My first instinct was to sort and simulate, which works but I fumbled explaining why a min-heap on end times is the cleaner approach.
Clarify the problem and edge cases, then propose an efficient algorithm such as sorting start and end times separately and using a two-pointer sweep to count concurrent meetings. Discuss time and space complexity, and consider alternative approaches like a min-heap to demonstrate depth.
Pro tip: Mention that the problem is equivalent to finding the maximum number of overlapping intervals, and that the sweep-line approach can be extended to handle other interval problems. Also, proactively discuss how you would handle edge cases like empty input or invalid intervals.
Ask questions to confirm input format, whether intervals are inclusive/exclusive, and if meetings can be split. Confirm that we need the minimum number of rooms to accommodate all meetings without overlap.
Start with a brute force approach (e.g., check all possible room assignments) to establish a baseline, then explain why it's inefficient and propose a better approach.
Describe the sweep-line algorithm: sort start and end times separately, use two pointers to count concurrent meetings, and track the maximum. Alternatively, use a min-heap to track end times of ongoing meetings.
State the time complexity (O(n log n) due to sorting) and space complexity (O(n) for the sorted arrays or heap). Compare with other approaches if applicable.
Walk through a simple example (e.g., [[0,30],[5,10],[15,20]]) to verify the algorithm and handle edge cases like empty input or single meeting.
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