Started with brute force just to make sure I understood the problem, which was fine.
First, clarify the problem constraints and edge cases, then propose a solution that balances time and space complexity. A common efficient approach is to sort the array while keeping track of original indices, then use a sliding window or two-pointer technique to find the minimum difference among pairs with index gap at least k. Discuss trade-offs between sorting and other methods like using a balanced BST or segment tree.
Pro tip: Mention that sorting changes the original order, so you must retain original indices; this shows attention to detail. Also, consider if the array is static or dynamic, as that affects the choice of data structure.
Restate the problem in your own words and ask clarifying questions about constraints, input size, and expected output. Confirm whether the array can be modified and if there are duplicate heights.
Mention the naive O(n^2) approach of checking all pairs with index gap >= k, and its inefficiency for large n. This sets the stage for optimization.
Describe an O(n log n) solution: create pairs of (height, index), sort by height, then use a sliding window to find the minimum difference where the index gap condition is satisfied. Alternatively, use a balanced BST to maintain a window of indices.
Compare sorting-based approach with other methods like using a segment tree or heap, discussing time/space complexity and suitability for different scenarios (e.g., streaming data).
Walk through edge cases such as k=0, k>=n, all equal heights, and negative heights. Suggest testing with small examples to verify correctness.
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