1 | /* -*- C++ -*- |
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2 | * lemon/euler.h - Part of LEMON, a generic C++ optimization library |
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3 | * |
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4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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6 | * |
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7 | * Permission to use, modify and distribute this software is granted |
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8 | * provided that this copyright notice appears in all copies. For |
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9 | * precise terms see the accompanying LICENSE file. |
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10 | * |
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11 | * This software is provided "AS IS" with no warranty of any kind, |
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12 | * express or implied, and with no claim as to its suitability for any |
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13 | * purpose. |
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14 | * |
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15 | */ |
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16 | #include<lemon/invalid.h> |
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17 | #include<lemon/topology.h> |
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18 | #include <list> |
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19 | |
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20 | /// \ingroup topology |
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21 | /// \file |
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22 | /// \brief Euler tour |
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23 | /// |
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24 | ///This file provides an Euler tour iterator and ways to check |
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25 | ///if a graph is euler. |
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26 | |
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27 | |
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28 | namespace lemon { |
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29 | |
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30 | ///Euler iterator for directed graphs. |
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31 | |
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32 | /// \ingroup topology |
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33 | ///This iterator converts to the \c Edge type of the graph and using |
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34 | ///operator ++ it provides an Euler tour of the graph (if there exists). |
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35 | /// |
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36 | ///For example |
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37 | ///if the given graph if Euler (i.e it has only one nontrivial component |
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38 | ///and the in-degree is equal to the out-degree for all nodes), |
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39 | ///the following code will print the edge IDs according to an |
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40 | ///Euler tour of \c g. |
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41 | ///\code |
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42 | /// for(EulerIt<ListGraph> e(g),e!=INVALID;++e) { |
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43 | /// std::cout << g.id(e) << std::eol; |
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44 | /// } |
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45 | ///\endcode |
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46 | ///If \c g is not Euler then the resulted tour will not be full or closed. |
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47 | ///\todo Test required |
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48 | template<class Graph> |
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49 | class EulerIt |
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50 | { |
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51 | typedef typename Graph::Node Node; |
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52 | typedef typename Graph::NodeIt NodeIt; |
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53 | typedef typename Graph::Edge Edge; |
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54 | typedef typename Graph::EdgeIt EdgeIt; |
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55 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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56 | typedef typename Graph::InEdgeIt InEdgeIt; |
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57 | |
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58 | const Graph &g; |
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59 | typename Graph::NodeMap<OutEdgeIt> nedge; |
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60 | std::list<Edge> euler; |
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61 | |
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62 | public: |
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63 | |
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64 | ///Constructor |
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65 | |
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66 | ///\param _g A directed graph. |
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67 | ///\param start The starting point of the tour. If it is not given |
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68 | /// the tour will start from the first node. |
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69 | EulerIt(const Graph &_g,typename Graph::Node start=INVALID) |
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70 | : g(_g), nedge(g) |
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71 | { |
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72 | if(start==INVALID) start=NodeIt(g); |
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73 | for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutEdgeIt(g,n); |
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74 | while(nedge[start]!=INVALID) { |
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75 | euler.push_back(nedge[start]); |
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76 | Node next=g.target(nedge[start]); |
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77 | ++nedge[start]; |
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78 | start=next; |
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79 | } |
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80 | } |
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81 | |
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82 | ///Edge Conversion |
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83 | operator Edge() { return euler.empty()?INVALID:euler.front(); } |
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84 | bool operator==(Invalid) { return euler.empty(); } |
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85 | bool operator!=(Invalid) { return !euler.empty(); } |
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86 | |
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87 | ///Next edge of the tour |
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88 | EulerIt &operator++() { |
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89 | Node s=g.target(euler.front()); |
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90 | euler.pop_front(); |
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91 | //This produces a warning.Strange. |
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92 | //std::list<Edge>::iterator next=euler.begin(); |
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93 | typename std::list<Edge>::iterator next=euler.begin(); |
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94 | while(nedge[s]!=INVALID) { |
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95 | euler.insert(next,nedge[s]); |
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96 | Node n=g.target(nedge[s]); |
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97 | ++nedge[s]; |
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98 | s=n; |
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99 | } |
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100 | return *this; |
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101 | } |
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102 | ///Postfix incrementation |
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103 | |
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104 | ///\warning This incrementation |
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105 | ///returns an \c Edge, not an \ref EulerIt, as one may |
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106 | ///expect. |
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107 | Edge operator++(int) |
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108 | { |
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109 | Edge e=*this; |
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110 | ++(*this); |
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111 | return e; |
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112 | } |
