/****************************************************************************** * Compilation: javac KosarajuSharirSCC.java * Execution: java KosarajuSharirSCC filename.txt * Dependencies: Digraph.java TransitiveClosure.java StdOut.java In.java * Data files: https://algs4.cs.princeton.edu/42digraph/tinyDG.txt * https://algs4.cs.princeton.edu/42digraph/mediumDG.txt * https://algs4.cs.princeton.edu/42digraph/largeDG.txt * * Compute the strongly-connected components of a digraph using the * Kosaraju-Sharir algorithm. * * Runs in O(E + V) time. * * % java KosarajuSharirSCC tinyDG.txt * 5 strong components * 1 * 0 2 3 4 5 * 9 10 11 12 * 6 8 * 7 * * % java KosarajuSharirSCC mediumDG.txt * 10 strong components * 21 * 2 5 6 8 9 11 12 13 15 16 18 19 22 23 25 26 28 29 30 31 32 33 34 35 37 38 39 40 42 43 44 46 47 48 49 * 14 * 3 4 17 20 24 27 36 * 41 * 7 * 45 * 1 * 0 * 10 * * % java -Xss50m KosarajuSharirSCC mediumDG.txt * 25 strong components * 7 11 32 36 61 84 95 116 121 128 230 ... * 28 73 80 104 115 143 149 164 184 185 ... * 38 40 200 201 207 218 286 387 418 422 ... * 12 14 56 78 87 103 216 269 271 272 ... * 42 48 112 135 160 217 243 246 273 346 ... * 46 76 96 97 224 237 297 303 308 309 ... * 9 15 21 22 27 90 167 214 220 225 227 ... * 74 99 133 146 161 166 202 205 245 262 ... * 43 83 94 120 125 183 195 206 244 254 ... * 1 13 54 91 92 93 106 140 156 194 208 ... * 10 39 67 69 131 144 145 154 168 258 ... * 6 52 66 113 118 122 139 147 212 213 ... * 8 127 150 182 203 204 249 367 400 432 ... * 63 65 101 107 108 136 169 170 171 173 ... * 55 71 102 155 159 198 228 252 325 419 ... * 4 25 34 58 70 152 172 196 199 210 226 ... * 2 44 50 88 109 138 141 178 197 211 ... * 57 89 129 162 174 179 188 209 238 276 ... * 33 41 49 119 126 132 148 181 215 221 ... * 3 18 23 26 35 64 105 124 157 186 251 ... * 5 16 17 20 31 47 81 98 158 180 187 ... * 24 29 51 59 75 82 100 114 117 134 151 ... * 30 45 53 60 72 85 111 130 137 142 163 ... * 19 37 62 77 79 110 153 352 353 361 ... * 0 68 86 123 165 176 193 239 289 336 ... * ******************************************************************************/ package edu.princeton.cs.algs4; /** * The {@code KosarajuSharirSCC} class represents a data type for * determining the strong components in a digraph. * The id operation determines in which strong component * a given vertex lies; the areStronglyConnected operation * determines whether two vertices are in the same strong component; * and the count operation determines the number of strong * components. *
* 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