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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_HARTMANN_ORLIN_H |
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20 #define LEMON_HARTMANN_ORLIN_H |
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21 |
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22 /// \ingroup shortest_path |
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23 /// |
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24 /// \file |
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25 /// \brief Hartmann-Orlin'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 HartmannOrlin algorithm. |
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37 /// |
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38 /// Default traits class of HartmannOrlin 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::Rea_data "Rea_data" 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 HartmannOrlinDefaultTraits |
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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 addBack() 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 HartmannOrlinDefaultTraits<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 shortest_path |
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94 /// @{ |
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95 |
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96 /// \brief Implementation of the Hartmann-Orlin algorithm for finding |
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97 /// a minimum mean cycle. |
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98 /// |
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99 /// This class implements the Hartmann-Orlin algorithm for finding |
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100 /// a directed cycle of minimum mean length (cost) in a digraph. |
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101 /// It is an improved version of \ref Karp "Karp's original algorithm", |
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102 /// it applies an efficient early termination scheme. |
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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 #ifdef DOXYGEN |
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108 template <typename GR, typename LEN, typename TR> |
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109 #else |
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110 template < typename GR, |
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111 typename LEN = typename GR::template ArcMap<int>, |
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112 typename TR = HartmannOrlinDefaultTraits<GR, LEN> > |
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113 #endif |
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114 class HartmannOrlin |
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115 { |
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116 public: |
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117 |
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118 /// The type of the digraph |
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119 typedef typename TR::Digraph Digraph; |
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120 /// The type of the length map |
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121 typedef typename TR::LengthMap LengthMap; |
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122 /// The type of the arc lengths |
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123 typedef typename TR::Value Value; |
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124 |
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125 /// \brief The large value type |
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126 /// |
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127 /// The large value type used for internal computations. |
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128 /// Using the \ref HartmannOrlinDefaultTraits "default traits class", |
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129 /// it is \c long \c long if the \c Value type is integer, |
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130 /// otherwise it is \c double. |
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131 typedef typename TR::LargeValue LargeValue; |
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132 |
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133 /// The tolerance type |
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134 typedef typename TR::Tolerance Tolerance; |
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135 |
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136 /// \brief The path type of the found cycles |
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137 /// |
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138 /// The path type of the found cycles. |
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139 /// Using the \ref HartmannOrlinDefaultTraits "default traits class", |
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140 /// it is \ref lemon::Path "Path<Digraph>". |
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141 typedef typename TR::Path Path; |
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142 |
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143 /// The \ref HartmannOrlinDefaultTraits "traits class" of the algorithm |
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144 typedef TR Traits; |
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145 |
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146 private: |
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147 |
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148 TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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149 |
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150 // Data sturcture for path data |
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151 struct PathData |
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152 { |
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153 bool found; |
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154 LargeValue dist; |
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155 Arc pred; |
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156 PathData(bool f = false, LargeValue d = 0, Arc p = INVALID) : |
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157 found(f), dist(d), pred(p) {} |
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158 }; |
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159 |
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160 typedef typename Digraph::template NodeMap<std::vector<PathData> > |
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161 PathDataNodeMap; |
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162 |
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163 private: |
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164 |
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165 // The digraph the algorithm runs on |
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166 const Digraph &_gr; |
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167 // The length of the arcs |
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168 const LengthMap &_length; |
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169 |
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170 // Data for storing the strongly connected components |
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171 int _comp_num; |
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172 typename Digraph::template NodeMap<int> _comp; |
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173 std::vector<std::vector<Node> > _comp_nodes; |
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174 std::vector<Node>* _nodes; |
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175 typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs; |
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176 |
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177 // Data for the found cycles |
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178 bool _curr_found, _best_found; |
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179 LargeValue _curr_length, _best_length; |
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180 int _curr_size, _best_size; |
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181 Node _curr_node, _best_node; |
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182 int _curr_level, _best_level; |
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183 |
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184 Path *_cycle_path; |
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185 bool _local_path; |
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186 |
