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59 lines
2.0 KiB
Java
59 lines
2.0 KiB
Java
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import edu.princeton.cs.introcs.StdOut;
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import edu.princeton.cs.introcs.StdRandom;
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/*************************************************************************
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* Compilation: javac BipartiteMatching.java
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* Execution: java BipartiteMatching N E
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* Dependencies: FordFulkerson.java FlowNetwork.java FlowEdge.java
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*
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* Find a maximum matching in a bipartite graph. Solve by reducing
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* to maximum flow.
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*
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* The order of growth of the running time in the worst case is E V
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* because each augmentation increases the cardinality of the matching
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* by one.
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*
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* The Hopcroft-Karp algorithm improves this to E V^1/2 by finding
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* a maximal set of shortest augmenting paths in each phase.
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*
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*********************************************************************/
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public class BipartiteMatching {
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public static void main(String[] args) {
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// read in bipartite network with 2N vertices and E edges
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// we assume the vertices on one side of the bipartition
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// are named 0 to N-1 and on the other side are N to 2N-1.
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int N = Integer.parseInt(args[0]);
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int E = Integer.parseInt(args[1]);
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int s = 2*N, t = 2*N + 1;
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FlowNetwork G = new FlowNetwork(2*N + 2);
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for (int i = 0; i < E; i++) {
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int v = StdRandom.uniform(N);
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int w = StdRandom.uniform(N) + N;
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G.addEdge(new FlowEdge(v, w, Double.POSITIVE_INFINITY));
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StdOut.println(v + "-" + w);
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}
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for (int i = 0; i < N; i++) {
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G.addEdge(new FlowEdge(s, i, 1.0));
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G.addEdge(new FlowEdge(i + N, t, 1.0));
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}
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// compute maximum flow and minimum cut
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FordFulkerson maxflow = new FordFulkerson(G, s, t);
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StdOut.println();
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StdOut.println("Size of maximum matching = " + (int) maxflow.value());
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for (int v = 0; v < N; v++) {
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for (FlowEdge e : G.adj(v)) {
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if (e.from() == v && e.flow() > 0)
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StdOut.println(e.from() + "-" + e.to());
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}
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}
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}
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}
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