Approach

To effectively answer the question "How would you write a function to sort a stack using only one additional stack?", follow a structured framework:

1. Understand the Problem: Clarify what is being asked. You need to sort a stack using only one additional stack for temporary storage.

2. Outline the Steps: Break down the sorting process into logical steps.

3. Explain Your Thought Process: Walk through your logic as you would in a coding interview.

4. Present the Code: Write a clear and functional code snippet.

5. Discuss Complexity: Mention the time and space complexity of your approach.

Key Points

When crafting a response, consider the following essential aspects:

• Clarity and Structure: Ensure your explanation is easy to follow.

• Algorithm Understanding: Demonstrate a solid understanding of stack operations.

• Efficiency: Discuss the efficiency of your solution regarding time and space complexity.

• Problem-Solving Skills: Showcase your ability to approach problems logically.

Standard Response

Here is a comprehensive sample answer that incorporates best practices:

Understanding the Problem

To sort a stack using another stack, we can utilize the property of stacks (LIFO - Last In First Out) to arrange the elements in ascending order. The main challenge is to ensure that we can only use one additional stack for temporary storage.

Steps to Sort the Stack

• Initialize a Temporary Stack: Create a second stack to hold the sorted elements.

• Pop Elements from the Original Stack: Continuously pop elements from the original stack until it is empty.

• Insert into the Temporary Stack: For each popped element, compare it with the top of the temporary stack:

• If the temporary stack is empty or the popped element is greater than the top of the temporary stack, push it onto the temporary stack.

• If the popped element is smaller, pop elements from the temporary stack and push them back to the original stack until the correct position for the popped element is found.

• Repeat Until Original Stack is Empty: This process continues until all elements from the original stack are transferred to the temporary stack in sorted order.

• Transfer Back: Finally, transfer the sorted elements back to the original stack, if needed.

Code Implementation

Here’s how this logic can be translated into Python code:

def sort_stack(original_stack):
 temp_stack = []

 while original_stack:
 # Pop the top element
 current = original_stack.pop()

 # While temp_stack is not empty and top of temp_stack is greater than current
 while temp_stack and temp_stack[-1] > current:
 original_stack.append(temp_stack.pop())

 # Push current onto temp_stack
 temp_stack.append(current)

 # If needed, transfer sorted elements back to original stack
 while temp_stack:
 original_stack.append(temp_stack.pop())

 return original_stack

Complexity Analysis

• Time Complexity: O(n^2) in the worst case, where n is the number of elements in the stack. This is due to the nested operations of popping and pushing elements between the stacks.

• Space Complexity: O(n) for the temporary stack.

Tips & Variations

Common Mistakes to Avoid

• Not Clarifying Requirements: Ensure you understand the constraints of using only one additional stack.

• Ignoring Edge Cases: Consider edge cases, such as an empty stack or a stack with identical elements.

• Assuming Input Types: Make sure to note the type of elements in the stack (integers, strings, etc.) when discussing sorting.

Alternative Ways to Answer

• Using Recursion: Another method could involve using recursive functions to sort the stack, but this may use more than one additional stack in terms of call stack space.

• Using a List as a Stack: If the language allows, you might discuss using a list as a stack for easier operations.

Role-Specific Variations

• For Technical Roles: Emphasize your understanding of data structures and algorithm complexity.

• For Managerial Positions: Focus on how you would communicate the solution to your team and ensure they understand the reasoning behind the approach.

• For Creative Roles: Highlight creative problem-solving and alternative methods of sorting if applicable.

Follow-Up Questions

• Can you explain why the time complexity is O(n^2)?

• How would you modify your solution if you were allowed to use additional data structures?

• What would you do if the stack contained objects instead of simple integers?

This structured response not only provides a clear answer to the interview question but also engages the interviewer in a discussion that showcases your problem-solving skills and technical knowledge