What is the worst-case time complexity of sorting a stack using another stack?

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Question: What is the worst-case time complexity of sorting a stack using another stack?

Options:

Correct Answer: O(n^2)

Solution:

The worst-case time complexity of sorting a stack using another stack is O(n^2) due to the need to repeatedly pop and push elements.

What is the worst-case time complexity of sorting a stack using another stack?

What is the worst-case time complexity of sorting a stack using another stack?

Step 1: Understand that we have one stack that we want to sort using another empty stack.
Step 2: Realize that to sort the elements, we will need to pop elements from the first stack.
Step 3: When we pop an element from the first stack, we need to compare it with the elements in the second stack to find the correct position.
Step 4: If the second stack has elements, we may need to pop elements from it and push them back to the first stack until we find the right spot for the popped element.
Step 5: This process of popping from one stack and pushing back to the other can take time, especially if we have to do it for every element in the first stack.
Step 6: If we have 'n' elements in the first stack, we may end up doing this for each element, leading to a total of n * n operations in the worst case.
Step 7: Therefore, the worst-case time complexity of sorting a stack using another stack is O(n^2).

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