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_NEAREST_NEIGHBOUR_TSP_H |
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20 | #define LEMON_NEAREST_NEIGHBOUR_TSP_H |
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21 | |
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22 | /// \ingroup tsp |
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23 | /// \file |
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24 | /// \brief Nearest neighbor algorithm for symmetric TSP |
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25 | |
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26 | #include <deque> |
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27 | #include <vector> |
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28 | #include <limits> |
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29 | #include <lemon/full_graph.h> |
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30 | #include <lemon/maps.h> |
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31 | |
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32 | namespace lemon { |
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33 | |
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34 | /// \ingroup tsp |
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35 | /// |
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36 | /// \brief Nearest neighbor algorithm for symmetric TSP. |
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37 | /// |
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38 | /// NearestNeighborTsp implements the nearest neighbor heuristic for solving |
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39 | /// symmetric \ref tsp "TSP". |
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40 | /// |
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41 | /// This is probably the simplest TSP heuristic. |
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42 | /// It starts with a minimum cost edge and at each step, it connects the |
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43 | /// nearest unvisited node to the current path. |
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44 | /// Finally, it connects the two end points of the path to form a tour. |
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45 | /// |
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46 | /// This method runs in O(n<sup>2</sup>) time. |
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47 | /// It quickly finds a relatively short tour for most TSP instances, |
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48 | /// but it could also yield a really bad (or even the worst) solution |
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49 | /// in special cases. |
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50 | /// |
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51 | /// \tparam CM Type of the cost map. |
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52 | template <typename CM> |
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53 | class NearestNeighborTsp |
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54 | { |
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55 | public: |
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56 | |
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57 | /// Type of the cost map |
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58 | typedef CM CostMap; |
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59 | /// Type of the edge costs |
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60 | typedef typename CM::Value Cost; |
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61 | |
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62 | private: |
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63 | |
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64 | GRAPH_TYPEDEFS(FullGraph); |
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65 | |
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66 | const FullGraph &_gr; |
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67 | const CostMap &_cost; |
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68 | Cost _sum; |
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69 | std::vector<Node> _path; |
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70 | |
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71 | public: |
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72 | |
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73 | /// \brief Constructor |
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74 | /// |
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75 | /// Constructor. |
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76 | /// \param gr The \ref FullGraph "full graph" the algorithm runs on. |
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77 | /// \param cost The cost map. |
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78 | NearestNeighborTsp(const FullGraph &gr, const CostMap &cost) |
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79 | : _gr(gr), _cost(cost) {} |
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80 | |
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81 | /// \name Execution Control |
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82 | /// @{ |
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83 | |
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84 | /// \brief Runs the algorithm. |
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85 | /// |
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86 | /// This function runs the algorithm. |
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87 | /// |
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88 | /// \return The total cost of the found tour. |
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89 | Cost run() { |
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90 | _path.clear(); |
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91 | if (_gr.nodeNum() == 0) { |
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92 | return _sum = 0; |
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93 | } |
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94 | else if (_gr.nodeNum() == 1) { |
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95 | _path.push_back(_gr(0)); |
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96 | return _sum = 0; |
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97 | } |
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98 | |
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99 | std::deque<Node> path_dq; |
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100 | Edge min_edge1 = INVALID, |
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101 | min_edge2 = INVALID; |
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102 | |
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103 | min_edge1 = mapMin(_gr, _cost); |
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104 | Node n1 = _gr.u(min_edge1), |
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105 | n2 = _gr.v(min_edge1); |
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106 | path_dq.push_back(n1); |
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107 | path_dq.push_back(n2); |
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108 | |
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109 | FullGraph::NodeMap<bool> used(_gr, false); |
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110 | used[n1] = true; |
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111 | used[n2] = true; |
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112 | |
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113 | min_edge1 = INVALID; |
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114 | while (int(path_dq.size()) != _gr.nodeNum()) { |
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115 | if (min_edge1 == INVALID) { |
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116 | for (IncEdgeIt e(_gr, n1); e != INVALID; ++e) { |
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117 | if (!used[_gr.runningNode(e)] && |
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118 | (_cost[e] < _cost[min_edge1] || min_edge1 == INVALID)) { |
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119 | min_edge1 = e; |
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120 | } |
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121 | } |
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122 | } |
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123 | |
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124 | if (min_edge2 == INVALID) { |
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125 | for (IncEdgeIt e(_gr, n2); e != INVALID; ++e) { |
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126 | if (!used[_gr.runningNode(e)] && |
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127 | (_cost[e] < _cost[min_edge2] || min_edge2 == INVALID)) { |
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128 | min_edge2 = e; |
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129 | } |
