TarjanSCC.java

Below is the syntax highlighted version of TarjanSCC.java from §4.2 Directed Graphs.

/*************************************************************************
 *  Compilation:  javac TarjanSCC.java
 *  Execution:    Java TarjanSCC V E
 *  Dependencies: Digraph.java Stack.java TransitiveClosure.java StdOut.java
 *
 *  Compute the strongly-connected components of a digraph using 
 *  Tarjan's algorithm.
 *
 *  Runs in O(E + V) time.
 *
 *  % java TarjanSCC tinyDG.txt
 *  5 components
 *  1 
 *  0 2 3 4 5 
 *  9 10 11 12 
 *  6 
 *  7 8 
 *
 *************************************************************************/

public class TarjanSCC {

    private boolean[] marked;        // marked[v] = has v been visited?
    private int[] id;                // id[v] = id of strong component containing v
    private int[] low;               // low[v] = low number of v
    private int pre;                 // preorder number counter
    private int count;               // number of strongly-connected components
    private Stack<Integer> stack;


    public TarjanSCC(Digraph G) {
        marked = new boolean[G.V()];
        stack = new Stack<Integer>();
        id = new int[G.V()]; 
        low = new int[G.V()];
        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;
        low[v] = pre++;
        int min = low[v];
        stack.push(v);
        for (int w : G.adj(v)) {
            if (!marked[w]) dfs(G, w);
            if (low[w] < min) min = low[w];
        }
        if (min < low[v]) { low[v] = min; return; }
        int w;
        do {
            w = stack.pop();
            id[w] = count;
            low[w] = G.V();
        } while (w != v);
        count++;
    }



    // return the number of strongly connected components
    public int count() { return count; }


    // are v and w strongly connected?
    public boolean stronglyConnected(int v, int w) {
        return id[v] == id[w];
    }

    // in which strongly connected component is 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;
    }

    public static void main(String[] args) {
        In in = new In(args[0]);
        Digraph G = new Digraph(in);
        TarjanSCC scc = new TarjanSCC(G);

        // number of connected components
        int M = scc.count();
        StdOut.println(M + " components");

        // compute list of vertices in each strong component
        Queue<Integer>[] components = (Queue<Integer>[]) new Queue[M];
        for (int i = 0; i < M; i++) {
            components[i] = new Queue<Integer>();
        }
        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();
        }

    }

}