers of Hanoi) Modify Listing 15.8, TowersOfHanoi.py, so that the program
finds the number of moves needed to move n disks from tower A to tower B.
(Hint: Use a global variable and increment it for every move.)
*15.19 (Decimal to binary) Write a recursive function that converts a decimal number
into a binary number as a string. The function header is as follows:
def decimalToBinary(value):
Write a test program that prompts the user to enter a decimal number and dis-
plays its binary equivalent.
*15.20 (Decimal to hex) Write a recursive function that converts a decimal number into
a hex number as a string. The function header is as follows:
def decimalToHex(value):
Write a test program that prompts the user to enter a decimal number and dis-
plays its hex equivalent.
*15.21 (Binary to decimal) Write a recursive function that parses a binary number as a
string into a decimal integer. The function header is as follows:
def binaryToDecimal(binaryString):
Write a test program that prompts the user to enter a binary string and displays its
decimal equivalent.
*15.22 (Hex to decimal) Write a recursive function that parses a hex number as a string
into a decimal integer. The function header is as follows:
def hexToDecimal(hexString):
Write a test program that prompts the user to enter a hex string and displays its
decimal equivalent.
**15.23 (String permutation) Write a recursive function to print all the permutations of a
string. For example, for the string abc, the printout is:
abc
acb
bac
bca
cab
cba
(Hint: Define the following two functions. The second function is a helper function.
def displayPermuation(s):
def displayPermuationHelper(s1, s2):

526 Chapter 15 Recursion
The first function simply invokes displayPermuation(” “, s). The second
function uses a loop to move a character from s2 to s1 and recursively invokes
it with a new s1 and s2. The base case is that s2 is empty and prints s1 to the
console.)
Write a test program that prompts the user to enter a string and displays all its
permutations.
*15.24 (Number of files in a directory) Write a program that prompts the user to enter a
directory and displays the number of files in the directory.
**15.25 (Tkinter: Koch snowflake fractal ) Section 15.8 presented the Sierpinski triangle
fractal. In this exercise, you will write a program to display another fractal,
called the Koch snowflake, named after a famous Swedish mathematician. A
Koch snowflake is created as follows:
1. Begin with an equilateral triangle, which is considered to be the Koch fractal
of order (or level) 0, as shown in Figure 15.14a.
2. Divide each line in the shape into three equal line segments and draw an out-
ward equilateral triangle with the middle line segment as the base to create a
Koch fractal of order 1, as shown in Figure 15.14b.
3. Repeat Step 2 to create a Koch fractal of order 2, 3, …, and so on, as shown in
Figure 15.14c–d.
(a) (b) (c) (d)
FIGURE 15.14 A Koch snowflake is a fractal starting with a triangle.
**15.26 (Turtle: Koch snowflake fractal) Rewrite the Koch snowflake program in Exer-
cise 15.25 using Turtle, as shown in Figure 15.15. Your program should prompt
the user to enter the order and display the corresponding fractal for the order.
(a) (b) (c) (d)
FIGURE 15.15 The Koch snowflake fractal is drawn using Turtle.

Programming Exercises 527
**15.27 (All eight queens) Modify Listing 15.10, EightQueens.py, to find all the possible
solutions to the Eight Queens problem.
**15.28 (Find words) Write a program that finds all the occurrences of a word in all the
files under a directory, recursively. Your program should prompt the user to enter
a directory name.
**15.29 (Tkinter: H-tree fractal) An H-tree is a fractal defined as follows:
1. Begin with a letter H. The three lines of the H are of the same length, as shown
in Figure 15.1a.
2. The letter H (in its sans-serif form, H) has four endpoints. Draw an H centered
at each of the four endpoints to an H-tree of order 1, as shown in Figure 15.1b.
These Hs are half the size of the H that contains the four endpoints.
3. Repeat Step 2 to create an H-tree of order 2, 3, …, and so on, as shown in
Figure 15.1c–d.
Write a Python program that draws an H-tree, as shown in Figure 15.1.
**15.30 (Turtle: H-tree fractal) Rewrite the H-tree fractal in Exercise 15.29 using Turtle,
as shown in Figure 15.16. Your program should prompt the user to enter the
order and display the corresponding fractal for the order.
(a) (b) (c) (d)
FIGURE 15.16 An H-tree fractal is drawn using Turtle for order of 0 in (a), 1 in (b), 2 in (c), and 3 in (d).
**15.31 (Tkinter: Recursive tree) Write a program to display a recursive tree, as shown in
Figure 15.17.
(a) (b) (c) (d)
FIGURE 15.17 A recursive tree with the specified depth is drawn.
**15.32 (Turtle: Recursive tree) Rewrite the recursive tree in Exercise 15.31 using Turtle,
as shown in Figure 15.18. Your program should prompt the user to enter the
order and display the corresponding fractal for the order.

528 Chapter 15 Recursion
**15.33 (Tkinter: Hilbert curve) The Hilbert curve, first described by German mathe-
matician David Hilbert in 1891, is a space-filling curve that visits every point in
a square grid with a size of or any other power
of 2. Write a program that displays a Hilbert curve for the specified order, as
shown in Figure 15.19.
2 * 2, 4 * 4, 8 * 8, 16 * 16,
**15.34 (Turtle: Hilbert curve) Rewrite the Hilbert curve in Exercise 15.33 using Turtle,
as shown in Figure 15.20. Your prsogram should prompt the user to enter the
order and display the corresponding fractal for the order.
(a) (b) (c) (d)
FIGURE 15.18 A recursive tree is drawn using Turtle with depth 0 in (a), 1 in (b), 2 in (c), and 3 in (d).
(a) (b) (c) (d)
FIGURE 15.19 A Hilbert curve with the specified order is drawn.
(a) (b) (c) (d)
FIGURE 15.20 A Hilbert curve is drawn using Turtle with order 0 in (a), 1 in (b), 2 in (c), and 3 in (d).

Programming Exercises 529
15.35 (Tkinter: Sierpinski triangle) Revise Listing 15.9, SierpinskiTriangle.py, to dis-
play the filled Sierpinski triangles, as shown in Figure 15.21.
15.36 (Turtle: Sierpinski triangle) Rewrite Listing 15.9, SierpinskiTriangle.py, using
Turtle.
FIGURE 15.21 Filled Sierpinski triangles are displayed.

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APPENDIXES
Appendix A
Python Keywords
Appendix B
The ASCII Character Set
Appendix C
Number Systems
531

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APPENDIX A
Python Keywords
The following keywords are reserved by the Python language. They should not be used for
anything other than their predefined purpose in Python.
and
as
assert
break
class
continue
def
del
elif
else
except
False
finally
for
from
global
if
import
in
is
lambda
None
nonlocal
not
or
pass
raise
return
True
try
while
with
yield
533

APPENDIX B
The ASCII Character Set
Tables B.1 and B.2 show ASCII characters and their respective decimal and hexadecimal
codes. The decimal or hexadecimal code of a character is a combination of its row index and
column index. For example, in Table B.1, the letter A is at row 6 and column 5, so its decimal
equivalent is 65; in Table B.2, letter A is at row 4 and column 1, so its hexadecimal equiva-
lent is 41.
534

TABLE B.1 ASCII Character Set in the Decimal Index
0 1 2 3 4 5 6 7 8 9
0 nul soh stx etx eot enq ack bel bs ht
1 nl vt ff cr so si dle dcl dc2 dc3
2 dc4 nak syn etb can em sub esc fs gs
3 rs us sp ! ” # $ % & ’
4 ( ) * + , – . / 0 1
5 2 3 4 5 6 7 8 9 : ;
6 6 = 7 ? @ A B C D E
7 F G H I J K L M N O
8 P Q R S T U V W X Y
9 Z [ \ ] ¿ – ‘ a b c
10 d e f g h i j k l m
11 n o p q r s t u v w
12 x y z { � } + del
TABLE B.2 ASCII Character Set in the Hexadecimal Index
0 1 2 3 4 5 6 7 8 9 A B C D E F
0 nul soh stx etx eot enq ack bel bs ht nl vt ff cr so si
1 dle dcl dc2 dc3 dc4 nak syn etb can em sub esc fs gs rs us
2 sp ! ” # $ % & ’ ( ) * + , – . /
3 0 1 2 3 4 5 6 7 8 9 : ; 6 = 7 ?
4 @ A B C D E F G H I J K L M N O
5 P Q R S T U V W X Y Z [ \ ] ¿ –
6 ‘ a b c d e f g h i j k l m n o
7 p q r s t u v w x y z { � } + del535

APPENDIX C
Number Systems
C.1 Introduction
Computers use binary numbers internally, because computers are made naturally to store and
process 0s and 1s. The binary number system has two digits, 0 and 1. A number or character
is stored as a sequence of 0s and 1s. Each 0 or 1 is called a bit (binary digit).
In our daily life we use decimal numbers. When we write a number such as 20 in a pro-
gram, it is assumed to be a decimal number. Internally, computer software is used to convert
decimal numbers into binary numbers, and vice versa.
We write computer programs using decimal numbers. However, to deal with an operating
system, we need to reach down to the “machine level” by using binary numbers. Binary num-
bers tend to be very long and cumbersome. Often hexadecimal numbers are used to abbrevi-
ate them, with each hexadecimal digit representing four binary digits. The hexadecimal
number system has 16 digits: 0–9 and A–F. The letters A, B, C, D, E, and F correspond to the
decimal numbers 10, 11, 12, 13, 14, and 15.
The digits in the decimal number system are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. A decimal num-
ber is represented by a sequence of one or more of these digits. The value that each digit rep-
resents depends on its position, which denotes an integral power of 10. For example, the digits
7, 4, 2, and 3 in decimal number 7423 represent 7000, 400, 20, and 3, respectively, as shown
below:
The decimal number system has ten digits, and the position values are integral powers of 10.
We say that 10 is the base or radix of the decimal number system. Similarly, since the binary
number system has two digits, its base is 2, and since the hex number system has 16 digits, its
base is 16.
If 1101 is a binary number, the digits 1, 1, 0, and 1 represent and
respectively:
If 7423 is a hex number, the digits 7, 4, 2, and 3 represent and
respectively:
163 162 161 160 = 28672 + 1024 + 32 + 3 = 29731
� 7 � 4 � 2 � 3 � = 7 * 163 + 4 * 162 + 2 * 161 + 3 * 160
3 * 160,
7 * 163, 4 * 162, 2 * 161,
23 ˛ 22 21 20 = 8 + 4 + 0 + 1 = 13
� 1 � 1 � 0 � 1 � = 1 * 23 + 1 * 22 + 0 * 21 + 1 * 20
1 * 20,
1 * 23, 1 * 22, 0 * 21,
103 102 101 100 = 7000 + 400 + 20 + 3 = 7423
� 7 � 4 � 2 � 3 � = 7 * 103 + 4 * 102 + 2 * 101 + 3 * 100
536
hexadecimal number
decimal numbers
binary numbers
radix
base

