michael/programming-examples
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity
599b63599b
programming-examples/java/Data_Structures/GraphGenerator.java
Michael Reber b880c3ccde Initial commit
2019-11-15 12:59:38 +01:00

408 lines
14 KiB
Java
Raw Blame History

import edu.princeton.cs.introcs.StdRandom;
/*************************************************************************
* 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
*
*************************************************************************/
/**
* The 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 <a href="http://algs4.cs.princeton.edu/41undirected">Section 4.1</a> 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<Edge> {
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;
}
}
/**
* Returns a random simple graph containing V vertices and E edges.
* @param V the number of vertices
* @param E the number of vertices
* @return a random simple graph on V vertices, containing a total
* of 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<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 graph on V vertices, with an
* edge between any two vertices with probability 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 V vertices, with an edge between
* any two vertices with probability 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 V vertices.
* @param V the number of vertices
* @return the complete graph on V vertices
*/
public static Graph complete(int V) {
return simple(V, 1.0);
}
/**
* Returns a complete bipartite graph on V1 and 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 V1 and 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 V1 and V2 vertices
* with 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 V1 and V2 vertices,
* containing a total of 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<Edge> set = new SET<Edge>();
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 V1 and V2 vertices,
* containing each possible edge with probability 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 V1 and V2 vertices,
* containing each possible edge with probability 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 V vertices.
* @param V the number of vertices in the path
* @return a path graph on 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 V vertices.
* @param V the number of vertices in the binary tree
* @return a complete binary tree graph on 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 V vertices.
* @param V the number of vertices in the cycle
* @return a cycle graph on 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 a wheel graph on V vertices.
* @param V the number of vertices in the wheel
* @return a wheel graph on V vertices: a single vertex connected to
* every vertex in a cycle on 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 V vertices.
* @param V the number of vertices in the star
* @return a star graph on 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 k -regular graph on 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
* @return a uniformly random k -regular graph on 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 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 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<Integer> pq = new MinPQ<Integer>();
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 GraphGenerator library.
*/
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;
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("Erdos-Renyi");
double p = (double) E / (V*(V-1)/2);
System.out.println(simple(V, p));
System.out.println();
System.out.println("complete bipartite");
System.out.println(completeBipartite(V1, V2));
System.out.println();
System.out.println("bipartite");
System.out.println(bipartite(V1, V2, E));
System.out.println();
System.out.println("Erdos Renyi bipartite");
double q = (double) E / (V1*V2);
System.out.println(bipartite(V1, V2, q));
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("tree");
System.out.println(tree(V));
System.out.println();
System.out.println("4-regular");
System.out.println(regular(V, 4));
System.out.println();
System.out.println("star");
System.out.println(star(V));
System.out.println();
System.out.println("wheel");
System.out.println(wheel(V));
System.out.println();
}
}
Reference in New Issue View Git Blame Copy Permalink