Approach

To effectively answer the interview question regarding designing and implementing a stack that supports push, pop, top, and retrieving the minimum element in constant time, follow a structured framework. Here’s a step-by-step breakdown:

1. Understanding the Requirements: Clearly define what operations must be supported by the stack.

2. Data Structure Selection: Choose appropriate data structures to maintain the stack and track the minimum element.

3. Algorithm Design: Outline how each operation will be implemented to ensure efficiency.

4. Complexity Analysis: Discuss the time and space complexity of the solution.

5. Edge Cases: Consider edge cases to ensure robustness.

Key Points

• Operations: The stack must support push, pop, top, and getMin (retrieving the minimum element).

• Efficiency: All operations must run in O(1) time complexity.

• Data Structures: Utilize two stacks or a tuple within a single stack for optimal performance.

• Clarity: Ensure your explanation is clear and concise, demonstrating your thought process to the interviewer.

Standard Response

Here’s a comprehensive sample answer to the interview question.

To design a stack that supports the operations push, pop, top, and retrieving the minimum element in constant time, I would implement a dual-stack system. This solution ensures that all operations are executed in O(1) time complexity. Below is the approach:

• Data Structures:

• Main Stack: This stack will store all the elements.

• Min Stack: This auxiliary stack will keep track of the minimum elements.

• Algorithm Implementation:

• Push Operation:

• Push the element onto the main stack.

• If the min stack is empty or the new element is less than or equal to the top of the min stack, push the new element onto the min stack.

• Pop Operation:

• Pop the top element from the main stack.

• If the popped element is the same as the top of the min stack, pop from the min stack as well.

• Top Operation:

• Return the top element of the main stack without removing it.

• Get Min Operation:

• Return the top element of the min stack, which is the minimum element in constant time.

• Complexity Analysis:

• Time Complexity: Each operation (push, pop, top, getMin) runs in O(1) time.

• Space Complexity: The space used is O(n) in the worst case, where n is the number of elements in the stack (due to the main stack and potentially the min stack).

• Edge Cases:

• Handle cases where the stack is empty during pop and getMin operations to avoid errors.

• Ensure that the implementation correctly maintains the minimum value when duplicate minimum values are present.

This design efficiently meets the requirements while ensuring clarity and robustness.

Tips & Variations

Common Mistakes to Avoid

• Not Using Two Stacks: Failing to implement a secondary data structure to track the minimum can lead to non-constant time retrieval.

• Ignoring Edge Cases: Overlooking edge cases, such as operations on an empty stack, can lead to runtime errors.

Alternative Ways to Answer

• Single Stack with Tuple: Another approach is to store tuples in the stack. Each element would be a tuple of the value and the current minimum.

Role-Specific Variations

• Technical Roles: Focus on the complexity analysis and optimizations in memory usage.

• Managerial Roles: Emphasize your ability to analyze performance and lead a team in implementing efficient algorithms.

• Creative Roles