Clarify the problem and constraints, then propose an efficient O(n) solution using a monotonic stack. Walk through the algorithm with a small example, analyze time and space complexity, and discuss edge cases.
Pro tip: Mention that this is a classic 'Next Greater Element' problem and that the monotonic stack approach is optimal; also note that you can process the array from right to left to maintain the stack of candidates.
Restate the problem to ensure understanding, ask about input size, duplicates, and expected output format. Confirm that 'greater' means strictly greater.
Start with the brute-force O(n^2) solution, then introduce the optimal O(n) monotonic stack approach. Explain why the stack approach is more efficient.
Explain the monotonic stack algorithm step-by-step: iterate from right to left, maintain a stack of indices with decreasing values, pop elements smaller than or equal to the current, and the top of the stack (if any) is the next greater element.
Choose a small array (e.g., [2, 5, 3, 7]) and demonstrate how the stack evolves and how the next greater elements are determined.
State that time complexity is O(n) because each element is pushed and popped at most once, and space complexity is O(n) for the stack. Discuss edge cases: empty array, all decreasing, all increasing, duplicates.
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