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Refactor ConnectedComponents: rename to UnionFind, clean up (#1299)
* Refactor ConnectedComponentsAdjacencyList: rename, clean up, add docs - Rename to ConnectedComponentsUnionFind to distinguish from DFS solver - Replace Map<Integer, List<Edge>> with List<List<Integer>> adjacency list - Remove unnecessary Edge class with cost field - Move package-level UnionFind to private inner class - Add Javadoc with complexity, graph diagram, and 0-indexed component ids - Fix misleading "strongly connected" reference in old Javadoc Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * Simplify component IDs by reusing Union-Find roots directly Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * Add componentSize method and comprehensive tests Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * Update README link for ConnectedComponentsUnionFind rename Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>
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‎README.md‎

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- [:movie_camera:](https://www.youtube.com/watch?v=oDqjPvD54Ss) [Breadth first search (adjacency list)](src/main/java/com/williamfiset/algorithms/graphtheory/BreadthFirstSearchAdjacencyList.java) **- O(V+E)**
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- [Bridges/cut edges (adjacency list)](src/main/java/com/williamfiset/algorithms/graphtheory/BridgesAdjacencyList.java) **- O(V+E)**
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- [Boruvkas (adjacency list, min spanning tree algorithm)](src/main/java/com/williamfiset/algorithms/graphtheory/Boruvkas.java) **- O(Elog(V))**
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- [Find connected components (adjacency list, union find)](src/main/java/com/williamfiset/algorithms/graphtheory/ConnectedComponentsAdjacencyList.java) **- O(Elog(E))**
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- [Find connected components (adjacency list, union find)](src/main/java/com/williamfiset/algorithms/graphtheory/ConnectedComponentsUnionFind.java) **- O(V+E)**
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- [Find connected components (adjacency list, DFS)](src/main/java/com/williamfiset/algorithms/graphtheory/ConnectedComponentsDfsSolverAdjacencyList.java) **- O(V+E)**
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- [Depth first search (adjacency list, iterative)](src/main/java/com/williamfiset/algorithms/graphtheory/DepthFirstSearchAdjacencyListIterative.java) **- O(V+E)**
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- [Depth first search (adjacency list, iterative, fast stack)](src/main/java/com/williamfiset/algorithms/graphtheory/DepthFirstSearchAdjacencyListIterativeFastStack.java) **- O(V+E)**

‎src/main/java/com/williamfiset/algorithms/graphtheory/BUILD‎

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runtime_deps = [":graphtheory"],
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)
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# bazel run //src/main/java/com/williamfiset/algorithms/graphtheory:ConnectedComponentsAdjacencyList
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# bazel run //src/main/java/com/williamfiset/algorithms/graphtheory:ConnectedComponentsUnionFind
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java_binary(
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name = "ConnectedComponentsAdjacencyList",
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main_class = "com.williamfiset.algorithms.graphtheory.ConnectedComponentsAdjacencyList",
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name = "ConnectedComponentsUnionFind",
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main_class = "com.williamfiset.algorithms.graphtheory.ConnectedComponentsUnionFind",
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runtime_deps = [":graphtheory"],
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)
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‎src/main/java/com/williamfiset/algorithms/graphtheory/ConnectedComponentsAdjacencyList.java‎

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‎src/main/java/com/williamfiset/algorithms/graphtheory/ConnectedComponentsUnionFind.java‎

