I happened to read on Wikipedia that the amortized time per operation on a disjoint set (union two elements, find parent of a specific element) is O(a(n)), where a(n) is the inverse Ackermann function, which grows very fast.
Can anyone explain why this is true?
Well, that would be rather hard to explain, because it isn't true. It's the non-inverse Ackermann function that grows like a rocket on steroids, the inverse Ackermann grows very slowly.
This gives you the theoretical background.
There is a proof of the fact in Introduction to Algorithms. It's a fairly popular read it seems, and your city or school library might have a copy. I've also seen copies floating about on the Internet but the legality of those is probably questionable.
EDIT: a chunk of the proof appears to be readable on Google Books.
Well, the Wikipedia page has a citation. If you're that interested, check it out. If you're at college that should be easy, if not, just find a nearby college and use their library (they don't care if you're not a student).
