Minimum of stack in O(1)

#include <iostream>
#include <iomanip>
#include <stack>
#include <conio.h>

/*
Push() and Pop() methods of stack are given. Write a function to get the minimum of stack in O(1) time

- can be done by maintaining the following invariant in all the operations in the stack
"The top element of the stack is always the smallest number"
- an auxillary stack is used to maintain this invariant during push operations
*/
std::stack<int> stack;

/*
- check if x < stack.top() 
- if yes, push it in
- if no, 
    - pop all the elements from the stack till we get x < stack.top() 
    and push into aux stack
    - push x
    - push all the elements from aux stack back to main stack
    - This maintains above stated invariant
*/
void push(int x)
{
    std::stack<int> aux;
    // using loop and a half idiom ... 
    while(true && stack.size() > 0)
    {
        if(stack.top() > x)
            break;
        else
        {
            aux.push(stack.top());
            stack.pop();
        }
    }
    
    // now we have two stacks, stack with all elements > x and aux with 
    // all elements < x
    stack.push(x);
    while(aux.size() > 0)
    {
        stack.push(aux.top());
        aux.pop();
    }
}

int main()
{
    push(3);
    push(1);
    push(2);
    push(6);
    push(4);
    push(12);
    push(10);
    push(8);
    
    // some tests
    assert(stack.top() == 1);
    stack.pop();
    assert(stack.top() == 2);
    stack.pop();
    assert(stack.top() == 3);    
    
    getch();
}