104 lines
2.7 KiB
Java
104 lines
2.7 KiB
Java
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import java.util.*;
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import java.util.stream.Stream;
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public class Biconnectivity {
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List<Integer>[] graph;
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boolean[] visited;
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Stack<Integer> stack;
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int time;
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int[] tin;
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int[] lowlink;
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List<List<Integer>> edgeBiconnectedComponents;
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List<Integer> cutPoints;
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List<String> bridges;
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public List<List<Integer>> biconnectivity(List<Integer>[] graph) {
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int n = graph.length;
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this.graph = graph;
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visited = new boolean[n];
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stack = new Stack<>();
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time = 0;
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tin = new int[n];
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lowlink = new int[n];
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edgeBiconnectedComponents = new ArrayList<>();
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cutPoints = new ArrayList<>();
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bridges = new ArrayList<>();
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for (int u = 0; u < n; u++)
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if (!visited[u])
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dfs(u, -1);
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return edgeBiconnectedComponents;
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}
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void dfs(int u, int p) {
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visited[u] = true;
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lowlink[u] = tin[u] = time++;
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stack.add(u);
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int children = 0;
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boolean cutPoint = false;
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for (int v : graph[u]) {
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if (v == p)
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continue;
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if (visited[v]) {
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lowlink[u] = Math.min(lowlink[u], tin[v]); // or lowlink[u] = Math.min(lowlink[u], lowlink[v]);
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} else {
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dfs(v, u);
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lowlink[u] = Math.min(lowlink[u], lowlink[v]);
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cutPoint |= tin[u] <= lowlink[v];
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if (tin[u] < lowlink[v]) // or if (lowlink[v] == tin[v])
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bridges.add("(" + u + "," + v + ")");
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++children;
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}
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}
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if (p == -1)
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cutPoint = children >= 2;
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if (cutPoint)
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cutPoints.add(u);
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if (tin[u] == lowlink[u]) {
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List<Integer> component = new ArrayList<>();
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while (true) {
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int x = stack.pop();
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component.add(x);
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if (x == u)
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break;
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}
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edgeBiconnectedComponents.add(component);
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}
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}
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// tree of edge-biconnected components
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public static List<Integer>[] ebcTree(List<Integer>[] graph, List<List<Integer>> components) {
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int[] comp = new int[graph.length];
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for (int i = 0; i < components.size(); i++)
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for (int u : components.get(i))
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comp[u] = i;
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List<Integer>[] g = Stream.generate(ArrayList::new).limit(components.size()).toArray(List[]::new);
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for (int u = 0; u < graph.length; u++)
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for (int v : graph[u])
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if (comp[u] != comp[v])
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g[comp[u]].add(comp[v]);
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return g;
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}
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// Usage example
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public static void main(String[] args) {
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List<Integer>[] graph = Stream.generate(ArrayList::new).limit(6).toArray(List[]::new);
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int[][] esges = {{0, 1}, {1, 2}, {0, 2}, {2, 3}, {1, 4}, {4, 5}, {5, 1}};
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for (int[] edge : esges) {
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graph[edge[0]].add(edge[1]);
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graph[edge[1]].add(edge[0]);
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}
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Biconnectivity bc = new Biconnectivity();
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List<List<Integer>> components = bc.biconnectivity(graph);
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System.out.println("edge-biconnected components:" + components);
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System.out.println("cut points: " + bc.cutPoints);
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System.out.println("bridges:" + bc.bridges);
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System.out.println("condensation tree:" + Arrays.toString(ebcTree(graph, components)));
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}
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}
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