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1 /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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2 * |
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3 * This file is a part of LEMON, a generic C++ optimization library. |
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4 * |
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5 * Copyright (C) 2003-2009 |
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6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 * |
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9 * Permission to use, modify and distribute this software is granted |
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10 * provided that this copyright notice appears in all copies. For |
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11 * precise terms see the accompanying LICENSE file. |
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12 * |
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13 * This software is provided "AS IS" with no warranty of any kind, |
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14 * express or implied, and with no claim as to its suitability for any |
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15 * purpose. |
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16 * |
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17 */ |
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18 |
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19 #ifndef LEMON_EULER_H |
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20 #define LEMON_EULER_H |
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21 |
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22 #include<lemon/core.h> |
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23 #include<lemon/adaptors.h> |
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24 #include<lemon/connectivity.h> |
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25 #include <list> |
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26 |
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27 /// \ingroup graph_prop |
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28 /// \file |
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29 /// \brief Euler tour |
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30 /// |
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31 ///This file provides an Euler tour iterator and ways to check |
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32 ///if a digraph is euler. |
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33 |
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34 |
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35 namespace lemon { |
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36 |
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37 ///Euler iterator for digraphs. |
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38 |
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39 /// \ingroup graph_prop |
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40 ///This iterator converts to the \c Arc type of the digraph and using |
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41 ///operator ++, it provides an Euler tour of a \e directed |
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42 ///graph (if there exists). |
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43 /// |
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44 ///For example |
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45 ///if the given digraph is Euler (i.e it has only one nontrivial component |
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46 ///and the in-degree is equal to the out-degree for all nodes), |
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47 ///the following code will put the arcs of \c g |
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48 ///to the vector \c et according to an |
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49 ///Euler tour of \c g. |
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50 ///\code |
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51 /// std::vector<ListDigraph::Arc> et; |
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52 /// for(DiEulerIt<ListDigraph> e(g),e!=INVALID;++e) |
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53 /// et.push_back(e); |
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54 ///\endcode |
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55 ///If \c g is not Euler then the resulted tour will not be full or closed. |
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56 ///\sa EulerIt |
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57 ///\todo Test required |
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58 template<class Digraph> |
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59 class DiEulerIt |
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60 { |
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61 typedef typename Digraph::Node Node; |
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62 typedef typename Digraph::NodeIt NodeIt; |
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63 typedef typename Digraph::Arc Arc; |
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64 typedef typename Digraph::ArcIt ArcIt; |
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65 typedef typename Digraph::OutArcIt OutArcIt; |
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66 typedef typename Digraph::InArcIt InArcIt; |
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67 |
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68 const Digraph &g; |
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69 typename Digraph::template NodeMap<OutArcIt> nedge; |
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70 std::list<Arc> euler; |
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71 |
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72 public: |
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73 |
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74 ///Constructor |
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75 |
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76 ///\param _g A digraph. |
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77 ///\param start The starting point of the tour. If it is not given |
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78 /// the tour will start from the first node. |
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79 DiEulerIt(const Digraph &_g,typename Digraph::Node start=INVALID) |
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80 : g(_g), nedge(g) |
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81 { |
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82 if(start==INVALID) start=NodeIt(g); |
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83 for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutArcIt(g,n); |
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84 while(nedge[start]!=INVALID) { |
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85 euler.push_back(nedge[start]); |
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86 Node next=g.target(nedge[start]); |
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87 ++nedge[start]; |
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88 start=next; |
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89 } |
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90 } |
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91 |
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92 ///Arc Conversion |
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93 operator Arc() { return euler.empty()?INVALID:euler.front(); } |
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94 bool operator==(Invalid) { return euler.empty(); } |
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95 bool operator!=(Invalid) { return !euler.empty(); } |
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96 |
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97 ///Next arc of the tour |
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98 DiEulerIt &operator++() { |
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99 Node s=g.target(euler.front()); |
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100 euler.pop_front(); |
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101 //This produces a warning.Strange. |
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102 //std::list<Arc>::iterator next=euler.begin(); |
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103 typename std::list<Arc>::iterator next=euler.begin(); |
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104 while(nedge[s]!=INVALID) { |
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105 euler.insert(next,nedge[s]); |
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106 Node n=g.target(nedge[s]); |
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107 ++nedge[s]; |
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108 s=n; |
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109 } |
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110 return *this; |
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111 } |
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112 ///Postfix incrementation |
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113 |
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114 ///\warning This incrementation |
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115 ///returns an \c Arc, not an \ref DiEulerIt, as one may |
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116 ///expect. |
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117 Arc operator++(int) |
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118 { |
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119 Arc e=*this; |
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120 ++(*this); |
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121 return e; |
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122 } |
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123 }; |
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124 |
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125 ///Euler iterator for graphs. |
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126 |
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127 /// \ingroup graph_prop |
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128 ///This iterator converts to the \c Arc (or \c Edge) |
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129 ///type of the digraph and using |
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130 ///operator ++, it provides an Euler tour of an undirected |
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131 ///digraph (if there exists). |
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132 /// |
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133 ///For example |
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134 ///if the given digraph if Euler (i.e it has only one nontrivial component |
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135 ///and the degree of each node is even), |
