They wanted the real solution, not just a two-stack hack that passes most cases.
Use two stacks: one for the main elements and another to keep track of the maximum values. When pushing, compare the new value with the current maximum and push the larger onto the max stack. When popping, pop from both stacks to maintain consistency.
Pro tip: Discuss the trade-offs between this two-stack approach and alternatives like storing (value, max) pairs or using a doubly linked list with a tree map. Mention that the two-stack solution is optimal for O(1) time and O(n) space, but consider edge cases like popping the maximum element.
Confirm that all operations must be O(1) time and discuss space complexity expectations. Ask about handling duplicate maximum values and popping when empty.
Explain how to use a main stack for elements and a max stack to track the maximum at each level. Describe push, pop, top, and peekMax operations.
Demonstrate with a sequence of operations (e.g., push 5, push 1, push 5, pop, top, peekMax) to show how the stacks evolve and ensure correctness.
State that each operation is O(1) time and O(n) space. Discuss edge cases: popping the maximum, duplicate maxima, and empty stack operations.
Mention other solutions like storing pairs or using a linked list with a balanced BST, and compare their time/space trade-offs.
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