1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library. |
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4 | * |
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5 | * Copyright (C) 2003-2009 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #include <iostream> |
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20 | |
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21 | #include <lemon/list_graph.h> |
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22 | #include <lemon/lgf_reader.h> |
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23 | #include <lemon/path.h> |
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24 | #include <lemon/suurballe.h> |
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25 | #include <lemon/concepts/digraph.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 | char test_lgf[] = |
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32 | "@nodes\n" |
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33 | "label\n" |
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34 | "1\n" |
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35 | "2\n" |
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36 | "3\n" |
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37 | "4\n" |
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38 | "5\n" |
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39 | "6\n" |
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40 | "7\n" |
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41 | "8\n" |
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42 | "9\n" |
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43 | "10\n" |
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44 | "11\n" |
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45 | "12\n" |
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46 | "@arcs\n" |
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47 | " length\n" |
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48 | " 1 2 70\n" |
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49 | " 1 3 150\n" |
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50 | " 1 4 80\n" |
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51 | " 2 8 80\n" |
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52 | " 3 5 140\n" |
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53 | " 4 6 60\n" |
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54 | " 4 7 80\n" |
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55 | " 4 8 110\n" |
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56 | " 5 7 60\n" |
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57 | " 5 11 120\n" |
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58 | " 6 3 0\n" |
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59 | " 6 9 140\n" |
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60 | " 6 10 90\n" |
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61 | " 7 1 30\n" |
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62 | " 8 12 60\n" |
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63 | " 9 12 50\n" |
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64 | "10 12 70\n" |
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65 | "10 2 100\n" |
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66 | "10 7 60\n" |
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67 | "11 10 20\n" |
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68 | "12 11 30\n" |
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69 | "@attributes\n" |
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70 | "source 1\n" |
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71 | "target 12\n" |
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72 | "@end\n"; |
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73 | |
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74 | // Check the interface of Suurballe |
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75 | void checkSuurballeCompile() |
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76 | { |
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77 | typedef int VType; |
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78 | typedef concepts::Digraph Digraph; |
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79 | |
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80 | typedef Digraph::Node Node; |
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81 | typedef Digraph::Arc Arc; |
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82 | typedef concepts::ReadMap<Arc, VType> LengthMap; |
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83 | |
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84 | typedef Suurballe<Digraph, LengthMap> SuurballeType; |
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85 | |
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86 | Digraph g; |
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87 | Node n; |
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88 | Arc e; |
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89 | LengthMap len; |
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90 | SuurballeType::FlowMap flow(g); |
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91 | SuurballeType::PotentialMap pi(g); |
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92 | |
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93 | SuurballeType suurb_test(g, len); |
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94 | const SuurballeType& const_suurb_test = suurb_test; |
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95 | |
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96 | suurb_test |
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97 | .flowMap(flow) |
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98 | .potentialMap(pi); |
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99 | |
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100 | int k; |
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101 | k = suurb_test.run(n, n); |
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102 | k = suurb_test.run(n, n, k); |
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103 | suurb_test.init(n); |
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104 | suurb_test.fullInit(n); |
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105 | suurb_test.start(n); |
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106 | suurb_test.start(n, k); |
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107 | k = suurb_test.findFlow(n); |
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108 | k = suurb_test.findFlow(n, k); |
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109 | suurb_test.findPaths(); |
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110 | |
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111 | int f; |
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112 | VType c; |
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113 | c = const_suurb_test.totalLength(); |
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114 | f = const_suurb_test.flow(e); |
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115 | const SuurballeType::FlowMap& fm = |
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116 | const_suurb_test.flowMap(); |
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117 | c = const_suurb_test.potential(n); |
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118 | const SuurballeType::PotentialMap& pm = |
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119 | const_suurb_test.potentialMap(); |
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120 | k = const_suurb_test.pathNum(); |
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121 | Path<Digraph> p = const_suurb_test.path(k); |
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122 | |
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123 | ignore_unused_variable_warning(fm); |
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124 | ignore_unused_variable_warning(pm); |
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125 | } |
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126 | |
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127 | // Check the feasibility of the flow |
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128 | template <typename Digraph, typename FlowMap> |
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129 | bool checkFlow( const Digraph& gr, const FlowMap& flow, |
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130 | typename Digraph::Node s, typename Digraph::Node t, |
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131 | int value ) |
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132 | { |
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133 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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134 | for (ArcIt e(gr); e != INVALID; ++e) |
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135 | if (!(flow[e] == 0 || flow[e] == 1)) return false; |
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136 | |
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137 | for (NodeIt n(gr); n != INVALID; ++n) { |
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138 | int sum = 0; |
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139 | for (OutArcIt e(gr, n); e != INVALID; ++e) |
