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) 2003-2011 |
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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 | #include <iostream> |
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20 | #include <fstream> |
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21 | #include <limits> |
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22 | |
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23 | #include <lemon/list_graph.h> |
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24 | #include <lemon/lgf_reader.h> |
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25 | |
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26 | #include <lemon/network_simplex.h> |
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27 | |
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28 | #include <lemon/concepts/digraph.h> |
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29 | #include <lemon/concept_check.h> |
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30 | |
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31 | #include "test_tools.h" |
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32 | |
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33 | using namespace lemon; |
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34 | |
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35 | char test_lgf[] = |
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36 | "@nodes\n" |
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37 | "label sup1 sup2 sup3 sup4 sup5 sup6\n" |
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38 | " 1 20 27 0 30 20 30\n" |
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39 | " 2 -4 0 0 0 -8 -3\n" |
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40 | " 3 0 0 0 0 0 0\n" |
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41 | " 4 0 0 0 0 0 0\n" |
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42 | " 5 9 0 0 0 6 11\n" |
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43 | " 6 -6 0 0 0 -5 -6\n" |
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44 | " 7 0 0 0 0 0 0\n" |
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45 | " 8 0 0 0 0 0 3\n" |
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46 | " 9 3 0 0 0 0 0\n" |
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47 | " 10 -2 0 0 0 -7 -2\n" |
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48 | " 11 0 0 0 0 -10 0\n" |
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49 | " 12 -20 -27 0 -30 -30 -20\n" |
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50 | "\n" |
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51 | "@arcs\n" |
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52 | " cost cap low1 low2 low3\n" |
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53 | " 1 2 70 11 0 8 8\n" |
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54 | " 1 3 150 3 0 1 0\n" |
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55 | " 1 4 80 15 0 2 2\n" |
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56 | " 2 8 80 12 0 0 0\n" |
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57 | " 3 5 140 5 0 3 1\n" |
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58 | " 4 6 60 10 0 1 0\n" |
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59 | " 4 7 80 2 0 0 0\n" |
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60 | " 4 8 110 3 0 0 0\n" |
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61 | " 5 7 60 14 0 0 0\n" |
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62 | " 5 11 120 12 0 0 0\n" |
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63 | " 6 3 0 3 0 0 0\n" |
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64 | " 6 9 140 4 0 0 0\n" |
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65 | " 6 10 90 8 0 0 0\n" |
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66 | " 7 1 30 5 0 0 -5\n" |
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67 | " 8 12 60 16 0 4 3\n" |
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68 | " 9 12 50 6 0 0 0\n" |
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69 | "10 12 70 13 0 5 2\n" |
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70 | "10 2 100 7 0 0 0\n" |
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71 | "10 7 60 10 0 0 -3\n" |
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72 | "11 10 20 14 0 6 -20\n" |
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73 | "12 11 30 10 0 0 -10\n" |
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74 | "\n" |
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75 | "@attributes\n" |
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76 | "source 1\n" |
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77 | "target 12\n"; |
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78 | |
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79 | |
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80 | enum SupplyType { |
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81 | EQ, |
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82 | GEQ, |
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83 | LEQ |
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84 | }; |
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85 | |
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86 | // Check the interface of an MCF algorithm |
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87 | template <typename GR, typename Value, typename Cost> |
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88 | class McfClassConcept |
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89 | { |
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90 | public: |
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91 | |
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92 | template <typename MCF> |
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93 | struct Constraints { |
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94 | void constraints() { |
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95 | checkConcept<concepts::Digraph, GR>(); |
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96 | |
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97 | const Constraints& me = *this; |
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98 | |
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99 | MCF mcf(me.g); |
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100 | const MCF& const_mcf = mcf; |
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101 | |
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102 | b = mcf.reset() |
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103 | .lowerMap(me.lower) |
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104 | .upperMap(me.upper) |
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105 | .costMap(me.cost) |
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106 | .supplyMap(me.sup) |
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107 | .stSupply(me.n, me.n, me.k) |
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108 | .run(); |
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109 | |
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110 | c = const_mcf.totalCost(); |
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111 | x = const_mcf.template totalCost<double>(); |
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112 | v = const_mcf.flow(me.a); |
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113 | c = const_mcf.potential(me.n); |
