/* -*- 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/fractional_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 = 4;

 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",

   "@nodes\n"

   "label\n"

   "0\n"

   "@edges\n"

   "     label  weight\n"

   "0 0  0      100\n"

 };

 void checkMaxFractionalMatchingCompile()

 {

   typedef concepts::Graph Graph;

   typedef Graph::Node Node;

   typedef Graph::Edge Edge;

   Graph g;

   Node n;

   Edge e;

   MaxFractionalMatching<Graph> mat_test(g);

   const MaxFractionalMatching<Graph>&

     const_mat_test = mat_test;

   mat_test.init();

   mat_test.start();

   mat_test.start(true);

   mat_test.startPerfect();

   mat_test.startPerfect(true);

   mat_test.run();

   mat_test.run(true);

   mat_test.runPerfect();

   mat_test.runPerfect(true);

   const_mat_test.matchingSize();

   const_mat_test.matching(e);

   const_mat_test.matching(n);

   const MaxFractionalMatching<Graph>::MatchingMap& mmap =

     const_mat_test.matchingMap();

   e = mmap[n];

   const_mat_test.barrier(n);

 }

 void checkMaxWeightedFractionalMatchingCompile()

 {

   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);

   MaxWeightedFractionalMatching<Graph> mat_test(g, w);

   const MaxWeightedFractionalMatching<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 MaxWeightedFractionalMatching<Graph>::MatchingMap& mmap =

     const_mat_test.matchingMap();

   e = mmap[n];

   const_mat_test.dualValue();

   const_mat_test.nodeValue(n);

 }

 void checkMaxWeightedPerfectFractionalMatchingCompile()

 {

   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);

   MaxWeightedPerfectFractionalMatching<Graph> mat_test(g, w);

   const MaxWeightedPerfectFractionalMatching<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 MaxWeightedPerfectFractionalMatching<Graph>::MatchingMap& mmap =

     const_mat_test.matchingMap();

   e = mmap[n];

   const_mat_test.dualValue();

   const_mat_test.nodeValue(n);

 }

 void checkFractionalMatching(const SmartGraph& graph,

                              const MaxFractionalMatching<SmartGraph>& mfm,

                              bool allow_loops = true) {

   int pv = 0;

   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {

     int indeg = 0;

     for (InArcIt a(graph, n); a != INVALID; ++a) {

       if (mfm.matching(graph.source(a)) == a) {

         ++indeg;

       }

     }

     if (mfm.matching(n) != INVALID) {

       check(indeg == 1, "Invalid matching");

       ++pv;

     } else {

       check(indeg == 0, "Invalid matching");

     }

   }

   check(pv == mfm.matchingSize(), "Wrong matching size");

   for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {

     check((e == mfm.matching(graph.u(e)) ? 1 : 0) +

           (e == mfm.matching(graph.v(e)) ? 1 : 0) ==

           mfm.matching(e), "Invalid matching");

   }

   SmartGraph::NodeMap<bool> processed(graph, false);

   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {

     if (processed[n]) continue;

     processed[n] = true;

     if (mfm.matching(n) == INVALID) continue;

     int num = 1;

     Node v = graph.target(mfm.matching(n));

     while (v != n) {

       processed[v] = true;

       ++num;

       v = graph.target(mfm.matching(v));

     }

     check(num == 2 || num % 2 == 1, "Wrong cycle size");

     check(allow_loops || num != 1, "Wrong cycle size");

   }

   int anum = 0, bnum = 0;

   SmartGraph::NodeMap<bool> neighbours(graph, false);

   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {

     if (!mfm.barrier(n)) continue;

     ++anum;

     for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) {

       Node u = graph.source(a);

       if (!allow_loops && u == n) continue;

       if (!neighbours[u]) {

         neighbours[u] = true;

         ++bnum;

       }

     }

   }

   check(anum - bnum + mfm.matchingSize() == countNodes(graph),

         "Wrong barrier");

 }

 void checkPerfectFractionalMatching(const SmartGraph& graph,

                              const MaxFractionalMatching<SmartGraph>& mfm,

                              bool perfect, bool allow_loops = true) {

   if (perfect) {

     for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {

       int indeg = 0;

       for (InArcIt a(graph, n); a != INVALID; ++a) {

         if (mfm.matching(graph.source(a)) == a) {

           ++indeg;

         }

       }

       check(mfm.matching(n) != INVALID, "Invalid matching");

       check(indeg == 1, "Invalid matching");

     }

     for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {

       check((e == mfm.matching(graph.u(e)) ? 1 : 0) +

             (e == mfm.matching(graph.v(e)) ? 1 : 0) ==

             mfm.matching(e), "Invalid matching");

     }

   } else {

     int anum = 0, bnum = 0;

     SmartGraph::NodeMap<bool> neighbours(graph, false);

     for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {

       if (!mfm.barrier(n)) continue;

       ++anum;

       for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) {

         Node u = graph.source(a);

         if (!allow_loops && u == n) continue;

         if (!neighbours[u]) {

           neighbours[u] = true;

           ++bnum;

         }

       }

     }

     check(anum - bnum > 0, "Wrong barrier");

   }

 }

 void checkWeightedFractionalMatching(const SmartGraph& graph,

                    const SmartGraph::EdgeMap<int>& weight,

                    const MaxWeightedFractionalMatching<SmartGraph>& mwfm,

                    bool allow_loops = true) {

   for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {

     if (graph.u(e) == graph.v(e) && !allow_loops) continue;

     int rw = mwfm.nodeValue(graph.u(e)) + mwfm.nodeValue(graph.v(e))

       - weight[e] * mwfm.dualScale;

     check(rw >= 0, "Negative reduced weight");

     check(rw == 0 || !mwfm.matching(e),

           "Non-zero reduced weight on matching edge");

