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mercor·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Mercor software engineer interview hit me with a classic data structures problem. Pretty standard coding round, nothing too surprising, but it's the kind of question that trips you up if you haven't thought about the auxiliary structure angle before.

Questions Asked (1)

Q1

Design a stack that supports push, pop, and a min operation, all in O(1) time.

Algorithms & Data Structures
Author's notes

I knew this one but still fumbled explaining the why behind the auxiliary stack.

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AI HintsAI Generated

Suggested Approach

Use an auxiliary stack that tracks the minimum value at each level of the main stack. When pushing, push the new value onto the main stack and push the new minimum onto the auxiliary stack. When popping, pop from both stacks. The min operation simply returns the top of the auxiliary stack.

Pro tip: Mention that this approach uses O(n) extra space, but you can optimize to O(1) extra space by storing the difference between the value and the current minimum, or by using a single stack with encoded values. Also, clarify that the min operation should return the minimum element in the current stack, not remove it.

1. Clarify requirements

Confirm that all operations (push, pop, min) must be O(1) time, and that min returns the minimum element without removing it. Ask about constraints like memory usage or thread safety if relevant.

2. Propose auxiliary stack approach

Explain that you will maintain two stacks: one for the actual elements and one for the minimum values. The auxiliary stack's top always holds the current minimum.

3. Detail push and pop operations

For push: push value onto main stack; if auxiliary stack is empty or value <= current min, push value onto auxiliary stack. For pop: pop from main stack; if popped value equals auxiliary stack's top, pop from auxiliary stack as well.

4. Implement min operation

The min operation simply returns the top of the auxiliary stack (or None if stack is empty). This is O(1).

5. Discuss optimizations and edge cases

Mention the O(1) space optimization using difference encoding or a single stack with a min variable. Handle edge cases like popping from an empty stack or pushing duplicate minimums.

Key Points to Mention

  • Time complexity: all operations are O(1).
  • Space complexity: O(n) extra space for auxiliary stack, but can be optimized to O(1).
  • Handling duplicate minimum values: push to auxiliary stack when value <= current min.
  • Edge cases: empty stack, popping when stack has one element, pushing negative numbers.
  • Alternative approaches: using a single stack with encoded values or storing (value, min) pairs.
  • Thread safety considerations if the stack is used in a concurrent environment.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.