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130 | } |
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131 | } |
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132 | |
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133 | if (_cost[min_edge1] < _cost[min_edge2]) { |
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134 | n1 = _gr.oppositeNode(n1, min_edge1); |
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135 | path_dq.push_front(n1); |
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136 | |
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137 | used[n1] = true; |
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138 | min_edge1 = INVALID; |
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139 | |
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140 | if (_gr.u(min_edge2) == n1 || _gr.v(min_edge2) == n1) |
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141 | min_edge2 = INVALID; |
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142 | } else { |
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143 | n2 = _gr.oppositeNode(n2, min_edge2); |
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144 | path_dq.push_back(n2); |
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145 | |
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146 | used[n2] = true; |
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147 | min_edge2 = INVALID; |
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148 | |
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149 | if (_gr.u(min_edge1) == n2 || _gr.v(min_edge1) == n2) |
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150 | min_edge1 = INVALID; |
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151 | } |
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152 | } |
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153 | |
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154 | n1 = path_dq.back(); |
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155 | n2 = path_dq.front(); |
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156 | _path.push_back(n2); |
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157 | _sum = _cost[_gr.edge(n1, n2)]; |
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158 | for (int i = 1; i < int(path_dq.size()); ++i) { |
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159 | n1 = n2; |
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160 | n2 = path_dq[i]; |
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161 | _path.push_back(n2); |
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162 | _sum += _cost[_gr.edge(n1, n2)]; |
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163 | } |
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164 | |
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165 | return _sum; |
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166 | } |
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167 | |
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168 | /// @} |
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169 | |
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170 | /// \name Query Functions |
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171 | /// @{ |
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172 | |
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173 | /// \brief The total cost of the found tour. |
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174 | /// |
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175 | /// This function returns the total cost of the found tour. |
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176 | /// |
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177 | /// \pre run() must be called before using this function. |
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178 | Cost tourCost() const { |
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179 | return _sum; |
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180 | } |
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181 | |
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182 | /// \brief Returns a const reference to the node sequence of the |
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183 | /// found tour. |
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184 | /// |
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185 | /// This function returns a const reference to a vector |
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186 | /// that stores the node sequence of the found tour. |
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187 | /// |
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188 | /// \pre run() must be called before using this function. |
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189 | const std::vector<Node>& tourNodes() const { |
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190 | return _path; |
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191 | } |
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192 | |
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193 | /// \brief Gives back the node sequence of the found tour. |
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194 | /// |
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195 | /// This function copies the node sequence of the found tour into |
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196 | /// an STL container through the given output iterator. The |
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197 | /// <tt>value_type</tt> of the container must be <tt>FullGraph::Node</tt>. |
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198 | /// For example, |
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199 | /// \code |
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200 | /// std::vector<FullGraph::Node> nodes(countNodes(graph)); |
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201 | /// tsp.tourNodes(nodes.begin()); |
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202 | /// \endcode |
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203 | /// or |
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204 | /// \code |
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205 | /// std::list<FullGraph::Node> nodes; |
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206 | /// tsp.tourNodes(std::back_inserter(nodes)); |
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207 | /// \endcode |
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208 | /// |
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209 | /// \pre run() must be called before using this function. |
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210 | template <typename Iterator> |
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211 | void tourNodes(Iterator out) const { |
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212 | std::copy(_path.begin(), _path.end(), out); |
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213 | } |
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214 | |
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215 | /// \brief Gives back the found tour as a path. |
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216 | /// |
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217 | /// This function copies the found tour as a list of arcs/edges into |
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218 | /// the given \ref lemon::concepts::Path "path structure". |
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219 | /// |
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220 | /// \pre run() must be called before using this function. |
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221 | template <typename Path> |
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222 | void tour(Path &path) const { |
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223 | path.clear(); |
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224 | for (int i = 0; i < int(_path.size()) - 1; ++i) { |
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225 | path.addBack(_gr.arc(_path[i], _path[i+1])); |
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226 | } |
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227 | if (int(_path.size()) >= 2) { |
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228 | path.addBack(_gr.arc(_path.back(), _path.front())); |
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229 | } |
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230 | } |
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231 | |
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232 | /// @} |
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233 | |
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234 | }; |
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235 | |
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236 | }; // namespace lemon |
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237 | |
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238 | #endif |
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