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) 2003-2007 |
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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_BELMANN_FORD_H |
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20 | #define LEMON_BELMANN_FORD_H |
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21 | |
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22 | /// \ingroup shortest_path |
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23 | /// \file |
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24 | /// \brief BellmanFord 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/bits/path_dump.h> |
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29 | #include <lemon/bits/invalid.h> |
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30 | #include <lemon/graph_utils.h> |
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31 | #include <lemon/error.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 BellmanFord 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 Bellman-Ford 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 BellmanFordDefaultOperationTraits { |
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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 BellmanFordDefaultOperationTraits<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 BellmanFord class. |
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85 | /// |
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86 | /// Default traits class of BellmanFord 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 BellmanFordDefaultTraits { |
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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 concepts::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 Bellman-Ford 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 BellmanFordDefaultOperationTraits |
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108 | typedef BellmanFordDefaultOperationTraits<Value> OperationTraits; |
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109 | |
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110 | /// \brief The type of the 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 |
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114 | /// edges of the shortest paths. |
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115 | /// It must meet the \ref concepts::WriteMap "WriteMap" concept. |
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116 | /// |
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117 | typedef typename Graph::template NodeMap<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, to which we would like to define the PredMap. |
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123 | static PredMap *createPredMap(const _Graph& graph) { |
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124 | return new PredMap(graph); |
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125 | } |
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126 | |
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127 | /// \brief The type of the map that stores the dists of the nodes. |
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128 | /// |
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129 | /// The type of the map that stores the dists of the nodes. |
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130 | /// It must meet the \ref concepts::WriteMap "WriteMap" concept. |
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131 | /// |
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132 | typedef typename Graph::template NodeMap<typename _LengthMap::Value> |
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133 | DistMap; |
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134 | |
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135 | /// \brief Instantiates a DistMap. |
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136 | /// |
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137 | /// This function instantiates a \ref DistMap. |
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138 | /// \param graph is the graph, to which we would like to define the |
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139 | /// \ref DistMap |
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140 | static DistMap *createDistMap(const _Graph& graph) { |
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141 | return new DistMap(graph); |
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142 | } |
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143 | |
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144 | }; |
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145 | |
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146 | /// \brief %BellmanFord algorithm class. |
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147 | /// |
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148 | /// \ingroup shortest_path |
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149 | /// This class provides an efficient implementation of \c Bellman-Ford |
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150 | /// algorithm. The edge lengths are passed to the algorithm using a |
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151 | /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any |
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152 | /// kind of length. |
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153 | /// |
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154 | /// The Bellman-Ford algorithm solves the shortest path from one node |
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155 | /// problem when the edges can have negative length but the graph should |
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156 | /// not contain cycles with negative sum of length. If we can assume |
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157 | /// that all edge is non-negative in the graph then the dijkstra algorithm |
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158 | /// should be used rather. |
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159 | /// |
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160 | /// The maximal time complexity of the algorithm is \f$ O(ne) \f$. |
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161 | /// |
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162 | /// The type of the length is determined by the |
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163 | /// \ref concepts::ReadMap::Value "Value" of the length map. |
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164 | /// |
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165 | /// \param _Graph The graph type the algorithm runs on. The default value |
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166 | /// is \ref ListGraph. The value of _Graph is not used directly by |
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167 | /// BellmanFord, it is only passed to \ref BellmanFordDefaultTraits. |
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168 | /// \param _LengthMap This read-only EdgeMap determines the lengths of the |
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169 | /// edges. The default map type is \ref concepts::Graph::EdgeMap |
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170 | /// "Graph::EdgeMap<int>". The value of _LengthMap is not used directly |
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171 | /// by BellmanFord, it is only passed to \ref BellmanFordDefaultTraits. |
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172 | /// \param _Traits Traits class to set various data types used by the |
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173 | /// algorithm. The default traits class is \ref BellmanFordDefaultTraits |
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174 | /// "BellmanFordDefaultTraits<_Graph,_LengthMap>". See \ref |
