Do you mean "design a stack where you can find the minimum value in O(1) both time and space complexity"? Because I don't see how you can do O(1) with an arbitrary stack.
Anyways I had failed to give proper answer and I was rejected in the interview. This was the last question of my last round!
Spoiler: Here is one such solution using a simple but very clever trick: http://www.geeksforgeeks.org/design-a-stack-that-supports-ge...