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Interval Scheduling Maximization - Interval Trees | Data Structures | Repovive

Repovive.

Data Structures19 sections · 729 units49h total

Open in Course

Interval Scheduling Maximization

Select non-overlapping set

Given intervals, select the maximum number of non-overlapping intervals.

Greedy approach: always pick the interval that ends earliest.

function maxNonOverlapping(intervals)
    sort intervals by end time
    count := 0
    lastEnd := -infinity

    for interval in intervals
        if interval.start >= lastEnd then
            count := count + 1
            lastEnd := interval.end

    return count

Why greedy works: picking the earliest-ending interval leaves the most room for future intervals. Any other choice can only do worse.

Time: $O(n \log n)$ . Space: $O(1)$ .