1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2008 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_BELLMAN_FORD_H |
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20 | #define LEMON_BELLMAN_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 Bellman-Ford algorithm. |
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25 | |
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26 | #include <lemon/list_graph.h> |
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27 | #include <lemon/bits/path_dump.h> |
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28 | #include <lemon/core.h> |
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29 | #include <lemon/error.h> |
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30 | #include <lemon/maps.h> |
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31 | #include <lemon/path.h> |
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32 | |
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33 | #include <limits> |
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34 | |
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35 | namespace lemon { |
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36 | |
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37 | /// \brief Default OperationTraits for the BellmanFord algorithm class. |
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38 | /// |
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39 | /// This operation traits class defines all computational operations |
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40 | /// and constants that are used in the Bellman-Ford algorithm. |
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41 | /// The default implementation is based on the \c numeric_limits class. |
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42 | /// If the numeric type does not have infinity value, then the maximum |
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43 | /// value is used as extremal infinity value. |
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44 | template < |
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45 | typename V, |
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46 | bool has_inf = std::numeric_limits<V>::has_infinity> |
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47 | struct BellmanFordDefaultOperationTraits { |
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48 | /// \e |
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49 | typedef V Value; |
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50 | /// \brief Gives back the zero value of the type. |
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51 | static Value zero() { |
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52 | return static_cast<Value>(0); |
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53 | } |
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54 | /// \brief Gives back the positive infinity value of the type. |
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55 | static Value infinity() { |
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56 | return std::numeric_limits<Value>::infinity(); |
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57 | } |
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58 | /// \brief Gives back the sum of the given two elements. |
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59 | static Value plus(const Value& left, const Value& right) { |
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60 | return left + right; |
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61 | } |
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62 | /// \brief Gives back \c true only if the first value is less than |
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63 | /// the second. |
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64 | static bool less(const Value& left, const Value& right) { |
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65 | return left < right; |
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66 | } |
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67 | }; |
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68 | |
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69 | template <typename V> |
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70 | struct BellmanFordDefaultOperationTraits<V, false> { |
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71 | typedef V Value; |
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72 | static Value zero() { |
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73 | return static_cast<Value>(0); |
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74 | } |
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75 | static Value infinity() { |
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76 | return std::numeric_limits<Value>::max(); |
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77 | } |
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78 | static Value plus(const Value& left, const Value& right) { |
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79 | if (left == infinity() || right == infinity()) return infinity(); |
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80 | return left + right; |
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81 | } |
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82 | static bool less(const Value& left, const Value& right) { |
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83 | return left < right; |
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84 | } |
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85 | }; |
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86 | |
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87 | /// \brief Default traits class of BellmanFord class. |
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88 | /// |
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89 | /// Default traits class of BellmanFord class. |
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90 | /// \param GR The type of the digraph. |
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91 | /// \param LEN The type of the length map. |
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92 | template<typename GR, typename LEN> |
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93 | struct BellmanFordDefaultTraits { |
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94 | /// The type of the digraph the algorithm runs on. |
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95 | typedef GR Digraph; |
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96 | |
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97 | /// \brief The type of the map that stores the arc lengths. |
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98 | /// |
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99 | /// The type of the map that stores the arc lengths. |
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100 | /// It must conform to the \ref concepts::ReadMap "ReadMap" concept. |
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101 | typedef LEN LengthMap; |
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102 | |
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103 | /// The type of the arc lengths. |
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104 | typedef typename LEN::Value Value; |
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105 | |
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106 | /// \brief Operation traits for Bellman-Ford algorithm. |
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107 | /// |
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108 | /// It defines the used operations and the infinity value for the |
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109 | /// given \c Value type. |
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110 | /// \see BellmanFordDefaultOperationTraits |
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111 | typedef BellmanFordDefaultOperationTraits<Value> OperationTraits; |
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112 | |
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113 | /// \brief The type of the map that stores the last arcs of the |
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114 | /// shortest paths. |
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115 | /// |
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116 | /// The type of the map that stores the last |
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117 | /// arcs of the shortest paths. |
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118 | /// It must conform to the \ref concepts::WriteMap "WriteMap" concept. |
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119 | typedef typename GR::template NodeMap<typename GR::Arc> PredMap; |
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120 | |
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121 | /// \brief Instantiates a \c PredMap. |
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122 | /// |
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123 | /// This function instantiates a \ref PredMap. |
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124 | /// \param g is the digraph to which we would like to define the |
