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) 2003-2006 |
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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_FLOYD_WARSHALL_H |
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20 | #define LEMON_FLOYD_WARSHALL_H |
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21 | |
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22 | ///\ingroup flowalgs |
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23 | /// \file |
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24 | /// \brief FloydWarshall algorithm. |
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25 | /// |
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26 | |
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27 | #include <lemon/list_graph.h> |
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28 | #include <lemon/graph_utils.h> |
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29 | #include <lemon/bits/invalid.h> |
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30 | #include <lemon/error.h> |
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31 | #include <lemon/matrix_maps.h> |
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32 | #include <lemon/maps.h> |
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33 | |
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34 | #include <limits> |
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35 | |
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36 | namespace lemon { |
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37 | |
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38 | /// \brief Default OperationTraits for the FloydWarshall algorithm class. |
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39 | /// |
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40 | /// It defines all computational operations and constants which are |
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41 | /// used in the Floyd-Warshall algorithm. The default implementation |
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42 | /// is based on the numeric_limits class. If the numeric type does not |
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43 | /// have infinity value then the maximum value is used as extremal |
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44 | /// infinity value. |
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45 | template < |
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46 | typename Value, |
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47 | bool has_infinity = std::numeric_limits<Value>::has_infinity> |
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48 | struct FloydWarshallDefaultOperationTraits { |
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49 | /// \brief Gives back the zero value of the type. |
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50 | static Value zero() { |
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51 | return static_cast<Value>(0); |
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52 | } |
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53 | /// \brief Gives back the positive infinity value of the type. |
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54 | static Value infinity() { |
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55 | return std::numeric_limits<Value>::infinity(); |
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56 | } |
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57 | /// \brief Gives back the sum of the given two elements. |
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58 | static Value plus(const Value& left, const Value& right) { |
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59 | return left + right; |
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60 | } |
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61 | /// \brief Gives back true only if the first value less than the second. |
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62 | static bool less(const Value& left, const Value& right) { |
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63 | return left < right; |
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64 | } |
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65 | }; |
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66 | |
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67 | template <typename Value> |
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68 | struct FloydWarshallDefaultOperationTraits<Value, false> { |
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69 | static Value zero() { |
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70 | return static_cast<Value>(0); |
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71 | } |
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72 | static Value infinity() { |
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73 | return std::numeric_limits<Value>::max(); |
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74 | } |
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75 | static Value plus(const Value& left, const Value& right) { |
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76 | if (left == infinity() || right == infinity()) return infinity(); |
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77 | return left + right; |
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78 | } |
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79 | static bool less(const Value& left, const Value& right) { |
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80 | return left < right; |
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81 | } |
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82 | }; |
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83 | |
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84 | /// \brief Default traits class of FloydWarshall class. |
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85 | /// |
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86 | /// Default traits class of FloydWarshall class. |
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87 | /// \param _Graph Graph type. |
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88 | /// \param _LegthMap Type of length map. |
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89 | template<class _Graph, class _LengthMap> |
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90 | struct FloydWarshallDefaultTraits { |
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91 | /// The graph type the algorithm runs on. |
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92 | typedef _Graph Graph; |
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93 | |
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94 | /// \brief The type of the map that stores the edge lengths. |
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95 | /// |
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96 | /// The type of the map that stores the edge lengths. |
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97 | /// It must meet the \ref concept::ReadMap "ReadMap" concept. |
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98 | typedef _LengthMap LengthMap; |
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99 | |
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100 | // The type of the length of the edges. |
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101 | typedef typename _LengthMap::Value Value; |
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102 | |
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103 | /// \brief Operation traits for floyd-warshall algorithm. |
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104 | /// |
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105 | /// It defines the infinity type on the given Value type |
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106 | /// and the used operation. |
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107 | /// \see FloydWarshallDefaultOperationTraits |
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108 | typedef FloydWarshallDefaultOperationTraits<Value> OperationTraits; |
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109 | |
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110 | /// \brief The type of the matrix map that stores the last edges of the |
