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_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 Bellman-Ford algorithm. |
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25 | /// |
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26 | |
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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 | |
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32 | #include <limits> |
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33 | |
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34 | namespace lemon { |
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35 | |
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36 | /// \brief Default OperationTraits for the BellmanFord algorithm class. |
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37 | /// |
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38 | /// It defines all computational operations and constants which are |
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39 | /// used in the Bellman-Ford algorithm. The default implementation |
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40 | /// is based on the numeric_limits class. If the numeric type does not |
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41 | /// have infinity value then the maximum value is used as extremal |
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42 | /// infinity value. |
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43 | template < |
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44 | typename Value, |
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45 | bool has_infinity = std::numeric_limits<Value>::has_infinity> |
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46 | struct BellmanFordDefaultOperationTraits { |
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47 | /// \brief Gives back the zero value of the type. |
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48 | static Value zero() { |
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49 | return static_cast<Value>(0); |
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50 | } |
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51 | /// \brief Gives back the positive infinity value of the type. |
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52 | static Value infinity() { |
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53 | return std::numeric_limits<Value>::infinity(); |
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54 | } |
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55 | /// \brief Gives back the sum of the given two elements. |
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56 | static Value plus(const Value& left, const Value& right) { |
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57 | return left + right; |
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58 | } |
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59 | /// \brief Gives back true only if the first value less than the second. |
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60 | static bool less(const Value& left, const Value& right) { |
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61 | return left < right; |
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62 | } |
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63 | }; |
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64 | |
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65 | template <typename Value> |
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66 | struct BellmanFordDefaultOperationTraits<Value, false> { |
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67 | static Value zero() { |
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68 | return static_cast<Value>(0); |
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69 | } |
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70 | static Value infinity() { |
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71 | return std::numeric_limits<Value>::max(); |
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72 | } |
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73 | static Value plus(const Value& left, const Value& right) { |
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74 | if (left == infinity() || right == infinity()) return infinity(); |
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75 | return left + right; |
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76 | } |
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77 | static bool less(const Value& left, const Value& right) { |
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78 | return left < right; |
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79 | } |
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80 | }; |
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81 | |
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82 | /// \brief Default traits class of BellmanFord class. |
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83 | /// |
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84 | /// Default traits class of BellmanFord class. |
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85 | /// \param _Digraph Digraph type. |
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86 | /// \param _LegthMap Type of length map. |
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87 | template<class _Digraph, class _LengthMap> |
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88 | struct BellmanFordDefaultTraits { |
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89 | /// The digraph type the algorithm runs on. |
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90 | typedef _Digraph Digraph; |
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91 | |
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92 | /// \brief The type of the map that stores the arc lengths. |
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93 | /// |
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94 | /// The type of the map that stores the arc lengths. |
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95 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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96 | typedef _LengthMap LengthMap; |
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97 | |
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98 | // The type of the length of the arcs. |
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99 | typedef typename _LengthMap::Value Value; |
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100 | |
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101 | /// \brief Operation traits for Bellman-Ford algorithm. |
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102 | /// |
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103 | /// It defines the infinity type on the given Value type |
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104 | /// and the used operation. |
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105 | /// \see BellmanFordDefaultOperationTraits |
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106 | typedef BellmanFordDefaultOperationTraits<Value> OperationTraits; |
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107 | |
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108 | /// \brief The type of the map that stores the last arcs of the |
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109 | /// shortest paths. |
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110 | /// |
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111 | /// The type of the map that stores the last |
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112 | /// arcs of the shortest paths. |
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113 | /// It must meet the \ref concepts::WriteMap "WriteMap" concept. |
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114 | /// |
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115 | typedef typename Digraph::template NodeMap<typename _Digraph::Arc> PredMap; |
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116 | |
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117 | /// \brief Instantiates a PredMap. |
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118 | /// |
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119 | /// This function instantiates a \ref PredMap. |
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120 | /// \param digraph is the digraph, to which we would like to define the PredMap. |
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121 | static PredMap *createPredMap(const _Digraph& digraph) { |