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125 | /// \ref PredMap. |
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126 | static PredMap *createPredMap(const GR& g) { |
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127 | return new PredMap(g); |
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128 | } |
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129 | |
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130 | /// \brief The type of the map that stores the distances of the nodes. |
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131 | /// |
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132 | /// The type of the map that stores the distances of the nodes. |
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133 | /// It must conform to the \ref concepts::WriteMap "WriteMap" concept. |
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134 | typedef typename GR::template NodeMap<typename LEN::Value> DistMap; |
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135 | |
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136 | /// \brief Instantiates a \c DistMap. |
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137 | /// |
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138 | /// This function instantiates a \ref DistMap. |
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139 | /// \param g is the digraph to which we would like to define the |
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140 | /// \ref DistMap. |
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141 | static DistMap *createDistMap(const GR& g) { |
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142 | return new DistMap(g); |
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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 %BellmanFord algorithm class. |
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148 | /// |
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149 | /// \ingroup shortest_path |
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150 | /// This class provides an efficient implementation of the Bellman-Ford |
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151 | /// algorithm. The maximum time complexity of the algorithm is |
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152 | /// <tt>O(ne)</tt>. |
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153 | /// |
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154 | /// The Bellman-Ford algorithm solves the single-source shortest path |
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155 | /// problem when the arcs can have negative lengths, but the digraph |
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156 | /// should not contain directed cycles with negative total length. |
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157 | /// If all arc costs are non-negative, consider to use the Dijkstra |
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158 | /// algorithm instead, since it is more efficient. |
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159 | /// |
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160 | /// The arc lengths are passed to the algorithm using a |
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161 | /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any |
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162 | /// kind of length. The type of the length values is determined by the |
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163 | /// \ref concepts::ReadMap::Value "Value" type of the length map. |
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164 | /// |
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165 | /// There is also a \ref bellmanFord() "function-type interface" for the |
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166 | /// Bellman-Ford algorithm, which is convenient in the simplier cases and |
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167 | /// it can be used easier. |
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168 | /// |
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169 | /// \tparam GR The type of the digraph the algorithm runs on. |
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170 | /// The default type is \ref ListDigraph. |
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171 | /// \tparam LEN A \ref concepts::ReadMap "readable" arc map that specifies |
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172 | /// the lengths of the arcs. The default map type is |
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173 | /// \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
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174 | #ifdef DOXYGEN |
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175 | template <typename GR, typename LEN, typename TR> |
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176 | #else |
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177 | template <typename GR=ListDigraph, |
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178 | typename LEN=typename GR::template ArcMap<int>, |
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179 | typename TR=BellmanFordDefaultTraits<GR,LEN> > |
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180 | #endif |
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181 | class BellmanFord { |
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182 | public: |
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183 | |
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184 | ///The type of the underlying digraph. |
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185 | typedef typename TR::Digraph Digraph; |
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186 | |
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187 | /// \brief The type of the arc lengths. |
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188 | typedef typename TR::LengthMap::Value Value; |
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189 | /// \brief The type of the map that stores the arc lengths. |
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190 | typedef typename TR::LengthMap LengthMap; |
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191 | /// \brief The type of the map that stores the last |
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192 | /// arcs of the shortest paths. |
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193 | typedef typename TR::PredMap PredMap; |
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194 | /// \brief The type of the map that stores the distances of the nodes. |
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195 | typedef typename TR::DistMap DistMap; |
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196 | /// The type of the paths. |
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197 | typedef PredMapPath<Digraph, PredMap> Path; |
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198 | ///\brief The \ref BellmanFordDefaultOperationTraits |
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199 | /// "operation traits class" of the algorithm. |
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200 | typedef typename TR::OperationTraits OperationTraits; |
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201 | |
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202 | ///The \ref BellmanFordDefaultTraits "traits class" of the algorithm. |
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203 | typedef TR Traits; |
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204 | |
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205 | private: |
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206 | |
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207 | typedef typename Digraph::Node Node; |
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208 | typedef typename Digraph::NodeIt NodeIt; |
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209 | typedef typename Digraph::Arc Arc; |
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210 | typedef typename Digraph::OutArcIt OutArcIt; |
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211 | |
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212 | // Pointer to the underlying digraph. |
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213 | const Digraph *_gr; |
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214 | // Pointer to the length map |
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215 | const LengthMap *_length; |
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216 | // Pointer to the map of predecessors arcs. |
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217 | PredMap *_pred; |
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218 | // Indicates if _pred is locally allocated (true) or not. |
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219 | bool _local_pred; |
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220 | // Pointer to the map of distances. |
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221 | DistMap *_dist; |
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222 | // Indicates if _dist is locally allocated (true) or not. |
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223 | bool _local_dist; |
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224 | |