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175 | /// BellmanFordDefaultTraits for the documentation of a BellmanFord traits |
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176 | /// class. |
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177 | /// |
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178 | /// \author Balazs Dezso |
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179 | |
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180 | #ifdef DOXYGEN |
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181 | template <typename _Graph, typename _LengthMap, typename _Traits> |
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182 | #else |
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183 | template <typename _Graph=ListGraph, |
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184 | typename _LengthMap=typename _Graph::template EdgeMap<int>, |
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185 | typename _Traits=BellmanFordDefaultTraits<_Graph,_LengthMap> > |
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186 | #endif |
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187 | class BellmanFord { |
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188 | public: |
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189 | |
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190 | /// \brief \ref Exception for uninitialized parameters. |
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191 | /// |
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192 | /// This error represents problems in the initialization |
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193 | /// of the parameters of the algorithms. |
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194 | |
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195 | class UninitializedParameter : public lemon::UninitializedParameter { |
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196 | public: |
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197 | virtual const char* what() const throw() { |
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198 | return "lemon::BellmanFord::UninitializedParameter"; |
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199 | } |
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200 | }; |
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201 | |
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202 | typedef _Traits Traits; |
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203 | ///The type of the underlying graph. |
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204 | typedef typename _Traits::Graph Graph; |
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205 | |
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206 | typedef typename Graph::Node Node; |
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207 | typedef typename Graph::NodeIt NodeIt; |
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208 | typedef typename Graph::Edge Edge; |
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209 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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210 | |
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211 | /// \brief The type of the length of the edges. |
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212 | typedef typename _Traits::LengthMap::Value Value; |
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213 | /// \brief The type of the map that stores the edge lengths. |
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214 | typedef typename _Traits::LengthMap LengthMap; |
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215 | /// \brief The type of the map that stores the last |
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216 | /// edges of the shortest paths. |
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217 | typedef typename _Traits::PredMap PredMap; |
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218 | /// \brief The type of the map that stores the dists of the nodes. |
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219 | typedef typename _Traits::DistMap DistMap; |
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220 | /// \brief The operation traits. |
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221 | typedef typename _Traits::OperationTraits OperationTraits; |
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222 | private: |
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223 | /// Pointer to the underlying graph. |
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224 | const Graph *graph; |
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225 | /// Pointer to the length map |
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226 | const LengthMap *length; |
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227 | ///Pointer to the map of predecessors edges. |
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228 | PredMap *_pred; |
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229 | ///Indicates if \ref _pred is locally allocated (\c true) or not. |
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230 | bool local_pred; |
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231 | ///Pointer to the map of distances. |
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232 | DistMap *_dist; |
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233 | ///Indicates if \ref _dist is locally allocated (\c true) or not. |
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234 | bool local_dist; |
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235 | |
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236 | typedef typename Graph::template NodeMap<bool> MaskMap; |
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237 | MaskMap *_mask; |
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238 | |
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239 | std::vector<Node> _process; |
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240 | |
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241 | /// Creates the maps if necessary. |
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242 | void create_maps() { |
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243 | if(!_pred) { |
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244 | local_pred = true; |
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245 | _pred = Traits::createPredMap(*graph); |
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246 | } |
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247 | if(!_dist) { |
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248 | local_dist = true; |
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249 | _dist = Traits::createDistMap(*graph); |
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250 | } |
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251 | _mask = new MaskMap(*graph, false); |
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252 | } |
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253 | |
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254 | public : |
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255 | |
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256 | typedef BellmanFord Create; |
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257 | |
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258 | /// \name Named template parameters |
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259 | |
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260 | ///@{ |
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261 | |
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262 | template <class T> |
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263 | struct DefPredMapTraits : public Traits { |
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264 | typedef T PredMap; |
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265 | static PredMap *createPredMap(const Graph&) { |