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111 | /// shortest paths. |
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112 | /// |
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113 | /// The type of the map that stores the last edges of the shortest paths. |
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114 | /// It must be a matrix map with \c Graph::Edge value type. |
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115 | /// |
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116 | typedef DynamicMatrixMap<Graph, typename Graph::Node, |
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117 | typename Graph::Edge> PredMap; |
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118 | |
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119 | /// \brief Instantiates a PredMap. |
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120 | /// |
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121 | /// This function instantiates a \ref PredMap. |
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122 | /// \param graph is the graph, |
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123 | /// to which we would like to define the PredMap. |
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124 | /// \todo The graph alone may be insufficient for the initialization |
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125 | static PredMap *createPredMap(const _Graph& graph) { |
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126 | return new PredMap(graph); |
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127 | } |
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128 | |
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129 | /// \brief The type of the map that stores the dists of the nodes. |
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130 | /// |
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131 | /// The type of the map that stores the dists of the nodes. |
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132 | /// It must meet the \ref concept::WriteMatrixMap "WriteMatrixMap" concept. |
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133 | /// |
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134 | typedef DynamicMatrixMap<Graph, typename Graph::Node, Value> DistMap; |
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135 | |
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136 | /// \brief Instantiates a DistMap. |
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137 | /// |
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138 | /// This function instantiates a \ref DistMap. |
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139 | /// \param graph is the graph, to which we would like to define the |
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140 | /// \ref DistMap |
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141 | static DistMap *createDistMap(const _Graph& graph) { |
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142 | return new DistMap(graph); |
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143 | } |
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144 | |
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145 | }; |
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146 | |
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147 | /// \brief %FloydWarshall algorithm class. |
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148 | /// |
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149 | /// \ingroup flowalgs |
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150 | /// This class provides an efficient implementation of \c Floyd-Warshall |
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151 | /// algorithm. The edge lengths are passed to the algorithm using a |
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152 | /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any |
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153 | /// kind of length. |
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154 | /// |
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155 | /// The algorithm solves the shortest path problem for each pair |
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156 | /// of node when the edges can have negative length but the graph should |
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157 | /// not contain cycles with negative sum of length. If we can assume |
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158 | /// that all edge is non-negative in the graph then the dijkstra algorithm |
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159 | /// should be used from each node rather and if the graph is sparse and |
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160 | /// there are negative circles then the johnson algorithm. |
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161 | /// |
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162 | /// The complexity of this algorithm is \f$ O(n^3+e) \f$. |
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163 | /// |
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164 | /// The type of the length is determined by the |
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165 | /// \ref concept::ReadMap::Value "Value" of the length map. |
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166 | /// |
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167 | /// \param _Graph The graph type the algorithm runs on. The default value |
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168 | /// is \ref ListGraph. The value of _Graph is not used directly by |
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169 | /// FloydWarshall, it is only passed to \ref FloydWarshallDefaultTraits. |
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170 | /// \param _LengthMap This read-only EdgeMap determines the lengths of the |
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171 | /// edges. It is read once for each edge, so the map may involve in |
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172 | /// relatively time consuming process to compute the edge length if |
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173 | /// it is necessary. The default map type is \ref |
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174 | /// concept::Graph::EdgeMap "Graph::EdgeMap<int>". The value |
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175 | /// of _LengthMap is not used directly by FloydWarshall, it is only passed |
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176 | /// to \ref FloydWarshallDefaultTraits. \param _Traits Traits class to set |
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177 | /// various data types used by the algorithm. The default traits |
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178 | /// class is \ref FloydWarshallDefaultTraits |
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179 | /// "FloydWarshallDefaultTraits<_Graph,_LengthMap>". See \ref |
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180 | /// FloydWarshallDefaultTraits for the documentation of a FloydWarshall |
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181 | /// traits class. |
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182 | /// |
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183 | /// \author Balazs Dezso |
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184 | |
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185 | #ifdef DOXYGEN |
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186 | template <typename _Graph, typename _LengthMap typename _Traits > |
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187 | #else |
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188 | template <typename _Graph=ListGraph, |
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189 | typename _LengthMap=typename _Graph::template EdgeMap<int>, |
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190 | typename _Traits=FloydWarshallDefaultTraits<_Graph,_LengthMap> > |
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191 | #endif |
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192 | class FloydWarshall { |
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193 | public: |