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225 | typedef typename Digraph::template NodeMap<bool> MaskMap; |
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226 | MaskMap *_mask; |
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227 | |
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228 | std::vector<Node> _process; |
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229 | |
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230 | // Creates the maps if necessary. |
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231 | void create_maps() { |
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232 | if(!_pred) { |
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233 | _local_pred = true; |
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234 | _pred = Traits::createPredMap(*_gr); |
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235 | } |
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236 | if(!_dist) { |
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237 | _local_dist = true; |
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238 | _dist = Traits::createDistMap(*_gr); |
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239 | } |
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240 | _mask = new MaskMap(*_gr, false); |
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241 | } |
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242 | |
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243 | public : |
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244 | |
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245 | typedef BellmanFord Create; |
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246 | |
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247 | /// \name Named Template Parameters |
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248 | |
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249 | ///@{ |
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250 | |
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251 | template <class T> |
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252 | struct SetPredMapTraits : public Traits { |
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253 | typedef T PredMap; |
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254 | static PredMap *createPredMap(const Digraph&) { |
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255 | LEMON_ASSERT(false, "PredMap is not initialized"); |
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256 | return 0; // ignore warnings |
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257 | } |
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258 | }; |
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259 | |
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260 | /// \brief \ref named-templ-param "Named parameter" for setting |
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261 | /// \c PredMap type. |
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262 | /// |
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263 | /// \ref named-templ-param "Named parameter" for setting |
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264 | /// \c PredMap type. |
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265 | /// It must conform to the \ref concepts::WriteMap "WriteMap" concept. |
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266 | template <class T> |
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267 | struct SetPredMap |
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268 | : public BellmanFord< Digraph, LengthMap, SetPredMapTraits<T> > { |
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269 | typedef BellmanFord< Digraph, LengthMap, SetPredMapTraits<T> > Create; |
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270 | }; |
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271 | |
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272 | template <class T> |
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273 | struct SetDistMapTraits : public Traits { |
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274 | typedef T DistMap; |
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275 | static DistMap *createDistMap(const Digraph&) { |
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276 | LEMON_ASSERT(false, "DistMap is not initialized"); |
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277 | return 0; // ignore warnings |
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278 | } |
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279 | }; |
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280 | |
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281 | /// \brief \ref named-templ-param "Named parameter" for setting |
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282 | /// \c DistMap type. |
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283 | /// |
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284 | /// \ref named-templ-param "Named parameter" for setting |
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285 | /// \c DistMap type. |
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286 | /// It must conform to the \ref concepts::WriteMap "WriteMap" concept. |
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287 | template <class T> |
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288 | struct SetDistMap |
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289 | : public BellmanFord< Digraph, LengthMap, SetDistMapTraits<T> > { |
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290 | typedef BellmanFord< Digraph, LengthMap, SetDistMapTraits<T> > Create; |
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291 | }; |
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292 | |
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293 | template <class T> |
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294 | struct SetOperationTraitsTraits : public Traits { |
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295 | typedef T OperationTraits; |
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296 | }; |
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297 | |
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298 | /// \brief \ref named-templ-param "Named parameter" for setting |
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299 | /// \c OperationTraits type. |
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300 | /// |
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301 | /// \ref named-templ-param "Named parameter" for setting |
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302 | /// \c OperationTraits type. |
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303 | /// For more information see \ref BellmanFordDefaultOperationTraits. |
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304 | template <class T> |
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305 | struct SetOperationTraits |
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306 | : public BellmanFord< Digraph, LengthMap, SetOperationTraitsTraits<T> > { |
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307 | typedef BellmanFord< Digraph, LengthMap, SetOperationTraitsTraits<T> > |
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308 | Create; |
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309 | }; |
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310 | |
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311 | ///@} |
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312 | |
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313 | protected: |
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314 | |
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315 | BellmanFord() {} |
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316 | |
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317 | public: |
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318 | |
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319 | /// \brief Constructor. |
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320 | /// |
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321 | /// Constructor. |
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322 | /// \param g The digraph the algorithm runs on. |
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323 | /// \param length The length map used by the algorithm. |
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324 | BellmanFord(const Digraph& g, const LengthMap& length) : |
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325 | _gr(&g), _length(&length), |
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326 | _pred(0), _local_pred(false), |
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327 | _dist(0), _local_dist(false), _mask(0) {} |
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328 | |
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329 | ///Destructor. |
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330 | ~BellmanFord() { |
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331 | if(_local_pred) delete _pred; |
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332 | if(_local_dist) delete _dist; |
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333 | if(_mask) delete _mask; |
