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) 2003-2010 |
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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_CAPACITY_SCALING_H |
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20 | #define LEMON_CAPACITY_SCALING_H |
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21 | |
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22 | /// \ingroup min_cost_flow_algs |
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23 | /// |
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24 | /// \file |
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25 | /// \brief Capacity Scaling algorithm for finding a minimum cost flow. |
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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/core.h> |
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30 | #include <lemon/bin_heap.h> |
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31 | |
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32 | namespace lemon { |
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33 | |
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34 | /// \brief Default traits class of CapacityScaling algorithm. |
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35 | /// |
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36 | /// Default traits class of CapacityScaling algorithm. |
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37 | /// \tparam GR Digraph type. |
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38 | /// \tparam V The number type used for flow amounts, capacity bounds |
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39 | /// and supply values. By default it is \c int. |
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40 | /// \tparam C The number type used for costs and potentials. |
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41 | /// By default it is the same as \c V. |
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42 | template <typename GR, typename V = int, typename C = V> |
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43 | struct CapacityScalingDefaultTraits |
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44 | { |
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45 | /// The type of the digraph |
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46 | typedef GR Digraph; |
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47 | /// The type of the flow amounts, capacity bounds and supply values |
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48 | typedef V Value; |
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49 | /// The type of the arc costs |
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50 | typedef C Cost; |
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51 | |
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52 | /// \brief The type of the heap used for internal Dijkstra computations. |
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53 | /// |
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54 | /// The type of the heap used for internal Dijkstra computations. |
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55 | /// It must conform to the \ref lemon::concepts::Heap "Heap" concept, |
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56 | /// its priority type must be \c Cost and its cross reference type |
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57 | /// must be \ref RangeMap "RangeMap<int>". |
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58 | typedef BinHeap<Cost, RangeMap<int> > Heap; |
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59 | }; |
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60 | |
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61 | /// \addtogroup min_cost_flow_algs |
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62 | /// @{ |
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63 | |
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64 | /// \brief Implementation of the Capacity Scaling algorithm for |
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65 | /// finding a \ref min_cost_flow "minimum cost flow". |
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66 | /// |
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67 | /// \ref CapacityScaling implements the capacity scaling version |
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68 | /// of the successive shortest path algorithm for finding a |
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69 | /// \ref min_cost_flow "minimum cost flow" \ref amo93networkflows, |
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70 | /// \ref edmondskarp72theoretical. It is an efficient dual |
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71 | /// solution method. |
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72 | /// |
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73 | /// Most of the parameters of the problem (except for the digraph) |
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74 | /// can be given using separate functions, and the algorithm can be |
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75 | /// executed using the \ref run() function. If some parameters are not |
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76 | /// specified, then default values will be used. |
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77 | /// |
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78 | /// \tparam GR The digraph type the algorithm runs on. |
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79 | /// \tparam V The number type used for flow amounts, capacity bounds |
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80 | /// and supply values in the algorithm. By default, it is \c int. |
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81 | /// \tparam C The number type used for costs and potentials in the |
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82 | /// algorithm. By default, it is the same as \c V. |
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83 | /// \tparam TR The traits class that defines various types used by the |
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84 | /// algorithm. By default, it is \ref CapacityScalingDefaultTraits |
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85 | /// "CapacityScalingDefaultTraits<GR, V, C>". |
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86 | /// In most cases, this parameter should not be set directly, |
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87 | /// consider to use the named template parameters instead. |
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88 | /// |
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89 | /// \warning Both \c V and \c C must be signed number types. |
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90 | /// \warning All input data (capacities, supply values, and costs) must |
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91 | /// be integer. |
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92 | /// \warning This algorithm does not support negative costs for |
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93 | /// arcs having infinite upper bound. |
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94 | #ifdef DOXYGEN |
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95 | template <typename GR, typename V, typename C, typename TR> |
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96 | #else |
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97 | template < typename GR, typename V = int, typename C = V, |
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98 | typename TR = CapacityScalingDefaultTraits<GR, V, C> > |
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99 | #endif |
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100 | class CapacityScaling |
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101 | { |
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102 | public: |
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103 | |
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104 | /// The type of the digraph |
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105 | typedef typename TR::Digraph Digraph; |
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106 | /// The type of the flow amounts, capacity bounds and supply values |
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107 | typedef typename TR::Value Value; |
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108 | /// The type of the arc costs |
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109 | typedef typename TR::Cost Cost; |
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110 | |
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111 | /// The type of the heap used for internal Dijkstra computations |
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112 | typedef typename TR::Heap Heap; |
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113 | |
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114 | /// The \ref CapacityScalingDefaultTraits "traits class" of the algorithm |
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115 | typedef TR Traits; |
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116 | |
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117 | public: |
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118 | |
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119 | /// \brief Problem type constants for the \c run() function. |
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120 | /// |
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121 | /// Enum type containing the problem type constants that can be |
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122 | /// returned by the \ref run() function of the algorithm. |
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123 | enum ProblemType { |
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124 | /// The problem has no feasible solution (flow). |
