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/******************************************************************************
* Compilation: javac GraphGenerator.java
* Execution: java GraphGenerator V E
* Dependencies: Graph.java
*
* A graph generator.
*
* For many more graph generators, see
* http://networkx.github.io/documentation/latest/reference/generators.html
*
******************************************************************************/
package edu.princeton.cs.algs4;
/**
* The {@code GraphGenerator} class provides static methods for creating
* various graphs, including Erdos-Renyi random graphs, random bipartite
* graphs, random k-regular graphs, and random rooted trees.
*
* For additional documentation, see Section 4.1 of
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class GraphGenerator {
private static final class Edge implements Comparable {
private int v;
private int w;
private Edge(int v, int w) {
if (v < w) {
this.v = v;
this.w = w;
}
else {
this.v = w;
this.w = v;
}
}
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;
}
}
// this class cannot be instantiated
private GraphGenerator() { }
/**
* Returns a random simple graph containing {@code V} vertices and {@code E} edges.
* @param V the number of vertices
* @param E the number of vertices
* @return a random simple graph on {@code V} vertices, containing a total
* of {@code E} edges
* @throws IllegalArgumentException if no such simple graph exists
*/
public static Graph simple(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");
Graph G = new Graph(V);
SET 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 graph on {@code V} vertices, with an
* edge between any two vertices with probability {@code p}. This is sometimes
* referred to as the Erdos-Renyi random graph model.
* @param V the number of vertices
* @param p the probability of choosing an edge
* @return a random simple graph on {@code V} vertices, with an edge between
* any two vertices with probability {@code p}
* @throws IllegalArgumentException if probability is not between 0 and 1
*/
public static Graph simple(int V, double p) {
if (p < 0.0 || p > 1.0)
throw new IllegalArgumentException("Probability must be between 0 and 1");
Graph G = new Graph(V);
for (int v = 0; v < V; v++)
for (int w = v+1; w < V; w++)
if (StdRandom.bernoulli(p))
G.addEdge(v, w);
return G;
}
/**
* Returns the complete graph on {@code V} vertices.
* @param V the number of vertices
* @return the complete graph on {@code V} vertices
*/
public static Graph complete(int V) {
return simple(V, 1.0);
}
/**
* Returns a complete bipartite graph on {@code V1} and {@code V2} vertices.
* @param V1 the number of vertices in one partition
* @param V2 the number of vertices in the other partition
* @return a complete bipartite graph on {@code V1} and {@code V2} vertices
* @throws IllegalArgumentException if probability is not between 0 and 1
*/
public static Graph completeBipartite(int V1, int V2) {
return bipartite(V1, V2, V1*V2);
}
/**
* Returns a random simple bipartite graph on {@code V1} and {@code V2} vertices
* with {@code E} edges.
* @param V1 the number of vertices in one partition
* @param V2 the number of vertices in the other partition
* @param E the number of edges
* @return a random simple bipartite graph on {@code V1} and {@code V2} vertices,
* containing a total of {@code E} edges
* @throws IllegalArgumentException if no such simple bipartite graph exists
*/
public static Graph bipartite(int V1, int V2, int E) {
if (E > (long) V1*V2) throw new IllegalArgumentException("Too many edges");
if (E < 0) throw new IllegalArgumentException("Too few edges");
Graph G = new Graph(V1 + V2);
int[] vertices = new int[V1 + V2];
for (int i = 0; i < V1 + V2; i++)
vertices[i] = i;
StdRandom.shuffle(vertices);
SET set = new SET();
while (G.E() < E) {
int i = StdRandom.uniform(V1);
int j = V1 + StdRandom.uniform(V2);
Edge e = new Edge(vertices[i], vertices[j]);
if (!set.contains(e)) {
set.add(e);
G.addEdge(vertices[i], vertices[j]);
}
}
return G;
}
/**
* Returns a random simple bipartite graph on {@code V1} and {@code V2} vertices,
* containing each possible edge with probability {@code p}.