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114 | const_mcf.flowMap(fm); |
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115 | const_mcf.potentialMap(pm); |
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116 | } |
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117 | |
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118 | typedef typename GR::Node Node; |
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119 | typedef typename GR::Arc Arc; |
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120 | typedef concepts::ReadMap<Node, Value> NM; |
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121 | typedef concepts::ReadMap<Arc, Value> VAM; |
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122 | typedef concepts::ReadMap<Arc, Cost> CAM; |
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123 | typedef concepts::WriteMap<Arc, Value> FlowMap; |
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124 | typedef concepts::WriteMap<Node, Cost> PotMap; |
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125 | |
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126 | GR g; |
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127 | VAM lower; |
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128 | VAM upper; |
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129 | CAM cost; |
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130 | NM sup; |
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131 | Node n; |
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132 | Arc a; |
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133 | Value k; |
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134 | |
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135 | FlowMap fm; |
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136 | PotMap pm; |
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137 | bool b; |
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138 | double x; |
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139 | typename MCF::Value v; |
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140 | typename MCF::Cost c; |
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141 | }; |
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142 | |
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143 | }; |
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144 | |
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145 | |
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146 | // Check the feasibility of the given flow (primal soluiton) |
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147 | template < typename GR, typename LM, typename UM, |
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148 | typename SM, typename FM > |
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149 | bool checkFlow( const GR& gr, const LM& lower, const UM& upper, |
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150 | const SM& supply, const FM& flow, |
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151 | SupplyType type = EQ ) |
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152 | { |
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153 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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154 | |
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155 | for (ArcIt e(gr); e != INVALID; ++e) { |
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156 | if (flow[e] < lower[e] || flow[e] > upper[e]) return false; |
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157 | } |
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158 | |
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159 | for (NodeIt n(gr); n != INVALID; ++n) { |
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160 | typename SM::Value sum = 0; |
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161 | for (OutArcIt e(gr, n); e != INVALID; ++e) |
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162 | sum += flow[e]; |
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163 | for (InArcIt e(gr, n); e != INVALID; ++e) |
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164 | sum -= flow[e]; |
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165 | bool b = (type == EQ && sum == supply[n]) || |
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166 | (type == GEQ && sum >= supply[n]) || |
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167 | (type == LEQ && sum <= supply[n]); |
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168 | if (!b) return false; |
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169 | } |
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170 | |
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171 | return true; |
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172 | } |
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173 | |
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174 | // Check the feasibility of the given potentials (dual soluiton) |
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175 | // using the "Complementary Slackness" optimality condition |
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176 | template < typename GR, typename LM, typename UM, |
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177 | typename CM, typename SM, typename FM, typename PM > |
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178 | bool checkPotential( const GR& gr, const LM& lower, const UM& upper, |
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179 | const CM& cost, const SM& supply, const FM& flow, |
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180 | const PM& pi, SupplyType type ) |
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181 | { |
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182 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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183 | |
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184 | bool opt = true; |
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185 | for (ArcIt e(gr); opt && e != INVALID; ++e) { |
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186 | typename CM::Value red_cost = |
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187 | cost[e] + pi[gr.source(e)] - pi[gr.target(e)]; |
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188 | opt = red_cost == 0 || |
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189 | (red_cost > 0 && flow[e] == lower[e]) || |
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190 | (red_cost < 0 && flow[e] == upper[e]); |
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191 | } |
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192 | |
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193 | for (NodeIt n(gr); opt && n != INVALID; ++n) { |
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194 | typename SM::Value sum = 0; |
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195 | for (OutArcIt e(gr, n); e != INVALID; ++e) |
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196 | sum += flow[e]; |
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197 | for (InArcIt e(gr, n); e != INVALID; ++e) |
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198 | sum -= flow[e]; |
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199 | if (type != LEQ) { |
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200 | opt = (pi[n] <= 0) && (sum == supply[n] || pi[n] == 0); |
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201 | } else { |
