1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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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) 2003-2009 |
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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_SUURBALLE_H |
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20 | #define LEMON_SUURBALLE_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 An algorithm for finding arc-disjoint paths between two |
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25 | /// nodes having minimum total length. |
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26 | |
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27 | #include <vector> |
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28 | #include <limits> |
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29 | #include <lemon/bin_heap.h> |
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30 | #include <lemon/path.h> |
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31 | #include <lemon/list_graph.h> |
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32 | #include <lemon/dijkstra.h> |
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33 | #include <lemon/maps.h> |
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34 | |
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35 | namespace lemon { |
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36 | |
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37 | /// \brief Default traits class of Suurballe algorithm. |
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38 | /// |
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39 | /// Default traits class of Suurballe algorithm. |
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40 | /// \tparam GR The digraph type the algorithm runs on. |
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41 | /// \tparam LEN The type of the length map. |
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42 | /// The default value is <tt>GR::ArcMap<int></tt>. |
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43 | #ifdef DOXYGEN |
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44 | template <typename GR, typename LEN> |
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45 | #else |
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46 | template < typename GR, |
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47 | typename LEN = typename GR::template ArcMap<int> > |
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48 | #endif |
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49 | struct SuurballeDefaultTraits |
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50 | { |
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51 | /// The type of the digraph. |
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52 | typedef GR Digraph; |
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53 | /// The type of the length map. |
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54 | typedef LEN LengthMap; |
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55 | /// The type of the lengths. |
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56 | typedef typename LEN::Value Length; |
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57 | /// The type of the flow map. |
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58 | typedef typename GR::template ArcMap<int> FlowMap; |
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59 | /// The type of the potential map. |
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60 | typedef typename GR::template NodeMap<Length> PotentialMap; |
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61 | |
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62 | /// \brief The path type |
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63 | /// |
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64 | /// The type used for storing the found arc-disjoint paths. |
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65 | /// It must conform to the \ref lemon::concepts::Path "Path" concept |
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66 | /// and it must have an \c addBack() function. |
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67 | typedef lemon::Path<Digraph> Path; |
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68 | |
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69 | /// The cross reference type used for the heap. |
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70 | typedef typename GR::template NodeMap<int> HeapCrossRef; |
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71 | |
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72 | /// \brief The heap type used for internal Dijkstra computations. |
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73 | /// |
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74 | /// The type of the heap used for internal Dijkstra computations. |
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75 | /// It must conform to the \ref lemon::concepts::Heap "Heap" concept |
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76 | /// and its priority type must be \c Length. |
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77 | typedef BinHeap<Length, HeapCrossRef> Heap; |
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78 | }; |
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79 | |
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80 | /// \addtogroup shortest_path |
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81 | /// @{ |
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82 | |
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83 | /// \brief Algorithm for finding arc-disjoint paths between two nodes |
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84 | /// having minimum total length. |
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85 | /// |
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86 | /// \ref lemon::Suurballe "Suurballe" implements an algorithm for |
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87 | /// finding arc-disjoint paths having minimum total length (cost) |
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88 | /// from a given source node to a given target node in a digraph. |
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89 | /// |
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90 | /// Note that this problem is a special case of the \ref min_cost_flow |
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91 | /// "minimum cost flow problem". This implementation is actually an |
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92 | /// efficient specialized version of the \ref CapacityScaling |
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93 | /// "successive shortest path" algorithm directly for this problem. |
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94 | /// Therefore this class provides query functions for flow values and |
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95 | /// node potentials (the dual solution) just like the minimum cost flow |
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96 | /// algorithms. |
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97 | /// |
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98 | /// \tparam GR The digraph type the algorithm runs on. |
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99 | /// \tparam LEN The type of the length map. |
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100 | /// The default value is <tt>GR::ArcMap<int></tt>. |
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101 | /// |
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102 | /// \warning Length values should be \e non-negative. |
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103 | /// |
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104 | /// \note For finding \e node-disjoint paths, this algorithm can be used |
