test/fractional_matching_test.cc
author Alpar Juttner <alpar@cs.elte.hu>
Mon, 03 May 2010 10:56:24 +0200
changeset 889 0bca98cbebbb
parent 872 41d7ac528c3a
child 999 00f8d9f9920d
permissions -rw-r--r--
Merge bugfix #368
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library.
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 *
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 * Copyright (C) 2003-2010
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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#include <iostream>
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#include <sstream>
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#include <vector>
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#include <queue>
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#include <cstdlib>
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#include <lemon/fractional_matching.h>
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#include <lemon/smart_graph.h>
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#include <lemon/concepts/graph.h>
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#include <lemon/concepts/maps.h>
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#include <lemon/lgf_reader.h>
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#include <lemon/math.h>
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#include "test_tools.h"
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using namespace std;
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using namespace lemon;
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GRAPH_TYPEDEFS(SmartGraph);
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const int lgfn = 4;
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const std::string lgf[lgfn] = {
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  "@nodes\n"
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  "label\n"
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  "0\n"
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  "1\n"
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  "2\n"
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  "3\n"
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  "4\n"
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  "5\n"
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  "6\n"
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  "7\n"
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  "@edges\n"
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  "     label  weight\n"
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  "7 4  0      984\n"
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  "0 7  1      73\n"
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  "7 1  2      204\n"
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  "2 3  3      583\n"
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  "2 7  4      565\n"
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  "2 1  5      582\n"
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  "0 4  6      551\n"
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  "2 5  7      385\n"
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  "1 5  8      561\n"
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  "5 3  9      484\n"
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  "7 5  10     904\n"
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  "3 6  11     47\n"
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  "7 6  12     888\n"
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  "3 0  13     747\n"
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  "6 1  14     310\n",
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  "@nodes\n"
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  "label\n"
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  "0\n"
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  "1\n"
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  "2\n"
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  "3\n"
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  "4\n"
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  "5\n"
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  "6\n"
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  "7\n"
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  "@edges\n"
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  "     label  weight\n"
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  "2 5  0      710\n"
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  "0 5  1      241\n"
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  "2 4  2      856\n"
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  "2 6  3      762\n"
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  "4 1  4      747\n"
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  "6 1  5      962\n"
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  "4 7  6      723\n"
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  "1 7  7      661\n"
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  "2 3  8      376\n"
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  "1 0  9      416\n"
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  "6 7  10     391\n",
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  "@nodes\n"
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  "label\n"
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  "0\n"
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  "1\n"
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  "2\n"
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  "3\n"
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  "4\n"
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  "5\n"
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  "6\n"
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  "7\n"
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  "@edges\n"
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  "     label  weight\n"
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  "6 2  0      553\n"
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  "0 7  1      653\n"
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  "6 3  2      22\n"
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  "4 7  3      846\n"
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  "7 2  4      981\n"
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  "7 6  5      250\n"
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  "5 2  6      539\n",
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  "@nodes\n"
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  "label\n"
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  "0\n"
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  "@edges\n"
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  "     label  weight\n"
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  "0 0  0      100\n"
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};
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void checkMaxFractionalMatchingCompile()
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{
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  typedef concepts::Graph Graph;
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  typedef Graph::Node Node;
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  typedef Graph::Edge Edge;
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  Graph g;
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  Node n;
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  Edge e;
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  MaxFractionalMatching<Graph> mat_test(g);
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  const MaxFractionalMatching<Graph>&
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    const_mat_test = mat_test;
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  mat_test.init();
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  mat_test.start();
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  mat_test.start(true);
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  mat_test.startPerfect();
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  mat_test.startPerfect(true);
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  mat_test.run();
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  mat_test.run(true);
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  mat_test.runPerfect();
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  mat_test.runPerfect(true);
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  const_mat_test.matchingSize();
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  const_mat_test.matching(e);
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  const_mat_test.matching(n);
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  const MaxFractionalMatching<Graph>::MatchingMap& mmap =
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    const_mat_test.matchingMap();
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  e = mmap[n];
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  const_mat_test.barrier(n);
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}
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void checkMaxWeightedFractionalMatchingCompile()
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{
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  typedef concepts::Graph Graph;
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  typedef Graph::Node Node;
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  typedef Graph::Edge Edge;
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  typedef Graph::EdgeMap<int> WeightMap;
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  Graph g;
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  Node n;
