1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2008 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #include <iostream> |
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20 | #include <fstream> |
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21 | |
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22 | #include <lemon/list_graph.h> |
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23 | #include <lemon/lgf_reader.h> |
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24 | #include <lemon/path.h> |
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25 | #include <lemon/suurballe.h> |
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26 | |
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27 | #include "test_tools.h" |
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28 | |
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29 | using namespace lemon; |
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30 | |
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31 | // Check the feasibility of the flow |
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32 | template <typename Digraph, typename FlowMap> |
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33 | bool checkFlow( const Digraph& gr, const FlowMap& flow, |
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34 | typename Digraph::Node s, typename Digraph::Node t, |
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35 | int value ) |
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36 | { |
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37 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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38 | for (ArcIt e(gr); e != INVALID; ++e) |
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39 | if (!(flow[e] == 0 || flow[e] == 1)) return false; |
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40 | |
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41 | for (NodeIt n(gr); n != INVALID; ++n) { |
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42 | int sum = 0; |
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43 | for (OutArcIt e(gr, n); e != INVALID; ++e) |
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44 | sum += flow[e]; |
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45 | for (InArcIt e(gr, n); e != INVALID; ++e) |
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46 | sum -= flow[e]; |
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47 | if (n == s && sum != value) return false; |
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48 | if (n == t && sum != -value) return false; |
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49 | if (n != s && n != t && sum != 0) return false; |
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50 | } |
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51 | |
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52 | return true; |
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53 | } |
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54 | |
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55 | // Check the optimalitiy of the flow |
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56 | template < typename Digraph, typename CostMap, |
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57 | typename FlowMap, typename PotentialMap > |
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58 | bool checkOptimality( const Digraph& gr, const CostMap& cost, |
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59 | const FlowMap& flow, const PotentialMap& pi ) |
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60 | { |
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61 | // Check the "Complementary Slackness" optimality condition |
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62 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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63 | bool opt = true; |
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64 | for (ArcIt e(gr); e != INVALID; ++e) { |
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65 | typename CostMap::Value red_cost = |
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66 | cost[e] + pi[gr.source(e)] - pi[gr.target(e)]; |
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67 | opt = (flow[e] == 0 && red_cost >= 0) || |
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68 | (flow[e] == 1 && red_cost <= 0); |
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69 | if (!opt) break; |
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70 | } |
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71 | return opt; |
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72 | } |
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73 | |
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74 | // Check a path |
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75 | template <typename Digraph, typename Path> |
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76 | bool checkPath( const Digraph& gr, const Path& path, |
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77 | typename Digraph::Node s, typename Digraph::Node t) |
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78 | { |
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79 | // Check the "Complementary Slackness" optimality condition |
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80 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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81 | Node n = s; |
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82 | for (int i = 0; i < path.length(); ++i) { |
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83 | if (gr.source(path.nth(i)) != n) return false; |
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84 | n = gr.target(path.nth(i)); |
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85 | } |
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86 | return n == t; |
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87 | } |
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88 | |
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89 | |
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90 | int main() |
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91 | { |
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92 | DIGRAPH_TYPEDEFS(ListDigraph); |
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93 | |
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94 | // Read the test digraph |
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95 | ListDigraph digraph; |
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96 | ListDigraph::ArcMap<int> length(digraph); |
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97 | Node source, target; |
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98 | |
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99 | std::string fname; |
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100 | if(getenv("srcdir")) |
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101 | fname = std::string(getenv("srcdir")); |
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102 | else fname = "."; |
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103 | fname += "/test/min_cost_flow_test.lgf"; |
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104 | |
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105 | std::ifstream input(fname.c_str()); |
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106 | check(input, "Input file '" << fname << "' not found"); |
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107 | DigraphReader<ListDigraph>(digraph, input). |
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108 | arcMap("cost", length). |
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109 | node("source", source). |
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110 | node("target", target). |
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111 | run(); |
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112 | input.close(); |
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113 | |
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114 | // Find 2 paths |
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115 | { |
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116 | Suurballe<ListDigraph> suurballe(digraph, length, source, target); |
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117 | check(suurballe.run(2) == 2, "Wrong number of paths"); |
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118 | check(checkFlow(digraph, suurballe.flowMap(), source, target, 2), |
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119 | "The flow is not feasible"); |
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120 | check(suurballe.totalLength() == 510, "The flow is not optimal"); |
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121 | check(checkOptimality(digraph, length, suurballe.flowMap(), |
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122 | suurballe.potentialMap()), |
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123 | "Wrong potentials"); |
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124 | for (int i = 0; i < suurballe.pathNum(); ++i) |
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125 | check(checkPath(digraph, suurballe.path(i), source, target), |
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126 | "Wrong path"); |
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127 | } |
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128 | |
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129 | // Find 3 paths |
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130 | { |
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131 | Suurballe<ListDigraph> suurballe(digraph, length, source, target); |
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132 | check(suurballe.run(3) == 3, "Wrong number of paths"); |
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133 | check(checkFlow(digraph, suurballe.flowMap(), source, target, 3), |
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134 | "The flow is not feasible"); |
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135 | check(suurballe.totalLength() == 1040, "The flow is not optimal"); |
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136 | check(checkOptimality(digraph, length, suurballe.flowMap(), |
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137 | suurballe.potentialMap()), |
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138 | "Wrong potentials"); |
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139 | for (int i = 0; i < suurballe.pathNum(); ++i) |
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140 | check(checkPath(digraph, suurballe.path(i), source, target), |
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141 | "Wrong path"); |
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142 | } |
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143 | |
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144 | // Find 5 paths (only 3 can be found) |
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145 | { |
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146 | Suurballe<ListDigraph> suurballe(digraph, length, source, target); |
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147 | check(suurballe.run(5) == 3, "Wrong number of paths"); |
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148 | check(checkFlow(digraph, suurballe.flowMap(), source, target, 3), |
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149 | "The flow is not feasible"); |
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150 | check(suurballe.totalLength() == 1040, "The flow is not optimal"); |
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151 | check(checkOptimality(digraph, length, suurballe.flowMap(), |
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152 | suurballe.potentialMap()), |
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153 | "Wrong potentials"); |
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154 | for (int i = 0; i < suurballe.pathNum(); ++i) |
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155 | check(checkPath(digraph, suurballe.path(i), source, target), |
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156 | "Wrong path"); |
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157 | } |
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158 | |
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159 | return 0; |
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160 | } |
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