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) 2003-2007 |
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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 <lemon/list_graph.h> |
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20 | #include <lemon/graph_utils.h> |
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21 | #include <lemon/random.h> |
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22 | #include <lemon/dim2.h> |
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23 | #include <lemon/bfs.h> |
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24 | #include <lemon/counter.h> |
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25 | #include <lemon/suurballe.h> |
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26 | #include <lemon/graph_to_eps.h> |
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27 | #include <lemon/graph_writer.h> |
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28 | #include <lemon/arg_parser.h> |
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29 | #include <lemon/euler.h> |
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30 | #include <cmath> |
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31 | #include <algorithm> |
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32 | #include <lemon/unionfind.h> |
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33 | #include <lemon/time_measure.h> |
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34 | |
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35 | using namespace lemon; |
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36 | |
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37 | typedef dim2::Point<double> Point; |
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38 | |
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39 | UGRAPH_TYPEDEFS(ListUGraph); |
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40 | |
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41 | bool progress=true; |
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42 | |
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43 | int N; |
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44 | // int girth; |
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45 | |
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46 | ListUGraph g; |
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47 | |
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48 | std::vector<Node> nodes; |
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49 | ListUGraph::NodeMap<Point> coords(g); |
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50 | |
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51 | |
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52 | double totalLen(){ |
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53 | double tlen=0; |
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54 | for(UEdgeIt e(g);e!=INVALID;++e) |
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55 | tlen+=sqrt((coords[g.source(e)]-coords[g.target(e)]).normSquare()); |
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56 | return tlen; |
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57 | } |
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58 | |
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59 | int tsp_impr_num=0; |
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60 | |
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61 | const double EPSILON=1e-8; |
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62 | bool tsp_improve(Node u, Node v) |
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63 | { |
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64 | double luv=std::sqrt((coords[v]-coords[u]).normSquare()); |
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65 | Node u2=u; |
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66 | Node v2=v; |
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67 | do { |
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68 | Node n; |
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69 | for(IncEdgeIt e(g,v2);(n=g.runningNode(e))==u2;++e); |
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70 | u2=v2; |
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71 | v2=n; |
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72 | if(luv+std::sqrt((coords[v2]-coords[u2]).normSquare())-EPSILON> |
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73 | std::sqrt((coords[u]-coords[u2]).normSquare())+ |
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74 | std::sqrt((coords[v]-coords[v2]).normSquare())) |
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75 | { |
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76 | g.erase(findUEdge(g,u,v)); |
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77 | g.erase(findUEdge(g,u2,v2)); |
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78 | g.addEdge(u2,u); |
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79 | g.addEdge(v,v2); |
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80 | tsp_impr_num++; |
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81 | return true; |
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82 | } |
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83 | } while(v2!=u); |
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84 | return false; |
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85 | } |
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86 | |
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87 | bool tsp_improve(Node u) |
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88 | { |
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89 | for(IncEdgeIt e(g,u);e!=INVALID;++e) |
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90 | if(tsp_improve(u,g.runningNode(e))) return true; |
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91 | return false; |
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92 | } |
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93 | |
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94 | void tsp_improve() |
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95 | { |
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96 | bool b; |
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97 | do { |
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98 | b=false; |
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99 | for(NodeIt n(g);n!=INVALID;++n) |
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100 | if(tsp_improve(n)) b=true; |
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101 | } while(b); |
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102 | } |
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103 | |
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104 | void tsp() |
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105 | { |
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106 | for(int i=0;i<N;i++) g.addEdge(nodes[i],nodes[(i+1)%N]); |
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107 | tsp_improve(); |
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108 | } |
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109 | |
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110 | class Line |
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111 | { |
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112 | public: |
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113 | Point a; |
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114 | Point b; |
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115 | Line(Point _a,Point _b) :a(_a),b(_b) {} |
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116 | Line(Node _a,Node _b) : a(coords[_a]),b(coords[_b]) {} |
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117 | Line(const Edge &e) : a(coords[g.source(e)]),b(coords[g.target(e)]) {} |
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118 | Line(const UEdge &e) : a(coords[g.source(e)]),b(coords[g.target(e)]) {} |
