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Classic problem but I fumbled the edge case where one interval completely swallows the next.
Start by sorting the intervals based on their start times, then iterate through them while maintaining a result list of merged intervals. For each interval, if it overlaps with the last merged interval, merge them by updating the end time; otherwise, add it to the result.
Pro tip: Clarify edge cases upfront, such as empty input, single interval, or intervals with the same start but different ends. Also, mention that the solution runs in O(n log n) time due to sorting, which is optimal for comparison-based approaches.
Confirm that intervals are closed and may be unsorted. Discuss edge cases like empty list, single interval, and intervals that touch (e.g., [1,2] and [2,3] are considered overlapping).
Sort the input list of intervals based on their start values. This ensures that any overlapping intervals will be adjacent, simplifying the merging process.
Initialize an empty result list. For each interval in the sorted list, if the result list is empty or the current interval does not overlap with the last interval in the result, append it. Otherwise, merge by updating the end of the last interval to the maximum of its end and the current interval's end.
After processing all intervals, return the result list, which contains non-overlapping intervals sorted by start time.
State that time complexity is O(n log n) due to sorting, and space complexity is O(n) for the output. Walk through a few test cases to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the problem and edge cases, then propose a brute-force O(n^2) solution as a baseline. Follow up with an optimized O(n) approach using a monotonic stack to find the largest rectangle in linear time, explaining the intuition and handling edge cases.
Pro tip: Emphasize that the stack stores indices of bars in increasing height order, and that you can avoid sentinel values by handling the final flush carefully—this shows attention to code robustness and edge cases.
Confirm the problem: given an array of bar heights, find the maximum rectangular area formed by consecutive bars. Discuss edge cases like empty array, single bar, and all equal heights.
Describe the O(n^2) approach: for each bar, expand left and right until a shorter bar is found, computing area. This sets a baseline and shows you can think simply first.
Introduce the monotonic stack: iterate through bars, maintain a stack of indices with increasing heights. When a shorter bar is encountered, pop and calculate area with the popped bar as the smallest height.
After iteration, pop remaining bars in the stack, treating the right boundary as the end of the array. Compute areas similarly.
State time and space complexity: O(n) time, O(n) space. Discuss edge cases like empty input, single bar, and decreasing/increasing heights.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.