Iterating over classes in a disjoint set data structure

Question

I've implemented a disjoint set data structure for my program and I realized I need to iterate over all equivalence classes.

Searching the web, I didn't find any useful information on the best way to implement that or how it influences complexity. I'm quite surprised since it seems like something that would be needed quite often.

Is there a standard way of doing this? I'm thinking about using a linked list (I use C so I plan to store some pointers in the top element of each equivalence class) and updating it on each union operation. Is there a better way?

Answer 1

You can store pointers to top elements in hash-based set or in any balanced binary search tree. You only need to delete and add elements - both operations in these structures run in O(1)* and in O(logN) respectively. In linked list they run in O(N).

Answer 2

Your proposal seems very reasonable. If you thread a doubly-linked list through the representatives, you can splice out an element from the representatives list in time O(1) and then walk the list each time you need to list representatives.

@ardenit has mentioned that you can also use an external hash table or BST to store the representatives. That's certainly simpler to code up, though I suspect it won't be as fast as just threading a linked list through the items.