Question

Can anyone please help me with the Algorithm for this problem (its an Interview Question):

You are given a stack. Devise an algorithm to find the maximum number
using PUSH/POP Operations only.

Answer 1

Given the lack of constraints in the original post, you can just pop off all the data and compute a running maximum:

if empty(st) -> raise exception
m <- pop(st)
while not empty(st)
    n <- pop(st)
    if n > m
        m <- n

Edit (with the new restriction that the original stack is unchanged and the new resource of a second available stack):

if empty(st) -> raise exception
m <- pop(st)
push(alt_st, m)
while not empty(st)
    n <- pop(st)
    push(alt_st, n)
    if n > m
        m <- n
while not empty(alt_st):
    n <- pop(alt_st)
    push(st, n)