Appendix C 537
binary to decimal
C.2 Conversions Between Binary and Decimal Numbers
Given a binary number the equivalent decimal value is
Here are some examples of converting binary numbers to decimals:
bn * 2n + bn-1 * 2n-1 + bn-2 * 2n-2 + c + b2 * 22 + b1 * 21 + b0 * 20
bnbn-1bn-2 c b2b1b0,
Binary Conversion Formula Decimal
10 1 * 21 + 0 * 20 2
1000 1 * 23 + 0 * 22 + 0 * 21 + 0 * 20 8
10101011
1 * 21 + 1 * 20
1 * 27 + 0 * 26 + 1 * 25 + 0 * 24 + 1 * 23 + 0 * 22 + 171
To convert a decimal number d to a binary number is to find the bits
and such that
These bits can be found by successively dividing d by 2 until the quotient is 0. The remainders
are and
For example, the decimal number 123 is 1111011 in binary. The conversion is done as follows:
bn., bn-2, bn-1,b0, b1, b2,c
d = bn * 2n + bn-1 * 2n-1 + bn-2 * 2n-2 + c + b2 * 22 + b1 * 21 + b0 * 20
b0
, b2, b1,bn, bn-1, bn-2,c
2 1
0
1
b6
0
2 3
2
1
2 7
6
b4
1
3
b5
1
2
Quotient
Remainder
15
14
b3
1
7
2
30
b2
0
15
2
60
61
b1
1
30
b0
2
122
1
61
12330
Tip
The Windows Calculator, as shown in Figure C.1, is a useful tool for performing number
conversions. To run it, search for Calculator from the Start button and launch Calculator,
then under View select Scientific.
BinaryDecimal
Hex
FIGURE C.1 You can perform number conversions using the Windows Calculator.
decimal to binary

Hexadecimal Conversion Formula Decimal
7F 7 * 161 + 15 * 160 127
FFFF 15 * 163 + 15 * 162 + 15 * 161 + 15 * 160 65535
431 4 * 162 + 3 * 161 + 1 * 160 1073
538 Appendix C
binary to hex
hex to binary
decimal to hex
hex to decimal
C.3 Conversions Between Hexadecimal and Decimal
Numbers
Given a hexadecimal number the equivalent decimal value is
Here are some examples of converting hexadecimal numbers to decimals:
+ h2 * 162 + h1 * 161 + h0 * 160hn * 16n + hn-1 * 16n-1 + hn-2 * 16n-2 + c
hnhn-1hn-2 c h2h1h0,
To convert a decimal number d to a hexadecimal number is to find the hexadecimal digits
and such that
These numbers can be found by successively dividing d by 16 until the quotient is 0. The
remainders are and
For example, the decimal number 123 is 7B in hexadecimal. The conversion is done as
follows:
hn., hn-2, hn-1,h0, h1, h2,c
+ h1 * 161 + h0 * 160
+ h2 * 162d = hn * 16n + hn-1 * 16n-1 + hn-2 * 16n-2 + c
h0, h2, h1,hn, hn-1, hn-2,c
Quotient
Remainder
16 7
0
7
h1
0
16 123
112
11
h0
7
C.4 Conversions Between Binary and Hexadecimal
Numbers
To convert a hexadecimal to a binary number, simply convert each digit in the hexadecimal
number into a four-digit binary number, using Table C.1.
For example, the hexadecimal number 7B is 1111011, where 7 is 111 in binary, and B is
1011 in binary.
To convert a binary number to a hexadecimal, convert every four binary digits from right to
left in the binary number into a hexadecimal number.
For example, the binary number 1110001101 is 38D, since 1101 is D, 1000 is 8, and 11 is
3, as shown below.
1 1 1 0 0 0 1 1 0 1
D83

Appendix C 539
TABLE C.1 Converting Hexadecimal to Binary
Hexadecimal Binary Decimal
0 0000 0
1 0001 1
2 0010 2
3 0011 3
4 0100 4
5 0101 5
6 0110 6
7 0111 7
8 1000 8
9 1001 9
A 1010 10
B 1011 11
C 1100 12
D 1101 13
E 1110 14
F 1111 15
Note
Octal numbers are also useful. The octal number system has eight digits, 0 to 7. A deci-
mal number 8 is represented in the octal system as 10.
Here are some good online resources for practicing number conversions:
■ http://forums.cisco.com/CertCom/game/binary_game_page.htm
■ http://people.sinclair.edu/nickreeder/Flash/binDec.htm
■ http://people.sinclair.edu/nickreeder/Flash/binHex.htm
REVIEW QUESTIONS
1. Convert the following decimal numbers into hexadecimal and binary numbers:
100; 4340; 2000
2. Convert the following binary numbers into hexadecimal and decimal numbers:
1000011001; 100000000; 100111
3. Convert the following hexadecimal numbers into binary and decimal numbers:
FEFA9; 93; 2000

http://forums.cisco.com/CertCom/game/binary_game_page.htm

http://people.sinclair.edu/nickreeder/Flash/binDec.htm

http://people.sinclair.edu/nickreeder/Flash/binHex.htm

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INDEX
Symbols and numbers
” (double quotes), 67–68
‘ (single quotes), 68
– (subtraction) operator, 40, 43–44
” ” (quotation marks), 16
/ (float division) operator, 40–41, 44
// (integer division) operator, 40–41, 43–44
\’ character, 70
\\ character, 70
\” character, 70
\ character, 72
\b character, 72
\f character, 71
\n character, 71–72
\r character, 71–72
\t character, 72
_ (underscore), identifiers, 36
__ (underscores)
__init__ method. see __init__ method
overview of, 227–229
+ (addition) operator, 40, 43–44, 71
+ (concatenation) operator, 71, 245, 318
+= (augmented assignment) operator, 44, 71
= (assignment) operator, 37, 117
”’ ”’ (paragraph comments), 16–17
% (remainder or modulo) operator, 41–44
( ) parentheses, 16, 476
* (multiplication) operator, 40, 43–44
* (repetition) operator, 245, 318
** (exponentiation) operator, 40–41, 43–44
[ ]. see Index operator [ ]
{} (curly braces), 479, 488
< (left-justification), 79 >>> (statement prompt), 15–16
1000BaseT, 8
A
Abbreviations, avoiding in identifiers, 36
abs(), 64–65
Absolute filenames, 440–441
Accessor (getter), 227, 232
accumulate(), 366
acos(), 65–67
Activation record, functions, 175
Activefill argument, Canvas, 283
Actual parameter, 173
Add button, 467–470
add method
add element to set, 479, 495
bouncing balls, 347
add_cascade method, 290, 292
add_command method, 290–293
Addition operator
concatenating two strings, 71
defined, 40
forming augmented assignment operators, 44
operator precedence rule, 43–44
addPoint(), 371–372
Address book case study, 467–470
addThisPoint(), 371–372
Aggregated object, 419–421
Aggregating class, 419–421
Aggregating object, 419–421
Aggregation relationships, 419–421
Algorithms, translating into programs, 32
and operator, 110–113
animate method, 300, 347
Animations
bouncing balls, 345–347
defined, 332
developing in Tkinter, 297–300
Anonymous objects, 219
append method, list class, 320
Appending data to end of file, 447
Arcs
displaying figures, 425–427
displaying in canvas, 280–283
Arguments
defining functions with default, 189–190
passing by reference values, 180–183
positional and keyword, 179–180
Arithmetic operators, 117
Arithmetic/logic unit, CPU, 3
Arrays, 314
arrow argument, Canvas, 283
Arrow keys, 8
ASCII
character sets, 534
generating random characters with, 191–192
ord() and chr(), 69
overview of, 68
asin(), 65–67
askfloat(), 302
askinteger(), 302
askokcancel(), 302
askopenfilename(), 448–449, 451
asksaveasfilename(), 448–449, 451
askstring(), 302
askyesno(), 301
askyesnocancel(), 302
Assemblers, 10
Assembly language, 10
Assign value, to variable, 33
(+)
541

