Q6. Stack Life Cycle doubt

#1

Let S be a stack of size n >= 1. Starting with the empty stack, suppose we push the first n natural numbers in sequence, and then perform n pop operations. Assume that Push and Pop operation take X seconds each, and Y seconds elapse between the end of one such stack operation and the start of the next operation. For m >= 1, define the stack-life of m as the time elapsed from the end of Push(m) to the start of the pop operation that removes m from S. The average stack-life of an element of this stack is:

Why is the answer to this n(X+Y)-X and not n(X+Y)?

#2

Time for last element Y as it is just popped
time for second last element (time for previous)+2X + 2Y=y+2X+2Y
Time for third last (time for previous)+2X + 2Y=2X+3Y + 2X +2Y
similary doing it for all n element and suming them all and dividing it by N we will get answer.

n(X + Y)-X

#3

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