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136 ///the following code will print the arc IDs according to an |
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137 ///Euler tour of \c g. |
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138 ///\code |
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139 /// for(EulerIt<ListGraph> e(g),e!=INVALID;++e) { |
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140 /// std::cout << g.id(Edge(e)) << std::eol; |
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141 /// } |
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142 ///\endcode |
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143 ///Although the iterator provides an Euler tour of an graph, |
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144 ///it still returns Arcs in order to indicate the direction of the tour. |
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145 ///(But Arc will convert to Edges, of course). |
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146 /// |
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147 ///If \c g is not Euler then the resulted tour will not be full or closed. |
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148 ///\sa EulerIt |
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149 ///\todo Test required |
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150 template<class Digraph> |
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151 class EulerIt |
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152 { |
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153 typedef typename Digraph::Node Node; |
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154 typedef typename Digraph::NodeIt NodeIt; |
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155 typedef typename Digraph::Arc Arc; |
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156 typedef typename Digraph::Edge Edge; |
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157 typedef typename Digraph::ArcIt ArcIt; |
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158 typedef typename Digraph::OutArcIt OutArcIt; |
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159 typedef typename Digraph::InArcIt InArcIt; |
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160 |
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161 const Digraph &g; |
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162 typename Digraph::template NodeMap<OutArcIt> nedge; |
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163 typename Digraph::template EdgeMap<bool> visited; |
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164 std::list<Arc> euler; |
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165 |
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166 public: |
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167 |
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168 ///Constructor |
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169 |
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170 ///\param _g An graph. |
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171 ///\param start The starting point of the tour. If it is not given |
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172 /// the tour will start from the first node. |
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173 EulerIt(const Digraph &_g,typename Digraph::Node start=INVALID) |
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174 : g(_g), nedge(g), visited(g,false) |
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175 { |
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176 if(start==INVALID) start=NodeIt(g); |
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177 for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutArcIt(g,n); |
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178 while(nedge[start]!=INVALID) { |
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179 euler.push_back(nedge[start]); |
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180 visited[nedge[start]]=true; |
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181 Node next=g.target(nedge[start]); |
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182 ++nedge[start]; |
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183 start=next; |
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184 while(nedge[start]!=INVALID && visited[nedge[start]]) ++nedge[start]; |
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185 } |
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186 } |
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187 |
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188 ///Arc Conversion |
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189 operator Arc() const { return euler.empty()?INVALID:euler.front(); } |
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190 ///Arc Conversion |
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191 operator Edge() const { return euler.empty()?INVALID:euler.front(); } |
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192 ///\e |
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193 bool operator==(Invalid) const { return euler.empty(); } |
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194 ///\e |
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195 bool operator!=(Invalid) const { return !euler.empty(); } |
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196 |
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197 ///Next arc of the tour |
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198 EulerIt &operator++() { |
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199 Node s=g.target(euler.front()); |
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200 euler.pop_front(); |
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201 typename std::list<Arc>::iterator next=euler.begin(); |
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202 |
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203 while(nedge[s]!=INVALID) { |
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204 while(nedge[s]!=INVALID && visited[nedge[s]]) ++nedge[s]; |
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205 if(nedge[s]==INVALID) break; |
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206 else { |
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207 euler.insert(next,nedge[s]); |
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208 visited[nedge[s]]=true; |
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209 Node n=g.target(nedge[s]); |
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210 ++nedge[s]; |
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211 s=n; |
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212 } |
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213 } |
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214 return *this; |
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215 } |
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216 |
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217 ///Postfix incrementation |
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218 |
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219 ///\warning This incrementation |
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220 ///returns an \c Arc, not an \ref EulerIt, as one may |
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221 ///expect. |
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222 Arc operator++(int) |
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223 { |
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224 Arc e=*this; |
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225 ++(*this); |
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226 return e; |
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227 } |
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228 }; |
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229 |
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230 |
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231 ///Checks if the graph is Euler |
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232 |
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233 /// \ingroup graph_prop |
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234 ///Checks if the graph is Euler. It works for both directed and undirected |
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235 ///graphs. |
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236 ///\note By definition, a digraph is called \e Euler if |
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237 ///and only if it is connected and the number of its incoming and outgoing |
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238 ///arcs are the same for each node. |
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239 ///Similarly, an undirected graph is called \e Euler if |
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240 ///and only if it is connected and the number of incident arcs is even |
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241 ///for each node. <em>Therefore, there are digraphs which are not Euler, but |
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242 ///still have an Euler tour</em>. |
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243 ///\todo Test required |
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244 template<class Digraph> |
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245 #ifdef DOXYGEN |
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246 bool |
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247 #else |
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248 typename enable_if<UndirectedTagIndicator<Digraph>,bool>::type |
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249 euler(const Digraph &g) |
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250 { |
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251 for(typename Digraph::NodeIt n(g);n!=INVALID;++n) |
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252 if(countIncEdges(g,n)%2) return false; |
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253 return connected(g); |
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254 } |
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255 template<class Digraph> |
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256 typename disable_if<UndirectedTagIndicator<Digraph>,bool>::type |
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257 #endif |
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258 euler(const Digraph &g) |
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259 { |
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260 for(typename Digraph::NodeIt n(g);n!=INVALID;++n) |
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261 if(countInArcs(g,n)!=countOutArcs(g,n)) return false; |
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262 return connected(Undirector<const Digraph>(g)); |
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263 } |
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264 |
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265 } |
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266 |
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267 #endif |