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) 2003-2008 |
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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_KARP_H |
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20 #define LEMON_KARP_H |
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21 |
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22 /// \ingroup min_mean_cycle |
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23 /// |
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24 /// \file |
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25 /// \brief Karp's algorithm for finding a minimum mean cycle. |
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26 |
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27 #include <vector> |
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28 #include <limits> |
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29 #include <lemon/core.h> |
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30 #include <lemon/path.h> |
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31 #include <lemon/tolerance.h> |
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32 #include <lemon/connectivity.h> |
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33 |
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34 namespace lemon { |
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35 |
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36 /// \brief Default traits class of Karp algorithm. |
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37 /// |
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38 /// Default traits class of Karp algorithm. |
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39 /// \tparam GR The type of the digraph. |
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40 /// \tparam LEN The type of the length map. |
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41 /// It must conform to the \ref concepts::ReadMap "ReadMap" concept. |
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42 #ifdef DOXYGEN |
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43 template <typename GR, typename LEN> |
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44 #else |
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45 template <typename GR, typename LEN, |
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46 bool integer = std::numeric_limits<typename LEN::Value>::is_integer> |
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47 #endif |
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48 struct KarpDefaultTraits |
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49 { |
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50 /// The type of the digraph |
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51 typedef GR Digraph; |
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52 /// The type of the length map |
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53 typedef LEN LengthMap; |
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54 /// The type of the arc lengths |
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55 typedef typename LengthMap::Value Value; |
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56 |
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57 /// \brief The large value type used for internal computations |
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58 /// |
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59 /// The large value type used for internal computations. |
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60 /// It is \c long \c long if the \c Value type is integer, |
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61 /// otherwise it is \c double. |
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62 /// \c Value must be convertible to \c LargeValue. |
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63 typedef double LargeValue; |
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64 |
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65 /// The tolerance type used for internal computations |
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66 typedef lemon::Tolerance<LargeValue> Tolerance; |
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67 |
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68 /// \brief The path type of the found cycles |
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69 /// |
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70 /// The path type of the found cycles. |
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71 /// It must conform to the \ref lemon::concepts::Path "Path" concept |
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72 /// and it must have an \c addFront() function. |
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73 typedef lemon::Path<Digraph> Path; |
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74 }; |
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75 |
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76 // Default traits class for integer value types |
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77 template <typename GR, typename LEN> |
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78 struct KarpDefaultTraits<GR, LEN, true> |
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79 { |
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80 typedef GR Digraph; |
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81 typedef LEN LengthMap; |
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82 typedef typename LengthMap::Value Value; |
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83 #ifdef LEMON_HAVE_LONG_LONG |
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84 typedef long long LargeValue; |
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85 #else |
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86 typedef long LargeValue; |
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87 #endif |
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88 typedef lemon::Tolerance<LargeValue> Tolerance; |
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89 typedef lemon::Path<Digraph> Path; |
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90 }; |
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91 |
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92 |
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93 /// \addtogroup min_mean_cycle |
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94 /// @{ |
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95 |
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96 /// \brief Implementation of Karp's algorithm for finding a minimum |
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97 /// mean cycle. |
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98 /// |
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99 /// This class implements Karp's algorithm for finding a directed |
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100 /// cycle of minimum mean length (cost) in a digraph |
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101 /// \ref amo93networkflows, \ref dasdan98minmeancycle. |
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102 /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e). |
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103 /// |
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104 /// \tparam GR The type of the digraph the algorithm runs on. |
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105 /// \tparam LEN The type of the length map. The default |
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106 /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
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107 /// \tparam TR The traits class that defines various types used by the |
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108 /// algorithm. By default, it is \ref KarpDefaultTraits |
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109 /// "KarpDefaultTraits<GR, LEN>". |
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110 /// In most cases, this parameter should not be set directly, |
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111 /// consider to use the named template parameters instead. |
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112 #ifdef DOXYGEN |
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113 template <typename GR, typename LEN, typename TR> |
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114 #else |
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115 template < typename GR, |
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116 typename LEN = typename GR::template ArcMap<int>, |
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117 typename TR = KarpDefaultTraits<GR, LEN> > |
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118 #endif |
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119 class Karp |
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120 { |
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121 public: |
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122 |
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123 /// The type of the digraph |
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124 typedef typename TR::Digraph Digraph; |
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125 /// The type of the length map |
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126 typedef typename TR::LengthMap LengthMap; |
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127 /// The type of the arc lengths |
