/* -*- 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;

}