Union-Find for Connected Components

Union-Find, also known as Disjoint Set Union, is a data structure that efficiently maintains a collection of disjoint sets with two primary operations: find (determine which set an element belongs to) and union (merge two sets into one). With path compression and union by rank optimizations, both operations run in nearly O(1) amortized time, specifically O(alpha(n)) where alpha is the inverse Ackermann function. For this problem, we initialize each element as its own set. When we encounter a rel