Assignment operators
augmented, 44
defined, 37
operator precedence and associativity, 117
Assignment statements
assigning values to variables, 37
copying lists with, 330
overview of, 36–38
simultaneous, 38–39
Association
aggregation and composition as, 419–421
overview of, 418–419
Associativity, operator, 117–118
Attributes, as object state, 216
Augmented assignment operator (+=), 44, 71
B
Backslash (\), 69–70
Ball class, bouncing balls, 343–345
Base (radix), decimal number system, 536
Base case
computing factorials, 500–502
computing Fibonacci numbers, 504–505
finding directory size, 511
problem solving using recursion, 506–507
recursive selection sort, 508–509
Towers of Hanoi, 514
BaseException class, custom exceptions, 460–461
Behavior of objects, 216
Binary digits (bits), 4–5
Binary files, vs. text, 440
Binary I/O, using pickling
address book, 467–470
detecting end of file, 466–467
overview of, 465–466
Binary numbers
conversions between decimal and, 537
conversions between hexadecimals and, 538–539
defined, 536
Binary operator, 40
Binary search, lists
overview of, 339–341
recursive, 509–510
bind method, mouse events, 294–297
Binding global variables, 188
Bindings, Tkinter, 294–297
Birthdays, guessing, 96–99, 379–381
Bits (binary digits), 4–5
Blind extensions, inheritance, 404
Blueprint, 216–217, 222
BMI (body mass index), case study, 107–108, 233–235
bool(), 93
Boolean (logical) operators, 110–116
Boolean accessor, 227
Boolean expression, 92–93
Bottom-up implementation, large programs, 196–198
Bouncing balls, case study, 345–347
Brackets [ ], 315, 319–320
break keyword
adding to loops, 151–152
displaying prime numbers, 155
use with caution, 152–153
break statement, exception handling, 455–456
Bus, for computer components, 2–3
Button widget, Tkinter
defined, 275
example, 279
processing events, 273–275
Buttons
adding image, 288–290
creating, 272–273
creating address book with binary I/O, 469
creating bouncing balls, 346
creating menus, 291
creating reusable clock GUI, 415
Bytes, 4–5
C
Cable modem, 8
Call stacks, 175–176
Callback functions
binding mouse event, 294–297
defined, 303
GUI programming in Tkinter, 292, 294, 296
processing events in Tkinter, 274, 287
Callback handler
binding mouse event with, 294
reusable clock, 415
Sodoku GUI, 377
Callback method, 291, 451
Caller, 173
Calling functions
call stacks and, 175–176
defined, 15
overview of, 173–175
camelCase, variables, 36
Canvas widget
creating animations in Tkinter, 297–300
creating bouncing balls, 346
creating pop-up menu, 293
defined, 275
displaying images, 288–289
reusable clock GUI, 414–418
scrolling contents in, 300–301
as source for key event, 295–296
using, 280–283
capitalize method, 249–250
Case sensitivity
converting strings, 249–250
identifiers, 36
named constants, 39, 108
Python programs and, 16
Case studies
body mass index, 107–108
bouncing balls, 345–347
convert decimals to hexadecimals, 185–187
542 Index

convert hexadecimals to decimals, 254–256
counting occurrences of each letter, 335–338, 451–452
counting occurrences of words, 492–494
Course class design, 421–423
current time, 46–48
deck of cards, 327–329
deck of cards GUI, 329–330
directory size, 510–511
distances, 52–53
Eight Queens, 518–520
factorials, 500–503
Fibonacci numbers, 503–505
fractals, 515–517
generate random ASCII characters, 191–192
guessing birthdays, 96–99, 379–381
guessing numbers, 136–138
leap years, 113–114
loan calculator, 287–288
lottery, 114–116
lotto numbers, 325–327
Monte Carlo simulation, 150–151
multiple subtraction quiz, 139–140
palindromes, 253–254
palindromes, recursive, 506–507
predict future tuition, 149–150
prime numbers, 154–155
random walk, 156–157
Rational class, 258–263
repeat subtraction quiz, 136
reusable clock, 414–418
reusable graphics functions, 199–201
subtraction quiz, multiple, 139–140
subtraction quiz, repeat, 136
taxes, 108–110
Towers of Hanoi, 512–515
CD-Rs, 6
CD-RWs, 6
CDs (compact discs), 6
ceil(), 65–67
center method, strings, 251–252
Central processing unit (CPU), 3–4
ch(), 69
Characters
accessing in strings, 234
ASCII, 68, 534
escape sequences for special, 69–70
generating random ASCII, 191–192
ord() and chr() and, 69
strings and, 67–68
stripping whitespace from string, 250–251
Unicode, 68
Checkbutton widget, Tkinter
adding image, 288–290
defined, 275
examples of, 276–279
Chinese zodiac signs, 103–105
chr(), 69
circle() command, Turtle, 22–24
circle method, 81–82
Circles
computing area of, 32–34
computing area with if statement, 95–96
computing in high-level language, 10
defining class for, 217–221
defining own exception classes, 461–462
displaying on canvas, 296–297
drawing in Turtle, 23–24, 81–83
with exceptions, 458–459
hiding data fields, 227–228
location of point in, 118–119
Monte Carlo simulation, 150–151
reusable graphics functions for, 199–201
Class abstraction, 229–232
Class definition, 217
Class encapsulation, 229–232
Classes
abstraction and encapsulation, 229–232
constructing objects with, 218–219
defining for objects, 216–218
designing Course class, 421–423
designing for stacks, 423–425
developing FigureCanvas class, 425–427
example using, 220–222
hiding data fields, 227–229
immutable vs. mutable objects and, 225–226
in OOP, 13, 233–235
overview of, 216
relationships among, 418–421
review, 235–239
self parameter and, 219–220
Tkinter GUI widget, 275–280
UML class diagrams, 222–225
Client, class, 221
Clock speed, CPUs, 3–4
Closest pair problem, 368–372
Coding
functions for reusable, 172
incrementally, 137
loop design strategies, 138–139
think before, 137, 148
Color
bouncing balls, 346–347
constructing Tkinter widget, 276, 278–279
drawing in Turtle, 21–22, 83–84
drawing Olympics rings logo, 23–24
Column indexes, 362–364
columnspan parameter, grid manager, 284
Command option, Tkinter, 274
Command window, 14–16
Commas, separating elements in lists, 315
Comments, 16–19
Common errors, 19
Communication devices, 8
Compact keyboards, 7
Comparing strings, 246
Comparison operators
comparing lists, 319
comparing strings, 246–247
Index 543

Comparison operators (continued )
operator precedence and associativity, 117
overview of, 92
special methods and, 257
Compiler, translating source code, 10–11
Composition
aggregation and, 419–421
designing Stack class, 423–425
Compound expressions, 110–111
Computers
hardware. see Hardware components
operating system, 12–13
overview of, 2–3
programming languages, 9–12
review, 25–29
Concatenation operator (+)
lists, 318
strings, 71, 245
Conditional expressions, 116
Conditional operator, 113
Condition-controlled loops, 134
config method, menus, 292
Confirmation, controlling loop with user, 140
Console
defined, 14
reading input from, 34–35
reading strings from, 71–72
Console input, 14
Console output, 14
Constants
named, 39, 108, 276
overview of, 39
Constructor
creating objects from classes, 218–219
creating strings, 242
UML class diagrams, 222
continue keyword, 151–153
Contract (template or blueprint), 216–217, 222
Control unit, CPU, 3
Conversion code
formatting floating-point numbers, 77–78
formatting in scientific notation, 78
formatting integers, 79
formatting strings, 79–80
Converting strings, 249–250, 254–256
Coordinate system, canvas, 282
Copy reference, lists, 330
Copying lists, 330–331
Core, CPU, 4
cos(), 65–67
Count backward, range(), 144
count method, 248–249, 320
Counter-controlled loops, 134, 143
Counting keywords, case study, 486–487
Counting occurrences of each letter, case study, 335–338, 451–452
Counting occurrences of words, case study, 492–494
countLetters()
counting each letter in file, 337–338, 452
exception handling, 455
retrieving data from Web, 453–454
Course class, 421–423
CPU (central processing unit), 3–4
create_arc method, 282
create_image method, 288–290
create_line method, 282
create_oval method, 282
create_polygon method, 282
create_text method, 282
createList(), 336–337
Curly braces { }, 479, 488
Current time
displaying, 46–48
GUI class to display reusable clock, 414–418
currentHour, 47
currentMinute, 47
currentSecond, 47
Cursor, mouse, 8
D
Daily temperature and humidity problem, 378–379
Data fields
defined, 216
hiding, 227–229
implementing associations with, 419
as instance variables, 219
rational number, 259–262
subclass, 400–401
in UML class diagrams, 222
Data hiding, 227–229
Data structure, 476
Data types
numeric, 40
Python coding and, 33
datetime class, reusable clock GUI, 415–418
De Morgan’s law, 112
Debugging, and stepwise refinement, 199
Decimal index, ASCII character set in, 534
Decimals
conversions between binary numbers and, 537
conversions between hexadecimals and, 185–187, 254–256, 538
defined, 536
decimalToHex(), 184–185
Deck of cards, case study, 327–330
def keyword, 173
Default arguments, 189–190, 333–334
degrees(), 65–67
Delete items from dictionary, 489
Delete key, 8
denominator field, rational number, 259–262
Deployment, software development process, 49
Descriptive names
constants, 39
identifiers, 36
variables, 32
Design
Course class, 418
strategies for loop, 138–139
Dialog boxes, 301–302, 448–451
dict class, 491
544 Index

