Largest Overlap of Intervals

The problem asks you to find the maximum number of overlapping time intervals within a given set. This tests your ability to efficiently manage and analyze intervals, a common pattern in scheduling and resource allocation problems.

intervalssortingsweeping linealgorithmoverlap

Problem Statement

You are given a list of time intervals, where each interval is represented as a pair of integers [start, end). The interval includes the start time but excludes the end time. Your task is to determine the maximum number of intervals that overlap at any single point in time.

Example 1

Input: [[0, 5), [1, 3), [2, 4)]

Output: 3

The intervals [0, 5), [1, 3), and [2, 4) all overlap between times 2 and 3, resulting in a maximum overlap of 3.

Example 2

Input: [[1, 4), [5, 8), [2, 6), [9, 12]]

Output: 2

The intervals [1, 4) and [2, 6) overlap between times 2 and 4, resulting in a maximum overlap of 2. No other point in time has more than 2 overlapping intervals.

Constraints

-The input list will contain at least one interval.
-For each interval [start, end), start will always be less than end.
-Interval start and end times will be non-negative integers.
-The input list will not be empty.
-Intervals may be unsorted.

Brute Force Approach

The brute force approach involves checking every possible time point within the entire range of intervals to see how many intervals overlap at that point. Imagine you're a security guard checking a hallway every minute. For each minute, you'd walk down the hallway and count how many people are currently in rooms that include that minute. The highest number you ever see is the maximum overlap. This approach is inefficient because it requires checking every possible time point.

TimeO(n*m)

SpaceO(1)

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