1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2006 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_BIPARTITE_MATCHING |
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20 | #define LEMON_BIPARTITE_MATCHING |
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21 | |
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22 | #include <lemon/bpugraph_adaptor.h> |
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23 | #include <lemon/bfs.h> |
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24 | |
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25 | #include <iostream> |
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26 | |
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27 | ///\ingroup matching |
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28 | ///\file |
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29 | ///\brief Maximum matching algorithms in bipartite graphs. |
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30 | |
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31 | namespace lemon { |
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32 | |
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33 | /// \ingroup matching |
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34 | /// |
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35 | /// \brief Bipartite Max Cardinality Matching algorithm |
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36 | /// |
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37 | /// Bipartite Max Cardinality Matching algorithm. This class implements |
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38 | /// the Hopcroft-Karp algorithm wich has \f$ O(e\sqrt{n}) \f$ time |
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39 | /// complexity. |
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40 | template <typename BpUGraph> |
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41 | class MaxBipartiteMatching { |
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42 | protected: |
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43 | |
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44 | typedef BpUGraph Graph; |
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45 | |
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46 | typedef typename Graph::Node Node; |
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47 | typedef typename Graph::ANodeIt ANodeIt; |
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48 | typedef typename Graph::BNodeIt BNodeIt; |
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49 | typedef typename Graph::UEdge UEdge; |
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50 | typedef typename Graph::UEdgeIt UEdgeIt; |
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51 | typedef typename Graph::IncEdgeIt IncEdgeIt; |
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52 | |
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53 | typedef typename BpUGraph::template ANodeMap<UEdge> ANodeMatchingMap; |
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54 | typedef typename BpUGraph::template BNodeMap<UEdge> BNodeMatchingMap; |
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55 | |
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56 | |
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57 | public: |
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58 | |
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59 | /// \brief Constructor. |
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60 | /// |
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61 | /// Constructor of the algorithm. |
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62 | MaxBipartiteMatching(const BpUGraph& _graph) |
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63 | : anode_matching(_graph), bnode_matching(_graph), graph(&_graph) {} |
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64 | |
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65 | /// \name Execution control |
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66 | /// The simplest way to execute the algorithm is to use |
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67 | /// one of the member functions called \c run(). |
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68 | /// \n |
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69 | /// If you need more control on the execution, |
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70 | /// first you must call \ref init() or one alternative for it. |
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71 | /// Finally \ref start() will perform the matching computation or |
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72 | /// with step-by-step execution you can augment the solution. |
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73 | |
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74 | /// @{ |
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75 | |
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76 | /// \brief Initalize the data structures. |
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77 | /// |
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78 | /// It initalizes the data structures and creates an empty matching. |
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79 | void init() { |
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80 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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81 | anode_matching[it] = INVALID; |
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82 | } |
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83 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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84 | bnode_matching[it] = INVALID; |
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85 | } |
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86 | matching_value = 0; |
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87 | } |
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88 | |
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89 | /// \brief Initalize the data structures. |
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90 | /// |
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91 | /// It initalizes the data structures and creates a greedy |
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92 | /// matching. From this matching sometimes it is faster to get |
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93 | /// the matching than from the initial empty matching. |
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94 | void greedyInit() { |
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95 | matching_value = 0; |
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96 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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97 | bnode_matching[it] = INVALID; |
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98 | } |
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99 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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100 | anode_matching[it] = INVALID; |
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101 | for (IncEdgeIt jt(*graph, it); jt != INVALID; ++jt) { |
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102 | if (bnode_matching[graph->bNode(jt)] == INVALID) { |
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103 | anode_matching[it] = jt; |
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104 | bnode_matching[graph->bNode(jt)] = jt; |
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105 | ++matching_value; |
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106 | break; |
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107 | } |
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108 | } |
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109 | } |
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110 | } |
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111 | |
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112 | /// \brief Initalize the data structures with an initial matching. |
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113 | /// |
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114 | /// It initalizes the data structures with an initial matching. |
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115 | template <typename MatchingMap> |
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116 | void matchingInit(const MatchingMap& matching) { |
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117 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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118 | anode_matching[it] = INVALID; |
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119 | } |
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120 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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121 | bnode_matching[it] = INVALID; |
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122 | } |
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123 | matching_value = 0; |
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124 | for (UEdgeIt it(*graph); it != INVALID; ++it) { |
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125 | if (matching[it]) { |
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126 | ++matching_value; |
