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 <cmath> |
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30 | #include <algorithm> |
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31 | #include <lemon/unionfind.h> |
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32 | |
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33 | using namespace lemon; |
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34 | |
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35 | typedef dim2::Point<double> Point; |
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36 | |
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37 | UGRAPH_TYPEDEFS(ListUGraph); |
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38 | |
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39 | int N; |
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40 | int girth; |
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41 | |
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42 | ListUGraph g; |
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43 | |
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44 | std::vector<Node> nodes; |
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45 | ListUGraph::NodeMap<Point> coords(g); |
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46 | |
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47 | int tsp_impr_num=0; |
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48 | |
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49 | const double EPSILON=1e-8; |
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50 | bool tsp_improve(Node u, Node v) |
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51 | { |
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52 | double luv=std::sqrt((coords[v]-coords[u]).normSquare()); |
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53 | Node u2=u; |
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54 | Node v2=v; |
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55 | do { |
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56 | Node n; |
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57 | for(IncEdgeIt e(g,v2);(n=g.runningNode(e))==u2;++e); |
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58 | u2=v2; |
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59 | v2=n; |
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60 | if(luv+std::sqrt((coords[v2]-coords[u2]).normSquare())-EPSILON> |
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61 | std::sqrt((coords[u]-coords[u2]).normSquare())+ |
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62 | std::sqrt((coords[v]-coords[v2]).normSquare())) |
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63 | { |
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64 | g.erase(findUEdge(g,u,v)); |
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65 | g.erase(findUEdge(g,u2,v2)); |
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66 | g.addEdge(u2,u); |
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67 | g.addEdge(v,v2); |
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68 | tsp_impr_num++; |
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69 | return true; |
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70 | } |
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71 | } while(v2!=u); |
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72 | return false; |
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73 | } |
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74 | |
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75 | bool tsp_improve(Node u) |
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76 | { |
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77 | for(IncEdgeIt e(g,u);e!=INVALID;++e) |
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78 | if(tsp_improve(u,g.runningNode(e))) return true; |
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79 | return false; |
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80 | } |
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81 | |
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82 | void tsp_improve() |
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83 | { |
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84 | bool b; |
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85 | do { |
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86 | b=false; |
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87 | for(NodeIt n(g);n!=INVALID;++n) |
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88 | if(tsp_improve(n)) b=true; |
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89 | } while(b); |
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90 | } |
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91 | |
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92 | void tsp() |
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93 | { |
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94 | for(int i=0;i<N;i++) g.addEdge(nodes[i],nodes[(i+1)%N]); |
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95 | tsp_improve(); |
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96 | } |
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97 | |
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98 | class Line |
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99 | { |
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100 | public: |
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101 | Point a; |
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102 | Point b; |
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103 | Line(Point _a,Point _b) :a(_a),b(_b) {} |
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104 | Line(Node _a,Node _b) : a(coords[_a]),b(coords[_b]) {} |
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105 | Line(const Edge &e) : a(coords[g.source(e)]),b(coords[g.target(e)]) {} |
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106 | Line(const UEdge &e) : a(coords[g.source(e)]),b(coords[g.target(e)]) {} |
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107 | }; |
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108 | |
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109 | inline std::ostream& operator<<(std::ostream &os, const Line &l) |
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110 | { |
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111 | os << l.a << "->" << l.b; |
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112 | return os; |
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113 | } |
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114 | |
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115 | bool cross(Line a, Line b) |
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116 | { |
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117 | Point ao=rot90(a.b-a.a); |
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118 | Point bo=rot90(b.b-b.a); |
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119 | return (ao*(b.a-a.a))*(ao*(b.b-a.a))<0 && |
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120 | (bo*(a.a-b.a))*(bo*(a.b-b.a))<0; |
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121 | } |
