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 directed cycle. |
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26 | |
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27 | #include <vector> |
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28 | #include <lemon/graph_utils.h> |
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29 | #include <lemon/topology.h> |
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30 | #include <lemon/path.h> |
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31 | #include <lemon/tolerance.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 directed 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 | /// minimum mean directed cycle. |
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43 | /// |
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44 | /// \param Graph The directed graph type the algorithm runs on. |
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45 | /// \param LengthMap The type of the length (cost) map. |
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46 | /// |
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47 | /// \warning \c LengthMap::Value must be convertible to \c double. |
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48 | /// |
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49 | /// \author Peter Kovacs |
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50 | |
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51 | template < typename Graph, |
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52 | typename LengthMap = typename Graph::template EdgeMap<int> > |
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53 | class MinMeanCycle |
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54 | { |
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55 | GRAPH_TYPEDEFS(typename Graph); |
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56 | |
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57 | typedef typename LengthMap::Value Length; |
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58 | typedef Path<Graph> Path; |
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59 | |
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60 | protected: |
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61 | |
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62 | typename Graph::template NodeMap<bool> _reached; |
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63 | typename Graph::template NodeMap<double> _dist; |
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64 | typename Graph::template NodeMap<Edge> _policy; |
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65 | |
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66 | /// The directed graph the algorithm runs on. |
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67 | const Graph &_graph; |
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68 | /// The length of the edges. |
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69 | const LengthMap &_length; |
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70 | |
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71 | /// The total length of the found cycle. |
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72 | Length _cycle_length; |
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73 | /// The number of edges on the found cycle. |
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74 | int _cycle_size; |
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75 | /// The found cycle. |
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76 | Path *_cycle_path; |
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77 | |
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78 | bool _local_path; |
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79 | bool _cycle_found; |
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80 | Node _cycle_node; |
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81 | |
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82 | typename Graph::template NodeMap<int> _component; |
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83 | int _component_num; |
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84 | |
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85 | std::vector<Node> _nodes; |
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86 | std::vector<Edge> _edges; |
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87 | Tolerance<double> _tolerance; |
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88 | |
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89 | public: |
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90 | |
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91 | /// \brief The constructor of the class. |
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92 | /// |
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93 | /// The constructor of the class. |
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94 | /// |
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95 | /// \param graph The directed graph the algorithm runs on. |
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96 | /// \param length The length (cost) of the edges. |
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97 | MinMeanCycle( const Graph &graph, |
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98 | const LengthMap &length ) : |
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99 | _graph(graph), _length(length), _dist(graph), _reached(graph), |
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100 | _policy(graph), _component(graph), _cycle_length(0), |
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101 | _cycle_size(-1), _cycle_path(NULL), _local_path(false) |
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102 | { } |
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103 | |
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104 | /// The destructor of the class. |
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105 | ~MinMeanCycle() { |
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106 | if (_local_path) delete _cycle_path; |
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107 | } |
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108 | |
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109 | protected: |
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110 | |
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111 | // Initializes the internal data structures for the current strongly |
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112 | // connected component and creating the policy graph. |
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113 | // The policy graph can be represented by the _policy map because |
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114 | // the out degree of every node is 1. |
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115 | bool initCurrentComponent(int comp) { |
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116 | // Finding the nodes of the current component |
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117 | _nodes.clear(); |
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118 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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119 | if (_component[n] == comp) _nodes.push_back(n); |
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120 | } |
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121 | if (_nodes.size() <= 1) return false; |
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122 | // Finding the edges of the current component |
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123 | _edges.clear(); |
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124 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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125 | if ( _component[_graph.source(e)] == comp && |
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126 | _component[_graph.target(e)] == comp ) |
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127 | _edges.push_back(e); |
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128 | } |
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129 | // Initializing _reached, _dist, _policy maps |
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130 | for (int i = 0; i < _nodes.size(); ++i) { |
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131 | _reached[_nodes[i]] = false; |
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132 | _policy[_nodes[i]] = INVALID; |
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133 | } |