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127 | anode_matching[graph->aNode(it)] = it; |
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128 | bnode_matching[graph->bNode(it)] = it; |
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129 | } |
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130 | } |
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131 | } |
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132 | |
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133 | /// \brief Initalize the data structures with an initial matching. |
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134 | /// |
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135 | /// It initalizes the data structures with an initial matching. |
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136 | /// \return %True when the given map contains really a matching. |
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137 | template <typename MatchingMap> |
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138 | void checkedMatchingInit(const MatchingMap& matching) { |
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139 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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140 | anode_matching[it] = INVALID; |
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141 | } |
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142 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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143 | bnode_matching[it] = INVALID; |
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144 | } |
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145 | matching_value = 0; |
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146 | for (UEdgeIt it(*graph); it != INVALID; ++it) { |
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147 | if (matching[it]) { |
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148 | ++matching_value; |
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149 | if (anode_matching[graph->aNode(it)] != INVALID) { |
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150 | return false; |
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151 | } |
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152 | anode_matching[graph->aNode(it)] = it; |
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153 | if (bnode_matching[graph->aNode(it)] != INVALID) { |
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154 | return false; |
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155 | } |
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156 | bnode_matching[graph->bNode(it)] = it; |
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157 | } |
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158 | } |
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159 | return false; |
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160 | } |
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161 | |
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162 | /// \brief An augmenting phase of the Hopcroft-Karp algorithm |
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163 | /// |
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164 | /// It runs an augmenting phase of the Hopcroft-Karp |
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165 | /// algorithm. The phase finds maximum count of edge disjoint |
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166 | /// augmenting paths and augments on these paths. The algorithm |
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167 | /// consists at most of \f$ O(\sqrt{n}) \f$ phase and one phase is |
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168 | /// \f$ O(e) \f$ long. |
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169 | bool augment() { |
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170 | |
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171 | typename Graph::template ANodeMap<bool> areached(*graph, false); |
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172 | typename Graph::template BNodeMap<bool> breached(*graph, false); |
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173 | |
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174 | typename Graph::template BNodeMap<UEdge> bpred(*graph, INVALID); |
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175 | |
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176 | std::vector<Node> queue, bqueue; |
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177 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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178 | if (anode_matching[it] == INVALID) { |
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179 | queue.push_back(it); |
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180 | areached[it] = true; |
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181 | } |
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182 | } |
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183 | |
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184 | bool success = false; |
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185 | |
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186 | while (!success && !queue.empty()) { |
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187 | std::vector<Node> newqueue; |
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188 | for (int i = 0; i < (int)queue.size(); ++i) { |
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189 | Node anode = queue[i]; |
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190 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
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191 | Node bnode = graph->bNode(jt); |
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192 | if (breached[bnode]) continue; |
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193 | breached[bnode] = true; |
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194 | bpred[bnode] = jt; |
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195 | if (bnode_matching[bnode] == INVALID) { |
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196 | bqueue.push_back(bnode); |
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197 | success = true; |
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198 | } else { |
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199 | Node newanode = graph->aNode(bnode_matching[bnode]); |
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200 | if (!areached[newanode]) { |
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201 | areached[newanode] = true; |
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202 | newqueue.push_back(newanode); |
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203 | } |
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204 | } |
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205 | } |
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206 | } |
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207 | queue.swap(newqueue); |
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208 | } |
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209 | |
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210 | if (success) { |
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211 | |
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212 | typename Graph::template ANodeMap<bool> aused(*graph, false); |
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213 | |
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214 | for (int i = 0; i < (int)bqueue.size(); ++i) { |
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215 | Node bnode = bqueue[i]; |
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216 | |
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217 | bool used = false; |
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218 | |
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219 | while (bnode != INVALID) { |
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220 | UEdge uedge = bpred[bnode]; |
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221 | Node anode = graph->aNode(uedge); |
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222 | |
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223 | if (aused[anode]) { |
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224 | used = true; |
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225 | break; |
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226 | } |
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227 | |
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228 | bnode = anode_matching[anode] != INVALID ? |
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229 | graph->bNode(anode_matching[anode]) : INVALID; |
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230 | |
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231 | } |
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232 | |
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233 | if (used) continue; |
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234 | |
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235 | bnode = bqueue[i]; |
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236 | while (bnode != INVALID) { |
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237 | UEdge uedge = bpred[bnode]; |
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238 | Node anode = graph->aNode(uedge); |
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239 | |
