1 | /* -*- C++ -*- |
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2 | * lemon/johnson.h - Part of LEMON, a generic C++ optimization library |
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3 | * |
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4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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6 | * |
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7 | * Permission to use, modify and distribute this software is granted |
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8 | * provided that this copyright notice appears in all copies. For |
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9 | * precise terms see the accompanying LICENSE file. |
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10 | * |
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11 | * This software is provided "AS IS" with no warranty of any kind, |
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12 | * express or implied, and with no claim as to its suitability for any |
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13 | * purpose. |
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14 | * |
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15 | */ |
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16 | |
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17 | #ifndef LEMON_JOHNSON_H |
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18 | #define LEMON_JOHNSON_H |
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19 | |
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20 | ///\ingroup flowalgs |
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21 | /// \file |
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22 | /// \brief Johnson algorithm. |
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23 | /// |
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24 | |
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25 | #include <lemon/list_graph.h> |
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26 | #include <lemon/graph_utils.h> |
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27 | #include <lemon/dijkstra.h> |
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28 | #include <lemon/belmann_ford.h> |
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29 | #include <lemon/invalid.h> |
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30 | #include <lemon/error.h> |
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31 | #include <lemon/maps.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 Johnson algorithm class. |
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38 | /// |
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39 | /// It defines all computational operations and constants which are |
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40 | /// used in the Floyd-Warshall algorithm. The default implementation |
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41 | /// is based on the numeric_limits class. If the numeric type does not |
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42 | /// have infinity value then the maximum value is used as extremal |
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43 | /// infinity value. |
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44 | template < |
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45 | typename Value, |
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46 | bool has_infinity = std::numeric_limits<Value>::has_infinity> |
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47 | struct JohnsonDefaultOperationTraits { |
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48 | /// \brief Gives back the zero value of the type. |
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49 | static Value zero() { |
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50 | return static_cast<Value>(0); |
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51 | } |
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52 | /// \brief Gives back the positive infinity value of the type. |
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53 | static Value infinity() { |
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54 | return std::numeric_limits<Value>::infinity(); |
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55 | } |
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56 | /// \brief Gives back the sum of the given two elements. |
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57 | static Value plus(const Value& left, const Value& right) { |
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58 | return left + right; |
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59 | } |
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60 | /// \brief Gives back true only if the first value less than the second. |
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61 | static bool less(const Value& left, const Value& right) { |
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62 | return left < right; |
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63 | } |
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64 | }; |
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65 | |
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66 | template <typename Value> |
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67 | struct JohnsonDefaultOperationTraits<Value, false> { |
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68 | static Value zero() { |
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69 | return static_cast<Value>(0); |
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70 | } |
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71 | static Value infinity() { |
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72 | return std::numeric_limits<Value>::max(); |
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73 | } |
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74 | static Value plus(const Value& left, const Value& right) { |
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75 | if (left == infinity() || right == infinity()) return infinity(); |
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76 | return left + right; |
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77 | } |
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78 | static bool less(const Value& left, const Value& right) { |
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79 | return left < right; |
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80 | } |
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81 | }; |
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82 | |
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83 | /// \brief Default traits class of Johnson class. |
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84 | /// |
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85 | /// Default traits class of Johnson class. |
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86 | /// \param _Graph Graph type. |
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87 | /// \param _LegthMap Type of length map. |
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88 | template<class _Graph, class _LengthMap> |
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89 | struct JohnsonDefaultTraits { |
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90 | /// The graph type the algorithm runs on. |
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91 | typedef _Graph Graph; |
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92 | |
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93 | /// \brief The type of the map that stores the edge lengths. |
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94 | /// |
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95 | /// The type of the map that stores the edge lengths. |
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96 | /// It must meet the \ref concept::ReadMap "ReadMap" concept. |
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97 | typedef _LengthMap LengthMap; |
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98 | |
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99 | // The type of the length of the edges. |
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100 | typedef typename _LengthMap::Value Value; |
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101 | |
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102 | /// \brief Operation traits for belmann-ford algorithm. |
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103 | /// |
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104 | /// It defines the infinity type on the given Value type |
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105 | /// and the used operation. |
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106 | /// \see JohnsonDefaultOperationTraits |
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107 | typedef JohnsonDefaultOperationTraits<Value> OperationTraits; |
