I'd seen this problem before so I wasn't panicking, but I fumbled explaining why a min-heap on end times actually works.
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 maximum overlaps. Walk through a small example to validate the approach, and analyze time and space complexity.
Pro tip: Mention that the minimum number of rooms equals the maximum number of concurrent meetings, and that this can also be solved with a min-heap, but the two-pointer method is more space-efficient. This shows you understand the problem deeply and can compare trade-offs.
Ask about input format, whether intervals are inclusive/exclusive, if the list can be empty, and if intervals are sorted. Confirm that overlapping means any intersection, even at endpoints.
Explain that the minimum rooms needed is the maximum number of overlapping meetings at any point. Propose sorting start and end times separately and using two pointers to count active meetings.
Choose a small set of intervals, e.g., [[0,30],[5,10],[15,20]], and demonstrate how the two-pointer sweep yields the answer 2. This validates the algorithm.
State that sorting takes O(n log n) time and O(n) space for the sorted arrays. Mention that a min-heap approach also works in O(n log n) time but uses O(n) space for the heap, and compare trade-offs.
Discuss empty input, single meeting, and meetings that touch at endpoints (non-overlapping). Summarize that the algorithm is optimal and scalable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.