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128 typedef typename TR::Value Value; |
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129 |
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130 /// \brief The large value type |
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131 /// |
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132 /// The large value type used for internal computations. |
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133 /// By default, it is \c long \c long if the \c Value type is integer, |
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134 /// otherwise it is \c double. |
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135 typedef typename TR::LargeValue LargeValue; |
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136 |
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137 /// The tolerance type |
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138 typedef typename TR::Tolerance Tolerance; |
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139 |
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140 /// \brief The path type of the found cycles |
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141 /// |
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142 /// The path type of the found cycles. |
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143 /// Using the \ref KarpDefaultTraits "default traits class", |
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144 /// it is \ref lemon::Path "Path<Digraph>". |
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145 typedef typename TR::Path Path; |
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146 |
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147 /// The \ref KarpDefaultTraits "traits class" of the algorithm |
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148 typedef TR Traits; |
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149 |
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150 private: |
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151 |
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152 TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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153 |
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154 // Data sturcture for path data |
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155 struct PathData |
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156 { |
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157 LargeValue dist; |
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158 Arc pred; |
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159 PathData(LargeValue d, Arc p = INVALID) : |
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160 dist(d), pred(p) {} |
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161 }; |
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162 |
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163 typedef typename Digraph::template NodeMap<std::vector<PathData> > |
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164 PathDataNodeMap; |
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165 |
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166 private: |
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167 |
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168 // The digraph the algorithm runs on |
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169 const Digraph &_gr; |
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170 // The length of the arcs |
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171 const LengthMap &_length; |
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172 |
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173 // Data for storing the strongly connected components |
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174 int _comp_num; |
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175 typename Digraph::template NodeMap<int> _comp; |
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176 std::vector<std::vector<Node> > _comp_nodes; |
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177 std::vector<Node>* _nodes; |
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178 typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs; |
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179 |
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180 // Data for the found cycle |
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181 LargeValue _cycle_length; |
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182 int _cycle_size; |
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183 Node _cycle_node; |
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184 |
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185 Path *_cycle_path; |
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186 bool _local_path; |
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187 |
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188 // Node map for storing path data |
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189 PathDataNodeMap _data; |
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190 // The processed nodes in the last round |
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191 std::vector<Node> _process; |
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192 |
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193 Tolerance _tolerance; |
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194 |
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195 // Infinite constant |
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196 const LargeValue INF; |
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197 |
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198 public: |
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199 |
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200 /// \name Named Template Parameters |
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201 /// @{ |
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202 |
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203 template <typename T> |
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204 struct SetLargeValueTraits : public Traits { |
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205 typedef T LargeValue; |
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206 typedef lemon::Tolerance<T> Tolerance; |
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207 }; |
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208 |
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209 /// \brief \ref named-templ-param "Named parameter" for setting |
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210 /// \c LargeValue type. |
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211 /// |
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212 /// \ref named-templ-param "Named parameter" for setting \c LargeValue |
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213 /// type. It is used for internal computations in the algorithm. |
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214 template <typename T> |
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215 struct SetLargeValue |
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216 : public Karp<GR, LEN, SetLargeValueTraits<T> > { |
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217 typedef Karp<GR, LEN, SetLargeValueTraits<T> > Create; |
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218 }; |
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219 |
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220 template <typename T> |
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221 struct SetPathTraits : public Traits { |
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222 typedef T Path; |
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223 }; |
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224 |
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225 /// \brief \ref named-templ-param "Named parameter" for setting |
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226 /// \c %Path type. |
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227 /// |
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228 /// \ref named-templ-param "Named parameter" for setting the \c %Path |
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229 /// type of the found cycles. |
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230 /// It must conform to the \ref lemon::concepts::Path "Path" concept |
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231 /// and it must have an \c addFront() function. |
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232 template <typename T> |
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233 struct SetPath |
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234 : public Karp<GR, LEN, SetPathTraits<T> > { |
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235 typedef Karp<GR, LEN, SetPathTraits<T> > Create; |
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236 }; |
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237 |
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238 /// @} |
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239 |
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240 protected: |
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241 |
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242 Karp() {} |
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243 |
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244 public: |
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245 |