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119 | }; |
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120 | |
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121 | inline std::ostream& operator<<(std::ostream &os, const Line &l) |
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122 | { |
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123 | os << l.a << "->" << l.b; |
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124 | return os; |
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125 | } |
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126 | |
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127 | bool cross(Line a, Line b) |
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128 | { |
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129 | Point ao=rot90(a.b-a.a); |
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130 | Point bo=rot90(b.b-b.a); |
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131 | return (ao*(b.a-a.a))*(ao*(b.b-a.a))<0 && |
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132 | (bo*(a.a-b.a))*(bo*(a.b-b.a))<0; |
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133 | } |
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134 | |
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135 | struct Pedge |
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136 | { |
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137 | Node a; |
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138 | Node b; |
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139 | double len; |
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140 | }; |
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141 | |
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142 | bool pedgeLess(Pedge a,Pedge b) |
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143 | { |
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144 | return a.len<b.len; |
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145 | } |
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146 | |
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147 | std::vector<UEdge> edges; |
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148 | |
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149 | void triangle() |
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150 | { |
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151 | Counter cnt("Number of edges added: "); |
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152 | std::vector<Pedge> pedges; |
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153 | for(NodeIt n(g);n!=INVALID;++n) |
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154 | for(NodeIt m=++(NodeIt(n));m!=INVALID;++m) |
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155 | { |
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156 | Pedge p; |
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157 | p.a=n; |
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158 | p.b=m; |
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159 | p.len=(coords[m]-coords[n]).normSquare(); |
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160 | pedges.push_back(p); |
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161 | } |
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162 | std::sort(pedges.begin(),pedges.end(),pedgeLess); |
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163 | for(std::vector<Pedge>::iterator pi=pedges.begin();pi!=pedges.end();++pi) |
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164 | { |
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165 | Line li(pi->a,pi->b); |
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166 | UEdgeIt e(g); |
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167 | for(;e!=INVALID && !cross(e,li);++e) ; |
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168 | UEdge ne; |
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169 | if(e==INVALID) { |
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170 | ne=g.addEdge(pi->a,pi->b); |
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171 | edges.push_back(ne); |
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172 | cnt++; |
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173 | } |
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174 | } |
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175 | } |
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176 | |
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177 | void sparse(int d) |
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178 | { |
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179 | Counter cnt("Number of edges removed: "); |
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180 | Bfs<ListUGraph> bfs(g); |
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181 | for(std::vector<UEdge>::reverse_iterator ei=edges.rbegin(); |
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182 | ei!=edges.rend();++ei) |
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183 | { |
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184 | Node a=g.source(*ei); |
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185 | Node b=g.target(*ei); |
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186 | g.erase(*ei); |
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187 | bfs.run(a,b); |
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188 | if(bfs.predEdge(b)==INVALID || bfs.dist(b)>d) |
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189 | g.addEdge(a,b); |
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190 | else cnt++; |
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191 | } |
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192 | } |
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193 | |
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194 | void sparse2(int d) |
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195 | { |
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196 | Counter cnt("Number of edges removed: "); |
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197 | for(std::vector<UEdge>::reverse_iterator ei=edges.rbegin(); |
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198 | ei!=edges.rend();++ei) |
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199 | { |
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200 | Node a=g.source(*ei); |
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201 | Node b=g.target(*ei); |
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202 | g.erase(*ei); |
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203 | ConstMap<Edge,int> cegy(1); |
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204 | Suurballe<ListUGraph,ConstMap<Edge,int> > sur(g,cegy,a,b); |
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205 | int k=sur.run(2); |
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206 | if(k<2 || sur.totalLength()>d) |
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207 | g.addEdge(a,b); |
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208 | else cnt++; |
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209 | // else std::cout << "Remove edge " << g.id(a) << "-" << g.id(b) << '\n'; |
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210 | } |
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211 | } |
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212 | |
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213 | void sparseTriangle(int d) |
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214 | { |
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215 | Counter cnt("Number of edges added: "); |
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216 | std::vector<Pedge> pedges; |
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217 | for(NodeIt n(g);n!=INVALID;++n) |
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218 | for(NodeIt m=++(NodeIt(n));m!=INVALID;++m) |
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219 | { |
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220 | Pedge p; |
