408 lines
14 KiB
Java
408 lines
14 KiB
Java
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import edu.princeton.cs.introcs.StdRandom;
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/*************************************************************************
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* Compilation: javac GraphGenerator.java
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* Execution: java GraphGenerator V E
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* Dependencies: Graph.java
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*
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* A graph generator.
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*
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* For many more graph generators, see
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* http://networkx.github.io/documentation/latest/reference/generators.html
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*
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*************************************************************************/
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/**
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* The GraphGenerator class provides static methods for creating
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* various graphs, including Erdos-Renyi random graphs, random bipartite
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* graphs, random k-regular graphs, and random rooted trees.
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*
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* For additional documentation, see <a href="http://algs4.cs.princeton.edu/41undirected">Section 4.1</a> of
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* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
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*
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* @author Robert Sedgewick
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* @author Kevin Wayne
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*/
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public class GraphGenerator {
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private static final class Edge implements Comparable<Edge> {
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private int v;
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private int w;
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private Edge(int v, int w) {
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if (v < w) {
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this.v = v;
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this.w = w;
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}
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else {
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this.v = w;
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this.w = v;
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}
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}
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public int compareTo(Edge that) {
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if (this.v < that.v) return -1;
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if (this.v > that.v) return +1;
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if (this.w < that.w) return -1;
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if (this.w > that.w) return +1;
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return 0;
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}
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}
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/**
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* Returns a random simple graph containing V vertices and E edges.
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* @param V the number of vertices
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* @param E the number of vertices
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* @return a random simple graph on V vertices, containing a total
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* of E edges
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* @throws IllegalArgumentException if no such simple graph exists
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*/
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public static Graph simple(int V, int E) {
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if (E > (long) V*(V-1)/2) throw new IllegalArgumentException("Too many edges");
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if (E < 0) throw new IllegalArgumentException("Too few edges");
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Graph G = new Graph(V);
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SET<Edge> set = new SET<Edge>();
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while (G.E() < E) {
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int v = StdRandom.uniform(V);
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int w = StdRandom.uniform(V);
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Edge e = new Edge(v, w);
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if ((v != w) && !set.contains(e)) {
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set.add(e);
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G.addEdge(v, w);
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}
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}
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return G;
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}
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/**
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* Returns a random simple graph on V vertices, with an
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* edge between any two vertices with probability p . This is sometimes
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* referred to as the Erdos-Renyi random graph model.
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* @param V the number of vertices
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* @param p the probability of choosing an edge
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* @return a random simple graph on V vertices, with an edge between
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* any two vertices with probability p
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* @throws IllegalArgumentException if probability is not between 0 and 1
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*/
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public static Graph simple(int V, double p) {
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if (p < 0.0 || p > 1.0)
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throw new IllegalArgumentException("Probability must be between 0 and 1");
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Graph G = new Graph(V);
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for (int v = 0; v < V; v++)
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for (int w = v+1; w < V; w++)
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if (StdRandom.bernoulli(p))
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G.addEdge(v, w);
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return G;
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}
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/**
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* Returns the complete graph on V vertices.
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* @param V the number of vertices
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* @return the complete graph on V vertices
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*/
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public static Graph complete(int V) {
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return simple(V, 1.0);
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}
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/**
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* Returns a complete bipartite graph on V1 and V2 vertices.
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* @param V1 the number of vertices in one partition
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* @param V2 the number of vertices in the other partition
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* @return a complete bipartite graph on V1 and V2 vertices
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* @throws IllegalArgumentException if probability is not between 0 and 1
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*/
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public static Graph completeBipartite(int V1, int V2) {
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return bipartite(V1, V2, V1*V2);
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}
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/**
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* Returns a random simple bipartite graph on V1 and V2 vertices
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* with E edges.
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* @param V1 the number of vertices in one partition
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* @param V2 the number of vertices in the other partition
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* @param E the number of edges
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* @return a random simple bipartite graph on V1 and V2 vertices,
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* containing a total of E edges
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* @throws IllegalArgumentException if no such simple bipartite graph exists
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*/
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public static Graph bipartite(int V1, int V2, int E) {
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if (E > (long) V1*V2) throw new IllegalArgumentException("Too many edges");
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if (E < 0) throw new IllegalArgumentException("Too few edges");
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Graph G = new Graph(V1 + V2);
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int[] vertices = new int[V1 + V2];
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for (int i = 0; i < V1 + V2; i++) vertices[i] = i;
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StdRandom.shuffle(vertices);
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SET<Edge> set = new SET<Edge>();
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while (G.E() < E) {
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int i = StdRandom.uniform(V1);
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int j = V1 + StdRandom.uniform(V2);
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Edge e = new Edge(vertices[i], vertices[j]);
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if (!set.contains(e)) {
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set.add(e);
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G.addEdge(vertices[i], vertices[j]);
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}
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}
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return G;
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}
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/**
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* Returns a random simple bipartite graph on V1 and V2 vertices,
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* containing each possible edge with probability p .