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122 | return new PredMap(digraph); |
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123 | } |
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124 | |
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125 | /// \brief The type of the map that stores the dists of the nodes. |
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126 | /// |
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127 | /// The type of the map that stores the dists of the nodes. |
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128 | /// It must meet the \ref concepts::WriteMap "WriteMap" concept. |
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129 | /// |
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130 | typedef typename Digraph::template NodeMap<typename _LengthMap::Value> |
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131 | DistMap; |
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132 | |
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133 | /// \brief Instantiates a DistMap. |
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134 | /// |
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135 | /// This function instantiates a \ref DistMap. |
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136 | /// \param digraph is the digraph, to which we would like to define the |
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137 | /// \ref DistMap |
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138 | static DistMap *createDistMap(const _Digraph& digraph) { |
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139 | return new DistMap(digraph); |
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140 | } |
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141 | |
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142 | }; |
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143 | |
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144 | /// \brief %BellmanFord algorithm class. |
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145 | /// |
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146 | /// \ingroup shortest_path |
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147 | /// This class provides an efficient implementation of \c Bellman-Ford |
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148 | /// algorithm. The arc lengths are passed to the algorithm using a |
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149 | /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any |
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150 | /// kind of length. |
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151 | /// |
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152 | /// The Bellman-Ford algorithm solves the shortest path from one node |
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153 | /// problem when the arcs can have negative length but the digraph should |
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154 | /// not contain cycles with negative sum of length. If we can assume |
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155 | /// that all arc is non-negative in the digraph then the dijkstra algorithm |
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156 | /// should be used rather. |
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157 | /// |
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158 | /// The maximal time complexity of the algorithm is \f$ O(ne) \f$. |
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159 | /// |
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160 | /// The type of the length is determined by the |
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161 | /// \ref concepts::ReadMap::Value "Value" of the length map. |
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162 | /// |
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163 | /// \param _Digraph The digraph type the algorithm runs on. The default value |
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164 | /// is \ref ListDigraph. The value of _Digraph is not used directly by |
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165 | /// BellmanFord, it is only passed to \ref BellmanFordDefaultTraits. |
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166 | /// \param _LengthMap This read-only ArcMap determines the lengths of the |
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167 | /// arcs. The default map type is \ref concepts::Digraph::ArcMap |
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168 | /// "Digraph::ArcMap<int>". The value of _LengthMap is not used directly |
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169 | /// by BellmanFord, it is only passed to \ref BellmanFordDefaultTraits. |
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170 | /// \param _Traits Traits class to set various data types used by the |
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171 | /// algorithm. The default traits class is \ref BellmanFordDefaultTraits |
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172 | /// "BellmanFordDefaultTraits<_Digraph,_LengthMap>". See \ref |
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173 | /// BellmanFordDefaultTraits for the documentation of a BellmanFord traits |
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174 | /// class. |
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175 | #ifdef DOXYGEN |
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176 | template <typename _Digraph, typename _LengthMap, typename _Traits> |
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177 | #else |
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178 | template <typename _Digraph, |
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179 | typename _LengthMap=typename _Digraph::template ArcMap<int>, |
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180 | typename _Traits=BellmanFordDefaultTraits<_Digraph,_LengthMap> > |
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181 | #endif |
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182 | class BellmanFord { |
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183 | public: |
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184 | |
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185 | typedef _Traits Traits; |
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186 | ///The type of the underlying digraph. |
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187 | typedef typename _Traits::Digraph Digraph; |
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188 | |
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189 | typedef typename Digraph::Node Node; |
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190 | typedef typename Digraph::NodeIt NodeIt; |
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191 | typedef typename Digraph::Arc Arc; |
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192 | typedef typename Digraph::OutArcIt OutArcIt; |
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193 | |
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194 | /// \brief The type of the length of the arcs. |
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195 | typedef typename _Traits::LengthMap::Value Value; |
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196 | /// \brief The type of the map that stores the arc lengths. |
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197 | typedef typename _Traits::LengthMap LengthMap; |
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198 | /// \brief The type of the map that stores the last |
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199 | /// arcs of the shortest paths. |
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200 | typedef typename _Traits::PredMap PredMap; |
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201 | /// \brief The type of the map that stores the dists of the nodes. |
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202 | typedef typename _Traits::DistMap DistMap; |
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203 | /// \brief The operation traits. |
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204 | typedef typename _Traits::OperationTraits OperationTraits; |
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205 | private: |
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206 | /// Pointer to the underlying digraph. |
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207 | const Digraph *digraph; |
