amortized analysis question

Please find attached and please have it typed, thank you.

Q6.2 Potential functions
16 Points
Define a column to be tall if it contains at least vk cards.
For each of the following potential functions, describe why it would work or describe what is
wrong in the sense that nothing can be done to fix whatever issue exists).
The answers don’t need to be long, but please try to be specific and convincing.
(a)
Φ,
li = number of cards in the column that is moved at iteration (i.e., move) i.
(meaning, we observe that it existed at iteration 1–1 but no longer exists after the move; for
example if we move a column with size x, we report a potential difference of -x)
O This function is ok.
O Something is wrong.
Enter your answer here
(b)
Φ; =
Vk · (number of tall columns)
This function is ok.
O Something is wrong.
(c)
Φ, = number of cards in all tall columns
O This function is ok.
O Something is wrong.
Enter your answer here
(d)
Φ; – = – (number of cards below the v k level)
O This function is ok.
O Something is wrong.