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108 | |
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109 | /// \brief The type of the map that stores the last edges of the |
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110 | /// shortest paths. |
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111 | /// |
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112 | /// The type of the map that stores the last |
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113 | /// edges of the shortest paths. |
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114 | /// It must be a matrix map with \c Graph::Edge value type. |
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115 | /// |
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116 | typedef NodeMatrixMap<Graph, typename Graph::Edge> PredMap; |
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117 | |
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118 | /// \brief Instantiates a PredMap. |
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119 | /// |
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120 | /// This function instantiates a \ref PredMap. |
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121 | /// \param G is the graph, to which we would like to define the PredMap. |
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122 | /// \todo The graph alone may be insufficient for the initialization |
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123 | static PredMap *createPredMap(const _Graph& graph) { |
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124 | return new PredMap(graph); |
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125 | } |
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126 | |
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127 | /// \brief The type of the map that stores the dists of the nodes. |
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128 | /// |
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129 | /// The type of the map that stores the dists of the nodes. |
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130 | /// It must meet the \ref concept::WriteMap "WriteMap" concept. |
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131 | /// |
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132 | typedef NodeMatrixMap<Graph, Value> DistMap; |
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133 | |
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134 | /// \brief Instantiates a DistMap. |
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135 | /// |
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136 | /// This function instantiates a \ref DistMap. |
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137 | /// \param G is the graph, to which we would like to define the |
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138 | /// \ref DistMap |
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139 | static DistMap *createDistMap(const _Graph& graph) { |
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140 | return new DistMap(graph); |
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141 | } |
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142 | |
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143 | }; |
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144 | |
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145 | /// \brief Johnson algorithm class. |
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146 | /// |
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147 | /// \ingroup flowalgs |
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148 | /// This class provides an efficient implementation of \c Johnson |
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149 | /// algorithm. The edge lengths are passed to the algorithm using a |
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150 | /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any |
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151 | /// kind of length. |
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152 | /// |
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153 | /// The type of the length is determined by the |
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154 | /// \ref concept::ReadMap::Value "Value" of the length map. |
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155 | /// |
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156 | /// \param _Graph The graph type the algorithm runs on. The default value |
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157 | /// is \ref ListGraph. The value of _Graph is not used directly by |
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158 | /// Johnson, it is only passed to \ref JohnsonDefaultTraits. |
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159 | /// \param _LengthMap This read-only EdgeMap determines the lengths of the |
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160 | /// edges. It is read once for each edge, so the map may involve in |
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161 | /// relatively time consuming process to compute the edge length if |
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162 | /// it is necessary. The default map type is \ref |
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163 | /// concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>". The value |
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164 | /// of _LengthMap is not used directly by Johnson, it is only passed |
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165 | /// to \ref JohnsonDefaultTraits. \param _Traits Traits class to set |
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166 | /// various data types used by the algorithm. The default traits |
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167 | /// class is \ref JohnsonDefaultTraits |
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168 | /// "JohnsonDefaultTraits<_Graph,_LengthMap>". See \ref |
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169 | /// JohnsonDefaultTraits for the documentation of a Johnson traits |
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170 | /// class. |
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171 | /// |
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172 | /// \author Balazs Dezso |
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173 | |
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174 | #ifdef DOXYGEN |
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175 | template <typename _Graph, typename _LengthMap, typename _Traits> |
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176 | #else |
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177 | template <typename _Graph=ListGraph, |
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178 | typename _LengthMap=typename _Graph::template EdgeMap<int>, |
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179 | typename _Traits=JohnsonDefaultTraits<_Graph,_LengthMap> > |
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180 | #endif |
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181 | class Johnson { |
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182 | public: |
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183 | |
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184 | /// \brief \ref Exception for uninitialized parameters. |
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185 | /// |
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186 | /// This error represents problems in the initialization |
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187 | /// of the parameters of the algorithms. |
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188 | |
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189 | class UninitializedParameter : public lemon::UninitializedParameter { |
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190 | public: |
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191 | virtual const char* exceptionName() const { |
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192 | return "lemon::Johnson::UninitializedParameter"; |
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193 | } |
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194 | }; |
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195 | |
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196 | typedef _Traits Traits; |
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197 | ///The type of the underlying graph. |
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198 | typedef typename _Traits::Graph Graph; |
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199 | |
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200 | typedef typename Graph::Node Node; |
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201 | typedef typename Graph::NodeIt NodeIt; |