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208 | /// Pointer to the length map |
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209 | const LengthMap *length; |
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210 | ///Pointer to the map of predecessors arcs. |
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211 | PredMap *_pred; |
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212 | ///Indicates if \ref _pred is locally allocated (\c true) or not. |
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213 | bool local_pred; |
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214 | ///Pointer to the map of distances. |
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215 | DistMap *_dist; |
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216 | ///Indicates if \ref _dist is locally allocated (\c true) or not. |
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217 | bool local_dist; |
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218 | |
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219 | typedef typename Digraph::template NodeMap<bool> MaskMap; |
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220 | MaskMap *_mask; |
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221 | |
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222 | std::vector<Node> _process; |
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223 | |
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224 | /// Creates the maps if necessary. |
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225 | void create_maps() { |
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226 | if(!_pred) { |
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227 | local_pred = true; |
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228 | _pred = Traits::createPredMap(*digraph); |
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229 | } |
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230 | if(!_dist) { |
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231 | local_dist = true; |
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232 | _dist = Traits::createDistMap(*digraph); |
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233 | } |
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234 | _mask = new MaskMap(*digraph, false); |
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235 | } |
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236 | |
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237 | public : |
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238 | |
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239 | typedef BellmanFord Create; |
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240 | |
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241 | /// \name Named template parameters |
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242 | |
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243 | ///@{ |
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244 | |
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245 | template <class T> |
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246 | struct DefPredMapTraits : public Traits { |
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247 | typedef T PredMap; |
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248 | static PredMap *createPredMap(const Digraph&) { |
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249 | LEMON_ASSERT(false, "PredMap is not initialized"); |
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250 | return 0; // ignore warnings |
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251 | } |
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252 | }; |
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253 | |
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254 | /// \brief \ref named-templ-param "Named parameter" for setting PredMap |
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255 | /// type |
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256 | /// \ref named-templ-param "Named parameter" for setting PredMap type |
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257 | /// |
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258 | template <class T> |
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259 | struct SetPredMap |
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260 | : public BellmanFord< Digraph, LengthMap, DefPredMapTraits<T> > { |
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261 | typedef BellmanFord< Digraph, LengthMap, DefPredMapTraits<T> > Create; |
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262 | }; |
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263 | |
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264 | template <class T> |
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265 | struct DefDistMapTraits : public Traits { |
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266 | typedef T DistMap; |
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267 | static DistMap *createDistMap(const Digraph&) { |
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268 | LEMON_ASSERT(false, "DistMap is not initialized"); |
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269 | return 0; // ignore warnings |
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270 | } |
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271 | }; |
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272 | |
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273 | /// \brief \ref named-templ-param "Named parameter" for setting DistMap |
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274 | /// type |
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275 | /// |
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276 | /// \ref named-templ-param "Named parameter" for setting DistMap type |
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277 | /// |
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278 | template <class T> |
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279 | struct SetDistMap |
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280 | : public BellmanFord< Digraph, LengthMap, DefDistMapTraits<T> > { |
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281 | typedef BellmanFord< Digraph, LengthMap, DefDistMapTraits<T> > Create; |
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282 | }; |
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283 | |
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284 | template <class T> |
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285 | struct DefOperationTraitsTraits : public Traits { |
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286 | typedef T OperationTraits; |
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287 | }; |
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288 | |
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289 | /// \brief \ref named-templ-param "Named parameter" for setting |
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290 | /// OperationTraits type |
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291 | /// |
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292 | /// \ref named-templ-param "Named parameter" for setting OperationTraits |
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293 | /// type |
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294 | template <class T> |
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295 | struct SetOperationTraits |
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296 | : public BellmanFord< Digraph, LengthMap, DefOperationTraitsTraits<T> > { |
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297 | typedef BellmanFord< Digraph, LengthMap, DefOperationTraitsTraits<T> > |
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298 | Create; |
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299 | }; |
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300 | |
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301 | ///@} |
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302 | |
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303 | protected: |
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304 | |
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305 | BellmanFord() {} |
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306 | |
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307 | public: |
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308 | |
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309 | /// \brief Constructor. |
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310 | /// |