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334 | } |
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335 | |
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336 | /// \brief Sets the length map. |
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337 | /// |
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338 | /// Sets the length map. |
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339 | /// \return <tt>(*this)</tt> |
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340 | BellmanFord &lengthMap(const LengthMap &map) { |
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341 | _length = ↦ |
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342 | return *this; |
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343 | } |
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344 | |
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345 | /// \brief Sets the map that stores the predecessor arcs. |
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346 | /// |
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347 | /// Sets the map that stores the predecessor arcs. |
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348 | /// If you don't use this function before calling \ref run() |
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349 | /// or \ref init(), an instance will be allocated automatically. |
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350 | /// The destructor deallocates this automatically allocated map, |
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351 | /// of course. |
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352 | /// \return <tt>(*this)</tt> |
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353 | BellmanFord &predMap(PredMap &map) { |
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354 | if(_local_pred) { |
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355 | delete _pred; |
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356 | _local_pred=false; |
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357 | } |
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358 | _pred = ↦ |
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359 | return *this; |
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360 | } |
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361 | |
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362 | /// \brief Sets the map that stores the distances of the nodes. |
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363 | /// |
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364 | /// Sets the map that stores the distances of the nodes calculated |
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365 | /// by the algorithm. |
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366 | /// If you don't use this function before calling \ref run() |
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367 | /// or \ref init(), an instance will be allocated automatically. |
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368 | /// The destructor deallocates this automatically allocated map, |
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369 | /// of course. |
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370 | /// \return <tt>(*this)</tt> |
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371 | BellmanFord &distMap(DistMap &map) { |
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372 | if(_local_dist) { |
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373 | delete _dist; |
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374 | _local_dist=false; |
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375 | } |
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376 | _dist = ↦ |
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377 | return *this; |
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378 | } |
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379 | |
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380 | /// \name Execution Control |
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381 | /// The simplest way to execute the Bellman-Ford algorithm is to use |
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382 | /// one of the member functions called \ref run().\n |
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383 | /// If you need better control on the execution, you have to call |
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384 | /// \ref init() first, then you can add several source nodes |
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385 | /// with \ref addSource(). Finally the actual path computation can be |
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386 | /// performed with \ref start(), \ref checkedStart() or |
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387 | /// \ref limitedStart(). |
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388 | |
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389 | ///@{ |
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390 | |
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391 | /// \brief Initializes the internal data structures. |
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392 | /// |
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393 | /// Initializes the internal data structures. The optional parameter |
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394 | /// is the initial distance of each node. |
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395 | void init(const Value value = OperationTraits::infinity()) { |
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396 | create_maps(); |
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397 | for (NodeIt it(*_gr); it != INVALID; ++it) { |
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398 | _pred->set(it, INVALID); |
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399 | _dist->set(it, value); |
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400 | } |
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401 | _process.clear(); |
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402 | if (OperationTraits::less(value, OperationTraits::infinity())) { |
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403 | for (NodeIt it(*_gr); it != INVALID; ++it) { |
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404 | _process.push_back(it); |
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405 | _mask->set(it, true); |
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406 | } |
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407 | } |
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408 | } |
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409 | |
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410 | /// \brief Adds a new source node. |
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411 | /// |
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412 | /// This function adds a new source node. The optional second parameter |
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413 | /// is the initial distance of the node. |
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414 | void addSource(Node source, Value dst = OperationTraits::zero()) { |
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415 | _dist->set(source, dst); |
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416 | if (!(*_mask)[source]) { |
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417 | _process.push_back(source); |
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418 | _mask->set(source, true); |
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419 | } |
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420 | } |
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421 | |
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422 | /// \brief Executes one round from the Bellman-Ford algorithm. |
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423 | /// |
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424 | /// If the algoritm calculated the distances in the previous round |
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425 | /// exactly for the paths of at most \c k arcs, then this function |
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426 | /// will calculate the distances exactly for the paths of at most |
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427 | /// <tt>k+1</tt> arcs. Performing \c k iterations using this function |
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428 | /// calculates the shortest path distances exactly for the paths |
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429 | /// consisting of at most \c k arcs. |
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430 | /// |
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431 | /// \warning The paths with limited arc number cannot be retrieved |
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432 | /// easily with \ref path() or \ref predArc() functions. If you also |
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433 | /// need the shortest paths and not only the distances, you should |
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434 | /// store the \ref predMap() "predecessor map" after each iteration |
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435 | /// and build the path manually. |