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* @param V1 the number of vertices in one partition
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* @param V2 the number of vertices in the other partition
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* @param p the probability that the graph contains an edge with one endpoint in either side
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* @return a random simple bipartite graph on V1 and V2 vertices,
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* containing each possible edge with probability p
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* @throws IllegalArgumentException if probability is not between 0 and 1
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*/
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public static Graph bipartite(int V1, int V2, double p) {
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if (p < 0.0 || p > 1.0)
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throw new IllegalArgumentException("Probability must be between 0 and 1");
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int[] vertices = new int[V1 + V2];
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for (int i = 0; i < V1 + V2; i++) vertices[i] = i;
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StdRandom.shuffle(vertices);
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Graph G = new Graph(V1 + V2);
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for (int i = 0; i < V1; i++)
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for (int j = 0; j < V2; j++)
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if (StdRandom.bernoulli(p))
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G.addEdge(vertices[i], vertices[V1+j]);
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return G;
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}
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/**
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* Returns a path graph on V vertices.
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* @param V the number of vertices in the path
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* @return a path graph on V vertices
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*/
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public static Graph path(int V) {
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Graph G = new Graph(V);
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int[] vertices = new int[V];
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for (int i = 0; i < V; i++) vertices[i] = i;
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StdRandom.shuffle(vertices);
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for (int i = 0; i < V-1; i++) {
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G.addEdge(vertices[i], vertices[i+1]);
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}
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return G;
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}
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/**
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* Returns a complete binary tree graph on V vertices.
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* @param V the number of vertices in the binary tree
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* @return a complete binary tree graph on V vertices
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*/
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public static Graph binaryTree(int V) {
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Graph G = new Graph(V);
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int[] vertices = new int[V];
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for (int i = 0; i < V; i++) vertices[i] = i;
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StdRandom.shuffle(vertices);
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for (int i = 1; i < V; i++) {
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G.addEdge(vertices[i], vertices[(i-1)/2]);
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}
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return G;
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}
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/**
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* Returns a cycle graph on V vertices.
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* @param V the number of vertices in the cycle
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* @return a cycle graph on V vertices
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*/
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public static Graph cycle(int V) {
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Graph G = new Graph(V);
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int[] vertices = new int[V];
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for (int i = 0; i < V; i++) vertices[i] = i;
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StdRandom.shuffle(vertices);
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for (int i = 0; i < V-1; i++) {
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G.addEdge(vertices[i], vertices[i+1]);
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}
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G.addEdge(vertices[V-1], vertices[0]);
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return G;
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}
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/**
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* Returns a wheel graph on V vertices.
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* @param V the number of vertices in the wheel
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* @return a wheel graph on V vertices: a single vertex connected to
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* every vertex in a cycle on V-1 vertices
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*/
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public static Graph wheel(int V) {
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if (V <= 1) throw new IllegalArgumentException("Number of vertices must be at least 2");
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Graph G = new Graph(V);
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int[] vertices = new int[V];
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for (int i = 0; i < V; i++) vertices[i] = i;
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StdRandom.shuffle(vertices);
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// simple cycle on V-1 vertices
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for (int i = 1; i < V-1; i++) {
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G.addEdge(vertices[i], vertices[i+1]);
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}
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G.addEdge(vertices[V-1], vertices[1]);
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// connect vertices[0] to every vertex on cycle
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for (int i = 1; i < V; i++) {
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G.addEdge(vertices[0], vertices[i]);
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}
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return G;
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}
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/**
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* Returns a star graph on V vertices.
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* @param V the number of vertices in the star
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* @return a star graph on V vertices: a single vertex connected to
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* every other vertex
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*/
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public static Graph star(int V) {
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if (V <= 0) throw new IllegalArgumentException("Number of vertices must be at least 1");
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Graph G = new Graph(V);
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int[] vertices = new int[V];
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for (int i = 0; i < V; i++) vertices[i] = i;
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StdRandom.shuffle(vertices);
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// connect vertices[0] to every other vertex
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for (int i = 1; i < V; i++) {
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G.addEdge(vertices[0], vertices[i]);
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}
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return G;
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}
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/**
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* Returns a uniformly random k -regular graph on V vertices
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* (not necessarily simple). The graph is simple with probability only about e^(-k^2/4),
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* which is tiny when k = 14.