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125 | INFEASIBLE, |
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126 | /// The problem has optimal solution (i.e. it is feasible and |
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127 | /// bounded), and the algorithm has found optimal flow and node |
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128 | /// potentials (primal and dual solutions). |
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129 | OPTIMAL, |
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130 | /// The digraph contains an arc of negative cost and infinite |
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131 | /// upper bound. It means that the objective function is unbounded |
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132 | /// on that arc, however, note that it could actually be bounded |
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133 | /// over the feasible flows, but this algroithm cannot handle |
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134 | /// these cases. |
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135 | UNBOUNDED |
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136 | }; |
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137 | |
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138 | private: |
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139 | |
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140 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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141 | |
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142 | typedef std::vector<int> IntVector; |
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143 | typedef std::vector<Value> ValueVector; |
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144 | typedef std::vector<Cost> CostVector; |
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145 | typedef std::vector<char> BoolVector; |
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146 | // Note: vector<char> is used instead of vector<bool> for efficiency reasons |
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147 | |
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148 | private: |
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149 | |
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150 | // Data related to the underlying digraph |
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151 | const GR &_graph; |
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152 | int _node_num; |
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153 | int _arc_num; |
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154 | int _res_arc_num; |
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155 | int _root; |
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156 | |
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157 | // Parameters of the problem |
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158 | bool _have_lower; |
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159 | Value _sum_supply; |
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160 | |
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161 | // Data structures for storing the digraph |
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162 | IntNodeMap _node_id; |
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163 | IntArcMap _arc_idf; |
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164 | IntArcMap _arc_idb; |
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165 | IntVector _first_out; |
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166 | BoolVector _forward; |
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167 | IntVector _source; |
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168 | IntVector _target; |
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169 | IntVector _reverse; |
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170 | |
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171 | // Node and arc data |
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172 | ValueVector _lower; |
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173 | ValueVector _upper; |
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174 | CostVector _cost; |
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175 | ValueVector _supply; |
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176 | |
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177 | ValueVector _res_cap; |
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178 | CostVector _pi; |
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179 | ValueVector _excess; |
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180 | IntVector _excess_nodes; |
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181 | IntVector _deficit_nodes; |
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182 | |
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183 | Value _delta; |
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184 | int _factor; |
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185 | IntVector _pred; |
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186 | |
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187 | public: |
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188 | |
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189 | /// \brief Constant for infinite upper bounds (capacities). |
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190 | /// |
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191 | /// Constant for infinite upper bounds (capacities). |
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192 | /// It is \c std::numeric_limits<Value>::infinity() if available, |
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193 | /// \c std::numeric_limits<Value>::max() otherwise. |
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194 | const Value INF; |
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195 | |
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196 | private: |
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197 | |
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198 | // Special implementation of the Dijkstra algorithm for finding |
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199 | // shortest paths in the residual network of the digraph with |
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200 | // respect to the reduced arc costs and modifying the node |
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201 | // potentials according to the found distance labels. |
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202 | class ResidualDijkstra |
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203 | { |
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204 | private: |
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205 | |
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206 | int _node_num; |
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207 | bool _geq; |
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208 | const IntVector &_first_out; |
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209 | const IntVector &_target; |
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210 | const CostVector &_cost; |
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211 | const ValueVector &_res_cap; |
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212 | const ValueVector &_excess; |
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213 | CostVector &_pi; |
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214 | IntVector &_pred; |
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215 | |
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216 | IntVector _proc_nodes; |
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217 | CostVector _dist; |
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218 | |
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219 | public: |
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220 | |
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221 | ResidualDijkstra(CapacityScaling& cs) : |
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222 | _node_num(cs._node_num), _geq(cs._sum_supply < 0), |
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223 | _first_out(cs._first_out), _target(cs._target), _cost(cs._cost), |
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224 | _res_cap(cs._res_cap), _excess(cs._excess), _pi(cs._pi), |
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225 | _pred(cs._pred), _dist(cs._node_num) |
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226 | {} |
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227 | |
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228 | int run(int s, Value delta = 1) { |
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229 | RangeMap<int> heap_cross_ref(_node_num, 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] = -1; |
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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() && _excess[heap.top()] > -delta) { |
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237 | int u = heap.top(), v; |
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238 | Cost 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 residual arcs |
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244 | int last_out = _geq ? _first_out[u+1] : _first_out[u+1] - 1; |
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245 | for (int a = _first_out[u]; a != last_out; ++a) { |
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246 | if (_res_cap[a] < delta) continue; |
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247 | v = _target[a]; |
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248 | switch (heap.state(v)) { |
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249 | case Heap::PRE_HEAP: |
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250 | heap.push(v, d + _cost[a] - _pi[v]); |