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202 | typedef typename Graph::Edge Edge; |
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203 | typedef typename Graph::EdgeIt EdgeIt; |
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204 | |
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205 | /// \brief The type of the length of the edges. |
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206 | typedef typename _Traits::LengthMap::Value Value; |
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207 | /// \brief The type of the map that stores the edge lengths. |
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208 | typedef typename _Traits::LengthMap LengthMap; |
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209 | /// \brief The type of the map that stores the last |
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210 | /// edges of the shortest paths. The type of the PredMap |
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211 | /// is a matrix map for Edges |
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212 | typedef typename _Traits::PredMap PredMap; |
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213 | /// \brief The type of the map that stores the dists of the nodes. |
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214 | /// The type of the DistMap is a matrix map for Values |
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215 | typedef typename _Traits::DistMap DistMap; |
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216 | /// \brief The operation traits. |
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217 | typedef typename _Traits::OperationTraits OperationTraits; |
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218 | private: |
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219 | /// Pointer to the underlying graph. |
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220 | const Graph *graph; |
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221 | /// Pointer to the length map |
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222 | const LengthMap *length; |
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223 | ///Pointer to the map of predecessors edges. |
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224 | PredMap *_pred; |
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225 | ///Indicates if \ref _pred is locally allocated (\c true) or not. |
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226 | bool local_pred; |
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227 | ///Pointer to the map of distances. |
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228 | DistMap *_dist; |
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229 | ///Indicates if \ref _dist is locally allocated (\c true) or not. |
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230 | bool local_dist; |
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231 | |
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232 | /// Creates the maps if necessary. |
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233 | void create_maps() { |
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234 | if(!_pred) { |
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235 | local_pred = true; |
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236 | _pred = Traits::createPredMap(*graph); |
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237 | } |
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238 | if(!_dist) { |
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239 | local_dist = true; |
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240 | _dist = Traits::createDistMap(*graph); |
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241 | } |
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242 | } |
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243 | |
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244 | public : |
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245 | |
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246 | /// \name Named template parameters |
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247 | |
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248 | ///@{ |
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249 | |
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250 | template <class T> |
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251 | struct DefPredMapTraits : public Traits { |
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252 | typedef T PredMap; |
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253 | static PredMap *createPredMap(const Graph& graph) { |
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254 | throw UninitializedParameter(); |
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255 | } |
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256 | }; |
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257 | |
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258 | /// \brief \ref named-templ-param "Named parameter" for setting PredMap |
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259 | /// type |
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260 | /// \ref named-templ-param "Named parameter" for setting PredMap type |
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261 | /// |
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262 | template <class T> |
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263 | struct DefPredMap |
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264 | : public Johnson< Graph, LengthMap, DefPredMapTraits<T> > { |
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265 | typedef Johnson< Graph, LengthMap, DefPredMapTraits<T> > Create; |
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266 | }; |
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267 | |
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268 | template <class T> |
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269 | struct DefDistMapTraits : public Traits { |
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270 | typedef T DistMap; |
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271 | static DistMap *createDistMap(const Graph& graph) { |
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272 | throw UninitializedParameter(); |
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273 | } |
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274 | }; |
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275 | /// \brief \ref named-templ-param "Named parameter" for setting DistMap |
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276 | /// type |
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277 | /// |
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278 | /// \ref named-templ-param "Named parameter" for setting DistMap type |
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279 | /// |
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280 | template <class T> |
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281 | struct DefDistMap |
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282 | : public Johnson< Graph, LengthMap, DefDistMapTraits<T> > { |
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283 | typedef Johnson< Graph, LengthMap, DefDistMapTraits<T> > Create; |
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284 | }; |
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285 | |
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286 | template <class T> |
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287 | struct DefOperationTraitsTraits : public Traits { |
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288 | typedef T OperationTraits; |
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289 | }; |
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290 | |
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291 | /// \brief \ref named-templ-param "Named parameter" for setting |
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292 | /// OperationTraits type |
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293 | /// |
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294 | /// \ref named-templ-param "Named parameter" for setting |
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295 | /// OperationTraits type |
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296 | template <class T> |
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297 | struct DefOperationTraits |
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298 | : public Johnson< Graph, LengthMap, DefOperationTraitsTraits<T> > { |
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299 | typedef Johnson< Graph, LengthMap, DefOperationTraitsTraits<T> > Create; |
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300 | }; |
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301 | |
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302 | ///@} |
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303 | |