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134 | Node u; Edge e; |
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135 | for (int j = 0; j < _edges.size(); ++j) { |
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136 | e = _edges[j]; |
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137 | u = _graph.source(e); |
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138 | if (!_reached[u] || _length[e] < _dist[u]) { |
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139 | _dist[u] = _length[e]; |
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140 | _policy[u] = e; |
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141 | _reached[u] = true; |
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142 | } |
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143 | } |
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144 | return true; |
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145 | } |
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146 | |
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147 | // Finds all cycles in the policy graph. |
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148 | // Sets _cycle_found to true if a cycle is found and sets |
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149 | // _cycle_length, _cycle_size, _cycle_node to represent the minimum |
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150 | // mean cycle in the policy graph. |
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151 | bool findPolicyCycles(int comp) { |
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152 | typename Graph::template NodeMap<int> level(_graph, -1); |
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153 | _cycle_found = false; |
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154 | Length clength; |
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155 | int csize; |
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156 | int path_cnt = 0; |
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157 | Node u, v; |
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158 | // Searching for cycles |
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159 | for (int i = 0; i < _nodes.size(); ++i) { |
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160 | if (level[_nodes[i]] < 0) { |
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161 | u = _nodes[i]; |
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162 | level[u] = path_cnt; |
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163 | while (level[u = _graph.target(_policy[u])] < 0) |
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164 | level[u] = path_cnt; |
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165 | if (level[u] == path_cnt) { |
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166 | // A cycle is found |
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167 | clength = _length[_policy[u]]; |
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168 | csize = 1; |
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169 | for (v = u; (v = _graph.target(_policy[v])) != u; ) { |
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170 | clength += _length[_policy[v]]; |
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171 | ++csize; |
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172 | } |
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173 | if ( !_cycle_found || |
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174 | clength * _cycle_size < _cycle_length * csize ) { |
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175 | _cycle_found = true; |
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176 | _cycle_length = clength; |
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177 | _cycle_size = csize; |
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178 | _cycle_node = u; |
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179 | } |
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180 | } |
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181 | ++path_cnt; |
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182 | } |
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183 | } |
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184 | return _cycle_found; |
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185 | } |
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186 | |
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187 | // Contracts the policy graph to be connected by cutting all cycles |
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188 | // except for the main cycle (i.e. the minimum mean cycle). |
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189 | void contractPolicyGraph(int comp) { |
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190 | // Finding the component of the main cycle using |
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191 | // reverse BFS search |
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192 | typename Graph::template NodeMap<int> found(_graph, false); |
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193 | std::deque<Node> queue; |
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194 | queue.push_back(_cycle_node); |
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195 | found[_cycle_node] = true; |
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196 | Node u, v; |
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197 | while (!queue.empty()) { |
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198 | v = queue.front(); queue.pop_front(); |
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199 | for (InEdgeIt e(_graph, v); e != INVALID; ++e) { |
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200 | u = _graph.source(e); |
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201 | if (_component[u] == comp && !found[u] && _policy[u] == e) { |
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202 | found[u] = true; |
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203 | queue.push_back(u); |
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204 | } |
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205 | } |
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206 | } |
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207 | // Connecting all other nodes to this component using |
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208 | // reverse BFS search |
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209 | queue.clear(); |
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210 | for (int i = 0; i < _nodes.size(); ++i) |
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211 | if (found[_nodes[i]]) queue.push_back(_nodes[i]); |
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212 | int found_cnt = queue.size(); |
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213 | while (found_cnt < _nodes.size() && !queue.empty()) { |
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214 | v = queue.front(); queue.pop_front(); |
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215 | for (InEdgeIt e(_graph, v); e != INVALID; ++e) { |
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216 | u = _graph.source(e); |
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217 | if (_component[u] == comp && !found[u]) { |
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218 | found[u] = true; |
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219 | ++found_cnt; |
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220 | _policy[u] = e; |
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221 | queue.push_back(u); |
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222 | } |
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223 | } |
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224 | } |
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225 | } |
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226 | |
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227 | // Computes node distances in the policy graph and updates the |
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228 | // policy graph if the node distances can be improved. |
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229 | bool computeNodeDistances(int comp) { |
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230 | // Computing node distances using reverse BFS search |
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231 | double cycle_mean = (double)_cycle_length / _cycle_size; |
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232 | typename Graph::template NodeMap<int> found(_graph, false); |