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202 | opt = (pi[n] >= 0) && (sum == supply[n] || pi[n] == 0); |
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203 | } |
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204 | } |
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205 | |
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206 | return opt; |
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207 | } |
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208 | |
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209 | // Check whether the dual cost is equal to the primal cost |
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210 | template < typename GR, typename LM, typename UM, |
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211 | typename CM, typename SM, typename PM > |
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212 | bool checkDualCost( const GR& gr, const LM& lower, const UM& upper, |
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213 | const CM& cost, const SM& supply, const PM& pi, |
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214 | typename CM::Value total ) |
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215 | { |
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216 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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217 | |
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218 | typename CM::Value dual_cost = 0; |
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219 | SM red_supply(gr); |
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220 | for (NodeIt n(gr); n != INVALID; ++n) { |
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221 | red_supply[n] = supply[n]; |
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222 | } |
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223 | for (ArcIt a(gr); a != INVALID; ++a) { |
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224 | if (lower[a] != 0) { |
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225 | dual_cost += lower[a] * cost[a]; |
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226 | red_supply[gr.source(a)] -= lower[a]; |
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227 | red_supply[gr.target(a)] += lower[a]; |
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228 | } |
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229 | } |
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230 | |
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231 | for (NodeIt n(gr); n != INVALID; ++n) { |
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232 | dual_cost -= red_supply[n] * pi[n]; |
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233 | } |
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234 | for (ArcIt a(gr); a != INVALID; ++a) { |
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235 | typename CM::Value red_cost = |
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236 | cost[a] + pi[gr.source(a)] - pi[gr.target(a)]; |
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237 | dual_cost -= (upper[a] - lower[a]) * std::max(-red_cost, 0); |
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238 | } |
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239 | |
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240 | return dual_cost == total; |
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241 | } |
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242 | |
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243 | // Run a minimum cost flow algorithm and check the results |
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244 | template < typename MCF, typename GR, |
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245 | typename LM, typename UM, |
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246 | typename CM, typename SM, |
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247 | typename PT > |
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248 | void checkMcf( const MCF& mcf, PT mcf_result, |
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249 | const GR& gr, const LM& lower, const UM& upper, |
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250 | const CM& cost, const SM& supply, |
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251 | PT result, bool optimal, typename CM::Value total, |
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252 | const std::string &test_id = "", |
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253 | SupplyType type = EQ ) |
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254 | { |
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255 | check(mcf_result == result, "Wrong result " + test_id); |
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256 | if (optimal) { |
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257 | typename GR::template ArcMap<typename SM::Value> flow(gr); |
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258 | typename GR::template NodeMap<typename CM::Value> pi(gr); |
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259 | mcf.flowMap(flow); |
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260 | mcf.potentialMap(pi); |
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261 | check(checkFlow(gr, lower, upper, supply, flow, type), |
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262 | "The flow is not feasible " + test_id); |
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263 | check(mcf.totalCost() == total, "The flow is not optimal " + test_id); |
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264 | check(checkPotential(gr, lower, upper, cost, supply, flow, pi, type), |
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265 | "Wrong potentials " + test_id); |
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266 | check(checkDualCost(gr, lower, upper, cost, supply, pi, total), |
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267 | "Wrong dual cost " + test_id); |
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268 | } |
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269 | } |
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270 | |
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271 | int main() |
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272 | { |
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273 | // Check the interfaces |
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274 | { |
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275 | typedef concepts::Digraph GR; |
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276 | checkConcept< McfClassConcept<GR, int, int>, |
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277 | NetworkSimplex<GR> >(); |
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278 | checkConcept< McfClassConcept<GR, double, double>, |
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279 | NetworkSimplex<GR, double> >(); |
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280 | checkConcept< McfClassConcept<GR, int, double>, |
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281 | NetworkSimplex<GR, int, double> >(); |
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282 | } |
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283 | |
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284 | // Run various MCF tests |
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285 | typedef ListDigraph Digraph; |
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286 | DIGRAPH_TYPEDEFS(ListDigraph); |
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287 | |
