DigraphGenerator.java

/*************************************************************************
 *  Compilation:  javac DigraphGenerator.java
 *  Execution:    java DigraphGenerator V E
 *  Dependencies: Digraph.java
 *
 *  A digraph generator.
 *  
 *************************************************************************/

/**
 *  The <tt>DigraphGenerator</tt> class provides static methods for creating
 *  various digraphs, including Erdos-Renyi random digraphs, random DAGs,
 *  random rooted trees, random rooted DAGs, random tournaments, path digraphs,
 *  cycle digraphs, and the complete digraph.
 *  <p>
 *  For additional documentation, see <a href="http://algs4.cs.princeton.edu/42digraph">Section 4.2</a> of
 *  <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
 *
 *  @author Robert Sedgewick
 *  @author Kevin Wayne
 */
public class DigraphGenerator {
    private static final class Edge implements Comparable<Edge> {
        private int v;
        private int w;
        private Edge(int v, int w) {
            this.v = v;
            this.w = w;
        }
        public int compareTo(Edge that) {
            if (this.v < that.v) return -1;
            if (this.v > that.v) return +1;
            if (this.w < that.w) return -1;
            if (this.w > that.w) return +1;
            return 0;
        }
    }

    /**
     * Returns a random simple digraph containing <tt>V</tt> vertices and <tt>E</tt> edges.
     * @param V the number of vertices
     * @param E the number of vertices
     * @return a random simple digraph on <tt>V</tt> vertices, containing a total
     *     of <tt>E</tt> edges
     * @throws IllegalArgumentException if no such simple digraph exists
     */
    public static Digraph simple(int V, int E) {
        if (E > (long) V*(V-1)) throw new IllegalArgumentException("Too many edges");
        if (E < 0)              throw new IllegalArgumentException("Too few edges");
        Digraph G = new Digraph(V);
        SET<Edge> set = new SET<Edge>();
        while (G.E() < E) {
            int v = StdRandom.uniform(V);
            int w = StdRandom.uniform(V);
            Edge e = new Edge(v, w);
            if ((v != w) && !set.contains(e)) {
                set.add(e);
                G.addEdge(v, w);
            }
        }
        return G;
    }

   /**
     * Returns a random simple digraph on <tt>V</tt> vertices, with an 
     * edge between any two vertices with probability <tt>p</tt>. This is sometimes
     * referred to as the Erdos-Renyi random digraph model.
     * @param V the number of vertices
     * @param p the probability of choosing an edge
     * @return a random simple digraph on <tt>V</tt> vertices, with an edge between
     *     any two vertices with probability <tt>p</tt>
     * @throws IllegalArgumentException if probability is not between 0 and 1
     */
    public static Digraph simple(int V, double p) {
        if (p < 0.0 || p > 1.0)
            throw new IllegalArgumentException("Probability must be between 0 and 1");
        Digraph G = new Digraph(V);
        for (int v = 0; v < V; v++)
            for (int w = 0; w < V; w++)
                if (v != w)
                    if (StdRandom.bernoulli(p))
                        G.addEdge(v, w);
        return G;
    }

    /**
     * Returns the complete digraph on <tt>V</tt> vertices.
     * @param V the number of vertices
     * @return the complete digraph on <tt>V</tt> vertices
     */
    public static Digraph complete(int V) {
        return simple(V, V*(V-1));
    }