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* @param V the number of vertices in the graph
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* @return a uniformly random k -regular graph on V vertices.
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*/
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public static Graph regular(int V, int k) {
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if (V*k % 2 != 0) throw new IllegalArgumentException("Number of vertices * k must be even");
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Graph G = new Graph(V);
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// create k copies of each vertex
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int[] vertices = new int[V*k];
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for (int v = 0; v < V; v++) {
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for (int j = 0; j < k; j++) {
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vertices[v + V*j] = v;
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}
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}
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// pick a random perfect matching
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StdRandom.shuffle(vertices);
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for (int i = 0; i < V*k/2; i++) {
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G.addEdge(vertices[2*i], vertices[2*i + 1]);
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}
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return G;
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}
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// http://www.proofwiki.org/wiki/Labeled_Tree_from_Prüfer_Sequence
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// http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.36.6484&rep=rep1&type=pdf
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/**
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* Returns a uniformly random tree on V vertices.
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* This algorithm uses a Prufer sequence and takes time proportional to V log V .
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* @param V the number of vertices in the tree
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* @return a uniformly random tree on V vertices
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*/
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public static Graph tree(int V) {
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Graph G = new Graph(V);
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// special case
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if (V == 1) return G;
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// Cayley's theorem: there are V^(V-2) labeled trees on V vertices
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// Prufer sequence: sequence of V-2 values between 0 and V-1
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// Prufer's proof of Cayley's theorem: Prufer sequences are in 1-1
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// with labeled trees on V vertices
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int[] prufer = new int[V-2];
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for (int i = 0; i < V-2; i++)
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prufer[i] = StdRandom.uniform(V);
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// degree of vertex v = 1 + number of times it appers in Prufer sequence
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int[] degree = new int[V];
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for (int v = 0; v < V; v++)
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degree[v] = 1;
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for (int i = 0; i < V-2; i++)
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degree[prufer[i]]++;
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// pq contains all vertices of degree 1
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MinPQ<Integer> pq = new MinPQ<Integer>();
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for (int v = 0; v < V; v++)
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if (degree[v] == 1) pq.insert(v);
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// repeatedly delMin() degree 1 vertex that has the minimum index
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for (int i = 0; i < V-2; i++) {
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int v = pq.delMin();
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G.addEdge(v, prufer[i]);
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degree[v]--;
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degree[prufer[i]]--;
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if (degree[prufer[i]] == 1) pq.insert(prufer[i]);
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}
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G.addEdge(pq.delMin(), pq.delMin());
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return G;
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}
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/**
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* Unit tests the GraphGenerator library.
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*/
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public static void main(String[] args) {
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int V = Integer.parseInt(args[0]);
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int E = Integer.parseInt(args[1]);
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int V1 = V/2;
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int V2 = V - V1;
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System.out.println("complete graph");
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System.out.println(complete(V));
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System.out.println();
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System.out.println("simple");
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System.out.println(simple(V, E));
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System.out.println();
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System.out.println("Erdos-Renyi");
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double p = (double) E / (V*(V-1)/2);
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System.out.println(simple(V, p));
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System.out.println();
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System.out.println("complete bipartite");
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System.out.println(completeBipartite(V1, V2));
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System.out.println();
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System.out.println("bipartite");
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System.out.println(bipartite(V1, V2, E));
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System.out.println();
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System.out.println("Erdos Renyi bipartite");
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double q = (double) E / (V1*V2);
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System.out.println(bipartite(V1, V2, q));
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System.out.println();
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System.out.println("path");
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System.out.println(path(V));
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System.out.println();
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System.out.println("cycle");
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System.out.println(cycle(V));
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System.out.println();
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System.out.println("binary tree");
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System.out.println(binaryTree(V));
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System.out.println();
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System.out.println("tree");
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System.out.println(tree(V));
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System.out.println();
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System.out.println("4-regular");
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System.out.println(regular(V, 4));
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System.out.println();
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System.out.println("star");
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System.out.println(star(V));
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System.out.println();
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System.out.println("wheel");
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System.out.println(wheel(V));
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System.out.println();
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}
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}
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