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251 | _pred[v] = a; |
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252 | break; |
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253 | case Heap::IN_HEAP: |
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254 | dn = d + _cost[a] - _pi[v]; |
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255 | if (dn < heap[v]) { |
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256 | heap.decrease(v, dn); |
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257 | _pred[v] = a; |
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258 | } |
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259 | break; |
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260 | case Heap::POST_HEAP: |
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261 | break; |
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262 | } |
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263 | } |
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264 | } |
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265 | if (heap.empty()) return -1; |
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266 | |
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267 | // Update potentials of processed nodes |
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268 | int t = heap.top(); |
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269 | Cost dt = heap.prio(); |
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270 | for (int i = 0; i < int(_proc_nodes.size()); ++i) { |
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271 | _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - dt; |
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272 | } |
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273 | |
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274 | return t; |
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275 | } |
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276 | |
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277 | }; //class ResidualDijkstra |
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278 | |
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279 | public: |
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280 | |
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281 | /// \name Named Template Parameters |
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282 | /// @{ |
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283 | |
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284 | template <typename T> |
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285 | struct SetHeapTraits : public Traits { |
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286 | typedef T Heap; |
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287 | }; |
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288 | |
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289 | /// \brief \ref named-templ-param "Named parameter" for setting |
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290 | /// \c Heap type. |
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291 | /// |
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292 | /// \ref named-templ-param "Named parameter" for setting \c Heap |
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293 | /// type, which is used for internal Dijkstra computations. |
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294 | /// It must conform to the \ref lemon::concepts::Heap "Heap" concept, |
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295 | /// its priority type must be \c Cost and its cross reference type |
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296 | /// must be \ref RangeMap "RangeMap<int>". |
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297 | template <typename T> |
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298 | struct SetHeap |
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299 | : public CapacityScaling<GR, V, C, SetHeapTraits<T> > { |
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300 | typedef CapacityScaling<GR, V, C, SetHeapTraits<T> > Create; |
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301 | }; |
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302 | |
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303 | /// @} |
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304 | |
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305 | protected: |
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306 | |
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307 | CapacityScaling() {} |
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308 | |
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309 | public: |
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310 | |
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311 | /// \brief Constructor. |
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312 | /// |
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313 | /// The constructor of the class. |
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314 | /// |
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315 | /// \param graph The digraph the algorithm runs on. |
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316 | CapacityScaling(const GR& graph) : |
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317 | _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph), |
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318 | INF(std::numeric_limits<Value>::has_infinity ? |
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319 | std::numeric_limits<Value>::infinity() : |
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320 | std::numeric_limits<Value>::max()) |
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321 | { |
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322 | // Check the number types |
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323 | LEMON_ASSERT(std::numeric_limits<Value>::is_signed, |
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324 | "The flow type of CapacityScaling must be signed"); |
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325 | LEMON_ASSERT(std::numeric_limits<Cost>::is_signed, |
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326 | "The cost type of CapacityScaling must be signed"); |
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327 | |
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328 | // Reset data structures |
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329 | reset(); |
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330 | } |
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331 | |
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332 | /// \name Parameters |
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333 | /// The parameters of the algorithm can be specified using these |
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334 | /// functions. |
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335 | |
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336 | /// @{ |
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337 | |
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338 | /// \brief Set the lower bounds on the arcs. |
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339 | /// |
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340 | /// This function sets the lower bounds on the arcs. |
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341 | /// If it is not used before calling \ref run(), the lower bounds |
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342 | /// will be set to zero on all arcs. |
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343 | /// |
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344 | /// \param map An arc map storing the lower bounds. |
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345 | /// Its \c Value type must be convertible to the \c Value type |
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346 | /// of the algorithm. |
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347 | /// |
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348 | /// \return <tt>(*this)</tt> |
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349 | template <typename LowerMap> |
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350 | CapacityScaling& lowerMap(const LowerMap& map) { |
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351 | _have_lower = true; |
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352 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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353 | _lower[_arc_idf[a]] = map[a]; |
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354 | _lower[_arc_idb[a]] = map[a]; |
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355 | } |
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356 | return *this; |
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357 | } |
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358 | |
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359 | /// \brief Set the upper bounds (capacities) on the arcs. |
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360 | /// |
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361 | /// This function sets the upper bounds (capacities) on the arcs. |
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362 | /// If it is not used before calling \ref run(), the upper bounds |
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363 | /// will be set to \ref INF on all arcs (i.e. the flow value will be |
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364 | /// unbounded from above). |
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365 | /// |
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366 | /// \param map An arc map storing the upper bounds. |
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367 | /// Its \c Value type must be convertible to the \c Value type |