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140 | sum += flow[e]; |
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141 | for (InArcIt e(gr, n); e != INVALID; ++e) |
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142 | sum -= flow[e]; |
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143 | if (n == s && sum != value) return false; |
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144 | if (n == t && sum != -value) return false; |
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145 | if (n != s && n != t && sum != 0) return false; |
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146 | } |
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147 | |
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148 | return true; |
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149 | } |
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150 | |
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151 | // Check the optimalitiy of the flow |
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152 | template < typename Digraph, typename CostMap, |
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153 | typename FlowMap, typename PotentialMap > |
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154 | bool checkOptimality( const Digraph& gr, const CostMap& cost, |
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155 | const FlowMap& flow, const PotentialMap& pi ) |
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156 | { |
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157 | // Check the "Complementary Slackness" optimality condition |
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158 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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159 | bool opt = true; |
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160 | for (ArcIt e(gr); e != INVALID; ++e) { |
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161 | typename CostMap::Value red_cost = |
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162 | cost[e] + pi[gr.source(e)] - pi[gr.target(e)]; |
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163 | opt = (flow[e] == 0 && red_cost >= 0) || |
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164 | (flow[e] == 1 && red_cost <= 0); |
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165 | if (!opt) break; |
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166 | } |
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167 | return opt; |
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168 | } |
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169 | |
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170 | // Check a path |
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171 | template <typename Digraph, typename Path> |
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172 | bool checkPath( const Digraph& gr, const Path& path, |
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173 | typename Digraph::Node s, typename Digraph::Node t) |
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174 | { |
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175 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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176 | Node n = s; |
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177 | for (int i = 0; i < path.length(); ++i) { |
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178 | if (gr.source(path.nth(i)) != n) return false; |
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179 | n = gr.target(path.nth(i)); |
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180 | } |
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181 | return n == t; |
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182 | } |
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183 | |
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184 | |
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185 | int main() |
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186 | { |
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187 | DIGRAPH_TYPEDEFS(ListDigraph); |
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188 | |
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189 | // Read the test digraph |
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190 | ListDigraph digraph; |
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191 | ListDigraph::ArcMap<int> length(digraph); |
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192 | Node s, t; |
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193 | |
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194 | std::istringstream input(test_lgf); |
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195 | DigraphReader<ListDigraph>(digraph, input). |
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196 | arcMap("length", length). |
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197 | node("source", s). |
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198 | node("target", t). |
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199 | run(); |
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200 | |
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201 | // Find 2 paths |
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202 | { |
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203 | Suurballe<ListDigraph> suurballe(digraph, length); |
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204 | check(suurballe.run(s, t) == 2, "Wrong number of paths"); |
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205 | check(checkFlow(digraph, suurballe.flowMap(), s, t, 2), |
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206 | "The flow is not feasible"); |
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207 | check(suurballe.totalLength() == 510, "The flow is not optimal"); |
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208 | check(checkOptimality(digraph, length, suurballe.flowMap(), |
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209 | suurballe.potentialMap()), |
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210 | "Wrong potentials"); |
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211 | for (int i = 0; i < suurballe.pathNum(); ++i) |
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212 | check(checkPath(digraph, suurballe.path(i), s, t), "Wrong path"); |
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213 | } |
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214 | |
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215 | // Find 3 paths |
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216 | { |
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217 | Suurballe<ListDigraph> suurballe(digraph, length); |
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218 | check(suurballe.run(s, t, 3) == 3, "Wrong number of paths"); |
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219 | check(checkFlow(digraph, suurballe.flowMap(), s, t, 3), |
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220 | "The flow is not feasible"); |
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221 | check(suurballe.totalLength() == 1040, "The flow is not optimal"); |
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222 | check(checkOptimality(digraph, length, suurballe.flowMap(), |
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223 | suurballe.potentialMap()), |
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224 | "Wrong potentials"); |
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225 | for (int i = 0; i < suurballe.pathNum(); ++i) |
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226 | check(checkPath(digraph, suurballe.path(i), s, t), "Wrong path"); |
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227 | } |
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228 | |
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229 | // Find 5 paths (only 3 can be found) |
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230 | { |
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231 | Suurballe<ListDigraph> suurballe(digraph, length); |
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232 | check(suurballe.run(s, t, 5) == 3, "Wrong number of paths"); |
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233 | check(checkFlow(digraph, suurballe.flowMap(), s, t, 3), |
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234 | "The flow is not feasible"); |
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235 | check(suurballe.totalLength() == 1040, "The flow is not optimal"); |
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236 | check(checkOptimality(digraph, length, suurballe.flowMap(), |
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237 | suurballe.potentialMap()), |
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238 | "Wrong potentials"); |
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239 | for (int i = 0; i < suurballe.pathNum(); ++i) |
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240 | check(checkPath(digraph, suurballe.path(i), s, t), "Wrong path"); |
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241 | } |
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242 | |
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243 | return 0; |
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244 | } |
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