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_MIN_MEAN_CYCLE_H |
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20 | #define LEMON_MIN_MEAN_CYCLE_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 Howard'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 <lemon/core.h> |
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29 | #include <lemon/path.h> |
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30 | #include <lemon/tolerance.h> |
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31 | #include <lemon/connectivity.h> |
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32 | |
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33 | namespace lemon { |
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34 | |
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35 | /// \addtogroup shortest_path |
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36 | /// @{ |
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37 | |
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38 | /// \brief Implementation of Howard's algorithm for finding a minimum |
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39 | /// mean cycle. |
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40 | /// |
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41 | /// \ref MinMeanCycle implements Howard's algorithm for finding a |
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42 | /// directed cycle of minimum mean length (cost) in a digraph. |
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43 | /// |
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44 | /// \tparam GR The type of the digraph the algorithm runs on. |
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45 | /// \tparam LEN The type of the length map. The default |
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46 | /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
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47 | /// |
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48 | /// \warning \c LEN::Value must be convertible to \c double. |
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49 | #ifdef DOXYGEN |
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50 | template <typename GR, typename LEN> |
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51 | #else |
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52 | template < typename GR, |
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53 | typename LEN = typename GR::template ArcMap<int> > |
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54 | #endif |
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55 | class MinMeanCycle |
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56 | { |
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57 | public: |
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58 | |
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59 | /// The type of the digraph the algorithm runs on |
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60 | typedef GR Digraph; |
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61 | /// The type of the length map |
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62 | typedef LEN LengthMap; |
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63 | /// The type of the arc lengths |
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64 | typedef typename LengthMap::Value Value; |
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65 | /// The type of the paths |
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66 | typedef lemon::Path<Digraph> Path; |
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67 | |
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68 | private: |
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69 | |
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70 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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71 | |
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72 | // The digraph the algorithm runs on |
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73 | const Digraph &_gr; |
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74 | // The length of the arcs |
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75 | const LengthMap &_length; |
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76 | |
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77 | // Data for the found cycles |
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78 | bool _curr_found, _best_found; |
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79 | Value _curr_length, _best_length; |
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80 | int _curr_size, _best_size; |
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81 | Node _curr_node, _best_node; |
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82 | |
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83 | Path *_cycle_path; |
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84 | bool _local_path; |
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85 | |
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86 | // Internal data used by the algorithm |
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87 | typename Digraph::template NodeMap<Arc> _policy; |
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88 | typename Digraph::template NodeMap<bool> _reached; |
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89 | typename Digraph::template NodeMap<int> _level; |
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90 | typename Digraph::template NodeMap<double> _dist; |
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91 | |
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92 | // Data for storing the strongly connected components |
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93 | int _comp_num; |
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94 | typename Digraph::template NodeMap<int> _comp; |
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95 | std::vector<std::vector<Node> > _comp_nodes; |
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96 | std::vector<Node>* _nodes; |
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97 | typename Digraph::template NodeMap<std::vector<Arc> > _in_arcs; |
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98 | |
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99 | // Queue used for BFS search |
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100 | std::vector<Node> _queue; |
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101 | int _qfront, _qback; |
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102 | |
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103 | Tolerance<double> _tol; |
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104 | |
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105 | public: |
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106 | |
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107 | /// \brief Constructor. |
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108 | /// |
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109 | /// The constructor of the class. |
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110 | /// |
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111 | /// \param digraph The digraph the algorithm runs on. |
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112 | /// \param length The lengths (costs) of the arcs. |
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113 | MinMeanCycle( const Digraph &digraph, |
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114 | const LengthMap &length ) : |
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115 | _gr(digraph), _length(length), _cycle_path(NULL), _local_path(false), |
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116 | _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph), |
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117 | _comp(digraph), _in_arcs(digraph) |
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118 | {} |
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119 | |
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120 | /// Destructor. |
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121 | ~MinMeanCycle() { |
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122 | if (_local_path) delete _cycle_path; |
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123 | } |
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124 | |
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125 | /// \brief Set the path structure for storing the found cycle. |
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126 | /// |
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127 | /// This function sets an external path structure for storing the |
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128 | /// found cycle. |
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129 | /// |
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130 | /// If you don't call this function before calling \ref run() or |
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131 | /// \ref findMinMean(), it will allocate a local \ref Path "path" |
