How to sort a stack using only Push, Pop, Top, IsEmpty, IsFull?

Question

Given a stack S, need to sort the stack using only Push, Pop, Top, IsEmpty, IsFull.

Looking for most sim

Answer 1

What temporary data structures can you use? With push and pop, and no temporary storage for n elements, accessing data near the bottom of the stack would be impossible without storing the rest -somewhere-.

If top (equiv to {x=pop();push(x);return x}) was replaced with shift, it would be perfectly doable - the stack would change into fifo (shift+push; pop would fall into disuse) and it would allow for an easy bubblesort on currently available elements.