    /**
     * Returns a random simple DAG containing <tt>V</tt> vertices and <tt>E</tt> edges.
     * Note: it is not uniformly selected at random among all such DAGs.
     * @param V the number of vertices
     * @param E the number of vertices
     * @return a random simple DAG on <tt>V</tt> vertices, containing a total
     *     of <tt>E</tt> edges
     * @throws IllegalArgumentException if no such simple DAG exists
     */
    public static Digraph dag(int V, int E) {
        if (E > (long) V*(V-1) / 2) throw new IllegalArgumentException("Too many edges");
        if (E < 0)                  throw new IllegalArgumentException("Too few edges");
        Digraph G = new Digraph(V);
        SET<Edge> set = new SET<Edge>();
        int[] vertices = new int[V];
        for (int i = 0; i < V; i++) vertices[i] = i;
        StdRandom.shuffle(vertices);
        while (G.E() < E) {
            int v = StdRandom.uniform(V);
            int w = StdRandom.uniform(V);
            Edge e = new Edge(v, w);
            if ((v < w) && !set.contains(e)) {
                set.add(e);
                G.addEdge(vertices[v], vertices[w]);
            }
        }
        return G;
    }

    // tournament
    /**
     * Returns a random tournament digraph on <tt>V</tt> vertices. A tournament digraph
     * is a DAG in which for every two vertices <tt>v != w<tt>, there is either
     * a directed edge from <tt>v</tt> to <tt>w</tt> or a directed edge
     * from <tt>w</tt> to <tt>v</tt>.
     * @param V the number of vertices
     * @return a random tournament digraph on <tt>V</tt> vertices
     */
    public static Digraph tournament(int V) {
        return dag(V, V*(V-1)/2);
    }

    /**
     * Returns a random rooted-in DAG on <tt>V</tt> vertices and <tt>E</tt> edges.
     * The DAG returned is not chosen uniformly at random among all such DAGs.
     * @param V the number of vertices
     * @param E the number of edges
     * @return a random rooted-in DAG on <tt>V</tt> vertices and <tt>E</tt> edges
     */
    public static Digraph rootedInDAG(int V, int E) {
        if (E > (long) V*(V-1) / 2) throw new IllegalArgumentException("Too many edges");
        if (E < V-1)                throw new IllegalArgumentException("Too few edges");
        Digraph G = new Digraph(V);
        SET<Edge> set = new SET<Edge>();

        // fix a topological order
        int[] vertices = new int[V];
        for (int i = 0; i < V; i++) vertices[i] = i;
        StdRandom.shuffle(vertices);

        // one edge pointing from each vertex, other than the root = vertices[V-1]
        for (int v = 0; v < V-1; v++) {
            int w = StdRandom.uniform(v+1, V);
            Edge e = new Edge(v, w);
            set.add(e);
            G.addEdge(vertices[v], vertices[w]);
        }

        while (G.E() < E) {
            int v = StdRandom.uniform(V);
            int w = StdRandom.uniform(V);
            Edge e = new Edge(v, w);
            if ((v < w) && !set.contains(e)) {
                set.add(e);
                G.addEdge(vertices[v], vertices[w]);
            }
        }
        return G;
    }

    /**
     * Returns a random rooted-out DAG on <tt>V</tt> vertices and <tt>E</tt> edges.
     * The DAG returned is not chosen uniformly at random among all such DAGs.
     * @param V the number of vertices
     * @param E the number of edges
     * @return a random rooted-out DAG on <tt>V</tt> vertices and <tt>E</tt> edges
     */
    public static Digraph rootedOutDAG(int V, int E) {
        if (E > (long) V*(V-1) / 2) throw new IllegalArgumentException("Too many edges");
        if (E < V-1)                throw new IllegalArgumentException("Too few edges");
        Digraph G = new Digraph(V);
        SET<Edge> set = new SET<Edge>();

        // fix a topological order
        int[] vertices = new int[V];
        for (int i = 0; i < V; i++) vertices[i] = i;
        StdRandom.shuffle(vertices);

        // one edge pointing from each vertex, other than the root = vertices[V-1]
        for (int v = 0; v < V-1; v++) {
            int w = StdRandom.uniform(v+1, V);
            Edge e = new Edge(v, w);
            set.add(e);
            G.addEdge(vertices[w], vertices[v]);
        }

        while (G.E() < E) {
            int v = StdRandom.uniform(V);
            int w = StdRandom.uniform(V);
            Edge e = new Edge(v, w);
            if ((v < w) && !set.contains(e)) {
                set.add(e);
                G.addEdge(vertices[w], vertices[v]);
            }
        }
        return G;
    }