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187 // Node map for storing path data |
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188 PathDataNodeMap _data; |
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189 // The processed nodes in the last round |
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190 std::vector<Node> _process; |
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191 |
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192 Tolerance _tolerance; |
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193 |
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194 public: |
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195 |
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196 /// \name Named Template Parameters |
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197 /// @{ |
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198 |
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199 template <typename T> |
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200 struct SetLargeValueTraits : public Traits { |
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201 typedef T LargeValue; |
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202 typedef lemon::Tolerance<T> Tolerance; |
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203 }; |
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204 |
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205 /// \brief \ref named-templ-param "Named parameter" for setting |
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206 /// \c LargeValue type. |
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207 /// |
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208 /// \ref named-templ-param "Named parameter" for setting \c LargeValue |
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209 /// type. It is used for internal computations in the algorithm. |
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210 template <typename T> |
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211 struct SetLargeValue |
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212 : public HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > { |
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213 typedef HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > Create; |
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214 }; |
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215 |
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216 template <typename T> |
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217 struct SetPathTraits : public Traits { |
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218 typedef T Path; |
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219 }; |
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220 |
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221 /// \brief \ref named-templ-param "Named parameter" for setting |
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222 /// \c %Path type. |
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223 /// |
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224 /// \ref named-templ-param "Named parameter" for setting the \c %Path |
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225 /// type of the found cycles. |
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226 /// It must conform to the \ref lemon::concepts::Path "Path" concept |
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227 /// and it must have an \c addFront() function. |
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228 template <typename T> |
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229 struct SetPath |
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230 : public HartmannOrlin<GR, LEN, SetPathTraits<T> > { |
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231 typedef HartmannOrlin<GR, LEN, SetPathTraits<T> > Create; |
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232 }; |
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233 |
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234 /// @} |
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235 |
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236 public: |
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237 |
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238 /// \brief Constructor. |
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239 /// |
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240 /// The constructor of the class. |
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241 /// |
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242 /// \param digraph The digraph the algorithm runs on. |
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243 /// \param length The lengths (costs) of the arcs. |
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244 HartmannOrlin( const Digraph &digraph, |
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245 const LengthMap &length ) : |
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246 _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph), |
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247 _best_found(false), _best_length(0), _best_size(1), |
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248 _cycle_path(NULL), _local_path(false), _data(digraph) |
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249 {} |
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250 |
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251 /// Destructor. |
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252 ~HartmannOrlin() { |
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253 if (_local_path) delete _cycle_path; |
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254 } |
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255 |
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256 /// \brief Set the path structure for storing the found cycle. |
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257 /// |
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258 /// This function sets an external path structure for storing the |
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259 /// found cycle. |
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260 /// |
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261 /// If you don't call this function before calling \ref run() or |
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262 /// \ref findMinMean(), it will allocate a local \ref Path "path" |
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263 /// structure. The destuctor deallocates this automatically |
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264 /// allocated object, of course. |
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265 /// |
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266 /// \note The algorithm calls only the \ref lemon::Path::addFront() |
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267 /// "addFront()" function of the given path structure. |
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268 /// |
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269 /// \return <tt>(*this)</tt> |
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270 HartmannOrlin& cycle(Path &path) { |
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271 if (_local_path) { |
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272 delete _cycle_path; |
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273 _local_path = false; |
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274 } |
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275 _cycle_path = &path; |
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276 return *this; |
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277 } |
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278 |
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279 /// \name Execution control |
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280 /// The simplest way to execute the algorithm is to call the \ref run() |
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281 /// function.\n |
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282 /// If you only need the minimum mean length, you may call |
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283 /// \ref findMinMean(). |
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284 |
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285 /// @{ |
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286 |
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287 /// \brief Run the algorithm. |
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288 /// |
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289 /// This function runs the algorithm. |
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290 /// It can be called more than once (e.g. if the underlying digraph |
