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+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2010
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#include <iostream>
+#include <sstream>
+#include <vector>
+#include <queue>
+#include <cstdlib>
+
+#include <lemon/matching.h>
+#include <lemon/smart_graph.h>
+#include <lemon/concepts/graph.h>
+#include <lemon/concepts/maps.h>
+#include <lemon/lgf_reader.h>
+#include <lemon/math.h>
+
+#include "test_tools.h"
+
+using namespace std;
+using namespace lemon;
+
+GRAPH_TYPEDEFS(SmartGraph);
+
+
+const int lgfn = 3;
+const std::string lgf[lgfn] = {
+ "@nodes\n"
+ "label\n"
+ "0\n"
+ "1\n"
+ "2\n"
+ "3\n"
+ "4\n"
+ "5\n"
+ "6\n"
+ "7\n"
+ "@edges\n"
+ " label weight\n"
+ "7 4 0 984\n"
+ "0 7 1 73\n"
+ "7 1 2 204\n"
+ "2 3 3 583\n"
+ "2 7 4 565\n"
+ "2 1 5 582\n"
+ "0 4 6 551\n"
+ "2 5 7 385\n"
+ "1 5 8 561\n"
+ "5 3 9 484\n"
+ "7 5 10 904\n"
+ "3 6 11 47\n"
+ "7 6 12 888\n"
+ "3 0 13 747\n"
+ "6 1 14 310\n",
+
+ "@nodes\n"
+ "label\n"
+ "0\n"
+ "1\n"
+ "2\n"
+ "3\n"
+ "4\n"
+ "5\n"
+ "6\n"
+ "7\n"
+ "@edges\n"
+ " label weight\n"
+ "2 5 0 710\n"
+ "0 5 1 241\n"
+ "2 4 2 856\n"
+ "2 6 3 762\n"
+ "4 1 4 747\n"
+ "6 1 5 962\n"
+ "4 7 6 723\n"
+ "1 7 7 661\n"
+ "2 3 8 376\n"
+ "1 0 9 416\n"
+ "6 7 10 391\n",
+
+ "@nodes\n"
+ "label\n"
+ "0\n"
+ "1\n"
+ "2\n"
+ "3\n"
+ "4\n"
+ "5\n"
+ "6\n"
+ "7\n"
+ "@edges\n"
+ " label weight\n"
+ "6 2 0 553\n"
+ "0 7 1 653\n"
+ "6 3 2 22\n"
+ "4 7 3 846\n"
+ "7 2 4 981\n"
+ "7 6 5 250\n"
+ "5 2 6 539\n",
+};
+
+void checkMaxMatchingCompile()
+{
+ typedef concepts::Graph Graph;
+ typedef Graph::Node Node;
+ typedef Graph::Edge Edge;
+ typedef Graph::EdgeMap<bool> MatMap;
+
+ Graph g;
+ Node n;
+ Edge e;
+ MatMap mat(g);
+
+ MaxMatching<Graph> mat_test(g);
+ const MaxMatching<Graph>&
+ const_mat_test = mat_test;
+
+ mat_test.init();
+ mat_test.greedyInit();
+ mat_test.matchingInit(mat);
+ mat_test.startSparse();
+ mat_test.startDense();
+ mat_test.run();
+
+ const_mat_test.matchingSize();
+ const_mat_test.matching(e);
+ const_mat_test.matching(n);
+ const MaxMatching<Graph>::MatchingMap& mmap =
+ const_mat_test.matchingMap();
+ e = mmap[n];
+ const_mat_test.mate(n);
+
+ MaxMatching<Graph>::Status stat =
+ const_mat_test.status(n);
+ const MaxMatching<Graph>::StatusMap& smap =
+ const_mat_test.statusMap();
+ stat = smap[n];
+ const_mat_test.barrier(n);
+}
+
+void checkMaxWeightedMatchingCompile()
+{
+ typedef concepts::Graph Graph;
+ typedef Graph::Node Node;
+ typedef Graph::Edge Edge;
+ typedef Graph::EdgeMap<int> WeightMap;
+
+ Graph g;
+ Node n;
+ Edge e;
+ WeightMap w(g);
+
+ MaxWeightedMatching<Graph> mat_test(g, w);
+ const MaxWeightedMatching<Graph>&
+ const_mat_test = mat_test;
+
+ mat_test.init();
+ mat_test.start();
+ mat_test.run();
+
+ const_mat_test.matchingWeight();
+ const_mat_test.matchingSize();
+ const_mat_test.matching(e);
+ const_mat_test.matching(n);
+ const MaxWeightedMatching<Graph>::MatchingMap& mmap =
+ const_mat_test.matchingMap();
+ e = mmap[n];
+ const_mat_test.mate(n);
+
+ int k = 0;
+ const_mat_test.dualValue();
+ const_mat_test.nodeValue(n);
+ const_mat_test.blossomNum();
+ const_mat_test.blossomSize(k);
+ const_mat_test.blossomValue(k);
+}
+
+void checkMaxWeightedPerfectMatchingCompile()
+{
+ typedef concepts::Graph Graph;
+ typedef Graph::Node Node;
+ typedef Graph::Edge Edge;
+ typedef Graph::EdgeMap<int> WeightMap;