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304 | protected: |
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305 | |
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306 | Johnson() {} |
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307 | |
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308 | public: |
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309 | |
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310 | /// \brief Constructor. |
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311 | /// |
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312 | /// \param _graph the graph the algorithm will run on. |
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313 | /// \param _length the length map used by the algorithm. |
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314 | Johnson(const Graph& _graph, const LengthMap& _length) : |
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315 | graph(&_graph), length(&_length), |
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316 | _pred(0), local_pred(false), |
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317 | _dist(0), local_dist(false) {} |
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318 | |
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319 | ///Destructor. |
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320 | ~Johnson() { |
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321 | if(local_pred) delete _pred; |
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322 | if(local_dist) delete _dist; |
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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 | Johnson &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 edges. |
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335 | /// |
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336 | /// Sets the map storing the predecessor edges. |
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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 | Johnson &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 | Johnson &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 | /// Finally \ref start() will perform the actual path |
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372 | /// computation. |
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373 | |
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374 | ///@{ |
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375 | |
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376 | /// \brief Initializes the internal data structures. |
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377 | /// |
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378 | /// Initializes the internal data structures. |
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379 | void init() { |
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380 | create_maps(); |
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381 | } |
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382 | |
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383 | /// \brief Executes the algorithm. |
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384 | /// |
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385 | /// This method runs the %Johnson algorithm in order to compute |
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386 | /// the shortest path to each node pairs. The algorithm |
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387 | /// computes |
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388 | /// - The shortest path tree for each node. |
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389 | /// - The distance between each node pairs. |
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390 | void start() { |
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391 | typedef typename BelmannFord<Graph, LengthMap>:: |
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392 | template DefOperationTraits<OperationTraits>:: |
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393 | template DefPredMap<NullMap<Node, Edge> >:: |
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394 | Create BelmannFordType; |
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395 | |
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396 | BelmannFordType belmannford(*graph, *length); |
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397 | |
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398 | NullMap<Node, Edge> predMap; |
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399 | |
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400 | belmannford.predMap(predMap); |
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401 | |
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402 | belmannford.init(OperationTraits::zero()); |
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403 | belmannford.start(); |
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404 | |
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405 | for (NodeIt it(*graph); it != INVALID; ++it) { |
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406 | typedef PotentialDifferenceMap<Graph, |
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407 | typename BelmannFordType::DistMap> PotDiffMap; |
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408 | PotDiffMap potdiff(*graph, belmannford.distMap()); |
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409 | typedef SubMap<LengthMap, PotDiffMap> ShiftLengthMap; |
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410 | ShiftLengthMap shiftlen(*length, potdiff); |
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411 | Dijkstra<Graph, ShiftLengthMap> dijkstra(*graph, shiftlen); |
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412 | dijkstra.run(it); |
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413 | for (NodeIt jt(*graph); jt != INVALID; ++jt) { |
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414 | if (dijkstra.reached(jt)) { |
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415 | _dist->set(it, jt, dijkstra.dist(jt) + |
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416 | belmannford.dist(jt) - belmannford.dist(it)); |
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417 | _pred->set(it, jt, dijkstra.pred(jt)); |
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418 | } else { |
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419 | _dist->set(it, jt, OperationTraits::infinity()); |
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420 | _pred->set(it, jt, INVALID); |
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421 | } |
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422 | } |
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423 | } |
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424 | } |
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425 | |
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426 | /// \brief Runs %Johnson algorithm. |
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427 | /// |
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428 | /// This method runs the %Johnson algorithm from a each node |
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429 | /// in order to compute the shortest path to each node pairs. |
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430 | /// The algorithm computes |
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431 | /// - The shortest path tree for each node. |
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432 | /// - The distance between each node pairs. |
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433 | /// |
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434 | /// \note d.run(s) is just a shortcut of the following code. |
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435 | /// \code |
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436 | /// d.init(); |
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437 | /// d.start(); |
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438 | /// \endcode |
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439 | void run() { |
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440 | init(); |
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441 | start(); |
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442 | } |
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443 | |
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444 | ///@} |
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445 | |
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446 | /// \name Query Functions |
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447 | /// The result of the %Johnson algorithm can be obtained using these |
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448 | /// functions.\n |
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449 | /// Before the use of these functions, |
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450 | /// either run() or start() must be called. |
