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_GREEDY_TSP_H |
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20 | #define LEMON_GREEDY_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 Greedy algorithm for symmetric TSP |
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25 | |
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26 | #include <vector> |
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27 | #include <algorithm> |
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28 | #include <lemon/full_graph.h> |
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29 | #include <lemon/unionfind.h> |
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30 | |
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31 | namespace lemon { |
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32 | |
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33 | /// \ingroup tsp |
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34 | /// |
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35 | /// \brief Greedy algorithm for symmetric TSP. |
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36 | /// |
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37 | /// GreedyTsp implements the greedy heuristic for solving |
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38 | /// symmetric \ref tsp "TSP". |
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39 | /// |
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40 | /// This algorithm is quite similar to the \ref NearestNeighborTsp |
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41 | /// "nearest neighbor" heuristic, but it maintains a set of disjoint paths. |
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42 | /// At each step, the shortest possible edge is added to these paths |
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43 | /// as long as it does not create a cycle of less than n edges and it does |
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44 | /// not increase the degree of any node above two. |
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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 GreedyTsp |
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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 | private: |
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72 | |
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73 | // Functor class to compare edges by their costs |
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74 | class EdgeComp { |
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75 | private: |
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76 | const CostMap &_cost; |
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77 | |
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78 | public: |
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79 | EdgeComp(const CostMap &cost) : _cost(cost) {} |
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80 | |
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81 | bool operator()(const Edge &a, const Edge &b) const { |
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82 | return _cost[a] < _cost[b]; |
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83 | } |
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84 | }; |
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85 | |
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86 | public: |
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87 | |
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88 | /// \brief Constructor |
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89 | /// |
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90 | /// Constructor. |
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91 | /// \param gr The \ref FullGraph "full graph" the algorithm runs on. |
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92 | /// \param cost The cost map. |
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93 | GreedyTsp(const FullGraph &gr, const CostMap &cost) |
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94 | : _gr(gr), _cost(cost) {} |
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95 | |
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96 | /// \name Execution Control |
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97 | /// @{ |
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98 | |
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99 | /// \brief Runs the algorithm. |
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100 | /// |
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101 | /// This function runs the algorithm. |
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102 | /// |
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103 | /// \return The total cost of the found tour. |
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104 | Cost run() { |
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105 | _path.clear(); |
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106 | |
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107 | if (_gr.nodeNum() == 0) return _sum = 0; |
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108 | else if (_gr.nodeNum() == 1) { |
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109 | _path.push_back(_gr(0)); |
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110 | return _sum = 0; |
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111 | } |
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112 | |
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113 | std::vector<int> plist; |
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114 | plist.resize(_gr.nodeNum()*2, -1); |
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115 | |
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116 | std::vector<Edge> sorted_edges; |
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117 | sorted_edges.reserve(_gr.edgeNum()); |
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118 | for (EdgeIt e(_gr); e != INVALID; ++e) |
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119 | sorted_edges.push_back(e); |
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120 | std::sort(sorted_edges.begin(), sorted_edges.end(), EdgeComp(_cost)); |
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121 | |
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122 | FullGraph::NodeMap<int> item_int_map(_gr); |
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123 | UnionFind<FullGraph::NodeMap<int> > union_find(item_int_map); |
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124 | for (NodeIt n(_gr); n != INVALID; ++n) |
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125 | union_find.insert(n); |
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126 | |
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127 | FullGraph::NodeMap<int> degree(_gr, 0); |
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128 | |
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129 | int nodesNum = 0, i = 0; |
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130 | while (nodesNum != _gr.nodeNum()-1) { |
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131 | Edge e = sorted_edges[i++]; |
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132 | Node u = _gr.u(e), |
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133 | v = _gr.v(e); |
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134 | |
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135 | if (degree[u] <= 1 && degree[v] <= 1) { |
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136 | if (union_find.join(u, v)) { |
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137 | const int uid = _gr.id(u), |
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138 | vid = _gr.id(v); |
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139 | |
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140 | plist[uid*2 + degree[u]] = vid; |
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141 | plist[vid*2 + degree[v]] = uid; |
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142 | |
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143 | ++degree[u]; |
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144 | ++degree[v]; |
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145 | ++nodesNum; |
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146 | } |
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147 | } |
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148 | } |
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149 | |
