Find Minimum Rooms Needed

Problem Statement

You are given an array of meeting time intervals intervals where each interval is represented as a pair of integers [start, end]. Each pair signifies that a meeting begins at start and finishes at end (start < end).

A single room can host at most one meeting at any given time. If a meeting ends at time T, another meeting can begin in the same room at time T without conflict.

Write a function that calculates the minimum number of conference rooms required to schedule all meetings without overlap.

Interface

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

Examples

Example 1

Input:

intervals = [[0, 30], [5, 10], [15, 20]]

Output:

2

Explanation:

• Room 1 hosts [0, 30].
• Meeting [5, 10] conflicts with [0, 30], so it needs Room 2.
• Meeting [15, 20] starts after [5, 10] ends at time 10, so it can reuse Room 2. Total rooms needed: 2.

Example 2

Input:

intervals = [[7, 10], [2, 4]]

Output:

1

Explanation: The meetings do not overlap in time, so a single room can host both.

Constraints

• 1 <= len(intervals) <= 10^5
• intervals[i].length == 2
• 0 <= intervals[i][0] < intervals[i][1] <= 10^9

Edge Cases to Consider

• Consecutive meetings that share a boundary (e.g., [1, 5] and [5, 10]) do not require separate rooms.
• Completely nested intervals (e.g., [1, 10] and [2, 5]).
• Multiple intervals starting or ending at identical times.