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/**
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* Connected Components — Adjacency List (Union-Find)
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*
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* <p>Finds all connected components of an undirected graph using a Union-Find
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* data structure. Each edge merges the two endpoint components; the final number
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* of disjoint sets is the component count.
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*
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* <p>For directed graphs, use Tarjan's or Kosaraju's algorithm to find
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* <em>strongly</em> connected components instead.
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*
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* <p>Time: O(V + E * α(V)) ≈ O(V + E)
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* <p>Space: O(V)
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*
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* @author William Fiset, william.alexandre.fiset@gmail.com
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*/
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package com.williamfiset.algorithms.graphtheory;
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import java.util.ArrayList;
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import java.util.List;
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public class ConnectedComponentsUnionFind {
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private final int n;
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private final List<List<Integer>> graph;
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private boolean solved;
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private UnionFind uf;
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public ConnectedComponentsUnionFind(List<List<Integer>> graph) {
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if (graph == null) {
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throw new IllegalArgumentException();
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}
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this.n = graph.size();
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this.graph = graph;
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}
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/**
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* Returns the number of connected components.
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*/
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public int countComponents() {
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solve();
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return uf.components;
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}
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/**
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* Returns the component id (root node) of the given node.
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*/
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public int componentId(int node) {
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solve();
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return uf.find(node);
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}
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/**
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* Returns the size of the component that the given node belongs to.
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*/
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public int componentSize(int node) {
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solve();
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return uf.sz[uf.find(node)];
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}
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private void solve() {
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if (solved) {
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return;
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}
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uf = new UnionFind(n);
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for (int u = 0; u < n; u++) {
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for (int v : graph.get(u)) {
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uf.union(u, v);
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}
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}
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solved = true;
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}
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// ==================== Main ====================
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//
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// 0 --- 1 3 --- 6
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// | / | |
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// | / | |
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// 2 4 9
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//
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// 5 7 --- 8 10
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//
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// Components: {0,1,2}, {3,4,6,9}, {5}, {7,8}, {10}
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// Count: 5
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//
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public static void main(String[] args) {
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int n = 11;
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List<List<Integer>> graph = createGraph(n);
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addUndirectedEdge(graph, 0, 1);
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addUndirectedEdge(graph, 0, 2);
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addUndirectedEdge(graph, 1, 2);
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addUndirectedEdge(graph, 3, 4);
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addUndirectedEdge(graph, 3, 6);
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addUndirectedEdge(graph, 6, 9);
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addUndirectedEdge(graph, 7, 8);
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ConnectedComponentsUnionFind solver =
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new ConnectedComponentsUnionFind(graph);
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System.out.printf("Number of components: %d%n", solver.countComponents());
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for (int i = 0; i < n; i++) {
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System.out.printf("Node %d -> component %d%n", i, solver.componentId(i));
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}
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}
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private static List<List<Integer>> createGraph(int n) {
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List<List<Integer>> graph = new ArrayList<>(n);
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for (int i = 0; i < n; i++) {
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graph.add(new ArrayList<>());
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}
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return graph;
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}
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private static void addUndirectedEdge(List<List<Integer>> graph, int from, int to) {
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graph.get(from).add(to);
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graph.get(to).add(from);
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}
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// Union-Find with path compression and union by size.
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private static class UnionFind {
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int components;
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private final int[] id;
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private final int[] sz;
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UnionFind(int n) {
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components = n;
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id = new int[n];
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sz = new int[n];
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for (int i = 0; i < n; i++) {
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id[i] = i;
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sz[i] = 1;
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}
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}
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int find(int p) {
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if (id[p] != p) {
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id[p] = find(id[p]);
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}
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return id[p];
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}
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void union(int p, int q) {
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int root1 = find(p);
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int root2 = find(q);
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if (root1 == root2) {
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return;
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}
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if (sz[root1] < sz[root2]) {
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sz[root2] += sz[root1];
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id[root1] = root2;
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} else {
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sz[root1] += sz[root2];
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id[root2] = root1;
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}
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components--;
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}
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}
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}

‎src/test/java/com/williamfiset/algorithms/graphtheory/BUILD‎

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# Core graphtheory tests
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# bazel test //src/test/java/com/williamfiset/algorithms/graphtheory:ConnectedComponentsUnionFindTest
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java_test(
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name = "ConnectedComponentsUnionFindTest",
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srcs = ["ConnectedComponentsUnionFindTest.java"],
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main_class = "org.junit.platform.console.ConsoleLauncher",
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use_testrunner = False,
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args = ["--select-class=com.williamfiset.algorithms.graphtheory.ConnectedComponentsUnionFindTest"],
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runtime_deps = JUNIT5_RUNTIME_DEPS,
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deps = TEST_DEPS,
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)
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# bazel test //src/test/java/com/williamfiset/algorithms/graphtheory:BoruvkasTest
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java_test(
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name = "BoruvkasTest",

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