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451 | |
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452 | ///@{ |
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453 | |
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454 | /// \brief Copies the shortest path to \c t into \c p |
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455 | /// |
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456 | /// This function copies the shortest path to \c t into \c p. |
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457 | /// If it \c t is a source itself or unreachable, then it does not |
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458 | /// alter \c p. |
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459 | /// \todo Is it the right way to handle unreachable nodes? |
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460 | /// \return Returns \c true if a path to \c t was actually copied to \c p, |
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461 | /// \c false otherwise. |
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462 | /// \sa DirPath |
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463 | template <typename Path> |
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464 | bool getPath(Path &p, Node source, Node target) { |
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465 | if (connected(source, target)) { |
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466 | p.clear(); |
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467 | typename Path::Builder b(target); |
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468 | for(b.setStartNode(target); pred(source, target) != INVALID; |
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469 | target = predNode(target)) { |
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470 | b.pushFront(pred(source, target)); |
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471 | } |
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472 | b.commit(); |
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473 | return true; |
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474 | } |
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475 | return false; |
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476 | } |
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477 | |
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478 | /// \brief The distance between two nodes. |
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479 | /// |
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480 | /// Returns the distance between two nodes. |
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481 | /// \pre \ref run() must be called before using this function. |
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482 | /// \warning If node \c v in unreachable from the root the return value |
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483 | /// of this funcion is undefined. |
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484 | Value dist(Node source, Node target) const { |
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485 | return (*_dist)(source, target); |
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486 | } |
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487 | |
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488 | /// \brief Returns the 'previous edge' of the shortest path tree. |
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489 | /// |
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490 | /// For the node \c node it returns the 'previous edge' of the shortest |
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491 | /// path tree to direction of the node \c root |
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492 | /// i.e. it returns the last edge of a shortest path from the node \c root |
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493 | /// to \c node. It is \ref INVALID if \c node is unreachable from the root |
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494 | /// or if \c node=root. The shortest path tree used here is equal to the |
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495 | /// shortest path tree used in \ref predNode(). |
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496 | /// \pre \ref run() must be called before using this function. |
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497 | /// \todo predEdge could be a better name. |
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498 | Edge pred(Node root, Node node) const { |
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499 | return (*_pred)(root, node); |
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500 | } |
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501 | |
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502 | /// \brief Returns the 'previous node' of the shortest path tree. |
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503 | /// |
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504 | /// For a node \c node it returns the 'previous node' of the shortest path |
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505 | /// tree to direction of the node \c root, i.e. it returns the last but |
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506 | /// one node from a shortest path from the \c root to \c node. It is |
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507 | /// INVALID if \c node is unreachable from the root or if \c node=root. |
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508 | /// The shortest path tree used here is equal to the |
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509 | /// shortest path tree used in \ref pred(). |
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510 | /// \pre \ref run() must be called before using this function. |
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511 | Node predNode(Node root, Node node) const { |
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512 | return (*_pred)(root, node) == INVALID ? |
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513 | INVALID : graph->source((*_pred)(root, node)); |
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514 | } |
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515 | |
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516 | /// \brief Returns a reference to the matrix node map of distances. |
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517 | /// |
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518 | /// Returns a reference to the matrix node map of distances. |
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519 | /// |
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520 | /// \pre \ref run() must be called before using this function. |
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521 | const DistMap &distMap() const { return *_dist;} |
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522 | |
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523 | /// \brief Returns a reference to the shortest path tree map. |
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524 | /// |
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525 | /// Returns a reference to the matrix node map of the edges of the |
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526 | /// shortest path tree. |
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527 | /// \pre \ref run() must be called before using this function. |
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528 | const PredMap &predMap() const { return *_pred;} |
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529 | |
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530 | /// \brief Checks if a node is reachable from the root. |
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531 | /// |
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532 | /// Returns \c true if \c v is reachable from the root. |
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533 | /// \pre \ref run() must be called before using this function. |
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534 | /// |
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535 | bool connected(Node source, Node target) { |
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536 | return (*_dist)(source, target) != OperationTraits::infinity(); |
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537 | } |
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538 | |
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539 | ///@} |
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540 | }; |
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541 | |
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542 | } //END OF NAMESPACE LEMON |
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543 | |
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544 | #endif |
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