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233 | std::deque<Node> queue; |
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234 | queue.push_back(_cycle_node); |
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235 | found[_cycle_node] = true; |
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236 | Node u, v; |
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237 | while (!queue.empty()) { |
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238 | v = queue.front(); queue.pop_front(); |
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239 | for (InEdgeIt e(_graph, v); e != INVALID; ++e) { |
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240 | u = _graph.source(e); |
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241 | if (_component[u] == comp && !found[u] && _policy[u] == e) { |
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242 | found[u] = true; |
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243 | _dist[u] = _dist[v] + _length[e] - cycle_mean; |
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244 | queue.push_back(u); |
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245 | } |
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246 | } |
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247 | } |
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248 | // Improving node distances |
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249 | bool improved = false; |
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250 | for (int j = 0; j < _edges.size(); ++j) { |
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251 | Edge e = _edges[j]; |
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252 | u = _graph.source(e); v = _graph.target(e); |
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253 | double delta = _dist[v] + _length[e] - cycle_mean; |
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254 | if (_tolerance.less(delta, _dist[u])) { |
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255 | improved = true; |
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256 | _dist[u] = delta; |
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257 | _policy[u] = e; |
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258 | } |
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259 | } |
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260 | return improved; |
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261 | } |
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262 | |
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263 | public: |
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264 | |
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265 | /// \brief Runs the algorithm. |
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266 | /// |
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267 | /// Runs the algorithm. |
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268 | /// |
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269 | /// \return Returns \c true if a directed cycle exists in the graph. |
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270 | /// |
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271 | /// \note Apart from the return value, <tt>mmc.run()</tt> is just a |
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272 | /// shortcut of the following code. |
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273 | /// \code |
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274 | /// mmc.init(); |
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275 | /// mmc.findMinMean(); |
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276 | /// mmc.findCycle(); |
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277 | /// \endcode |
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278 | bool run() { |
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279 | init(); |
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280 | return findMinMean() && findCycle(); |
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281 | } |
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282 | |
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283 | /// \brief Initializes the internal data structures. |
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284 | /// |
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285 | /// Initializes the internal data structures. |
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286 | /// |
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287 | /// \sa reset() |
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288 | void init() { |
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289 | _tolerance.epsilon(1e-8); |
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290 | if (!_cycle_path) { |
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291 | _local_path = true; |
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292 | _cycle_path = new Path; |
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293 | } |
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294 | _cycle_found = false; |
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295 | _component_num = stronglyConnectedComponents(_graph, _component); |
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296 | } |
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297 | |
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298 | /// \brief Resets the internal data structures. |
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299 | /// |
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300 | /// Resets the internal data structures so that \ref findMinMean() |
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301 | /// and \ref findCycle() can be called again (e.g. when the |
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302 | /// underlaying graph has been modified). |
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303 | /// |
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304 | /// \sa init() |
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305 | void reset() { |
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306 | if (_cycle_path) _cycle_path->clear(); |
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307 | _cycle_found = false; |
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308 | _component_num = stronglyConnectedComponents(_graph, _component); |
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309 | } |
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310 | |
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311 | /// \brief Finds the minimum cycle mean length in the graph. |
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312 | /// |
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313 | /// Computes all the required data and finds the minimum cycle mean |
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314 | /// length in the graph. |
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315 | /// |
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316 | /// \return Returns \c true if a directed cycle exists in the graph. |
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317 | /// |
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318 | /// \pre \ref init() must be called before using this function. |
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319 | bool findMinMean() { |
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320 | // Finding the minimum mean cycle in the components |
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321 | for (int comp = 0; comp < _component_num; ++comp) { |
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322 | if (!initCurrentComponent(comp)) continue; |
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323 | while (true) { |
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324 | if (!findPolicyCycles(comp)) return false; |
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325 | contractPolicyGraph(comp); |
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326 | if (!computeNodeDistances(comp)) return true; |
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327 | } |
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328 | } |
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329 | } |
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330 | |
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331 | /// \brief Finds a critical (minimum mean) directed cycle. |
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332 | /// |
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333 | /// Finds a critical (minimum mean) directed cycle using the data |
