Find Right Interval

Find Right Interval - Problem

You are given an array of intervals, where intervals[i] = [start_i, end_i] and each start_i is unique.

The right interval for an interval i is an interval j such that start_j >= end_i and start_j is minimized.

Note that i may equal j.

Return an array of right interval indices for each interval i. If no right interval exists for interval i, then put -1 at index i.

Input & Output

Example 1 — Basic Case

$ Input: intervals = [[1,2]]

› Output: [-1]

💡 Note: There is only one interval, no right interval exists for [1,2], so return -1

Example 2 — Multiple Intervals

$ Input: intervals = [[3,4],[2,3],[1,2]]

› Output: [-1,0,1]

💡 Note: For [3,4]: no interval starts >= 4, return -1. For [2,3]: [3,4] starts at 3 >= 3, return index 0. For [1,2]: [2,3] starts at 2 >= 2, return index 1

Example 3 — Self Reference

$ Input: intervals = [[1,4],[2,3],[3,4]]

› Output: [-1,2,-1]

💡 Note: For [1,4]: no start >= 4, return -1. For [2,3]: [3,4] starts at 3 >= 3, return index 2. For [3,4]: no start >= 4, return -1

Constraints

1 ≤ intervals.length ≤ 2 × 10⁴
intervals[i].length == 2
-10⁶ ≤ start_i ≤ end_i ≤ 10⁶
The start point of each interval is unique.

Visualization

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Asked in

G Google 15 f Facebook 12 a Amazon 8

The key insight is to sort intervals by start time to enable binary search. The brute force approach checks all intervals for each query in O(n²) time. The optimal approach sorts start times with indices, then uses binary search to find the smallest valid start time in O(log n) per query. Overall time: O(n log n), space: O(n).

Common Approaches

✓ One Pass Hash

⏱️ Time: N/A Space: N/A

Brute Force

⏱️ Time: O(n²) Space: O(1)

For each interval, iterate through all intervals to find the one with the smallest start time that is >= current interval's end time.

Sort + Binary Search

⏱️ Time: O(n log n) Space: O(n)

Create a sorted array of start times with their original indices, then for each interval use binary search to find the smallest start time >= end time.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

⚡ Linearithmic

Space Complexity

⚡ Linearithmic Space

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Smart Actions

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