deba@869: /* -*- mode: C++; indent-tabs-mode: nil; -*-
deba@869:  *
deba@869:  * This file is a part of LEMON, a generic C++ optimization library.
deba@869:  *
alpar@877:  * Copyright (C) 2003-2010
deba@869:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@869:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@869:  *
deba@869:  * Permission to use, modify and distribute this software is granted
deba@869:  * provided that this copyright notice appears in all copies. For
deba@869:  * precise terms see the accompanying LICENSE file.
deba@869:  *
deba@869:  * This software is provided "AS IS" with no warranty of any kind,
deba@869:  * express or implied, and with no claim as to its suitability for any
deba@869:  * purpose.
deba@869:  *
deba@869:  */
deba@869: 
deba@869: #include <iostream>
deba@869: #include <sstream>
deba@869: #include <vector>
deba@869: #include <queue>
deba@869: #include <cstdlib>
deba@869: 
deba@869: #include <lemon/fractional_matching.h>
deba@869: #include <lemon/smart_graph.h>
deba@869: #include <lemon/concepts/graph.h>
deba@869: #include <lemon/concepts/maps.h>
deba@869: #include <lemon/lgf_reader.h>
deba@869: #include <lemon/math.h>
deba@869: 
deba@869: #include "test_tools.h"
deba@869: 
deba@869: using namespace std;
deba@869: using namespace lemon;
deba@869: 
deba@869: GRAPH_TYPEDEFS(SmartGraph);
deba@869: 
deba@869: 
deba@869: const int lgfn = 4;
deba@869: const std::string lgf[lgfn] = {
deba@869:   "@nodes\n"
deba@869:   "label\n"
deba@869:   "0\n"
deba@869:   "1\n"
deba@869:   "2\n"
deba@869:   "3\n"
deba@869:   "4\n"
deba@869:   "5\n"
deba@869:   "6\n"
deba@869:   "7\n"
deba@869:   "@edges\n"
deba@869:   "     label  weight\n"
deba@869:   "7 4  0      984\n"
deba@869:   "0 7  1      73\n"
deba@869:   "7 1  2      204\n"
deba@869:   "2 3  3      583\n"
deba@869:   "2 7  4      565\n"
deba@869:   "2 1  5      582\n"
deba@869:   "0 4  6      551\n"
deba@869:   "2 5  7      385\n"
deba@869:   "1 5  8      561\n"
deba@869:   "5 3  9      484\n"
deba@869:   "7 5  10     904\n"
deba@869:   "3 6  11     47\n"
deba@869:   "7 6  12     888\n"
deba@869:   "3 0  13     747\n"
deba@869:   "6 1  14     310\n",
deba@869: 
deba@869:   "@nodes\n"
deba@869:   "label\n"
deba@869:   "0\n"
deba@869:   "1\n"
deba@869:   "2\n"
deba@869:   "3\n"
deba@869:   "4\n"
deba@869:   "5\n"
deba@869:   "6\n"
deba@869:   "7\n"
deba@869:   "@edges\n"
deba@869:   "     label  weight\n"
deba@869:   "2 5  0      710\n"
deba@869:   "0 5  1      241\n"
deba@869:   "2 4  2      856\n"
deba@869:   "2 6  3      762\n"
deba@869:   "4 1  4      747\n"
deba@869:   "6 1  5      962\n"
deba@869:   "4 7  6      723\n"
deba@869:   "1 7  7      661\n"
deba@869:   "2 3  8      376\n"
deba@869:   "1 0  9      416\n"
deba@869:   "6 7  10     391\n",
deba@869: 
deba@869:   "@nodes\n"
deba@869:   "label\n"
deba@869:   "0\n"
deba@869:   "1\n"
deba@869:   "2\n"
deba@869:   "3\n"
deba@869:   "4\n"
deba@869:   "5\n"
deba@869:   "6\n"
deba@869:   "7\n"
deba@869:   "@edges\n"
deba@869:   "     label  weight\n"
deba@869:   "6 2  0      553\n"
deba@869:   "0 7  1      653\n"
deba@869:   "6 3  2      22\n"
deba@869:   "4 7  3      846\n"
deba@869:   "7 2  4      981\n"
deba@869:   "7 6  5      250\n"
deba@869:   "5 2  6      539\n",
deba@869: 
deba@869:   "@nodes\n"
deba@869:   "label\n"
deba@869:   "0\n"
deba@869:   "@edges\n"
deba@869:   "     label  weight\n"
deba@869:   "0 0  0      100\n"
deba@869: };
deba@869: 
deba@869: void checkMaxFractionalMatchingCompile()
deba@869: {
deba@869:   typedef concepts::Graph Graph;
deba@869:   typedef Graph::Node Node;
deba@869:   typedef Graph::Edge Edge;
deba@869: 
deba@869:   Graph g;
deba@869:   Node n;
deba@869:   Edge e;
deba@869: 
deba@869:   MaxFractionalMatching<Graph> mat_test(g);
deba@869:   const MaxFractionalMatching<Graph>&
deba@869:     const_mat_test = mat_test;
deba@869: 