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246 /// \brief Constructor. |
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247 /// |
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248 /// The constructor of the class. |
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249 /// |
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250 /// \param digraph The digraph the algorithm runs on. |
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251 /// \param length The lengths (costs) of the arcs. |
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252 Karp( const Digraph &digraph, |
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253 const LengthMap &length ) : |
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254 _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph), |
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255 _cycle_length(0), _cycle_size(1), _cycle_node(INVALID), |
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256 _cycle_path(NULL), _local_path(false), _data(digraph), |
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257 INF(std::numeric_limits<LargeValue>::has_infinity ? |
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258 std::numeric_limits<LargeValue>::infinity() : |
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259 std::numeric_limits<LargeValue>::max()) |
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260 {} |
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261 |
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262 /// Destructor. |
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263 ~Karp() { |
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264 if (_local_path) delete _cycle_path; |
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265 } |
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266 |
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267 /// \brief Set the path structure for storing the found cycle. |
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268 /// |
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269 /// This function sets an external path structure for storing the |
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270 /// found cycle. |
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271 /// |
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272 /// If you don't call this function before calling \ref run() or |
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273 /// \ref findMinMean(), it will allocate a local \ref Path "path" |
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274 /// structure. The destuctor deallocates this automatically |
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275 /// allocated object, of course. |
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276 /// |
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277 /// \note The algorithm calls only the \ref lemon::Path::addFront() |
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278 /// "addFront()" function of the given path structure. |
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279 /// |
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280 /// \return <tt>(*this)</tt> |
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281 Karp& cycle(Path &path) { |
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282 if (_local_path) { |
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283 delete _cycle_path; |
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284 _local_path = false; |
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285 } |
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286 _cycle_path = &path; |
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287 return *this; |
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288 } |
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289 |
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290 /// \brief Set the tolerance used by the algorithm. |
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291 /// |
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292 /// This function sets the tolerance object used by the algorithm. |
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293 /// |
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294 /// \return <tt>(*this)</tt> |
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295 Karp& tolerance(const Tolerance& tolerance) { |
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296 _tolerance = tolerance; |
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297 return *this; |
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298 } |
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299 |
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300 /// \brief Return a const reference to the tolerance. |
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301 /// |
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302 /// This function returns a const reference to the tolerance object |
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303 /// used by the algorithm. |
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304 const Tolerance& tolerance() const { |
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305 return _tolerance; |
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306 } |
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307 |
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308 /// \name Execution control |
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309 /// The simplest way to execute the algorithm is to call the \ref run() |
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310 /// function.\n |
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311 /// If you only need the minimum mean length, you may call |
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312 /// \ref findMinMean(). |
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313 |
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314 /// @{ |
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315 |
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316 /// \brief Run the algorithm. |
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317 /// |
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318 /// This function runs the algorithm. |
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319 /// It can be called more than once (e.g. if the underlying digraph |
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320 /// and/or the arc lengths have been modified). |
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321 /// |
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322 /// \return \c true if a directed cycle exists in the digraph. |
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323 /// |
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324 /// \note <tt>mmc.run()</tt> is just a shortcut of the following code. |
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325 /// \code |
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326 /// return mmc.findMinMean() && mmc.findCycle(); |
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327 /// \endcode |
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328 bool run() { |
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329 return findMinMean() && findCycle(); |
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330 } |
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331 |
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332 /// \brief Find the minimum cycle mean. |
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333 /// |
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334 /// This function finds the minimum mean length of the directed |
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335 /// cycles in the digraph. |
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336 /// |
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337 /// \return \c true if a directed cycle exists in the digraph. |
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338 bool findMinMean() { |
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339 // Initialization and find strongly connected components |
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340 init(); |
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341 findComponents(); |
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342 |
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343 // Find the minimum cycle mean in the components |
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344 for (int comp = 0; comp < _comp_num; ++comp) { |
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345 if (!initComponent(comp)) continue; |
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346 processRounds(); |
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347 updateMinMean(); |
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348 } |
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349 return (_cycle_node != INVALID); |
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350 } |
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351 |
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352 /// \brief Find a minimum mean directed cycle. |
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353 /// |
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354 /// This function finds a directed cycle of minimum mean length |
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355 /// in the digraph using the data computed by findMinMean(). |
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356 /// |