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288 | // Read the test digraph |
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289 | Digraph gr; |
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290 | Digraph::ArcMap<int> c(gr), l1(gr), l2(gr), l3(gr), u(gr); |
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291 | Digraph::NodeMap<int> s1(gr), s2(gr), s3(gr), s4(gr), s5(gr), s6(gr); |
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292 | ConstMap<Arc, int> cc(1), cu(std::numeric_limits<int>::max()); |
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293 | Node v, w; |
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294 | |
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295 | std::istringstream input(test_lgf); |
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296 | DigraphReader<Digraph>(gr, input) |
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297 | .arcMap("cost", c) |
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298 | .arcMap("cap", u) |
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299 | .arcMap("low1", l1) |
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300 | .arcMap("low2", l2) |
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301 | .arcMap("low3", l3) |
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302 | .nodeMap("sup1", s1) |
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303 | .nodeMap("sup2", s2) |
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304 | .nodeMap("sup3", s3) |
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305 | .nodeMap("sup4", s4) |
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306 | .nodeMap("sup5", s5) |
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307 | .nodeMap("sup6", s6) |
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308 | .node("source", v) |
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309 | .node("target", w) |
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310 | .run(); |
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311 | |
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312 | // Build test digraphs with negative costs |
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313 | Digraph neg_gr; |
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314 | Node n1 = neg_gr.addNode(); |
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315 | Node n2 = neg_gr.addNode(); |
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316 | Node n3 = neg_gr.addNode(); |
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317 | Node n4 = neg_gr.addNode(); |
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318 | Node n5 = neg_gr.addNode(); |
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319 | Node n6 = neg_gr.addNode(); |
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320 | Node n7 = neg_gr.addNode(); |
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321 | |
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322 | Arc a1 = neg_gr.addArc(n1, n2); |
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323 | Arc a2 = neg_gr.addArc(n1, n3); |
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324 | Arc a3 = neg_gr.addArc(n2, n4); |
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325 | Arc a4 = neg_gr.addArc(n3, n4); |
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326 | Arc a5 = neg_gr.addArc(n3, n2); |
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327 | Arc a6 = neg_gr.addArc(n5, n3); |
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328 | Arc a7 = neg_gr.addArc(n5, n6); |
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329 | Arc a8 = neg_gr.addArc(n6, n7); |
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330 | Arc a9 = neg_gr.addArc(n7, n5); |
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331 | |
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332 | Digraph::ArcMap<int> neg_c(neg_gr), neg_l1(neg_gr, 0), neg_l2(neg_gr, 0); |
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333 | ConstMap<Arc, int> neg_u1(std::numeric_limits<int>::max()), neg_u2(5000); |
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334 | Digraph::NodeMap<int> neg_s(neg_gr, 0); |
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335 | |
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336 | neg_l2[a7] = 1000; |
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337 | neg_l2[a8] = -1000; |
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338 | |
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339 | neg_s[n1] = 100; |
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340 | neg_s[n4] = -100; |
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341 | |
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342 | neg_c[a1] = 100; |
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343 | neg_c[a2] = 30; |
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344 | neg_c[a3] = 20; |
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345 | neg_c[a4] = 80; |
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346 | neg_c[a5] = 50; |
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347 | neg_c[a6] = 10; |
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348 | neg_c[a7] = 80; |
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349 | neg_c[a8] = 30; |
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350 | neg_c[a9] = -120; |
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351 | |
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352 | Digraph negs_gr; |
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353 | Digraph::NodeMap<int> negs_s(negs_gr); |
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354 | Digraph::ArcMap<int> negs_c(negs_gr); |
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355 | ConstMap<Arc, int> negs_l(0), negs_u(1000); |
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356 | n1 = negs_gr.addNode(); |
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357 | n2 = negs_gr.addNode(); |
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358 | negs_s[n1] = 100; |
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359 | negs_s[n2] = -300; |
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360 | negs_c[negs_gr.addArc(n1, n2)] = -1; |
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361 | |
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362 | |
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363 | // A. Test NetworkSimplex with the default pivot rule |
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364 | { |
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365 | NetworkSimplex<Digraph> mcf(gr); |
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366 | |
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367 | // Check the equality form |
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368 | mcf.upperMap(u).costMap(c); |
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369 | checkMcf(mcf, mcf.supplyMap(s1).run(), |
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370 | gr, l1, u, c, s1, mcf.OPTIMAL, true, 5240, "#A1"); |
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371 | checkMcf(mcf, mcf.stSupply(v, w, 27).run(), |
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372 | gr, l1, u, c, s2, mcf.OPTIMAL, true, 7620, "#A2"); |
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373 | mcf.lowerMap(l2); |
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374 | checkMcf(mcf, mcf.supplyMap(s1).run(), |
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375 | gr, l2, u, c, s1, mcf.OPTIMAL, true, 5970, "#A3"); |