deba@869:   mat_test.init();
deba@869:   mat_test.start();
deba@869:   mat_test.start(true);
deba@869:   mat_test.startPerfect();
deba@869:   mat_test.startPerfect(true);
deba@869:   mat_test.run();
deba@869:   mat_test.run(true);
deba@869:   mat_test.runPerfect();
deba@869:   mat_test.runPerfect(true);
deba@869: 
deba@869:   const_mat_test.matchingSize();
deba@869:   const_mat_test.matching(e);
deba@869:   const_mat_test.matching(n);
deba@869:   const MaxFractionalMatching<Graph>::MatchingMap& mmap =
deba@869:     const_mat_test.matchingMap();
deba@869:   e = mmap[n];
deba@869: 
deba@869:   const_mat_test.barrier(n);
deba@869: }
deba@869: 
deba@869: void checkMaxWeightedFractionalMatchingCompile()
deba@869: {
deba@869:   typedef concepts::Graph Graph;
deba@869:   typedef Graph::Node Node;
deba@869:   typedef Graph::Edge Edge;
deba@869:   typedef Graph::EdgeMap<int> WeightMap;
deba@869: 
deba@869:   Graph g;
deba@869:   Node n;
deba@869:   Edge e;
deba@869:   WeightMap w(g);
deba@869: 
deba@869:   MaxWeightedFractionalMatching<Graph> mat_test(g, w);
deba@869:   const MaxWeightedFractionalMatching<Graph>&
deba@869:     const_mat_test = mat_test;
deba@869: 
deba@869:   mat_test.init();
deba@869:   mat_test.start();
deba@869:   mat_test.run();
deba@869: 
deba@869:   const_mat_test.matchingWeight();
deba@869:   const_mat_test.matchingSize();
deba@869:   const_mat_test.matching(e);
deba@869:   const_mat_test.matching(n);
deba@869:   const MaxWeightedFractionalMatching<Graph>::MatchingMap& mmap =
deba@869:     const_mat_test.matchingMap();
deba@869:   e = mmap[n];
deba@869: 
deba@869:   const_mat_test.dualValue();
deba@869:   const_mat_test.nodeValue(n);
deba@869: }
deba@869: 
deba@869: void checkMaxWeightedPerfectFractionalMatchingCompile()
deba@869: {
deba@869:   typedef concepts::Graph Graph;
deba@869:   typedef Graph::Node Node;
deba@869:   typedef Graph::Edge Edge;
deba@869:   typedef Graph::EdgeMap<int> WeightMap;
deba@869: 
deba@869:   Graph g;
deba@869:   Node n;
deba@869:   Edge e;
deba@869:   WeightMap w(g);
deba@869: 
deba@869:   MaxWeightedPerfectFractionalMatching<Graph> mat_test(g, w);
deba@869:   const MaxWeightedPerfectFractionalMatching<Graph>&
deba@869:     const_mat_test = mat_test;
deba@869: 
deba@869:   mat_test.init();
deba@869:   mat_test.start();
deba@869:   mat_test.run();
deba@869: 
deba@869:   const_mat_test.matchingWeight();
deba@869:   const_mat_test.matching(e);
deba@869:   const_mat_test.matching(n);
deba@869:   const MaxWeightedPerfectFractionalMatching<Graph>::MatchingMap& mmap =
deba@869:     const_mat_test.matchingMap();
deba@869:   e = mmap[n];
deba@869: 
deba@869:   const_mat_test.dualValue();
deba@869:   const_mat_test.nodeValue(n);
deba@869: }
deba@869: 
deba@869: void checkFractionalMatching(const SmartGraph& graph,
deba@869:                              const MaxFractionalMatching<SmartGraph>& mfm,
deba@869:                              bool allow_loops = true) {
deba@869:   int pv = 0;
deba@869:   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@869:     int indeg = 0;
deba@869:     for (InArcIt a(graph, n); a != INVALID; ++a) {
deba@869:       if (mfm.matching(graph.source(a)) == a) {
deba@869:         ++indeg;
deba@869:       }
deba@869:     }
deba@869:     if (mfm.matching(n) != INVALID) {
deba@869:       check(indeg == 1, "Invalid matching");
deba@869:       ++pv;
deba@869:     } else {
deba@869:       check(indeg == 0, "Invalid matching");
deba@869:     }
deba@869:   }
deba@869:   check(pv == mfm.matchingSize(), "Wrong matching size");
deba@869: 
deba@872:   for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
deba@872:     check((e == mfm.matching(graph.u(e)) ? 1 : 0) +
alpar@877:           (e == mfm.matching(graph.v(e)) ? 1 : 0) ==
deba@872:           mfm.matching(e), "Invalid matching");
deba@872:   }
deba@872: 