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240 | bnode_matching[bnode] = uedge; |
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241 | |
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242 | bnode = anode_matching[anode] != INVALID ? |
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243 | graph->bNode(anode_matching[anode]) : INVALID; |
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244 | |
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245 | anode_matching[anode] = uedge; |
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246 | |
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247 | aused[anode] = true; |
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248 | } |
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249 | ++matching_value; |
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250 | |
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251 | } |
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252 | } |
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253 | return success; |
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254 | } |
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255 | |
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256 | /// \brief An augmenting phase of the Ford-Fulkerson algorithm |
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257 | /// |
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258 | /// It runs an augmenting phase of the Ford-Fulkerson |
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259 | /// algorithm. The phase finds only one augmenting path and |
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260 | /// augments only on this paths. The algorithm consists at most |
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261 | /// of \f$ O(n) \f$ simple phase and one phase is at most |
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262 | /// \f$ O(e) \f$ long. |
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263 | bool simpleAugment() { |
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264 | |
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265 | typename Graph::template ANodeMap<bool> areached(*graph, false); |
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266 | typename Graph::template BNodeMap<bool> breached(*graph, false); |
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267 | |
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268 | typename Graph::template BNodeMap<UEdge> bpred(*graph, INVALID); |
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269 | |
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270 | std::vector<Node> queue; |
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271 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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272 | if (anode_matching[it] == INVALID) { |
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273 | queue.push_back(it); |
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274 | areached[it] = true; |
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275 | } |
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276 | } |
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277 | |
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278 | while (!queue.empty()) { |
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279 | std::vector<Node> newqueue; |
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280 | for (int i = 0; i < (int)queue.size(); ++i) { |
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281 | Node anode = queue[i]; |
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282 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
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283 | Node bnode = graph->bNode(jt); |
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284 | if (breached[bnode]) continue; |
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285 | breached[bnode] = true; |
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286 | bpred[bnode] = jt; |
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287 | if (bnode_matching[bnode] == INVALID) { |
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288 | while (bnode != INVALID) { |
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289 | UEdge uedge = bpred[bnode]; |
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290 | anode = graph->aNode(uedge); |
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291 | |
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292 | bnode_matching[bnode] = uedge; |
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293 | |
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294 | bnode = anode_matching[anode] != INVALID ? |
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295 | graph->bNode(anode_matching[anode]) : INVALID; |
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296 | |
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297 | anode_matching[anode] = uedge; |
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298 | |
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299 | } |
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300 | ++matching_value; |
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301 | return true; |
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302 | } else { |
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303 | Node newanode = graph->aNode(bnode_matching[bnode]); |
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304 | if (!areached[newanode]) { |
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305 | areached[newanode] = true; |
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306 | newqueue.push_back(newanode); |
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307 | } |
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308 | } |
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309 | } |
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310 | } |
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311 | queue.swap(newqueue); |
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312 | } |
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313 | |
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314 | return false; |
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315 | } |
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316 | |
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317 | /// \brief Starts the algorithm. |
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318 | /// |
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319 | /// Starts the algorithm. It runs augmenting phases until the optimal |
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320 | /// solution reached. |
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321 | void start() { |
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322 | while (augment()) {} |
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323 | } |
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324 | |
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325 | /// \brief Runs the algorithm. |
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326 | /// |
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327 | /// It just initalize the algorithm and then start it. |
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328 | void run() { |
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329 | init(); |
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330 | start(); |
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331 | } |
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332 | |
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333 | /// @} |
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334 | |
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335 | /// \name Query Functions |
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336 | /// The result of the %Matching algorithm can be obtained using these |
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337 | /// functions.\n |
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338 | /// Before the use of these functions, |
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339 | /// either run() or start() must be called. |
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340 | |
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341 | ///@{ |
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342 | |
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343 | /// \brief Returns an minimum covering of the nodes. |
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344 | /// |
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345 | /// The minimum covering set problem is the dual solution of the |
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346 | /// maximum bipartite matching. It provides an solution for this |
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347 | /// problem what is proof of the optimality of the matching. |
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348 | /// \return The size of the cover set. |
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349 | template <typename CoverMap> |
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350 | int coverSet(CoverMap& covering) { |
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351 | |
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352 | typename Graph::template ANodeMap<bool> areached(*graph, false); |
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353 | typename Graph::template BNodeMap<bool> breached(*graph, false); |
