Clarify that the problem is to find any three elements whose indices are increasing and values are strictly increasing. Then present an O(n) time, O(1) space solution that tracks the smallest and second smallest values while scanning, and finally returns the third element that completes the increasing triplet.
Pro tip: Emphasize that the algorithm only needs to return one valid triplet, not all triplets, and that the O(n) greedy approach is optimal because any solution must examine all elements in the worst case. Also mention that the indices of the stored smallest and second smallest values are maintained to ensure the order condition.
Confirm that the array is unsorted and that we need to find any three elements with increasing indices and strictly increasing values. Ask about edge cases like duplicates or arrays with fewer than three elements.
Mention that a triple nested loop would be O(n^3) and is too slow for large inputs. This shows you consider naive solutions before optimizing.
Explain that you scan the array once, keeping track of the smallest value seen so far (with its index) and the second smallest value that appears after the smallest (with its index). When you find a value greater than the second smallest, you have found a valid triplet.
Use a concrete example like [2, 1, 5, 0, 4, 6] to demonstrate how the algorithm updates the smallest and second smallest and eventually finds the triplet (1, 4, 6) or (0, 4, 6).
State that the algorithm runs in O(n) time and uses O(1) extra space. Discuss edge cases such as no triplet existing, duplicates, and negative numbers.
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