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105 | /// along with the \ref SplitNodes adaptor. |
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106 | #ifdef DOXYGEN |
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107 | template <typename GR, typename LEN, typename TR> |
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108 | #else |
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109 | template < typename GR, |
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110 | typename LEN = typename GR::template ArcMap<int>, |
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111 | typename TR = SuurballeDefaultTraits<GR, LEN> > |
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112 | #endif |
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113 | class Suurballe |
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114 | { |
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115 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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116 | |
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117 | typedef ConstMap<Arc, int> ConstArcMap; |
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118 | typedef typename GR::template NodeMap<Arc> PredMap; |
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119 | |
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120 | public: |
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121 | |
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122 | /// The type of the digraph. |
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123 | typedef typename TR::Digraph Digraph; |
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124 | /// The type of the length map. |
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125 | typedef typename TR::LengthMap LengthMap; |
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126 | /// The type of the lengths. |
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127 | typedef typename TR::Length Length; |
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128 | |
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129 | /// The type of the flow map. |
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130 | typedef typename TR::FlowMap FlowMap; |
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131 | /// The type of the potential map. |
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132 | typedef typename TR::PotentialMap PotentialMap; |
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133 | /// The type of the path structures. |
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134 | typedef typename TR::Path Path; |
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135 | /// The cross reference type used for the heap. |
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136 | typedef typename TR::HeapCrossRef HeapCrossRef; |
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137 | /// The heap type used for internal Dijkstra computations. |
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138 | typedef typename TR::Heap Heap; |
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139 | |
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140 | /// The \ref SuurballeDefaultTraits "traits class" of the algorithm. |
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141 | typedef TR Traits; |
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142 | |
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143 | private: |
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144 | |
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145 | // ResidualDijkstra is a special implementation of the |
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146 | // Dijkstra algorithm for finding shortest paths in the |
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147 | // residual network with respect to the reduced arc lengths |
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148 | // and modifying the node potentials according to the |
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149 | // distance of the nodes. |
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150 | class ResidualDijkstra |
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151 | { |
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152 | private: |
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153 | |
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154 | const Digraph &_graph; |
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155 | const LengthMap &_length; |
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156 | const FlowMap &_flow; |
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157 | PotentialMap &_pi; |
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158 | PredMap &_pred; |
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159 | Node _s; |
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160 | Node _t; |
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161 | |
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162 | PotentialMap _dist; |
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163 | std::vector<Node> _proc_nodes; |
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164 | |
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165 | public: |
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166 | |
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167 | // Constructor |
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168 | ResidualDijkstra(Suurballe &srb) : |
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169 | _graph(srb._graph), _length(srb._length), |
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170 | _flow(*srb._flow), _pi(*srb._potential), _pred(srb._pred), |
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171 | _s(srb._s), _t(srb._t), _dist(_graph) {} |
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172 | |
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173 | // Run the algorithm and return true if a path is found |
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174 | // from the source node to the target node. |
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175 | bool run(int cnt) { |
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176 | return cnt == 0 ? startFirst() : start(); |
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177 | } |
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178 | |
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179 | private: |
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180 | |
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181 | // Execute the algorithm for the first time (the flow and potential |
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182 | // functions have to be identically zero). |
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183 | bool startFirst() { |
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184 | HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP); |
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185 | Heap heap(heap_cross_ref); |
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186 | heap.push(_s, 0); |
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187 | _pred[_s] = INVALID; |
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188 | _proc_nodes.clear(); |
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189 | |
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190 | // Process nodes |
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191 | while (!heap.empty() && heap.top() != _t) { |
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192 | Node u = heap.top(), v; |
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193 | Length d = heap.prio(), dn; |
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194 | _dist[u] = heap.prio(); |
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195 | _proc_nodes.push_back(u); |
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196 | heap.pop(); |