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150 | for (int i=0, n=-1; i<_gr.nodeNum()*2; ++i) { |
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151 | if (plist[i] == -1) { |
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152 | if (n==-1) { |
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153 | n = i; |
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154 | } else { |
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155 | plist[n] = i/2; |
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156 | plist[i] = n/2; |
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157 | break; |
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158 | } |
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159 | } |
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160 | } |
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161 | |
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162 | for (int i=0, next=0, last=-1; i!=_gr.nodeNum(); ++i) { |
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163 | _path.push_back(_gr.nodeFromId(next)); |
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164 | if (plist[2*next] != last) { |
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165 | last = next; |
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166 | next = plist[2*next]; |
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167 | } else { |
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168 | last = next; |
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169 | next = plist[2*next+1]; |
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170 | } |
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171 | } |
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172 | |
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173 | _sum = _cost[_gr.edge(_path.back(), _path.front())]; |
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174 | for (int i = 0; i < int(_path.size())-1; ++i) { |
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175 | _sum += _cost[_gr.edge(_path[i], _path[i+1])]; |
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176 | } |
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177 | |
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178 | return _sum; |
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179 | } |
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180 | |
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181 | /// @} |
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182 | |
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183 | /// \name Query Functions |
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184 | /// @{ |
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185 | |
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186 | /// \brief The total cost of the found tour. |
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187 | /// |
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188 | /// This function returns the total cost of the found tour. |
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189 | /// |
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190 | /// \pre run() must be called before using this function. |
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191 | Cost tourCost() const { |
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192 | return _sum; |
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193 | } |
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194 | |
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195 | /// \brief Returns a const reference to the node sequence of the |
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196 | /// found tour. |
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197 | /// |
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198 | /// This function returns a const reference to a vector |
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199 | /// that stores the node sequence of the found tour. |
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200 | /// |
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201 | /// \pre run() must be called before using this function. |
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202 | const std::vector<Node>& tourNodes() const { |
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203 | return _path; |
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204 | } |
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205 | |
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206 | /// \brief Gives back the node sequence of the found tour. |
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207 | /// |
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208 | /// This function copies the node sequence of the found tour into |
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209 | /// an STL container through the given output iterator. The |
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210 | /// <tt>value_type</tt> of the container must be <tt>FullGraph::Node</tt>. |
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211 | /// For example, |
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212 | /// \code |
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213 | /// std::vector<FullGraph::Node> nodes(countNodes(graph)); |
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214 | /// tsp.tourNodes(nodes.begin()); |
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215 | /// \endcode |
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216 | /// or |
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217 | /// \code |
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218 | /// std::list<FullGraph::Node> nodes; |
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219 | /// tsp.tourNodes(std::back_inserter(nodes)); |
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220 | /// \endcode |
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221 | /// |
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222 | /// \pre run() must be called before using this function. |
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223 | template <typename Iterator> |
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224 | void tourNodes(Iterator out) const { |
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225 | std::copy(_path.begin(), _path.end(), out); |
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226 | } |
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227 | |
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228 | /// \brief Gives back the found tour as a path. |
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229 | /// |
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230 | /// This function copies the found tour as a list of arcs/edges into |
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231 | /// the given \ref lemon::concepts::Path "path structure". |
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232 | /// |
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233 | /// \pre run() must be called before using this function. |
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234 | template <typename Path> |
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235 | void tour(Path &path) const { |
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236 | path.clear(); |
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237 | for (int i = 0; i < int(_path.size()) - 1; ++i) { |
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238 | path.addBack(_gr.arc(_path[i], _path[i+1])); |
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239 | } |
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240 | if (int(_path.size()) >= 2) { |
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241 | path.addBack(_gr.arc(_path.back(), _path.front())); |
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242 | } |
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243 | } |
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244 | |
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245 | /// @} |
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246 | |
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247 | }; |
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248 | |
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249 | }; // namespace lemon |
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250 | |
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251 | #endif |
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