This leads to a question about the nature of the problem:
Do we REALLY need to evaluate all of those 4M values?

If the end result will be sampled in only a few places, then there are definitely more efficient ways to go about it on-demand. If the interesting points are those with certain specific properties (local maxima?) then there will likely be a way to simplify there too.

Nice catch. I do care about local maxima. How does this help?

Correct me if I'm wrong, but wouldn't all local maxima have to be at the center of at least one range? If not, you'd be able to move one place towards the midpoint and get a higher value. (Since you can't use two ranges at the same time to make a bigger range)

Rather than testing 4M points, just grab the 25k ranges, delete the ones that are subsets of another range, and then the midpoints of what are left are your local maxima.

Conversely, local minima would be found at the midpoints between the midpoints of overlapping ranges. You would still have to test three values to ensure it is a true minima and not a flat spot.




In this case, you might get to use the buckets technique from back up the thread. 25k+1 midpoints between adjacent ranges * 3 sampled values * ~30 ranges in the bucket = 2.3M compares instead of 120M