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354 | |
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355 | std::vector<Node> queue; |
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356 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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357 | if (anode_matching[it] == INVALID) { |
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358 | queue.push_back(it); |
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359 | } |
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360 | } |
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361 | |
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362 | while (!queue.empty()) { |
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363 | std::vector<Node> newqueue; |
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364 | for (int i = 0; i < (int)queue.size(); ++i) { |
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365 | Node anode = queue[i]; |
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366 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
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367 | Node bnode = graph->bNode(jt); |
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368 | if (breached[bnode]) continue; |
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369 | breached[bnode] = true; |
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370 | if (bnode_matching[bnode] != INVALID) { |
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371 | Node newanode = graph->aNode(bnode_matching[bnode]); |
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372 | if (!areached[newanode]) { |
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373 | areached[newanode] = true; |
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374 | newqueue.push_back(newanode); |
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375 | } |
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376 | } |
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377 | } |
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378 | } |
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379 | queue.swap(newqueue); |
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380 | } |
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381 | |
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382 | int size = 0; |
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383 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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384 | covering[it] = !areached[it] && anode_matching[it] != INVALID; |
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385 | if (!areached[it] && anode_matching[it] != INVALID) { |
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386 | ++size; |
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387 | } |
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388 | } |
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389 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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390 | covering[it] = breached[it]; |
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391 | if (breached[it]) { |
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392 | ++size; |
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393 | } |
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394 | } |
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395 | return size; |
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396 | } |
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397 | |
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398 | /// \brief Set true all matching uedge in the map. |
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399 | /// |
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400 | /// Set true all matching uedge in the map. It does not change the |
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401 | /// value mapped to the other uedges. |
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402 | /// \return The number of the matching edges. |
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403 | template <typename MatchingMap> |
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404 | int quickMatching(MatchingMap& matching) { |
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405 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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406 | if (anode_matching[it] != INVALID) { |
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407 | matching[anode_matching[it]] = true; |
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408 | } |
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409 | } |
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410 | return matching_value; |
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411 | } |
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412 | |
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413 | /// \brief Set true all matching uedge in the map and the others to false. |
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414 | /// |
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415 | /// Set true all matching uedge in the map and the others to false. |
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416 | /// \return The number of the matching edges. |
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417 | template <typename MatchingMap> |
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418 | int matching(MatchingMap& matching) { |
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419 | for (UEdgeIt it(*graph); it != INVALID; ++it) { |
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420 | matching[it] = it == anode_matching[graph->aNode(it)]; |
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421 | } |
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422 | return matching_value; |
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423 | } |
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424 | |
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425 | |
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426 | /// \brief Return true if the given uedge is in the matching. |
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427 | /// |
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428 | /// It returns true if the given uedge is in the matching. |
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429 | bool matchingEdge(const UEdge& edge) { |
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430 | return anode_matching[graph->aNode(edge)] == edge; |
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431 | } |
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432 | |
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433 | /// \brief Returns the matching edge from the node. |
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434 | /// |
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435 | /// Returns the matching edge from the node. If there is not such |
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436 | /// edge it gives back \c INVALID. |
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437 | UEdge matchingEdge(const Node& node) { |
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438 | if (graph->aNode(node)) { |
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439 | return anode_matching[node]; |
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440 | } else { |
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441 | return bnode_matching[node]; |
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442 | } |
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443 | } |
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444 | |
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445 | /// \brief Gives back the number of the matching edges. |
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446 | /// |
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447 | /// Gives back the number of the matching edges. |
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448 | int matchingValue() const { |
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449 | return matching_value; |
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450 | } |
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451 | |
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452 | /// @} |
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453 | |
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454 | private: |
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455 | |
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456 | ANodeMatchingMap anode_matching; |
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457 | BNodeMatchingMap bnode_matching; |
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458 | const Graph *graph; |
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459 | |
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460 | int matching_value; |
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461 | |
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462 | }; |
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463 | |
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464 | } |
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465 | |
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466 | #endif |
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