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291 /// and/or the arc lengths have been modified). |
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292 /// |
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293 /// \return \c true if a directed cycle exists in the digraph. |
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294 /// |
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295 /// \note <tt>mmc.run()</tt> is just a shortcut of the following code. |
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296 /// \code |
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297 /// return mmc.findMinMean() && mmc.findCycle(); |
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298 /// \endcode |
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299 bool run() { |
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300 return findMinMean() && findCycle(); |
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301 } |
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302 |
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303 /// \brief Find the minimum cycle mean. |
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304 /// |
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305 /// This function finds the minimum mean length of the directed |
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306 /// cycles in the digraph. |
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307 /// |
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308 /// \return \c true if a directed cycle exists in the digraph. |
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309 bool findMinMean() { |
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310 // Initialization and find strongly connected components |
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311 init(); |
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312 findComponents(); |
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313 |
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314 // Find the minimum cycle mean in the components |
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315 for (int comp = 0; comp < _comp_num; ++comp) { |
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316 if (!initComponent(comp)) continue; |
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317 processRounds(); |
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318 |
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319 // Update the best cycle (global minimum mean cycle) |
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320 if ( _curr_found && (!_best_found || |
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321 _curr_length * _best_size < _best_length * _curr_size) ) { |
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322 _best_found = true; |
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323 _best_length = _curr_length; |
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324 _best_size = _curr_size; |
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325 _best_node = _curr_node; |
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326 _best_level = _curr_level; |
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327 } |
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328 } |
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329 return _best_found; |
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330 } |
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331 |
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332 /// \brief Find a minimum mean directed cycle. |
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333 /// |
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334 /// This function finds a directed cycle of minimum mean length |
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335 /// in the digraph using the data computed by findMinMean(). |
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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 /// |
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339 /// \pre \ref findMinMean() must be called before using this function. |
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340 bool findCycle() { |
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341 if (!_best_found) return false; |
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342 IntNodeMap reached(_gr, -1); |
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343 int r = _best_level + 1; |
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344 Node u = _best_node; |
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345 while (reached[u] < 0) { |
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346 reached[u] = --r; |
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347 u = _gr.source(_data[u][r].pred); |
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348 } |
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349 r = reached[u]; |
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350 Arc e = _data[u][r].pred; |
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351 _cycle_path->addFront(e); |
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352 _best_length = _length[e]; |
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353 _best_size = 1; |
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354 Node v; |
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355 while ((v = _gr.source(e)) != u) { |
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356 e = _data[v][--r].pred; |
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357 _cycle_path->addFront(e); |
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358 _best_length += _length[e]; |
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359 ++_best_size; |
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360 } |
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361 return true; |
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362 } |
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363 |
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364 /// @} |
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365 |
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366 /// \name Query Functions |
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367 /// The results of the algorithm can be obtained using these |
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368 /// functions.\n |
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369 /// The algorithm should be executed before using them. |
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370 |
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371 /// @{ |
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372 |
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373 /// \brief Return the total length of the found cycle. |
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374 /// |
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375 /// This function returns the total length of the found cycle. |
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376 /// |
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377 /// \pre \ref run() or \ref findMinMean() must be called before |
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378 /// using this function. |
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379 LargeValue cycleLength() const { |
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380 return _best_length; |
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381 } |
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382 |
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383 /// \brief Return the number of arcs on the found cycle. |
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384 /// |
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385 /// This function returns the number of arcs on the found cycle. |
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386 /// |
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387 /// \pre \ref run() or \ref findMinMean() must be called before |
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388 /// using this function. |
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389 int cycleArcNum() const { |
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390 return _best_size; |
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391 } |
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392 |
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393 /// \brief Return the mean length of the found cycle. |
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394 /// |
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395 /// This function returns the mean length of the found cycle. |
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396 /// |
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397 /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the |
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398 /// following code. |
