The push/pop/top part is trivial and I kind of rushed through it, which in hindsight was dumb because I should've used that time to think about the max operations.
Start by clarifying the requirements and edge cases, especially the duplicate handling for popMax. Then propose a solution using two stacks (one for values, one for maximums) and implement it, analyzing time complexities. Discuss trade-offs and possible optimizations.
Pro tip: Mention that the two-stack approach gives O(1) for push, pop, top, and peekMax, but popMax is O(n) in the worst case; however, you can optimize popMax to O(log n) using a balanced BST or a heap with lazy deletion, but that adds complexity. Showing awareness of these trade-offs demonstrates maturity.
Ask about duplicate handling, empty stack behavior, and whether popMax should remove the topmost maximum. Confirm that operations should be efficient.
Suggest using two stacks: one to store all elements, and another to keep track of the maximum values. Explain how they work together.
Write code for push, pop, top, peekMax, and popMax. For popMax, temporarily pop elements until the max is found, then push back the remaining elements.
State that push, pop, top, and peekMax are O(1), while popMax is O(n) in the worst case due to the need to pop and push back elements.
Mention alternative approaches like using a balanced BST or heap with lazy deletion to achieve O(log n) for popMax, but note the added complexity and space overhead.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.