What is the time complexity of finding the minimum element in a stack that supports getMin() operation in O(1) time?O(1)O(n)O(log n)O(n^2)

To determine the time complexity of finding the minimum element in a stack that supports a getMin() operation in O(1) time, we can analyze how this is achieved.

Step 1: Stack Design

1. The stack must maintain the properties of a typical stack (LIFO - Last In First Out).
2. Alongside the normal stack operations (push and pop), it must also keep track of the minimum element efficiently.

Step 2: Auxiliary Structure

1. An auxiliary stack (let's call it minStack) is often employed to store the minimum values.
2. Whenever a new element is added to the main stack, the minimum is compared with the new element, and the smaller value is pushed onto minStack.

Step 3: Operations Analysis

1. Push Operation:
   • When a new element is pushed, it involves comparing the new element with the current minimum (top of minStack). Thus, the time complexity is O(1).
2. Pop Operation:
   • When an element is popped, if it is the same as the top of minStack, the minimum must be popped from there as well. This also takes O(1) time.
3. getMin Operation:
   • Retrieving the minimum element simply involves accessing the top of minStack, which is again O(1).

Final Answer

The time complexity for finding the minimum element in a stack that supports the getMin() operation in O(1) time is O(1).