The basic push/pop/top part was fine, I've done stack problems before.
Start by clarifying the requirements and edge cases, especially the duplicate handling in popMax. Then propose a solution using two stacks or a doubly linked list with a tree map, explaining how each operation maintains the max tracking. Finally, analyze time and space complexity and discuss trade-offs.
Pro tip: Demonstrate awareness of the trade-off between simplicity and efficiency: a two-stack solution is easy but popMax is O(n), while a balanced BST or heap with lazy deletion can achieve O(log n) but adds complexity. Mention that in an interview, you'd start with the simpler solution and then optimize if needed.
Ask about duplicate handling, expected time complexity, and whether all operations need to be O(1) or if O(log n) is acceptable. Confirm that popMax removes the topmost maximum element.
Describe a two-stack approach: one stack for all elements, another for tracking maximums. Explain how push, pop, top, and peekMax work in O(1), but popMax requires O(n) to remove the topmost max.
Introduce a more efficient structure, such as a doubly linked list for the stack and a balanced BST (or heap with lazy deletion) to track maximums, achieving O(log n) for popMax and O(1) for other operations.
Compare time and space complexity of both approaches. Discuss when the simpler solution suffices and when the optimized version is necessary, considering real-world constraints.
Walk through a sequence of operations, including duplicates, to verify correctness and consistency of max tracking.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.