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132 | /// structure. The destuctor deallocates this automatically |
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133 | /// allocated object, of course. |
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134 | /// |
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135 | /// \note The algorithm calls only the \ref lemon::Path::addBack() |
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136 | /// "addBack()" function of the given path structure. |
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137 | /// |
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138 | /// \return <tt>(*this)</tt> |
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139 | /// |
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140 | /// \sa cycle() |
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141 | MinMeanCycle& cyclePath(Path &path) { |
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142 | if (_local_path) { |
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143 | delete _cycle_path; |
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144 | _local_path = false; |
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145 | } |
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146 | _cycle_path = &path; |
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147 | return *this; |
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148 | } |
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149 | |
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150 | /// \name Execution control |
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151 | /// The simplest way to execute the algorithm is to call the \ref run() |
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152 | /// function.\n |
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153 | /// If you only need the minimum mean length, you may call |
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154 | /// \ref findMinMean(). |
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155 | |
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156 | /// @{ |
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157 | |
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158 | /// \brief Run the algorithm. |
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159 | /// |
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160 | /// This function runs the algorithm. |
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161 | /// It can be called more than once (e.g. if the underlying digraph |
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162 | /// and/or the arc lengths have been modified). |
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163 | /// |
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164 | /// \return \c true if a directed cycle exists in the digraph. |
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165 | /// |
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166 | /// \note <tt>mmc.run()</tt> is just a shortcut of the following code. |
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167 | /// \code |
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168 | /// return mmc.findMinMean() && mmc.findCycle(); |
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169 | /// \endcode |
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170 | bool run() { |
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171 | return findMinMean() && findCycle(); |
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172 | } |
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173 | |
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174 | /// \brief Find the minimum cycle mean. |
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175 | /// |
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176 | /// This function finds the minimum mean length of the directed |
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177 | /// cycles in the digraph. |
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178 | /// |
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179 | /// \return \c true if a directed cycle exists in the digraph. |
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180 | bool findMinMean() { |
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181 | // Initialize and find strongly connected components |
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182 | init(); |
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183 | findComponents(); |
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184 | |
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185 | // Find the minimum cycle mean in the components |
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186 | for (int comp = 0; comp < _comp_num; ++comp) { |
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187 | // Find the minimum mean cycle in the current component |
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188 | if (!buildPolicyGraph(comp)) continue; |
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189 | while (true) { |
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190 | findPolicyCycle(); |
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191 | if (!computeNodeDistances()) break; |
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192 | } |
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193 | // Update the best cycle (global minimum mean cycle) |
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194 | if ( !_best_found || (_curr_found && |
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195 | _curr_length * _best_size < _best_length * _curr_size) ) { |
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196 | _best_found = true; |
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197 | _best_length = _curr_length; |
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198 | _best_size = _curr_size; |
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199 | _best_node = _curr_node; |
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200 | } |
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201 | } |
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202 | return _best_found; |
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203 | } |
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204 | |
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205 | /// \brief Find a minimum mean directed cycle. |
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206 | /// |
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207 | /// This function finds a directed cycle of minimum mean length |
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208 | /// in the digraph using the data computed by findMinMean(). |
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209 | /// |
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210 | /// \return \c true if a directed cycle exists in the digraph. |
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211 | /// |
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212 | /// \pre \ref findMinMean() must be called before using this function. |
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213 | bool findCycle() { |
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214 | if (!_best_found) return false; |
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215 | _cycle_path->addBack(_policy[_best_node]); |
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216 | for ( Node v = _best_node; |
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217 | (v = _gr.target(_policy[v])) != _best_node; ) { |
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218 | _cycle_path->addBack(_policy[v]); |
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219 | } |
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220 | return true; |
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221 | } |
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222 | |
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223 | /// @} |
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224 | |
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225 | /// \name Query Functions |
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226 | /// The results of the algorithm can be obtained using these |
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227 | /// functions.\n |
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228 | /// The algorithm should be executed before using them. |
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229 | |
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230 | /// @{ |
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231 | |
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232 | /// \brief Return the total length of the found cycle. |
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233 | /// |
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234 | /// This function returns the total length of the found cycle. |
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235 | /// |
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236 | /// \pre \ref run() or \ref findMinMean() must be called before |