   }

   int pv = 0;

   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {

     int indeg = 0;

     for (InArcIt a(graph, n); a != INVALID; ++a) {

       if (mwfm.matching(graph.source(a)) == a) {

         ++indeg;

       }

     }

     check(indeg <= 1, "Invalid matching");

     if (mwfm.matching(n) != INVALID) {

       check(mwfm.nodeValue(n) >= 0, "Invalid node value");

       check(indeg == 1, "Invalid matching");

       pv += weight[mwfm.matching(n)];

       SmartGraph::Node o = graph.target(mwfm.matching(n));

     } else {

       check(mwfm.nodeValue(n) == 0, "Invalid matching");

       check(indeg == 0, "Invalid matching");

     }

   }

   for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {

     check((e == mwfm.matching(graph.u(e)) ? 1 : 0) +

           (e == mwfm.matching(graph.v(e)) ? 1 : 0) ==

           mwfm.matching(e), "Invalid matching");

   }

   int dv = 0;

   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {

     dv += mwfm.nodeValue(n);

   }

   check(pv * mwfm.dualScale == dv * 2, "Wrong duality");

   SmartGraph::NodeMap<bool> processed(graph, false);

   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {

     if (processed[n]) continue;

     processed[n] = true;

     if (mwfm.matching(n) == INVALID) continue;

     int num = 1;

     Node v = graph.target(mwfm.matching(n));

     while (v != n) {

       processed[v] = true;

       ++num;

       v = graph.target(mwfm.matching(v));

     }

     check(num == 2 || num % 2 == 1, "Wrong cycle size");

     check(allow_loops || num != 1, "Wrong cycle size");

   }

   return;

 }

 void checkWeightedPerfectFractionalMatching(const SmartGraph& graph,

                 const SmartGraph::EdgeMap<int>& weight,

                 const MaxWeightedPerfectFractionalMatching<SmartGraph>& mwpfm,

                 bool allow_loops = true) {

   for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {

     if (graph.u(e) == graph.v(e) && !allow_loops) continue;

     int rw = mwpfm.nodeValue(graph.u(e)) + mwpfm.nodeValue(graph.v(e))

       - weight[e] * mwpfm.dualScale;

     check(rw >= 0, "Negative reduced weight");

     check(rw == 0 || !mwpfm.matching(e),

           "Non-zero reduced weight on matching edge");

   }

   int pv = 0;

   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {

     int indeg = 0;

     for (InArcIt a(graph, n); a != INVALID; ++a) {

       if (mwpfm.matching(graph.source(a)) == a) {

         ++indeg;

       }

     }

     check(mwpfm.matching(n) != INVALID, "Invalid perfect matching");

     check(indeg == 1, "Invalid perfect matching");

     pv += weight[mwpfm.matching(n)];

     SmartGraph::Node o = graph.target(mwpfm.matching(n));

   }

   for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {

     check((e == mwpfm.matching(graph.u(e)) ? 1 : 0) +

           (e == mwpfm.matching(graph.v(e)) ? 1 : 0) ==

           mwpfm.matching(e), "Invalid matching");

   }

   int dv = 0;

   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {

     dv += mwpfm.nodeValue(n);

   }

   check(pv * mwpfm.dualScale == dv * 2, "Wrong duality");

   SmartGraph::NodeMap<bool> processed(graph, false);

   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {

     if (processed[n]) continue;

     processed[n] = true;

     if (mwpfm.matching(n) == INVALID) continue;

     int num = 1;

     Node v = graph.target(mwpfm.matching(n));

     while (v != n) {

       processed[v] = true;

       ++num;

       v = graph.target(mwpfm.matching(v));

     }

     check(num == 2 || num % 2 == 1, "Wrong cycle size");

     check(allow_loops || num != 1, "Wrong cycle size");

   }

   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_with_loops;

     {

       MaxFractionalMatching<SmartGraph> mfm(graph, true);

       mfm.run();

       checkFractionalMatching(graph, mfm, true);

       perfect_with_loops = mfm.matchingSize() == countNodes(graph);

     }

     bool perfect_without_loops;

     {

       MaxFractionalMatching<SmartGraph> mfm(graph, false);

       mfm.run();

       checkFractionalMatching(graph, mfm, false);

       perfect_without_loops = mfm.matchingSize() == countNodes(graph);

     }

     {

       MaxFractionalMatching<SmartGraph> mfm(graph, true);

       bool result = mfm.runPerfect();

       checkPerfectFractionalMatching(graph, mfm, result, true);

       check(result == perfect_with_loops, "Wrong perfect matching");

     }

     {

       MaxFractionalMatching<SmartGraph> mfm(graph, false);

       bool result = mfm.runPerfect();

       checkPerfectFractionalMatching(graph, mfm, result, false);

       check(result == perfect_without_loops, "Wrong perfect matching");

     }

     {

       MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, true);

       mwfm.run();

       checkWeightedFractionalMatching(graph, weight, mwfm, true);

     }

     {

       MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, false);

       mwfm.run();

       checkWeightedFractionalMatching(graph, weight, mwfm, false);

     }

     {

       MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight,

                                                              true);

       bool perfect = mwpfm.run();

       check(perfect == (mwpfm.matchingSize() == countNodes(graph)),

             "Perfect matching found");

       check(perfect == perfect_with_loops, "Wrong perfect matching");

       if (perfect) {

         checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, true);

       }

     }

     {

       MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight,

                                                              false);

       bool perfect = mwpfm.run();

       check(perfect == (mwpfm.matchingSize() == countNodes(graph)),

             "Perfect matching found");

       check(perfect == perfect_without_loops, "Wrong perfect matching");

       if (perfect) {

         checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, false);

       }

     }

   }

   return 0;

 }