deba@869:   SmartGraph::NodeMap<bool> processed(graph, false);
deba@869:   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@869:     if (processed[n]) continue;
deba@869:     processed[n] = true;
deba@869:     if (mfm.matching(n) == INVALID) continue;
deba@869:     int num = 1;
deba@869:     Node v = graph.target(mfm.matching(n));
deba@869:     while (v != n) {
deba@869:       processed[v] = true;
deba@869:       ++num;
deba@869:       v = graph.target(mfm.matching(v));
deba@869:     }
deba@869:     check(num == 2 || num % 2 == 1, "Wrong cycle size");
deba@869:     check(allow_loops || num != 1, "Wrong cycle size");
deba@869:   }
deba@869: 
deba@869:   int anum = 0, bnum = 0;
deba@869:   SmartGraph::NodeMap<bool> neighbours(graph, false);
deba@869:   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@869:     if (!mfm.barrier(n)) continue;
deba@869:     ++anum;
deba@869:     for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) {
deba@869:       Node u = graph.source(a);
deba@869:       if (!allow_loops && u == n) continue;
deba@869:       if (!neighbours[u]) {
deba@869:         neighbours[u] = true;
deba@869:         ++bnum;
deba@869:       }
deba@869:     }
deba@869:   }
deba@869:   check(anum - bnum + mfm.matchingSize() == countNodes(graph),
deba@869:         "Wrong barrier");
deba@869: }
deba@869: 
deba@869: void checkPerfectFractionalMatching(const SmartGraph& graph,
deba@869:                              const MaxFractionalMatching<SmartGraph>& mfm,
deba@869:                              bool perfect, bool allow_loops = true) {
deba@869:   if (perfect) {
deba@869:     for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@869:       int indeg = 0;
deba@869:       for (InArcIt a(graph, n); a != INVALID; ++a) {
deba@869:         if (mfm.matching(graph.source(a)) == a) {
deba@869:           ++indeg;
deba@869:         }
deba@869:       }
deba@869:       check(mfm.matching(n) != INVALID, "Invalid matching");
deba@869:       check(indeg == 1, "Invalid matching");
deba@869:     }
deba@872:     for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
deba@872:       check((e == mfm.matching(graph.u(e)) ? 1 : 0) +
alpar@877:             (e == mfm.matching(graph.v(e)) ? 1 : 0) ==
deba@872:             mfm.matching(e), "Invalid matching");
deba@872:     }
deba@869:   } else {
deba@869:     int anum = 0, bnum = 0;
deba@869:     SmartGraph::NodeMap<bool> neighbours(graph, false);
deba@869:     for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@869:       if (!mfm.barrier(n)) continue;
deba@869:       ++anum;
deba@869:       for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) {
deba@869:         Node u = graph.source(a);
deba@869:         if (!allow_loops && u == n) continue;
deba@869:         if (!neighbours[u]) {
deba@869:           neighbours[u] = true;
deba@869:           ++bnum;
deba@869:         }
deba@869:       }
deba@869:     }
deba@869:     check(anum - bnum > 0, "Wrong barrier");
deba@869:   }
deba@869: }
deba@869: 
deba@869: void checkWeightedFractionalMatching(const SmartGraph& graph,
deba@869:                    const SmartGraph::EdgeMap<int>& weight,
deba@869:                    const MaxWeightedFractionalMatching<SmartGraph>& mwfm,
deba@869:                    bool allow_loops = true) {
deba@869:   for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
deba@869:     if (graph.u(e) == graph.v(e) && !allow_loops) continue;
deba@869:     int rw = mwfm.nodeValue(graph.u(e)) + mwfm.nodeValue(graph.v(e))
deba@869:       - weight[e] * mwfm.dualScale;
deba@869: 
deba@869:     check(rw >= 0, "Negative reduced weight");
deba@869:     check(rw == 0 || !mwfm.matching(e),
deba@869:           "Non-zero reduced weight on matching edge");
deba@869:   }
deba@869: 
deba@869:   int pv = 0;
deba@869:   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@869:     int indeg = 0;
deba@869:     for (InArcIt a(graph, n); a != INVALID; ++a) {