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197 | |
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198 | // Traverse outgoing arcs |
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199 | for (OutArcIt e(_graph, u); e != INVALID; ++e) { |
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200 | v = _graph.target(e); |
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201 | switch(heap.state(v)) { |
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202 | case Heap::PRE_HEAP: |
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203 | heap.push(v, d + _length[e]); |
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204 | _pred[v] = e; |
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205 | break; |
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206 | case Heap::IN_HEAP: |
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207 | dn = d + _length[e]; |
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208 | if (dn < heap[v]) { |
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209 | heap.decrease(v, dn); |
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210 | _pred[v] = e; |
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211 | } |
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212 | break; |
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213 | case Heap::POST_HEAP: |
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214 | break; |
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215 | } |
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216 | } |
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217 | } |
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218 | if (heap.empty()) return false; |
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219 | |
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220 | // Update potentials of processed nodes |
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221 | Length t_dist = heap.prio(); |
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222 | for (int i = 0; i < int(_proc_nodes.size()); ++i) |
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223 | _pi[_proc_nodes[i]] = _dist[_proc_nodes[i]] - t_dist; |
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224 | return true; |
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225 | } |
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226 | |
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227 | // Execute the algorithm. |
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228 | bool start() { |
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229 | HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP); |
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230 | Heap heap(heap_cross_ref); |
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231 | heap.push(_s, 0); |
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232 | _pred[_s] = INVALID; |
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233 | _proc_nodes.clear(); |
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234 | |
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235 | // Process nodes |
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236 | while (!heap.empty() && heap.top() != _t) { |
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237 | Node u = heap.top(), v; |
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238 | Length d = heap.prio() + _pi[u], dn; |
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239 | _dist[u] = heap.prio(); |
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240 | _proc_nodes.push_back(u); |
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241 | heap.pop(); |
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242 | |
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243 | // Traverse outgoing arcs |
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244 | for (OutArcIt e(_graph, u); e != INVALID; ++e) { |
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245 | if (_flow[e] == 0) { |
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246 | v = _graph.target(e); |
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247 | switch(heap.state(v)) { |
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248 | case Heap::PRE_HEAP: |
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249 | heap.push(v, d + _length[e] - _pi[v]); |
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250 | _pred[v] = e; |
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251 | break; |
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252 | case Heap::IN_HEAP: |
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253 | dn = d + _length[e] - _pi[v]; |
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254 | if (dn < heap[v]) { |
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255 | heap.decrease(v, dn); |
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256 | _pred[v] = e; |
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257 | } |
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258 | break; |
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259 | case Heap::POST_HEAP: |
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260 | break; |
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261 | } |
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262 | } |
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263 | } |
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264 | |
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265 | // Traverse incoming arcs |
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266 | for (InArcIt e(_graph, u); e != INVALID; ++e) { |
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267 | if (_flow[e] == 1) { |
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268 | v = _graph.source(e); |
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269 | switch(heap.state(v)) { |
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270 | case Heap::PRE_HEAP: |
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271 | heap.push(v, d - _length[e] - _pi[v]); |
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272 | _pred[v] = e; |
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273 | break; |
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274 | case Heap::IN_HEAP: |
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275 | dn = d - _length[e] - _pi[v]; |
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276 | if (dn < heap[v]) { |
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277 | heap.decrease(v, dn); |
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278 | _pred[v] = e; |
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279 | } |
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280 | break; |
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281 | case Heap::POST_HEAP: |
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282 | break; |
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283 | } |
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284 | } |
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285 | } |
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286 | } |
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287 | if (heap.empty()) return false; |
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288 | |
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289 | // Update potentials of processed nodes |
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290 | Length t_dist = heap.prio(); |
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291 | for (int i = 0; i < int(_proc_nodes.size()); ++i) |
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292 | _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist; |
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293 | return true; |
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294 | } |
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295 | |
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296 | }; //class ResidualDijkstra |
