206 lines
6.5 KiB
Java
206 lines
6.5 KiB
Java
|
|
||
|
|
|
||
|
|
import edu.princeton.cs.introcs.In;
|
||
|
|
import edu.princeton.cs.introcs.StdOut;
|
||
|
|
|
||
|
|
/*************************************************************************
|
||
|
|
* Compilation: javac KosarajuSharirSCC.java
|
||
|
|
* Execution: java KosarajuSharirSCC filename.txt
|
||
|
|
* Dependencies: Digraph.java TransitiveClosure.java StdOut.java In.java
|
||
|
|
* Data files: http://algs4.cs.princeton.edu/42directed/tinyDG.txt
|
||
|
|
*
|
||
|
|
* Compute the strongly-connected components of a digraph using the
|
||
|
|
* Kosaraju-Sharir algorithm.
|
||
|
|
*
|
||
|
|
* Runs in O(E + V) time.
|
||
|
|
*
|
||
|
|
* % java KosarajuSCC tinyDG.txt
|
||
|
|
* 5 components
|
||
|
|
* 1
|
||
|
|
* 0 2 3 4 5
|
||
|
|
* 9 10 11 12
|
||
|
|
* 6 8
|
||
|
|
* 7
|
||
|
|
*
|
||
|
|
* % java KosarajuSharirSCC mediumDG.txt
|
||
|
|
* 10 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 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 ...
|
||
|
|
*
|
||
|
|
*************************************************************************/
|
||
|
|
|
||
|
|
/**
|
||
|
|
* The 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 time proportional to V + E
|
||
|
|
* (in the worst case),
|
||
|
|
* where V is the number of vertices and E is the number of edges.
|
||
|
|
* Afterwards, the id , count , and areStronglyConnected
|
||
|
|
* operations take constant time.
|
||
|
|
* For alternate implementations of the same API, see
|
||
|
|
* {@link TarjanSCC} and {@link GabowSCC}.
|
||
|
|
*
|
||
|
|
* For additional documentation, see <a href="/algs4/42digraph">Section 4.2</a> 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 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 v and w in the same strong component?
|
||
|
|
* @param v one vertex
|
||
|
|
* @param w the other vertex
|
||
|
|
* @return true if vertices v and w are in the same
|
||
|
|
* strong component, and false otherwise
|
||
|
|
*/
|
||
|
|
public boolean stronglyConnected(int v, int w) {
|
||
|
|
return id[v] == id[w];
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the component id of the strong component containing vertex v .
|
||
|
|
* @param v the vertex
|
||
|
|
* @return the component id of the strong component containing vertex v
|
||
|
|
*/
|
||
|
|
public int id(int 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;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Unit tests the KosarajuSharirSCC data type.
|
||
|
|
*/
|
||
|
|
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 + " components");
|
||
|
|
|
||
|
|
// compute list of vertices in each strong component
|
||
|
|
Queue<Integer>[] components = (Queue<Integer>[]) new Queue[M];
|
||
|
|
for (int i = 0; i < M; i++) {
|
||
|
|
components[i] = new Queue<Integer>();
|
||
|
|
}
|
||
|
|
for (int v = 0; v < G.V(); v++) {
|
||
|
|
components[scc.id(v)].enqueue(v);
|
||
|
|
}
|
||
|
|
|
||
|
|
// print results
|
||
|
|
for (int i = 0; i < M; i++) {
|
||
|
|
for (int v : components[i]) {
|
||
|
|
StdOut.print(v + " ");
|
||
|
|
}
|
||
|
|
StdOut.println();
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|