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194 | |
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195 | /// \brief \ref Exception for uninitialized parameters. |
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196 | /// |
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197 | /// This error represents problems in the initialization |
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198 | /// of the parameters of the algorithms. |
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199 | |
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200 | class UninitializedParameter : public lemon::UninitializedParameter { |
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201 | public: |
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202 | virtual const char* exceptionName() const { |
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203 | return "lemon::FloydWarshall::UninitializedParameter"; |
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204 | } |
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205 | }; |
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206 | |
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207 | typedef _Traits Traits; |
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208 | ///The type of the underlying graph. |
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209 | typedef typename _Traits::Graph Graph; |
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210 | |
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211 | typedef typename Graph::Node Node; |
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212 | typedef typename Graph::NodeIt NodeIt; |
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213 | typedef typename Graph::Edge Edge; |
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214 | typedef typename Graph::EdgeIt EdgeIt; |
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215 | |
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216 | /// \brief The type of the length of the edges. |
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217 | typedef typename _Traits::LengthMap::Value Value; |
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218 | /// \brief The type of the map that stores the edge lengths. |
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219 | typedef typename _Traits::LengthMap LengthMap; |
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220 | /// \brief The type of the map that stores the last |
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221 | /// edges of the shortest paths. The type of the PredMap |
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222 | /// is a matrix map for Edges |
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223 | typedef typename _Traits::PredMap PredMap; |
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224 | /// \brief The type of the map that stores the dists of the nodes. |
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225 | /// The type of the DistMap is a matrix map for Values |
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226 | typedef typename _Traits::DistMap DistMap; |
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227 | /// \brief The operation traits. |
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228 | typedef typename _Traits::OperationTraits OperationTraits; |
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229 | private: |
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230 | /// Pointer to the underlying graph. |
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231 | const Graph *graph; |
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232 | /// Pointer to the length map |
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233 | const LengthMap *length; |
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234 | ///Pointer to the map of predecessors edges. |
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235 | PredMap *_pred; |
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236 | ///Indicates if \ref _pred is locally allocated (\c true) or not. |
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237 | bool local_pred; |
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238 | ///Pointer to the map of distances. |
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239 | DistMap *_dist; |
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240 | ///Indicates if \ref _dist is locally allocated (\c true) or not. |
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241 | bool local_dist; |
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242 | |
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243 | /// Creates the maps if necessary. |
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244 | void create_maps() { |
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245 | if(!_pred) { |
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246 | local_pred = true; |
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247 | _pred = Traits::createPredMap(*graph); |
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248 | } |
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249 | if(!_dist) { |
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250 | local_dist = true; |
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251 | _dist = Traits::createDistMap(*graph); |
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252 | } |
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253 | } |
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254 | |
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255 | public : |
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256 | |
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257 | /// \name Named template parameters |
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258 | |
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259 | ///@{ |
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260 | |
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261 | template <class T> |
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262 | struct DefPredMapTraits : public Traits { |
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263 | typedef T PredMap; |
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264 | static PredMap *createPredMap(const Graph& graph) { |
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265 | throw UninitializedParameter(); |
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266 | } |
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267 | }; |
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268 | |
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269 | /// \brief \ref named-templ-param "Named parameter" for setting PredMap |
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270 | /// type |
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271 | /// \ref named-templ-param "Named parameter" for setting PredMap type |
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272 | /// |
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273 | template <class T> |
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274 | struct DefPredMap |
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275 | : public FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > { |
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276 | typedef FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > Create; |
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277 | }; |
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278 | |
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279 | template <class T> |
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280 | struct DefDistMapTraits : public Traits { |
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281 | typedef T DistMap; |
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282 | static DistMap *createDistMap(const Graph& graph) { |
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283 | throw UninitializedParameter(); |
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284 | } |
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285 | }; |
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286 | /// \brief \ref named-templ-param "Named parameter" for setting DistMap |
