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package algs42;
import algs35.SET;
import  stdlib.*;

/*************************************************************************
 *  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 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;
    }
  }

  /**
   * Create a random digraph with V vertices and E edges.
   * Expected running time is proportional to V + E.
   */
  public static Digraph random(int V, int E) {
    if (E < 0) throw new Error("Number of edges must be nonnegative");
    Digraph G = new Digraph(V);

    for (int i = 0; i < E; i++) {
      int v = (int) (Math.random() * V);
      int w = (int) (Math.random() * V);
      G.addEdge(v, w);
    }
    return G;
  }
  /**
   * 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<>();
    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.
   * This implementations takes time propotional to V^2 (even if <tt>p</tt> is small).
   * @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<>();
    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;
  }

  /**
   * Returns a random tournament digraph on <tt>V</tt> vertices. A tournament digraph
   * is a DAG in which for every two vertices, there is one directed edge.
   * A tournament is an oriented complete graph.
   * @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.
   * A rooted in-tree is a DAG in which there is a single vertex
   * reachable from every other vertex.
   * 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<>();

    // 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.
   * A rooted out-tree is a DAG in which every vertex is reachable from a
   * single vertex.
   * 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<>();

    // 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(w, v);
      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(w, v);
      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.
   * A rooted in-tree is an oriented tree in which there is a single vertex
   * reachable from every other vertex.
   * 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. A rooted out-tree
   * is an oriented tree in which each vertex is reachable from a single vertex.
   * It is also known as a <em>arborescence</em> or <em>branching</em>.
   * 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;
  }

  /**
   * Returns a random simple digraph on <tt>V</tt> vertices, <tt>E</tt>
   * edges and (at most) <tt>c</tt> strong components. The vertices are randomly
   * assigned integer labels between  <tt>0</tt> and <tt>c-1</tt> (corresponding to
   * strong components). Then, a strong component is created among the vertices
   * with the same label. Next, random edges (either between two vertices with
   * the same labels or from a vertex with a smaller label to a vertex with a
   * larger label). The number of components will be equal to the number of
   * distinct labels that are assigned to vertices.
   *
   * @param V the number of vertices
   * @param E the number of edges
   * @param c the (maximum) number of strong components
   * @return a random simple digraph on <tt>V</tt> vertices and
               <tt>E</tt> edges, with (at most) <tt>c</tt> strong components
   * @throws IllegalArgumentException if <tt>c</tt> is larger than <tt>V</tt>
   */
  public static Digraph strong(int V, int E, int c) {
    if (c >= V || c <= 0)
      throw new IllegalArgumentException("Number of components must be between 1 and V");
    if (E <= 2*(V-c))
      throw new IllegalArgumentException("Number of edges must be at least 2(V-c)");
    if (E > (long) V*(V-1) / 2)
      throw new IllegalArgumentException("Too many edges");

    // the digraph
    Digraph G = new Digraph(V);

    // edges added to G (to avoid duplicate edges)
    SET<Edge> set = new SET<>();

    int[] label = new int[V];
    for (int v = 0; v < V; v++)
      label[v] = StdRandom.uniform(c);

    // make all vertices with label c a strong component by
    // combining a rooted in-tree and a rooted out-tree
    for (int i = 0; i < c; i++) {
      // how many vertices in component c
      int count = 0;
      for (int v = 0; v < G.V(); v++) {
        if (label[v] == i) count++;
      }

      // if (count == 0) System.err.println("less than desired number of strong components");

      int[] vertices = new int[count];
      int j = 0;
      for (int v = 0; v < V; v++) {
        if (label[v] == i) vertices[j++] = v;
      }
      StdRandom.shuffle(vertices);

      // rooted-in tree with root = vertices[count-1]
      for (int v = 0; v < count-1; v++) {
        int w = StdRandom.uniform(v+1, count);
        Edge e = new Edge(w, v);
        set.add(e);
        G.addEdge(vertices[w], vertices[v]);
      }

      // rooted-out tree with root = vertices[count-1]
      for (int v = 0; v < count-1; v++) {
        int w = StdRandom.uniform(v+1, count);
        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 (!set.contains(e) && v != w && label[v] <= label[w]) {
        set.add(e);
        G.addEdge(v, w);
      }
    }

    return G;
  }

  /**
   * Unit tests the <tt>DigraphGenerator</tt> library.
   */
  private static void print (Digraph G, String filename) {
    System.out.println(filename);
    System.out.println(G);
    System.out.println();
    G.toGraphviz (filename + ".png");
  }
  public static void main(String[] args) {
    args = new String [] { "6", "10", "0.25", "3" };

    int V = Integer.parseInt(args[0]);
    int E = Integer.parseInt(args[1]);
    double p = Double.parseDouble (args[2]);
    int c = Integer.parseInt(args[3]);

    print(DigraphGenerator.random(V,E), "random-" + V + "-" + E);
    print(DigraphGenerator.simple(V,E), "simpleA-" + V + "-" + E);
    print(DigraphGenerator.simple(V,p), "simpleB-" + V + "-" + p);
    print(DigraphGenerator.complete(V), "complete-" + V);
    print(DigraphGenerator.dag(V,E), "dag-" + V + "-" + E);
    print(DigraphGenerator.tournament(V), "tournament-" + V);
    print(DigraphGenerator.rootedInDAG(V,E), "rootedInDAG-" + V + "-" + E);
    print(DigraphGenerator.rootedOutDAG(V,E), "rootedOutDAG-" + V + "-" + E);
    print(DigraphGenerator.rootedInTree(V), "rootedInTree-" + V);
    print(DigraphGenerator.rootedOutTree(V), "rootedOutTree-" + V);
    print(DigraphGenerator.path(V), "path-" + V);
    print(DigraphGenerator.binaryTree(V), "rootedInTreeBinary-" + V);
    print(DigraphGenerator.cycle(V), "cycle-" + V);
    if (E <= 2*(V-c)) E = 2*(V-c)+1;
    print(DigraphGenerator.strong(V,E,c), "strong-" + V + "-" + E + "-" + c);
  }
}