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311 | /// \param _graph the digraph the algorithm will run on. |
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312 | /// \param _length the length map used by the algorithm. |
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313 | BellmanFord(const Digraph& _graph, const LengthMap& _length) : |
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314 | digraph(&_graph), length(&_length), |
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315 | _pred(0), local_pred(false), |
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316 | _dist(0), local_dist(false), _mask(0) {} |
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317 | |
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318 | ///Destructor. |
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319 | ~BellmanFord() { |
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320 | if(local_pred) delete _pred; |
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321 | if(local_dist) delete _dist; |
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322 | if(_mask) delete _mask; |
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323 | } |
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324 | |
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325 | /// \brief Sets the length map. |
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326 | /// |
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327 | /// Sets the length map. |
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328 | /// \return \c (*this) |
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329 | BellmanFord &lengthMap(const LengthMap &m) { |
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330 | length = &m; |
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331 | return *this; |
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332 | } |
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333 | |
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334 | /// \brief Sets the map storing the predecessor arcs. |
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335 | /// |
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336 | /// Sets the map storing the predecessor arcs. |
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337 | /// If you don't use this function before calling \ref run(), |
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338 | /// it will allocate one. The destuctor deallocates this |
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339 | /// automatically allocated map, of course. |
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340 | /// \return \c (*this) |
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341 | BellmanFord &predMap(PredMap &m) { |
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342 | if(local_pred) { |
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343 | delete _pred; |
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344 | local_pred=false; |
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345 | } |
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346 | _pred = &m; |
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347 | return *this; |
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348 | } |
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349 | |
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350 | /// \brief Sets the map storing the distances calculated by the algorithm. |
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351 | /// |
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352 | /// Sets the map storing the distances calculated by the algorithm. |
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353 | /// If you don't use this function before calling \ref run(), |
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354 | /// it will allocate one. The destuctor deallocates this |
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355 | /// automatically allocated map, of course. |
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356 | /// \return \c (*this) |
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357 | BellmanFord &distMap(DistMap &m) { |
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358 | if(local_dist) { |
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359 | delete _dist; |
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360 | local_dist=false; |
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361 | } |
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362 | _dist = &m; |
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363 | return *this; |
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364 | } |
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365 | |
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366 | /// \name Execution control |
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367 | /// The simplest way to execute the algorithm is to use |
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368 | /// one of the member functions called \c run(...). |
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369 | /// \n |
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370 | /// If you need more control on the execution, |
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371 | /// first you must call \ref init(), then you can add several source nodes |
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372 | /// with \ref addSource(). |
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373 | /// Finally \ref start() will perform the actual path |
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374 | /// computation. |
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375 | |
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376 | ///@{ |
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377 | |
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378 | /// \brief Initializes the internal data structures. |
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379 | /// |
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380 | /// Initializes the internal data structures. |
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381 | void init(const Value value = OperationTraits::infinity()) { |
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382 | create_maps(); |
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383 | for (NodeIt it(*digraph); it != INVALID; ++it) { |
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384 | _pred->set(it, INVALID); |
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385 | _dist->set(it, value); |
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386 | } |
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387 | _process.clear(); |
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388 | if (OperationTraits::less(value, OperationTraits::infinity())) { |
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389 | for (NodeIt it(*digraph); it != INVALID; ++it) { |
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390 | _process.push_back(it); |
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391 | _mask->set(it, true); |
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392 | } |
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393 | } |
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394 | } |
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395 | |
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396 | /// \brief Adds a new source node. |
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397 | /// |
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398 | /// Adds a new source node. The optional second parameter is the |
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399 | /// initial distance of the node. It just sets the distance of the |
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400 | /// node to the given value. |
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401 | void addSource(Node source, Value dst = OperationTraits::zero()) { |
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402 | _dist->set(source, dst); |
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403 | if (!(*_mask)[source]) { |
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404 | _process.push_back(source); |
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405 | _mask->set(source, true); |
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406 | } |
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407 | } |
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408 | |
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409 | /// \brief Executes one round from the Bellman-Ford algorithm. |
