Describe the Painting

Given half-open colored segments that overlap and mix (where a mixed color is the set-sum of active colors), produce the minimal list of non-overlapping half-open segments that describe the painting by reporting, for each contiguous range, the sum of distinct colors present. This is solved by a sweep-line over endpoints (or sorting events), tracking the current set/sum of active colors and emitting/merging ranges whenever that sum changes.