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I was able to come up with a O(N^2) solution pretty quickly with no memory overhead. I'm having trouble coming up with anything that's much faster for all cases.
My basic algorithm:
1. Beginning at the 0th index and increasing by one, select an interval I --> (i, j)
2. Compare the selected interval to the intervals after it, J. If there is overlap between intervals, take the min(I.i, J.i) as the new start and the max(I.j, J.j) as the end. Update interval I. Delete interval J from the array. Continue comparing again from the index of I, plus 1.
3. If no interval in the array had an overlap, interval I is part of the solution set. Move on to the next index.
C++
Output:
- Salsa October 19, 2015