Knew this was a monotonic stack problem pretty fast but then spent like two minutes convincing myself I was wrong.
Clarify the problem first: for each element, find the nearest greater element to its right; if none, output -1. Then propose an O(n) solution using a monotonic decreasing stack, explaining how it efficiently tracks candidates for the next greater element.
Pro tip: Mention that the monotonic stack approach is optimal and commonly used in similar problems like daily temperatures; also discuss how to handle duplicates and circular arrays if asked.
Confirm that 'next greater' means the first greater element to the right, and that if no such element exists, the answer is -1. Ask about input size, duplicates, and whether the array is circular.
Mention the O(n^2) brute force approach: for each element, scan to the right until a greater element is found. This shows you understand the baseline and can optimize.
Explain that a stack maintaining indices of elements in decreasing order can be used. Iterate through the array, and for each element, pop from the stack while the current element is greater than the element at the top index, setting the next greater for those popped.
Trace the algorithm on a small array like [2, 1, 2, 4, 3] to demonstrate how the stack updates and results are assigned. This clarifies the process and catches edge cases.
State that time complexity is O(n) because each element is pushed and popped at most once, and space is O(n) for the stack. Discuss edge cases: empty array, all decreasing, all increasing, duplicates.
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