/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2008

 * 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 <lemon/math.h>

#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;

}