c programming

Question

Let S be a stack k 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 the one such stack operation and the start of the next operation. For
m > 1, define the stack-life of mcs the time elapsed from the end or 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
(A) n(X+Y) (B) 3Y+2X
(C) n(X+Y)-X (D) Y+ 2X

Comments

https://gateoverflow.in/951/gate2003_64

Answer 1

here numbers are entered in natural order from 1,2,---------n these are coming in AP so simply do this.... first first element 1... n-1  nelements has to push and n-1 elements has to pop so total time=2(n-1)X and b/w each y sec elapse so total elapse=[2(n-1)+1]Y.

 now for last element just y unit elapse...so total time=2(n-1)x+2(n-1)y+y+[y]/2=n(x+y)-x