I did some simple benchmarks of a `Vec<(u32, u32)>` to a `BTreeMap<u32, u32>` for the test case and found them to be roughly comparable. The intervals are relatively dense so I was hoping for the vector to perform better than it did.

The binary search was useful to find the start position if there are more than a few hundred elements or so (whatever the breakeven point for linear search vs. binary search is on your CPU).