Interval Scheduling Maximization
Select the maximum number of non-overlapping intervals from a collection. This is identical to the Activity Selection problem and demonstrates the greedy choice property: always selecting the interval that finishes earliest leaves the maximum room for remaining intervals. Used in resource allocation, meeting scheduling, and event planning. Optimal solution in O(n log n) time.
Visualization
Interactive visualization for Interval Scheduling Maximization
Interval Scheduling:
- • Greedy: sort by end time
- • Select non-overlapping intervals
Interactive visualization with step-by-step execution
Implementation
1function maxIntervals(intervals: [number, number][]): number {
2 intervals.sort((a, b) => a[1] - b[1]);
3 let count = 1;
4 let lastEnd = intervals[0][1];
5
6 for (let i = 1; i < intervals.length; i++) {
7 if (intervals[i][0] >= lastEnd) {
8 count++;
9 lastEnd = intervals[i][1];
10 }
11 }
12 return count;
13}Deep Dive
Theoretical Foundation
Interval Scheduling Maximization is solved optimally with the greedy algorithm: sort intervals by ending time (ascending), then greedily select intervals that don't overlap with the previously selected one. Why optimal? Exchange argument: suppose optimal solution doesn't include earliest-finishing interval. Replace first interval in optimal with earliest-finishing; this doesn't cause conflicts (finishes earlier or same), proving greedy choice is safe. Time: O(n log n) for sorting + O(n) for selection = O(n log n).
Complexity
Time
O(n log n)
O(n log n)
O(n log n)
Space
O(1)
Applications
Industry Use
Conference room scheduling (maximize meetings)
CPU task scheduling
Event planning (maximize events attended)
Manufacturing job scheduling
TV program scheduling
Resource allocation
Use Cases
Related Algorithms
Huffman Coding
Huffman Coding is a lossless data compression algorithm that creates optimal prefix-free variable-length codes based on character frequencies. Developed by David A. Huffman in 1952 as a student at MIT, it uses a greedy approach to build a binary tree where frequent characters get shorter codes. This algorithm is fundamental in ZIP, JPEG, MP3, and many compression formats.
Activity Selection Problem
Select the maximum number of non-overlapping activities from a set, where each activity has a start and end time. This classic greedy algorithm demonstrates the greedy choice property: always selecting the activity that finishes earliest leaves the most room for remaining activities. Used in scheduling problems, resource allocation, and interval management. Achieves optimal solution with O(n log n) time complexity.
Fractional Knapsack Problem
Given items with values and weights, and a knapsack with capacity, select items (or fractions thereof) to maximize total value. Unlike the 0/1 knapsack where items must be taken whole, the fractional knapsack allows taking fractions of items. The greedy approach of taking items in order of value-to-weight ratio yields the optimal solution in O(n log n) time. This demonstrates when greedy algorithms work vs. when dynamic programming is needed.
Job Sequencing with Deadlines
Schedule jobs with deadlines and profits to maximize total profit. Each job takes 1 unit time and has a deadline and profit. The greedy strategy is to sort jobs by profit (descending) and greedily schedule each job as late as possible before its deadline. This maximizes profit while respecting constraints. Used in task scheduling, CPU job management, and project planning.