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266 | throw UninitializedParameter(); |
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267 | } |
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268 | }; |
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269 | |
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270 | /// \brief \ref named-templ-param "Named parameter" for setting PredMap |
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271 | /// type |
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272 | /// \ref named-templ-param "Named parameter" for setting PredMap type |
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273 | /// |
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274 | template <class T> |
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275 | struct DefPredMap |
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276 | : public BellmanFord< Graph, LengthMap, DefPredMapTraits<T> > { |
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277 | typedef BellmanFord< Graph, LengthMap, DefPredMapTraits<T> > Create; |
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278 | }; |
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279 | |
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280 | template <class T> |
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281 | struct DefDistMapTraits : public Traits { |
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282 | typedef T DistMap; |
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283 | static DistMap *createDistMap(const Graph&) { |
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284 | throw UninitializedParameter(); |
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285 | } |
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286 | }; |
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287 | |
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288 | /// \brief \ref named-templ-param "Named parameter" for setting DistMap |
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289 | /// type |
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290 | /// |
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291 | /// \ref named-templ-param "Named parameter" for setting DistMap type |
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292 | /// |
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293 | template <class T> |
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294 | struct DefDistMap |
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295 | : public BellmanFord< Graph, LengthMap, DefDistMapTraits<T> > { |
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296 | typedef BellmanFord< Graph, LengthMap, DefDistMapTraits<T> > Create; |
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297 | }; |
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298 | |
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299 | template <class T> |
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300 | struct DefOperationTraitsTraits : public Traits { |
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301 | typedef T OperationTraits; |
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302 | }; |
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303 | |
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304 | /// \brief \ref named-templ-param "Named parameter" for setting |
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305 | /// OperationTraits type |
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306 | /// |
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307 | /// \ref named-templ-param "Named parameter" for setting OperationTraits |
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308 | /// type |
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309 | template <class T> |
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310 | struct DefOperationTraits |
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311 | : public BellmanFord< Graph, LengthMap, DefOperationTraitsTraits<T> > { |
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312 | typedef BellmanFord< Graph, LengthMap, DefOperationTraitsTraits<T> > |
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313 | Create; |
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314 | }; |
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315 | |
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316 | ///@} |
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317 | |
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318 | protected: |
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319 | |
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320 | BellmanFord() {} |
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321 | |
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322 | public: |
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323 | |
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324 | /// \brief Constructor. |
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325 | /// |
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326 | /// \param _graph the graph the algorithm will run on. |
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327 | /// \param _length the length map used by the algorithm. |
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328 | BellmanFord(const Graph& _graph, const LengthMap& _length) : |
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329 | graph(&_graph), length(&_length), |
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330 | _pred(0), local_pred(false), |
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331 | _dist(0), local_dist(false), _mask(0) {} |
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332 | |
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333 | ///Destructor. |
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334 | ~BellmanFord() { |
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335 | if(local_pred) delete _pred; |
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336 | if(local_dist) delete _dist; |
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337 | if(_mask) delete _mask; |
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338 | } |
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339 | |
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340 | /// \brief Sets the length map. |
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341 | /// |
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342 | /// Sets the length map. |
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343 | /// \return \c (*this) |
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344 | BellmanFord &lengthMap(const LengthMap &m) { |
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345 | length = &m; |
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346 | return *this; |
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347 | } |
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348 | |
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349 | /// \brief Sets the map storing the predecessor edges. |
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350 | /// |
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351 | /// Sets the map storing the predecessor edges. |
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352 | /// If you don't use this function before calling \ref run(), |
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353 | /// it will allocate one. The destuctor deallocates this |
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354 | /// automatically allocated map, of course. |
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355 | /// \return \c (*this) |
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356 | BellmanFord &predMap(PredMap &m) { |
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357 | if(local_pred) { |
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358 | delete _pred; |