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  Edge e;
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  WeightMap w(g);
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  MaxWeightedFractionalMatching<Graph> mat_test(g, w);
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  const MaxWeightedFractionalMatching<Graph>&
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    const_mat_test = mat_test;
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  mat_test.init();
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  mat_test.start();
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  mat_test.run();
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  const_mat_test.matchingWeight();
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  const_mat_test.matchingSize();
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  const_mat_test.matching(e);
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  const_mat_test.matching(n);
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  const MaxWeightedFractionalMatching<Graph>::MatchingMap& mmap =
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    const_mat_test.matchingMap();
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  e = mmap[n];
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  const_mat_test.dualValue();
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  const_mat_test.nodeValue(n);
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}
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void checkMaxWeightedPerfectFractionalMatchingCompile()
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{
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  typedef concepts::Graph Graph;
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  typedef Graph::Node Node;
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  typedef Graph::Edge Edge;
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  typedef Graph::EdgeMap<int> WeightMap;
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  Graph g;
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  Node n;
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  Edge e;
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  WeightMap w(g);
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  MaxWeightedPerfectFractionalMatching<Graph> mat_test(g, w);
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  const MaxWeightedPerfectFractionalMatching<Graph>&
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    const_mat_test = mat_test;
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  mat_test.init();
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  mat_test.start();
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  mat_test.run();
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  const_mat_test.matchingWeight();
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  const_mat_test.matching(e);
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  const_mat_test.matching(n);
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  const MaxWeightedPerfectFractionalMatching<Graph>::MatchingMap& mmap =
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    const_mat_test.matchingMap();
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  e = mmap[n];
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  const_mat_test.dualValue();
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  const_mat_test.nodeValue(n);
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}
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void checkFractionalMatching(const SmartGraph& graph,
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                             const MaxFractionalMatching<SmartGraph>& mfm,
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                             bool allow_loops = true) {
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  int pv = 0;
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  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
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    int indeg = 0;
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    for (InArcIt a(graph, n); a != INVALID; ++a) {
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      if (mfm.matching(graph.source(a)) == a) {
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        ++indeg;
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      }
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    }
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    if (mfm.matching(n) != INVALID) {
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      check(indeg == 1, "Invalid matching");
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      ++pv;
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    } else {
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      check(indeg == 0, "Invalid matching");
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    }
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  }
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  check(pv == mfm.matchingSize(), "Wrong matching size");
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  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
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    check((e == mfm.matching(graph.u(e)) ? 1 : 0) +
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          (e == mfm.matching(graph.v(e)) ? 1 : 0) ==
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          mfm.matching(e), "Invalid matching");
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  }
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  SmartGraph::NodeMap<bool> processed(graph, false);
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  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
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    if (processed[n]) continue;
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    processed[n] = true;
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    if (mfm.matching(n) == INVALID) continue;
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    int num = 1;
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    Node v = graph.target(mfm.matching(n));
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    while (v != n) {
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      processed[v] = true;
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      ++num;
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      v = graph.target(mfm.matching(v));
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    }
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    check(num == 2 || num % 2 == 1, "Wrong cycle size");
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    check(allow_loops || num != 1, "Wrong cycle size");
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  }
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  int anum = 0, bnum = 0;
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  SmartGraph::NodeMap<bool> neighbours(graph, false);
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  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
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    if (!mfm.barrier(n)) continue;
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    ++anum;
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    for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) {
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      Node u = graph.source(a);
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      if (!allow_loops && u == n) continue;
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      if (!neighbours[u]) {
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        neighbours[u] = true;
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        ++bnum;
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      }
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    }
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  }
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  check(anum - bnum + mfm.matchingSize() == countNodes(graph),
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        "Wrong barrier");
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}
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void checkPerfectFractionalMatching(const SmartGraph& graph,
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                             const MaxFractionalMatching<SmartGraph>& mfm,
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                             bool perfect, bool allow_loops = true) {
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  if (perfect) {
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    for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
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      int indeg = 0;
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      for (InArcIt a(graph, n); a != INVALID; ++a) {
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        if (mfm.matching(graph.source(a)) == a) {
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          ++indeg;
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        }
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      }
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      check(mfm.matching(n) != INVALID, "Invalid matching");
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      check(indeg == 1, "Invalid matching");
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    }
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    for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
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      check((e == mfm.matching(graph.u(e)) ? 1 : 0) +
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            (e == mfm.matching(graph.v(e)) ? 1 : 0) ==
