Generalizing Dijkstra's Dutch National Flag Algorithm Dijkstra's Dutch National Flag (DNF) algorithm is one of those deceptively simple ideas that becomes more interesting the deeper you look into it. At first glance, it solves a very narrow problem: sorting an array containing only 0 , 1 , and 2 in a single linear pass. Elegant, clever, and usually treated as a specialized trick. But hidden inside DNF is a much more general idea. The algorithm works because it understands the structure of the value space . It knows exactly which values belong on the left, which belong on the right, and which belong in the middle. Once you stop thinking of DNF as "sorting three values" and start thinking of it as "partitioning a known value space," the natural question becomes: Can this idea be generalized to arbitrary integer arrays?…