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368 | /// of the algorithm. |
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369 | /// |
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370 | /// \return <tt>(*this)</tt> |
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371 | template<typename UpperMap> |
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372 | CapacityScaling& upperMap(const UpperMap& map) { |
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373 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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374 | _upper[_arc_idf[a]] = map[a]; |
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375 | } |
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376 | return *this; |
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377 | } |
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378 | |
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379 | /// \brief Set the costs of the arcs. |
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380 | /// |
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381 | /// This function sets the costs of the arcs. |
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382 | /// If it is not used before calling \ref run(), the costs |
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383 | /// will be set to \c 1 on all arcs. |
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384 | /// |
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385 | /// \param map An arc map storing the costs. |
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386 | /// Its \c Value type must be convertible to the \c Cost type |
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387 | /// of the algorithm. |
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388 | /// |
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389 | /// \return <tt>(*this)</tt> |
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390 | template<typename CostMap> |
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391 | CapacityScaling& costMap(const CostMap& map) { |
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392 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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393 | _cost[_arc_idf[a]] = map[a]; |
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394 | _cost[_arc_idb[a]] = -map[a]; |
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395 | } |
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396 | return *this; |
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397 | } |
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398 | |
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399 | /// \brief Set the supply values of the nodes. |
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400 | /// |
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401 | /// This function sets the supply values of the nodes. |
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402 | /// If neither this function nor \ref stSupply() is used before |
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403 | /// calling \ref run(), the supply of each node will be set to zero. |
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404 | /// |
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405 | /// \param map A node map storing the supply values. |
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406 | /// Its \c Value type must be convertible to the \c Value type |
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407 | /// of the algorithm. |
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408 | /// |
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409 | /// \return <tt>(*this)</tt> |
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410 | template<typename SupplyMap> |
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411 | CapacityScaling& supplyMap(const SupplyMap& map) { |
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412 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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413 | _supply[_node_id[n]] = map[n]; |
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414 | } |
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415 | return *this; |
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416 | } |
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417 | |
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418 | /// \brief Set single source and target nodes and a supply value. |
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419 | /// |
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420 | /// This function sets a single source node and a single target node |
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421 | /// and the required flow value. |
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422 | /// If neither this function nor \ref supplyMap() is used before |
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423 | /// calling \ref run(), the supply of each node will be set to zero. |
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424 | /// |
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425 | /// Using this function has the same effect as using \ref supplyMap() |
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426 | /// with a map in which \c k is assigned to \c s, \c -k is |
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427 | /// assigned to \c t and all other nodes have zero supply value. |
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428 | /// |
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429 | /// \param s The source node. |
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430 | /// \param t The target node. |
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431 | /// \param k The required amount of flow from node \c s to node \c t |
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432 | /// (i.e. the supply of \c s and the demand of \c t). |
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433 | /// |
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434 | /// \return <tt>(*this)</tt> |
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435 | CapacityScaling& stSupply(const Node& s, const Node& t, Value k) { |
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436 | for (int i = 0; i != _node_num; ++i) { |
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437 | _supply[i] = 0; |
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438 | } |
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439 | _supply[_node_id[s]] = k; |
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440 | _supply[_node_id[t]] = -k; |
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441 | return *this; |
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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 Execution control |
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447 | /// The algorithm can be executed using \ref run(). |
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448 | |
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449 | /// @{ |
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450 | |
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451 | /// \brief Run the algorithm. |
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452 | /// |
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453 | /// This function runs the algorithm. |
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454 | /// The paramters can be specified using functions \ref lowerMap(), |
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455 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). |
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456 | /// For example, |
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457 | /// \code |
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458 | /// CapacityScaling<ListDigraph> cs(graph); |
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459 | /// cs.lowerMap(lower).upperMap(upper).costMap(cost) |
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460 | /// .supplyMap(sup).run(); |
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461 | /// \endcode |
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462 | /// |
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463 | /// This function can be called more than once. All the given parameters |
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464 | /// are kept for the next call, unless \ref resetParams() or \ref reset() |
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465 | /// is used, thus only the modified parameters have to be set again. |
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466 | /// If the underlying digraph was also modified after the construction |
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467 | /// of the class (or the last \ref reset() call), then the \ref reset() |
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468 | /// function must be called. |
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469 | /// |
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470 | /// \param factor The capacity scaling factor. It must be larger than |
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471 | /// one to use scaling. If it is less or equal to one, then scaling |
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472 | /// will be disabled. |
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473 | /// |
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474 | /// \return \c INFEASIBLE if no feasible flow exists, |
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475 | /// \n \c OPTIMAL if the problem has optimal solution |
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476 | /// (i.e. it is feasible and bounded), and the algorithm has found |
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477 | /// optimal flow and node potentials (primal and dual solutions), |
