Minimum Meeting Rooms Required with Capacity Constraints

You are organizing a conference and have a list of meetings to schedule. Each meeting is specified by its start and end time, represented as an interval [start_i, end_i] where start_i < end_i. All rooms are identical and can accommodate any number of attendees up to a given max_capacity, but you must reserve an entire room for each meeting; a room cannot host two meetings at the same time regardless of attendance. Calculate the fewest number of rooms needed so that no two…