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436 | /// |
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437 | /// \return \c true when the algorithm have not found more shorter |
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438 | /// paths. |
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439 | /// |
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440 | /// \see ActiveIt |
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441 | bool processNextRound() { |
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442 | for (int i = 0; i < int(_process.size()); ++i) { |
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443 | _mask->set(_process[i], false); |
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444 | } |
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445 | std::vector<Node> nextProcess; |
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446 | std::vector<Value> values(_process.size()); |
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447 | for (int i = 0; i < int(_process.size()); ++i) { |
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448 | values[i] = (*_dist)[_process[i]]; |
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449 | } |
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450 | for (int i = 0; i < int(_process.size()); ++i) { |
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451 | for (OutArcIt it(*_gr, _process[i]); it != INVALID; ++it) { |
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452 | Node target = _gr->target(it); |
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453 | Value relaxed = OperationTraits::plus(values[i], (*_length)[it]); |
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454 | if (OperationTraits::less(relaxed, (*_dist)[target])) { |
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455 | _pred->set(target, it); |
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456 | _dist->set(target, relaxed); |
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457 | if (!(*_mask)[target]) { |
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458 | _mask->set(target, true); |
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459 | nextProcess.push_back(target); |
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460 | } |
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461 | } |
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462 | } |
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463 | } |
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464 | _process.swap(nextProcess); |
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465 | return _process.empty(); |
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466 | } |
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467 | |
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468 | /// \brief Executes one weak round from the Bellman-Ford algorithm. |
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469 | /// |
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470 | /// If the algorithm calculated the distances in the previous round |
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471 | /// at least for the paths of at most \c k arcs, then this function |
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472 | /// will calculate the distances at least for the paths of at most |
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473 | /// <tt>k+1</tt> arcs. |
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474 | /// This function does not make it possible to calculate the shortest |
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475 | /// path distances exactly for paths consisting of at most \c k arcs, |
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476 | /// this is why it is called weak round. |
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477 | /// |
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478 | /// \return \c true when the algorithm have not found more shorter |
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479 | /// paths. |
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480 | /// |
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481 | /// \see ActiveIt |
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482 | bool processNextWeakRound() { |
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483 | for (int i = 0; i < int(_process.size()); ++i) { |
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484 | _mask->set(_process[i], false); |
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485 | } |
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486 | std::vector<Node> nextProcess; |
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487 | for (int i = 0; i < int(_process.size()); ++i) { |
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488 | for (OutArcIt it(*_gr, _process[i]); it != INVALID; ++it) { |
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489 | Node target = _gr->target(it); |
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490 | Value relaxed = |
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491 | OperationTraits::plus((*_dist)[_process[i]], (*_length)[it]); |
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492 | if (OperationTraits::less(relaxed, (*_dist)[target])) { |
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493 | _pred->set(target, it); |
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494 | _dist->set(target, relaxed); |
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495 | if (!(*_mask)[target]) { |
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496 | _mask->set(target, true); |
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497 | nextProcess.push_back(target); |
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498 | } |
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499 | } |
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500 | } |
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501 | } |
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502 | _process.swap(nextProcess); |
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503 | return _process.empty(); |
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504 | } |
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505 | |
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506 | /// \brief Executes the algorithm. |
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507 | /// |
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508 | /// Executes the algorithm. |
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509 | /// |
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510 | /// This method runs the Bellman-Ford algorithm from the root node(s) |
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511 | /// in order to compute the shortest path to each node. |
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512 | /// |
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513 | /// The algorithm computes |
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514 | /// - the shortest path tree (forest), |
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515 | /// - the distance of each node from the root(s). |
---|
516 | /// |
---|
517 | /// \pre init() must be called and at least one root node should be |
---|
518 | /// added with addSource() before using this function. |
---|
519 | void start() { |
---|
520 | int num = countNodes(*_gr) - 1; |
---|
521 | for (int i = 0; i < num; ++i) { |
---|
522 | if (processNextWeakRound()) break; |
---|
523 | } |
---|
524 | } |
---|
525 | |
---|
526 | /// \brief Executes the algorithm and checks the negative cycles. |
---|
527 | /// |
---|
528 | /// Executes the algorithm and checks the negative cycles. |
---|
529 | /// |
---|
530 | /// This method runs the Bellman-Ford algorithm from the root node(s) |
---|
531 | /// in order to compute the shortest path to each node and also checks |
---|
532 | /// if the digraph contains cycles with negative total length. |
---|
533 | /// |
---|
534 | /// The algorithm computes |
---|
535 | /// - the shortest path tree (forest), |
---|
536 | /// - the distance of each node from the root(s). |
---|
537 | /// |
---|
538 | /// \return \c false if there is a negative cycle in the digraph. |
---|
539 | /// |
---|
540 | /// \pre init() must be called and at least one root node should be |
---|
541 | /// added with addSource() before using this function. |
---|
542 | bool checkedStart() { |
---|
543 | int num = countNodes(*_gr); |
---|
544 | for (int i = 0; i < num; ++i) { |
---|
545 | if (processNextWeakRound()) return true; |
---|
546 | } |
---|
547 | return _process.empty(); |
---|
548 | } |
---|
549 | |
---|
550 | /// \brief Executes the algorithm with arc number limit. |
---|
551 | /// |
---|
552 | /// Executes the algorithm with arc number limit. |
---|
553 | /// |
---|
554 | /// This method runs the Bellman-Ford algorithm from the root node(s) |
---|
555 | /// in order to compute the shortest path distance for each node |
---|
556 | /// using only the paths consisting of at most \c num arcs. |
---|
557 | /// |
---|
558 | /// The algorithm computes |
---|
559 | /// - the limited distance of each node from the root(s), |
---|
560 | /// - the predecessor arc for each node. |
---|
561 | /// |
---|
562 | /// \warning The paths with limited arc number cannot be retrieved |