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297 | |
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298 | public: |
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299 | |
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300 | /// \name Named Template Parameters |
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301 | /// @{ |
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302 | |
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303 | template <typename T> |
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304 | struct SetFlowMapTraits : public Traits { |
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305 | typedef T FlowMap; |
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306 | }; |
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307 | |
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308 | /// \brief \ref named-templ-param "Named parameter" for setting |
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309 | /// \c FlowMap type. |
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310 | /// |
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311 | /// \ref named-templ-param "Named parameter" for setting |
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312 | /// \c FlowMap type. |
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313 | template <typename T> |
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314 | struct SetFlowMap |
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315 | : public Suurballe<GR, LEN, SetFlowMapTraits<T> > { |
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316 | typedef Suurballe<GR, LEN, SetFlowMapTraits<T> > Create; |
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317 | }; |
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318 | |
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319 | template <typename T> |
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320 | struct SetPotentialMapTraits : public Traits { |
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321 | typedef T PotentialMap; |
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322 | }; |
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323 | |
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324 | /// \brief \ref named-templ-param "Named parameter" for setting |
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325 | /// \c PotentialMap type. |
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326 | /// |
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327 | /// \ref named-templ-param "Named parameter" for setting |
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328 | /// \c PotentialMap type. |
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329 | template <typename T> |
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330 | struct SetPotentialMap |
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331 | : public Suurballe<GR, LEN, SetPotentialMapTraits<T> > { |
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332 | typedef Suurballe<GR, LEN, SetPotentialMapTraits<T> > Create; |
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333 | }; |
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334 | |
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335 | template <typename T> |
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336 | struct SetPathTraits : public Traits { |
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337 | typedef T Path; |
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338 | }; |
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339 | |
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340 | /// \brief \ref named-templ-param "Named parameter" for setting |
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341 | /// \c %Path type. |
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342 | /// |
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343 | /// \ref named-templ-param "Named parameter" for setting \c %Path type. |
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344 | /// It must conform to the \ref lemon::concepts::Path "Path" concept |
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345 | /// and it must have an \c addBack() function. |
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346 | template <typename T> |
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347 | struct SetPath |
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348 | : public Suurballe<GR, LEN, SetPathTraits<T> > { |
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349 | typedef Suurballe<GR, LEN, SetPathTraits<T> > Create; |
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350 | }; |
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351 | |
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352 | template <typename H, typename CR> |
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353 | struct SetHeapTraits : public Traits { |
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354 | typedef H Heap; |
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355 | typedef CR HeapCrossRef; |
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356 | }; |
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357 | |
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358 | /// \brief \ref named-templ-param "Named parameter" for setting |
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359 | /// \c Heap and \c HeapCrossRef types. |
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360 | /// |
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361 | /// \ref named-templ-param "Named parameter" for setting \c Heap |
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362 | /// and \c HeapCrossRef types with automatic allocation. |
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363 | /// They will be used for internal Dijkstra computations. |
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364 | /// The heap type must conform to the \ref lemon::concepts::Heap "Heap" |
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365 | /// concept and its priority type must be \c Length. |
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366 | template <typename H, |
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367 | typename CR = typename Digraph::template NodeMap<int> > |
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368 | struct SetHeap |
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369 | : public Suurballe<GR, LEN, SetHeapTraits<H, CR> > { |
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370 | typedef Suurballe<GR, LEN, SetHeapTraits<H, CR> > Create; |
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371 | }; |
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372 | |
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373 | /// @} |
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374 | |
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375 | private: |
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376 | |
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377 | // The digraph the algorithm runs on |
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378 | const Digraph &_graph; |
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379 | // The length map |
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380 | const LengthMap &_length; |
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381 | |
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382 | // Arc map of the current flow |
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383 | FlowMap *_flow; |
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384 | bool _local_flow; |
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385 | // Node map of the current potentials |
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386 | PotentialMap *_potential; |
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387 | bool _local_potential; |
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388 | |