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410 | /// |
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411 | /// If the algoritm calculated the distances in the previous round |
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412 | /// exactly for all at most \f$ k \f$ length path lengths then it will |
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413 | /// calculate the distances exactly for all at most \f$ k + 1 \f$ |
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414 | /// length path lengths. With \f$ k \f$ iteration this function |
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415 | /// calculates the at most \f$ k \f$ length path lengths. |
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416 | /// |
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417 | /// \warning The paths with limited arc number cannot be retrieved |
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418 | /// easily with \ref path() or \ref predArc() functions. If you |
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419 | /// need the shortest path and not just the distance you should store |
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420 | /// after each iteration the \ref predMap() map and manually build |
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421 | /// the path. |
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422 | /// |
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423 | /// \return \c true when the algorithm have not found more shorter |
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424 | /// paths. |
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425 | bool processNextRound() { |
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426 | for (int i = 0; i < int(_process.size()); ++i) { |
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427 | _mask->set(_process[i], false); |
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428 | } |
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429 | std::vector<Node> nextProcess; |
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430 | std::vector<Value> values(_process.size()); |
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431 | for (int i = 0; i < int(_process.size()); ++i) { |
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432 | values[i] = (*_dist)[_process[i]]; |
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433 | } |
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434 | for (int i = 0; i < int(_process.size()); ++i) { |
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435 | for (OutArcIt it(*digraph, _process[i]); it != INVALID; ++it) { |
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436 | Node target = digraph->target(it); |
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437 | Value relaxed = OperationTraits::plus(values[i], (*length)[it]); |
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438 | if (OperationTraits::less(relaxed, (*_dist)[target])) { |
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439 | _pred->set(target, it); |
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440 | _dist->set(target, relaxed); |
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441 | if (!(*_mask)[target]) { |
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442 | _mask->set(target, true); |
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443 | nextProcess.push_back(target); |
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444 | } |
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445 | } |
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446 | } |
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447 | } |
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448 | _process.swap(nextProcess); |
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449 | return _process.empty(); |
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450 | } |
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451 | |
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452 | /// \brief Executes one weak round from the Bellman-Ford algorithm. |
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453 | /// |
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454 | /// If the algorithm calculated the distances in the |
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455 | /// previous round at least for all at most k length paths then it will |
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456 | /// calculate the distances at least for all at most k + 1 length paths. |
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457 | /// This function does not make it possible to calculate strictly the |
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458 | /// at most k length minimal paths, this is why it is |
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459 | /// called just weak round. |
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460 | /// \return \c true when the algorithm have not found more shorter paths. |
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461 | bool processNextWeakRound() { |
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462 | for (int i = 0; i < int(_process.size()); ++i) { |
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463 | _mask->set(_process[i], false); |
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464 | } |
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465 | std::vector<Node> nextProcess; |
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466 | for (int i = 0; i < int(_process.size()); ++i) { |
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467 | for (OutArcIt it(*digraph, _process[i]); it != INVALID; ++it) { |
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468 | Node target = digraph->target(it); |
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469 | Value relaxed = |
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470 | OperationTraits::plus((*_dist)[_process[i]], (*length)[it]); |
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471 | if (OperationTraits::less(relaxed, (*_dist)[target])) { |
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472 | _pred->set(target, it); |
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473 | _dist->set(target, relaxed); |
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474 | if (!(*_mask)[target]) { |
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475 | _mask->set(target, true); |
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476 | nextProcess.push_back(target); |
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477 | } |
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478 | } |
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479 | } |
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480 | } |
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481 | _process.swap(nextProcess); |
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482 | return _process.empty(); |
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483 | } |
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484 | |
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485 | /// \brief Executes the algorithm. |
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486 | /// |
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487 | /// \pre init() must be called and at least one node should be added |
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488 | /// with addSource() before using this function. |
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489 | /// |
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490 | /// This method runs the %BellmanFord algorithm from the root node(s) |
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491 | /// in order to compute the shortest path to each node. The algorithm |
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492 | /// computes |
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493 | /// - The shortest path tree. |
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494 | /// - The distance of each node from the root(s). |
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495 | void start() { |
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496 | int num = countNodes(*digraph) - 1; |
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497 | for (int i = 0; i < num; ++i) { |
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498 | if (processNextWeakRound()) break; |
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499 | } |
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500 | } |
