Amortized analysis on Operations of stack

Question

Let's Suppose we perform a sequence of operations (i.e., top, push, and pop) on an initially empty stack so that the stack size does not exceed k. After every k operations, we make a copy of the entire stack for backup purposes. How can I use the accounting method to prove that each stack operation will have O(1) amortized complexity regardless of whether the stack is copied or not?

Answer 1

You have k simple operations and one copy operation that takes at most k time.

Together you make p elementary operations, and p < k + k = 2*k

So amortized complexity per operation is p/k <= 2*k/k = 2 = O(1)