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 | public: |
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241 | |
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242 | /// \brief Constructor. |
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243 | /// |
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244 | /// The constructor of the class. |
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245 | /// |
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246 | /// \param digraph The digraph the algorithm runs on. |
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247 | /// \param length The lengths (costs) of the arcs. |
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248 | Karp( const Digraph &digraph, |
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249 | const LengthMap &length ) : |
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250 | _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph), |
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251 | _cycle_length(0), _cycle_size(1), _cycle_node(INVALID), |
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252 | _cycle_path(NULL), _local_path(false), _data(digraph), |
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253 | INF(std::numeric_limits<LargeValue>::has_infinity ? |
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254 | std::numeric_limits<LargeValue>::infinity() : |
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255 | std::numeric_limits<LargeValue>::max()) |
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256 | {} |
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257 | |
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258 | /// Destructor. |
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259 | ~Karp() { |
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260 | if (_local_path) delete _cycle_path; |
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261 | } |
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262 | |
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263 | /// \brief Set the path structure for storing the found cycle. |
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264 | /// |
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265 | /// This function sets an external path structure for storing the |
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266 | /// found cycle. |
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267 | /// |
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268 | /// If you don't call this function before calling \ref run() or |
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269 | /// \ref findMinMean(), it will allocate a local \ref Path "path" |
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270 | /// structure. The destuctor deallocates this automatically |
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271 | /// allocated object, of course. |
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272 | /// |
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273 | /// \note The algorithm calls only the \ref lemon::Path::addFront() |
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274 | /// "addFront()" function of the given path structure. |
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275 | /// |
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276 | /// \return <tt>(*this)</tt> |
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277 | Karp& cycle(Path &path) { |
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278 | if (_local_path) { |
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279 | delete _cycle_path; |
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280 | _local_path = false; |
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281 | } |
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282 | _cycle_path = &path; |
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283 | return *this; |
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284 | } |
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285 | |
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286 | /// \brief Set the tolerance used by the algorithm. |
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287 | /// |
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288 | /// This function sets the tolerance object used by the algorithm. |
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289 | /// |
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290 | /// \return <tt>(*this)</tt> |
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291 | Karp& tolerance(const Tolerance& tolerance) { |
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292 | _tolerance = tolerance; |
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293 | return *this; |
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294 | } |
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295 | |
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296 | /// \brief Return a const reference to the tolerance. |
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297 | /// |
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298 | /// This function returns a const reference to the tolerance object |
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299 | /// used by the algorithm. |
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300 | const Tolerance& tolerance() const { |
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301 | return _tolerance; |
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302 | } |
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303 | |
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304 | /// \name Execution control |
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305 | /// The simplest way to execute the algorithm is to call the \ref run() |
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306 | /// function.\n |
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307 | /// If you only need the minimum mean length, you may call |
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308 | /// \ref findMinMean(). |
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309 | |
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310 | /// @{ |
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311 | |
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312 | /// \brief Run the algorithm. |
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313 | /// |
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314 | /// This function runs the algorithm. |
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315 | /// It can be called more than once (e.g. if the underlying digraph |
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316 | /// and/or the arc lengths have been modified). |
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317 | /// |
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318 | /// \return \c true if a directed cycle exists in the digraph. |
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319 | /// |
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320 | /// \note <tt>mmc.run()</tt> is just a shortcut of the following code. |
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321 | /// \code |
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322 | /// return mmc.findMinMean() && mmc.findCycle(); |
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323 | /// \endcode |
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324 | bool run() { |
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325 | return findMinMean() && findCycle(); |
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326 | } |
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327 | |
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328 | /// \brief Find the minimum cycle mean. |
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329 | /// |
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330 | /// This function finds the minimum mean length of the directed |
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331 | /// cycles in the digraph. |
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332 | /// |
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333 | /// \return \c true if a directed cycle exists in the digraph. |
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334 | bool findMinMean() { |
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335 | // Initialization and find strongly connected components |
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336 | init(); |
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337 | findComponents(); |
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338 | |
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339 | // Find the minimum cycle mean in the components |
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340 | for (int comp = 0; comp < _comp_num; ++comp) { |
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341 | if (!initComponent(comp)) continue; |
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342 | processRounds(); |
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343 | updateMinMean(); |
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344 | } |
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345 | return (_cycle_node != INVALID); |
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346 | } |
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347 | |
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348 | /// \brief Find a minimum mean directed cycle. |
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349 | /// |
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350 | /// This function finds a directed cycle of minimum mean length |
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351 | /// in the digraph using the data computed by findMinMean(). |