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334 | /// computed in the \ref findMinMean() function. |
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335 | /// |
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336 | /// \return Returns \c true if a directed cycle exists in the graph. |
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337 | /// |
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338 | /// \pre \ref init() and \ref findMinMean() must be called before |
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339 | /// using this function. |
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340 | bool findCycle() { |
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341 | if (!_cycle_found) return false; |
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342 | _cycle_path->addBack(_policy[_cycle_node]); |
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343 | for ( Node v = _cycle_node; |
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344 | (v = _graph.target(_policy[v])) != _cycle_node; ) { |
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345 | _cycle_path->addBack(_policy[v]); |
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346 | } |
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347 | return true; |
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348 | } |
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349 | |
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350 | /// \brief Returns the total length of the found cycle. |
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351 | /// |
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352 | /// Returns the total length of the found cycle. |
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353 | /// |
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354 | /// \pre \ref run() or \ref findMinMean() must be called before |
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355 | /// using this function. |
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356 | Length cycleLength() const { |
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357 | return _cycle_length; |
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358 | } |
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359 | |
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360 | /// \brief Returns the number of edges on the found cycle. |
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361 | /// |
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362 | /// Returns the number of edges on the found cycle. |
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363 | /// |
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364 | /// \pre \ref run() or \ref findMinMean() must be called before |
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365 | /// using this function. |
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366 | int cycleEdgeNum() const { |
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367 | return _cycle_size; |
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368 | } |
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369 | |
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370 | /// \brief Returns the mean length of the found cycle. |
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371 | /// |
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372 | /// Returns the mean length of the found cycle. |
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373 | /// |
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374 | /// \pre \ref run() or \ref findMinMean() must be called before |
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375 | /// using this function. |
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376 | /// |
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377 | /// \note <tt>mmc.cycleMean()</tt> is just a shortcut of the |
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378 | /// following code. |
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379 | /// \code |
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380 | /// return double(mmc.cycleLength()) / mmc.cycleEdgeNum(); |
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381 | /// \endcode |
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382 | double cycleMean() const { |
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383 | return (double)_cycle_length / _cycle_size; |
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384 | } |
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385 | |
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386 | /// \brief Returns a const reference to the \ref Path "path" |
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387 | /// structure storing the found cycle. |
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388 | /// |
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389 | /// Returns a const reference to the \ref Path "path" |
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390 | /// structure storing the found cycle. |
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391 | /// |
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392 | /// \pre \ref run() or \ref findCycle() must be called before using |
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393 | /// this function. |
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394 | /// |
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395 | /// \sa cyclePath() |
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396 | const Path& cycle() const { |
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397 | return *_cycle_path; |
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398 | } |
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399 | |
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400 | /// \brief Sets the \ref Path "path" structure for storing the found |
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401 | /// cycle. |
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402 | /// |
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403 | /// Sets an external \ref Path "path" structure for storing the |
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404 | /// found cycle. |
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405 | /// |
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406 | /// If you don't call this function before calling \ref run() or |
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407 | /// \ref init(), it will allocate a local \ref Path "path" |
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408 | /// structure. |
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409 | /// The destuctor deallocates this automatically allocated map, |
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410 | /// of course. |
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411 | /// |
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412 | /// \note The algorithm calls only the \ref lemon::Path::addBack() |
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413 | /// "addBack()" function of the given \ref Path "path" structure. |
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414 | /// |
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415 | /// \return <tt>(*this)</tt> |
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416 | /// |
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417 | /// \sa cycle() |
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418 | MinMeanCycle& cyclePath(Path &path) { |
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419 | if (_local_path) { |
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420 | delete _cycle_path; |
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421 | _local_path = false; |
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422 | } |
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423 | _cycle_path = &path; |
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424 | return *this; |
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425 | } |
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426 | |
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427 | }; //class MinMeanCycle |
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428 | |
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429 | ///@} |
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430 | |
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431 | } //namespace lemon |
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432 | |
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433 | #endif //LEMON_MIN_MEAN_CYCLE_H |
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