/**
* Returns a random simple digraph on {@code V} vertices, {@code E}
* edges and (at least) {@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 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 {@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<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;
}