Question

I just studied the disjoint set data structure and I know that it is also called “union-find data structures”, union and find are two main operations of this data structure. We can can perform union on disjoint sets, similarly we can perform find operations; I want to know what other operations we can perform on disjoint sets except union and find.

Answer 1

Disjoint sets structure is also called “union-find structure”. So union, find and MakeSet operations should be supported anyway. Other operations are not what this structure is all about, and whether they’re supported depends on implementation and the aims you have. Sometimes you’ll need to choose particular implementation specifically to fit your project’s needs of additional opertations.

Other than that it would be nice if we supported the other basic set-related operations. Let’s enumerate them:

• intersection of two sets. Since sets are disjoint, it’s always empty unless these two sets coincide.
• union of two sets — supported out of the box.
• get an element from the set — supported, it’s most likely the result of find.
• delete an element from the set — depends on implementation. When sets are implemented as forests, it’s tricky and requires slower additional operations. When sets are implemented as linked lists, it’s simple.
• enumerate the set, i.e. iterate each element in the given set. This one depends on implementation again: for linked lists it’s simple, for forest-like implementation it requires additional structures to support.