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352 | /// |
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353 | /// \return \c true if a directed cycle exists in the digraph. |
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354 | /// |
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355 | /// \pre \ref findMinMean() must be called before using this function. |
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356 | bool findCycle() { |
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357 | if (_cycle_node == INVALID) return false; |
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358 | IntNodeMap reached(_gr, -1); |
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359 | int r = _data[_cycle_node].size(); |
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360 | Node u = _cycle_node; |
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361 | while (reached[u] < 0) { |
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362 | reached[u] = --r; |
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363 | u = _gr.source(_data[u][r].pred); |
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364 | } |
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365 | r = reached[u]; |
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366 | Arc e = _data[u][r].pred; |
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367 | _cycle_path->addFront(e); |
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368 | _cycle_length = _length[e]; |
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369 | _cycle_size = 1; |
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370 | Node v; |
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371 | while ((v = _gr.source(e)) != u) { |
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372 | e = _data[v][--r].pred; |
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373 | _cycle_path->addFront(e); |
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374 | _cycle_length += _length[e]; |
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375 | ++_cycle_size; |
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376 | } |
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377 | return true; |
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378 | } |
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379 | |
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380 | /// @} |
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381 | |
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382 | /// \name Query Functions |
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383 | /// The results of the algorithm can be obtained using these |
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384 | /// functions.\n |
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385 | /// The algorithm should be executed before using them. |
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386 | |
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387 | /// @{ |
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388 | |
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389 | /// \brief Return the total length of the found cycle. |
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390 | /// |
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391 | /// This function returns the total length of the found cycle. |
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392 | /// |
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393 | /// \pre \ref run() or \ref findMinMean() must be called before |
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394 | /// using this function. |
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395 | LargeValue cycleLength() const { |
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396 | return _cycle_length; |
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397 | } |
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398 | |
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399 | /// \brief Return the number of arcs on the found cycle. |
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400 | /// |
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401 | /// This function returns the number of arcs on the found cycle. |
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402 | /// |
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403 | /// \pre \ref run() or \ref findMinMean() must be called before |
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404 | /// using this function. |
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405 | int cycleArcNum() const { |
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406 | return _cycle_size; |
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407 | } |
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408 | |
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409 | /// \brief Return the mean length of the found cycle. |
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410 | /// |
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411 | /// This function returns the mean length of the found cycle. |
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412 | /// |
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413 | /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the |
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414 | /// following code. |
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415 | /// \code |
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416 | /// return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum(); |
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417 | /// \endcode |
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418 | /// |
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419 | /// \pre \ref run() or \ref findMinMean() must be called before |
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420 | /// using this function. |
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421 | double cycleMean() const { |
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422 | return static_cast<double>(_cycle_length) / _cycle_size; |
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423 | } |
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424 | |
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425 | /// \brief Return the found cycle. |
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426 | /// |
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427 | /// This function returns a const reference to the path structure |
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428 | /// storing the found cycle. |
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429 | /// |
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430 | /// \pre \ref run() or \ref findCycle() must be called before using |
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431 | /// this function. |
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432 | const Path& cycle() const { |
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433 | return *_cycle_path; |
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434 | } |
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435 | |
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436 | ///@} |
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437 | |
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438 | private: |
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439 | |
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440 | // Initialization |
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441 | void init() { |
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442 | if (!_cycle_path) { |
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443 | _local_path = true; |
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444 | _cycle_path = new Path; |
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445 | } |
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446 | _cycle_path->clear(); |
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447 | _cycle_length = 0; |
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448 | _cycle_size = 1; |
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449 | _cycle_node = INVALID; |
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450 | for (NodeIt u(_gr); u != INVALID; ++u) |
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451 | _data[u].clear(); |
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452 | } |
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453 | |
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454 | // Find strongly connected components and initialize _comp_nodes |
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455 | // and _out_arcs |
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456 | void findComponents() { |
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457 | _comp_num = stronglyConnectedComponents(_gr, _comp); |
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458 | _comp_nodes.resize(_comp_num); |
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459 | if (_comp_num == 1) { |
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460 | _comp_nodes[0].clear(); |
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461 | for (NodeIt n(_gr); n != INVALID; ++n) { |
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462 | _comp_nodes[0].push_back(n); |
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463 | _out_arcs[n].clear(); |
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464 | for (OutArcIt a(_gr, n); a != INVALID; ++a) { |
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465 | _out_arcs[n].push_back(a); |
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466 | } |
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467 | } |
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468 | } else { |