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376 | checkMcf(mcf, mcf.stSupply(v, w, 27).run(), |
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377 | gr, l2, u, c, s2, mcf.OPTIMAL, true, 8010, "#A4"); |
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378 | mcf.reset(); |
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379 | checkMcf(mcf, mcf.supplyMap(s1).run(), |
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380 | gr, l1, cu, cc, s1, mcf.OPTIMAL, true, 74, "#A5"); |
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381 | checkMcf(mcf, mcf.lowerMap(l2).stSupply(v, w, 27).run(), |
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382 | gr, l2, cu, cc, s2, mcf.OPTIMAL, true, 94, "#A6"); |
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383 | mcf.reset(); |
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384 | checkMcf(mcf, mcf.run(), |
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385 | gr, l1, cu, cc, s3, mcf.OPTIMAL, true, 0, "#A7"); |
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386 | checkMcf(mcf, mcf.lowerMap(l2).upperMap(u).run(), |
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387 | gr, l2, u, cc, s3, mcf.INFEASIBLE, false, 0, "#A8"); |
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388 | mcf.reset().lowerMap(l3).upperMap(u).costMap(c).supplyMap(s4); |
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389 | checkMcf(mcf, mcf.run(), |
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390 | gr, l3, u, c, s4, mcf.OPTIMAL, true, 6360, "#A9"); |
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391 | |
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392 | // Check the GEQ form |
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393 | mcf.reset().upperMap(u).costMap(c).supplyMap(s5); |
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394 | checkMcf(mcf, mcf.run(), |
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395 | gr, l1, u, c, s5, mcf.OPTIMAL, true, 3530, "#A10", GEQ); |
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396 | mcf.supplyType(mcf.GEQ); |
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397 | checkMcf(mcf, mcf.lowerMap(l2).run(), |
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398 | gr, l2, u, c, s5, mcf.OPTIMAL, true, 4540, "#A11", GEQ); |
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399 | mcf.supplyMap(s6); |
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400 | checkMcf(mcf, mcf.run(), |
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401 | gr, l2, u, c, s6, mcf.INFEASIBLE, false, 0, "#A12", GEQ); |
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402 | |
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403 | // Check the LEQ form |
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404 | mcf.reset().supplyType(mcf.LEQ); |
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405 | mcf.upperMap(u).costMap(c).supplyMap(s6); |
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406 | checkMcf(mcf, mcf.run(), |
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407 | gr, l1, u, c, s6, mcf.OPTIMAL, true, 5080, "#A13", LEQ); |
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408 | checkMcf(mcf, mcf.lowerMap(l2).run(), |
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409 | gr, l2, u, c, s6, mcf.OPTIMAL, true, 5930, "#A14", LEQ); |
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410 | mcf.supplyMap(s5); |
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411 | checkMcf(mcf, mcf.run(), |
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412 | gr, l2, u, c, s5, mcf.INFEASIBLE, false, 0, "#A15", LEQ); |
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413 | |
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414 | // Check negative costs |
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415 | NetworkSimplex<Digraph> neg_mcf(neg_gr); |
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416 | neg_mcf.lowerMap(neg_l1).costMap(neg_c).supplyMap(neg_s); |
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417 | checkMcf(neg_mcf, neg_mcf.run(), neg_gr, neg_l1, neg_u1, |
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418 | neg_c, neg_s, neg_mcf.UNBOUNDED, false, 0, "#A16"); |
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419 | neg_mcf.upperMap(neg_u2); |
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420 | checkMcf(neg_mcf, neg_mcf.run(), neg_gr, neg_l1, neg_u2, |
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421 | neg_c, neg_s, neg_mcf.OPTIMAL, true, -40000, "#A17"); |
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422 | neg_mcf.reset().lowerMap(neg_l2).costMap(neg_c).supplyMap(neg_s); |
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423 | checkMcf(neg_mcf, neg_mcf.run(), neg_gr, neg_l2, neg_u1, |
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424 | neg_c, neg_s, neg_mcf.UNBOUNDED, false, 0, "#A18"); |
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425 | |
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426 | NetworkSimplex<Digraph> negs_mcf(negs_gr); |
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427 | negs_mcf.costMap(negs_c).supplyMap(negs_s); |
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428 | checkMcf(negs_mcf, negs_mcf.run(), negs_gr, negs_l, negs_u, |
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429 | negs_c, negs_s, negs_mcf.OPTIMAL, true, -300, "#A19", GEQ); |
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430 | } |
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431 | |
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432 | // B. Test NetworkSimplex with each pivot rule |
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433 | { |
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434 | NetworkSimplex<Digraph> mcf(gr); |
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435 | mcf.supplyMap(s1).costMap(c).upperMap(u).lowerMap(l2); |
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436 | |
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437 | checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::FIRST_ELIGIBLE), |
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438 | gr, l2, u, c, s1, mcf.OPTIMAL, true, 5970, "#B1"); |
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439 | checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::BEST_ELIGIBLE), |
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440 | gr, l2, u, c, s1, mcf.OPTIMAL, true, 5970, "#B2"); |
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441 | checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::BLOCK_SEARCH), |
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442 | gr, l2, u, c, s1, mcf.OPTIMAL, true, 5970, "#B3"); |
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443 | checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::CANDIDATE_LIST), |
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444 | gr, l2, u, c, s1, mcf.OPTIMAL, true, 5970, "#B4"); |
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445 | checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::ALTERING_LIST), |
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446 | gr, l2, u, c, s1, mcf.OPTIMAL, true, 5970, "#B5"); |
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447 | } |
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448 | |
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449 | return 0; |
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450 | } |
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