Dictionaries
adding, modifying, and retrieving values, 488–489
counting occurrences of words, 492–494
creating, 488
defined, 487–488
deleting items, 489
equality test, 490
len()and, 490
looping items, 489
methods, 491–492
overview of, 487–488
review, 495–498
testing if keys are in, 490
Dictionary entry, 488
Dictionary item, 488
difference method, sets, 481–483
Digital subscriber line (DSL), 8
Digital versatile or video discs (DVDs), 6
Digits, identifiers using, 36
Direct recursion, 503
Directory path, 440
Directory size, 510–511
Disks, 6
displayTriangles(), 517
Distance, computing, 52–54
Divide-and-conquer strategy, function abstraction
benefits of, 199
implementation details, 196–199
overview of, 192–193
top-down design, 193–195
top-down or bottom-up implementation, 195–196
Documentation, guidelines, 18–19
done() command, Turtle, 24
dot method, 119
dot operator (.), 219
Dot pitch, 8
Double quotes (“)
enclosing strings in, 67
use of in this book, 68
DoubleVar, 278
drawClock method, reusable clock, 417–418
Drawing
creating animations, 297–300
shapes, 81–83
Drives, 6
DSL (digital subscriber line), 8
dump(), 465–467
DVD-R, 6
DVD-RW, 6
DVDs (digital versatile or video discs), 6
Dynamic binding, and polymorphism, 410–411
E
Eight Queens, case study, 518–520
Elementary programming. see Programming, elementary
else clause, exception handling, 456
Encapsulation (information hiding), 192
Encoding scheme, 4
endswith method, strings, 248–249
Entry widget, Tkinter
defined, 275
example of, 277–278
Sudoku GUI problem, 375–377
EOFError, 466–467
EOL (end-of-line) character, 69–70
Equality operators
precedence rule for, 117
testing dictionaries, 490
testing sets, 480–481
Errors
programming, 19–21
selection statement, 105–106
Escape sequences, character, 69–70
eval(), 34, 45
Evaluate expressions, 43
Events
creating loan calculator, 287–288
processing in Tkinter, 273–275
Tkinter GUI program and, 273
Exception handling
binary IO using pickling, 465–467
creating address book, 467–470
defined, 440
defining custom classes for, 460–465
processing exceptions, 460
raising exceptions, 457–459
review, 470–474
writing code, 454–457
Exceptions, defined, 454
Execute program, 16
exp(), 65–67
expand option, pack manager, 284–285
Exponentiation operator (**), 40–41, 43–44
Expressions
Boolean, 92–93
conditional, 116
evaluating internally, 117–118
operator precedence and, 43–44
overview of, 36–38
extend method, list class, 320–321
F
fabs(), 65–67
factorial(), 500–503
Factorials, case study, 500–503
Faster button, animation, 300
Fibonacci numbers, computing, 503–505
FigureCanvas class, 425–427
File dialogs
creating text editor, 449–451
displaying Open and Save As, 448–449
filename, opening file, 440–441
Files
appending data, 447
binary IO using pickling, 465–467
counting each letter in, 451–452
creating address book, 467–470
custom exception classes, 460–465
Index 545

Files (continued )
detecting end of, 466–467
exception handling, 454–457
file dialogs, 448–451
opening, 440–441
processing exceptions, 460
raising exceptions, 457–459
reading all data from, 445–447
reading data from, 443–445
retrieving data from Web, 452–454
review, 470–474
storing data in, 440
testing existence of, 443
text input and output, 440
writing and reading numeric data, 447–448
writing data, 441–443
fill option, pack manager, 284–285
finally clause, exception handling, 456–457
find method, strings, 248–249
First half of list, binary searches, 339–341
Fixed cells, 372
Float division operator (/), 40, 44
Floating-point numbers
causing loop-continuation-condition errors, 147–148
formatting, 77–78
not using in loop control, 141–142
overview of, 40
scientific notation, 42–43
type conversions and rounding, 45–46
Flowcharts, 95, 100
Fonts
creating Tkinter widget, 276, 278–279
drawing in Turtle, 83–84
for clause, 319–320
for loops
iterating strings, 247
nesting, 145–146
overview of, 143–145
performance for lists vs. sets, 485–486
reading data from all files, 445–446
traversing all keys in dictionary, 489–490
traversing elements in tuple, 476–477
traversing list elements, 319
Formal parameters, function header, 173
format()
numbers, 76–79
strings, 79–80
format method, strings, 251–252
Formatting
numbers, 76–79
strings, 79–80, 251–253
Fractals, case study, 515–517
Frame widget, Tkinter, 275–279
Free cells, 372
Function abstraction
benefits of, 199
implementation details, 196–199
overview of, 192–193
top-down design, 193–195
top-down or bottom-up implementation, 195–196
Function header, 173
Function keys, 7
Functions
calling, 173–176
common, 64–65
converting decimals to hexadecimals, 185–187
default arguments, 189–190
defined, 15
generating random ASCII characters, 191–192
list, 316
lists, passing to, 332–334
lists, returning from, 334–335
mathematical, 65
modularizing code with, 183–185
object, 75–76
order of, 175
overview of, 172
parentheses for, 16
passing arguments by reference values, 180–183
passing mutable objects to, 225–226
passing two-dimensional lists to, 365–367
positional and keyword arguments, 179–180
recursive. see Recursion
reusable graphics, 199–201
review, 201–213
scope of variables, 187–189
string, 243
syntax for, 172–173
with/without return values, 176–179
G
Games, detecting location of object, 118–119
Garbage collection, 330
GBs (gigabytes), 5
gcd(), 183–184, 259
GCD (greatest common divisor)
finding, 148–149
modularizing code, 183–184
reducing rational number, 259–262
General-purpose programming language, 13
Geometic shapes. see Turtle
Geometry managers, Tkinter, 278, 283–286, 287–288
get method
class abstraction and encapsulation, 232
client access to data field, 227–228
dictionaries, 491
getGrade(), 177–178
getMatrix(), 366
getRandomLowerCaseLetter(), 335–337
getSize(), 511
getter (accessor), 227, 232
GHz (gigahertz), 4
Gigabytes (GBs), 5
Global statements, 188
Global variables, 187–188
goto(), 22–23, 83–84
Graphics programming
computing distance, 52–54
drawing with Canvas widget, 282
546 Index

reusable functions, 199–201
starting with Turtle. see Turtle
Greatest common divisor. see GCD (greatest common divisor)
Grid, 372–373
Grid manager, Tkinter, 277, 282–284
Guessing birthdays case study, 96–99, 379–381
Guessing lottery, 114–116
GUI modules, geometric shapes. see Turtle
GUI programming
closest pair problem, 370–372
creating bouncing balls, 347
reusable clock, 414–418
Sudoku problem, 375–377
using Tkinter. see Tkinter
H
Handlers, 274
Hard disks, 6
Hardware components
bits and bytes, 4–5
communication devices, 8
CPU, 3–4
input and output devices, 7–8
memory, 5
overview of, 2–3
review, 8–9
storage devices, 5–7
Hashable elements, sets, 479
Heap, 175
Helper functions, recursive, 507–510
Hertz (Hz), 3–4
Hexadecimal index, ASCII, 534
Hexadecimals
conversions between binary numbers and, 538–539
conversions between decimals and, 185–187,
254–256, 538
creating bouncing balls, 346–347
defined, 536
hexCharToDecimal(), 255–256
hexToDecimal(), 255–256
hideturtle(), 84
High-level languages, 10–11
History, Python’s, 13–14
Honer’s algorithm, 255
H-tree, 500
Hz (hertz), 3–4
I
id(), 74–75
Identifiers
named constants as, 39
overview of, 36
Identity, object, 216
IDLE (Interactive DeveLopment Environment), 14–15
if clause, list comprehensions, 319
if statements. see also Nested if statements
computing taxes, 108–109
example of, 96
overview of, 95–96
selection statement errors, 105–106
if-elif-else statements, 102–105
if-else statements
recursive functions, 505–506
two-way, 100–102
Images
deck of cards GUI program, 330
displaying with Tkinter, 288–290
Immutable objects
vs. mutable objects, 225–226
numbers and strings as, 181
with same content, storing in one object, 243
in tuples, 478
Implementation, software development, 49, 51
in operator
counting keywords program, 486–487
defined, 258
lists, 318
searching lists with, 338
sets, 479
strings, 245
testing if key is in dictionary, 490
tuples, 476–477
Incremental development and testing, 110
Indentation
avoiding for statements, 16
causing selection statement errors, 105–106
index method, list class, 320, 337–338
Index operator [ ]
creating lists, 315
overview of, 319–320
strings, 243
tuples, 477
Index variables, 316–317, 319
IndexError, 317
Indexes, list, 316–317
Indirect recursion, 503
Infinite loops, 135
Infinite recursion, 503
Information hiding (encapsulation), 192
Inheritance
object class and, 406–409
overriding methods, 405–406
overview of, 400
polymorphism and. see Polymorphism
review, 428–438
superclasses and subclasses, 400–405
__init__ method
constructing objects, 218–219
creating address book, 468, 470
defining classes, 217
initializing object, 407–409
invoking for superclass, 402
not including in UML diagram, 222
Initializer
class abstraction and encapsulation with, 231
constructing objects with, 218
defined, 217
hiding data fields with, 227–229
Index 547