deba@869:       if (mwfm.matching(graph.source(a)) == a) {
deba@869:         ++indeg;
deba@869:       }
deba@869:     }
deba@869:     check(indeg <= 1, "Invalid matching");
deba@869:     if (mwfm.matching(n) != INVALID) {
deba@869:       check(mwfm.nodeValue(n) >= 0, "Invalid node value");
deba@869:       check(indeg == 1, "Invalid matching");
deba@869:       pv += weight[mwfm.matching(n)];
deba@869:       SmartGraph::Node o = graph.target(mwfm.matching(n));
deba@869:     } else {
deba@869:       check(mwfm.nodeValue(n) == 0, "Invalid matching");
deba@869:       check(indeg == 0, "Invalid matching");
deba@869:     }
deba@869:   }
deba@869: 
deba@872:   for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
deba@872:     check((e == mwfm.matching(graph.u(e)) ? 1 : 0) +
alpar@877:           (e == mwfm.matching(graph.v(e)) ? 1 : 0) ==
deba@872:           mwfm.matching(e), "Invalid matching");
deba@872:   }
deba@872: 
deba@869:   int dv = 0;
deba@869:   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@869:     dv += mwfm.nodeValue(n);
deba@869:   }
deba@869: 
deba@869:   check(pv * mwfm.dualScale == dv * 2, "Wrong duality");
deba@869: 
deba@869:   SmartGraph::NodeMap<bool> processed(graph, false);
deba@869:   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@869:     if (processed[n]) continue;
deba@869:     processed[n] = true;
deba@869:     if (mwfm.matching(n) == INVALID) continue;
deba@869:     int num = 1;
deba@869:     Node v = graph.target(mwfm.matching(n));
deba@869:     while (v != n) {
deba@869:       processed[v] = true;
deba@869:       ++num;
deba@869:       v = graph.target(mwfm.matching(v));
deba@869:     }
deba@869:     check(num == 2 || num % 2 == 1, "Wrong cycle size");
deba@869:     check(allow_loops || num != 1, "Wrong cycle size");
deba@869:   }
deba@869: 
deba@869:   return;
deba@869: }
deba@869: 
deba@869: void checkWeightedPerfectFractionalMatching(const SmartGraph& graph,
deba@869:                 const SmartGraph::EdgeMap<int>& weight,
deba@869:                 const MaxWeightedPerfectFractionalMatching<SmartGraph>& mwpfm,
deba@869:                 bool allow_loops = true) {
deba@869:   for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
deba@869:     if (graph.u(e) == graph.v(e) && !allow_loops) continue;
deba@869:     int rw = mwpfm.nodeValue(graph.u(e)) + mwpfm.nodeValue(graph.v(e))
deba@869:       - weight[e] * mwpfm.dualScale;
deba@869: 
deba@869:     check(rw >= 0, "Negative reduced weight");
deba@869:     check(rw == 0 || !mwpfm.matching(e),
deba@869:           "Non-zero reduced weight on matching edge");
deba@869:   }
deba@869: 
deba@869:   int pv = 0;
deba@869:   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@869:     int indeg = 0;
deba@869:     for (InArcIt a(graph, n); a != INVALID; ++a) {
deba@869:       if (mwpfm.matching(graph.source(a)) == a) {
deba@869:         ++indeg;
deba@869:       }
deba@869:     }
deba@869:     check(mwpfm.matching(n) != INVALID, "Invalid perfect matching");
deba@869:     check(indeg == 1, "Invalid perfect matching");
deba@869:     pv += weight[mwpfm.matching(n)];
deba@869:     SmartGraph::Node o = graph.target(mwpfm.matching(n));
deba@869:   }
deba@869: 
deba@872:   for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
deba@872:     check((e == mwpfm.matching(graph.u(e)) ? 1 : 0) +
alpar@877:           (e == mwpfm.matching(graph.v(e)) ? 1 : 0) ==
deba@872:           mwpfm.matching(e), "Invalid matching");
deba@872:   }
deba@872: 
deba@869:   int dv = 0;
deba@869:   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@869:     dv += mwpfm.nodeValue(n);
deba@869:   }
deba@869: 
deba@869:   check(pv * mwpfm.dualScale == dv * 2, "Wrong duality");
deba@869: 
deba@869:   SmartGraph::NodeMap<bool> processed(graph, false);
deba@869:   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@869:     if (processed[n]) continue;