* @param V1 the number of vertices in one partition
* @param V2 the number of vertices in the other partition
* @param p the probability that the graph contains an edge with one endpoint in either side
* @return a random simple bipartite graph on {@code V1} and {@code V2} vertices,
* containing each possible edge with probability {@code p}
* @throws IllegalArgumentException if probability is not between 0 and 1
*/
public static Graph bipartite(int V1, int V2, double p) {
if (p < 0.0 || p > 1.0)
throw new IllegalArgumentException("Probability must be between 0 and 1");
int[] vertices = new int[V1 + V2];
for (int i = 0; i < V1 + V2; i++)
vertices[i] = i;
StdRandom.shuffle(vertices);
Graph G = new Graph(V1 + V2);
for (int i = 0; i < V1; i++)
for (int j = 0; j < V2; j++)
if (StdRandom.bernoulli(p))
G.addEdge(vertices[i], vertices[V1+j]);
return G;
}
/**
* Returns a path graph on {@code V} vertices.
* @param V the number of vertices in the path
* @return a path graph on {@code V} vertices
*/
public static Graph path(int V) {
Graph G = new Graph(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 graph on {@code V} vertices.
* @param V the number of vertices in the binary tree
* @return a complete binary tree graph on {@code V} vertices
*/
public static Graph binaryTree(int V) {
Graph G = new Graph(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 graph on {@code V} vertices.
* @param V the number of vertices in the cycle
* @return a cycle graph on {@code V} vertices
*/
public static Graph cycle(int V) {
Graph G = new Graph(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 an Eulerian cycle graph on {@code V} vertices.
*
* @param V the number of vertices in the cycle
* @param E the number of edges in the cycle
* @return a graph that is an Eulerian cycle on {@code V} vertices
* and {@code E} edges
* @throws IllegalArgumentException if either {@code V <= 0} or {@code E <= 0}
*/
public static Graph eulerianCycle(int V, int E) {
if (E <= 0)
throw new IllegalArgumentException("An Eulerian cycle must have at least one edge");
if (V <= 0)
throw new IllegalArgumentException("An Eulerian cycle must have at least one vertex");
Graph G = new Graph(V);
int[] vertices = new int[E];
for (int i = 0; i < E; i++)
vertices[i] = StdRandom.uniform(V);
for (int i = 0; i < E-1; i++) {
G.addEdge(vertices[i], vertices[i+1]);
}
G.addEdge(vertices[E-1], vertices[0]);
return G;
}
/**
* Returns an Eulerian path graph on {@code V} vertices.
*
* @param V the number of vertices in the path
* @param E the number of edges in the path
* @return a graph that is an Eulerian path on {@code V} vertices
* and {@code E} edges
* @throws IllegalArgumentException if either {@code V <= 0} or {@code E < 0}
*/
public static Graph eulerianPath(int V, int E) {
if (E < 0)
throw new IllegalArgumentException("negative number of edges");
if (V <= 0)
throw new IllegalArgumentException("An Eulerian path must have at least one vertex");
Graph G = new Graph(V);
int[] vertices = new int[E+1];
for (int i = 0; i < E+1; i++)
vertices[i] = StdRandom.uniform(V);
for (int i = 0; i < E; i++) {
G.addEdge(vertices[i], vertices[i+1]);
}
return G;
}
/**
* Returns a wheel graph on {@code V} vertices.
* @param V the number of vertices in the wheel
* @return a wheel graph on {@code V} vertices: a single vertex connected to
* every vertex in a cycle on {@code V-1} vertices
*/
public static Graph wheel(int V) {
if (V <= 1) throw new IllegalArgumentException("Number of vertices must be at least 2");
Graph G = new Graph(V);
int[] vertices = new int[V];
for (int i = 0; i < V; i++)
vertices[i] = i;
StdRandom.shuffle(vertices);
// simple cycle on V-1 vertices
for (int i = 1; i < V-1; i++) {
G.addEdge(vertices[i], vertices[i+1]);
}
G.addEdge(vertices[V-1], vertices[1]);
// connect vertices[0] to every vertex on cycle
for (int i = 1; i < V; i++) {
G.addEdge(vertices[0], vertices[i]);
}
return G;
}
/**
* Returns a star graph on {@code V} vertices.
* @param V the number of vertices in the star
* @return a star graph on {@code V} vertices: a single vertex connected to
* every other vertex
*/
public static Graph star(int V) {
if (V <= 0) throw new IllegalArgumentException("Number of vertices must be at least 1");
Graph G = new Graph(V);
int[] vertices = new int[V];
for (int i = 0; i < V; i++)
vertices[i] = i;
StdRandom.shuffle(vertices);
// connect vertices[0] to every other vertex
for (int i = 1; i < V; i++) {
G.addEdge(vertices[0], vertices[i]);
}
return G;
}
/**
* Returns a uniformly random {@code k}-regular graph on {@code V} vertices
* (not necessarily simple). The graph is simple with probability only about e^(-k^2/4),
* which is tiny when k = 14.