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287 | /// type |
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288 | /// |
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289 | /// \ref named-templ-param "Named parameter" for setting DistMap type |
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290 | /// |
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291 | template <class T> |
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292 | struct DefDistMap |
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293 | : public FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > { |
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294 | typedef FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > Create; |
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295 | }; |
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296 | |
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297 | template <class T> |
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298 | struct DefOperationTraitsTraits : public Traits { |
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299 | typedef T OperationTraits; |
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300 | }; |
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301 | |
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302 | /// \brief \ref named-templ-param "Named parameter" for setting |
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303 | /// OperationTraits type |
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304 | /// |
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305 | /// \ref named-templ-param "Named parameter" for setting PredMap type |
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306 | template <class T> |
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307 | struct DefOperationTraits |
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308 | : public FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> > { |
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309 | typedef FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> > |
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310 | Create; |
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311 | }; |
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312 | |
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313 | ///@} |
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314 | |
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315 | protected: |
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316 | |
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317 | FloydWarshall() {} |
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318 | |
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319 | public: |
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320 | |
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321 | typedef FloydWarshall Create; |
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322 | |
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323 | /// \brief Constructor. |
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324 | /// |
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325 | /// \param _graph the graph the algorithm will run on. |
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326 | /// \param _length the length map used by the algorithm. |
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327 | FloydWarshall(const Graph& _graph, const LengthMap& _length) : |
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328 | graph(&_graph), length(&_length), |
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329 | _pred(0), local_pred(false), |
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330 | _dist(0), local_dist(false) {} |
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331 | |
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332 | ///Destructor. |
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333 | ~FloydWarshall() { |
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334 | if(local_pred) delete _pred; |
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335 | if(local_dist) delete _dist; |
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336 | } |
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337 | |
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338 | /// \brief Sets the length map. |
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339 | /// |
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340 | /// Sets the length map. |
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341 | /// \return \c (*this) |
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342 | FloydWarshall &lengthMap(const LengthMap &m) { |
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343 | length = &m; |
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344 | return *this; |
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345 | } |
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346 | |
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347 | /// \brief Sets the map storing the predecessor edges. |
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348 | /// |
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349 | /// Sets the map storing the predecessor edges. |
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350 | /// If you don't use this function before calling \ref run(), |
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351 | /// it will allocate one. The destuctor deallocates this |
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352 | /// automatically allocated map, of course. |
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353 | /// \return \c (*this) |
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354 | FloydWarshall &predMap(PredMap &m) { |
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355 | if(local_pred) { |
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356 | delete _pred; |
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357 | local_pred=false; |
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358 | } |
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359 | _pred = &m; |
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360 | return *this; |
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361 | } |
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362 | |
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363 | /// \brief Sets the map storing the distances calculated by the algorithm. |
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364 | /// |
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365 | /// Sets the map storing the distances calculated by the algorithm. |
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366 | /// If you don't use this function before calling \ref run(), |
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367 | /// it will allocate one. The destuctor deallocates this |
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368 | /// automatically allocated map, of course. |
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369 | /// \return \c (*this) |
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370 | FloydWarshall &distMap(DistMap &m) { |
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371 | if(local_dist) { |
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372 | delete _dist; |
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373 | local_dist=false; |
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374 | } |
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375 | _dist = &m; |
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376 | return *this; |
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377 | } |
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378 | |
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379 | ///\name Execution control |
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380 | /// The simplest way to execute the algorithm is to use |
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381 | /// one of the member functions called \c run(...). |
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382 | /// \n |
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383 | /// If you need more control on the execution, |
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384 | /// Finally \ref start() will perform the actual path |