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389 | // The source node |
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390 | Node _s; |
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391 | // The target node |
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392 | Node _t; |
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393 | |
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394 | // Container to store the found paths |
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395 | std::vector<Path> _paths; |
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396 | int _path_num; |
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397 | |
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398 | // The pred arc map |
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399 | PredMap _pred; |
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400 | |
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401 | // Data for full init |
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402 | PotentialMap *_init_dist; |
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403 | PredMap *_init_pred; |
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404 | bool _full_init; |
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405 | |
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406 | public: |
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407 | |
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408 | /// \brief Constructor. |
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409 | /// |
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410 | /// Constructor. |
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411 | /// |
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412 | /// \param graph The digraph the algorithm runs on. |
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413 | /// \param length The length (cost) values of the arcs. |
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414 | Suurballe( const Digraph &graph, |
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415 | const LengthMap &length ) : |
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416 | _graph(graph), _length(length), _flow(0), _local_flow(false), |
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417 | _potential(0), _local_potential(false), _pred(graph), |
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418 | _init_dist(0), _init_pred(0) |
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419 | {} |
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420 | |
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421 | /// Destructor. |
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422 | ~Suurballe() { |
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423 | if (_local_flow) delete _flow; |
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424 | if (_local_potential) delete _potential; |
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425 | delete _init_dist; |
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426 | delete _init_pred; |
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427 | } |
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428 | |
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429 | /// \brief Set the flow map. |
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430 | /// |
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431 | /// This function sets the flow map. |
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432 | /// If it is not used before calling \ref run() or \ref init(), |
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433 | /// an instance will be allocated automatically. The destructor |
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434 | /// deallocates this automatically allocated map, of course. |
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435 | /// |
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436 | /// The found flow contains only 0 and 1 values, since it is the |
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437 | /// union of the found arc-disjoint paths. |
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438 | /// |
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439 | /// \return <tt>(*this)</tt> |
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440 | Suurballe& flowMap(FlowMap &map) { |
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441 | if (_local_flow) { |
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442 | delete _flow; |
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443 | _local_flow = false; |
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444 | } |
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445 | _flow = ↦ |
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446 | return *this; |
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447 | } |
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448 | |
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449 | /// \brief Set the potential map. |
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450 | /// |
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451 | /// This function sets the potential map. |
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452 | /// If it is not used before calling \ref run() or \ref init(), |
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453 | /// an instance will be allocated automatically. The destructor |
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454 | /// deallocates this automatically allocated map, of course. |
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455 | /// |
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456 | /// The node potentials provide the dual solution of the underlying |
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457 | /// \ref min_cost_flow "minimum cost flow problem". |
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458 | /// |
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459 | /// \return <tt>(*this)</tt> |
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460 | Suurballe& potentialMap(PotentialMap &map) { |
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461 | if (_local_potential) { |
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462 | delete _potential; |
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463 | _local_potential = false; |
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464 | } |
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465 | _potential = ↦ |
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466 | return *this; |
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467 | } |
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468 | |
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469 | /// \name Execution Control |
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470 | /// The simplest way to execute the algorithm is to call the run() |
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471 | /// function.\n |
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472 | /// If you need to execute the algorithm many times using the same |
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473 | /// source node, then you may call fullInit() once and start() |
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474 | /// for each target node.\n |
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475 | /// If you only need the flow that is the union of the found |
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476 | /// arc-disjoint paths, then you may call findFlow() instead of |
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477 | /// start(). |
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478 | |
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479 | /// @{ |
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480 | |
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481 | /// \brief Run the algorithm. |