Initializing two-dimensional lists, 364
input(), 254
Input
devices, 7–8
errors, 20
file, 370
reading from console, 34–35
input()
reading input from console, 34
reading strings from console, 71–72
returning string from keyboard, 242
Input redirection, loops, 142–143
Input values, initializing lists, 364
Inputting lists, 322
Insert key, 8
insert method, list class, 320–321
Insertion sort, lists, 345–347
Instance, as object, 217
Instance methods, 219, 231
Instance variables, 219–220
Instantiation, 217
int()
converting Boolean value to integer, 93
overview of, 40
type conversions, 45–46
Integer division operator (// ), 40, 43–44
Integers
converting Boolean value to, 93
formatting, 79
generating random numbers, 93–94
overview of, 40
type conversions and rounding, 45–46
Interactive DeveLopment Environment (IDLE),
14–15
Interactive mode, Python in, 16
Interpreted, Python as, 13
Interpreter
executing Python from, 13
translating source code with, 10–11
intersection method, sets, 481–483
IntVar, widgets, 278
InvalidRadiusException class, 461–462
Invoking functions, 15
IOError exception, 454–456
_io.TextIOWrapper class, 441–443
Is-a relationships, inheritance modeling, 404
isfile(), 443
isinstance(), 411–414
isPalindrome(), 506–508
isPalindromeHelper(), 508
isPrime(), 184–185
isStopped variable, 299–300, 347
isTooCloseToOtherPoints method,
371–372
isValidAt(grid), 374–375
isValid(grid), 373, 375–376
Iteration
of loops, 134
recursion vs., 520
of strings, 247
J
Joining lines implicitly, 35
Justify format
numbers, 79
text in widget, 276
K
KBs (kilobytes), 5
key element, searching lists, 338–341
Key events, Tkinter, 294–297
Keyboards, 7–8
Key/value pairs, dictionaries, 487–489
Keyword arguments, 179–180, 189
Keywords (reserved words)
counting program, 486–487
list of Python, 533
not used for identifiers, 36
kilobytes (KBs), 5
L
Labels
adding image to, 288–290
building deck of cards GUI, 330
using Tkinter widgets, 272–273, 275, 278–279
LANs (local area networks), 8
Launching Python, 14–15
Leap years, determining, 113–114
Left shift, for lists, 322
Left-justification 79
len()
dictionaries, 490
lists, 316
sets, 479, 482–483
strings, 234, 258
tuples, 476–477
len method, 258
__len__ function, strings, 258
Letters, used by identifiers, 36
Lexicographical ordering, 319
Line break character (\), 69–70
Line comments, 16
Line continuation symbol (\), 35
Line numbers, 16
Linear search, lists, 338–339
linearSearch(), 338–339
list class, 315
List comprehensions, 319–320
Listbox widget, scrolling contents, 300–301
Lists
bouncing balls, 345–347
coding simplification, 322–325
comparison operators vs., 319
concatenation operator and, 318
copying, 330–331
counting each letter in file, 451–452
counting occurrences of each letter, 335–338
creating, 315
creating from tuple, 477
+
(6),
548 Index

deck of cards, 327–329
deck of cards GUI, 329–330
functions for, 316
index operator [ ] and, 316–317
inputting, 322
list comprehensions, 319–320
lotto numbers, 325–327
methods, 320–321
in/not in operators and, 318
overview of, 314
passing to functions, 332–334
repetition operator (*) and, 318
returning from functions, 334–335
review, 348–359
searching, 338–341
sequence operations for, 315
sets vs., 479
shifting, 322
sorting elements in, 341–345
splitting strings into, 321–322
traversing elements in for loop, 319
tuples vs., 476
Literals
Boolean, 93
defined, 40
ljust() method, strings, 251–252
load(), binary IO using pickling, 465–467
loadAddress method, AddressBook, 470
Loan calculator program, 287–288
Local area networks (LANs), 8
Local variables, 187
log (), 65–67
Logic errors, 20
Logical operators
generating lottery program, 114–116
operator precedence and associativity, 117
overview of, 110–113
testing, 111–113
Loop body, 134
Loop-continuation-condition
defined, 134
numeric errors caused by, 147–148
terminating, 135
while loop and, 135
Loops
adding break and continue keywords to, 151–153
displaying prime numbers, 154–155
finding greatest common divisor, 148–149
for. see for loops
minimizing numerical errors, 147
Monte Carlo simulation, 150–151
nested, 145–146
overview of, 134
predicting future tuition, 149–150
random walk simulation, 156–157
review, 157–169
telling program to execute statements repeatedly, 134
traversing all keys in dictionary, 489
while. see while loops
Loss of precision, 74
Lottery, 114–116
Lottery, guessing, 114–116
Lotto numbers, case study, 325–327
lower method, 249–250, 451–452
Lowercase letters, random, 191–192
Low-level language, 10
lstrip method, strings, 251
M
Machine language, code in, 9–10
Machine stack, 175–176
Maintenance, software development, 49
Map, as dictionary, 488
Matched lists, binary searches, 339–341
Mathematical computations, performing, 18
Mathematical functions
case study, 72–74
common Python, 64–65
drawing various shapes, 81–83
drawing with colors and fonts, 83–85
formatting numbers, 76–79
formatting strings, 79–80
guessing birthdays, 99
objects and methods, 74–76
review, 85–89
strings and characters, 67–72
types of, 65–67
max()
defined, 64–65
lists, 316
sets, 479, 482–483
strings, 234
tuples, 476–477
Mbps (million bits per second), and high-speed NICs, 8
MBs (megabytes), 5
Megabytes (MBs), 5
Members, accessing object, 219–220
Memory, 5
Menu widget, Tkinter, 275
Menubutton widget, Tkinter, 275
Menus, creating, 290–293
Message widget, Tkinter, 275
Methods
defining for operators, 257
defining object’s behavior with, 216
dictionary, 491
implementing associations with, 419
as instance methods, 219
introduction to, 75–76
invoking, 220
list, 320–321
overriding, 405–406
searching for strings, 248–249
string testing, 247
subclass, 400–401
UML class diagrams, 222
Methods, special
checking palindromes, 253–254
converting hexadecimals to decimals, 254–256
Index 549

Methods, special (continued )
operator overloading and, 257–258
Rational class, 258–263
review, 263–270
Million bits per second (Mbps), and high-speed NICs, 8
min()
defined, 64–65
lists, 316
sets, 479, 482–483
tuples, 476–477
Minimum number of coins, case study, 72–74
Mixed arguments, 189
Mnemonics, for assembly language, 10
mode parameter, open(), 440–441
Modems, 8
Modifier keys, 8
Modularizing code, 183–185
Modules, 16, 183–184
Monitors, 8
Monte Carlo simulation, case study, 150–151
Motherboards, 3–4
Mouse
binding events, 294–297
as pointing device, 8
specifying style of cursor for Tkinter widget, 276
move method, animations in Tkinter, 297–300
Multicore CPUs, 4
Multidimensional lists
calculating daily temperature and humidity,
378–379
guessing birthdays, 379–381
overview of, 377–378
passing lists to functions, 332
review, 381–397
two-dimensional. see Two-dimensional lists
Multiple inheritance, 404–405
Multiple solutions, for programs, 149
Multiple values, returning, 190
Multiple-choice test, grading, 367–368
Multiplication operator (*), 40, 43–44
Multiplication table, nested loops, 145–146
Multiplicity of classes, in association, 419
Multiprocessing (parallel processing), 13
Multiprogramming, 13
Multithreading, 13
multi-way if-elif-else statements, 102–105
Mutable objects
vs. immutable objects, 225–226
passing lists to functions, 332
in tuples, 478
Mutator (setter), 227, 232
myList[index], 316–317
N
Named constants
computing body mass index, 108
formatting text in widget, 276
overview of, 39
NameError class, 460–461
Naming conventions
classes, 218
constant, 39
identifier, 36
variable, 36
nearestPoints(), closest pair problem, 369–372
Negative indexes, lists, 317–318
Nested if statements
computing body mass index, 107–108
computing taxes, 108–109
overview of, 102–105
Nested lists, 362, 368
Nested loops, 145–146
__new__ method, constructing objects, 407–408
Newline character (\n), 69–70
NICs (network interface cards), 8
No-Fly list, 492–494
None function, 178
not in operator
lists, 318, 338
sets, 479
strings, 245–246
testing if key is in dictionary, 490
tuples, 476
not operator
as logical operator, 110–111
testing, 111–113
Number systems, 536–539
Numbers. see also Mathematical functions;
Random numbers
computing factorials, 500–503
computing Fibonacci, 503–505
deck of cards, 327–329
deck of cards GUI, 329–330
displaying prime, 154–155
formatting, 76–79
formatting floating-point, 77–78
formatting in scientific notation, 78
guessing, 136–138
as immutable objects, 181
lotto numbers, 325–327
objects and methods, 74–76
performing mathematical computations, 18
writing and reading to file, 447–448
numerator field, rational numbers, 259–262
Numeric data types, 40–43
Numeric keypad, 7–8
Numeric operators
augmented assignment operators, 44
evaluating expressions and operator precedence,
43–44
overview of, 40–42
scientific notation, 42–43
type conversions and rounding, 45–46
Numerical errors, 141–142, 147–148
O
object class, 406–409
Object member access operator, 219
550 Index

