Got the two-heap approach out pretty quickly, free rooms as a min-heap on index, occupied rooms as a min-heap on (end_time, room_index).
Clarify the exact room assignment rules (delay handling, smallest available index, reuse priority) and edge cases before designing. Then, propose an efficient algorithm using a min-heap for room availability and a counter for meetings per room, discussing time/space complexity and trade-offs.
Pro tip: Explicitly state your assumptions about the rules and confirm them with the interviewer; this shows attention to detail and avoids solving the wrong problem. Also, mention that you would test with edge cases like simultaneous meetings and zero meetings.
Ask questions to pin down the exact assignment rules: how delays are handled, what 'smallest available room index' means, and the reuse priority. Also confirm input format, interval inclusivity, and constraints (e.g., n, number of meetings).
Choose a min-heap to track available room indices and another min-heap (or sorted structure) to track ongoing meetings by end time. Use an array to count meetings per room.
Process meetings in chronological order. For each meeting, free rooms whose meetings have ended, apply delay rules if any, assign the smallest available room, and update counters.
After processing all meetings, find the room with the maximum count, breaking ties by smaller index. State time complexity O(m log n) and space O(n + m).
Walk through edge cases (no meetings, all simultaneous, delays causing no available room). Discuss alternative approaches (e.g., sweep line) and trade-offs between simplicity and efficiency.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.