The two-heap setup is the move here: one min-heap tracking free rooms by index, another tracking busy rooms by end time.
Clarify that meetings are given as intervals and that we need to simulate assigning each meeting to the lowest-index available room, then count meetings per room. Use a min-heap to track room availability by end time, and a separate min-heap for free room indices to always pick the smallest index. After processing all meetings, return the room with the maximum count (tie-break by smallest index).
Pro tip: Mention that the problem is essentially a greedy interval scheduling with resource allocation, and that using two heaps (one for busy rooms by end time, one for free room indices) yields an O(n log n) solution. Also note that if meetings are not sorted by start time, sort them first; if they are, skip sorting.
Confirm that meetings are given as [start, end] intervals, rooms are indexed 0 to k-1, and that meetings are non-overlapping in time? Actually, they may overlap. Ask if meetings are sorted by start time. Clarify tie-breaking: smallest room index when multiple free.
Use a min-heap for free room indices (initialized with all rooms) and a min-heap for busy rooms keyed by end time. Also maintain an array to count meetings per room.
Sort meetings by start time if needed. For each meeting, release all busy rooms whose end time <= current start time (move them to free heap). Then assign the meeting to the smallest free room index, increment its count, and push the room into the busy heap with its end time.
After processing all meetings, scan the count array to find the room with the maximum count. If there's a tie, return the smallest index.
State time complexity O(n log n) due to sorting and heap operations, space O(n + k). Discuss edge cases: no meetings, more rooms than meetings, all meetings at same time, etc.
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