The Merge Intervals problem merges all overlapping intervals from a given collection and returns an array of the non-overlapping intervals.

Sort intervals by start times ascending. Maintain a list of merged intervals; if the current interval overlaps with the last merged one, merge them by extending the end boundary.

Sorting by start times ensures that once we process interval i and it does not overlap with the current merged range, no subsequent interval can overlap with it either.

Proof by induction: since intervals are sorted by start time, interval i has start >= previous start. If start > last_end, all subsequent intervals also have start > last_end, guaranteeing separation.