*
* @param V the number of vertices in the graph
* @param k degree of each vertex
* @return a uniformly random {@code k}-regular graph on {@code V} vertices.
*/
public static Graph regular(int V, int k) {
if (V*k % 2 != 0) throw new IllegalArgumentException("Number of vertices * k must be even");
Graph G = new Graph(V);
// create k copies of each vertex
int[] vertices = new int[V*k];
for (int v = 0; v < V; v++) {
for (int j = 0; j < k; j++) {
vertices[v + V*j] = v;
}
}
// pick a random perfect matching
StdRandom.shuffle(vertices);
for (int i = 0; i < V*k/2; i++) {
G.addEdge(vertices[2*i], vertices[2*i + 1]);
}
return G;
}
// http://www.proofwiki.org/wiki/Labeled_Tree_from_Prüfer_Sequence
// http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.36.6484&rep=rep1&type=pdf
/**
* Returns a uniformly random tree on {@code V} vertices.
* This algorithm uses a Prufer sequence and takes time proportional to V log V.
* @param V the number of vertices in the tree
* @return a uniformly random tree on {@code V} vertices
*/
public static Graph tree(int V) {
Graph G = new Graph(V);
// special case
if (V == 1) return G;
// Cayley's theorem: there are V^(V-2) labeled trees on V vertices
// Prufer sequence: sequence of V-2 values between 0 and V-1
// Prufer's proof of Cayley's theorem: Prufer sequences are in 1-1
// with labeled trees on V vertices
int[] prufer = new int[V-2];
for (int i = 0; i < V-2; i++)
prufer[i] = StdRandom.uniform(V);
// degree of vertex v = 1 + number of times it appers in Prufer sequence
int[] degree = new int[V];
for (int v = 0; v < V; v++)
degree[v] = 1;
for (int i = 0; i < V-2; i++)
degree[prufer[i]]++;
// pq contains all vertices of degree 1
MinPQ pq = new MinPQ();
for (int v = 0; v < V; v++)
if (degree[v] == 1) pq.insert(v);
// repeatedly delMin() degree 1 vertex that has the minimum index
for (int i = 0; i < V-2; i++) {
int v = pq.delMin();
G.addEdge(v, prufer[i]);
degree[v]--;
degree[prufer[i]]--;
if (degree[prufer[i]] == 1) pq.insert(prufer[i]);
}
G.addEdge(pq.delMin(), pq.delMin());
return G;
}
/**
* Unit tests the {@code GraphGenerator} library.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
int V = Integer.parseInt(args[0]);
int E = Integer.parseInt(args[1]);
int V1 = V/2;
int V2 = V - V1;
StdOut.println("complete graph");
StdOut.println(complete(V));
StdOut.println();
StdOut.println("simple");
StdOut.println(simple(V, E));
StdOut.println();
StdOut.println("Erdos-Renyi");
double p = (double) E / (V*(V-1)/2.0);
StdOut.println(simple(V, p));
StdOut.println();
StdOut.println("complete bipartite");
StdOut.println(completeBipartite(V1, V2));
StdOut.println();
StdOut.println("bipartite");
StdOut.println(bipartite(V1, V2, E));
StdOut.println();
StdOut.println("Erdos Renyi bipartite");
double q = (double) E / (V1*V2);
StdOut.println(bipartite(V1, V2, q));
StdOut.println();
StdOut.println("path");
StdOut.println(path(V));
StdOut.println();
StdOut.println("cycle");
StdOut.println(cycle(V));
StdOut.println();
StdOut.println("binary tree");
StdOut.println(binaryTree(V));
StdOut.println();
StdOut.println("tree");
StdOut.println(tree(V));
StdOut.println();
StdOut.println("4-regular");
StdOut.println(regular(V, 4));
StdOut.println();
StdOut.println("star");
StdOut.println(star(V));
StdOut.println();
StdOut.println("wheel");
StdOut.println(wheel(V));
StdOut.println();
}
}
/******************************************************************************
* Copyright 2002-2018, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.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.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.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.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/