---|
563 | /// easily with \ref path() or \ref predArc() functions. If you also |
---|
564 | /// need the shortest paths and not only the distances, you should |
---|
565 | /// store the \ref predMap() "predecessor map" after each iteration |
---|
566 | /// and build the path manually. |
---|
567 | /// |
---|
568 | /// \pre init() must be called and at least one root node should be |
---|
569 | /// added with addSource() before using this function. |
---|
570 | void limitedStart(int num) { |
---|
571 | for (int i = 0; i < num; ++i) { |
---|
572 | if (processNextRound()) break; |
---|
573 | } |
---|
574 | } |
---|
575 | |
---|
576 | /// \brief Runs the algorithm from the given root node. |
---|
577 | /// |
---|
578 | /// This method runs the Bellman-Ford algorithm from the given root |
---|
579 | /// node \c s in order to compute the shortest path to each node. |
---|
580 | /// |
---|
581 | /// The algorithm computes |
---|
582 | /// - the shortest path tree (forest), |
---|
583 | /// - the distance of each node from the root(s). |
---|
584 | /// |
---|
585 | /// \note bf.run(s) is just a shortcut of the following code. |
---|
586 | /// \code |
---|
587 | /// bf.init(); |
---|
588 | /// bf.addSource(s); |
---|
589 | /// bf.start(); |
---|
590 | /// \endcode |
---|
591 | void run(Node s) { |
---|
592 | init(); |
---|
593 | addSource(s); |
---|
594 | start(); |
---|
595 | } |
---|
596 | |
---|
597 | /// \brief Runs the algorithm from the given root node with arc |
---|
598 | /// number limit. |
---|
599 | /// |
---|
600 | /// This method runs the Bellman-Ford algorithm from the given root |
---|
601 | /// node \c s in order to compute the shortest path distance for each |
---|
602 | /// node using only the paths consisting of at most \c num arcs. |
---|
603 | /// |
---|
604 | /// The algorithm computes |
---|
605 | /// - the limited distance of each node from the root(s), |
---|
606 | /// - the predecessor arc for each node. |
---|
607 | /// |
---|
608 | /// \warning The paths with limited arc number cannot be retrieved |
---|
609 | /// easily with \ref path() or \ref predArc() functions. If you also |
---|
610 | /// need the shortest paths and not only the distances, you should |
---|
611 | /// store the \ref predMap() "predecessor map" after each iteration |
---|
612 | /// and build the path manually. |
---|
613 | /// |
---|
614 | /// \note bf.run(s, num) is just a shortcut of the following code. |
---|
615 | /// \code |
---|
616 | /// bf.init(); |
---|
617 | /// bf.addSource(s); |
---|
618 | /// bf.limitedStart(num); |
---|
619 | /// \endcode |
---|
620 | void run(Node s, int num) { |
---|
621 | init(); |
---|
622 | addSource(s); |
---|
623 | limitedStart(num); |
---|
624 | } |
---|
625 | |
---|
626 | ///@} |
---|
627 | |
---|
628 | /// \brief LEMON iterator for getting the active nodes. |
---|
629 | /// |
---|
630 | /// This class provides a common style LEMON iterator that traverses |
---|
631 | /// the active nodes of the Bellman-Ford algorithm after the last |
---|
632 | /// phase. These nodes should be checked in the next phase to |
---|
633 | /// find augmenting arcs outgoing from them. |
---|
634 | class ActiveIt { |
---|
635 | public: |
---|
636 | |
---|
637 | /// \brief Constructor. |
---|
638 | /// |
---|
639 | /// Constructor for getting the active nodes of the given BellmanFord |
---|
640 | /// instance. |
---|
641 | ActiveIt(const BellmanFord& algorithm) : _algorithm(&algorithm) |
---|
642 | { |
---|
643 | _index = _algorithm->_process.size() - 1; |
---|
644 | } |
---|
645 | |
---|
646 | /// \brief Invalid constructor. |
---|
647 | /// |
---|
648 | /// Invalid constructor. |
---|
649 | ActiveIt(Invalid) : _algorithm(0), _index(-1) {} |
---|
650 | |
---|
651 | /// \brief Conversion to \c Node. |
---|
652 | /// |
---|
653 | /// Conversion to \c Node. |
---|
654 | operator Node() const { |
---|
655 | return _index >= 0 ? _algorithm->_process[_index] : INVALID; |
---|
656 | } |
---|
657 | |
---|
658 | /// \brief Increment operator. |
---|
659 | /// |
---|
660 | /// Increment operator. |
---|
661 | ActiveIt& operator++() { |
---|
662 | --_index; |
---|
663 | return *this; |
---|
664 | } |
---|
665 | |
---|
666 | bool operator==(const ActiveIt& it) const { |
---|
667 | return static_cast<Node>(*this) == static_cast<Node>(it); |
---|
668 | } |
---|
669 | bool operator!=(const ActiveIt& it) const { |
---|
670 | return static_cast<Node>(*this) != static_cast<Node>(it); |
---|
671 | } |
---|
672 | bool operator<(const ActiveIt& it) const { |
---|
673 | return static_cast<Node>(*this) < static_cast<Node>(it); |
---|
674 | } |
---|
675 | |
---|
676 | private: |
---|
677 | const BellmanFord* _algorithm; |
---|
678 | int _index; |
---|
679 | }; |
---|
680 | |
---|
681 | /// \name Query Functions |
---|
682 | /// The result of the Bellman-Ford algorithm can be obtained using these |
---|
683 | /// functions.\n |
---|
684 | /// Either \ref run() or \ref init() should be called before using them. |
---|
685 | |
---|
686 | ///@{ |
---|
687 | |
---|
688 | /// \brief The shortest path to the given node. |
---|
689 | /// |
---|
690 | /// Gives back the shortest path to the given node from the root(s). |
---|
691 | /// |
---|
692 | /// \warning \c t should be reached from the root(s). |
---|
693 | /// |
---|
694 | /// \pre Either \ref run() or \ref init() must be called before |
---|
695 | /// using this function. |
---|
696 | Path path(Node t) const |
---|
697 | { |
---|
698 | return Path(*_gr, *_pred, t); |
---|
699 | } |
---|
700 | |
---|
701 | /// \brief The distance of the given node from the root(s). |
---|
702 | /// |
---|
703 | /// Returns the distance of the given node from the root(s). |
---|
704 | /// |
---|
705 | /// \warning If node \c v is not reached from the root(s), then |
---|
706 | /// the return value of this function is undefined. |
---|
707 | /// |
---|
708 | /// \pre Either \ref run() or \ref init() must be called before |
---|
709 | /// using this function. |
---|
710 | Value dist(Node v) const { return (*_dist)[v]; } |
---|
711 | |
---|
712 | /// \brief Returns the 'previous arc' of the shortest path tree for |
---|
713 | /// the given node. |
---|
714 | /// |
---|
715 | /// This function returns the 'previous arc' of the shortest path |
---|
716 | /// tree for node \c v, i.e. it returns the last arc of a |
---|
717 | /// shortest path from a root to \c v. It is \c INVALID if \c v |
---|
718 | /// is not reached from the root(s) or if \c v is a root. |
---|
719 | /// |
---|
720 | /// The shortest path tree used here is equal to the shortest path |
---|
721 | /// tree used in \ref predNode() and \predMap(). |
---|
722 | /// |
---|
723 | /// \pre Either \ref run() or \ref init() must be called before |
---|
724 | /// using this function. |
---|
725 | Arc predArc(Node v) const { return (*_pred)[v]; } |
---|
726 | |
---|
727 | /// \brief Returns the 'previous node' of the shortest path tree for |
---|
728 | /// the given node. |
---|
729 | /// |
---|
730 | /// This function returns the 'previous node' of the shortest path |
---|
731 | /// tree for node \c v, i.e. it returns the last but one node of |
---|
732 | /// a shortest path from a root to \c v. It is \c INVALID if \c v |
---|
733 | /// is not reached from the root(s) or if \c v is a root. |
---|
734 | /// |
---|
735 | /// The shortest path tree used here is equal to the shortest path |
---|
736 | /// tree used in \ref predArc() and \predMap(). |
---|
737 | /// |
---|
738 | /// \pre Either \ref run() or \ref init() must be called before |
---|
739 | /// using this function. |
---|
740 | Node predNode(Node v) const { |
---|
741 | return (*_pred)[v] == INVALID ? INVALID : _gr->source((*_pred)[v]); |
---|
742 | } |
---|
743 | |
---|
744 | /// \brief Returns a const reference to the node map that stores the |
---|
745 | /// distances of the nodes. |
---|
746 | /// |
---|
747 | /// Returns a const reference to the node map that stores the distances |
---|
748 | /// of the nodes calculated by the algorithm. |
---|
749 | /// |
---|
750 | /// \pre Either \ref run() or \ref init() must be called before |
---|
751 | /// using this function. |
---|
752 | const DistMap &distMap() const { return *_dist;} |
---|
753 | |
---|
754 | /// \brief Returns a const reference to the node map that stores the |
---|
755 | /// predecessor arcs. |
---|
756 | /// |
---|
757 | /// Returns a const reference to the node map that stores the predecessor |
---|
758 | /// arcs, which form the shortest path tree (forest). |
---|
759 | /// |
---|
760 | /// \pre Either \ref run() or \ref init() must be called before |
---|
761 | /// using this function. |
---|
762 | const PredMap &predMap() const { return *_pred; } |
---|
763 | |
---|
764 | /// \brief Checks if a node is reached from the root(s). |
---|
765 | /// |
---|
766 | /// Returns \c true if \c v is reached from the root(s). |
---|
767 | /// |
---|
768 | /// \pre Either \ref run() or \ref init() must be called before |
---|
769 | /// using this function. |
---|
770 | bool reached(Node v) const { |
---|
771 | return (*_dist)[v] != OperationTraits::infinity(); |
---|
772 | } |
---|
773 | |
---|
774 | /// \brief Gives back a negative cycle. |
---|
775 | /// |
---|
776 | /// This function gives back a directed cycle with negative total |
---|
777 | /// length if the algorithm has already found one. |