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            mfm.matching(e), "Invalid matching");
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    }
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  } else {
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    int anum = 0, bnum = 0;
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    SmartGraph::NodeMap<bool> neighbours(graph, false);
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    for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
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      if (!mfm.barrier(n)) continue;
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      ++anum;
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      for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) {
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        Node u = graph.source(a);
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        if (!allow_loops && u == n) continue;
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        if (!neighbours[u]) {
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          neighbours[u] = true;
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          ++bnum;
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        }
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      }
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    }
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    check(anum - bnum > 0, "Wrong barrier");
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  }
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}
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void checkWeightedFractionalMatching(const SmartGraph& graph,
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                   const SmartGraph::EdgeMap<int>& weight,
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                   const MaxWeightedFractionalMatching<SmartGraph>& mwfm,
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                   bool allow_loops = true) {
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  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
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    if (graph.u(e) == graph.v(e) && !allow_loops) continue;
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    int rw = mwfm.nodeValue(graph.u(e)) + mwfm.nodeValue(graph.v(e))
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      - weight[e] * mwfm.dualScale;
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    check(rw >= 0, "Negative reduced weight");
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    check(rw == 0 || !mwfm.matching(e),
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          "Non-zero reduced weight on matching edge");
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  }
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  int pv = 0;
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  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
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    int indeg = 0;
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    for (InArcIt a(graph, n); a != INVALID; ++a) {
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      if (mwfm.matching(graph.source(a)) == a) {
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        ++indeg;
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      }
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    }
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    check(indeg <= 1, "Invalid matching");
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    if (mwfm.matching(n) != INVALID) {
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      check(mwfm.nodeValue(n) >= 0, "Invalid node value");
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      check(indeg == 1, "Invalid matching");
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      pv += weight[mwfm.matching(n)];
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      SmartGraph::Node o = graph.target(mwfm.matching(n));
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    } else {
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      check(mwfm.nodeValue(n) == 0, "Invalid matching");
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      check(indeg == 0, "Invalid matching");
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    }
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  }
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  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
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    check((e == mwfm.matching(graph.u(e)) ? 1 : 0) +
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          (e == mwfm.matching(graph.v(e)) ? 1 : 0) ==
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          mwfm.matching(e), "Invalid matching");
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  }
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  int dv = 0;
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  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
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    dv += mwfm.nodeValue(n);
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  }
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  check(pv * mwfm.dualScale == dv * 2, "Wrong duality");
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  SmartGraph::NodeMap<bool> processed(graph, false);
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  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
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    if (processed[n]) continue;
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    processed[n] = true;
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    if (mwfm.matching(n) == INVALID) continue;
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    int num = 1;
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    Node v = graph.target(mwfm.matching(n));
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    while (v != n) {
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      processed[v] = true;
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      ++num;
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   374
      v = graph.target(mwfm.matching(v));
deba@869
   375
    }
deba@869
   376
    check(num == 2 || num % 2 == 1, "Wrong cycle size");
deba@869
   377
    check(allow_loops || num != 1, "Wrong cycle size");
deba@869
   378
  }
deba@869
   379
deba@869
   380
  return;
deba@869
   381
}
deba@869
   382
deba@869
   383
void checkWeightedPerfectFractionalMatching(const SmartGraph& graph,
deba@869
   384
                const SmartGraph::EdgeMap<int>& weight,
deba@869
   385
                const MaxWeightedPerfectFractionalMatching<SmartGraph>& mwpfm,
deba@869
   386
                bool allow_loops = true) {
deba@869
   387
  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
deba@869
   388
    if (graph.u(e) == graph.v(e) && !allow_loops) continue;
deba@869
   389
    int rw = mwpfm.nodeValue(graph.u(e)) + mwpfm.nodeValue(graph.v(e))
deba@869
   390
      - weight[e] * mwpfm.dualScale;
deba@869
   391
deba@869
   392
    check(rw >= 0, "Negative reduced weight");
deba@869
   393
    check(rw == 0 || !mwpfm.matching(e),
deba@869
   394
          "Non-zero reduced weight on matching edge");
deba@869
   395
  }
deba@869
   396
deba@869
   397
  int pv = 0;
deba@869
   398
  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@869
   399
    int indeg = 0;
deba@869
   400
    for (InArcIt a(graph, n); a != INVALID; ++a) {
deba@869
   401
      if (mwpfm.matching(graph.source(a)) == a) {
deba@869
   402
        ++indeg;
deba@869
   403
      }
deba@869
   404
    }
deba@869
   405
    check(mwpfm.matching(n) != INVALID, "Invalid perfect matching");
deba@869
   406
    check(indeg == 1, "Invalid perfect matching");
deba@869
   407
    pv += weight[mwpfm.matching(n)];
deba@869
   408
    SmartGraph::Node o = graph.target(mwpfm.matching(n));
deba@869
   409
  }
deba@869
   410
deba@872
   411
  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
deba@872
   412
    check((e == mwpfm.matching(graph.u(e)) ? 1 : 0) +
alpar@877
   413
          (e == mwpfm.matching(graph.v(e)) ? 1 : 0) ==
deba@872
   414
          mwpfm.matching(e), "Invalid matching");
deba@872
   415
  }
deba@872
   416
deba@869
   417
  int dv = 0;
deba@869
   418
  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@869
   419
    dv += mwpfm.nodeValue(n);
deba@869
   420
  }
deba@869
   421
deba@869
   422
  check(pv * mwpfm.dualScale == dv * 2, "Wrong duality");
deba@869
   423
deba@869
   424
  SmartGraph::NodeMap<bool> processed(graph, false);
deba@869
   425
  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@869
   426
    if (processed[n]) continue;
deba@869
   427
    processed[n] = true;
deba@869
   428
    if (mwpfm.matching(n) == INVALID) continue;
deba@869
   429
    int num = 1;
deba@869
   430
    Node v = graph.target(mwpfm.matching(n));
deba@869
   431
    while (v != n) {
deba@869
   432
      processed[v] = true;
deba@869
   433
      ++num;
deba@869
   434
      v = graph.target(mwpfm.matching(v));
deba@869
   435
    }
deba@869
   436
    check(num == 2 || num % 2 == 1, "Wrong cycle size");
deba@869
   437
    check(allow_loops || num != 1, "Wrong cycle size");
deba@869
   438
  }
deba@869
   439
deba@869
   440
  return;
deba@869
   441
}
deba@869
   442
deba@869
   443
deba@869
   444
int main() {
deba@869
   445
deba@869
   446
  for (int i = 0; i < lgfn; ++i) {
deba@869
   447
    SmartGraph graph;
deba@869
   448
    SmartGraph::EdgeMap<int> weight(graph);
deba@869
   449
deba@869
   450
    istringstream lgfs(lgf[i]);
deba@869
   451
    graphReader(graph, lgfs).