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122 | |
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123 | struct Pedge |
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124 | { |
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125 | Node a; |
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126 | Node b; |
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127 | double len; |
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128 | }; |
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129 | |
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130 | bool pedgeLess(Pedge a,Pedge b) |
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131 | { |
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132 | return a.len<b.len; |
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133 | } |
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134 | |
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135 | std::vector<UEdge> edges; |
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136 | |
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137 | void triangle() |
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138 | { |
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139 | Counter cnt("Number of edges added: "); |
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140 | std::vector<Pedge> pedges; |
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141 | for(NodeIt n(g);n!=INVALID;++n) |
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142 | for(NodeIt m=++(NodeIt(n));m!=INVALID;++m) |
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143 | { |
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144 | Pedge p; |
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145 | p.a=n; |
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146 | p.b=m; |
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147 | p.len=(coords[m]-coords[n]).normSquare(); |
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148 | pedges.push_back(p); |
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149 | } |
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150 | std::sort(pedges.begin(),pedges.end(),pedgeLess); |
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151 | for(std::vector<Pedge>::iterator pi=pedges.begin();pi!=pedges.end();++pi) |
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152 | { |
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153 | Line li(pi->a,pi->b); |
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154 | UEdgeIt e(g); |
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155 | for(;e!=INVALID && !cross(e,li);++e) ; |
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156 | UEdge ne; |
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157 | if(e==INVALID) { |
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158 | ne=g.addEdge(pi->a,pi->b); |
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159 | edges.push_back(ne); |
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160 | cnt++; |
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161 | } |
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162 | } |
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163 | } |
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164 | |
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165 | void sparse(int d) |
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166 | { |
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167 | Counter cnt("Number of edges removed: "); |
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168 | Bfs<ListUGraph> bfs(g); |
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169 | for(std::vector<UEdge>::reverse_iterator ei=edges.rbegin(); |
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170 | ei!=edges.rend();++ei) |
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171 | { |
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172 | Node a=g.source(*ei); |
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173 | Node b=g.target(*ei); |
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174 | g.erase(*ei); |
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175 | bfs.run(a,b); |
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176 | if(bfs.predEdge(b)==INVALID || bfs.dist(b)>d) |
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177 | g.addEdge(a,b); |
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178 | else cnt++; |
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179 | } |
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180 | } |
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181 | |
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182 | void sparse2(int d) |
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183 | { |
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184 | Counter cnt("Number of edges removed: "); |
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185 | for(std::vector<UEdge>::reverse_iterator ei=edges.rbegin(); |
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186 | ei!=edges.rend();++ei) |
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187 | { |
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188 | Node a=g.source(*ei); |
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189 | Node b=g.target(*ei); |
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190 | g.erase(*ei); |
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191 | ConstMap<Edge,int> cegy(1); |
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192 | Suurballe<ListUGraph,ConstMap<Edge,int> > sur(g,cegy,a,b); |
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193 | int k=sur.run(2); |
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194 | if(k<2 || sur.totalLength()>d) |
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195 | g.addEdge(a,b); |
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196 | else cnt++; |
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197 | // else std::cout << "Remove edge " << g.id(a) << "-" << g.id(b) << '\n'; |
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198 | } |
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199 | } |
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200 | |
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201 | void sparseTriangle(int d) |
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202 | { |
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203 | Counter cnt("Number of edges added: "); |
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204 | std::vector<Pedge> pedges; |
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205 | for(NodeIt n(g);n!=INVALID;++n) |
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206 | for(NodeIt m=++(NodeIt(n));m!=INVALID;++m) |
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207 | { |
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208 | Pedge p; |
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209 | p.a=n; |
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210 | p.b=m; |
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211 | p.len=(coords[m]-coords[n]).normSquare(); |
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212 | pedges.push_back(p); |
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213 | } |