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221 | p.a=n; |
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222 | p.b=m; |
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223 | p.len=(coords[m]-coords[n]).normSquare(); |
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224 | pedges.push_back(p); |
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225 | } |
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226 | std::sort(pedges.begin(),pedges.end(),pedgeLess); |
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227 | for(std::vector<Pedge>::iterator pi=pedges.begin();pi!=pedges.end();++pi) |
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228 | { |
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229 | Line li(pi->a,pi->b); |
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230 | UEdgeIt e(g); |
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231 | for(;e!=INVALID && !cross(e,li);++e) ; |
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232 | UEdge ne; |
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233 | if(e==INVALID) { |
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234 | ConstMap<Edge,int> cegy(1); |
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235 | Suurballe<ListUGraph,ConstMap<Edge,int> > |
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236 | sur(g,cegy,pi->a,pi->b); |
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237 | int k=sur.run(2); |
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238 | if(k<2 || sur.totalLength()>d) |
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239 | { |
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240 | ne=g.addEdge(pi->a,pi->b); |
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241 | edges.push_back(ne); |
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242 | cnt++; |
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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 | void minTree() { |
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249 | int en=0; |
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250 | int pr=0; |
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251 | std::vector<Pedge> pedges; |
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252 | Timer T; |
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253 | std::cout << T.realTime() << "s: Setting up the edges...\n"; |
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254 | for(NodeIt n(g);n!=INVALID;++n) |
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255 | { |
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256 | for(NodeIt m=++(NodeIt(n));m!=INVALID;++m) |
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257 | { |
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258 | Pedge p; |
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259 | p.a=n; |
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260 | p.b=m; |
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261 | p.len=(coords[m]-coords[n]).normSquare(); |
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262 | pedges.push_back(p); |
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263 | } |
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264 | if(progress && en>=pr*double(N)/100) |
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265 | { |
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266 | std::cout << pr << "% \r" << std::flush; |
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267 | pr++; |
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268 | } |
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269 | } |
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270 | std::cout << T.realTime() << "s: Sorting the edges...\n"; |
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271 | std::sort(pedges.begin(),pedges.end(),pedgeLess); |
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272 | std::cout << T.realTime() << "s: Creating the tree...\n"; |
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273 | ListUGraph::NodeMap<int> comp(g); |
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274 | UnionFind<ListUGraph::NodeMap<int> > uf(comp); |
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275 | for (NodeIt it(g); it != INVALID; ++it) |
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276 | uf.insert(it); |
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277 | for(std::vector<Pedge>::iterator pi=pedges.begin();pi!=pedges.end();++pi) |
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278 | { |
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279 | if ( uf.join(pi->a,pi->b) ) { |
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280 | g.addEdge(pi->a,pi->b); |
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281 | en++; |
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282 | if(en>=N-1) |
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283 | break; |
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284 | } |
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285 | } |
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286 | std::cout << T.realTime() << "s: Done\n"; |
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287 | } |
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288 | |
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289 | Node common(UEdge e, UEdge f) |
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290 | { |
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291 | return (g.source(e)==g.source(f)||g.source(e)==g.target(f))? |
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292 | g.source(e):g.target(e); |
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293 | } |
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294 | |
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295 | void tsp2() |
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296 | { |
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297 | std::cout << "Find a tree..." << std::endl; |
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298 | |
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299 | minTree(); |
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300 | |
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301 | std::cout << "Total edge length (tree) : " << totalLen() << std::endl; |
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302 | |
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303 | std::cout << "Make it Euler..." << std::endl; |
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304 | |
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305 | { |
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306 | std::vector<Node> leafs; |
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307 | for(NodeIt n(g);n!=INVALID;++n) |
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308 | if(countIncEdges(g,n)%2==1) leafs.push_back(n); |
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309 | for(unsigned int i=0;i<leafs.size();i+=2) |
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310 | g.addEdge(leafs[i],leafs[i+1]); |
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311 | } |
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312 | |
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313 | for(NodeIt n(g);n!=INVALID;++n) |
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314 | if(countIncEdges(g,n)%2) |
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315 | std::cout << "GEBASZ!!!" << std::endl; |
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316 | |
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317 | std::cout << "Number of edges : " << countUEdges(g) << std::endl; |
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318 | |
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319 | // for(NodeIt n(g);n!=INVALID;++n) |
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320 | // if(countIncEdges(g,n)>2) |
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321 | // std::cout << "+"; |