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385 | /// computation. |
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386 | |
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387 | ///@{ |
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388 | |
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389 | /// \brief Initializes the internal data structures. |
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390 | /// |
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391 | /// Initializes the internal data structures. |
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392 | void init() { |
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393 | create_maps(); |
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394 | for (NodeIt it(*graph); it != INVALID; ++it) { |
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395 | for (NodeIt jt(*graph); jt != INVALID; ++jt) { |
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396 | _pred->set(it, jt, INVALID); |
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397 | _dist->set(it, jt, OperationTraits::infinity()); |
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398 | } |
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399 | _dist->set(it, it, OperationTraits::zero()); |
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400 | } |
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401 | for (EdgeIt it(*graph); it != INVALID; ++it) { |
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402 | Node source = graph->source(it); |
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403 | Node target = graph->target(it); |
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404 | if (OperationTraits::less((*length)[it], (*_dist)(source, target))) { |
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405 | _dist->set(source, target, (*length)[it]); |
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406 | _pred->set(source, target, it); |
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407 | } |
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408 | } |
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409 | } |
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410 | |
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411 | /// \brief Executes the algorithm. |
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412 | /// |
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413 | /// This method runs the %FloydWarshall algorithm in order to compute |
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414 | /// the shortest path to each node pairs. The algorithm |
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415 | /// computes |
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416 | /// - The shortest path tree for each node. |
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417 | /// - The distance between each node pairs. |
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418 | void start() { |
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419 | for (NodeIt kt(*graph); kt != INVALID; ++kt) { |
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420 | for (NodeIt it(*graph); it != INVALID; ++it) { |
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421 | for (NodeIt jt(*graph); jt != INVALID; ++jt) { |
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422 | Value relaxed = OperationTraits::plus((*_dist)(it, kt), |
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423 | (*_dist)(kt, jt)); |
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424 | if (OperationTraits::less(relaxed, (*_dist)(it, jt))) { |
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425 | _dist->set(it, jt, relaxed); |
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426 | _pred->set(it, jt, (*_pred)(kt, jt)); |
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427 | } |
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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 | |
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433 | /// \brief Executes the algorithm and checks the negative cycles. |
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434 | /// |
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435 | /// This method runs the %FloydWarshall algorithm in order to compute |
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436 | /// the shortest path to each node pairs. If there is a negative cycle |
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437 | /// in the graph it gives back false. |
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438 | /// The algorithm computes |
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439 | /// - The shortest path tree for each node. |
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440 | /// - The distance between each node pairs. |
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441 | bool checkedStart() { |
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442 | start(); |
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443 | for (NodeIt it(*graph); it != INVALID; ++it) { |
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444 | if (OperationTraits::less((*dist)(it, it), OperationTraits::zero())) { |
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445 | return false; |
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446 | } |
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447 | } |
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448 | return true; |
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449 | } |
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450 | |
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451 | /// \brief Runs %FloydWarshall algorithm. |
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452 | /// |
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453 | /// This method runs the %FloydWarshall algorithm from a each node |
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454 | /// in order to compute the shortest path to each node pairs. |
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455 | /// The algorithm computes |
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456 | /// - The shortest path tree for each node. |
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457 | /// - The distance between each node pairs. |
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458 | /// |
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459 | /// \note d.run(s) is just a shortcut of the following code. |
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460 | ///\code |
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461 | /// d.init(); |
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462 | /// d.start(); |
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463 | ///\endcode |
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464 | void run() { |
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465 | init(); |
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466 | start(); |
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467 | } |
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468 | |
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469 | ///@} |
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470 | |
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471 | /// \name Query Functions |
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472 | /// The result of the %FloydWarshall algorithm can be obtained using these |
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473 | /// functions.\n |
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474 | /// Before the use of these functions, |
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475 | /// either run() or start() must be called. |
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476 | |
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477 | ///@{ |
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478 | |
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479 | /// \brief Copies the shortest path to \c t into \c p |
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480 | /// |
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481 | /// This function copies the shortest path to \c t into \c p. |