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359 | local_pred=false; |
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360 | } |
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361 | _pred = &m; |
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362 | return *this; |
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363 | } |
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364 | |
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365 | /// \brief Sets the map storing the distances calculated by the algorithm. |
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366 | /// |
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367 | /// Sets the map storing the distances calculated by the algorithm. |
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368 | /// If you don't use this function before calling \ref run(), |
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369 | /// it will allocate one. The destuctor deallocates this |
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370 | /// automatically allocated map, of course. |
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371 | /// \return \c (*this) |
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372 | BellmanFord &distMap(DistMap &m) { |
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373 | if(local_dist) { |
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374 | delete _dist; |
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375 | local_dist=false; |
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376 | } |
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377 | _dist = &m; |
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378 | return *this; |
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379 | } |
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380 | |
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381 | /// \name Execution control |
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382 | /// The simplest way to execute the algorithm is to use |
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383 | /// one of the member functions called \c run(...). |
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384 | /// \n |
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385 | /// If you need more control on the execution, |
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386 | /// first you must call \ref init(), then you can add several source nodes |
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387 | /// with \ref addSource(). |
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388 | /// Finally \ref start() will perform the actual path |
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389 | /// computation. |
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390 | |
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391 | ///@{ |
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392 | |
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393 | /// \brief Initializes the internal data structures. |
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394 | /// |
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395 | /// Initializes the internal data structures. |
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396 | void init(const Value value = OperationTraits::infinity()) { |
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397 | create_maps(); |
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398 | for (NodeIt it(*graph); it != INVALID; ++it) { |
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399 | _pred->set(it, INVALID); |
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400 | _dist->set(it, value); |
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401 | } |
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402 | _process.clear(); |
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403 | if (OperationTraits::less(value, OperationTraits::infinity())) { |
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404 | for (NodeIt it(*graph); it != INVALID; ++it) { |
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405 | _process.push_back(it); |
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406 | _mask->set(it, true); |
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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 Adds a new source node. |
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412 | /// |
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413 | /// Adds a new source node. The optional second parameter is the |
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414 | /// initial distance of the node. It just sets the distance of the |
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415 | /// node to the given value. |
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416 | void addSource(Node source, Value dst = OperationTraits::zero()) { |
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417 | _dist->set(source, dst); |
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418 | if (!(*_mask)[source]) { |
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419 | _process.push_back(source); |
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420 | _mask->set(source, true); |
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421 | } |
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422 | } |
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423 | |
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424 | /// \brief Executes one round from the Bellman-Ford algorithm. |
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425 | /// |
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426 | /// If the algoritm calculated the distances in the previous round |
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427 | /// exactly for all at most \f$ k \f$ length path lengths then it will |
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428 | /// calculate the distances exactly for all at most \f$ k + 1 \f$ |
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429 | /// length path lengths. With \f$ k \f$ iteration this function |
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430 | /// calculates the at most \f$ k \f$ length path lengths. |
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431 | /// |
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432 | /// \warning The paths with limited edge number cannot be retrieved |
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433 | /// easily with \ref path() or \ref predEdge() functions. If you |
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434 | /// need the shortest path and not just the distance you should store |
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435 | /// after each iteration the \ref predMap() map and manually build |
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436 | /// the path. |
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437 | /// |
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438 | /// \return %True when the algorithm have not found more shorter |
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439 | /// paths. |
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440 | bool processNextRound() { |
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441 | for (int i = 0; i < int(_process.size()); ++i) { |
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442 | _mask->set(_process[i], false); |
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443 | } |
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444 | std::vector<Node> nextProcess; |
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445 | std::vector<Value> values(_process.size()); |
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446 | for (int i = 0; i < int(_process.size()); ++i) { |
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447 | values[i] = (*_dist)[_process[i]]; |
