What’s the most efficient way to test two integer ranges for overlap

comparisonintegerperformancerange

Given two inclusive integer ranges [x1:x2] and [y1:y2], where x1 ≤ x2 and y1 ≤ y2, what is the most efficient way to test whether there is any overlap of the two ranges?

A simple implementation is as follows:

bool testOverlap(int x1, int x2, int y1, int y2) {
  return (x1 >= y1 && x1 <= y2) ||
         (x2 >= y1 && x2 <= y2) ||
         (y1 >= x1 && y1 <= x2) ||
         (y2 >= x1 && y2 <= x2);
}

But I expect there are more efficient ways to compute this.

What method would be the most efficient in terms of fewest operations.

Best Answer

What does it mean for the ranges to overlap? It means there exists some number C which is in both ranges, i.e.

x1 <= C <= x2

and

y1 <= C <= y2

To avoid confusion, considering the ranges are: [x1:x2] and [y1:y2]

Now, if we are allowed to assume that the ranges are well-formed (so that x1 <= x2 and y1 <= y2) then it is sufficient to test

x1 <= y2 && y1 <= x2

OR

(StartA <= EndB) and (EndA >= StartB)