Start by clarifying the problem and walking through a small example to ensure understanding. Then, discuss a brute-force approach and optimize it using precomputed left and right maximum arrays or a two-pointer technique. Finally, analyze time and space complexity and test with edge cases.
Pro tip: Mention that the two-pointer approach achieves O(n) time and O(1) space, which is optimal. Also, relate the problem to real-world scenarios like trapping rainwater between buildings to show practical insight.
Restate the problem in your own words and walk through a simple example to confirm understanding. Ask clarifying questions about input constraints and expected output.
Explain a naive solution that for each bar, finds the maximum height on the left and right, and adds the minimum of those minus the current height. This takes O(n^2) time.
Describe how to precompute left and right maximum arrays in O(n) time and O(n) space, or use two pointers to achieve O(n) time and O(1) space. Explain the logic clearly.
State the time and space complexity of your chosen approach. Compare with the brute force to highlight the improvement.
Walk through edge cases such as empty array, all bars of same height, strictly increasing/decreasing heights, and arrays with zeros. Verify the solution handles them correctly.
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