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56. Merge Intervals

mediumAsked at Atlassian

Merge Intervals is an Atlassian-favorite scheduling problem. Given an array of intervals [start, end], merge all overlapping ones and return the result. It maps directly to calendar coalescing in Atlassian's Confluence calendars and Jira time-tracking UIs.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Source citations

Public interview reports confirming this problem appears in Atlassian loops.

  • Glassdoor (2026-Q1)— Atlassian SWE-II onsite reports cite Merge Intervals as a recurring scheduling/calendar problem.
  • Blind (2025-10)— Atlassian Senior-engineer threads mention Merge Intervals as the warm-up before Meeting Rooms II.

Problem

Given an array of intervals where intervals[i] = [start_i, end_i], merge all overlapping intervals, and return an array of the non-overlapping intervals that cover all the intervals in the input.

Constraints

  • 1 <= intervals.length <= 10^4
  • intervals[i].length == 2
  • 0 <= start_i <= end_i <= 10^4

Examples

Example 1

Input
intervals = [[1,3],[2,6],[8,10],[15,18]]
Output
[[1,6],[8,10],[15,18]]

Explanation: [1,3] and [2,6] overlap so they merge into [1,6].

Example 2

Input
intervals = [[1,4],[4,5]]
Output
[[1,5]]

Explanation: Touching intervals are considered overlapping.

Approaches

1. Brute O(n^2) pairwise merge

Repeatedly scan all pairs; merge any overlapping pair into one; restart until no more merges happen.

Time
O(n^2)
Space
O(n)
function mergeBrute(intervals) {
  let result = intervals.slice();
  let changed = true;
  while (changed) {
    changed = false;
    outer: for (let i = 0; i < result.length; i++) {
      for (let j = i + 1; j < result.length; j++) {
        const [a, b] = result[i];
        const [c, d] = result[j];
        if (a <= d && c <= b) {
          result[i] = [Math.min(a, c), Math.max(b, d)];
          result.splice(j, 1);
          changed = true;
          continue outer;
        }
      }
    }
  }
  return result;
}

Tradeoff: Easy to explain in 30 seconds but obviously slow. Useful only to motivate the sort-first insight. Mention it, then immediately move to the sorted version.

2. Sort by start, single-pass merge (optimal)

Sort by start. Walk left-to-right; if the current interval's start <= the previous interval's end, extend the previous end; otherwise push the current interval as a new group.

Time
O(n log n)
Space
O(n) for the output
function merge(intervals) {
  if (intervals.length === 0) return [];
  intervals.sort((a, b) => a[0] - b[0]);
  const result = [intervals[0].slice()];
  for (let i = 1; i < intervals.length; i++) {
    const last = result[result.length - 1];
    const [start, end] = intervals[i];
    if (start <= last[1]) {
      last[1] = Math.max(last[1], end);
    } else {
      result.push([start, end]);
    }
  }
  return result;
}

Tradeoff: n log n from the sort dominates the linear scan. Mutates the result's last entry in place for clarity; you could push immutable copies but it costs an extra allocation per merge. Atlassian's preferred shape.

Atlassian-specific tips

Atlassian interviewers consistently ask 'what's the convention if two intervals touch at a point — say [1,4] and [4,5]?'. LeetCode treats them as overlapping. State the convention out loud before coding; failing to confirm this is the #1 lost-point on Atlassian's interview rubric for this question. After you finish, expect the follow-up 'now insert a new interval into an already-merged set' (LeetCode 57).

Common mistakes

  • Sorting by end instead of start — silently breaks merging on inputs like [[1,5],[2,3],[4,6]].
  • Mutating the input intervals[i] in place when copying into the result — the next test case sees corrupted state if the judge runs them in sequence.
  • Off-by-one on the touching-endpoint test — using < instead of <= drops [[1,4],[4,5]] into two intervals instead of [[1,5]].

Follow-up questions

An interviewer at Atlassian may pivot to one of these next:

  • Insert Interval (LeetCode 57) — given an already-sorted, already-merged list, insert a new interval in O(n).
  • Meeting Rooms II (LeetCode 253) — how many rooms (concurrent overlaps) do you need? Heap of end-times, or sweep-line.
  • Interval Intersection (LeetCode 986) — given two sorted lists, return their intersection.

Solve it now

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Output

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FAQ

Do I need to sort or can I use a different structure?

You need sorted order. You could use a self-balancing BST keyed on start for O(log n) inserts if the input were streaming, but for the static problem nothing beats sort + single-pass.

Why does Atlassian like this problem?

Because it's the same algorithm as 'collapse overlapping calendar events into a single block' which is what Confluence calendars and Jira time-logging UIs do internally. Interviewers will explicitly probe whether you see the connection.

Free learning resources

Curated free links for this problem.

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