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206 lines
6.5 KiB
Java
206 lines
6.5 KiB
Java
5 years ago
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import edu.princeton.cs.introcs.In;
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import edu.princeton.cs.introcs.StdOut;
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/*************************************************************************
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* Compilation: javac KosarajuSharirSCC.java
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* Execution: java KosarajuSharirSCC filename.txt
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* Dependencies: Digraph.java TransitiveClosure.java StdOut.java In.java
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* Data files: http://algs4.cs.princeton.edu/42directed/tinyDG.txt
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*
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* Compute the strongly-connected components of a digraph using the
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* Kosaraju-Sharir algorithm.
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*
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* Runs in O(E + V) time.
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*
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* % java KosarajuSCC tinyDG.txt
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* 5 components
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* 1
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* 0 2 3 4 5
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* 9 10 11 12
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* 6 8
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* 7
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*
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* % java KosarajuSharirSCC mediumDG.txt
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* 10 components
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* 21
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* 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
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* 14
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* 3 4 17 20 24 27 36
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* 41
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* 7
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* 45
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* 1
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* 0
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* 10
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*
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* % java -Xss50m KosarajuSharirSCC mediumDG.txt
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* 25 components
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* 7 11 32 36 61 84 95 116 121 128 230 ...
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* 28 73 80 104 115 143 149 164 184 185 ...
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* 38 40 200 201 207 218 286 387 418 422 ...
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* 12 14 56 78 87 103 216 269 271 272 ...
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* 42 48 112 135 160 217 243 246 273 346 ...
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* 46 76 96 97 224 237 297 303 308 309 ...
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* 9 15 21 22 27 90 167 214 220 225 227 ...
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* 74 99 133 146 161 166 202 205 245 262 ...
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* 43 83 94 120 125 183 195 206 244 254 ...
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* 1 13 54 91 92 93 106 140 156 194 208 ...
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* 10 39 67 69 131 144 145 154 168 258 ...
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* 6 52 66 113 118 122 139 147 212 213 ...
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* 8 127 150 182 203 204 249 367 400 432 ...
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* 63 65 101 107 108 136 169 170 171 173 ...
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* 55 71 102 155 159 198 228 252 325 419 ...
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* 4 25 34 58 70 152 172 196 199 210 226 ...
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* 2 44 50 88 109 138 141 178 197 211 ...
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* 57 89 129 162 174 179 188 209 238 276 ...
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* 33 41 49 119 126 132 148 181 215 221 ...
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* 3 18 23 26 35 64 105 124 157 186 251 ...
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* 5 16 17 20 31 47 81 98 158 180 187 ...
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* 24 29 51 59 75 82 100 114 117 134 151 ...
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* 30 45 53 60 72 85 111 130 137 142 163 ...
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* 19 37 62 77 79 110 153 352 353 361 ...
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* 0 68 86 123 165 176 193 239 289 336 ...
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*
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*************************************************************************/
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/**
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* The KosarajuSharirSCC class represents a data type for
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* determining the strong components in a digraph.
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* The id operation determines in which strong component
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* a given vertex lies; the areStronglyConnected operation
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* determines whether two vertices are in the same strong component;
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* and the count operation determines the number of strong
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* components.
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* The component identifier of a component is one of the
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* vertices in the strong component: two vertices have the same component
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* identifier if and only if they are in the same strong component.
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*
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* This implementation uses the Kosaraju-Sharir algorithm.
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* The constructor takes time proportional to V + E
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* (in the worst case),
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* where V is the number of vertices and E is the number of edges.
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* Afterwards, the id , count , and areStronglyConnected
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* operations take constant time.
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* For alternate implementations of the same API, see
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* {@link TarjanSCC} and {@link GabowSCC}.
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*
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* For additional documentation, see <a href="/algs4/42digraph">Section 4.2</a> of
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* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
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*
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* @author Robert Sedgewick
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* @author Kevin Wayne
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*/
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public class KosarajuSharirSCC {
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private boolean[] marked; // marked[v] = has vertex v been visited?
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private int[] id; // id[v] = id of strong component containing v
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private int count; // number of strongly-connected components
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/**
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* Computes the strong components of the digraph G .
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* @param G the digraph
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*/
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public KosarajuSharirSCC(Digraph G) {
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// compute reverse postorder of reverse graph
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DepthFirstOrder dfs = new DepthFirstOrder(G.reverse());
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// run DFS on G, using reverse postorder to guide calculation
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marked = new boolean[G.V()];
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id = new int[G.V()];
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for (int v : dfs.reversePost()) {
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if (!marked[v]) {
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dfs(G, v);
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count++;
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}
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}
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// check that id[] gives strong components
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assert check(G);
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}
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// DFS on graph G
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private void dfs(Digraph G, int v) {
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marked[v] = true;
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id[v] = count;
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for (int w : G.adj(v)) {
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if (!marked[w]) dfs(G, w);
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}
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}
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/**
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* Returns the number of strong components.
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* @return the number of strong components
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*/
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public int count() {
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return count;
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}
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/**
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* Are vertices v and w in the same strong component?
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* @param v one vertex
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* @param w the other vertex
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* @return true if vertices v and w are in the same
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* strong component, and false otherwise
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*/
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public boolean stronglyConnected(int v, int w) {
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return id[v] == id[w];
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}
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/**
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* Returns the component id of the strong component containing vertex v .
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* @param v the vertex
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* @return the component id of the strong component containing vertex v
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*/
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public int id(int v) {
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return id[v];
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}
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// does the id[] array contain the strongly connected components?
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private boolean check(Digraph G) {
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TransitiveClosure tc = new TransitiveClosure(G);
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for (int v = 0; v < G.V(); v++) {
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for (int w = 0; w < G.V(); w++) {
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if (stronglyConnected(v, w) != (tc.reachable(v, w) && tc.reachable(w, v)))
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return false;
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}
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}
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return true;
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}
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/**
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* Unit tests the KosarajuSharirSCC data type.
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*/
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public static void main(String[] args) {
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In in = new In(args[0]);
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Digraph G = new Digraph(in);
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KosarajuSharirSCC scc = new KosarajuSharirSCC(G);
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// number of connected components
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int M = scc.count();
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StdOut.println(M + " components");
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// compute list of vertices in each strong component
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Queue<Integer>[] components = (Queue<Integer>[]) new Queue[M];
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for (int i = 0; i < M; i++) {
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components[i] = new Queue<Integer>();
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}
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for (int v = 0; v < G.V(); v++) {
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components[scc.id(v)].enqueue(v);
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}
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// print results
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for (int i = 0; i < M; i++) {
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for (int v : components[i]) {
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StdOut.print(v + " ");
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}
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StdOut.println();
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}
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}
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}
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