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478 | /// \n \c UNBOUNDED if the digraph contains an arc of negative cost |
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479 | /// and infinite upper bound. It means that the objective function |
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480 | /// is unbounded on that arc, however, note that it could actually be |
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481 | /// bounded over the feasible flows, but this algroithm cannot handle |
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482 | /// these cases. |
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483 | /// |
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484 | /// \see ProblemType |
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485 | /// \see resetParams(), reset() |
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486 | ProblemType run(int factor = 4) { |
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487 | _factor = factor; |
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488 | ProblemType pt = init(); |
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489 | if (pt != OPTIMAL) return pt; |
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490 | return start(); |
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491 | } |
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492 | |
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493 | /// \brief Reset all the parameters that have been given before. |
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494 | /// |
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495 | /// This function resets all the paramaters that have been given |
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496 | /// before using functions \ref lowerMap(), \ref upperMap(), |
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497 | /// \ref costMap(), \ref supplyMap(), \ref stSupply(). |
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498 | /// |
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499 | /// It is useful for multiple \ref run() calls. Basically, all the given |
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500 | /// parameters are kept for the next \ref run() call, unless |
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501 | /// \ref resetParams() or \ref reset() is used. |
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502 | /// If the underlying digraph was also modified after the construction |
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503 | /// of the class or the last \ref reset() call, then the \ref reset() |
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504 | /// function must be used, otherwise \ref resetParams() is sufficient. |
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505 | /// |
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506 | /// For example, |
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507 | /// \code |
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508 | /// CapacityScaling<ListDigraph> cs(graph); |
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509 | /// |
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510 | /// // First run |
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511 | /// cs.lowerMap(lower).upperMap(upper).costMap(cost) |
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512 | /// .supplyMap(sup).run(); |
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513 | /// |
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514 | /// // Run again with modified cost map (resetParams() is not called, |
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515 | /// // so only the cost map have to be set again) |
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516 | /// cost[e] += 100; |
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517 | /// cs.costMap(cost).run(); |
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518 | /// |
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519 | /// // Run again from scratch using resetParams() |
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520 | /// // (the lower bounds will be set to zero on all arcs) |
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521 | /// cs.resetParams(); |
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522 | /// cs.upperMap(capacity).costMap(cost) |
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523 | /// .supplyMap(sup).run(); |
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524 | /// \endcode |
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525 | /// |
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526 | /// \return <tt>(*this)</tt> |
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527 | /// |
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528 | /// \see reset(), run() |
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529 | CapacityScaling& resetParams() { |
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530 | for (int i = 0; i != _node_num; ++i) { |
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531 | _supply[i] = 0; |
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532 | } |
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533 | for (int j = 0; j != _res_arc_num; ++j) { |
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534 | _lower[j] = 0; |
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535 | _upper[j] = INF; |
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536 | _cost[j] = _forward[j] ? 1 : -1; |
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537 | } |
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538 | _have_lower = false; |
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539 | return *this; |
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540 | } |
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541 | |
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542 | /// \brief Reset the internal data structures and all the parameters |
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543 | /// that have been given before. |
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544 | /// |
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545 | /// This function resets the internal data structures and all the |
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546 | /// paramaters that have been given before using functions \ref lowerMap(), |
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547 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). |
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548 | /// |
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549 | /// It is useful for multiple \ref run() calls. Basically, all the given |
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550 | /// parameters are kept for the next \ref run() call, unless |
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551 | /// \ref resetParams() or \ref reset() is used. |
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552 | /// If the underlying digraph was also modified after the construction |
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553 | /// of the class or the last \ref reset() call, then the \ref reset() |
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554 | /// function must be used, otherwise \ref resetParams() is sufficient. |
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555 | /// |
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556 | /// See \ref resetParams() for examples. |
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557 | /// |
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558 | /// \return <tt>(*this)</tt> |
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559 | /// |
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560 | /// \see resetParams(), run() |
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561 | CapacityScaling& reset() { |
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562 | // Resize vectors |
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563 | _node_num = countNodes(_graph); |
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564 | _arc_num = countArcs(_graph); |
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565 | _res_arc_num = 2 * (_arc_num + _node_num); |
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566 | _root = _node_num; |
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567 | ++_node_num; |
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568 | |
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569 | _first_out.resize(_node_num + 1); |
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570 | _forward.resize(_res_arc_num); |
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571 | _source.resize(_res_arc_num); |
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572 | _target.resize(_res_arc_num); |
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573 | _reverse.resize(_res_arc_num); |
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574 | |
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575 | _lower.resize(_res_arc_num); |
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576 | _upper.resize(_res_arc_num); |
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577 | _cost.resize(_res_arc_num); |
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578 | _supply.resize(_node_num); |
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579 | |
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580 | _res_cap.resize(_res_arc_num); |
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581 | _pi.resize(_node_num); |
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582 | _excess.resize(_node_num); |
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583 | _pred.resize(_node_num); |
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584 | |
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585 | // Copy the graph |
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586 | int i = 0, j = 0, k = 2 * _arc_num + _node_num - 1; |
