package edu.princeton.cs.algs4.ch55;
import edu.princeton.cs.algs4.SET;
import edu.princeton.cs.algs4.ch42.Digraph;
import edu.princeton.cs.introcs.*;
/*************************************************************************
* 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.
* 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<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, 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) {
Digraph G = new Digraph(V);
for (int v = 0; v < G.V(); v++) {
for (int w = v+1; w < G.V(); w++) {
if (StdRandom.bernoulli(0.5)) G.addEdge(v, w);
else G.addEdge(w, v);
}
}
return G;
}
/**
* 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<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.
* 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<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(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 least) <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 creates among the vertices
* with the same label. Next, random edges (either between two vertices with
* the same labels or from a vetex 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<Edge>();
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.
*/
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();
}
}
/*************************************************************************
* Copyright 2002-2012, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4-package.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4-package.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4-package.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
* You should have received a copy of the GNU General Public License
* along with algs4-package.jar. If not, see http://www.gnu.org/licenses.
*************************************************************************/