package algs42;
import algs35.SET;
import algs13.Stack;
import stdlib.*;
/*************************************************************************
* Compilation: javac DigraphGenerator.java
* Execution: java DigraphGenerator V E
* Dependencies: Digraph.java
*
* A digraph generator.
*
*************************************************************************/
/**
* The {@code DigraphGenerator} 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.
*
* For additional documentation, see Section 4.2 of
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class DigraphGenerator {
private static class Edge implements Comparable {
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;
}
}
public static Digraph fromIn(In in) {
Digraph G = new Digraph (in.readInt());
int E = in.readInt();
if (E < 0) throw new IllegalArgumentException("Number of edges in a Digraph must be nonnegative");
for (int i = 0; i < E; i++) {
int v = in.readInt();
int w = in.readInt();
G.addEdge(v, w);
}
return G;
}
public static Digraph copy (Digraph G) {
Digraph R = new Digraph (G.V());
for (int v = 0; v < G.V(); v++) {
// reverse so that adjacency list is in same order as original
Stack reverse = new Stack();
for (int w : G.adj(v)) {
reverse.push(w);
}
for (int w : reverse) {
R.addEdge (v, w);
}
}
return R;
}
/**
* 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 {@code V} vertices and {@code E} edges.
* @param V the number of vertices
* @param E the number of vertices
* @return a random simple digraph on {@code V} vertices, containing a total
* of {@code E} 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 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 {@code V} vertices, with an
* edge between any two vertices with probability {@code p}. This is sometimes
* referred to as the Erdos-Renyi random digraph model.
* This implementations takes time propotional to V^2 (even if {@code p} is small).
* @param V the number of vertices
* @param p the probability of choosing an edge
* @return a random simple digraph 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 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 {@code V} vertices.
* @param V the number of vertices
* @return the complete digraph on {@code V} vertices
*/
public static Digraph complete(int V) {
return simple(V, V*(V-1));
}
/**
* Returns a random simple DAG containing {@code V} vertices and {@code E} 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 {@code V} vertices, containing a total
* of {@code E} 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 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 {@code V} 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 {@code V} vertices
*/
public static Digraph tournament(int V) {
return dag(V, V*(V-1)/2);
}
/**
* Returns a random rooted-in DAG on {@code V} vertices and {@code E} 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 {@code V} vertices and {@code E} 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 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 {@code V} vertices and {@code E} 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 {@code V} vertices and {@code E} 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 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 {@code V} 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 {@code V} vertices
*/
public static Digraph rootedInTree(int V) {
return rootedInDAG(V, V-1);
}
/**
* Returns a random rooted-out tree on {@code V} 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 arborescence or branching.
* 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 {@code V} vertices
*/
public static Digraph rootedOutTree(int V) {
return rootedOutDAG(V, V-1);
}
/**
* Returns a path digraph on {@code V} vertices.
* @param V the number of vertices in the path
* @return a digraph that is a directed path on {@code V} 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 {@code V} vertices.
* @param V the number of vertices in the binary tree
* @return a digraph that is a complete binary tree on {@code V} 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 {@code V} vertices.
* @param V the number of vertices in the cycle
* @return a digraph that is a directed cycle on {@code V} 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 an Eulerian cycle digraph on {@code V} vertices.
*
* @param V the number of vertices in the cycle
* @param E the number of edges in the cycle
* @return a digraph that is a directed Eulerian cycle on {@code V} vertices
* and {@code E} edges
* @throws IllegalArgumentException if either {@code V <= 0} or {@code E <= 0}
*/
public static Digraph 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");
Digraph G = new Digraph(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 digraph on {@code V} vertices.
*
* @param V the number of vertices in the path
* @param E the number of edges in the path
* @return a digraph that is a directed Eulerian path on {@code V} vertices
* and {@code E} edges
* @throws IllegalArgumentException if either {@code V <= 0} or {@code E < 0}
*/
public static Digraph 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");
Digraph G = new Digraph(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 random simple digraph on {@code V} vertices, {@code E}
* edges and (at most) {@code c} strong components. The vertices are randomly
* assigned integer labels between {@code 0} and {@code c-1} (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 {@code V} vertices and
{@code E} edges, with (at most) {@code c} strong components
* @throws IllegalArgumentException if {@code c} is larger than {@code V}
*/
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 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 {@code DigraphGenerator} 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]);
for (int i=5; i>0; i--) {
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);
}
}
}