I knew this problem but still fumbled the explanation for the heap approach.
Clarify the problem constraints (e.g., intervals are half-open, input format) and then explain the sweep line algorithm: separate start and end times, sort them, and use a two-pointer technique to count the maximum number of concurrent meetings. Alternatively, mention the min-heap approach for a more intuitive solution, and analyze time/space complexity.
Pro tip: After presenting the optimal solution, briefly discuss trade-offs with the brute-force approach and how you would handle edge cases like empty input or back-to-back meetings. This shows you think about real-world robustness and scalability.
Ask about interval inclusivity (e.g., [start, end) vs [start, end]), input format, and whether meetings can be scheduled back-to-back without needing a new room.
Mention that a naive O(n^2) approach of comparing all pairs is inefficient for large inputs, setting the stage for a better solution.
Explain how to separate start and end times, sort them, and use two pointers to track the number of active meetings, updating the maximum.
State that the sweep line runs in O(n log n) time and O(n) space. Optionally, mention the min-heap approach which also achieves O(n log n) and is easier to reason about.
Discuss empty input, single meeting, and all overlapping meetings. Summarize why the chosen approach is optimal and scalable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.