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Design a max-stack with efficient operations

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MediumSoftware EngineerOnsiteCoding & Algorithms

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This interview question evaluates algorithm design, data structures, correctness, complexity, edge cases, and implementation details in a realistic interview setting. A strong answer for Design a max-stack with efficient operations states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

Design a stack that supports push (x), pop(), top(), peekMax(), and popMax(). The popMax operation must remove and return the maximum element; if there are multiple maximums, remove the most recently pushed one. Implement two approaches: (A) an amortized O(

  1. solution using auxiliary structures, and (B) an O(log n) popMax solution using a balanced tree or heap plus linked nodes. Explain how you will handle duplicates, empty-structure edge cases, and concurrency concerns for a high-throughput system. Provide time/space complexities and brief test cases.