Minimum number of rooms needed to hold overlapping meetings

You are given a list of meetings, each with a start time and an end time. A room can host at most one meeting at a time, and a meeting stays in the same room from its start to its end. Return the minimum number of rooms needed so that every meeting can be held in full.

Function Signature

def min_meeting_rooms(intervals: list[list[int]]) -> int:

intervals[i] = [start, end] describes meeting i, which occupies the half-open time interval [start, end).

Rules

• Two meetings conflict when their intervals overlap. A meeting that ends at time t does not conflict with a meeting that starts at time t, so the two can use the same room.
• The meetings are given in no particular order.
• Return 0 when the list is empty.

Constraints

• 0 <= len(intervals) <= 10^5
• 0 <= start < end <= 10^9 for every meeting

Examples

Example 1

Input: intervals = [[1, 5], [2, 6], [4, 8], [7, 9]]
Output: 3

Between times 4 and 5, the meetings [1, 5), [2, 6) and [4, 8) are all in progress, so three rooms are needed. Three is enough: by time 7 the meeting [2, 6) has ended, so [7, 9) can use its room.

Example 2

Input: intervals = [[1, 3], [3, 5], [5, 7]]
Output: 1

Each meeting starts exactly when the previous one ends, so one room hosts all three.

Example 3

Input: intervals = [[10, 20], [0, 10], [5, 15]]
Output: 2

[5, 15) overlaps both other meetings, but [0, 10) and [10, 20) do not overlap each other and can share a room.