    /**
     * Returns a random rooted-in tree on <tt>V</tt> vertices.
     * The tree returned is not chosen uniformly at random among all such trees.
     * @param V the number of vertices
     * @return a random rooted-in tree on <tt>V</tt> vertices
     */
    public static Digraph rootedInTree(int V) {
        return rootedInDAG(V, V-1);
    }

    /**
     * Returns a random rooted-out tree on <tt>V</tt> vertices.
     * The tree returned is not chosen uniformly at random among all such trees.
     * @param V the number of vertices
     * @return a random rooted-out tree on <tt>V</tt> vertices
     */
    public static Digraph rootedOutTree(int V) {
        return rootedOutDAG(V, V-1);
    }

    /**
     * Returns a path digraph on <tt>V</tt> vertices.
     * @param V the number of vertices in the path
     * @return a digraph that is a directed path on <tt>V</tt> vertices
     */
    public static Digraph path(int V) {
        Digraph G = new Digraph(V);
        int[] vertices = new int[V];
        for (int i = 0; i < V; i++) vertices[i] = i;
        StdRandom.shuffle(vertices);
        for (int i = 0; i < V-1; i++) {
            G.addEdge(vertices[i], vertices[i+1]);
        }
        return G;
    }

    /**
     * Returns a complete binary tree digraph on <tt>V</tt> vertices.
     * @param V the number of vertices in the binary tree
     * @return a digraph that is a complete binary tree on <tt>V</tt> vertices
     */
    public static Digraph binaryTree(int V) {
        Digraph G = new Digraph(V);
        int[] vertices = new int[V];
        for (int i = 0; i < V; i++) vertices[i] = i;
        StdRandom.shuffle(vertices);
        for (int i = 1; i < V; i++) {
            G.addEdge(vertices[i], vertices[(i-1)/2]);
        }
        return G;
    }

    /**
     * Returns a cycle digraph on <tt>V</tt> vertices.
     * @param V the number of vertices in the cycle
     * @return a digraph that is a directed cycle on <tt>V</tt> vertices
     */
    public static Digraph cycle(int V) {
        Digraph G = new Digraph(V);
        int[] vertices = new int[V];
        for (int i = 0; i < V; i++) vertices[i] = i;
        StdRandom.shuffle(vertices);
        for (int i = 0; i < V-1; i++) {
            G.addEdge(vertices[i], vertices[i+1]);
        }
        G.addEdge(vertices[V-1], vertices[0]);
        return G;
    }

    /**
     * Unit tests the <tt>DigraphGenerator</tt> library.
     */
    public static void main(String[] args) {
        int V = Integer.parseInt(args[0]);
        int E = Integer.parseInt(args[1]);
        System.out.println("complete graph");
        System.out.println(complete(V));
        System.out.println();

        System.out.println("simple");
        System.out.println(simple(V, E));
        System.out.println();

        System.out.println("path");
        System.out.println(path(V));
        System.out.println();

        System.out.println("cycle");
        System.out.println(cycle(V));
        System.out.println();

        System.out.println("binary tree");
        System.out.println(binaryTree(V));
        System.out.println();

        System.out.println("tournament");
        System.out.println(tournament(V));
        System.out.println();

        System.out.println("DAG");
        System.out.println(dag(V, E));
        System.out.println();

        System.out.println("rooted-in DAG");
        System.out.println(rootedInDAG(V, E));
        System.out.println();

        System.out.println("rooted-out DAG");
        System.out.println(rootedOutDAG(V, E));
        System.out.println();

        System.out.println("rooted-in tree");
        System.out.println(rootedInTree(V));
        System.out.println();

        System.out.println("rooted-out DAG");
        System.out.println(rootedOutTree(V));
        System.out.println();
    }

}