Maybe storing of all intersection intervals can help.
You need:
- boundaries of union of all intervals,
- for each intersection left boundary and list of intervals from which intersection is made.
Intersection intervals can be stored in a tree, because they are represented only with left boundary. Methods insert and delete interval look like (simplified):
Insert: find intersection intervals for left and right boundary of new interval, split these intersection intervals in 2 or 3 new intersection intervals. For each intersection intervals between add pointer to new interval.
Delete: find intersection intervals for left and right boundary, merge them to intersection intervals before. For each intersection intervals between remove pointer to deleted interval.