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357 /// \return \c true if a directed cycle exists in the digraph. |
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358 /// |
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359 /// \pre \ref findMinMean() must be called before using this function. |
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360 bool findCycle() { |
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361 if (_cycle_node == INVALID) return false; |
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362 IntNodeMap reached(_gr, -1); |
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363 int r = _data[_cycle_node].size(); |
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364 Node u = _cycle_node; |
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365 while (reached[u] < 0) { |
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366 reached[u] = --r; |
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367 u = _gr.source(_data[u][r].pred); |
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368 } |
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369 r = reached[u]; |
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370 Arc e = _data[u][r].pred; |
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371 _cycle_path->addFront(e); |
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372 _cycle_length = _length[e]; |
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373 _cycle_size = 1; |
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374 Node v; |
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375 while ((v = _gr.source(e)) != u) { |
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376 e = _data[v][--r].pred; |
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377 _cycle_path->addFront(e); |
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378 _cycle_length += _length[e]; |
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379 ++_cycle_size; |
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380 } |
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381 return true; |
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382 } |
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383 |
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384 /// @} |
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385 |
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386 /// \name Query Functions |
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387 /// The results of the algorithm can be obtained using these |
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388 /// functions.\n |
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389 /// The algorithm should be executed before using them. |
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390 |
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391 /// @{ |
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392 |
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393 /// \brief Return the total length of the found cycle. |
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394 /// |
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395 /// This function returns the total length of the found cycle. |
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396 /// |
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397 /// \pre \ref run() or \ref findMinMean() must be called before |
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398 /// using this function. |
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399 Value cycleLength() const { |
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400 return static_cast<Value>(_cycle_length); |
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401 } |
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402 |
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403 /// \brief Return the number of arcs on the found cycle. |
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404 /// |
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405 /// This function returns the number of arcs on the found cycle. |
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406 /// |
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407 /// \pre \ref run() or \ref findMinMean() must be called before |
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408 /// using this function. |
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409 int cycleArcNum() const { |
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410 return _cycle_size; |
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411 } |
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412 |
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413 /// \brief Return the mean length of the found cycle. |
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414 /// |
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415 /// This function returns the mean length of the found cycle. |
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416 /// |
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417 /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the |
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418 /// following code. |
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419 /// \code |
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420 /// return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum(); |
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421 /// \endcode |
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422 /// |
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423 /// \pre \ref run() or \ref findMinMean() must be called before |
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424 /// using this function. |
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425 double cycleMean() const { |
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426 return static_cast<double>(_cycle_length) / _cycle_size; |
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427 } |
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428 |
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429 /// \brief Return the found cycle. |
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430 /// |
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431 /// This function returns a const reference to the path structure |
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432 /// storing the found cycle. |
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433 /// |
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434 /// \pre \ref run() or \ref findCycle() must be called before using |
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435 /// this function. |
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436 const Path& cycle() const { |
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437 return *_cycle_path; |
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438 } |
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439 |
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440 ///@} |
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441 |
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442 private: |
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443 |
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444 // Initialization |
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445 void init() { |
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446 if (!_cycle_path) { |
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447 _local_path = true; |
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448 _cycle_path = new Path; |
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449 } |
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450 _cycle_path->clear(); |
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451 _cycle_length = 0; |
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452 _cycle_size = 1; |
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453 _cycle_node = INVALID; |
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454 for (NodeIt u(_gr); u != INVALID; ++u) |
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455 _data[u].clear(); |
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456 } |
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457 |
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458 // Find strongly connected components and initialize _comp_nodes |
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459 // and _out_arcs |
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460 void findComponents() { |
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461 _comp_num = stronglyConnectedComponents(_gr, _comp); |
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462 _comp_nodes.resize(_comp_num); |
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463 if (_comp_num == 1) { |
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464 _comp_nodes[0].clear(); |
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465 for (NodeIt n(_gr); n != INVALID; ++n) { |
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466 _comp_nodes[0].push_back(n); |
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467 _out_arcs[n].clear(); |
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468 for (OutArcIt a(_gr, n); a != INVALID; ++a) { |
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469 _out_arcs[n].push_back(a); |
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470 } |
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471 } |
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472 } else { |
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473 for (int i = 0; i < _comp_num; ++i) |
