* The component identifier of a component is one of the * vertices in the strong component: two vertices have the same component * identifier if and only if they are in the same strong component. *
* This implementation uses the Kosaraju-Sharir algorithm. * The constructor takes Θ(V + E) time, * where V is the number of vertices and E * is the number of edges. * Each instance method takes Θ(1) time. * It uses Θ(V) extra space (not including the digraph). * For alternative implementations of the same API, see * {@link TarjanSCC} and {@link GabowSCC}. *
* 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 KosarajuSharirSCC {
private boolean[] marked; // marked[v] = has vertex v been visited?
private int[] id; // id[v] = id of strong component containing v
private int count; // number of strongly-connected components
/**
* Computes the strong components of the digraph {@code G}.
* @param G the digraph
*/
public KosarajuSharirSCC(Digraph G) {
// compute reverse postorder of reverse graph
DepthFirstOrder dfs = new DepthFirstOrder(G.reverse());
// run DFS on G, using reverse postorder to guide calculation
marked = new boolean[G.V()];
id = new int[G.V()];
for (int v : dfs.reversePost()) {
if (!marked[v]) {
dfs(G, v);
count++;
}
}
// check that id[] gives strong components
assert check(G);
}
// DFS on graph G
private void dfs(Digraph G, int v) {
marked[v] = true;
id[v] = count;
for (int w : G.adj(v)) {
if (!marked[w]) dfs(G, w);
}
}
/**
* Returns the number of strong components.
* @return the number of strong components
*/
public int count() {
return count;
}
/**
* Are vertices {@code v} and {@code w} in the same strong component?
* @param v one vertex
* @param w the other vertex
* @return {@code true} if vertices {@code v} and {@code w} are in the same
* strong component, and {@code false} otherwise
* @throws IllegalArgumentException unless {@code 0 <= v < V}
* @throws IllegalArgumentException unless {@code 0 <= w < V}
*/
public boolean stronglyConnected(int v, int w) {
validateVertex(v);
validateVertex(w);
return id[v] == id[w];
}
/**
* Returns the component id of the strong component containing vertex {@code v}.
* @param v the vertex
* @return the component id of the strong component containing vertex {@code v}
* @throws IllegalArgumentException unless {@code 0 <= s < V}
*/
public int id(int v) {
validateVertex(v);
return id[v];
}
// does the id[] array contain the strongly connected components?
private boolean check(Digraph G) {
TransitiveClosure tc = new TransitiveClosure(G);
for (int v = 0; v < G.V(); v++) {
for (int w = 0; w < G.V(); w++) {
if (stronglyConnected(v, w) != (tc.reachable(v, w) && tc.reachable(w, v)))
return false;
}
}
return true;
}
// throw an IllegalArgumentException unless {@code 0 <= v < V}
private void validateVertex(int v) {
int V = marked.length;
if (v < 0 || v >= V)
throw new IllegalArgumentException("vertex " + v + " is not between 0 and " + (V-1));
}
/**
* Unit tests the {@code KosarajuSharirSCC} data type.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
In in = new In(args[0]);
Digraph G = new Digraph(in);
KosarajuSharirSCC scc = new KosarajuSharirSCC(G);
// number of connected components
int m = scc.count();
StdOut.println(m + " strong components");
// compute list of vertices in each strong component
Queue