package edu.princeton.cs.algs4.ch60;
import edu.princeton.cs.algs4.FlowEdge;
import edu.princeton.cs.algs4.FlowNetwork;
import edu.princeton.cs.algs4.FordFulkerson;
import edu.princeton.cs.introcs.*;
/*************************************************************************
* Compilation: javac BipartiteMatching.java
* Execution: java BipartiteMatching N E
* Dependencies: FordFulkerson.java FlowNetwork.java FlowEdge.java
*
* Find a maximum matching in a bipartite graph. Solve by reducing
* to maximum flow.
*
* The order of growth of the running time in the worst case is E V
* because each augmentation increases the cardinality of the matching
* by one.
*
* The Hopcroft-Karp algorithm improves this to E V^1/2 by finding
* a maximal set of shortest augmenting paths in each phase.
*
*********************************************************************/
public class BipartiteMatching {
public static void main(String[] args) {
// read in bipartite network with 2N vertices and E edges
// we assume the vertices on one side of the bipartition
// are named 0 to N-1 and on the other side are N to 2N-1.
int N = Integer.parseInt(args[0]);
int E = Integer.parseInt(args[1]);
int s = 2*N, t = 2*N + 1;
FlowNetwork G = new FlowNetwork(2*N + 2);
for (int i = 0; i < E; i++) {
int v = StdRandom.uniform(N);
int w = StdRandom.uniform(N) + N;
G.addEdge(new FlowEdge(v, w, Double.POSITIVE_INFINITY));
StdOut.println(v + "-" + w);
}
for (int i = 0; i < N; i++) {
G.addEdge(new FlowEdge(s, i, 1.0));
G.addEdge(new FlowEdge(i + N, t, 1.0));
}
// compute maximum flow and minimum cut
FordFulkerson maxflow = new FordFulkerson(G, s, t);
StdOut.println();
StdOut.println("Size of maximum matching = " + (int) maxflow.value());
for (int v = 0; v < N; v++) {
for (FlowEdge e : G.adj(v)) {
if (e.from() == v && e.flow() > 0)
StdOut.println(e.from() + "-" + e.to());
}
}
}
}
/*************************************************************************
* Copyright 2002-2012, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4-package.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4-package.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4-package.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
* You should have received a copy of the GNU General Public License
* along with algs4-package.jar. If not, see http://www.gnu.org/licenses.
*************************************************************************/