Union-Find, also called disjoint set union, maintains a collection of disjoint sets with two operations: find, which returns a set representative, and union, which merges two sets. Path compression and union by rank make it near-constant amortized time.
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Union-Find, also called disjoint set union, maintains a collection of disjoint sets with two operations: find, which returns a set representative, and union, which merges two sets. Path compression and union by rank make it near-constant amortized time.
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Find returns the root of an element, and union merges two trees under a single root.
Path compression flattens trees and union by rank keeps them shallow, giving near-constant amortized time.
Use it for connectivity, cycle detection in undirected graphs, and Kruskal minimum spanning trees.
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Connected components, cycle detection in undirected graphs, and building minimum spanning trees with Kruskal.
With path compression and union by rank, operations run in near-constant amortized time, the inverse Ackermann function.
