Clarify the problem constraints 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 compare with alternative approaches like min-heap or sweep line with events.
Pro tip: Mention that the problem is equivalent to finding the maximum number of overlapping intervals, and that sorting start and end times separately avoids the overhead of a heap. Also, proactively discuss how to handle edge cases like empty input or zero-length meetings.
Ask about input size, whether intervals are inclusive/exclusive, and if meetings can be back-to-back. Confirm expected output and any constraints on time/space.
Briefly mention a naive O(n^2) solution that checks each meeting against all others to establish a baseline, then explain why it's inefficient.
Describe the two-pointer sweep: sort start and end times separately, then iterate through starts, incrementing room count when a start is before the next end, else decrement. Alternatively, use a min-heap of end times.
State that sorting takes O(n log n) time and O(n) space, and compare with heap approach which also is O(n log n) but may have higher constant factors. Discuss when one might be preferred.
Walk through a simple example like [[0,30],[5,10],[15,20]] to show the algorithm yields 2 rooms. Mention edge cases: empty array, single meeting, all overlapping, no overlaps.
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