What is Union Find and what problems does it solve?

Union Find, also called Disjoint Set Union, maintains a collection of disjoint sets and supports two operations: find, which determines which set an element belongs to, and union, which merges two sets. With path compression in find and union by rank, both operations run in nearly O of one amortized time. Union Find efficiently solves connected component problems, cycle detection in undirected graphs, Kruskal's minimum spanning tree algorithm, and determining if two nodes are in the same group.