Start by clarifying the problem and walking through a brute-force approach to establish understanding. Then introduce the optimal monotonic stack solution, explaining how it efficiently finds the largest rectangle by identifying boundaries for each bar. Emphasize the time and space complexity trade-offs.
Pro tip: Mention that the monotonic stack approach can be implemented in a single pass with a stack of indices, and highlight that adding a sentinel bar of height 0 at the end simplifies handling remaining bars. This shows attention to implementation details and edge cases.
Restate the problem to ensure understanding: given an array of bar heights, find the maximum area rectangle formed by a contiguous range where height is the minimum bar in that range. Confirm input constraints and expected output.
Describe a naive O(n^2) solution: for each bar, expand left and right until a shorter bar is encountered, computing area. This demonstrates baseline understanding and sets the stage for optimization.
Explain the O(n) monotonic stack approach: maintain a stack of indices with increasing heights. When a shorter bar is found, pop and calculate area using the popped bar's height and the distance to the previous smaller bar.
State that the optimal solution runs in O(n) time and O(n) space, as each bar is pushed and popped at most once. Contrast with the brute force O(n^2) time.
Discuss edge cases: empty array, single bar, strictly increasing/decreasing heights, and equal heights. Mention adding a sentinel 0 at the end to flush the stack.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.