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587 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
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588 | _node_id[n] = i; |
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589 | } |
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590 | i = 0; |
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591 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
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592 | _first_out[i] = j; |
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593 | for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) { |
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594 | _arc_idf[a] = j; |
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595 | _forward[j] = true; |
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596 | _source[j] = i; |
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597 | _target[j] = _node_id[_graph.runningNode(a)]; |
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598 | } |
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599 | for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) { |
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600 | _arc_idb[a] = j; |
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601 | _forward[j] = false; |
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602 | _source[j] = i; |
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603 | _target[j] = _node_id[_graph.runningNode(a)]; |
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604 | } |
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605 | _forward[j] = false; |
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606 | _source[j] = i; |
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607 | _target[j] = _root; |
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608 | _reverse[j] = k; |
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609 | _forward[k] = true; |
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610 | _source[k] = _root; |
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611 | _target[k] = i; |
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612 | _reverse[k] = j; |
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613 | ++j; ++k; |
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614 | } |
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615 | _first_out[i] = j; |
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616 | _first_out[_node_num] = k; |
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617 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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618 | int fi = _arc_idf[a]; |
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619 | int bi = _arc_idb[a]; |
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620 | _reverse[fi] = bi; |
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621 | _reverse[bi] = fi; |
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622 | } |
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623 | |
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624 | // Reset parameters |
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625 | resetParams(); |
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626 | return *this; |
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627 | } |
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628 | |
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629 | /// @} |
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630 | |
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631 | /// \name Query Functions |
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632 | /// The results of the algorithm can be obtained using these |
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633 | /// functions.\n |
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634 | /// The \ref run() function must be called before using them. |
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635 | |
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636 | /// @{ |
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637 | |
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638 | /// \brief Return the total cost of the found flow. |
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639 | /// |
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640 | /// This function returns the total cost of the found flow. |
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641 | /// Its complexity is O(e). |
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642 | /// |
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643 | /// \note The return type of the function can be specified as a |
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644 | /// template parameter. For example, |
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645 | /// \code |
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646 | /// cs.totalCost<double>(); |
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647 | /// \endcode |
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648 | /// It is useful if the total cost cannot be stored in the \c Cost |
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649 | /// type of the algorithm, which is the default return type of the |
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650 | /// function. |
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651 | /// |
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652 | /// \pre \ref run() must be called before using this function. |
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653 | template <typename Number> |
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654 | Number totalCost() const { |
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655 | Number c = 0; |
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656 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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657 | int i = _arc_idb[a]; |
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658 | c += static_cast<Number>(_res_cap[i]) * |
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659 | (-static_cast<Number>(_cost[i])); |
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660 | } |
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661 | return c; |
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662 | } |
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663 | |
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664 | #ifndef DOXYGEN |
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665 | Cost totalCost() const { |
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666 | return totalCost<Cost>(); |
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667 | } |
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668 | #endif |
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669 | |
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670 | /// \brief Return the flow on the given arc. |
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671 | /// |
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672 | /// This function returns the flow on the given arc. |
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673 | /// |
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674 | /// \pre \ref run() must be called before using this function. |
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675 | Value flow(const Arc& a) const { |
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676 | return _res_cap[_arc_idb[a]]; |
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677 | } |
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678 | |
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679 | /// \brief Return the flow map (the primal solution). |
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680 | /// |
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681 | /// This function copies the flow value on each arc into the given |
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682 | /// map. The \c Value type of the algorithm must be convertible to |
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683 | /// the \c Value type of the map. |
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684 | /// |
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685 | /// \pre \ref run() must be called before using this function. |
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686 | template <typename FlowMap> |
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687 | void flowMap(FlowMap &map) const { |
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688 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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689 | map.set(a, _res_cap[_arc_idb[a]]); |
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690 | } |
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691 | } |
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692 | |
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693 | /// \brief Return the potential (dual value) of the given node. |
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694 | /// |
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695 | /// This function returns the potential (dual value) of the |
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696 | /// given node. |
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697 | /// |
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698 | /// \pre \ref run() must be called before using this function. |
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699 | Cost potential(const Node& n) const { |
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700 | return _pi[_node_id[n]]; |
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701 | } |
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702 | |
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703 | /// \brief Return the potential map (the dual solution). |
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704 | /// |