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448 | } |
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449 | for (int i = 0; i < int(_process.size()); ++i) { |
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450 | for (OutEdgeIt it(*graph, _process[i]); it != INVALID; ++it) { |
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451 | Node target = graph->target(it); |
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452 | Value relaxed = OperationTraits::plus(values[i], (*length)[it]); |
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453 | if (OperationTraits::less(relaxed, (*_dist)[target])) { |
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454 | _pred->set(target, it); |
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455 | _dist->set(target, relaxed); |
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456 | if (!(*_mask)[target]) { |
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457 | _mask->set(target, true); |
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458 | nextProcess.push_back(target); |
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459 | } |
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460 | } |
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461 | } |
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462 | } |
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463 | _process.swap(nextProcess); |
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464 | return _process.empty(); |
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465 | } |
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466 | |
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467 | /// \brief Executes one weak round from the Bellman-Ford algorithm. |
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468 | /// |
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469 | /// If the algorithm calculated the distances in the |
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470 | /// previous round at least for all at most k length paths then it will |
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471 | /// calculate the distances at least for all at most k + 1 length paths. |
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472 | /// This function does not make it possible to calculate strictly the |
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473 | /// at most k length minimal paths, this is why it is |
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474 | /// called just weak round. |
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475 | /// \return %True when the algorithm have not found more shorter paths. |
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476 | bool processNextWeakRound() { |
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477 | for (int i = 0; i < int(_process.size()); ++i) { |
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478 | _mask->set(_process[i], false); |
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479 | } |
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480 | std::vector<Node> nextProcess; |
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481 | for (int i = 0; i < int(_process.size()); ++i) { |
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482 | for (OutEdgeIt it(*graph, _process[i]); it != INVALID; ++it) { |
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483 | Node target = graph->target(it); |
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484 | Value relaxed = |
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485 | OperationTraits::plus((*_dist)[_process[i]], (*length)[it]); |
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486 | if (OperationTraits::less(relaxed, (*_dist)[target])) { |
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487 | _pred->set(target, it); |
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488 | _dist->set(target, relaxed); |
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489 | if (!(*_mask)[target]) { |
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490 | _mask->set(target, true); |
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491 | nextProcess.push_back(target); |
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492 | } |
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493 | } |
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494 | } |
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495 | } |
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496 | _process.swap(nextProcess); |
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497 | return _process.empty(); |
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498 | } |
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499 | |
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500 | /// \brief Executes the algorithm. |
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501 | /// |
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502 | /// \pre init() must be called and at least one node should be added |
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503 | /// with addSource() before using this function. |
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504 | /// |
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505 | /// This method runs the %BellmanFord algorithm from the root node(s) |
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506 | /// in order to compute the shortest path to each node. The algorithm |
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507 | /// computes |
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508 | /// - The shortest path tree. |
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509 | /// - The distance of each node from the root(s). |
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510 | void start() { |
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511 | int num = countNodes(*graph) - 1; |
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512 | for (int i = 0; i < num; ++i) { |
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513 | if (processNextWeakRound()) break; |
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514 | } |
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515 | } |
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516 | |
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517 | /// \brief Executes the algorithm and checks the negative cycles. |
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518 | /// |
---|
519 | /// \pre init() must be called and at least one node should be added |
---|
520 | /// with addSource() before using this function. If there is |
---|
521 | /// a negative cycle in the graph it gives back false. |
---|
522 | /// |
---|
523 | /// This method runs the %BellmanFord algorithm from the root node(s) |
---|
524 | /// in order to compute the shortest path to each node. The algorithm |
---|
525 | /// computes |
---|
526 | /// - The shortest path tree. |
---|
527 | /// - The distance of each node from the root(s). |
---|
528 | bool checkedStart() { |
---|
529 | int num = countNodes(*graph); |
---|
530 | for (int i = 0; i < num; ++i) { |
---|
531 | if (processNextWeakRound()) return true; |
---|
532 | } |
---|
533 | return _process.empty(); |
---|
534 | } |
---|
535 | |
---|
536 | /// \brief Executes the algorithm with path length limit. |
---|
537 | /// |
---|
538 | /// \pre init() must be called and at least one node should be added |
---|
539 | /// with addSource() before using this function. |
---|
540 | /// |
---|
541 | /// This method runs the %BellmanFord algorithm from the root |
---|
542 | /// node(s) in order to compute the shortest path lengths with at |
---|
543 | /// most \c num edge. |
---|
544 | /// |
---|
545 | /// \warning The paths with limited edge number cannot be retrieved |
---|
546 | /// easily with \ref path() or \ref predEdge() functions. If you |
---|
547 | /// need the shortest path and not just the distance you should store |