Object-oriented programming. see OOP (object-oriented
programming)
Object-oriented thinking, 233–235
Objects
accessing members of, 219
class abstraction and encapsulation, 229–232
constructing, 218–219
defining classes for, 216–218
detecting location of, 118–119
example using classes, 220–222
hiding data fields, 227–229
immutable vs. mutable, 225–226
introduction to, 74–76
object-oriented thinking, 233–235
overview of, 216
review, 235–239
self parameter, 219–220
strings with same content are the same, 242
UML class diagrams, 222–225
Off-by-one-error, loops, 135, 317
Olympics rings logo program, 23–24
OOP (object-oriented programming)
creating GUI objects, 216
procedural programming vs., 233–235
Python using, 13
open(), files, 440–442
Open dialog box, 448–449
openFile method, 451
Opening files, 440–441
Operands, 40, 45–46
Operations
list, 315
set, 481–485
tuple, 476
Operator associativity, 117–118
Operator overloading, 257–258
Operator precedence, 43–44, 117–118
Operators
augmented assignment operators, 44
logical, 110–113
numeric, 40–43
or operator, 110–113
ord(), 69
Order of functions, 175
OS (operating system), 12–13
os module, 510–511
os.path module, 443
outfile object, 447–448
Output devices, 7–8
Output redirection, loops, 142–143
Ovals
bouncing balls program, 347
creating pop-up menu, 293
displaying with Canvas widget, 280–283
displaying with FigureCanvas, 425–427
drawing on canvas, 281–283
enlarge/shrink circle program, 296
Overflow, and floating-point numbers, 42
Overhead, recursion, 520
Overriding methods, inheritance, 405–406
P
Pack manager, Tkinter, 273, 284–285
padx option, grid manager, 284
pady option, grid manager, 284
Page Down key, 8
Page Up key, 8
Palindromes
checking if strings are, 253–254
recursive helper functions, 508
solving using recursion, 506–507
Parallel processing (multiprocessing), 13
Parameters
function header, 173
passing positional or keywords arguments to, 179–180
Parentheses ( ), 16, 476
Pass-by-value, 180
Passing arguments by reference values, 180–183
Pen, in Turtle, 22–23
pendown(), Turtle
drawing Olympics rings logo, 24
drawing various shapes, 81–82
drawing with colors and fonts, 83–84
moving pen to any location, 23
pensize(), Turtle, 81–84
penup(), Turtle
drawing Olympics rings logo, 24
drawing various shapes, 81–82
drawing with colors and fonts, 83–84
moving pen to any location, 23
Performance
avoiding recursion if concerned about, 520
lists vs. sets and, 485–486
Personal income tax, computing, 108–109
PhotoImage objects
creating menu, 291–292
displaying images, 288–289
Pickling, binary I/O using, 465–467
Pixels, and screen resolution, 8
Place manger, Tkinter, 286
Points, drawing in circle, 118–119
Polygons, drawing in canvas, 280–283
Polymorphism
class relationships, 418–421
defined, 409
designing class for stacks, 423–425
designing Course class, 421–423
and dynamic binding, 409–411
FigureCanvas class, 425–427
inheritance and. see Inheritance
isintance() and, 411–414
reusable clock program and, 414–418
review, 428–438
pop method, list class, 321
pop(key) method, dictionaries, 491
Pop-up menus, 292–294
Positional arguments, 179–180, 189
pound sign (#), preceding comment line, 16
pow(), 64–65
Precedence rule, operator, 43–44
Prime numbers, 154–155, 184–185
Index 551

print()
defined, 15
displaying string on monitor, 242
printing without newline character, 70
writing simple program, 34
print statement
creating Python source code files, 17
defined, 15
joining lines explicitly and, 35
printGrade(), 176–178
printPrimeNumbers(), 184–185
Private data fields, 227–229
Private methods, 227–229
Problems
executing statements based on conditions, 92
solving using recursion, 505–507
solving with elementary programming, 32
writing simple program, 32–34
Procedural programming, 233–235
processAdd method, address book, 470
processFirst method, address book, 470
processKeyEvent callback function, 295–296
processLine(), dictionary, 493–494
processMouseEvent callback function, 295–296
processNext method, address book, 470
Programming
documentation and style, 18–19
errors, 19–21
graphics, 21–24
overview of, 2
review, 25–29
writing simple programs, 32–34
Programming, elementary
augmented assignment operators, 44
computing distances, 52–53
displaying current time, 46–48
evaluating expressions and operator precedence, 43–44
identifiers, 36
named constants, 39
numeric data types and operators, 40–43
reading input from console, 34–35
review, 54–61
simultaneous assignments, 38–39
software development, 48–52
type conversions and rounding, 45
variables, assignment statements, and expressions, 36–38
writing simple program, 32–34
Programming languages
assembly, 10
defined, 9
high-level, 10–11
machine, 9–10
overview of, 2
review, 11–12
Programs, 2
Properties
creating Tkinter widget, 276
mouse and key event, 295
as object state, 216
Pseudocode, algorithms in, 32
Punctuation, avoiding at end of statements, 16
.py extension, 16, 183–184
Python, introduction
creating source files, 16–17
graphics programming. see Turtle
history of, 13–14
launching, 14–15
mathematical computations, 18
as programming language, 2
Python 2 vs. 3, 13
review, 25–29
Q
Quotation marks (” “), strings, 16
R
radian(), 65–67
Radiobutton widget, 275–280, 288–290
Radix (base), decimal number system, 536
raise keyword, processing exceptions, 460
Raising exceptions, 457–459
RAM (random-access memory), 5
randint()
bouncing balls, 346
defined, 93
denoting constants with, 39
guess number, 138
lottery program, 115
multiple subtraction quiz, 139
random ASCII characters, 191
random numbers, 93–95
random shuffling, 364–365
random walk, 156
reading and writing numbers to files, 447
repeat subtraction quiz, 136
subtraction quiz, 101–102
random(), 94–95
Random ASCII characters, case study, 191–192
random module
lottery program, 114–116
random numbers, 93–94
shuffling elements in lists randomly, 316
Random numbers
generating, 93–95
generating lottery program, 115
two-way if-else statements, 100–102
writing to files using strings, 447–448
Random walk, case study, 156–157
RandomCharacter module, 335–338
randrange(), 94–95
range(), 143–146
Rational class, case study, 258–263
Rational numbers, 258–263
Raw string, absolute filenames, 441, 444
read method
reading data from all files, 445–447
reading data from file, 440, 443–445
readASolution(), 373, 375
552 Index

Reading
data from all files, 445–447
data from files, 443–445
data from Web, 452–454
numbers in files, 447–448
readline(), 443–445
readlines(), 443–447
Real types, 40
Rectangles
creating pop-up menu, 293
displaying with canvas, 280–283
displaying with FigureCanvas, 425–427
Recursion
computing factorials, 500–503
computing Fibonacci numbers, 503–505
Eight Queens problem, 518–520
finding directory size, 510–511
fractals, 515–517
iteration vs., 520
overhead, 520
overview of, 500
problem solving using, 505–507
recursive helper functions, 507–510
review, 522–529
tail, 520–522
Towers of Hanoi, 512–515
Recursive calls, 500–501, 506
Recursive functions, 500–503, 505–506
recursiveBinarySearch(), 509–510
redisplayBall method, 347
Reference values
passing arguments by, 180–183
returning lists from functions, 334–335
Regular expressions, 322
Relationships among classes
aggregation and composition, 419–421
association, 418–419
is-a relationship, 404
using inheritance to model is-a, 418
Relative filenames, 440
Remainder or modulo operator (%), 40–44
remove method
list class, 321, 347
manipulating sets, 479–480
Repetition operator (*), 245, 318
replace method, strings, 249–250
replacePunctuations(), 493–494
repr(), 444
Requirements specification, software development, 48–50
Reserved words (keywords)
case study, 486–487
list of Python, 533
not used for identifiers, 36
Resources, OS allocating and assigning, 12
Resume button, animation, 300
Retrieving data from Web files, 452–454
return None statement, 178
return statement, 178, 190–191
Return value, functions, 173, 176–179
Reusable clock GUI, case study, 414–418
Reusable code, 172, 199–201
reverse method, list class, 321, 334–335
rfind method, strings, 248–249
rjust method, strings, 251–252
round(), 45, 64–65
Rounding, 45–46
Rows, two-dimensional lists, 362–364
rowspan parameter, grid manager, 284
rstrip method, strings, 251
Rules, identifier, 36
Runtime errors, 20, 35
Runtime stack, 175–176
RuntimeError class, 457–459, 461
S
Save As dialog box, displaying, 448–449
saveAddress method, AddressBook, 470
saveFile method, text editor, 451
Scheduling operations, OS, 13
Scientific notation, 42–43, 78
Scope of instance variable, 220
Scope of variables, 37, 187–189
Screen resolution, 8
Script files, 16
Scrollbars, 300–302
Searching
lists, 338–341, 509–510
substrings, 248–249
Second half of list, binary search approach, 339–341
Selection sort
lists, 342–343
recursive, 508–509
Selections
boolean types, values, and expressions, 92–93
common errors, 105–106
computing body mass index, 107–108
computing taxes, 108–110
conditional expressions, 116
detecting location of object, 118–119
determining leap years, 113–114
generating random numbers, 93–95
guessing birthdays, 96–99
if statements, 95–96
logical operators, 110–113
lottery program, 114–116
nested if and multi-way if-elif-else statements, 102–105
operator precedence and associativity, 117–118
overview of, 92
review, 119–132
two-way if-else statements, 100–102
self parameter
__init__ method, 218
not including in UML diagram, 222
working with, 219–220
Self-avoiding walk, simulating, 157
Sentinel-controlled loop, 140–142
Sequence operations, lists, 315
Sequence types. see lists; strings
Set difference, 481–483
Index 553

