Meeting Rooms II
Given an array of meeting time intervals [start, end], find the minimum number of conference rooms required.
Input format: intervals as start,end pairs separated by semicolons.
Example:
0,30;5,10;15,20
2
- The input intervals are first parsed into individual meeting times: (0,30), (5,10), (15,20)
- We then determine the overlap of these intervals to find the maximum number of meetings happening at the same time: (0,30) overlaps with (5,10) and (15,20), while (5,10) and (15,20) also overlap with each other
- The maximum overlap occurs at time 15, when meetings (0,30), (5,10), and (15,20) are all happening, but (5,10) ends before (15,20) ends, and only (0,30) and (15,20) are happening at time 20, thus the maximum number of rooms required is 2, when (0,30) and (5,10) are happening at time 5, and also at time 15 when (0,30) and (15,20) are happening, and (5,10) has already started
- The final output is the minimum number of conference rooms required, which is 2​
Constraints:
- 1 <= len(intervals) <= 10^4
- 0 <= start < end <= 10^6
Background Knowledge
The "Meeting Rooms II" problem is a classic example of a scheduling problem, which involves allocating resources (in this case, conference rooms) to a set of tasks (meetings) with specific time constraints. To solve this problem, you need to understand the concept of interval scheduling, where each meeting is represented by a start and end time. The goal is to find the minimum number of rooms required to accommodate all meetings without any conflicts.
The key concept here is overlapping intervals. When two meetings overlap, they cannot be assigned to the same room. To determine if two intervals overlap, you can use a simple comparison: if the start time of one meeting is less than the end time of another meeting, they overlap. This concept is crucial in solving the problem, as you need to identify the maximum number of overlapping intervals to determine the minimum number of rooms required.
In terms of data structures, you can use a priority queue or a sorted array to keep track of the end times of the meetings. This allows you to efficiently find the meeting that ends earliest and assign a new meeting to the same room if possible. Understanding how to use these data structures to manage the meetings and rooms is essential to solving the problem.
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