Merge Overlapping Intervals

You have a list of time blocks — think busy slots on a calendar, each a [start, end] pair. Some of them overlap or butt up against each other, and you want one clean view: the consolidated stretches of busy time, with no two blocks touching. Implement intervalsCombineOverlapping(intervals), which takes a list of intervals in any order and returns a new list of merged, non-overlapping intervals sorted by start.

Signature

// intervals: Array<[number, number]>
//   A list of [start, end] pairs. CLOSED intervals: each one includes both
//   endpoints, so [1, 3] covers 1, 3, and everything between. The list may be
//   in any order; start <= end for every pair.
// returns: Array<[number, number]>
//   A NEW array of merged, non-overlapping intervals, sorted by start.
//   Two intervals merge if they overlap OR merely touch at an endpoint:
//   [1, 3] and [3, 5] become [1, 5].
function intervalsCombineOverlapping(intervals): Array<[number, number]>;

Examples

// An overlapping set collapses; the gap-separated blocks stay apart.
intervalsCombineOverlapping([
  [1, 3],
  [2, 6],
  [8, 10],
  [15, 18],
]);
// → [[1, 6], [8, 10], [15, 18]]
//   [1, 3] and [2, 6] overlap → [1, 6]; the other two have gaps, so they stay.

// Touching at an endpoint counts as overlapping (closed intervals).
intervalsCombineOverlapping([
  [1, 3],
  [3, 5],
]);
// → [[1, 5]]
//   They share the point 3, so they merge into one block.

// Unsorted input with a chain only reachable after sorting.
intervalsCombineOverlapping([
  [1, 4],
  [5, 6],
  [2, 5],
]);
// → [[1, 6]]
//   Sorted, this is [1,4],[2,5],[5,6]: [1,4]+[2,5]=[1,5], then +[5,6]=[1,6].

Notes

• Closed intervals. Each interval includes both endpoints. [1, 3] covers everything from 1 to 3 inclusive.
• Touching merges. Intervals that share only an endpoint — [1, 3] and [3, 5] — merge into [1, 5]. A one-unit gap like [1, 2] and [3, 4] does not merge; 2 and 3 are distinct points.
• Output is sorted by start and contains no two overlapping or touching intervals.
• Input order is arbitrary. You cannot assume the intervals arrive sorted; a correct solution sorts them itself.
• Do not mutate the input. Neither the outer array nor any inner [start, end] pair should change — return fresh arrays.
• Don't worry about open/half-open intervals, intervals where start > end, or non-numeric coordinates — those are out of scope.