+
+ Graph g;
+ Node n;
+ Edge e;
+ WeightMap w(g);
+
+ MaxWeightedPerfectMatching<Graph> mat_test(g, w);
+ const MaxWeightedPerfectMatching<Graph>&
+ const_mat_test = mat_test;
+
+ mat_test.init();
+ mat_test.start();
+ mat_test.run();
+
+ const_mat_test.matchingWeight();
+ const_mat_test.matching(e);
+ const_mat_test.matching(n);
+ const MaxWeightedPerfectMatching<Graph>::MatchingMap& mmap =
+ const_mat_test.matchingMap();
+ e = mmap[n];
+ const_mat_test.mate(n);
+
+ int k = 0;
+ const_mat_test.dualValue();
+ const_mat_test.nodeValue(n);
+ const_mat_test.blossomNum();
+ const_mat_test.blossomSize(k);
+ const_mat_test.blossomValue(k);
+}
+
+void checkMatching(const SmartGraph& graph,
+ const MaxMatching<SmartGraph>& mm) {
+ int num = 0;
+
+ IntNodeMap comp_index(graph);
+ UnionFind<IntNodeMap> comp(comp_index);
+
+ int barrier_num = 0;
+
+ for (NodeIt n(graph); n != INVALID; ++n) {
+ check(mm.status(n) == MaxMatching<SmartGraph>::EVEN ||
+ mm.matching(n) != INVALID, "Wrong Gallai-Edmonds decomposition");
+ if (mm.status(n) == MaxMatching<SmartGraph>::ODD) {
+ ++barrier_num;
+ } else {
+ comp.insert(n);
+ }
+ }
+
+ for (EdgeIt e(graph); e != INVALID; ++e) {
+ if (mm.matching(e)) {
+ check(e == mm.matching(graph.u(e)), "Wrong matching");
+ check(e == mm.matching(graph.v(e)), "Wrong matching");
+ ++num;
+ }
+ check(mm.status(graph.u(e)) != MaxMatching<SmartGraph>::EVEN ||
+ mm.status(graph.v(e)) != MaxMatching<SmartGraph>::MATCHED,
+ "Wrong Gallai-Edmonds decomposition");
+
+ check(mm.status(graph.v(e)) != MaxMatching<SmartGraph>::EVEN ||
+ mm.status(graph.u(e)) != MaxMatching<SmartGraph>::MATCHED,
+ "Wrong Gallai-Edmonds decomposition");
+
+ if (mm.status(graph.u(e)) != MaxMatching<SmartGraph>::ODD &&
+ mm.status(graph.v(e)) != MaxMatching<SmartGraph>::ODD) {
+ comp.join(graph.u(e), graph.v(e));
+ }
+ }
+
+ std::set<int> comp_root;
+ int odd_comp_num = 0;
+ for (NodeIt n(graph); n != INVALID; ++n) {
+ if (mm.status(n) != MaxMatching<SmartGraph>::ODD) {
+ int root = comp.find(n);
+ if (comp_root.find(root) == comp_root.end()) {
+ comp_root.insert(root);
+ if (comp.size(n) % 2 == 1) {
+ ++odd_comp_num;
+ }
+ }
+ }
+ }
+
+ check(mm.matchingSize() == num, "Wrong matching");
+ check(2 * num == countNodes(graph) - (odd_comp_num - barrier_num),
+ "Wrong matching");
+ return;
+}
+
+void checkWeightedMatching(const SmartGraph& graph,
+ const SmartGraph::EdgeMap<int>& weight,
+ const MaxWeightedMatching<SmartGraph>& mwm) {
+ for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
+ if (graph.u(e) == graph.v(e)) continue;
+ int rw = mwm.nodeValue(graph.u(e)) + mwm.nodeValue(graph.v(e));
+
+ for (int i = 0; i < mwm.blossomNum(); ++i) {
+ bool s = false, t = false;
+ for (MaxWeightedMatching<SmartGraph>::BlossomIt n(mwm, i);
+ n != INVALID; ++n) {
+ if (graph.u(e) == n) s = true;
+ if (graph.v(e) == n) t = true;
+ }
+ if (s == true && t == true) {
+ rw += mwm.blossomValue(i);
+ }
+ }
+ rw -= weight[e] * mwm.dualScale;
+
+ check(rw >= 0, "Negative reduced weight");
+ check(rw == 0 || !mwm.matching(e),
+ "Non-zero reduced weight on matching edge");
+ }
+
+ int pv = 0;
+ for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
+ if (mwm.matching(n) != INVALID) {
+ check(mwm.nodeValue(n) >= 0, "Invalid node value");
+ pv += weight[mwm.matching(n)];
+ SmartGraph::Node o = graph.target(mwm.matching(n));
+ check(mwm.mate(n) == o, "Invalid matching");