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705 | /// This function copies the potential (dual value) of each node |
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706 | /// into the given map. |
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707 | /// The \c Cost type of the algorithm must be convertible to the |
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708 | /// \c Value type of the map. |
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709 | /// |
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710 | /// \pre \ref run() must be called before using this function. |
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711 | template <typename PotentialMap> |
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712 | void potentialMap(PotentialMap &map) const { |
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713 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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714 | map.set(n, _pi[_node_id[n]]); |
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715 | } |
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716 | } |
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717 | |
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718 | /// @} |
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719 | |
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720 | private: |
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721 | |
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722 | // Initialize the algorithm |
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723 | ProblemType init() { |
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724 | if (_node_num <= 1) return INFEASIBLE; |
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725 | |
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726 | // Check the sum of supply values |
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727 | _sum_supply = 0; |
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728 | for (int i = 0; i != _root; ++i) { |
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729 | _sum_supply += _supply[i]; |
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730 | } |
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731 | if (_sum_supply > 0) return INFEASIBLE; |
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732 | |
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733 | // Initialize vectors |
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734 | for (int i = 0; i != _root; ++i) { |
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735 | _pi[i] = 0; |
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736 | _excess[i] = _supply[i]; |
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737 | } |
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738 | |
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739 | // Remove non-zero lower bounds |
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740 | const Value MAX = std::numeric_limits<Value>::max(); |
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741 | int last_out; |
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742 | if (_have_lower) { |
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743 | for (int i = 0; i != _root; ++i) { |
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744 | last_out = _first_out[i+1]; |
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745 | for (int j = _first_out[i]; j != last_out; ++j) { |
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746 | if (_forward[j]) { |
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747 | Value c = _lower[j]; |
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748 | if (c >= 0) { |
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749 | _res_cap[j] = _upper[j] < MAX ? _upper[j] - c : INF; |
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750 | } else { |
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751 | _res_cap[j] = _upper[j] < MAX + c ? _upper[j] - c : INF; |
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752 | } |
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753 | _excess[i] -= c; |
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754 | _excess[_target[j]] += c; |
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755 | } else { |
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756 | _res_cap[j] = 0; |
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757 | } |
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758 | } |
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759 | } |
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760 | } else { |
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761 | for (int j = 0; j != _res_arc_num; ++j) { |
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762 | _res_cap[j] = _forward[j] ? _upper[j] : 0; |
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763 | } |
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764 | } |
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765 | |
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766 | // Handle negative costs |
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767 | for (int i = 0; i != _root; ++i) { |
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768 | last_out = _first_out[i+1] - 1; |
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769 | for (int j = _first_out[i]; j != last_out; ++j) { |
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770 | Value rc = _res_cap[j]; |
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771 | if (_cost[j] < 0 && rc > 0) { |
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772 | if (rc >= MAX) return UNBOUNDED; |
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773 | _excess[i] -= rc; |
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774 | _excess[_target[j]] += rc; |
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775 | _res_cap[j] = 0; |
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776 | _res_cap[_reverse[j]] += rc; |
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777 | } |
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778 | } |
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779 | } |
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780 | |
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781 | // Handle GEQ supply type |
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782 | if (_sum_supply < 0) { |
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783 | _pi[_root] = 0; |
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784 | _excess[_root] = -_sum_supply; |
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785 | for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
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786 | int ra = _reverse[a]; |
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787 | _res_cap[a] = -_sum_supply + 1; |
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788 | _res_cap[ra] = 0; |
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789 | _cost[a] = 0; |
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790 | _cost[ra] = 0; |
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791 | } |
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792 | } else { |
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793 | _pi[_root] = 0; |
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794 | _excess[_root] = 0; |
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795 | for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
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796 | int ra = _reverse[a]; |
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797 | _res_cap[a] = 1; |
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798 | _res_cap[ra] = 0; |
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799 | _cost[a] = 0; |
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800 | _cost[ra] = 0; |
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801 | } |
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802 | } |
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803 | |
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804 | // Initialize delta value |
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805 | if (_factor > 1) { |
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806 | // With scaling |
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807 | Value max_sup = 0, max_dem = 0, max_cap = 0; |
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808 | for (int i = 0; i != _root; ++i) { |
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809 | Value ex = _excess[i]; |
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810 | if ( ex > max_sup) max_sup = ex; |
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811 | if (-ex > max_dem) max_dem = -ex; |
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812 | int last_out = _first_out[i+1] - 1; |
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813 | for (int j = _first_out[i]; j != last_out; ++j) { |
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814 | if (_res_cap[j] > max_cap) max_cap = _res_cap[j]; |
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815 | } |
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816 | } |
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817 | max_sup = std::min(std::min(max_sup, max_dem), max_cap); |
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818 | for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) ; |
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819 | } else { |
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820 | // Without scaling |
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821 | _delta = 1; |
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822 | } |
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823 | |
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824 | return OPTIMAL; |
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825 | } |
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826 | |
