Maximum White Tiles Covered by a Carpet

Slide the carpet start

Sort intervals by start. For each left interval as a possible carpet start, move right while the carpet ending at tiles[left][0] + carpetLen - 1 fully covers complete intervals, maintaining their total length. If the next interval is only partly reached, add max(0, carpetEnd - nextStart + 1) for that candidate, then remove the left interval before advancing left. The right pointer never moves backward.

Boundary discipline

Use inclusive interval lengths end - start + 1, and clamp partial coverage because a gap may put the next interval beyond the carpet. The usual statement guarantees non-overlapping intervals; if it does not, merge first. Every interval enters and leaves the running total once after sorting, so time is O(n log n) and extra space is O(1) beyond sorting. Test a carpet shorter than one interval, a carpet ending exactly on a tile, and large gaps between intervals.