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322 | // std::cout << std::endl; |
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323 | |
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324 | std::cout << "Total edge length (euler) : " << totalLen() << std::endl; |
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325 | |
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326 | ListUGraph::UEdgeMap<UEdge> enext(g); |
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327 | { |
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328 | UEulerIt<ListUGraph> e(g); |
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329 | UEdge eo=e; |
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330 | UEdge ef=e; |
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331 | // std::cout << "Tour edge: " << g.id(UEdge(e)) << std::endl; |
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332 | for(++e;e!=INVALID;++e) |
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333 | { |
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334 | // std::cout << "Tour edge: " << g.id(UEdge(e)) << std::endl; |
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335 | enext[eo]=e; |
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336 | eo=e; |
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337 | } |
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338 | enext[eo]=ef; |
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339 | } |
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340 | |
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341 | std::cout << "Creating a tour from that..." << std::endl; |
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342 | |
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343 | int nnum = countNodes(g); |
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344 | int ednum = countUEdges(g); |
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345 | |
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346 | for(UEdge p=UEdgeIt(g);ednum>nnum;p=enext[p]) |
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347 | { |
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348 | // std::cout << "Checking edge " << g.id(p) << std::endl; |
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349 | UEdge e=enext[p]; |
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350 | UEdge f=enext[e]; |
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351 | Node n2=common(e,f); |
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352 | Node n1=g.oppositeNode(n2,e); |
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353 | Node n3=g.oppositeNode(n2,f); |
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354 | if(countIncEdges(g,n2)>2) |
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355 | { |
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356 | // std::cout << "Remove an Edge" << std::endl; |
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357 | UEdge ff=enext[f]; |
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358 | g.erase(e); |
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359 | g.erase(f); |
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360 | UEdge ne=g.addEdge(n1,n3); |
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361 | enext[p]=ne; |
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362 | enext[ne]=ff; |
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363 | ednum--; |
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364 | } |
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365 | } |
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366 | |
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367 | std::cout << "Total edge length (tour) : " << totalLen() << std::endl; |
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368 | |
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369 | tsp_improve(); |
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370 | |
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371 | std::cout << "Total edge length (2-opt tour) : " << totalLen() << std::endl; |
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372 | } |
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373 | |
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374 | |
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375 | int main(int argc,const char **argv) |
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376 | { |
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377 | ArgParser ap(argc,argv); |
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378 | |
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379 | // bool eps; |
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380 | bool disc_d, square_d, gauss_d; |
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381 | // bool tsp_a,two_a,tree_a; |
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382 | int num_of_cities=1; |
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383 | double area=1; |
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384 | N=100; |
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385 | // girth=10; |
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386 | std::string ndist("disc"); |
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387 | ap.refOption("n", "Number of nodes (default is 100)", N) |
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388 | .intOption("g", "Girth parameter (default is 10)", 10) |
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389 | .refOption("cities", "Number of cities (default is 1)", num_of_cities) |
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390 | .refOption("area", "Full relative area of the cities (default is 1)", area) |
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391 | .refOption("disc", "Nodes are evenly distributed on a unit disc (default)",disc_d) |
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392 | .optionGroup("dist", "disc") |
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393 | .refOption("square", "Nodes are evenly distributed on a unit square", square_d) |
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394 | .optionGroup("dist", "square") |
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395 | .refOption("gauss", |
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396 | "Nodes are located according to a two-dim gauss distribution", |
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397 | gauss_d) |
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398 | .optionGroup("dist", "gauss") |
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399 | // .mandatoryGroup("dist") |
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400 | .onlyOneGroup("dist") |
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401 | .boolOption("eps", "Also generate .eps output (prefix.eps)") |
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402 | .boolOption("dir", "Directed graph is generated (each edges are replaced by two directed ones)") |
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403 | .boolOption("2con", "Create a two connected planar graph") |
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404 | .optionGroup("alg","2con") |
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405 | .boolOption("tree", "Create a min. cost spanning tree") |
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406 | .optionGroup("alg","tree") |
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407 | .boolOption("tsp", "Create a TSP tour") |
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408 | .optionGroup("alg","tsp") |
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409 | .boolOption("tsp2", "Create a TSP tour (tree based)") |
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410 | .optionGroup("alg","tsp2") |
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411 | .onlyOneGroup("alg") |
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412 | .other("[prefix]","Prefix of the output files. Default is 'lgf-gen-out'") |
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413 | .run(); |