---|
778 | /// Otherwise it gives back an empty path. |
---|
779 | lemon::Path<Digraph> negativeCycle() const { |
---|
780 | typename Digraph::template NodeMap<int> state(*_gr, -1); |
---|
781 | lemon::Path<Digraph> cycle; |
---|
782 | for (int i = 0; i < int(_process.size()); ++i) { |
---|
783 | if (state[_process[i]] != -1) continue; |
---|
784 | for (Node v = _process[i]; (*_pred)[v] != INVALID; |
---|
785 | v = _gr->source((*_pred)[v])) { |
---|
786 | if (state[v] == i) { |
---|
787 | cycle.addFront((*_pred)[v]); |
---|
788 | for (Node u = _gr->source((*_pred)[v]); u != v; |
---|
789 | u = _gr->source((*_pred)[u])) { |
---|
790 | cycle.addFront((*_pred)[u]); |
---|
791 | } |
---|
792 | return cycle; |
---|
793 | } |
---|
794 | else if (state[v] >= 0) { |
---|
795 | break; |
---|
796 | } |
---|
797 | state[v] = i; |
---|
798 | } |
---|
799 | } |
---|
800 | return cycle; |
---|
801 | } |
---|
802 | |
---|
803 | ///@} |
---|
804 | }; |
---|
805 | |
---|
806 | /// \brief Default traits class of bellmanFord() function. |
---|
807 | /// |
---|
808 | /// Default traits class of bellmanFord() function. |
---|
809 | /// \tparam GR The type of the digraph. |
---|
810 | /// \tparam LEN The type of the length map. |
---|
811 | template <typename GR, typename LEN> |
---|
812 | struct BellmanFordWizardDefaultTraits { |
---|
813 | /// The type of the digraph the algorithm runs on. |
---|
814 | typedef GR Digraph; |
---|
815 | |
---|
816 | /// \brief The type of the map that stores the arc lengths. |
---|
817 | /// |
---|
818 | /// The type of the map that stores the arc lengths. |
---|
819 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
---|
820 | typedef LEN LengthMap; |
---|
821 | |
---|
822 | /// The type of the arc lengths. |
---|
823 | typedef typename LEN::Value Value; |
---|
824 | |
---|
825 | /// \brief Operation traits for Bellman-Ford algorithm. |
---|
826 | /// |
---|
827 | /// It defines the used operations and the infinity value for the |
---|
828 | /// given \c Value type. |
---|
829 | /// \see BellmanFordDefaultOperationTraits |
---|
830 | typedef BellmanFordDefaultOperationTraits<Value> OperationTraits; |
---|
831 | |
---|
832 | /// \brief The type of the map that stores the last |
---|
833 | /// arcs of the shortest paths. |
---|
834 | /// |
---|
835 | /// The type of the map that stores the last arcs of the shortest paths. |
---|
836 | /// It must conform to the \ref concepts::WriteMap "WriteMap" concept. |
---|
837 | typedef typename GR::template NodeMap<typename GR::Arc> PredMap; |
---|
838 | |
---|
839 | /// \brief Instantiates a \c PredMap. |
---|
840 | /// |
---|
841 | /// This function instantiates a \ref PredMap. |
---|
842 | /// \param g is the digraph to which we would like to define the |
---|
843 | /// \ref PredMap. |
---|
844 | static PredMap *createPredMap(const GR &g) { |
---|
845 | return new PredMap(g); |
---|
846 | } |
---|
847 | |
---|
848 | /// \brief The type of the map that stores the distances of the nodes. |
---|
849 | /// |
---|
850 | /// The type of the map that stores the distances of the nodes. |
---|
851 | /// It must conform to the \ref concepts::WriteMap "WriteMap" concept. |
---|
852 | typedef typename GR::template NodeMap<Value> DistMap; |
---|
853 | |
---|
854 | /// \brief Instantiates a \c DistMap. |
---|
855 | /// |
---|
856 | /// This function instantiates a \ref DistMap. |
---|
857 | /// \param g is the digraph to which we would like to define the |
---|
858 | /// \ref DistMap. |
---|
859 | static DistMap *createDistMap(const GR &g) { |
---|
860 | return new DistMap(g); |
---|
861 | } |
---|
862 | |
---|
863 | ///The type of the shortest paths. |
---|
864 | |
---|
865 | ///The type of the shortest paths. |
---|
866 | ///It must meet the \ref concepts::Path "Path" concept. |
---|
867 | typedef lemon::Path<Digraph> Path; |
---|
868 | }; |
---|
869 | |
---|
870 | /// \brief Default traits class used by BellmanFordWizard. |
---|
871 | /// |
---|
872 | /// Default traits class used by BellmanFordWizard. |
---|
873 | /// \tparam GR The type of the digraph. |
---|
874 | /// \tparam LEN The type of the length map. |
---|
875 | template <typename GR, typename LEN> |
---|
876 | class BellmanFordWizardBase |
---|
877 | : public BellmanFordWizardDefaultTraits<GR, LEN> { |
---|
878 | |
---|
879 | typedef BellmanFordWizardDefaultTraits<GR, LEN> Base; |
---|
880 | protected: |
---|
881 | // Type of the nodes in the digraph. |
---|
882 | typedef typename Base::Digraph::Node Node; |
---|
883 | |
---|
884 | // Pointer to the underlying digraph. |
---|
885 | void *_graph; |
---|
886 | // Pointer to the length map |
---|
887 | void *_length; |
---|
888 | // Pointer to the map of predecessors arcs. |
---|
889 | void *_pred; |
---|
890 | // Pointer to the map of distances. |
---|
891 | void *_dist; |
---|
892 | //Pointer to the shortest path to the target node. |
---|
893 | void *_path; |
---|
894 | //Pointer to the distance of the target node. |
---|
895 | void *_di; |
---|
896 | |
---|
897 | public: |
---|
898 | /// Constructor. |
---|
899 | |
---|
900 | /// This constructor does not require parameters, it initiates |
---|
901 | /// all of the attributes to default values \c 0. |
---|
902 | BellmanFordWizardBase() : |
---|
903 | _graph(0), _length(0), _pred(0), _dist(0), _path(0), _di(0) {} |
---|
904 | |
---|
905 | /// Constructor. |
---|
906 | |
---|
907 | /// This constructor requires two parameters, |
---|
908 | /// others are initiated to \c 0. |
---|
909 | /// \param gr The digraph the algorithm runs on. |
---|
910 | /// \param len The length map. |
---|
911 | BellmanFordWizardBase(const GR& gr, |
---|
912 | const LEN& len) : |
---|
913 | _graph(reinterpret_cast<void*>(const_cast<GR*>(&gr))), |
---|
914 | _length(reinterpret_cast<void*>(const_cast<LEN*>(&len))), |
---|
915 | _pred(0), _dist(0), _path(0), _di(0) {} |
---|
916 | |
---|
917 | }; |
---|
918 | |
---|
919 | /// \brief Auxiliary class for the function-type interface of the |
---|
920 | /// \ref BellmanFord "Bellman-Ford" algorithm. |
---|
921 | /// |
---|
922 | /// This auxiliary class is created to implement the |
---|
923 | /// \ref bellmanFord() "function-type interface" of the |
---|
924 | /// \ref BellmanFord "Bellman-Ford" algorithm. |
---|
925 | /// It does not have own \ref run() method, it uses the |
---|
926 | /// functions and features of the plain \ref BellmanFord. |
---|
927 | /// |
---|
928 | /// This class should only be used through the \ref bellmanFord() |
---|
929 | /// function, which makes it easier to use the algorithm. |
---|
930 | template<class TR> |
---|
931 | class BellmanFordWizard : public TR { |
---|
932 | typedef TR Base; |
---|
933 | |
---|
934 | typedef typename TR::Digraph Digraph; |
---|
935 | |
---|
936 | typedef typename Digraph::Node Node; |
---|
937 | typedef typename Digraph::NodeIt NodeIt; |
---|
938 | typedef typename Digraph::Arc Arc; |
---|
939 | typedef typename Digraph::OutArcIt ArcIt; |
---|
940 | |
---|
941 | typedef typename TR::LengthMap LengthMap; |
---|
942 | typedef typename LengthMap::Value Value; |
---|
943 | typedef typename TR::PredMap PredMap; |
---|
944 | typedef typename TR::DistMap DistMap; |
---|
945 | typedef typename TR::Path Path; |
---|
946 | |
---|
947 | public: |
---|
948 | /// Constructor. |
---|
949 | BellmanFordWizard() : TR() {} |
---|
950 | |
---|
951 | /// \brief Constructor that requires parameters. |
---|
952 | /// |
---|
953 | /// Constructor that requires parameters. |
---|
954 | /// These parameters will be the default values for the traits class. |
---|
955 | /// \param gr The digraph the algorithm runs on. |
---|
956 | /// \param len The length map. |
---|
957 | BellmanFordWizard(const Digraph& gr, const LengthMap& len) |
---|
958 | : TR(gr, len) {} |
---|
959 | |
---|
960 | /// \brief Copy constructor |
---|
961 | BellmanFordWizard(const TR &b) : TR(b) {} |
---|
962 | |
---|
963 | ~BellmanFordWizard() {} |
---|
964 | |
---|
965 | /// \brief Runs the Bellman-Ford algorithm from the given source node. |
---|
966 | /// |
---|
967 | /// This method runs the Bellman-Ford algorithm from the given source |
---|
968 | /// node in order to compute the shortest path to each node. |
---|
969 | void run(Node s) { |
---|
970 | BellmanFord<Digraph,LengthMap,TR> |
---|
971 | bf(*reinterpret_cast<const Digraph*>(Base::_graph), |
---|
972 | *reinterpret_cast<const LengthMap*>(Base::_length)); |
---|
973 | if (Base::_pred) bf.predMap(*reinterpret_cast<PredMap*>(Base::_pred)); |
---|
974 | if (Base::_dist) bf.distMap(*reinterpret_cast<DistMap*>(Base::_dist)); |
---|
975 | bf.run(s); |
---|
976 | } |
---|
977 | |
---|
978 | /// \brief Runs the Bellman-Ford algorithm to find the shortest path |
---|
979 | /// between \c s and \c t. |
---|
980 | /// |
---|
981 | /// This method runs the Bellman-Ford algorithm from node \c s |
---|
982 | /// in order to compute the shortest path to node \c t. |
---|
983 | /// Actually, it computes the shortest path to each node, but using |
---|
984 | /// this function you can retrieve the distance and the shortest path |
---|
985 | /// for a single target node easier. |
---|
986 | /// |
---|
987 | /// \return \c true if \c t is reachable form \c s. |
---|
988 | bool run(Node s, Node t) { |
---|
989 | BellmanFord<Digraph,LengthMap,TR> |
---|
990 | bf(*reinterpret_cast<const Digraph*>(Base::_graph), |