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237 | /// using this function. |
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238 | Value cycleLength() const { |
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239 | return _best_length; |
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240 | } |
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241 | |
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242 | /// \brief Return the number of arcs on the found cycle. |
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243 | /// |
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244 | /// This function returns the number of arcs on the found cycle. |
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245 | /// |
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246 | /// \pre \ref run() or \ref findMinMean() must be called before |
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247 | /// using this function. |
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248 | int cycleArcNum() const { |
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249 | return _best_size; |
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250 | } |
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251 | |
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252 | /// \brief Return the mean length of the found cycle. |
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253 | /// |
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254 | /// This function returns the mean length of the found cycle. |
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255 | /// |
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256 | /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the |
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257 | /// following code. |
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258 | /// \code |
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259 | /// return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum(); |
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260 | /// \endcode |
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261 | /// |
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262 | /// \pre \ref run() or \ref findMinMean() must be called before |
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263 | /// using this function. |
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264 | double cycleMean() const { |
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265 | return static_cast<double>(_best_length) / _best_size; |
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266 | } |
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267 | |
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268 | /// \brief Return the found cycle. |
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269 | /// |
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270 | /// This function returns a const reference to the path structure |
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271 | /// storing the found cycle. |
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272 | /// |
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273 | /// \pre \ref run() or \ref findCycle() must be called before using |
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274 | /// this function. |
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275 | /// |
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276 | /// \sa cyclePath() |
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277 | const Path& cycle() const { |
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278 | return *_cycle_path; |
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279 | } |
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280 | |
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281 | ///@} |
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282 | |
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283 | private: |
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284 | |
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285 | // Initialize |
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286 | void init() { |
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287 | _tol.epsilon(1e-6); |
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288 | if (!_cycle_path) { |
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289 | _local_path = true; |
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290 | _cycle_path = new Path; |
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291 | } |
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292 | _queue.resize(countNodes(_gr)); |
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293 | _best_found = false; |
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294 | _best_length = 0; |
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295 | _best_size = 1; |
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296 | _cycle_path->clear(); |
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297 | } |
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298 | |
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299 | // Find strongly connected components and initialize _comp_nodes |
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300 | // and _in_arcs |
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301 | void findComponents() { |
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302 | _comp_num = stronglyConnectedComponents(_gr, _comp); |
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303 | _comp_nodes.resize(_comp_num); |
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304 | if (_comp_num == 1) { |
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305 | _comp_nodes[0].clear(); |
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306 | for (NodeIt n(_gr); n != INVALID; ++n) { |
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307 | _comp_nodes[0].push_back(n); |
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308 | _in_arcs[n].clear(); |
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309 | for (InArcIt a(_gr, n); a != INVALID; ++a) { |
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310 | _in_arcs[n].push_back(a); |
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311 | } |
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312 | } |
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313 | } else { |
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314 | for (int i = 0; i < _comp_num; ++i) |
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315 | _comp_nodes[i].clear(); |
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316 | for (NodeIt n(_gr); n != INVALID; ++n) { |
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317 | int k = _comp[n]; |
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318 | _comp_nodes[k].push_back(n); |
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319 | _in_arcs[n].clear(); |
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320 | for (InArcIt a(_gr, n); a != INVALID; ++a) { |
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321 | if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a); |
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322 | } |
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323 | } |
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324 | } |
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325 | } |
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326 | |
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327 | // Build the policy graph in the given strongly connected component |
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328 | // (the out-degree of every node is 1) |
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329 | bool buildPolicyGraph(int comp) { |
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330 | _nodes = &(_comp_nodes[comp]); |
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331 | if (_nodes->size() < 1 || |
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332 | (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) { |
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333 | return false; |
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334 | } |
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335 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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336 | _dist[(*_nodes)[i]] = std::numeric_limits<double>::max(); |
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337 | } |
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338 | Node u, v; |
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339 | Arc e; |
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340 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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341 | v = (*_nodes)[i]; |
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342 | for (int j = 0; j < int(_in_arcs[v].size()); ++j) { |
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343 | e = _in_arcs[v][j]; |
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344 | u = _gr.source(e); |