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414 | |
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415 | std::string prefix; |
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416 | switch(ap.files().size()) |
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417 | { |
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418 | case 0: |
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419 | prefix="lgf-gen-out"; |
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420 | break; |
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421 | case 1: |
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422 | prefix=ap.files()[0]; |
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423 | break; |
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424 | default: |
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425 | std::cerr << "\nAt most one prefix can be given\n\n"; |
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426 | exit(1); |
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427 | } |
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428 | |
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429 | double sum_sizes=0; |
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430 | std::vector<double> sizes; |
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431 | std::vector<double> cum_sizes; |
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432 | for(int s=0;s<num_of_cities;s++) |
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433 | { |
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434 | // sum_sizes+=rnd.exponential(); |
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435 | double d=rnd(); |
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436 | sum_sizes+=d; |
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437 | sizes.push_back(d); |
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438 | cum_sizes.push_back(sum_sizes); |
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439 | } |
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440 | int i=0; |
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441 | for(int s=0;s<num_of_cities;s++) |
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442 | { |
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443 | Point center=(num_of_cities==1?Point(0,0):rnd.disc()); |
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444 | if(gauss_d) |
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445 | for(;i<N*(cum_sizes[s]/sum_sizes);i++) { |
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446 | Node n=g.addNode(); |
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447 | nodes.push_back(n); |
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448 | coords[n]=center+rnd.gauss2()*area* |
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449 | std::sqrt(sizes[s]/sum_sizes); |
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450 | } |
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451 | else if(square_d) |
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452 | for(;i<N*(cum_sizes[s]/sum_sizes);i++) { |
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453 | Node n=g.addNode(); |
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454 | nodes.push_back(n); |
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455 | coords[n]=center+Point(rnd()*2-1,rnd()*2-1)*area* |
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456 | std::sqrt(sizes[s]/sum_sizes); |
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457 | } |
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458 | else if(disc_d || true) |
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459 | for(;i<N*(cum_sizes[s]/sum_sizes);i++) { |
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460 | Node n=g.addNode(); |
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461 | nodes.push_back(n); |
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462 | coords[n]=center+rnd.disc()*area* |
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463 | std::sqrt(sizes[s]/sum_sizes); |
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464 | } |
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465 | } |
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466 | |
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467 | if(ap["tsp"]) { |
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468 | tsp(); |
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469 | std::cout << "#2-opt improvements: " << tsp_impr_num << std::endl; |
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470 | } |
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471 | if(ap["tsp2"]) { |
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472 | tsp2(); |
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473 | std::cout << "#2-opt improvements: " << tsp_impr_num << std::endl; |
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474 | } |
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475 | else if(ap["2con"]) { |
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476 | std::cout << "Make triangles\n"; |
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477 | // triangle(); |
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478 | sparseTriangle(ap["g"]); |
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479 | std::cout << "Make it sparser\n"; |
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480 | sparse2(ap["g"]); |
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481 | } |
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482 | else if(ap["tree"]) { |
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483 | minTree(); |
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484 | } |
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485 | |
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486 | |
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487 | std::cout << "Number of nodes : " << countNodes(g) << std::endl; |
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488 | std::cout << "Number of edges : " << countUEdges(g) << std::endl; |
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489 | double tlen=0; |
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490 | for(UEdgeIt e(g);e!=INVALID;++e) |
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491 | tlen+=sqrt((coords[g.source(e)]-coords[g.target(e)]).normSquare()); |
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492 | std::cout << "Total edge length : " << tlen << std::endl; |
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493 | if(ap["eps"]) |
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494 | graphToEps(g,prefix+".eps"). |
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495 | scale(600).nodeScale(.2).edgeWidthScale(.001).preScale(false). |
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496 | coords(coords).run(); |
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497 | |
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498 | if(ap["dir"]) |
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499 | GraphWriter<ListUGraph>(prefix+".lgf",g). |
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500 | writeNodeMap("coordinates_x",scaleMap(xMap(coords),600)). |
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501 | writeNodeMap("coordinates_y",scaleMap(yMap(coords),600)). |
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502 | run(); |
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503 | else UGraphWriter<ListUGraph>(prefix+".lgf",g). |
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504 | writeNodeMap("coordinates_x",scaleMap(xMap(coords),600)). |
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505 | writeNodeMap("coordinates_y",scaleMap(yMap(coords),600)). |
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506 | run(); |
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507 | } |
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508 | |
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