---|
991 | *reinterpret_cast<const LengthMap*>(Base::_length)); |
---|
992 | if (Base::_pred) bf.predMap(*reinterpret_cast<PredMap*>(Base::_pred)); |
---|
993 | if (Base::_dist) bf.distMap(*reinterpret_cast<DistMap*>(Base::_dist)); |
---|
994 | bf.run(s); |
---|
995 | if (Base::_path) *reinterpret_cast<Path*>(Base::_path) = bf.path(t); |
---|
996 | if (Base::_di) *reinterpret_cast<Value*>(Base::_di) = bf.dist(t); |
---|
997 | return bf.reached(t); |
---|
998 | } |
---|
999 | |
---|
1000 | template<class T> |
---|
1001 | struct SetPredMapBase : public Base { |
---|
1002 | typedef T PredMap; |
---|
1003 | static PredMap *createPredMap(const Digraph &) { return 0; }; |
---|
1004 | SetPredMapBase(const TR &b) : TR(b) {} |
---|
1005 | }; |
---|
1006 | |
---|
1007 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
1008 | /// the predecessor map. |
---|
1009 | /// |
---|
1010 | /// \ref named-templ-param "Named parameter" for setting |
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1011 | /// the map that stores the predecessor arcs of the nodes. |
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1012 | template<class T> |
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1013 | BellmanFordWizard<SetPredMapBase<T> > predMap(const T &t) { |
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1014 | Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t)); |
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1015 | return BellmanFordWizard<SetPredMapBase<T> >(*this); |
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1016 | } |
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1017 | |
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1018 | template<class T> |
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1019 | struct SetDistMapBase : public Base { |
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1020 | typedef T DistMap; |
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1021 | static DistMap *createDistMap(const Digraph &) { return 0; }; |
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1022 | SetDistMapBase(const TR &b) : TR(b) {} |
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1023 | }; |
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1024 | |
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1025 | /// \brief \ref named-templ-param "Named parameter" for setting |
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1026 | /// the distance map. |
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1027 | /// |
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1028 | /// \ref named-templ-param "Named parameter" for setting |
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1029 | /// the map that stores the distances of the nodes calculated |
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1030 | /// by the algorithm. |
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1031 | template<class T> |
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1032 | BellmanFordWizard<SetDistMapBase<T> > distMap(const T &t) { |
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1033 | Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t)); |
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1034 | return BellmanFordWizard<SetDistMapBase<T> >(*this); |
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1035 | } |
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1036 | |
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1037 | template<class T> |
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1038 | struct SetPathBase : public Base { |
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1039 | typedef T Path; |
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1040 | SetPathBase(const TR &b) : TR(b) {} |
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1041 | }; |
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1042 | |
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1043 | /// \brief \ref named-func-param "Named parameter" for getting |
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1044 | /// the shortest path to the target node. |
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1045 | /// |
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1046 | /// \ref named-func-param "Named parameter" for getting |
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1047 | /// the shortest path to the target node. |
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1048 | template<class T> |
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1049 | BellmanFordWizard<SetPathBase<T> > path(const T &t) |
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1050 | { |
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1051 | Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t)); |
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1052 | return BellmanFordWizard<SetPathBase<T> >(*this); |
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1053 | } |
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1054 | |
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1055 | /// \brief \ref named-func-param "Named parameter" for getting |
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1056 | /// the distance of the target node. |
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1057 | /// |
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1058 | /// \ref named-func-param "Named parameter" for getting |
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1059 | /// the distance of the target node. |
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1060 | BellmanFordWizard dist(const Value &d) |
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1061 | { |
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1062 | Base::_di=reinterpret_cast<void*>(const_cast<Value*>(&d)); |
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1063 | return *this; |
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1064 | } |
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1065 | |
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1066 | }; |
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1067 | |
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1068 | /// \brief Function type interface for the \ref BellmanFord "Bellman-Ford" |
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1069 | /// algorithm. |
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1070 | /// |
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1071 | /// \ingroup shortest_path |
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1072 | /// Function type interface for the \ref BellmanFord "Bellman-Ford" |
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1073 | /// algorithm. |
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1074 | /// |
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1075 | /// This function also has several \ref named-templ-func-param |
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1076 | /// "named parameters", they are declared as the members of class |
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1077 | /// \ref BellmanFordWizard. |
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1078 | /// The following examples show how to use these parameters. |
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1079 | /// \code |
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1080 | /// // Compute shortest path from node s to each node |
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1081 | /// bellmanFord(g,length).predMap(preds).distMap(dists).run(s); |
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1082 | /// |
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1083 | /// // Compute shortest path from s to t |
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1084 | /// bool reached = bellmanFord(g,length).path(p).dist(d).run(s,t); |
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1085 | /// \endcode |
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1086 | /// \warning Don't forget to put the \ref BellmanFordWizard::run() "run()" |
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1087 | /// to the end of the parameter list. |
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1088 | /// \sa BellmanFordWizard |
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1089 | /// \sa BellmanFord |
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1090 | template<typename GR, typename LEN> |
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1091 | BellmanFordWizard<BellmanFordWizardBase<GR,LEN> > |
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1092 | bellmanFord(const GR& digraph, |
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1093 | const LEN& length) |
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1094 | { |
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1095 | return BellmanFordWizard<BellmanFordWizardBase<GR,LEN> >(digraph, length); |
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1096 | } |
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1097 | |
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1098 | } //END OF NAMESPACE LEMON |
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1099 | |
---|
1100 | #endif |
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1101 | |
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