/* -*- C++ -*-

  *

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

  *

  * Copyright (C) 2003-2007

  * 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 <cmath>

 #include <cstdlib>

 #include "test_tools.h"

 #include <lemon/smart_graph.h>

 #include <lemon/max_matching.h>

 #include <lemon/graph_reader.h>

 UGRAPH_TYPEDEFS(SmartUGraph);

 using namespace std;

 using namespace lemon;

 const int lgfn = 3;

 const std::string lgf[lgfn] = {   

   "@nodeset\n"

   "label\n"

   "0\n"

   "1\n"

   "2\n"

   "3\n"

   "4\n"

   "5\n"

   "6\n"

   "7\n"

   "@uedgeset\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"

   "@end\n",

   "@nodeset\n"

   "label\n"

   "0\n"

   "1\n"

   "2\n"

   "3\n"

   "4\n"

   "5\n"

   "6\n"

   "7\n"

   "@uedgeset\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"

   "@end\n",

   "@nodeset\n"

   "label\n"

   "0\n"

   "1\n"

   "2\n"

   "3\n"

   "4\n"

   "5\n"

   "6\n"

   "7\n"

   "@uedgeset\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"

   "@end\n"

 };

 void checkMatching(const SmartUGraph& ugraph,

 		   const SmartUGraph::UEdgeMap<int>& weight,

 		   const MaxWeightedMatching<SmartUGraph>& mwm) {

   for (SmartUGraph::UEdgeIt e(ugraph); e != INVALID; ++e) {

     if (ugraph.source(e) == ugraph.target(e)) continue;

     int rw = 

       mwm.nodeValue(ugraph.source(e)) + mwm.nodeValue(ugraph.target(e));

     for (int i = 0; i < mwm.blossomNum(); ++i) {

       bool s = false, t = false;

       for (MaxWeightedMatching<SmartUGraph>::BlossomIt n(mwm, i); 

 	   n != INVALID; ++n) {

 	if (ugraph.source(e) == n) s = true;

 	if (ugraph.target(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 (SmartUGraph::NodeIt n(ugraph); n != INVALID; ++n) {

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

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

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

       SmartUGraph::Node o = ugraph.target(mwm.matching(n));

       check(mwm.mate(n) == o, "Invalid matching");

       check(mwm.matching(n) == ugraph.oppositeEdge(mwm.matching(o)), 

 	    "Invalid matching");

     } else {

       check(mwm.mate(n) == INVALID, "Invalid matching");

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

     }

   }

   int dv = 0;

   for (SmartUGraph::NodeIt n(ugraph); 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 checkPerfectMatching(const SmartUGraph& ugraph,

 			  const SmartUGraph::UEdgeMap<int>& weight,

 			  const MaxWeightedPerfectMatching<SmartUGraph>& mwpm) {

   for (SmartUGraph::UEdgeIt e(ugraph); e != INVALID; ++e) {

     if (ugraph.source(e) == ugraph.target(e)) continue;

     int rw = 

       mwpm.nodeValue(ugraph.source(e)) + mwpm.nodeValue(ugraph.target(e));

     for (int i = 0; i < mwpm.blossomNum(); ++i) {

       bool s = false, t = false;

       for (MaxWeightedPerfectMatching<SmartUGraph>::BlossomIt n(mwpm, i); 

 	   n != INVALID; ++n) {

 	if (ugraph.source(e) == n) s = true;

 	if (ugraph.target(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 (SmartUGraph::NodeIt n(ugraph); n != INVALID; ++n) {

     check(mwpm.matching(n) != INVALID, "Non perfect");

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

     SmartUGraph::Node o = ugraph.target(mwpm.matching(n));

     check(mwpm.mate(n) == o, "Invalid matching");

     check(mwpm.matching(n) == ugraph.oppositeEdge(mwpm.matching(o)), 

 	  "Invalid matching");

   }

   int dv = 0;

   for (SmartUGraph::NodeIt n(ugraph); 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) {

     SmartUGraph ugraph;

     SmartUGraph::UEdgeMap<int> weight(ugraph);

     istringstream lgfs(lgf[i]);

     UGraphReader<SmartUGraph>(lgfs, ugraph).

       readUEdgeMap("weight", weight).run();

     MaxWeightedMatching<SmartUGraph> mwm(ugraph, weight);

     mwm.run();

     checkMatching(ugraph, weight, mwm);

     MaxMatching<SmartUGraph> mm(ugraph);

     mm.run();

     MaxWeightedPerfectMatching<SmartUGraph> mwpm(ugraph, weight);

     bool perfect = mwpm.run();

     check(perfect == (mm.size() * 2 == countNodes(ugraph)), 

 	  "Perfect matching found");

     if (perfect) {

       checkPerfectMatching(ugraph, weight, mwpm);

     }

   }

   return 0;

 }