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501 | |
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502 | /// \brief Executes the algorithm and checks the negative cycles. |
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503 | /// |
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504 | /// \pre init() must be called and at least one node should be added |
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505 | /// with addSource() before using this function. |
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506 | /// |
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507 | /// This method runs the %BellmanFord algorithm from the root node(s) |
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508 | /// in order to compute the shortest path to each node. The algorithm |
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509 | /// computes |
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510 | /// - The shortest path tree. |
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511 | /// - The distance of each node from the root(s). |
---|
512 | /// |
---|
513 | /// \return \c false if there is a negative cycle in the digraph. |
---|
514 | bool checkedStart() { |
---|
515 | int num = countNodes(*digraph); |
---|
516 | for (int i = 0; i < num; ++i) { |
---|
517 | if (processNextWeakRound()) return true; |
---|
518 | } |
---|
519 | return _process.empty(); |
---|
520 | } |
---|
521 | |
---|
522 | /// \brief Executes the algorithm with path length limit. |
---|
523 | /// |
---|
524 | /// \pre init() must be called and at least one node should be added |
---|
525 | /// with addSource() before using this function. |
---|
526 | /// |
---|
527 | /// This method runs the %BellmanFord algorithm from the root |
---|
528 | /// node(s) in order to compute the shortest path lengths with at |
---|
529 | /// most \c num arc. |
---|
530 | /// |
---|
531 | /// \warning The paths with limited arc number cannot be retrieved |
---|
532 | /// easily with \ref path() or \ref predArc() functions. If you |
---|
533 | /// need the shortest path and not just the distance you should store |
---|
534 | /// after each iteration the \ref predMap() map and manually build |
---|
535 | /// the path. |
---|
536 | /// |
---|
537 | /// The algorithm computes |
---|
538 | /// - The predecessor arc from each node. |
---|
539 | /// - The limited distance of each node from the root(s). |
---|
540 | void limitedStart(int num) { |
---|
541 | for (int i = 0; i < num; ++i) { |
---|
542 | if (processNextRound()) break; |
---|
543 | } |
---|
544 | } |
---|
545 | |
---|
546 | /// \brief Runs %BellmanFord algorithm from node \c s. |
---|
547 | /// |
---|
548 | /// This method runs the %BellmanFord algorithm from a root node \c s |
---|
549 | /// in order to compute the shortest path to each node. The algorithm |
---|
550 | /// computes |
---|
551 | /// - The shortest path tree. |
---|
552 | /// - The distance of each node from the root. |
---|
553 | /// |
---|
554 | /// \note d.run(s) is just a shortcut of the following code. |
---|
555 | ///\code |
---|
556 | /// d.init(); |
---|
557 | /// d.addSource(s); |
---|
558 | /// d.start(); |
---|
559 | ///\endcode |
---|
560 | void run(Node s) { |
---|
561 | init(); |
---|
562 | addSource(s); |
---|
563 | start(); |
---|
564 | } |
---|
565 | |
---|
566 | /// \brief Runs %BellmanFord algorithm with limited path length |
---|
567 | /// from node \c s. |
---|
568 | /// |
---|
569 | /// This method runs the %BellmanFord algorithm from a root node \c s |
---|
570 | /// in order to compute the shortest path with at most \c len arcs |
---|
571 | /// to each node. The algorithm computes |
---|
572 | /// - The shortest path tree. |
---|
573 | /// - The distance of each node from the root. |
---|
574 | /// |
---|
575 | /// \note d.run(s, num) is just a shortcut of the following code. |
---|
576 | ///\code |
---|
577 | /// d.init(); |
---|
578 | /// d.addSource(s); |
---|
579 | /// d.limitedStart(num); |
---|
580 | ///\endcode |
---|
581 | void run(Node s, int num) { |
---|
582 | init(); |
---|
583 | addSource(s); |
---|
584 | limitedStart(num); |
---|
585 | } |
---|
586 | |
---|
587 | ///@} |
---|
588 | |
---|
589 | /// \name Query Functions |
---|
590 | /// The result of the %BellmanFord algorithm can be obtained using these |
---|
591 | /// functions.\n |
---|
592 | /// Before the use of these functions, |
---|
593 | /// either run() or start() must be called. |
---|
594 | |
---|
595 | ///@{ |
---|
596 | |
---|
597 | /// \brief Lemon iterator for get the active nodes. |
---|
598 | /// |
---|
599 | /// Lemon iterator for get the active nodes. This class provides a |
---|
600 | /// common style lemon iterator which gives back a subset of the |
---|
601 | /// nodes. The iterated nodes are active in the algorithm after |
---|
602 | /// the last phase so these should be checked in the next phase to |
---|
603 | /// find augmenting arcs from these. |
---|
604 | class ActiveIt { |
---|
605 | public: |
---|
606 | |
---|
607 | /// \brief Constructor. |
---|
608 | /// |
---|
609 | /// Constructor for get the nodeset of the variable. |
---|
610 | ActiveIt(const BellmanFord& algorithm) : _algorithm(&algorithm) |
---|
611 | { |
---|
612 | _index = _algorithm->_process.size() - 1; |
---|
613 | } |
---|
614 | |
---|
615 | /// \brief Invalid constructor. |
---|
616 | /// |
---|
617 | /// Invalid constructor. |
---|
618 | ActiveIt(Invalid) : _algorithm(0), _index(-1) {} |
---|
619 | |
---|
620 | /// \brief Conversion to node. |
---|
621 | /// |
---|
622 | /// Conversion to node. |
---|
623 | operator Node() const { |
---|
624 | return _index >= 0 ? _algorithm->_process[_index] : INVALID; |
---|
625 | } |
---|
626 | |
---|
627 | /// \brief Increment operator. |
---|
628 | /// |
---|
629 | /// Increment operator. |
---|
630 | ActiveIt& operator++() { |
---|
631 | --_index; |
---|
632 | return *this; |
---|
633 | } |
---|
634 | |
---|
635 | bool operator==(const ActiveIt& it) const { |
---|
636 | return static_cast<Node>(*this) == static_cast<Node>(it); |
---|
637 | } |
---|
638 | bool operator!=(const ActiveIt& it) const { |
---|
639 | return static_cast<Node>(*this) != static_cast<Node>(it); |
---|
640 | } |
---|
641 | bool operator<(const ActiveIt& it) const { |
---|
642 | return static_cast<Node>(*this) < static_cast<Node>(it); |
---|
643 | } |
---|
644 | |
---|
645 | private: |
---|
646 | const BellmanFord* _algorithm; |
---|
647 | int _index; |
---|
648 | }; |
---|
649 | |
---|
650 | typedef PredMapPath<Digraph, PredMap> Path; |
---|
651 | |
---|
652 | /// \brief Gives back the shortest path. |
---|
653 | /// |
---|
654 | /// Gives back the shortest path. |
---|
655 | /// \pre The \c t should be reachable from the source. |
---|
656 | Path path(Node t) |
---|
657 | { |
---|
658 | return Path(*digraph, *_pred, t); |
---|
659 | } |
---|
660 | |
---|
661 | |
---|
662 | // TODO : implement negative cycle |
---|
663 | // /// \brief Gives back a negative cycle. |
---|
664 | // /// |
---|
665 | // /// This function gives back a negative cycle. |
---|
666 | // /// If the algorithm have not found yet negative cycle it will give back |
---|
667 | // /// an empty path. |
---|
668 | // Path negativeCycle() { |
---|
669 | // typename Digraph::template NodeMap<int> state(*digraph, 0); |
---|
670 | // for (ActiveIt it(*this); it != INVALID; ++it) { |
---|
671 | // if (state[it] == 0) { |
---|
672 | // for (Node t = it; predArc(t) != INVALID; t = predNode(t)) { |
---|
673 | // if (state[t] == 0) { |
---|
674 | // state[t] = 1; |
---|
675 | // } else if (state[t] == 2) { |
---|
676 | // break; |
---|
677 | // } else { |
---|
678 | // p.clear(); |
---|
679 | // typename Path::Builder b(p); |
---|
680 | // b.setStartNode(t); |
---|
681 | // b.pushFront(predArc(t)); |
---|
682 | // for(Node s = predNode(t); s != t; s = predNode(s)) { |
---|
683 | // b.pushFront(predArc(s)); |
---|
684 | // } |
---|
685 | // b.commit(); |
---|
686 | // return true; |
---|
687 | // } |
---|
688 | // } |
---|
689 | // for (Node t = it; predArc(t) != INVALID; t = predNode(t)) { |
---|
690 | // if (state[t] == 1) { |
---|
691 | // state[t] = 2; |
---|
692 | // } else { |
---|
693 | // break; |
---|
694 | // } |
---|
695 | // } |
---|
696 | // } |
---|
697 | // } |
---|
698 | // return false; |
---|
699 | // } |
---|
700 | |
---|
701 | /// \brief The distance of a node from the root. |
---|
702 | /// |
---|
703 | /// Returns the distance of a node from the root. |
---|
704 | /// \pre \ref run() must be called before using this function. |
---|