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399 /// \code |
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400 /// return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum(); |
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401 /// \endcode |
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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 double cycleMean() const { |
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406 return static_cast<double>(_best_length) / _best_size; |
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407 } |
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408 |
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409 /// \brief Return the found cycle. |
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410 /// |
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411 /// This function returns a const reference to the path structure |
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412 /// storing the found cycle. |
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413 /// |
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414 /// \pre \ref run() or \ref findCycle() must be called before using |
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415 /// this function. |
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416 const Path& cycle() const { |
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417 return *_cycle_path; |
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418 } |
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419 |
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420 ///@} |
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421 |
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422 private: |
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423 |
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424 // Initialization |
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425 void init() { |
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426 if (!_cycle_path) { |
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427 _local_path = true; |
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428 _cycle_path = new Path; |
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429 } |
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430 _cycle_path->clear(); |
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431 _best_found = false; |
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432 _best_length = 0; |
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433 _best_size = 1; |
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434 _cycle_path->clear(); |
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435 for (NodeIt u(_gr); u != INVALID; ++u) |
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436 _data[u].clear(); |
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437 } |
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438 |
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439 // Find strongly connected components and initialize _comp_nodes |
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440 // and _out_arcs |
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441 void findComponents() { |
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442 _comp_num = stronglyConnectedComponents(_gr, _comp); |
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443 _comp_nodes.resize(_comp_num); |
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444 if (_comp_num == 1) { |
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445 _comp_nodes[0].clear(); |
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446 for (NodeIt n(_gr); n != INVALID; ++n) { |
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447 _comp_nodes[0].push_back(n); |
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448 _out_arcs[n].clear(); |
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449 for (OutArcIt a(_gr, n); a != INVALID; ++a) { |
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450 _out_arcs[n].push_back(a); |
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451 } |
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452 } |
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453 } else { |
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454 for (int i = 0; i < _comp_num; ++i) |
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455 _comp_nodes[i].clear(); |
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456 for (NodeIt n(_gr); n != INVALID; ++n) { |
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457 int k = _comp[n]; |
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458 _comp_nodes[k].push_back(n); |
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459 _out_arcs[n].clear(); |
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460 for (OutArcIt a(_gr, n); a != INVALID; ++a) { |
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461 if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a); |
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462 } |
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463 } |
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464 } |
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465 } |
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466 |
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467 // Initialize path data for the current component |
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468 bool initComponent(int comp) { |
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469 _nodes = &(_comp_nodes[comp]); |
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470 int n = _nodes->size(); |
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471 if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) { |
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472 return false; |
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473 } |
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474 for (int i = 0; i < n; ++i) { |
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475 _data[(*_nodes)[i]].resize(n + 1); |
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476 } |
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477 return true; |
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478 } |
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479 |
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480 // Process all rounds of computing path data for the current component. |
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481 // _data[v][k] is the length of a shortest directed walk from the root |
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482 // node to node v containing exactly k arcs. |
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483 void processRounds() { |
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484 Node start = (*_nodes)[0]; |
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485 _data[start][0] = PathData(true, 0); |
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486 _process.clear(); |
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487 _process.push_back(start); |
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488 |
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489 int k, n = _nodes->size(); |
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490 int next_check = 4; |
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491 bool terminate = false; |
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492 for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) { |
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493 processNextBuildRound(k); |
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494 if (k == next_check || k == n) { |
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495 terminate = checkTermination(k); |
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496 next_check = next_check * 3 / 2; |
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497 } |
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498 } |
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499 for ( ; k <= n && !terminate; ++k) { |
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500 processNextFullRound(k); |
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501 if (k == next_check || k == n) { |
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502 terminate = checkTermination(k); |
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503 next_check = next_check * 3 / 2; |
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504 } |
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505 } |
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506 } |
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507 |
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508 // Process one round and rebuild _process |
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509 void processNextBuildRound(int k) { |