---|
548 | /// after each iteration the \ref predMap() map and manually build |
---|
549 | /// the path. |
---|
550 | /// |
---|
551 | /// The algorithm computes |
---|
552 | /// - The predecessor edge from each node. |
---|
553 | /// - The limited distance of each node from the root(s). |
---|
554 | void limitedStart(int num) { |
---|
555 | for (int i = 0; i < num; ++i) { |
---|
556 | if (processNextRound()) break; |
---|
557 | } |
---|
558 | } |
---|
559 | |
---|
560 | /// \brief Runs %BellmanFord algorithm from node \c s. |
---|
561 | /// |
---|
562 | /// This method runs the %BellmanFord algorithm from a root node \c s |
---|
563 | /// in order to compute the shortest path to each node. The algorithm |
---|
564 | /// computes |
---|
565 | /// - The shortest path tree. |
---|
566 | /// - The distance of each node from the root. |
---|
567 | /// |
---|
568 | /// \note d.run(s) is just a shortcut of the following code. |
---|
569 | ///\code |
---|
570 | /// d.init(); |
---|
571 | /// d.addSource(s); |
---|
572 | /// d.start(); |
---|
573 | ///\endcode |
---|
574 | void run(Node s) { |
---|
575 | init(); |
---|
576 | addSource(s); |
---|
577 | start(); |
---|
578 | } |
---|
579 | |
---|
580 | /// \brief Runs %BellmanFord algorithm with limited path length |
---|
581 | /// from node \c s. |
---|
582 | /// |
---|
583 | /// This method runs the %BellmanFord algorithm from a root node \c s |
---|
584 | /// in order to compute the shortest path with at most \c len edges |
---|
585 | /// to each node. The algorithm computes |
---|
586 | /// - The shortest path tree. |
---|
587 | /// - The distance of each node from the root. |
---|
588 | /// |
---|
589 | /// \note d.run(s, num) is just a shortcut of the following code. |
---|
590 | ///\code |
---|
591 | /// d.init(); |
---|
592 | /// d.addSource(s); |
---|
593 | /// d.limitedStart(num); |
---|
594 | ///\endcode |
---|
595 | void run(Node s, int num) { |
---|
596 | init(); |
---|
597 | addSource(s); |
---|
598 | limitedStart(num); |
---|
599 | } |
---|
600 | |
---|
601 | ///@} |
---|
602 | |
---|
603 | /// \name Query Functions |
---|
604 | /// The result of the %BellmanFord algorithm can be obtained using these |
---|
605 | /// functions.\n |
---|
606 | /// Before the use of these functions, |
---|
607 | /// either run() or start() must be called. |
---|
608 | |
---|
609 | ///@{ |
---|
610 | |
---|
611 | /// \brief Lemon iterator for get the active nodes. |
---|
612 | /// |
---|
613 | /// Lemon iterator for get the active nodes. This class provides a |
---|
614 | /// common style lemon iterator which gives back a subset of the |
---|
615 | /// nodes. The iterated nodes are active in the algorithm after |
---|
616 | /// the last phase so these should be checked in the next phase to |
---|
617 | /// find augmenting edges from these. |
---|
618 | class ActiveIt { |
---|
619 | public: |
---|
620 | |
---|
621 | /// \brief Constructor. |
---|
622 | /// |
---|
623 | /// Constructor for get the nodeset of the variable. |
---|
624 | ActiveIt(const BellmanFord& algorithm) : _algorithm(&algorithm) |
---|
625 | { |
---|
626 | _index = _algorithm->_process.size() - 1; |
---|
627 | } |
---|
628 | |
---|
629 | /// \brief Invalid constructor. |
---|
630 | /// |
---|
631 | /// Invalid constructor. |
---|
632 | ActiveIt(Invalid) : _algorithm(0), _index(-1) {} |
---|
633 | |
---|
634 | /// \brief Conversion to node. |
---|
635 | /// |
---|
636 | /// Conversion to node. |
---|
637 | operator Node() const { |
---|
638 | return _index >= 0 ? _algorithm->_process[_index] : INVALID; |
---|
639 | } |
---|
640 | |
---|
641 | /// \brief Increment operator. |
---|
642 | /// |
---|
643 | /// Increment operator. |
---|
644 | ActiveIt& operator++() { |
---|
645 | --_index; |
---|
646 | return *this; |
---|
647 | } |
---|
648 | |
---|
649 | bool operator==(const ActiveIt& it) const { |
---|
650 | return static_cast<Node>(*this) == static_cast<Node>(it); |
---|
651 | } |
---|
652 | bool operator!=(const ActiveIt& it) const { |
---|
653 | return static_cast<Node>(*this) != static_cast<Node>(it); |
---|
654 | } |
---|
655 | bool operator<(const ActiveIt& it) const { |
---|
656 | return static_cast<Node>(*this) < static_cast<Node>(it); |
---|
657 | } |
---|
658 | |
---|
659 | private: |
---|
660 | const BellmanFord* _algorithm; |
---|
661 | int _index; |
---|
662 | }; |
---|
663 | |
---|
664 | typedef PredMapPath<Graph, PredMap> Path; |
---|
665 | |
---|
666 | /// \brief Gives back the shortest path. |
---|
667 | /// |
---|
668 | /// Gives back the shortest path. |
---|
669 | /// \pre The \c t should be reachable from the source. |
---|
670 | Path path(Node t) |
---|
671 | { |
---|
672 | return Path(*graph, *_pred, t); |
---|
673 | } |
---|
674 | |
---|
675 | |
---|
676 | // TODO : implement negative cycle |
---|
677 | // /// \brief Gives back a negative cycle. |
---|
678 | // /// |
---|
679 | // /// This function gives back a negative cycle. |
---|
680 | // /// If the algorithm have not found yet negative cycle it will give back |
---|
681 | // /// an empty path. |
---|
682 | // Path negativeCycle() { |
---|
683 | // typename Graph::template NodeMap<int> state(*graph, 0); |
---|
684 | // for (ActiveIt it(*this); it != INVALID; ++it) { |
---|
685 | // if (state[it] == 0) { |
---|
686 | // for (Node t = it; predEdge(t) != INVALID; t = predNode(t)) { |
---|
687 | // if (state[t] == 0) { |
---|
688 | // state[t] = 1; |
---|
689 | // } else if (state[t] == 2) { |
---|
690 | // break; |
---|
691 | // } else { |
---|
692 | // p.clear(); |
---|
693 | // typename Path::Builder b(p); |
---|
694 | // b.setStartNode(t); |
---|
695 | // b.pushFront(predEdge(t)); |
---|
696 | // for(Node s = predNode(t); s != t; s = predNode(s)) { |
---|
697 | // b.pushFront(predEdge(s)); |
---|
698 | // } |
---|
699 | // b.commit(); |
---|
700 | // return true; |
---|
701 | // } |
---|
702 | // } |
---|
703 | // for (Node t = it; predEdge(t) != INVALID; t = predNode(t)) { |
---|
704 | // if (state[t] == 1) { |
---|
705 | // state[t] = 2; |
---|
706 | // } else { |
---|
707 | // break; |
---|
708 | // } |
---|
709 | // } |
---|
710 | // } |
---|
711 | // } |
---|
712 | // return false; |
---|
713 | // } |
---|
714 | |
---|
715 | /// \brief The distance of a node from the root. |
---|
716 | /// |
---|
717 | /// Returns the distance of a node from the root. |
---|
718 | /// \pre \ref run() must be called before using this function. |
---|
719 | /// \warning If node \c v in unreachable from the root the return value |
---|
720 | /// of this funcion is undefined. |
---|
721 | Value dist(Node v) const { return (*_dist)[v]; } |
---|
722 | |
---|
723 | /// \brief Returns the 'previous edge' of the shortest path tree. |
---|
724 | /// |
---|
725 | /// For a node \c v it returns the 'previous edge' of the shortest path |
---|
726 | /// tree, i.e. it returns the last edge of a shortest path from the root |
---|
727 | /// to \c v. It is \ref INVALID if \c v is unreachable from the root or |
---|
728 | /// if \c v=s. The shortest path tree used here is equal to the shortest |
---|
729 | /// path tree used in \ref predNode(). |
---|
730 | /// \pre \ref run() must be called before using |
---|
731 | /// this function. |
---|
732 | Edge predEdge(Node v) const { return (*_pred)[v]; } |
---|
733 | |
---|
734 | /// \brief Returns the 'previous node' of the shortest path tree. |
---|
735 | /// |
---|
736 | /// For a node \c v it returns the 'previous node' of the shortest path |
---|
737 | /// tree, i.e. it returns the last but one node from a shortest path from |
---|
738 | /// the root to \c /v. It is INVALID if \c v is unreachable from the root |
---|
739 | /// or if \c v=s. The shortest path tree used here is equal to the |
---|
740 | /// shortest path tree used in \ref predEdge(). \pre \ref run() must be |
---|
741 | /// called before using this function. |
---|
742 | Node predNode(Node v) const { |
---|
743 | return (*_pred)[v] == INVALID ? INVALID : graph->source((*_pred)[v]); |
