Merge Intervals — Calendars, Meetings & Ranges

Meetings, bookings, IP ranges, price windows — interval problems are everywhere in real systems, and they all start with the same two moves.

Move 1: know the overlap test

// [a1, a2] and [b1, b2] overlap when:
a1 <= b2 && b1 <= a2
// each starts before the other ends. Draw it once; remember it forever.

Move 2: sort by start, then sweep

function mergeIntervals(intervals) {
  intervals.sort((a, b) => a[0] - b[0]);       // sort by start
  const out = [intervals[0]];

  for (let i = 1; i < intervals.length; i++) {
    const last = out[out.length - 1];
    const cur  = intervals[i];
    if (cur[0] <= last[1]) {
      last[1] = Math.max(last[1], cur[1]);     // overlap → extend
    } else {
      out.push(cur);                            // gap → start new interval
    }
  }
  return out;
}
// [[1,3],[2,6],[8,10]] → [[1,6],[8,10]]

After sorting, you only ever compare with the last merged interval — earlier ones can't overlap anything new. That insight is the whole pattern.

The famous variants

• Insert interval — add one interval into a sorted list, merging as needed.
• Meeting rooms I — "can one person attend all meetings?" = does anything overlap after sorting?
• Meeting rooms II — "minimum rooms needed" = max simultaneous overlaps (sort starts and ends separately, sweep with a counter).

Spot it when…

• Input is pairs of [start, end]. That's it — the word "interval", "meeting", "range", or "booking" is the giveaway.

Complexity: O(n log n) from the sort; the sweep is O(n). Interviewers expect you to say the sort dominates. Next: Binary Search as a pattern — more than finding values.