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827 | ProblemType start() { |
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828 | // Execute the algorithm |
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829 | ProblemType pt; |
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830 | if (_delta > 1) |
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831 | pt = startWithScaling(); |
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832 | else |
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833 | pt = startWithoutScaling(); |
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834 | |
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835 | // Handle non-zero lower bounds |
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836 | if (_have_lower) { |
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837 | int limit = _first_out[_root]; |
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838 | for (int j = 0; j != limit; ++j) { |
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839 | if (!_forward[j]) _res_cap[j] += _lower[j]; |
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840 | } |
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841 | } |
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842 | |
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843 | // Shift potentials if necessary |
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844 | Cost pr = _pi[_root]; |
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845 | if (_sum_supply < 0 || pr > 0) { |
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846 | for (int i = 0; i != _node_num; ++i) { |
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847 | _pi[i] -= pr; |
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848 | } |
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849 | } |
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850 | |
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851 | return pt; |
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852 | } |
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853 | |
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854 | // Execute the capacity scaling algorithm |
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855 | ProblemType startWithScaling() { |
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856 | // Perform capacity scaling phases |
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857 | int s, t; |
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858 | ResidualDijkstra _dijkstra(*this); |
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859 | while (true) { |
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860 | // Saturate all arcs not satisfying the optimality condition |
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861 | int last_out; |
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862 | for (int u = 0; u != _node_num; ++u) { |
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863 | last_out = _sum_supply < 0 ? |
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864 | _first_out[u+1] : _first_out[u+1] - 1; |
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865 | for (int a = _first_out[u]; a != last_out; ++a) { |
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866 | int v = _target[a]; |
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867 | Cost c = _cost[a] + _pi[u] - _pi[v]; |
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868 | Value rc = _res_cap[a]; |
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869 | if (c < 0 && rc >= _delta) { |
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870 | _excess[u] -= rc; |
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871 | _excess[v] += rc; |
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872 | _res_cap[a] = 0; |
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873 | _res_cap[_reverse[a]] += rc; |
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874 | } |
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875 | } |
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876 | } |
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877 | |
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878 | // Find excess nodes and deficit nodes |
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879 | _excess_nodes.clear(); |
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880 | _deficit_nodes.clear(); |
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881 | for (int u = 0; u != _node_num; ++u) { |
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882 | Value ex = _excess[u]; |
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883 | if (ex >= _delta) _excess_nodes.push_back(u); |
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884 | if (ex <= -_delta) _deficit_nodes.push_back(u); |
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885 | } |
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886 | int next_node = 0, next_def_node = 0; |
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887 | |
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888 | // Find augmenting shortest paths |
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889 | while (next_node < int(_excess_nodes.size())) { |
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890 | // Check deficit nodes |
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891 | if (_delta > 1) { |
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892 | bool delta_deficit = false; |
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893 | for ( ; next_def_node < int(_deficit_nodes.size()); |
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894 | ++next_def_node ) { |
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895 | if (_excess[_deficit_nodes[next_def_node]] <= -_delta) { |
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896 | delta_deficit = true; |
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897 | break; |
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898 | } |
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899 | } |
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900 | if (!delta_deficit) break; |
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901 | } |
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902 | |
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903 | // Run Dijkstra in the residual network |
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904 | s = _excess_nodes[next_node]; |
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905 | if ((t = _dijkstra.run(s, _delta)) == -1) { |
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906 | if (_delta > 1) { |
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907 | ++next_node; |
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908 | continue; |
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909 | } |
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910 | return INFEASIBLE; |
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911 | } |
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912 | |
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913 | // Augment along a shortest path from s to t |
---|
914 | Value d = std::min(_excess[s], -_excess[t]); |
---|
915 | int u = t; |
---|
916 | int a; |
---|
917 | if (d > _delta) { |
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918 | while ((a = _pred[u]) != -1) { |
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919 | if (_res_cap[a] < d) d = _res_cap[a]; |
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920 | u = _source[a]; |
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921 | } |
---|
922 | } |
---|
923 | u = t; |
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924 | while ((a = _pred[u]) != -1) { |
---|
925 | _res_cap[a] -= d; |
---|
926 | _res_cap[_reverse[a]] += d; |
---|
927 | u = _source[a]; |
---|
928 | } |
---|
929 | _excess[s] -= d; |
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930 | _excess[t] += d; |
---|
931 | |
---|
932 | if (_excess[s] < _delta) ++next_node; |
---|
933 | } |
---|
934 | |
---|
935 | if (_delta == 1) break; |
---|
936 | _delta = _delta <= _factor ? 1 : _delta / _factor; |
---|
937 | } |
---|
938 | |
---|
939 | return OPTIMAL; |
---|
940 | } |
---|
941 | |
---|
942 | // Execute the successive shortest path algorithm |
---|
943 | ProblemType startWithoutScaling() { |
---|
944 | // Find excess nodes |
---|
945 | _excess_nodes.clear(); |
---|
946 | for (int i = 0; i != _node_num; ++i) { |
---|
947 | if (_excess[i] > 0) _excess_nodes.push_back(i); |
---|
948 | } |
---|
949 | if (_excess_nodes.size() == 0) return OPTIMAL; |
---|
950 | int next_node = 0; |
---|
951 | |
---|
952 | // Find shortest paths |
---|
953 | int s, t; |
---|
954 | ResidualDijkstra _dijkstra(*this); |
---|
955 | while ( _excess[_excess_nodes[next_node]] > 0 || |
---|
956 | ++next_node < int(_excess_nodes.size()) ) |
---|
957 | { |
---|
958 | // Run Dijkstra in the residual network |
---|
959 | s = _excess_nodes[next_node]; |
---|
960 | if ((t = _dijkstra.run(s)) == -1) return INFEASIBLE; |
---|
961 | |
---|
962 | // Augment along a shortest path from s to t |
---|
963 | Value d = std::min(_excess[s], -_excess[t]); |
---|
964 | int u = t; |
---|
965 | int a; |
---|
966 | if (d > 1) { |
---|
967 | while ((a = _pred[u]) != -1) { |
---|
968 | if (_res_cap[a] < d) d = _res_cap[a]; |
---|
969 | u = _source[a]; |
---|
970 | } |
---|
971 | } |
---|
972 | u = t; |
---|
973 | while ((a = _pred[u]) != -1) { |
---|
974 | _res_cap[a] -= d; |
---|
975 | _res_cap[_reverse[a]] += d; |
---|
976 | u = _source[a]; |
---|
977 | } |
---|
978 | _excess[s] -= d; |
---|
979 | _excess[t] += d; |
---|
980 | } |
---|
981 | |
---|
982 | return OPTIMAL; |
---|
983 | } |
---|
984 | |
---|
985 | }; //class CapacityScaling |
---|
986 | |
---|
987 | ///@} |
---|
988 | |
---|
989 | } //namespace lemon |
---|
990 | |
---|
991 | #endif //LEMON_CAPACITY_SCALING_H |
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