deba@869
   452
      edgeMap("weight", weight).run();
deba@869
   453
deba@869
   454
    bool perfect_with_loops;
deba@869
   455
    {
deba@869
   456
      MaxFractionalMatching<SmartGraph> mfm(graph, true);
deba@869
   457
      mfm.run();
deba@869
   458
      checkFractionalMatching(graph, mfm, true);
deba@869
   459
      perfect_with_loops = mfm.matchingSize() == countNodes(graph);
deba@869
   460
    }
deba@869
   461
deba@869
   462
    bool perfect_without_loops;
deba@869
   463
    {
deba@869
   464
      MaxFractionalMatching<SmartGraph> mfm(graph, false);
deba@869
   465
      mfm.run();
deba@869
   466
      checkFractionalMatching(graph, mfm, false);
deba@869
   467
      perfect_without_loops = mfm.matchingSize() == countNodes(graph);
deba@869
   468
    }
deba@869
   469
deba@869
   470
    {
deba@869
   471
      MaxFractionalMatching<SmartGraph> mfm(graph, true);
deba@869
   472
      bool result = mfm.runPerfect();
deba@869
   473
      checkPerfectFractionalMatching(graph, mfm, result, true);
deba@869
   474
      check(result == perfect_with_loops, "Wrong perfect matching");
deba@869
   475
    }
deba@869
   476
deba@869
   477
    {
deba@869
   478
      MaxFractionalMatching<SmartGraph> mfm(graph, false);
deba@869
   479
      bool result = mfm.runPerfect();
deba@869
   480
      checkPerfectFractionalMatching(graph, mfm, result, false);
deba@869
   481
      check(result == perfect_without_loops, "Wrong perfect matching");
deba@869
   482
    }
deba@869
   483
deba@869
   484
    {
deba@869
   485
      MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, true);
deba@869
   486
      mwfm.run();
deba@869
   487
      checkWeightedFractionalMatching(graph, weight, mwfm, true);
deba@869
   488
    }
deba@869
   489
deba@869
   490
    {
deba@869
   491
      MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, false);
deba@869
   492
      mwfm.run();
deba@869
   493
      checkWeightedFractionalMatching(graph, weight, mwfm, false);
deba@869
   494
    }
deba@869
   495
deba@869
   496
    {
deba@869
   497
      MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight,
deba@869
   498
                                                             true);
deba@869
   499
      bool perfect = mwpfm.run();
deba@869
   500
      check(perfect == (mwpfm.matchingSize() == countNodes(graph)),
deba@869
   501
            "Perfect matching found");
deba@869
   502
      check(perfect == perfect_with_loops, "Wrong perfect matching");
deba@869
   503
deba@869
   504
      if (perfect) {
deba@869
   505
        checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, true);
deba@869
   506
      }
deba@869
   507
    }
deba@869
   508
deba@869
   509
    {
deba@869
   510
      MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight,
deba@869
   511
                                                             false);
deba@869
   512
      bool perfect = mwpfm.run();
deba@869
   513
      check(perfect == (mwpfm.matchingSize() == countNodes(graph)),
deba@869
   514
            "Perfect matching found");
deba@869
   515
      check(perfect == perfect_without_loops, "Wrong perfect matching");
deba@869
   516
deba@869
   517
      if (perfect) {
deba@869
   518
        checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, false);
deba@869
   519
      }
deba@869
   520
    }
deba@869
   521
deba@869
   522
  }
deba@869
   523
deba@869
   524
  return 0;
deba@869
   525
}