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469 | for (int i = 0; i < _comp_num; ++i) |
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470 | _comp_nodes[i].clear(); |
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471 | for (NodeIt n(_gr); n != INVALID; ++n) { |
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472 | int k = _comp[n]; |
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473 | _comp_nodes[k].push_back(n); |
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474 | _out_arcs[n].clear(); |
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475 | for (OutArcIt a(_gr, n); a != INVALID; ++a) { |
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476 | if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a); |
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477 | } |
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478 | } |
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479 | } |
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480 | } |
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481 | |
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482 | // Initialize path data for the current component |
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483 | bool initComponent(int comp) { |
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484 | _nodes = &(_comp_nodes[comp]); |
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485 | int n = _nodes->size(); |
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486 | if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) { |
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487 | return false; |
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488 | } |
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489 | for (int i = 0; i < n; ++i) { |
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490 | _data[(*_nodes)[i]].resize(n + 1, PathData(INF)); |
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491 | } |
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492 | return true; |
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493 | } |
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494 | |
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495 | // Process all rounds of computing path data for the current component. |
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496 | // _data[v][k] is the length of a shortest directed walk from the root |
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497 | // node to node v containing exactly k arcs. |
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498 | void processRounds() { |
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499 | Node start = (*_nodes)[0]; |
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500 | _data[start][0] = PathData(0); |
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501 | _process.clear(); |
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502 | _process.push_back(start); |
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503 | |
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504 | int k, n = _nodes->size(); |
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505 | for (k = 1; k <= n && int(_process.size()) < n; ++k) { |
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506 | processNextBuildRound(k); |
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507 | } |
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508 | for ( ; k <= n; ++k) { |
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509 | processNextFullRound(k); |
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510 | } |
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511 | } |
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512 | |
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513 | // Process one round and rebuild _process |
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514 | void processNextBuildRound(int k) { |
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515 | std::vector<Node> next; |
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516 | Node u, v; |
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517 | Arc e; |
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518 | LargeValue d; |
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519 | for (int i = 0; i < int(_process.size()); ++i) { |
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520 | u = _process[i]; |
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521 | for (int j = 0; j < int(_out_arcs[u].size()); ++j) { |
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522 | e = _out_arcs[u][j]; |
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523 | v = _gr.target(e); |
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524 | d = _data[u][k-1].dist + _length[e]; |
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525 | if (_tolerance.less(d, _data[v][k].dist)) { |
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526 | if (_data[v][k].dist == INF) next.push_back(v); |
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527 | _data[v][k] = PathData(d, e); |
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528 | } |
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529 | } |
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530 | } |
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531 | _process.swap(next); |
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532 | } |
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533 | |
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534 | // Process one round using _nodes instead of _process |
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535 | void processNextFullRound(int k) { |
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536 | Node u, v; |
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537 | Arc e; |
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538 | LargeValue d; |
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539 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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540 | u = (*_nodes)[i]; |
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541 | for (int j = 0; j < int(_out_arcs[u].size()); ++j) { |
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542 | e = _out_arcs[u][j]; |
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543 | v = _gr.target(e); |
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544 | d = _data[u][k-1].dist + _length[e]; |
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545 | if (_tolerance.less(d, _data[v][k].dist)) { |
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546 | _data[v][k] = PathData(d, e); |
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547 | } |
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548 | } |
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549 | } |
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550 | } |
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551 | |
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552 | // Update the minimum cycle mean |
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553 | void updateMinMean() { |
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554 | int n = _nodes->size(); |
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555 | for (int i = 0; i < n; ++i) { |
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556 | Node u = (*_nodes)[i]; |
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557 | if (_data[u][n].dist == INF) continue; |
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558 | LargeValue length, max_length = 0; |
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559 | int size, max_size = 1; |
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560 | bool found_curr = false; |
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561 | for (int k = 0; k < n; ++k) { |
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562 | if (_data[u][k].dist == INF) continue; |
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563 | length = _data[u][n].dist - _data[u][k].dist; |
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564 | size = n - k; |
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565 | if (!found_curr || length * max_size > max_length * size) { |
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566 | found_curr = true; |
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567 | max_length = length; |
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568 | max_size = size; |
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569 | } |
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570 | } |
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571 | if ( found_curr && (_cycle_node == INVALID || |
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572 | max_length * _cycle_size < _cycle_length * max_size) ) { |
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573 | _cycle_length = max_length; |
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574 | _cycle_size = max_size; |
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575 | _cycle_node = u; |
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576 | } |
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577 | } |
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578 | } |
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579 | |
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580 | }; //class Karp |
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581 | |
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582 | ///@} |
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583 | |
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584 | } //namespace lemon |
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585 | |
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586 | #endif //LEMON_KARP_H |
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