Design a max-stack with efficient operations

Q: Design a max-stack with efficient operations

This question evaluates a candidate's ability to design and analyze a data structure that supports stack operations with efficient maximum retrieval and removal, testing algorithmic design, complexity analysis, and handling of edge cases such as duplicates and empty-structure behavior.

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Question

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(

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.

Design a max-stack with efficient operations

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