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345 | if (_length[e] < _dist[u]) { |
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346 | _dist[u] = _length[e]; |
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347 | _policy[u] = e; |
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348 | } |
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349 | } |
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350 | } |
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351 | return true; |
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352 | } |
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353 | |
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354 | // Find the minimum mean cycle in the policy graph |
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355 | void findPolicyCycle() { |
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356 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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357 | _level[(*_nodes)[i]] = -1; |
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358 | } |
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359 | Value clength; |
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360 | int csize; |
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361 | Node u, v; |
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362 | _curr_found = false; |
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363 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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364 | u = (*_nodes)[i]; |
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365 | if (_level[u] >= 0) continue; |
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366 | for (; _level[u] < 0; u = _gr.target(_policy[u])) { |
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367 | _level[u] = i; |
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368 | } |
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369 | if (_level[u] == i) { |
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370 | // A cycle is found |
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371 | clength = _length[_policy[u]]; |
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372 | csize = 1; |
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373 | for (v = u; (v = _gr.target(_policy[v])) != u; ) { |
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374 | clength += _length[_policy[v]]; |
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375 | ++csize; |
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376 | } |
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377 | if ( !_curr_found || |
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378 | (clength * _curr_size < _curr_length * csize) ) { |
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379 | _curr_found = true; |
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380 | _curr_length = clength; |
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381 | _curr_size = csize; |
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382 | _curr_node = u; |
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383 | } |
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384 | } |
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385 | } |
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386 | } |
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387 | |
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388 | // Contract the policy graph and compute node distances |
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389 | bool computeNodeDistances() { |
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390 | // Find the component of the main cycle and compute node distances |
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391 | // using reverse BFS |
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392 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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393 | _reached[(*_nodes)[i]] = false; |
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394 | } |
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395 | double curr_mean = double(_curr_length) / _curr_size; |
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396 | _qfront = _qback = 0; |
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397 | _queue[0] = _curr_node; |
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398 | _reached[_curr_node] = true; |
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399 | _dist[_curr_node] = 0; |
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400 | Node u, v; |
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401 | Arc e; |
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402 | while (_qfront <= _qback) { |
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403 | v = _queue[_qfront++]; |
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404 | for (int j = 0; j < int(_in_arcs[v].size()); ++j) { |
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405 | e = _in_arcs[v][j]; |
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406 | u = _gr.source(e); |
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407 | if (_policy[u] == e && !_reached[u]) { |
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408 | _reached[u] = true; |
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409 | _dist[u] = _dist[v] + _length[e] - curr_mean; |
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410 | _queue[++_qback] = u; |
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411 | } |
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412 | } |
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413 | } |
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414 | |
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415 | // Connect all other nodes to this component and compute node |
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416 | // distances using reverse BFS |
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417 | _qfront = 0; |
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418 | while (_qback < int(_nodes->size())-1) { |
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419 | v = _queue[_qfront++]; |
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420 | for (int j = 0; j < int(_in_arcs[v].size()); ++j) { |
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421 | e = _in_arcs[v][j]; |
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422 | u = _gr.source(e); |
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423 | if (!_reached[u]) { |
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424 | _reached[u] = true; |
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425 | _policy[u] = e; |
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426 | _dist[u] = _dist[v] + _length[e] - curr_mean; |
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427 | _queue[++_qback] = u; |
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428 | } |
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429 | } |
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430 | } |
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431 | |
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432 | // Improve node distances |
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433 | bool improved = false; |
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434 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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435 | v = (*_nodes)[i]; |
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436 | for (int j = 0; j < int(_in_arcs[v].size()); ++j) { |
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437 | e = _in_arcs[v][j]; |
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438 | u = _gr.source(e); |
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439 | double delta = _dist[v] + _length[e] - curr_mean; |
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440 | if (_tol.less(delta, _dist[u])) { |
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441 | _dist[u] = delta; |
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442 | _policy[u] = e; |
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443 | improved = true; |
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444 | } |
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445 | } |
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446 | } |
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447 | return improved; |
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448 | } |
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449 | |
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450 | }; //class MinMeanCycle |
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451 | |
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452 | ///@} |
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453 | |
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454 | } //namespace lemon |
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455 | |
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456 | #endif //LEMON_MIN_MEAN_CYCLE_H |
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