The push/pop/top part was fine, that's just a stack.
Start by clarifying the requirements and constraints, then propose a solution using two stacks: one for the main stack and another to keep track of the maximum values. For popMax, temporarily pop elements from the main stack until the maximum is removed, then push them back, ensuring O(1) amortized time for most operations and O(n) worst-case for popMax, but discuss trade-offs and potential optimizations.
Pro tip: Demonstrate awareness of the trade-off between time complexity and implementation complexity: a simple two-stack solution is easy to implement but popMax is O(n) worst-case; a more advanced solution using a doubly linked list and a tree map achieves O(log n) for all operations, but is harder to code. Discuss which is preferable based on expected usage patterns.
Ask about expected frequency of operations, whether all operations must be strictly better than O(n) worst-case, and if duplicates matter. Confirm that popMax should remove the top-most maximum.
Describe a two-stack approach: one stack for elements, another for tracking maximums. Explain how push, pop, top, peekMax work in O(1), and popMax in O(n) by temporarily popping elements.
Discuss that popMax is O(n) worst-case, which may not meet 'better than linear time' for all operations. Mention that amortized analysis might be acceptable if popMax is infrequent.
Introduce a doubly linked list to maintain stack order and a balanced BST (e.g., TreeMap) to track values and their positions, achieving O(log n) for all operations. Explain how to handle duplicates by storing a list of nodes for each value.
Summarize the trade-offs: simple two-stack is easier but popMax is O(n); optimized version is O(log n) but complex. Recommend based on interview context and expected use cases.
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