---|
744 | } |
---|
745 | |
---|
746 | /// \brief Returns a reference to the NodeMap of distances. |
---|
747 | /// |
---|
748 | /// Returns a reference to the NodeMap of distances. \pre \ref run() must |
---|
749 | /// be called before using this function. |
---|
750 | const DistMap &distMap() const { return *_dist;} |
---|
751 | |
---|
752 | /// \brief Returns a reference to the shortest path tree map. |
---|
753 | /// |
---|
754 | /// Returns a reference to the NodeMap of the edges of the |
---|
755 | /// shortest path tree. |
---|
756 | /// \pre \ref run() must be called before using this function. |
---|
757 | const PredMap &predMap() const { return *_pred; } |
---|
758 | |
---|
759 | /// \brief Checks if a node is reachable from the root. |
---|
760 | /// |
---|
761 | /// Returns \c true if \c v is reachable from the root. |
---|
762 | /// \pre \ref run() must be called before using this function. |
---|
763 | /// |
---|
764 | bool reached(Node v) { return (*_dist)[v] != OperationTraits::infinity(); } |
---|
765 | |
---|
766 | ///@} |
---|
767 | }; |
---|
768 | |
---|
769 | /// \brief Default traits class of BellmanFord function. |
---|
770 | /// |
---|
771 | /// Default traits class of BellmanFord function. |
---|
772 | /// \param _Graph Graph type. |
---|
773 | /// \param _LengthMap Type of length map. |
---|
774 | template <typename _Graph, typename _LengthMap> |
---|
775 | struct BellmanFordWizardDefaultTraits { |
---|
776 | /// \brief The graph type the algorithm runs on. |
---|
777 | typedef _Graph Graph; |
---|
778 | |
---|
779 | /// \brief The type of the map that stores the edge lengths. |
---|
780 | /// |
---|
781 | /// The type of the map that stores the edge lengths. |
---|
782 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
---|
783 | typedef _LengthMap LengthMap; |
---|
784 | |
---|
785 | /// \brief The value type of the length map. |
---|
786 | typedef typename _LengthMap::Value Value; |
---|
787 | |
---|
788 | /// \brief Operation traits for Bellman-Ford algorithm. |
---|
789 | /// |
---|
790 | /// It defines the infinity type on the given Value type |
---|
791 | /// and the used operation. |
---|
792 | /// \see BellmanFordDefaultOperationTraits |
---|
793 | typedef BellmanFordDefaultOperationTraits<Value> OperationTraits; |
---|
794 | |
---|
795 | /// \brief The type of the map that stores the last |
---|
796 | /// edges of the shortest paths. |
---|
797 | /// |
---|
798 | /// The type of the map that stores the last |
---|
799 | /// edges of the shortest paths. |
---|
800 | /// It must meet the \ref concepts::WriteMap "WriteMap" concept. |
---|
801 | typedef NullMap <typename _Graph::Node,typename _Graph::Edge> PredMap; |
---|
802 | |
---|
803 | /// \brief Instantiates a PredMap. |
---|
804 | /// |
---|
805 | /// This function instantiates a \ref PredMap. |
---|
806 | static PredMap *createPredMap(const _Graph &) { |
---|
807 | return new PredMap(); |
---|
808 | } |
---|
809 | /// \brief The type of the map that stores the dists of the nodes. |
---|
810 | /// |
---|
811 | /// The type of the map that stores the dists of the nodes. |
---|
812 | /// It must meet the \ref concepts::WriteMap "WriteMap" concept. |
---|
813 | typedef NullMap<typename Graph::Node, Value> DistMap; |
---|
814 | /// \brief Instantiates a DistMap. |
---|
815 | /// |
---|
816 | /// This function instantiates a \ref DistMap. |
---|
817 | static DistMap *createDistMap(const _Graph &) { |
---|
818 | return new DistMap(); |
---|
819 | } |
---|
820 | }; |
---|
821 | |
---|
822 | /// \brief Default traits used by \ref BellmanFordWizard |
---|
823 | /// |
---|
824 | /// To make it easier to use BellmanFord algorithm |
---|
825 | /// we have created a wizard class. |
---|
826 | /// This \ref BellmanFordWizard class needs default traits, |
---|
827 | /// as well as the \ref BellmanFord class. |
---|
828 | /// The \ref BellmanFordWizardBase is a class to be the default traits of the |
---|
829 | /// \ref BellmanFordWizard class. |
---|
830 | /// \todo More named parameters are required... |
---|
831 | template<class _Graph,class _LengthMap> |
---|
832 | class BellmanFordWizardBase |
---|
833 | : public BellmanFordWizardDefaultTraits<_Graph,_LengthMap> { |
---|
834 | |
---|
835 | typedef BellmanFordWizardDefaultTraits<_Graph,_LengthMap> Base; |
---|
836 | protected: |
---|
837 | /// Type of the nodes in the graph. |
---|
838 | typedef typename Base::Graph::Node Node; |
---|
839 | |
---|
840 | /// Pointer to the underlying graph. |
---|
841 | void *_graph; |
---|
842 | /// Pointer to the length map |
---|
843 | void *_length; |
---|
844 | ///Pointer to the map of predecessors edges. |
---|
845 | void *_pred; |
---|
846 | ///Pointer to the map of distances. |
---|
847 | void *_dist; |
---|
848 | ///Pointer to the source node. |
---|
849 | Node _source; |
---|
850 | |
---|
851 | public: |
---|
852 | /// Constructor. |
---|
853 | |
---|
854 | /// This constructor does not require parameters, therefore it initiates |
---|
855 | /// all of the attributes to default values (0, INVALID). |
---|
856 | BellmanFordWizardBase() : _graph(0), _length(0), _pred(0), |
---|
857 | _dist(0), _source(INVALID) {} |
---|
858 | |
---|
859 | /// Constructor. |
---|
860 | |
---|
861 | /// This constructor requires some parameters, |
---|
862 | /// listed in the parameters list. |
---|
863 | /// Others are initiated to 0. |
---|
864 | /// \param graph is the initial value of \ref _graph |
---|
865 | /// \param length is the initial value of \ref _length |
---|
866 | /// \param source is the initial value of \ref _source |
---|
867 | BellmanFordWizardBase(const _Graph& graph, |
---|
868 | const _LengthMap& length, |
---|
869 | Node source = INVALID) : |
---|
870 | _graph(reinterpret_cast<void*>(const_cast<_Graph*>(&graph))), |
---|
871 | _length(reinterpret_cast<void*>(const_cast<_LengthMap*>(&length))), |
---|
872 | _pred(0), _dist(0), _source(source) {} |
---|
873 | |
---|
874 | }; |
---|
875 | |
---|
876 | /// A class to make the usage of BellmanFord algorithm easier |
---|
877 | |
---|
878 | /// This class is created to make it easier to use BellmanFord algorithm. |
---|
879 | /// It uses the functions and features of the plain \ref BellmanFord, |
---|
880 | /// but it is much simpler to use it. |
---|
881 | /// |
---|
882 | /// Simplicity means that the way to change the types defined |
---|
883 | /// in the traits class is based on functions that returns the new class |
---|
884 | /// and not on templatable built-in classes. |
---|
885 | /// When using the plain \ref BellmanFord |
---|
886 | /// the new class with the modified type comes from |
---|
887 | /// the original class by using the :: |
---|
888 | /// operator. In the case of \ref BellmanFordWizard only |
---|
889 | /// a function have to be called and it will |
---|
890 | /// return the needed class. |
---|
891 | /// |
---|
892 | /// It does not have own \ref run method. When its \ref run method is called |
---|
893 | /// it initiates a plain \ref BellmanFord class, and calls the \ref |
---|
894 | /// BellmanFord::run method of it. |
---|
895 | template<class _Traits> |
---|
896 | class BellmanFordWizard : public _Traits { |
---|
897 | typedef _Traits Base; |
---|
898 | |
---|
899 | ///The type of the underlying graph. |
---|
900 | typedef typename _Traits::Graph Graph; |
---|
901 | |
---|
902 | typedef typename Graph::Node Node; |
---|
903 | typedef typename Graph::NodeIt NodeIt; |
---|
904 | typedef typename Graph::Edge Edge; |
---|
905 | typedef typename Graph::OutEdgeIt EdgeIt; |
---|
906 | |
---|
907 | ///The type of the map that stores the edge lengths. |
---|
908 | typedef typename _Traits::LengthMap LengthMap; |
---|
909 | |
---|
910 | ///The type of the length of the edges. |
---|
911 | typedef typename LengthMap::Value Value; |
---|
912 | |
---|
913 | ///\brief The type of the map that stores the last |
---|
914 | ///edges of the shortest paths. |
---|
