Two-pointer approach is the right move here but I spent a couple minutes convincing myself why the greedy logic actually works.
Start by clarifying the problem and constraints, then propose a brute-force solution to establish a baseline. Introduce the two-pointer technique as an optimized O(n) solution, explaining why it works and its trade-offs. Finally, discuss edge cases and potential optimizations.
Pro tip: Emphasize the greedy proof behind moving the pointer with the shorter line: it's the only way to potentially increase the area, since the width decreases and the height is limited by the shorter line. This shows deep understanding beyond just memorizing the algorithm.
Restate the problem in your own words and ask clarifying questions about input constraints, expected output, and edge cases (e.g., empty array, two lines, equal heights).
Mention that a naive solution would check all pairs of lines, calculating area as min(height[i], height[j]) * (j - i), with O(n^2) time complexity. This establishes a baseline.
Explain that starting with pointers at both ends and moving the pointer with the shorter line inward yields an O(n) solution. Describe the area calculation and pointer movement logic.
Argue why moving the shorter pointer is safe: the area is limited by the shorter line, so moving the taller line cannot increase the area, while moving the shorter line might find a taller line and increase the area.
State time complexity O(n) and space O(1). Discuss edge cases like empty input, two lines, and all equal heights, and confirm the algorithm handles them.
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