import edu.princeton.cs.introcs.In; import edu.princeton.cs.introcs.StdOut; /************************************************************************* * Compilation: javac GabowSCC.java * Execution: java GabowSCC V E * Dependencies: Digraph.java Stack.java TransitiveClosure.java StdOut.java * * Compute the strongly-connected components of a digraph using * Gabow's algorithm (aka Cheriyan-Mehlhorn algorithm). * * Runs in O(E + V) time. * * % java GabowSCC tinyDG.txt * 5 components * 1 * 0 2 3 4 5 * 9 10 11 12 * 6 8 * 7 * *************************************************************************/ /** * The GabowSCC class represents a data type for * determining the strong components in a digraph. * The id operation determines in which strong component * a given vertex lies; the areStronglyConnected operation * determines whether two vertices are in the same strong component; * and the count operation determines the number of strong * components. * The component identifier of a component is one of the * vertices in the strong component: two vertices have the same component * identifier if and only if they are in the same strong component. * * This implementation uses the Gabow's algorithm. * The constructor takes time proportional to V + E * (in the worst case), * where V is the number of vertices and E is the number of edges. * Afterwards, the id , count , and areStronglyConnected * operations take constant time. * For alternate implementations of the same API, see * {@link KosarajuSharirSCC} and {@link TarjanSCC}. * * For additional documentation, see Section 4.2 of * Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne. * * @author Robert Sedgewick * @author Kevin Wayne */ public class GabowSCC { private boolean[] marked; // marked[v] = has v been visited? private int[] id; // id[v] = id of strong component containing v private int[] preorder; // preorder[v] = preorder of v private int pre; // preorder number counter private int count; // number of strongly-connected components private Stack stack1; private Stack stack2; /** * Computes the strong components of the digraph G . * @param G the digraph */ public GabowSCC(Digraph G) { marked = new boolean[G.V()]; stack1 = new Stack(); stack2 = new Stack(); id = new int[G.V()]; preorder = new int[G.V()]; for (int v = 0; v < G.V(); v++) id[v] = -1; for (int v = 0; v < G.V(); v++) { if (!marked[v]) dfs(G, v); } // check that id[] gives strong components assert check(G); } private void dfs(Digraph G, int v) { marked[v] = true; preorder[v] = pre++; stack1.push(v); stack2.push(v); for (int w : G.adj(v)) { if (!marked[w]) dfs(G, w); else if (id[w] == -1) { while (preorder[stack2.peek()] > preorder[w]) stack2.pop(); } } // found strong component containing v if (stack2.peek() == v) { stack2.pop(); int w; do { w = stack1.pop(); id[w] = count; } while (w != v); count++; } } /** * Returns the number of strong components. * @return the number of strong components */ public int count() { return count; } /** * Are vertices v and w in the same strong component? * @param v one vertex * @param w the other vertex * @return true if vertices v and w are in the same * strong component, and false otherwise */ public boolean stronglyConnected(int v, int w) { return id[v] == id[w]; } /** * Returns the component id of the strong component containing vertex v . * @param v the vertex * @return the component id of the strong component containing vertex v */ public int id(int v) { return id[v]; } // does the id[] array contain the strongly connected components? private boolean check(Digraph G) { TransitiveClosure tc = new TransitiveClosure(G); for (int v = 0; v < G.V(); v++) { for (int w = 0; w < G.V(); w++) { if (stronglyConnected(v, w) != (tc.reachable(v, w) && tc.reachable(w, v))) return false; } } return true; } /** * Unit tests the GabowSCC data type. */ public static void main(String[] args) { In in = new In(args[0]); Digraph G = new Digraph(in); GabowSCC scc = new GabowSCC(G); // number of connected components int M = scc.count(); StdOut.println(M + " components"); // compute list of vertices in each strong component Queue[] components = (Queue[]) new Queue[M]; for (int i = 0; i < M; i++) { components[i] = new Queue(); } for (int v = 0; v < G.V(); v++) { components[scc.id(v)].enqueue(v); } // print results for (int i = 0; i < M; i++) { for (int v : components[i]) { StdOut.print(v + " "); } StdOut.println(); } } }