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482 | /// |
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483 | /// This function runs the algorithm. |
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484 | /// |
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485 | /// \param s The source node. |
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486 | /// \param t The target node. |
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487 | /// \param k The number of paths to be found. |
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488 | /// |
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489 | /// \return \c k if there are at least \c k arc-disjoint paths from |
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490 | /// \c s to \c t in the digraph. Otherwise it returns the number of |
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491 | /// arc-disjoint paths found. |
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492 | /// |
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493 | /// \note Apart from the return value, <tt>s.run(s, t, k)</tt> is |
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494 | /// just a shortcut of the following code. |
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495 | /// \code |
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496 | /// s.init(s); |
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497 | /// s.start(t, k); |
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498 | /// \endcode |
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499 | int run(const Node& s, const Node& t, int k = 2) { |
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500 | init(s); |
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501 | start(t, k); |
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502 | return _path_num; |
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503 | } |
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504 | |
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505 | /// \brief Initialize the algorithm. |
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506 | /// |
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507 | /// This function initializes the algorithm with the given source node. |
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508 | /// |
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509 | /// \param s The source node. |
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510 | void init(const Node& s) { |
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511 | _s = s; |
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512 | |
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513 | // Initialize maps |
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514 | if (!_flow) { |
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515 | _flow = new FlowMap(_graph); |
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516 | _local_flow = true; |
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517 | } |
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518 | if (!_potential) { |
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519 | _potential = new PotentialMap(_graph); |
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520 | _local_potential = true; |
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521 | } |
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522 | _full_init = false; |
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523 | } |
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524 | |
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525 | /// \brief Initialize the algorithm and perform Dijkstra. |
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526 | /// |
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527 | /// This function initializes the algorithm and performs a full |
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528 | /// Dijkstra search from the given source node. It makes consecutive |
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529 | /// executions of \ref start() "start(t, k)" faster, since they |
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530 | /// have to perform %Dijkstra only k-1 times. |
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531 | /// |
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532 | /// This initialization is usually worth using instead of \ref init() |
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533 | /// if the algorithm is executed many times using the same source node. |
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534 | /// |
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535 | /// \param s The source node. |
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536 | void fullInit(const Node& s) { |
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537 | // Initialize maps |
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538 | init(s); |
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539 | if (!_init_dist) { |
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540 | _init_dist = new PotentialMap(_graph); |
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541 | } |
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542 | if (!_init_pred) { |
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543 | _init_pred = new PredMap(_graph); |
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544 | } |
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545 | |
---|
546 | // Run a full Dijkstra |
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547 | typename Dijkstra<Digraph, LengthMap> |
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548 | ::template SetStandardHeap<Heap> |
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549 | ::template SetDistMap<PotentialMap> |
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550 | ::template SetPredMap<PredMap> |
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551 | ::Create dijk(_graph, _length); |
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552 | dijk.distMap(*_init_dist).predMap(*_init_pred); |
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553 | dijk.run(s); |
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554 | |
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555 | _full_init = true; |
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556 | } |
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557 | |
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558 | /// \brief Execute the algorithm. |
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559 | /// |
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560 | /// This function executes the algorithm. |
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561 | /// |
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562 | /// \param t The target node. |
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563 | /// \param k The number of paths to be found. |
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564 | /// |
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565 | /// \return \c k if there are at least \c k arc-disjoint paths from |
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566 | /// \c s to \c t in the digraph. Otherwise it returns the number of |
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567 | /// arc-disjoint paths found. |
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568 | /// |
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569 | /// \note Apart from the return value, <tt>s.start(t, k)</tt> is |
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570 | /// just a shortcut of the following code. |
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571 | /// \code |
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572 | /// s.findFlow(t, k); |
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573 | /// s.findPaths(); |
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574 | /// \endcode |
