Minimum Number of Rooms to Host All Meetings

Meetings are held in a set of identical rooms. Each meeting needs one room for its whole duration, and a room can host only one meeting at a time. Return the minimum number of rooms needed to host every meeting. ### Function Signature ```python def min_meeting_rooms(meetings: list[list[int]]) -> int: ``` ### Rules - `meetings[i] = [start, end]` occupies a room for the half-open interval `[start, end)`: the meeting is in progress at every time `t` with `start <= t < end`. - A room freed at time `t` can host another meeting that starts at time `t`. - Identical meetings listed twice are separate meetings, and each needs its own room. - Return `0` when there are no meetings. ### Constraints - `0 <= len(meetings) <= 10^5` - `0 <= start < end <= 10^9` for every meeting - Times are integers, so every value fits in a 32-bit signed integer. - `meetings` is in no particular order. ### Examples **Example 1** ```text Input: meetings = [[0, 6], [2, 4], [3, 8], [7, 9]] Output: 3 ``` At time `3`, the meetings `[0, 6)`, `[2, 4)` and `[3, 8)` are all in progress, so at least three rooms are needed. Three are enough: one room hosts `[0, 6)` and then `[7, 9)`, and the other two host `[2, 4)` and `[3, 8)`. **Example 2** ```text Input: meetings = [[1, 5], [5, 8], [8, 10]] Output: 1 ``` Each meeting starts exactly when the previous one ends, so one room hosts all three in turn. **Example 3** ```text Input: meetings = [[4, 9], [4, 9], [1, 3]] Output: 2 ``` The two copies of `[4, 9)` need separate rooms. The meeting `[1, 3)` ends before either starts, so it can use one of those two rooms.