Retrieving the Min element in a stack in O(1) Time

Question

The reason I\'m asking this question is because I cannot see why the way I think cannot be applied to this particular question

\"How would you design a stack which,

Answer 1

This wouldn't work if you popped numbers off the stack.

Ex. 2,4,5,3,1. After you pop 1 off, what is your minimum?

The solution is to keep a stack of minimums, not just a single value. If you encounter a value that is less than equal to the current minimum, you need to push it onto the min-stack.

Ex.

Push(4):
Stack: 4
Min-stack: 4

Push(2):
Stack: 4 2
Min-stack: 4 2

Push(2):
Stack: 4 2 2
Min-stack: 4 2 2

Push(5):
Stack: 4 2 2 5
Min-stack: 4 2 2

Push(3):
Stack: 4 2 2 5 3
Min-stack: 4 2 2

Push(1):
Stack: 4 2 2 5 3 1
Min-stack: 4 2 2 1

Pop():
Stack: 4 2 2 5 3
Min-stack: 4 2 2

Pop():
Stack: 4 2 2 5
Min-stack: 4 2 2

Pop():
Stack: 4 2 2
Min-stack: 4 2 2

Pop():
Stack: 4 2
Min-stack: 4 2

Pop():
Stack: 4
Min-stack: 4