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575 | int start(const Node& t, int k = 2) { |
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576 | findFlow(t, k); |
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577 | findPaths(); |
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578 | return _path_num; |
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579 | } |
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580 | |
---|
581 | /// \brief Execute the algorithm to find an optimal flow. |
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582 | /// |
---|
583 | /// This function executes the successive shortest path algorithm to |
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584 | /// find a minimum cost flow, which is the union of \c k (or less) |
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585 | /// arc-disjoint paths. |
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586 | /// |
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587 | /// \param t The target node. |
---|
588 | /// \param k The number of paths to be found. |
---|
589 | /// |
---|
590 | /// \return \c k if there are at least \c k arc-disjoint paths from |
---|
591 | /// the source node to the given node \c t in the digraph. |
---|
592 | /// Otherwise it returns the number of arc-disjoint paths found. |
---|
593 | /// |
---|
594 | /// \pre \ref init() must be called before using this function. |
---|
595 | int findFlow(const Node& t, int k = 2) { |
---|
596 | _t = t; |
---|
597 | ResidualDijkstra dijkstra(*this); |
---|
598 | |
---|
599 | // Initialization |
---|
600 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
601 | (*_flow)[e] = 0; |
---|
602 | } |
---|
603 | if (_full_init) { |
---|
604 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
605 | (*_potential)[n] = (*_init_dist)[n]; |
---|
606 | } |
---|
607 | Node u = _t; |
---|
608 | Arc e; |
---|
609 | while ((e = (*_init_pred)[u]) != INVALID) { |
---|
610 | (*_flow)[e] = 1; |
---|
611 | u = _graph.source(e); |
---|
612 | } |
---|
613 | _path_num = 1; |
---|
614 | } else { |
---|
615 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
616 | (*_potential)[n] = 0; |
---|
617 | } |
---|
618 | _path_num = 0; |
---|
619 | } |
---|
620 | |
---|
621 | // Find shortest paths |
---|
622 | while (_path_num < k) { |
---|
623 | // Run Dijkstra |
---|
624 | if (!dijkstra.run(_path_num)) break; |
---|
625 | ++_path_num; |
---|
626 | |
---|
627 | // Set the flow along the found shortest path |
---|
628 | Node u = _t; |
---|
629 | Arc e; |
---|
630 | while ((e = _pred[u]) != INVALID) { |
---|
631 | if (u == _graph.target(e)) { |
---|
632 | (*_flow)[e] = 1; |
---|
633 | u = _graph.source(e); |
---|
634 | } else { |
---|
635 | (*_flow)[e] = 0; |
---|
636 | u = _graph.target(e); |
---|
637 | } |
---|
638 | } |
---|
639 | } |
---|
640 | return _path_num; |
---|
641 | } |
---|
642 | |
---|
643 | /// \brief Compute the paths from the flow. |
---|
644 | /// |
---|
645 | /// This function computes arc-disjoint paths from the found minimum |
---|
646 | /// cost flow, which is the union of them. |
---|
647 | /// |
---|
648 | /// \pre \ref init() and \ref findFlow() must be called before using |
---|
649 | /// this function. |
---|
650 | void findPaths() { |
---|
651 | FlowMap res_flow(_graph); |
---|
652 | for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a]; |
---|
653 | |
---|
654 | _paths.clear(); |
---|
655 | _paths.resize(_path_num); |
---|
656 | for (int i = 0; i < _path_num; ++i) { |
---|
657 | Node n = _s; |
---|
658 | while (n != _t) { |
---|
659 | OutArcIt e(_graph, n); |
---|
660 | for ( ; res_flow[e] == 0; ++e) ; |
---|
661 | n = _graph.target(e); |
---|
662 | _paths[i].addBack(e); |
---|
663 | res_flow[e] = 0; |
---|
664 | } |
---|
665 | } |
---|
666 | } |
---|
667 | |
---|
668 | /// @} |
---|
669 | |
---|
670 | /// \name Query Functions |
---|
671 | /// The results of the algorithm can be obtained using these |
---|
672 | /// functions. |
---|
673 | /// \n The algorithm should be executed before using them. |
---|
674 | |
---|
675 | /// @{ |
---|
676 | |
---|
677 | /// \brief Return the total length of the found paths. |
---|
678 | /// |
---|
679 | /// This function returns the total length of the found paths, i.e. |
---|
680 | /// the total cost of the found flow. |
---|
681 | /// The complexity of the function is O(e). |
---|
682 | /// |
---|
683 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
684 | /// this function. |
---|
685 | Length totalLength() const { |
---|
686 | Length c = 0; |
---|
687 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
688 | c += (*_flow)[e] * _length[e]; |
---|
689 | return c; |
---|
690 | } |
---|
691 | |
---|
692 | /// \brief Return the flow value on the given arc. |
---|
693 | /// |
---|
694 | /// This function returns the flow value on the given arc. |
---|
695 | /// It is \c 1 if the arc is involved in one of the found arc-disjoint |
---|
696 | /// paths, otherwise it is \c 0. |
---|
697 | /// |
---|
698 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
699 | /// this function. |
---|
700 | int flow(const Arc& arc) const { |
---|
701 | return (*_flow)[arc]; |
---|
702 | } |
---|
703 | |
---|
704 | /// \brief Return a const reference to an arc map storing the |
---|
705 | /// found flow. |
---|
706 | /// |
---|
707 | /// This function returns a const reference to an arc map storing |
---|
708 | /// the flow that is the union of the found arc-disjoint paths. |
---|
709 | /// |
---|
710 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
711 | /// this function. |
---|
712 | const FlowMap& flowMap() const { |
---|
713 | return *_flow; |
---|
714 | } |
---|
715 | |
---|
716 | /// \brief Return the potential of the given node. |
---|
717 | /// |
---|
718 | /// This function returns the potential of the given node. |
---|
719 | /// The node potentials provide the dual solution of the |
---|
720 | /// underlying \ref min_cost_flow "minimum cost flow problem". |
---|
721 | /// |
---|
722 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
723 | /// this function. |
---|
724 | Length potential(const Node& node) const { |
---|
725 | return (*_potential)[node]; |
---|
726 | } |
---|
727 | |
---|
728 | /// \brief Return a const reference to a node map storing the |
---|
729 | /// found potentials (the dual solution). |
---|
730 | /// |
---|
731 | /// This function returns a const reference to a node map storing |
---|
732 | /// the found potentials that provide the dual solution of the |
---|
733 | /// underlying \ref min_cost_flow "minimum cost flow problem". |
---|
734 | /// |
---|
735 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
736 | /// this function. |
---|
737 | const PotentialMap& potentialMap() const { |
---|
738 | return *_potential; |
---|
739 | } |
---|
740 | |
---|
741 | /// \brief Return the number of the found paths. |
---|
742 | /// |
---|
743 | /// This function returns the number of the found paths. |
---|
744 | /// |
---|
745 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
746 | /// this function. |
---|
747 | int pathNum() const { |
---|
748 | return _path_num; |
---|
749 | } |
---|
750 | |
---|
751 | /// \brief Return a const reference to the specified path. |
---|
752 | /// |
---|
753 | /// This function returns a const reference to the specified path. |
---|
754 | /// |
---|
755 | /// \param i The function returns the <tt>i</tt>-th path. |
---|
756 | /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>. |
---|
757 | /// |
---|
758 | /// \pre \ref run() or \ref findPaths() must be called before using |
---|
759 | /// this function. |
---|
760 | const Path& path(int i) const { |
---|
761 | return _paths[i]; |
---|
762 | } |
---|
763 | |
---|
764 | /// @} |
---|
765 | |
---|
766 | }; //class Suurballe |
---|
767 | |
---|
768 | ///@} |
---|
769 | |
---|
770 | } //namespace lemon |
---|
771 | |
---|
772 | #endif //LEMON_SUURBALLE_H |
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