Set intersection, 481–483
set methods, 227, 232
Set symmetric difference, 482
Set union, 481–483
setAddress method, 470
Sets
counting keywords, 486–487
creating, 479
equality test, 480–481
lists vs., 479
manipulating and accessing, 479–480
operations, 481–485
performance of lists vs., 485–486
review, 495–498
subsets and supersets, 480
Setter (mutator)
class abstraction and encapsulation, 232
defined, 227
Shapes
displaying with Canvas widget, 280–283
drawing with colors and fonts, 83–84
drawing with turtle, 81–83
Shifting lists, 322
Short-circuit AND operator, 113
shortestDistance variable, closest pair problem, 369
showerror(), 301
showinfo(), 301
showwarning(), 301
shuffle(), 316, 329–330
Shuffle button, 329–330
side option, pack manager, 285
Sierpinski triangle, case study, 514–517
Simultaneous assignments, 38–39
sin(), 65–67
Single quotes (‘), 67–68
sleepTime variable, animation, 300, 346
Slicing operator
lists, 317–318
strings, 244–245
tuples, 477
Slower button, animation, 300
Software
for computer, 2
development process, 48–52
examples of, 2
sort method, list class
defined, 321
sorting elements in list, 341–345
sorting two-dimensional lists, 365
sortHelper(), 508–509
Source files, 16–17
Source program or source code, high-level languages, 10–11
Spacing style, programming, 19
Special characters, 16, 69–70
Special methods. see Methods, special
Specifiers, format, 76–80
Speed, CPU clock, 3–4
split method, str class, 321–322
Splitting strings, into lists, 321–322
sqrt(), 65–67
Stack-overflow exception, recursion, 520
Stack traceback, 454
Stacks
call, 175
designing Stack class for modeling, 423–425
overview of, 423
[start : end], slicing list, 317–318
startswith method, strings, 248–249
State, object, 216
Statement prompt (>>>), 15–16
Statements
high-level language, 10
invoking value-returning functions as, 173
Step value, range(), 144
Stepwise refinement
benefits of, 199
implementation details, 196–199
overview of, 192–193
top-down design, 193–195
top-down or bottom-up implementation, 195–196
sticky option, grid manager, 284
StillClock class, clock GUI, 414–418
Stop button, animation, 300
Stopping condition. see Base case
Storage devices, 5–7
str(), 71
str class
comparing strings, 246
concatenation operator 245
converting strings, 249–250
creating strings, 242–243
defined, 242
formatting strings, 251–253
functions for strings, 243
index operator [], 243
iterating string, 247
in operator, 245
repetition operator (*), 245
review, key terms and summary, 263
review, programming exercises, 263–270
searching for substrings, 248–249
slicing operator, 244–245
strings, 245–246
stripping whitespace characters from string, 250–251
testing strings, 247–248
__str__ method, 407–409
Strings
and characters, 67–70
comparing, 246
concatenation, 71
concatenation operator 245
converting, 249–250
converting numbers into, 71
creating, 242–243
creating tuples from, 476
defined, 15, 242
displaying with Canvas widget, 281
enclosing with quotation marks, 16
formatting, 79–80, 251–253
functions for, 243
(+ ),
(+ ),
554 Index

as immutable objects, 183
index operator [ ], 243
iterating, 247
not in operator, 245–246
objects and methods, 74–76
in operator, 245
overview of, 242
reading from the console, 71–72
repetition operator (*), 245
review, key terms and summary, 263
review, programming exercises, 263–270
searching for substrings, 248–249
slicing operator [start : end], 244–245
str class. see str class
stripping whitespace characters from, 250–251
testing, 247–248
writing numbers to files using, 447–448
strip(), strings, 76
strip method, strings, 251, 254
Stub, defined, 195–196
Subclasses
defined, 404
inheritance and, 400–405
method overriding and, 405–406
polymorphism and dynamic binding, 409–411
Subsets, 480
Substrings, searching for, 248–249
Subtraction operator (-), 40, 43–44
Subtraction quiz
loop, 139–140
repeating, 136
two-way if-else statements, 101–102
Sudoku problem, 371–372
sum()
lists, 316
sets, 479, 482–483
tuples, 476–477
Summing, two-dimensional lists, 364
Superclasses
inheritance and, 400–405
method overriding and, 405–406
polymorphism and dynamic binding, 409–411
Supersets, 480
swapCase method, strings, 249–250
switch statements, recursive functions, 505–506
symmetric_difference method, sets, 482
Syntax
errors, 19–20
rules, 19
SyntaxError class, exceptions, 456–457, 461
sys module, computing taxes, 109–110
System analysis and design, software development, 49–50
T
tags argument, Canvas, 282–283
Tail recursive, 520–522
tan(), 65–67
Tasks, controlling and monitoring, 12
Taxes, computing, 108–110
TBs (terabytes), 5
Teamwork, with stepwise refinement, 199
Templates, 216–217, 222
Testing
base cases, 511
Boolean operators, 111–113
custom exceptions, 462
exceptions, 458–459
existence of file, 443
incremental development and, 110
for key in dictionary, 490
software development process, 49, 52
stepwise refinement and, 199
strings, 247–248
Text editor, creating, 449–451
Text files, vs. binary files, 440
Text formatting, Tkinter widget, 276, 278–279
Text input and output, files
appending data, 447
counting each letter in, 451–452
file dialogs, 448–451
opening, 440–441
overview, 440
reading all data from, 445–447
reading data from, 443–445
testing existence of, 443
writing and reading numeric data, 447–448
writing data, 441–443
Text widget
creating, 277–278
creating text editor, 451
defined, 275
scrolling contents in, 300–301
Think before coding, 137, 148
Think recursively, 506
time(), 46–48
time module, current time, 46–48
title(), 249–250
Tk class, 272
Tkinter
animations, 297–300
Canvas widget, 280–283
deck of cards GUI, 329–330
defined, 21, 272
displaying dialog boxes, 448–449
displaying images, 288–290
geometry managers, 283–286
getting started, 272–273
loan calculator, 287–288
menus, 290–292
mouse, key events, and bindings, 294–297
overview of, 271
pop-up menus, 292–294
processing events, 273–275
review, 302–311
scrollbars, 300–302
widget classes, 275–280
toHexChar(), 185
Top-down implementation, large programs, 193–198
totalHours, 47
Index 555

totalMinutes, 47
totalSeconds, 47
Towers of Hanoi, case study, 512–515
Trace a program, 33
Traceback, 454
Transistors, CPUs built on, 3
Triangular arrow, denoting inheritance between two classes, 400
try/except block
catching and processing exceptions, 458–459
exception handling, 454–457
processing exceptions using exception object, 460
Tuition, predicting future, 149–150
Tuples
creating, 476–478
lists vs., 476
operations, 476
review, 495–498
using fixed elements, 476
Turtle
benefits of Tkinter vs., 329
computing distance, 52–54
detecting location of object in circle, 118–119
drawing and adding color to figure, 21–22
drawing Olympics rings logo, 23–24
drawing various shapes, 81–83
drawing with colors and fonts, 83–85
moving pen to any location, 22–23
simulating random walk, 156–157
Two-dimensional lists
check Sudoku GUI solution, 375–377
check Sudoku solution, 372–375
examples of, 363–365
grading multiple-choice test, 367–368
passing to functions, 365–367
processing, 362–363
review, 381–397
solving closest pair problem, 368–370
solving closest pair problem GUI, 370–372
two-way if-else statements, 100–102
type(), 74–75
Type conversions, 45–46
U
UML (Unified Modeling Language) class diagrams
example of, 230–232
overview of, 222–224
Rational class, 259
Unary operators, 40
Underflow, floating-point numbers, 42
Underscore (_), identifiers, 36
Underscores (__)
__init__ method, 217
private data fields and private methods, 227–229
Unhandled exceptions, 456
Unicode code, 68
union method, sets, 481–483
Unique address, 5
Unix epoch, current system time, 46–47
upper method, strings, 249–250
USB flash drives, 7
UsefulTurtleFunctions.py, 199–201
V
Value-returning functions, 173–175
Values, Boolean, 92–93
van Rossum, Guido, 13
Variables
assignment statements, expressions and, 36–38
Boolean, 93
classes storing data fields as, 216
naming conventions, 36
objects vs., 221
parameters as function header, 173
relationships between objects and, 75
simultaneous assignments, 38–39
writing programs using, 32–34
Void function, 176–178
W
Weather problem, 378–379
Web, reading data from, 452–454
while loops
controlling with sentinel value, 140–142
controlling with user confirmation, 140
converting for loop to, 144–145
design strategies, 138–139
guessing numbers, 136–138
input and output redirections, 142–143
multiple subtraction quiz, 139–140
overview of, 134–136
repeat subtraction quiz, 136
Whitespace characters
defined, 76
stripping from string, 250–251
Widgets, GUI
creating loan calculator, 287–288
Tkinter classes, 275–280
width argument, Canvas, 283
Windows Calculator, number conversions, 537
write method
drawing with colors and fonts, 84
writing data to file, 440–443
Writing
data to file, 441–443
object to file with binary I/O pickling, 465–470
testing file’s existence before, 443
Z
ZeroDivisonError class, 456–457, 460–461
556 Index

CREDITS
Cover and chapter opener art: “Life Aquatic” © Arthur Xanthopoulos from Damaged Photography
Figure 1.1 (CPU): © Shutterstock/Studio 37
Figure 1.1 (Memory): © Shutterstock/Arno van Dulmen
Figure 1.1 (Storage Devices/hard drive): © Shutterstock/Péter Gudella
Figure 1.1 (Storage Devices/USB flash drive): © Shutterstock/Vasilius
Figure 1.1 (Storage Devices/DVD): © Shutterstock/Nata-Lia
Figure 1.1 (Input Devices/keyboard): © Shutterstock/Dmitry Rukhlenko
Figure 1.1 (Input Devices/mouse): © Fotolia/Andrey Khrobostov
Figure 1.1 (Input Devices/joystick): © Shutterstock/George Dolgikh
Figure 1.1 (Output Devices/monitor): © Shutterstock/Nikola Spasenoski
Figure 1.1 (Output Devices/laser printer): © Shutterstock/restyler
Figure 1.1 (Communication Devices/cable modem): © Shutterstock/prism68
Figure 1.1 (Communication Devices/network interface card): © Shutterstock/moritorus
Figure 1.1 (Communication Devices/wireless modem): © Shutterstock/tuanyick
Figure 1.2: © Shutterstock/Xavier P
Figure 1.4: © Shutterstock/Péter Gudella
Figure 1.5 (USB flash drive/plugged in): © Shutterstock/xj
Figure 1.5 (USB flash drive/unplugged/cap off): © Shutterstock/Vasilius
Figure 1.6 (keyboard): © Shutterstock/Dmitry Rukhlenko
Figure 1.7 (network interface card): © Shutterstock/moritorus
Figure 1.7 (server): © Shutterstock/Madlen
Figure 1.7 (PC): © Shutterstock/Dmitry Melnikov
Figures 1.11, 1.12, 1.14–1.20, 2.3, 2.4, 3.1, 3.3–3.7, 4.7, 4.13–4.16, 5.2–5.6, 6.10–6.13, 7.1, 9.1, 9.3–9.6, 9.9–9.40, 10.5, 10.13,
10.15–10.21, 11.3, 11.8, 11.12, 11.14–11.19, 12.4, 12.15, 12.17–12.31, 13.3, 13.7, 13.8, 13.11–13.13, 14.9–14.12, 14.14, 15.1, 15.9,
15.14–15.21: Python, Turtle Graphics, and Tkinter are Copyright © 2001–2011 Python Software Foundation. All rights reserved.
557