+ check(mwm.matching(n) == graph.oppositeArc(mwm.matching(o)),
+ "Invalid matching");
+ } else {
+ check(mwm.mate(n) == INVALID, "Invalid matching");
+ check(mwm.nodeValue(n) == 0, "Invalid matching");
+ }
+ }
+
+ int dv = 0;
+ for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
+ dv += mwm.nodeValue(n);
+ }
+
+ for (int i = 0; i < mwm.blossomNum(); ++i) {
+ check(mwm.blossomValue(i) >= 0, "Invalid blossom value");
+ check(mwm.blossomSize(i) % 2 == 1, "Even blossom size");
+ dv += mwm.blossomValue(i) * ((mwm.blossomSize(i) - 1) / 2);
+ }
+
+ check(pv * mwm.dualScale == dv * 2, "Wrong duality");
+
+ return;
+}
+
+void checkWeightedPerfectMatching(const SmartGraph& graph,
+ const SmartGraph::EdgeMap<int>& weight,
+ const MaxWeightedPerfectMatching<SmartGraph>& mwpm) {
+ for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
+ if (graph.u(e) == graph.v(e)) continue;
+ int rw = mwpm.nodeValue(graph.u(e)) + mwpm.nodeValue(graph.v(e));
+
+ for (int i = 0; i < mwpm.blossomNum(); ++i) {
+ bool s = false, t = false;
+ for (MaxWeightedPerfectMatching<SmartGraph>::BlossomIt n(mwpm, i);
+ n != INVALID; ++n) {
+ if (graph.u(e) == n) s = true;
+ if (graph.v(e) == n) t = true;
+ }
+ if (s == true && t == true) {
+ rw += mwpm.blossomValue(i);
+ }
+ }
+ rw -= weight[e] * mwpm.dualScale;
+
+ check(rw >= 0, "Negative reduced weight");
+ check(rw == 0 || !mwpm.matching(e),
+ "Non-zero reduced weight on matching edge");
+ }
+
+ int pv = 0;
+ for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
+ check(mwpm.matching(n) != INVALID, "Non perfect");
+ pv += weight[mwpm.matching(n)];
+ SmartGraph::Node o = graph.target(mwpm.matching(n));
+ check(mwpm.mate(n) == o, "Invalid matching");
+ check(mwpm.matching(n) == graph.oppositeArc(mwpm.matching(o)),
+ "Invalid matching");
+ }
+
+ int dv = 0;
+ for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
+ dv += mwpm.nodeValue(n);
+ }
+
+ for (int i = 0; i < mwpm.blossomNum(); ++i) {
+ check(mwpm.blossomValue(i) >= 0, "Invalid blossom value");
+ check(mwpm.blossomSize(i) % 2 == 1, "Even blossom size");
+ dv += mwpm.blossomValue(i) * ((mwpm.blossomSize(i) - 1) / 2);
+ }
+
+ check(pv * mwpm.dualScale == dv * 2, "Wrong duality");
+
+ return;
+}
+
+
+int main() {
+
+ for (int i = 0; i < lgfn; ++i) {
+ SmartGraph graph;
+ SmartGraph::EdgeMap<int> weight(graph);
+
+ istringstream lgfs(lgf[i]);
+ graphReader(graph, lgfs).
+ edgeMap("weight", weight).run();
+
+ bool perfect;
+ {
+ MaxMatching<SmartGraph> mm(graph);
+ mm.run();
+ checkMatching(graph, mm);
+ perfect = 2 * mm.matchingSize() == countNodes(graph);
+ }
+
+ {
+ MaxWeightedMatching<SmartGraph> mwm(graph, weight);
+ mwm.run();
+ checkWeightedMatching(graph, weight, mwm);
+ }
+
+ {
+ MaxWeightedMatching<SmartGraph> mwm(graph, weight);
+ mwm.init();
+ mwm.start();
+ checkWeightedMatching(graph, weight, mwm);
+ }
+
+ {
+ MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);
+ bool result = mwpm.run();
+
+ check(result == perfect, "Perfect matching found");
+ if (perfect) {
+ checkWeightedPerfectMatching(graph, weight, mwpm);
+ }
+ }
+
+ {
+ MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);
+ mwpm.init();
+ bool result = mwpm.start();
+
+ check(result == perfect, "Perfect matching found");
+ if (perfect) {
+ checkWeightedPerfectMatching(graph, weight, mwpm);
+ }
+ }
+ }
+
+ return 0;
+}
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