Culture

I bring this up because it lets me tell you a nice little piece of CS culture.

The running time of a sequence of m JOINs (unions) and CONNECTEDs (finds) implemented this way on n objects is $O((n+m)\alpha(n+m))$.

Here, $\alpha(x)$ is the pseudoinverse of Ackermann's function. It's basically the world's slowest growing function. It's almost impossible to imagine an x large enough so that $\alpha(x)\gt 4$.

Big improvement over the $O((n+m)\log(n+m))$ data structure I gave earlier! Linear, for all intents and purposes.