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Merge Overlapping Intervals | J.P. Morgan Coding Question

Quick Overview

This question tests practical array manipulation and sorting skills by requiring candidates to consolidate overlapping numeric intervals into a minimal set. It evaluates algorithmic reasoning around interval overlap conditions and is a staple coding problem used to assess proficiency with greedy techniques and sorted data processing.

Merge Overlapping Intervals

Company: J.P. Morgan

Role: Software Engineer

Category: Coding & Algorithms

Difficulty: medium

Interview Round: Technical Screen

## Merge Overlapping Intervals You are given an array `intervals` where each element `intervals[i] = [start_i, end_i]` represents a closed interval on the number line. Merge all intervals that **overlap** (including those that merely touch at an endpoint) and return an array of the resulting non-overlapping intervals that together cover exactly the same set of points as the input. Two intervals `[a, b]` and `[c, d]` overlap when `c <= b` (assuming `a <= c`); for example `[1, 4]` and `[4, 5]` overlap and merge into `[1, 5]`. ### Example 1 ``` Input: intervals = [[1, 3], [2, 6], [8, 10], [15, 18]] Output: [[1, 6], [8, 10], [15, 18]] ``` `[1, 3]` and `[2, 6]` overlap and merge into `[1, 6]`. ### Example 2 ``` Input: intervals = [[1, 4], [4, 5]] Output: [[1, 5]] ``` The intervals touch at `4`, so they merge. ### Example 3 ``` Input: intervals = [[1, 4], [0, 4]] Output: [[0, 4]] ``` ### Constraints - `1 <= intervals.length <= 10^4` - `intervals[i].length == 2` - `0 <= start_i <= end_i <= 10^6` - The input is **not** guaranteed to be sorted. ### Required Output Return a list of merged intervals. The output should be sorted in ascending order by start value, and no two returned intervals may overlap.

Quick Answer: This question tests practical array manipulation and sorting skills by requiring candidates to consolidate overlapping numeric intervals into a minimal set. It evaluates algorithmic reasoning around interval overlap conditions and is a staple coding problem used to assess proficiency with greedy techniques and sorted data processing.

You are given an array `intervals` where each element `intervals[i] = [start_i, end_i]` represents a closed interval on the number line. Merge all intervals that **overlap** (including those that merely touch at an endpoint) and return an array of the resulting non-overlapping intervals that together cover exactly the same set of points as the input. Two intervals `[a, b]` and `[c, d]` overlap when `c <= b` (assuming `a <= c`); for example `[1, 4]` and `[4, 5]` overlap and merge into `[1, 5]`. ### Example 1 ``` Input: intervals = [[1, 3], [2, 6], [8, 10], [15, 18]] Output: [[1, 6], [8, 10], [15, 18]] ``` `[1, 3]` and `[2, 6]` overlap and merge into `[1, 6]`. ### Example 2 ``` Input: intervals = [[1, 4], [4, 5]] Output: [[1, 5]] ``` The intervals touch at `4`, so they merge. ### Example 3 ``` Input: intervals = [[1, 4], [0, 4]] Output: [[0, 4]] ``` The output must be sorted in ascending order by start value, and no two returned intervals may overlap. The input is **not** guaranteed to be sorted.

Constraints

1 <= intervals.length <= 10^4
intervals[i].length == 2
0 <= start_i <= end_i <= 10^6
The input is not guaranteed to be sorted.

Examples

Input: [[1, 3], [2, 6], [8, 10], [15, 18]]

Expected Output: [[1, 6], [8, 10], [15, 18]]

Explanation: [1,3] and [2,6] overlap (2 <= 3) and merge into [1,6]; the rest are disjoint.

Input: [[1, 4], [4, 5]]

Expected Output: [[1, 5]]

Explanation: The intervals touch at 4, which counts as overlapping, so they merge into [1,5].

Input: [[1, 4], [0, 4]]

Expected Output: [[0, 4]]

Explanation: After sorting, [0,4] and [1,4] overlap and merge; the result is sorted by start.

Input: [[1, 4], [2, 3]]

Expected Output: [[1, 4]]

Explanation: [2,3] is fully contained in [1,4]; the merged end stays max(4, 3) = 4.

Input: [[5, 6]]

Expected Output: [[5, 6]]

Explanation: A single interval cannot overlap anything and is returned unchanged.

Input: [[1, 2], [3, 4], [5, 6]]

Expected Output: [[1, 2], [3, 4], [5, 6]]

Explanation: All intervals are disjoint (gaps between them), so none merge.

Input: [[6, 8], [1, 9], [2, 4], [4, 7]]

Expected Output: [[1, 9]]

Explanation: Unsorted input. After sorting, [1,9] swallows all the others, leaving a single interval.

Hints

Sort the intervals by their start value first. After sorting, any interval that overlaps a later one must overlap the one immediately before it.
Sweep left to right, keeping the last merged interval. Treat intervals as overlapping when the next start is <= the current end (touching endpoints count as overlapping).
When the next interval overlaps, extend the current interval's end to max(current_end, next_end); otherwise start a new merged interval.

Quick Overview