Compute the Minimum Number of Meeting Rooms

Problem Statement

Given an array of meeting time intervals intervals where each interval is represented as [start, end], return the minimum number of conference rooms required to hold all meetings.

Intervals are half-open [start, end). This means that a meeting ending at time T and another meeting starting at time T do not overlap, and both can use the same room without conflict.

Your solution should not mutate the input array.

Function Signature

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

Input and Output Format

• Input: A list of lists of integers, where each inner list contains two integers [start, end] representing the start time and end time of a meeting.
• Output: An integer representing the minimum number of meeting rooms needed.

Constraints

• 0 <= len(intervals) <= 10^5
• intervals[i].length == 2
• 0 <= start < end <= 10^9

Examples

Example 1

Input: intervals = [[0, 30], [5, 10], [15, 20]]
Output: 2
Explanation: 
- Room 1 hosts: [0, 30]
- Room 2 hosts: [5, 10] and then [15, 20]
At most 2 meetings run concurrently.

Example 2

Input: intervals = [[7, 10], [2, 4]]
Output: 1
Explanation: 
Since neither interval overlaps, a single room is sufficient.

Example 3

Input: intervals = [[1, 5], [5, 10]]
Output: 1
Explanation: 
The first meeting ends at time 5, and the second meeting begins at time 5. Because intervals are half-open, they do not overlap.

Edge Cases to Consider

• Empty input: intervals = [] should return 0.
• Adjacent meetings sharing boundaries: e.g., [1, 3] and [3, 5] require only 1 room.
• Completely nested intervals: e.g., [1, 10] and [2, 5] require 2 rooms.
• Identical intervals: multiple meetings with identical start and end times must each receive their own room.