Python Quick Reference
Companion Web site: www.pearsonhighered.com/liang
selection statements
if condition:
statements
if condition:
statements
else:
statements
if condition1:
statements
elif condition2:
statements
else:
statements
loop statements
while condition:
statements
# strings, lists, tuples
# are examples of sequences
for e in sequence:
statements
for line in file:
statements
for key in dictionary:
statements
Defining Functions
def functionName(parameters):
statements
Simultaneous Assignment
x, y = y, x # Swap x with y
Logical Operators
and logical conjunction
or logical disjunction
not logical negation
Relational Operators
< less than <= less than or equal to > greater than
>= greater than or equal to
== equal to
!= not equal
Augmented Assignment Operators
= assignment
+= addition assignment
-= subtraction assignment
*= multiplication assignment
/= float division assignment
//= integer division assignment
%= remainder assignment
**= exponent assignment
Arithmetic Operators
+ addition
– subtraction
* multiplication
/ float division
// integer division
% remainder
** exponent
range Functions
range(a, b) # Returns a sequence a, a + 1, …, b – 1
range(b) # Same as range(0, b)
range(a, b, k) # Returns a sequence a, a + k, a + 2k, …, with the last number
# in the sequence less than b
Random Numbers
random.randint(a, b) # Return a random integer between a and b
random.randrange(a, b) # Return a random integer between a and b – 1
random.random() # Return a random float between 0.0 and 1.0, excluding 1.0
Console Input
string = input(“Enter a string: “)
number = eval(input(“Enter a number: “))
number1, number2, number3 = eval(input(“Enter three numbers, separated by commas: “)
Console Output
print(item1, item2, …)
print(item1, item2, …, end = “ending string”)
Conditional Expression
v = v1 if condition else v2

www.pearsonhighered.com/liang

FIGURE 1.17 The program draws the Olympics rings logo.
FIGURE 3.4 The program draws five shapes in different colors.
FIGURE 5.5 The program plots sine function in blue and cosine function in red.
FIGURE 3.5 The program draws an Olympic symbol.

FIGURE 9.36 Ten balls with random colors are displayed at random locations.
FIGURE 9.39 The blue circle is dragged with the mouse.
FIGURE 10.14 The program displays bouncing balls with control buttons.
FIGURE 11.17 The program displays 0s and 1s randomly with a click of the Refresh button.

FIGURE 12.28 The program uses the BarChart class to display bar charts.
FIGURE 12.25 The program enables two players to play the Connect Four game.
(a) (b)
FIGURE 12.26 A Mandelbrot image is shown in (a) and a Julia set image is shown in (b).

FIGURE 15.11 queens[i] denotes the position of the queen in row i.
FIGURE 12.29 The program uses the PieChart class to display pie charts.

Cover
Title Page
Copyright Page
PREFACE
Acknowledgments
Contents
Chapter 1 Introduction to Computers, Programs, and Python
1.1 Introduction
1.2 What Is a Computer?
1.3 Programming Languages
1.4 Operating Systems
1.5 The History of Python
1.6 Getting Started with Python
1.7 Programming Style and Documentation
1.8 Programming Errors
1.9 Getting Started with Graphics Programming
Chapter 2 Elementary Programming
2.1 Introduction
2.2 Writing a Simple Program
2.3 Reading Input from the Console
2.4 Identifiers
2.5 Variables, Assignment Statements, and Expressions
2.6 Simultaneous Assignments
2.7 Named Constants
2.8 Numeric Data Types and Operators
2.9 Evaluating Expressions and Operator Precedence
2.10 Augmented Assignment Operators
2.11 Type Conversions and Rounding
2.12 Case Study: Displaying the Current Time
2.13 Software Development Process
2.14 Case Study: Computing Distances
Chapter 3 Mathematical Functions, Strings, and Objects
3.1 Introduction
3.2 Common Python Functions
3.3 Strings and Characters
3.4 Case Study: Minimum Number of Coins
3.5 Introduction to Objects and Methods
3.6 Formatting Numbers and Strings
3.7 Drawing Various Shapes
3.8 Drawing with Colors and Fonts
Chapter 4 Selections
4.1 Introduction
4.2 Boolean Types, Values, and Expressions
4.3 Generating Random Numbers
4.4 if Statements
4.5 Case Study: Guessing Birthdays
4.6 Two-Way if-else Statements
4.7 Nested if and Multi-Way if-elif-else Statements
4.8 Common Errors in Selection Statements
4.9 Case Study: Computing Body Mass Index
4.10 Case Study: Computing Taxes
4.11 Logical Operators
4.12 Case Study: Determining Leap Years
4.13 Case Study: Lottery
4.14 Conditional Expressions
4.15 Operator Precedence and Associativity
4.16 Detecting the Location of an Object
Chapter 5 Loops
5.1 Introduction
5.2 The while Loop
5.3 The for Loop
5.4 Nested Loops
5.5 Minimizing Numerical Errors
5.6 Case Studies
5.7 Keywords break and continue
5.8 Case Study: Displaying Prime Numbers
5.9 Case Study: Random Walk
Chapter 6 Functions
6.1 Introduction
6.2 Defining a Function
6.3 Calling a Function
6.4 Functions with/without Return Values
6.5 Positional and Keyword Arguments
6.6 Passing Arguments by Reference Values
6.7 Modularizing Code
6.8 Case Study: Converting Decimals to Hexadecimals
6.9 The Scope of Variables
6.10 Default Arguments
6.11 Returning Multiple Values
6.12 Case Study: Generating Random ASCII Characters
6.13 Function Abstraction and Stepwise Refinement
6.14 Case Study: Reusable Graphics Functions
Chapter 7 Objects and Classes
7.1 Introduction
7.2 Defining Classes for Objects
7.3 UML Class Diagrams
7.4 Immutable Objects vs. Mutable Objects
7.5 Hiding Data Fields
7.6 Class Abstraction and Encapsulation
7.7 Object-Oriented Thinking
Chapter 8 More on Strings and Special Methods
8.1 Introduction
8.2 The str Class
8.3 Case Study: Checking Palindromes
8.4 Case Study: Converting Hexadecimals to Decimals
8.5 Operator Overloading and Special Methods
8.6 Case Study: The Rational Class
Chapter 9 GUI Programming Using Tkinter
9.1 Introduction
9.2 Getting Started with Tkinter
9.3 Processing Events
9.4 The Widget Classes
9.5 Canvas
9.6 The Geometry Managers
9.7 Case Study: Loan Calculator
9.8 Displaying Images
9.9 Menus
9.10 Popup Menus
9.11 Mouse, Key Events, and Bindings
9.12 Animations
9.13 Scrollbars
9.14 Standard Dialog Boxes
Chapter 10 Lists
10.1 Introduction
10.2 List Basics
10.3 Case Study: Lotto Numbers
10.4 Case Study: Deck of Cards
10.5 Deck of Cards GUI
10.6 Copying Lists
10.7 Passing Lists to Functions
10.8 Returning a List from a Function
10.9 Case Study: Counting the Occurrences of Each Letter
10.10 Searching Lists
10.11 Sorting Lists
10.12 Case Study: Bouncing Balls
Chapter 11 Multidimensional Lists
11.1 Introduction
11.2 Processing Two-Dimensional Lists
11.3 Passing Two-Dimensional Lists to Functions
11.4 Problem: Grading a Multiple-Choice Test
11.5 Problem: Finding the Closest Pair
11.6 GUI: Finding the Closest Pair
11.7 Problem: Sudoku
11.8 Case Study: Sudoku GUI
11.9 Multidimensional Lists
Chapter 12 Inheritance and Polymorphism
12.1 Introduction
12.2 Superclasses and Subclasses
12.3 Overriding Methods
12.4 The object Class
12.5 Polymorphism and Dynamic Binding
12.6 The isinstance Function
12.7 Case Study: A Reusable Clock
12.8 Class Relationships
12.9 Case Study: Designing the Course Class
12.10 Designing a Class for Stacks
12.11 Case Study: The FigureCanvas Class
Chapter 13 Files and Exception Handling
13.1 Introduction
13.2 Text Input and Output
13.3 File Dialogs
13.4 Case Study: Counting Each Letter in a File
13.5 Retrieving Data from the Web
13.6 Exception Handling
13.7 Raising Exceptions
13.8 Processing Exceptions Using Exception Objects
13.9 Defining Custom Exception Classes
13.10 Binary IO Using Pickling
13.11 Case Study: Address Book
Chapter 14 Tuples, Sets, and Dictionaries
14.1 Introduction
14.2 Tuples
14.3 Sets
14.4 Comparing the Performance of Sets and Lists
14.5 Case Study: Counting Keywords
14.6 Dictionaries
14.7 Case Study: Occurrences of Words
Chapter 15 Recursion
15.1 Introduction
15.2 Case Study: Computing Factorials
15.3 Case Study: Computing Fibonacci Numbers
15.4 Problem Solving Using Recursion
15.5 Recursive Helper Functions
15.6 Case Study: Finding the Directory Size
15.7 Case Study: Towers of Hanoi
15.8 Case Study: Fractals
15.9 Case Study: Eight Queens
15.10 Recursion vs. Iteration
15.11 Tail Recursion
APPENDIXES
Appendix A: Python Keywords
Appendix B: The ASCII Character Set
Appendix C: Number Systems
INDEX
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Z
CREDITS

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