deba@869:     processed[n] = true;
deba@869:     if (mwpfm.matching(n) == INVALID) continue;
deba@869:     int num = 1;
deba@869:     Node v = graph.target(mwpfm.matching(n));
deba@869:     while (v != n) {
deba@869:       processed[v] = true;
deba@869:       ++num;
deba@869:       v = graph.target(mwpfm.matching(v));
deba@869:     }
deba@869:     check(num == 2 || num % 2 == 1, "Wrong cycle size");
deba@869:     check(allow_loops || num != 1, "Wrong cycle size");
deba@869:   }
deba@869: 
deba@869:   return;
deba@869: }
deba@869: 
deba@869: 
deba@869: int main() {
deba@869: 
deba@869:   for (int i = 0; i < lgfn; ++i) {
deba@869:     SmartGraph graph;
deba@869:     SmartGraph::EdgeMap<int> weight(graph);
deba@869: 
deba@869:     istringstream lgfs(lgf[i]);
deba@869:     graphReader(graph, lgfs).
deba@869:       edgeMap("weight", weight).run();
deba@869: 
deba@869:     bool perfect_with_loops;
deba@869:     {
deba@869:       MaxFractionalMatching<SmartGraph> mfm(graph, true);
deba@869:       mfm.run();
deba@869:       checkFractionalMatching(graph, mfm, true);
deba@869:       perfect_with_loops = mfm.matchingSize() == countNodes(graph);
deba@869:     }
deba@869: 
deba@869:     bool perfect_without_loops;
deba@869:     {
deba@869:       MaxFractionalMatching<SmartGraph> mfm(graph, false);
deba@869:       mfm.run();
deba@869:       checkFractionalMatching(graph, mfm, false);
deba@869:       perfect_without_loops = mfm.matchingSize() == countNodes(graph);
deba@869:     }
deba@869: 
deba@869:     {
deba@869:       MaxFractionalMatching<SmartGraph> mfm(graph, true);
deba@869:       bool result = mfm.runPerfect();
deba@869:       checkPerfectFractionalMatching(graph, mfm, result, true);
deba@869:       check(result == perfect_with_loops, "Wrong perfect matching");
deba@869:     }
deba@869: 
deba@869:     {
deba@869:       MaxFractionalMatching<SmartGraph> mfm(graph, false);
deba@869:       bool result = mfm.runPerfect();
deba@869:       checkPerfectFractionalMatching(graph, mfm, result, false);
deba@869:       check(result == perfect_without_loops, "Wrong perfect matching");
deba@869:     }
deba@869: 
deba@869:     {
deba@869:       MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, true);
deba@869:       mwfm.run();
deba@869:       checkWeightedFractionalMatching(graph, weight, mwfm, true);
deba@869:     }
deba@869: 
deba@869:     {
deba@869:       MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, false);
deba@869:       mwfm.run();
deba@869:       checkWeightedFractionalMatching(graph, weight, mwfm, false);
deba@869:     }
deba@869: 
deba@869:     {
deba@869:       MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight,
deba@869:                                                              true);
deba@869:       bool perfect = mwpfm.run();
deba@869:       check(perfect == (mwpfm.matchingSize() == countNodes(graph)),
deba@869:             "Perfect matching found");
deba@869:       check(perfect == perfect_with_loops, "Wrong perfect matching");
deba@869: 
deba@869:       if (perfect) {
deba@869:         checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, true);
deba@869:       }
deba@869:     }
deba@869: 
deba@869:     {
deba@869:       MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight,
deba@869:                                                              false);
deba@869:       bool perfect = mwpfm.run();
deba@869:       check(perfect == (mwpfm.matchingSize() == countNodes(graph)),
deba@869:             "Perfect matching found");
deba@869:       check(perfect == perfect_without_loops, "Wrong perfect matching");
deba@869: 
deba@869:       if (perfect) {
deba@869:         checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, false);
deba@869:       }
deba@869:     }
deba@869: 
deba@869:   }
deba@869: 
deba@869:   return 0;
deba@869: }