 Solution

A disjoint-set data structure maintains a partition of a set into pairwise disjoint sets. Make-Set(v) creates the singleton containing a new vertex. Find-Set(v) returns the disjoint-set representative of its current set. Union(u,v) merges the two sets containing its arguments, preserving the partition; it has no effect if they are already the same set. A disjoint-set forest can implement these operations without explicitly moving every member when sets are joined.