705 | /// \warning If node \c v in unreachable from the root the return value |
---|
706 | /// of this funcion is undefined. |
---|
707 | Value dist(Node v) const { return (*_dist)[v]; } |
---|
708 | |
---|
709 | /// \brief Returns the 'previous arc' of the shortest path tree. |
---|
710 | /// |
---|
711 | /// For a node \c v it returns the 'previous arc' of the shortest path |
---|
712 | /// tree, i.e. it returns the last arc of a shortest path from the root |
---|
713 | /// to \c v. It is \ref INVALID if \c v is unreachable from the root or |
---|
714 | /// if \c v=s. The shortest path tree used here is equal to the shortest |
---|
715 | /// path tree used in \ref predNode(). |
---|
716 | /// \pre \ref run() must be called before using |
---|
717 | /// this function. |
---|
718 | Arc predArc(Node v) const { return (*_pred)[v]; } |
---|
719 | |
---|
720 | /// \brief Returns the 'previous node' of the shortest path tree. |
---|
721 | /// |
---|
722 | /// For a node \c v it returns the 'previous node' of the shortest path |
---|
723 | /// tree, i.e. it returns the last but one node from a shortest path from |
---|
724 | /// the root to \c /v. It is INVALID if \c v is unreachable from the root |
---|
725 | /// or if \c v=s. The shortest path tree used here is equal to the |
---|
726 | /// shortest path tree used in \ref predArc(). \pre \ref run() must be |
---|
727 | /// called before using this function. |
---|
728 | Node predNode(Node v) const { |
---|
729 | return (*_pred)[v] == INVALID ? INVALID : digraph->source((*_pred)[v]); |
---|
730 | } |
---|
731 | |
---|
732 | /// \brief Returns a reference to the NodeMap of distances. |
---|
733 | /// |
---|
734 | /// Returns a reference to the NodeMap of distances. \pre \ref run() must |
---|
735 | /// be called before using this function. |
---|
736 | const DistMap &distMap() const { return *_dist;} |
---|
737 | |
---|
738 | /// \brief Returns a reference to the shortest path tree map. |
---|
739 | /// |
---|
740 | /// Returns a reference to the NodeMap of the arcs of the |
---|
741 | /// shortest path tree. |
---|
742 | /// \pre \ref run() must be called before using this function. |
---|
743 | const PredMap &predMap() const { return *_pred; } |
---|
744 | |
---|
745 | /// \brief Checks if a node is reachable from the root. |
---|
746 | /// |
---|
747 | /// Returns \c true if \c v is reachable from the root. |
---|
748 | /// \pre \ref run() must be called before using this function. |
---|
749 | /// |
---|
750 | bool reached(Node v) { return (*_dist)[v] != OperationTraits::infinity(); } |
---|
751 | |
---|
752 | ///@} |
---|
753 | }; |
---|
754 | |
---|
755 | /// \brief Default traits class of BellmanFord function. |
---|
756 | /// |
---|
757 | /// Default traits class of BellmanFord function. |
---|
758 | /// \param _Digraph Digraph type. |
---|
759 | /// \param _LengthMap Type of length map. |
---|
760 | template <typename _Digraph, typename _LengthMap> |
---|
761 | struct BellmanFordWizardDefaultTraits { |
---|
762 | /// \brief The digraph type the algorithm runs on. |
---|
763 | typedef _Digraph Digraph; |
---|
764 | |
---|
765 | /// \brief The type of the map that stores the arc lengths. |
---|
766 | /// |
---|
767 | /// The type of the map that stores the arc lengths. |
---|
768 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
---|
769 | typedef _LengthMap LengthMap; |
---|
770 | |
---|
771 | /// \brief The value type of the length map. |
---|
772 | typedef typename _LengthMap::Value Value; |
---|
773 | |
---|
774 | /// \brief Operation traits for Bellman-Ford algorithm. |
---|
775 | /// |
---|
776 | /// It defines the infinity type on the given Value type |
---|
777 | /// and the used operation. |
---|
778 | /// \see BellmanFordDefaultOperationTraits |
---|
779 | typedef BellmanFordDefaultOperationTraits<Value> OperationTraits; |
---|
780 | |
---|
781 | /// \brief The type of the map that stores the last |
---|
782 | /// arcs of the shortest paths. |
---|
783 | /// |
---|
784 | /// The type of the map that stores the last |
---|
785 | /// arcs of the shortest paths. |
---|
786 | /// It must meet the \ref concepts::WriteMap "WriteMap" concept. |
---|
787 | typedef NullMap <typename _Digraph::Node,typename _Digraph::Arc> PredMap; |
---|
788 | |
---|
789 | /// \brief Instantiates a PredMap. |
---|
790 | /// |
---|
791 | /// This function instantiates a \ref PredMap. |
---|
792 | static PredMap *createPredMap(const _Digraph &) { |
---|
793 | return new PredMap(); |
---|
794 | } |
---|
795 | /// \brief The type of the map that stores the dists of the nodes. |
---|
796 | /// |
---|
797 | /// The type of the map that stores the dists of the nodes. |
---|
798 | /// It must meet the \ref concepts::WriteMap "WriteMap" concept. |
---|
799 | typedef NullMap<typename Digraph::Node, Value> DistMap; |
---|
800 | /// \brief Instantiates a DistMap. |
---|
801 | /// |
---|
802 | /// This function instantiates a \ref DistMap. |
---|
803 | static DistMap *createDistMap(const _Digraph &) { |
---|
804 | return new DistMap(); |
---|
805 | } |
---|
806 | }; |
---|
807 | |
---|
808 | /// \brief Default traits used by \ref BellmanFordWizard |
---|
809 | /// |
---|
810 | /// To make it easier to use BellmanFord algorithm |
---|
811 | /// we have created a wizard class. |
---|
812 | /// This \ref BellmanFordWizard class needs default traits, |
---|
813 | /// as well as the \ref BellmanFord class. |
---|
814 | /// The \ref BellmanFordWizardBase is a class to be the default traits of the |
---|
815 | /// \ref BellmanFordWizard class. |
---|
816 | /// \todo More named parameters are required... |
---|
817 | template<class _Digraph,class _LengthMap> |
---|
818 | class BellmanFordWizardBase |
---|
819 | : public BellmanFordWizardDefaultTraits<_Digraph,_LengthMap> { |
---|
820 | |
---|
821 | typedef BellmanFordWizardDefaultTraits<_Digraph,_LengthMap> Base; |
---|
822 | protected: |
---|
823 | /// Type of the nodes in the digraph. |
---|
824 | typedef typename Base::Digraph::Node Node; |
---|
825 | |
---|
826 | /// Pointer to the underlying digraph. |
---|
827 | void *_graph; |
---|
828 | /// Pointer to the length map |
---|
829 | void *_length; |
---|
830 | ///Pointer to the map of predecessors arcs. |
---|
831 | void *_pred; |
---|
832 | ///Pointer to the map of distances. |
---|
833 | void *_dist; |
---|
834 | ///Pointer to the source node. |
---|
835 | Node _source; |
---|
836 | |
---|
837 | public: |
---|
838 | /// Constructor. |
---|
839 | |
---|
840 | /// This constructor does not require parameters, therefore it initiates |
---|
841 | /// all of the attributes to default values (0, INVALID). |
---|
842 | BellmanFordWizardBase() : _graph(0), _length(0), _pred(0), |
---|
843 | _dist(0), _source(INVALID) {} |
---|
844 | |
---|
845 | /// Constructor. |
---|
846 | |
---|
847 | /// This constructor requires some parameters, |
---|
848 | /// listed in the parameters list. |
---|
849 | /// Others are initiated to 0. |
---|
850 | /// \param digraph is the initial value of \ref _graph |
---|
851 | /// \param length is the initial value of \ref _length |
---|
852 | /// \param source is the initial value of \ref _source |
---|
853 | BellmanFordWizardBase(const _Digraph& digraph, |
---|
854 | const _LengthMap& length, |
---|
855 | Node source = INVALID) : |
---|
856 | _graph(reinterpret_cast<void*>(const_cast<_Digraph*>(&digraph))), |
---|
857 | _length(reinterpret_cast<void*>(const_cast<_LengthMap*>(&length))), |
---|
858 | _pred(0), _dist(0), _source(source) {} |
---|
859 | |
---|
860 | }; |
---|
861 | |
---|
862 | /// A class to make the usage of BellmanFord algorithm easier |
---|
863 | |
---|
864 | /// This class is created to make it easier to use BellmanFord algorithm. |
---|
865 | /// It uses the functions and features of the plain \ref BellmanFord, |
---|
866 | /// but it is much simpler to use it. |
---|
867 | /// |
---|
868 | /// Simplicity means that the way to change the types defined |
---|
869 | /// in the traits class is based on functions that returns the new class |
---|
870 | /// and not on templatable built-in classes. |
---|
871 | /// When using the plain \ref BellmanFord |
---|
872 | /// the new class with the modified type comes from |
---|
873 | /// the original class by using the :: |
---|
874 | /// operator. In the case of \ref BellmanFordWizard only |
---|
875 | /// a function have to be called and it will |
---|
876 | /// return the needed class. |
---|
877 | /// |
---|
878 | /// It does not have own \ref run method. When its \ref run method is called |
---|
879 | /// it initiates a plain \ref BellmanFord class, and calls the \ref |
---|
880 | /// BellmanFord::run method of it. |