915 | typedef typename _Traits::PredMap PredMap; |
---|
916 | |
---|
917 | ///The type of the map that stores the dists of the nodes. |
---|
918 | typedef typename _Traits::DistMap DistMap; |
---|
919 | |
---|
920 | public: |
---|
921 | /// Constructor. |
---|
922 | BellmanFordWizard() : _Traits() {} |
---|
923 | |
---|
924 | /// \brief Constructor that requires parameters. |
---|
925 | /// |
---|
926 | /// Constructor that requires parameters. |
---|
927 | /// These parameters will be the default values for the traits class. |
---|
928 | BellmanFordWizard(const Graph& graph, const LengthMap& length, |
---|
929 | Node src = INVALID) |
---|
930 | : _Traits(graph, length, src) {} |
---|
931 | |
---|
932 | /// \brief Copy constructor |
---|
933 | BellmanFordWizard(const _Traits &b) : _Traits(b) {} |
---|
934 | |
---|
935 | ~BellmanFordWizard() {} |
---|
936 | |
---|
937 | /// \brief Runs BellmanFord algorithm from a given node. |
---|
938 | /// |
---|
939 | /// Runs BellmanFord algorithm from a given node. |
---|
940 | /// The node can be given by the \ref source function. |
---|
941 | void run() { |
---|
942 | if(Base::_source == INVALID) throw UninitializedParameter(); |
---|
943 | BellmanFord<Graph,LengthMap,_Traits> |
---|
944 | bf(*reinterpret_cast<const Graph*>(Base::_graph), |
---|
945 | *reinterpret_cast<const LengthMap*>(Base::_length)); |
---|
946 | if (Base::_pred) bf.predMap(*reinterpret_cast<PredMap*>(Base::_pred)); |
---|
947 | if (Base::_dist) bf.distMap(*reinterpret_cast<DistMap*>(Base::_dist)); |
---|
948 | bf.run(Base::_source); |
---|
949 | } |
---|
950 | |
---|
951 | /// \brief Runs BellmanFord algorithm from the given node. |
---|
952 | /// |
---|
953 | /// Runs BellmanFord algorithm from the given node. |
---|
954 | /// \param src is the given source. |
---|
955 | void run(Node src) { |
---|
956 | Base::_source = src; |
---|
957 | run(); |
---|
958 | } |
---|
959 | |
---|
960 | template<class T> |
---|
961 | struct DefPredMapBase : public Base { |
---|
962 | typedef T PredMap; |
---|
963 | static PredMap *createPredMap(const Graph &) { return 0; }; |
---|
964 | DefPredMapBase(const _Traits &b) : _Traits(b) {} |
---|
965 | }; |
---|
966 | |
---|
967 | ///\brief \ref named-templ-param "Named parameter" |
---|
968 | ///function for setting PredMap type |
---|
969 | /// |
---|
970 | /// \ref named-templ-param "Named parameter" |
---|
971 | ///function for setting PredMap type |
---|
972 | /// |
---|
973 | template<class T> |
---|
974 | BellmanFordWizard<DefPredMapBase<T> > predMap(const T &t) |
---|
975 | { |
---|
976 | Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t)); |
---|
977 | return BellmanFordWizard<DefPredMapBase<T> >(*this); |
---|
978 | } |
---|
979 | |
---|
980 | template<class T> |
---|
981 | struct DefDistMapBase : public Base { |
---|
982 | typedef T DistMap; |
---|
983 | static DistMap *createDistMap(const Graph &) { return 0; }; |
---|
984 | DefDistMapBase(const _Traits &b) : _Traits(b) {} |
---|
985 | }; |
---|
986 | |
---|
987 | ///\brief \ref named-templ-param "Named parameter" |
---|
988 | ///function for setting DistMap type |
---|
989 | /// |
---|
990 | /// \ref named-templ-param "Named parameter" |
---|
991 | ///function for setting DistMap type |
---|
992 | /// |
---|
993 | template<class T> |
---|
994 | BellmanFordWizard<DefDistMapBase<T> > distMap(const T &t) { |
---|
995 | Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t)); |
---|
996 | return BellmanFordWizard<DefDistMapBase<T> >(*this); |
---|
997 | } |
---|
998 | |
---|
999 | template<class T> |
---|
1000 | struct DefOperationTraitsBase : public Base { |
---|
1001 | typedef T OperationTraits; |
---|
1002 | DefOperationTraitsBase(const _Traits &b) : _Traits(b) {} |
---|
1003 | }; |
---|
1004 | |
---|
1005 | ///\brief \ref named-templ-param "Named parameter" |
---|
1006 | ///function for setting OperationTraits type |
---|
1007 | /// |
---|
1008 | /// \ref named-templ-param "Named parameter" |
---|
1009 | ///function for setting OperationTraits type |
---|
1010 | /// |
---|
1011 | template<class T> |
---|
1012 | BellmanFordWizard<DefOperationTraitsBase<T> > distMap() { |
---|
1013 | return BellmanFordWizard<DefDistMapBase<T> >(*this); |
---|
1014 | } |
---|
1015 | |
---|
1016 | /// \brief Sets the source node, from which the BellmanFord algorithm runs. |
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1017 | /// |
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1018 | /// Sets the source node, from which the BellmanFord algorithm runs. |
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1019 | /// \param src is the source node. |
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1020 | BellmanFordWizard<_Traits>& source(Node src) { |
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1021 | Base::_source = src; |
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1022 | return *this; |
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1023 | } |
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1024 | |
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1025 | }; |
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1026 | |
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1027 | /// \brief Function type interface for BellmanFord algorithm. |
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1028 | /// |
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1029 | /// \ingroup shortest_path |
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1030 | /// Function type interface for BellmanFord algorithm. |
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1031 | /// |
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1032 | /// This function also has several \ref named-templ-func-param |
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1033 | /// "named parameters", they are declared as the members of class |
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1034 | /// \ref BellmanFordWizard. |
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1035 | /// The following |
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1036 | /// example shows how to use these parameters. |
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1037 | ///\code |
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1038 | /// bellmanford(g,length,source).predMap(preds).run(); |
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1039 | ///\endcode |
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1040 | /// \warning Don't forget to put the \ref BellmanFordWizard::run() "run()" |
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1041 | /// to the end of the parameter list. |
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1042 | /// \sa BellmanFordWizard |
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1043 | /// \sa BellmanFord |
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1044 | template<class _Graph, class _LengthMap> |
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1045 | BellmanFordWizard<BellmanFordWizardBase<_Graph,_LengthMap> > |
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1046 | bellmanFord(const _Graph& graph, |
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1047 | const _LengthMap& length, |
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1048 | typename _Graph::Node source = INVALID) { |
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1049 | return BellmanFordWizard<BellmanFordWizardBase<_Graph,_LengthMap> > |
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1050 | (graph, length, source); |
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1051 | } |
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1052 | |
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1053 | } //END OF NAMESPACE LEMON |
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1054 | |
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1055 | #endif |
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1056 | |
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