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474 _comp_nodes[i].clear(); |
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475 for (NodeIt n(_gr); n != INVALID; ++n) { |
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476 int k = _comp[n]; |
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477 _comp_nodes[k].push_back(n); |
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478 _out_arcs[n].clear(); |
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479 for (OutArcIt a(_gr, n); a != INVALID; ++a) { |
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480 if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a); |
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481 } |
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482 } |
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483 } |
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484 } |
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485 |
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486 // Initialize path data for the current component |
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487 bool initComponent(int comp) { |
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488 _nodes = &(_comp_nodes[comp]); |
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489 int n = _nodes->size(); |
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490 if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) { |
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491 return false; |
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492 } |
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493 for (int i = 0; i < n; ++i) { |
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494 _data[(*_nodes)[i]].resize(n + 1, PathData(INF)); |
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495 } |
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496 return true; |
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497 } |
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498 |
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499 // Process all rounds of computing path data for the current component. |
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500 // _data[v][k] is the length of a shortest directed walk from the root |
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501 // node to node v containing exactly k arcs. |
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502 void processRounds() { |
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503 Node start = (*_nodes)[0]; |
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504 _data[start][0] = PathData(0); |
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505 _process.clear(); |
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506 _process.push_back(start); |
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507 |
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508 int k, n = _nodes->size(); |
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509 for (k = 1; k <= n && int(_process.size()) < n; ++k) { |
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510 processNextBuildRound(k); |
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511 } |
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512 for ( ; k <= n; ++k) { |
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513 processNextFullRound(k); |
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514 } |
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515 } |
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516 |
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517 // Process one round and rebuild _process |
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518 void processNextBuildRound(int k) { |
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519 std::vector<Node> next; |
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520 Node u, v; |
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521 Arc e; |
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522 LargeValue d; |
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523 for (int i = 0; i < int(_process.size()); ++i) { |
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524 u = _process[i]; |
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525 for (int j = 0; j < int(_out_arcs[u].size()); ++j) { |
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526 e = _out_arcs[u][j]; |
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527 v = _gr.target(e); |
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528 d = _data[u][k-1].dist + _length[e]; |
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529 if (_tolerance.less(d, _data[v][k].dist)) { |
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530 if (_data[v][k].dist == INF) next.push_back(v); |
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531 _data[v][k] = PathData(d, e); |
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532 } |
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533 } |
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534 } |
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535 _process.swap(next); |
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536 } |
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537 |
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538 // Process one round using _nodes instead of _process |
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539 void processNextFullRound(int k) { |
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540 Node u, v; |
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541 Arc e; |
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542 LargeValue d; |
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543 for (int i = 0; i < int(_nodes->size()); ++i) { |
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544 u = (*_nodes)[i]; |
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545 for (int j = 0; j < int(_out_arcs[u].size()); ++j) { |
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546 e = _out_arcs[u][j]; |
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547 v = _gr.target(e); |
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548 d = _data[u][k-1].dist + _length[e]; |
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549 if (_tolerance.less(d, _data[v][k].dist)) { |
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550 _data[v][k] = PathData(d, e); |
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551 } |
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552 } |
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553 } |
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554 } |
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555 |
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556 // Update the minimum cycle mean |
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557 void updateMinMean() { |
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558 int n = _nodes->size(); |
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559 for (int i = 0; i < n; ++i) { |
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560 Node u = (*_nodes)[i]; |
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561 if (_data[u][n].dist == INF) continue; |
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562 LargeValue length, max_length = 0; |
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563 int size, max_size = 1; |
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564 bool found_curr = false; |
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565 for (int k = 0; k < n; ++k) { |
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566 if (_data[u][k].dist == INF) continue; |
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567 length = _data[u][n].dist - _data[u][k].dist; |
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568 size = n - k; |
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569 if (!found_curr || length * max_size > max_length * size) { |
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570 found_curr = true; |
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571 max_length = length; |
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572 max_size = size; |
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573 } |
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574 } |
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575 if ( found_curr && (_cycle_node == INVALID || |
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576 max_length * _cycle_size < _cycle_length * max_size) ) { |
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577 _cycle_length = max_length; |
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578 _cycle_size = max_size; |
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579 _cycle_node = u; |
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580 } |
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581 } |
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582 } |
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583 |
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584 }; //class Karp |
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585 |
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586 ///@} |
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587 |
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588 } //namespace lemon |
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589 |
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590 #endif //LEMON_KARP_H |
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