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19. Merge Intervals

mediumAsked at SoFi

Merge all overlapping intervals — SoFi uses this constantly because loan-statement billing periods and recurring transaction windows are interval problems in disguise.

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

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

Example 2

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

Approaches

1. Brute force

Repeatedly scan pairs for overlap and merge until no more merges possible.

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

Tradeoff:

2. Sort + sweep

Sort by start, then walk through and merge into the last result if current.start <= last.end, else push as new interval.

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

Tradeoff:

SoFi-specific tips

SoFi engineers see this pattern weekly — interest-accrual periods, autopay schedules, and statement closing dates all merge as intervals, so candidates who immediately reach for sort+sweep score well.

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