---|
881 | template<class _Traits> |
---|
882 | class BellmanFordWizard : public _Traits { |
---|
883 | typedef _Traits Base; |
---|
884 | |
---|
885 | ///The type of the underlying digraph. |
---|
886 | typedef typename _Traits::Digraph Digraph; |
---|
887 | |
---|
888 | typedef typename Digraph::Node Node; |
---|
889 | typedef typename Digraph::NodeIt NodeIt; |
---|
890 | typedef typename Digraph::Arc Arc; |
---|
891 | typedef typename Digraph::OutArcIt ArcIt; |
---|
892 | |
---|
893 | ///The type of the map that stores the arc lengths. |
---|
894 | typedef typename _Traits::LengthMap LengthMap; |
---|
895 | |
---|
896 | ///The type of the length of the arcs. |
---|
897 | typedef typename LengthMap::Value Value; |
---|
898 | |
---|
899 | ///\brief The type of the map that stores the last |
---|
900 | ///arcs of the shortest paths. |
---|
901 | typedef typename _Traits::PredMap PredMap; |
---|
902 | |
---|
903 | ///The type of the map that stores the dists of the nodes. |
---|
904 | typedef typename _Traits::DistMap DistMap; |
---|
905 | |
---|
906 | public: |
---|
907 | /// Constructor. |
---|
908 | BellmanFordWizard() : _Traits() {} |
---|
909 | |
---|
910 | /// \brief Constructor that requires parameters. |
---|
911 | /// |
---|
912 | /// Constructor that requires parameters. |
---|
913 | /// These parameters will be the default values for the traits class. |
---|
914 | BellmanFordWizard(const Digraph& digraph, const LengthMap& length, |
---|
915 | Node src = INVALID) |
---|
916 | : _Traits(digraph, length, src) {} |
---|
917 | |
---|
918 | /// \brief Copy constructor |
---|
919 | BellmanFordWizard(const _Traits &b) : _Traits(b) {} |
---|
920 | |
---|
921 | ~BellmanFordWizard() {} |
---|
922 | |
---|
923 | /// \brief Runs BellmanFord algorithm from a given node. |
---|
924 | /// |
---|
925 | /// Runs BellmanFord algorithm from a given node. |
---|
926 | /// The node can be given by the \ref source function. |
---|
927 | void run() { |
---|
928 | LEMON_ASSERT(Base::_source != INVALID, "Source node is not given"); |
---|
929 | BellmanFord<Digraph,LengthMap,_Traits> |
---|
930 | bf(*reinterpret_cast<const Digraph*>(Base::_graph), |
---|
931 | *reinterpret_cast<const LengthMap*>(Base::_length)); |
---|
932 | if (Base::_pred) bf.predMap(*reinterpret_cast<PredMap*>(Base::_pred)); |
---|
933 | if (Base::_dist) bf.distMap(*reinterpret_cast<DistMap*>(Base::_dist)); |
---|
934 | bf.run(Base::_source); |
---|
935 | } |
---|
936 | |
---|
937 | /// \brief Runs BellmanFord algorithm from the given node. |
---|
938 | /// |
---|
939 | /// Runs BellmanFord algorithm from the given node. |
---|
940 | /// \param src is the given source. |
---|
941 | void run(Node src) { |
---|
942 | Base::_source = src; |
---|
943 | run(); |
---|
944 | } |
---|
945 | |
---|
946 | template<class T> |
---|
947 | struct DefPredMapBase : public Base { |
---|
948 | typedef T PredMap; |
---|
949 | static PredMap *createPredMap(const Digraph &) { return 0; }; |
---|
950 | DefPredMapBase(const _Traits &b) : _Traits(b) {} |
---|
951 | }; |
---|
952 | |
---|
953 | ///\brief \ref named-templ-param "Named parameter" |
---|
954 | ///function for setting PredMap type |
---|
955 | /// |
---|
956 | /// \ref named-templ-param "Named parameter" |
---|
957 | ///function for setting PredMap type |
---|
958 | /// |
---|
959 | template<class T> |
---|
960 | BellmanFordWizard<DefPredMapBase<T> > predMap(const T &t) |
---|
961 | { |
---|
962 | Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t)); |
---|
963 | return BellmanFordWizard<DefPredMapBase<T> >(*this); |
---|
964 | } |
---|
965 | |
---|
966 | template<class T> |
---|
967 | struct DefDistMapBase : public Base { |
---|
968 | typedef T DistMap; |
---|
969 | static DistMap *createDistMap(const Digraph &) { return 0; }; |
---|
970 | DefDistMapBase(const _Traits &b) : _Traits(b) {} |
---|
971 | }; |
---|
972 | |
---|
973 | ///\brief \ref named-templ-param "Named parameter" |
---|
974 | ///function for setting DistMap type |
---|
975 | /// |
---|
976 | /// \ref named-templ-param "Named parameter" |
---|
977 | ///function for setting DistMap type |
---|
978 | /// |
---|
979 | template<class T> |
---|
980 | BellmanFordWizard<DefDistMapBase<T> > distMap(const T &t) { |
---|
981 | Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t)); |
---|
982 | return BellmanFordWizard<DefDistMapBase<T> >(*this); |
---|
983 | } |
---|
984 | |
---|
985 | template<class T> |
---|
986 | struct DefOperationTraitsBase : public Base { |
---|
987 | typedef T OperationTraits; |
---|
988 | DefOperationTraitsBase(const _Traits &b) : _Traits(b) {} |
---|
989 | }; |
---|
990 | |
---|
991 | ///\brief \ref named-templ-param "Named parameter" |
---|
992 | ///function for setting OperationTraits type |
---|
993 | /// |
---|
994 | /// \ref named-templ-param "Named parameter" |
---|
995 | ///function for setting OperationTraits type |
---|
996 | /// |
---|
997 | template<class T> |
---|
998 | BellmanFordWizard<DefOperationTraitsBase<T> > distMap() { |
---|
999 | return BellmanFordWizard<DefDistMapBase<T> >(*this); |
---|
1000 | } |
---|
1001 | |
---|
1002 | /// \brief Sets the source node, from which the BellmanFord algorithm runs. |
---|
1003 | /// |
---|
1004 | /// Sets the source node, from which the BellmanFord algorithm runs. |
---|
1005 | /// \param src is the source node. |
---|
1006 | BellmanFordWizard<_Traits>& source(Node src) { |
---|
1007 | Base::_source = src; |
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1008 | return *this; |
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1009 | } |
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1010 | |
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1011 | }; |
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1012 | |
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1013 | /// \brief Function type interface for BellmanFord algorithm. |
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1014 | /// |
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1015 | /// \ingroup shortest_path |
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1016 | /// Function type interface for BellmanFord algorithm. |
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1017 | /// |
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1018 | /// This function also has several \ref named-templ-func-param |
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1019 | /// "named parameters", they are declared as the members of class |
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1020 | /// \ref BellmanFordWizard. |
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1021 | /// The following |
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1022 | /// example shows how to use these parameters. |
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1023 | ///\code |
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1024 | /// bellmanford(g,length,source).predMap(preds).run(); |
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1025 | ///\endcode |
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1026 | /// \warning Don't forget to put the \ref BellmanFordWizard::run() "run()" |
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1027 | /// to the end of the parameter list. |
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1028 | /// \sa BellmanFordWizard |
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1029 | /// \sa BellmanFord |
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1030 | template<class _Digraph, class _LengthMap> |
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1031 | BellmanFordWizard<BellmanFordWizardBase<_Digraph,_LengthMap> > |
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1032 | bellmanFord(const _Digraph& digraph, |
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1033 | const _LengthMap& length, |
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1034 | typename _Digraph::Node source = INVALID) { |
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1035 | return BellmanFordWizard<BellmanFordWizardBase<_Digraph,_LengthMap> > |
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1036 | (digraph, length, source); |
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1037 | } |
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1038 | |
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1039 | } //END OF NAMESPACE LEMON |
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1040 | |
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1041 | #endif |
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1042 | |
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