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510 std::vector<Node> next; |
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511 Node u, v; |
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512 Arc e; |
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513 LargeValue d; |
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514 for (int i = 0; i < int(_process.size()); ++i) { |
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515 u = _process[i]; |
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516 for (int j = 0; j < int(_out_arcs[u].size()); ++j) { |
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517 e = _out_arcs[u][j]; |
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518 v = _gr.target(e); |
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519 d = _data[u][k-1].dist + _length[e]; |
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520 if (!_data[v][k].found) { |
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521 next.push_back(v); |
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522 _data[v][k] = PathData(true, _data[u][k-1].dist + _length[e], e); |
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523 } |
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524 else if (_tolerance.less(d, _data[v][k].dist)) { |
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525 _data[v][k] = PathData(true, d, e); |
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526 } |
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527 } |
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528 } |
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529 _process.swap(next); |
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530 } |
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531 |
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532 // Process one round using _nodes instead of _process |
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533 void processNextFullRound(int k) { |
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534 Node u, v; |
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535 Arc e; |
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536 LargeValue d; |
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537 for (int i = 0; i < int(_nodes->size()); ++i) { |
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538 u = (*_nodes)[i]; |
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539 for (int j = 0; j < int(_out_arcs[u].size()); ++j) { |
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540 e = _out_arcs[u][j]; |
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541 v = _gr.target(e); |
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542 d = _data[u][k-1].dist + _length[e]; |
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543 if (!_data[v][k].found || _tolerance.less(d, _data[v][k].dist)) { |
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544 _data[v][k] = PathData(true, d, e); |
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545 } |
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546 } |
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547 } |
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548 } |
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549 |
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550 // Check early termination |
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551 bool checkTermination(int k) { |
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552 typedef std::pair<int, int> Pair; |
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553 typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0)); |
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554 typename GR::template NodeMap<LargeValue> pi(_gr); |
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555 int n = _nodes->size(); |
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556 LargeValue length; |
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557 int size; |
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558 Node u; |
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559 |
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560 // Search for cycles that are already found |
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561 _curr_found = false; |
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562 for (int i = 0; i < n; ++i) { |
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563 u = (*_nodes)[i]; |
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564 if (!_data[u][k].found) continue; |
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565 for (int j = k; j >= 0; --j) { |
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566 if (level[u].first == i && level[u].second > 0) { |
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567 // A cycle is found |
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568 length = _data[u][level[u].second].dist - _data[u][j].dist; |
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569 size = level[u].second - j; |
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570 if (!_curr_found || length * _curr_size < _curr_length * size) { |
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571 _curr_length = length; |
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572 _curr_size = size; |
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573 _curr_node = u; |
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574 _curr_level = level[u].second; |
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575 _curr_found = true; |
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576 } |
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577 } |
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578 level[u] = Pair(i, j); |
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579 u = _gr.source(_data[u][j].pred); |
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580 } |
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581 } |
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582 |
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583 // If at least one cycle is found, check the optimality condition |
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584 LargeValue d; |
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585 if (_curr_found && k < n) { |
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586 // Find node potentials |
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587 for (int i = 0; i < n; ++i) { |
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588 u = (*_nodes)[i]; |
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589 pi[u] = std::numeric_limits<LargeValue>::max(); |
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590 for (int j = 0; j <= k; ++j) { |
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591 d = _data[u][j].dist * _curr_size - j * _curr_length; |
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592 if (_data[u][j].found && _tolerance.less(d, pi[u])) { |
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593 pi[u] = d; |
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594 } |
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595 } |
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596 } |
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597 |
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598 // Check the optimality condition for all arcs |
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599 bool done = true; |
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600 for (ArcIt a(_gr); a != INVALID; ++a) { |
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601 if (_tolerance.less(_length[a] * _curr_size - _curr_length, |
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602 pi[_gr.target(a)] - pi[_gr.source(a)]) ) { |
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603 done = false; |
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604 break; |
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605 } |
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606 } |
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607 return done; |
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608 } |
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609 return (k == n); |
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610 } |
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611 |
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612 }; //class HartmannOrlin |
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613 |
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614 ///@} |
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615 |
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616 } //namespace lemon |
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617 |
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618 #endif //LEMON_HARTMANN_ORLIN_H |