A range intersection algorithm better than O(n)?

Question

Range intersection is a simple, but non-trivial problem.

Its has been answered twice already:

• Find number range intersection
• Comparing date ra

Answer 1

This depends on your exact problem, in the linked question, the ranges where distinct, no common part, and the searched ranged could span multiple ranges. If your problem is the same, its is really easy: Take an array of the ranges, sort them by their lowest values (since they do not overlap, this would be also the same order as sorted by their upper values).

Now just make a binsearch for the your target lower value (or smaller if not exact) and one for the target upper value(or bigger if not exact). The resulting indexes are the the ranges which are coverd. You have to check wheter the ranges at the indexes itself are in- or excluded, but that are just 2 checks. Overall complexity O(log n).