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214 | std::sort(pedges.begin(),pedges.end(),pedgeLess); |
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215 | for(std::vector<Pedge>::iterator pi=pedges.begin();pi!=pedges.end();++pi) |
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216 | { |
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217 | Line li(pi->a,pi->b); |
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218 | UEdgeIt e(g); |
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219 | for(;e!=INVALID && !cross(e,li);++e) ; |
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220 | UEdge ne; |
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221 | if(e==INVALID) { |
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222 | ConstMap<Edge,int> cegy(1); |
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223 | Suurballe<ListUGraph,ConstMap<Edge,int> > |
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224 | sur(g,cegy,pi->a,pi->b); |
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225 | int k=sur.run(2); |
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226 | if(k<2 || sur.totalLength()>d) |
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227 | { |
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228 | ne=g.addEdge(pi->a,pi->b); |
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229 | edges.push_back(ne); |
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230 | cnt++; |
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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 | void minTree() { |
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237 | std::vector<Pedge> pedges; |
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238 | for(NodeIt n(g);n!=INVALID;++n) |
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239 | for(NodeIt m=++(NodeIt(n));m!=INVALID;++m) |
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240 | { |
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241 | Pedge p; |
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242 | p.a=n; |
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243 | p.b=m; |
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244 | p.len=(coords[m]-coords[n]).normSquare(); |
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245 | pedges.push_back(p); |
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246 | } |
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247 | std::sort(pedges.begin(),pedges.end(),pedgeLess); |
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248 | ListUGraph::NodeMap<int> comp(g); |
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249 | UnionFind<ListUGraph::NodeMap<int> > uf(comp); |
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250 | for (NodeIt it(g); it != INVALID; ++it) |
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251 | uf.insert(it); |
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252 | |
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253 | int en=0; |
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254 | for(std::vector<Pedge>::iterator pi=pedges.begin();pi!=pedges.end();++pi) |
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255 | { |
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256 | if ( uf.join(pi->a,pi->b) ) { |
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257 | g.addEdge(pi->a,pi->b); |
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258 | en++; |
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259 | if(en>=N-1) return; |
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260 | } |
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261 | } |
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262 | } |
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263 | |
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264 | |
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265 | |
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266 | int main(int argc,char **argv) |
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267 | { |
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268 | ArgParser ap(argc,argv); |
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269 | |
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270 | bool eps; |
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271 | bool disc_d, square_d, gauss_d; |
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272 | bool tsp_a,two_a,tree_a; |
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273 | int num_of_cities=1; |
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274 | double area=1; |
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275 | N=100; |
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276 | girth=10; |
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277 | std::string ndist("disc"); |
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278 | ap.option("n", "Number of nodes (default is 100)", N) |
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279 | .option("g", "Girth parameter (default is 10)", girth) |
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280 | .option("cities", "Number of cities (default is 1)", num_of_cities) |
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281 | .option("area", "Full relative area of the cities (default is 1)", area) |
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282 | .option("disc", "Nodes are evenly distributed on a unit disc (default)",disc_d) |
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283 | .optionGroup("dist", "disc") |
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284 | .option("square", "Nodes are evenly distributed on a unit square", square_d) |
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285 | .optionGroup("dist", "square") |
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286 | .option("gauss", |
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287 | "Nodes are located according to a two-dim gauss distribution", |
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288 | gauss_d) |
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289 | .optionGroup("dist", "gauss") |
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290 | // .mandatoryGroup("dist") |
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291 | .onlyOneGroup("dist") |
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292 | .option("eps", "Also generate .eps output (prefix.eps)",eps) |
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293 | .option("2con", "Create a two connected planar graph",two_a) |
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294 | .optionGroup("alg","2con") |
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295 | .option("tree", "Create a min. cost spanning tree",tree_a) |
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296 | .optionGroup("alg","tree") |
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297 | .option("tsp", "Create a TSP tour",tsp_a) |
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298 | .optionGroup("alg","tsp") |
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299 | .onlyOneGroup("alg") |
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300 | .other("[prefix]","Prefix of the output files. Default is 'lgf-gen-out'") |
