Identifying the maximum overlap pattern
Some specific problems can be solved using the technique to find maximum overlapping intervals. These are generally easy or medium problems where we are given an array of intervals, and finding the maximum overlap partially or entirely solves the problem. If the problem statement or its solution follows the generic template below, it can be solved by applying the fixed-sized sliding window technique.
Example
Let's consider the following problem as an example to understand better how to identify and solve a problem that requires finding the maximum overlapping intervals.
Problem statement: Given an array of start and end times of a meeting, find the minimum number of meeting rooms needed.
Find the minimum number of meeting rooms needed for the given meeting times.
Maximum overlapping intervals
If no meetings overlap, the minimum number of meeting rooms needed would be one. For all other cases, the minimum number of meeting rooms needed is the maximum number of overlapping meetings. The problem solution fits the template for the maximum overlapping interval pattern.
Given an array of intervals (meeting times), find the maximum overlap
We can use the line sweep technique to find the maximum overlap between the meeting times and return it as the minimum number of meeting rooms needed. We create two variables rooms and minRooms to keep track of the number of meeting rooms required at any point and the maximum number needed at any point so far. The maximum number of meeting rooms needed at any point is the minimum number of meeting rooms we need for the given set of meetings, and hence the name minRooms.
Use the line sweep technique to find the maximum overlapping meetings in the meeting times array.
The implementation of the maximum overlapping interval solution is given as follows.
C++
Java
Typescript
Javascript
Python
As the code above demonstrates, using the line sweep technique to find the maximum overlap between meetings allows us to solve the problem in a single pass.
Example problems
Most problems that fall under this category are easy or medium problems; a list of a few is given below.
We will now solve these problems to understand the maximum overlap pattern better.