Meeting Rooms II

Meeting Rooms II

What is this problem about?

The "Meeting Rooms II" interview question asks you to determine the minimum number of conference rooms required to schedule a given set of meetings. Each meeting is represented by an interval with a start and end time. Unlike "Meeting Rooms I," which only checks for conflicts for a single person, this problem requires you to find the maximum number of meetings that are occurring simultaneously at any point in time. This is a classic problem in interval scheduling and resource allocation, testing your ability to manage overlapping events and efficiently track resource usage.

Why is this asked in interviews?

This "Meeting Rooms II" coding problem is a popular choice in technical interviews at companies like Apple, Google, and Amazon due to its ability to assess a candidate's understanding of greedy algorithms, sorting, and heap (priority queue) data structures. It's a step up from basic interval problems, requiring more sophisticated management of active intervals. Interviewers use this problem to evaluate structured thinking, efficiency in handling dynamic sets of data, and the ability to apply appropriate data structures to optimize solutions. Success demonstrates strong algorithmic intuition and practical problem-solving skills.

Algorithmic pattern used

The most efficient algorithmic pattern for the "Meeting Rooms II" interview question involves Sorting and a Min-Heap (Priority Queue).

1. Sort meetings: First, sort all meetings by their start times.
2. Process meetings with a Min-Heap: Initialize a min-heap to store the end times of the meetings currently occupying rooms. The size of the heap at any point represents the number of rooms currently in use.
3. Iterate and manage rooms: For each meeting (in sorted order):
   • If the heap is not empty and the current meeting's start time is greater than or equal to the smallest end time in the heap (i.e., heap.peek() <= current_meeting.start), it means a room has become free. Remove that end time from the heap (heap.poll()).
   • Add the current meeting's end time to the heap (heap.add(current_meeting.end)).
4. The maximum size of the heap observed during this process is the minimum number of rooms required.

Example explanation

Consider meetings: [[0, 30], [5, 10], [15, 20]].

1. Sort by start times: meetings = [[0, 30], [5, 10], [15, 20]] (already sorted)

2. Initialize min_heap = [], max_rooms = 0

3. Process meetings:

   • Meeting [0, 30]:

     • Heap is empty.
     • Add 30 (end time) to min_heap. min_heap = [30].
     • max_rooms = max(0, len(min_heap)) = max(0, 1) = 1.

   • Meeting [5, 10]:

     • min_heap.peek() is 30. Current start time is 5.
     • 5 < 30, so no room is free yet.
     • Add 10 (end time) to min_heap. min_heap = [10, 30] (heap property maintained).
     • max_rooms = max(1, len(min_heap)) = max(1, 2) = 2.

   • Meeting [15, 20]:

     • min_heap.peek() is 10. Current start time is 15.
     • 15 >= 10, so a room (the one ending at 10) is free. Remove 10 from min_heap. min_heap = [30].
     • Add 20 (end time) to min_heap. min_heap = [20, 30].
     • max_rooms = max(2, len(min_heap)) = max(2, 2) = 2.

Final max_rooms = 2. This is the minimum number of rooms needed.

Common mistakes candidates make

A common mistake in the "Meeting Rooms II" interview question is trying to solve it with a simpler approach that doesn't account for all overlaps, such as comparing every interval with every other interval, which is O(N^2) and inefficient. Another error is incorrectly implementing the logic with the min-heap, for instance, forgetting to remove old end times or not realizing that the heap should store end times only. Some candidates might struggle with sorting by start times and then incorrectly sorting by end times as a secondary condition, which is not needed for the heap-based approach.

Interview preparation tip

To excel at the Meeting Rooms II coding problem, make sure you have a strong grasp of Greedy Algorithms and the Min-Heap (Priority Queue) data structure. Practice using heapq in Python or PriorityQueue in Java. Work through multiple examples by hand, tracing the state of the sorted intervals and the min-heap. Pay attention to how the heap's size reflects the current number of occupied rooms. Understand why sorting by start time is essential and why comparing the current meeting's start with the heap's minimum end time is the correct greedy choice. Also, consider the "sweep line" approach as an alternative.