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MediumHigh Frequency30 min

Union Find (Disjoint Set)

Track connected components efficiently with union by rank and path compression.

Union-Find tracks connected components. find(x) returns representative, union(x,y) merges groups. With path compression + union by rank: O(α(n)) per operation.

Union-Find (Disjoint Set Union)

Union-Find Operations

Number of Connected Components

O(E ┬╖ ╬▒(n)) Γëê O(E)count starts at n, decrements on each successful union of two different components.
Step-by-step1 / 4
Graphnodes + edges
01234
01234

Init: parent[i]=i, count=5

Each node is its own root. 5 separate components.