/* -*- mode: C++; indent-tabs-mode: nil; -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library.

  *

  * Copyright (C) 2003-2009

  * 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/max_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();

     MaxMatching<SmartGraph> mm(graph);

     mm.run();

     checkMatching(graph, mm);

     MaxWeightedMatching<SmartGraph> mwm(graph, weight);

     mwm.run();

     checkWeightedMatching(graph, weight, mwm);

     MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);

     bool perfect = mwpm.run();

     check(perfect == (mm.matchingSize() * 2 == countNodes(graph)),

           "Perfect matching found");

     if (perfect) {

       checkWeightedPerfectMatching(graph, weight, mwpm);

     }

   }

   return 0;

 }