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482 | /// If it \c t is a source itself or unreachable, then it does not |
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483 | /// alter \c p. |
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484 | /// \return Returns \c true if a path to \c t was actually copied to \c p, |
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485 | /// \c false otherwise. |
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486 | /// \sa DirPath |
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487 | template <typename Path> |
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488 | bool getPath(Path &p, Node source, Node target) { |
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489 | if (connected(source, target)) { |
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490 | p.clear(); |
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491 | typename Path::Builder b(target); |
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492 | for(b.setStartNode(target); predEdge(source, target) != INVALID; |
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493 | target = predNode(target)) { |
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494 | b.pushFront(predEdge(source, target)); |
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495 | } |
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496 | b.commit(); |
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497 | return true; |
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498 | } |
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499 | return false; |
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500 | } |
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501 | |
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502 | /// \brief The distance between two nodes. |
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503 | /// |
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504 | /// Returns the distance between two nodes. |
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505 | /// \pre \ref run() must be called before using this function. |
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506 | /// \warning If node \c v in unreachable from the root the return value |
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507 | /// of this funcion is undefined. |
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508 | Value dist(Node source, Node target) const { |
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509 | return (*_dist)(source, target); |
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510 | } |
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511 | |
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512 | /// \brief Returns the 'previous edge' of the shortest path tree. |
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513 | /// |
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514 | /// For the node \c node it returns the 'previous edge' of the shortest |
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515 | /// path tree to direction of the node \c root |
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516 | /// i.e. it returns the last edge of a shortest path from the node \c root |
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517 | /// to \c node. It is \ref INVALID if \c node is unreachable from the root |
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518 | /// or if \c node=root. The shortest path tree used here is equal to the |
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519 | /// shortest path tree used in \ref predNode(). |
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520 | /// \pre \ref run() must be called before using this function. |
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521 | Edge predEdge(Node root, Node node) const { |
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522 | return (*_pred)(root, node); |
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523 | } |
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524 | |
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525 | /// \brief Returns the 'previous node' of the shortest path tree. |
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526 | /// |
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527 | /// For a node \c node it returns the 'previous node' of the shortest path |
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528 | /// tree to direction of the node \c root, i.e. it returns the last but |
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529 | /// one node from a shortest path from the \c root to \c node. It is |
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530 | /// INVALID if \c node is unreachable from the root or if \c node=root. |
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531 | /// The shortest path tree used here is equal to the |
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532 | /// shortest path tree used in \ref predEdge(). |
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533 | /// \pre \ref run() must be called before using this function. |
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534 | Node predNode(Node root, Node node) const { |
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535 | return (*_pred)(root, node) == INVALID ? |
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536 | INVALID : graph->source((*_pred)(root, node)); |
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537 | } |
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538 | |
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539 | /// \brief Returns a reference to the matrix node map of distances. |
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540 | /// |
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541 | /// Returns a reference to the matrix node map of distances. |
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542 | /// |
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543 | /// \pre \ref run() must be called before using this function. |
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544 | const DistMap &distMap() const { return *_dist;} |
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545 | |
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546 | /// \brief Returns a reference to the shortest path tree map. |
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547 | /// |
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548 | /// Returns a reference to the matrix node map of the edges of the |
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549 | /// shortest path tree. |
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550 | /// \pre \ref run() must be called before using this function. |
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551 | const PredMap &predMap() const { return *_pred;} |
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552 | |
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553 | /// \brief Checks if a node is reachable from the root. |
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554 | /// |
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555 | /// Returns \c true if \c v is reachable from the root. |
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556 | /// \pre \ref run() must be called before using this function. |
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557 | /// |
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558 | bool connected(Node source, Node target) { |
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559 | return (*_dist)(source, target) != OperationTraits::infinity(); |
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560 | } |
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561 | |
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562 | ///@} |
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563 | }; |
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564 | |
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565 | } //END OF NAMESPACE LEMON |
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566 | |
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567 | #endif |
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568 | |
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