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301 | .run(); |
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302 | |
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303 | std::string prefix; |
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304 | switch(ap.files().size()) |
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305 | { |
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306 | case 0: |
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307 | prefix="lgf-gen-out"; |
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308 | break; |
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309 | case 1: |
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310 | prefix=ap.files()[0]; |
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311 | break; |
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312 | default: |
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313 | std::cerr << "\nAt most one prefix can be given\n\n"; |
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314 | exit(1); |
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315 | } |
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316 | |
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317 | double sum_sizes=0; |
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318 | std::vector<double> sizes; |
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319 | std::vector<double> cum_sizes; |
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320 | for(int s=0;s<num_of_cities;s++) |
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321 | { |
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322 | // sum_sizes+=rnd.exponential(); |
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323 | double d=rnd(); |
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324 | sum_sizes+=d; |
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325 | sizes.push_back(d); |
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326 | cum_sizes.push_back(sum_sizes); |
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327 | } |
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328 | int i=0; |
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329 | for(int s=0;s<num_of_cities;s++) |
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330 | { |
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331 | Point center=(num_of_cities==1?Point(0,0):rnd.disc()); |
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332 | if(gauss_d) |
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333 | for(;i<N*(cum_sizes[s]/sum_sizes);i++) { |
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334 | Node n=g.addNode(); |
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335 | nodes.push_back(n); |
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336 | coords[n]=center+rnd.gauss2()*area* |
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337 | std::sqrt(sizes[s]/sum_sizes); |
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338 | } |
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339 | else if(square_d) |
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340 | for(;i<N*(cum_sizes[s]/sum_sizes);i++) { |
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341 | Node n=g.addNode(); |
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342 | nodes.push_back(n); |
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343 | coords[n]=center+Point(rnd()*2-1,rnd()*2-1)*area* |
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344 | std::sqrt(sizes[s]/sum_sizes); |
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345 | } |
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346 | else if(disc_d || true) |
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347 | for(;i<N*(cum_sizes[s]/sum_sizes);i++) { |
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348 | Node n=g.addNode(); |
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349 | nodes.push_back(n); |
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350 | coords[n]=center+rnd.disc()*area* |
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351 | std::sqrt(sizes[s]/sum_sizes); |
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352 | } |
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353 | } |
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354 | |
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355 | if(tsp_a) { |
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356 | tsp(); |
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357 | std::cout << "#2-opt improvements: " << tsp_impr_num << std::endl; |
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358 | } |
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359 | else if(two_a) { |
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360 | std::cout << "Make triangles\n"; |
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361 | // triangle(); |
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362 | sparseTriangle(girth); |
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363 | std::cout << "Make it sparser\n"; |
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364 | sparse2(girth); |
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365 | } |
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366 | else if(tree_a) { |
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367 | minTree(); |
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368 | } |
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369 | |
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370 | |
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371 | std::cout << "Number of nodes : " << countNodes(g) << std::endl; |
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372 | std::cout << "Number of edges : " << countUEdges(g) << std::endl; |
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373 | double tlen=0; |
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374 | for(UEdgeIt e(g);e!=INVALID;++e) |
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375 | tlen+=sqrt((coords[g.source(e)]-coords[g.target(e)]).normSquare()); |
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376 | std::cout << "Total edge length : " << tlen << std::endl; |
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377 | if(eps) |
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378 | graphToEps(g,prefix+".eps"). |
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379 | scale(600).nodeScale(.2).edgeWidthScale(.001).preScale(false). |
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380 | coords(coords).run(); |
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381 | |
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382 | UGraphWriter<ListUGraph>(prefix+".lgf",g). |
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383 | writeNodeMap("coordinates_x",scaleMap(xMap(coords),600)). |
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384 | writeNodeMap("coordinates_y",scaleMap(yMap(coords),600)). |
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385 | run(); |
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386 | } |
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387 | |
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