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113 | }; |
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114 | |
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115 | ///Euler iterator for undirected graphs. |
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116 | |
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117 | /// \ingroup topology |
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118 | ///This iterator converts to the \c Edge type of the graph and using |
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119 | ///operator ++ it provides an Euler tour of the graph (if there exists). |
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120 | /// |
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121 | ///For example |
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122 | ///if the given graph if Euler (i.e it has only one nontrivial component |
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123 | ///and the degree of each node is even), |
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124 | ///the following code will print the edge IDs according to an |
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125 | ///Euler tour of \c g. |
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126 | ///\code |
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127 | /// for(UndirEulerIt<UndirListGraph> e(g),e!=INVALID;++e) { |
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128 | /// std::cout << g.id(UndirEdge(e)) << std::eol; |
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129 | /// } |
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130 | ///\endcode |
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131 | ///Although the iterator provides an Euler tour of an undirected graph, |
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132 | ///in order to indicate the direction of the tour, UndirEulerIt |
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133 | ///returns directed edges (that convert to the undirected ones, of course). |
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134 | /// |
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135 | ///If \c g is not Euler then the resulted tour will not be full or closed. |
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136 | ///\todo Test required |
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137 | template<class Graph> |
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138 | class UndirEulerIt |
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139 | { |
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140 | typedef typename Graph::Node Node; |
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141 | typedef typename Graph::NodeIt NodeIt; |
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142 | typedef typename Graph::Edge Edge; |
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143 | typedef typename Graph::EdgeIt EdgeIt; |
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144 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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145 | typedef typename Graph::InEdgeIt InEdgeIt; |
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146 | |
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147 | const Graph &g; |
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148 | typename Graph::NodeMap<OutEdgeIt> nedge; |
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149 | typename Graph::UndirEdgeMap<bool> visited; |
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150 | std::list<Edge> euler; |
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151 | |
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152 | public: |
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153 | |
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154 | ///Constructor |
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155 | |
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156 | ///\param _g An undirected graph. |
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157 | ///\param start The starting point of the tour. If it is not given |
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158 | /// the tour will start from the first node. |
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159 | UndirEulerIt(const Graph &_g,typename Graph::Node start=INVALID) |
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160 | : g(_g), nedge(g), visited(g,false) |
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161 | { |
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162 | if(start==INVALID) start=NodeIt(g); |
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163 | for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutEdgeIt(g,n); |
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164 | while(nedge[start]!=INVALID) { |
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165 | euler.push_back(nedge[start]); |
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166 | Node next=g.target(nedge[start]); |
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167 | ++nedge[start]; |
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168 | start=next; while(nedge[start]!=INVALID && visited[nedge[start]]) ++nedge[start]; |
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169 | } |
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170 | } |
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171 | |
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172 | ///Edge Conversion |
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173 | operator Edge() { return euler.empty()?INVALID:euler.front(); } |
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174 | bool operator==(Invalid) { return euler.empty(); } |
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175 | bool operator!=(Invalid) { return !euler.empty(); } |
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176 | |
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177 | ///Next edge of the tour |
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178 | UndirEulerIt &operator++() { |
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179 | Node s=g.target(euler.front()); |
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180 | euler.pop_front(); |
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181 | typename std::list<Edge>::iterator next=euler.begin(); |
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182 | |
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183 | while(nedge[s]!=INVALID) { |
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184 | while(nedge[s]!=INVALID && visited[nedge[s]]) ++nedge[s]; |
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185 | if(nedge[s]==INVALID) break; |
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186 | else { |
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187 | euler.insert(next,nedge[s]); |
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188 | Node n=g.target(nedge[s]); |
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189 | ++nedge[s]; |
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190 | s=n; |
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191 | } |
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192 | } |
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193 | return *this; |
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194 | } |
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195 | |
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196 | ///Postfix incrementation |
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197 | |
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198 | ///\warning This incrementation |
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199 | ///returns an \c Edge, not an \ref UndirEulerIt, as one may |
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200 | ///expect. |
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201 | Edge operator++(int) |
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202 | { |
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203 | Edge e=*this; |
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204 | ++(*this); |
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205 | return e; |
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206 | } |
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207 | }; |
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208 | |
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209 | |
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210 | ///Checks if the graph is Euler |
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211 | |
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212 | /// \ingroup topology |
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213 | ///Checks if the graph is Euler. It works for both directed and |
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214 | ///undirected graphs. |
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215 | ///\note By definition, a directed graph is called \e Euler if |
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216 | ///and only if connected and the number of it is incoming and outgoing edges |
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217 | ///are the same for each node. |
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218 | ///Similarly, an undirected graph is called \e Euler if |
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219 | ///and only if it is connected and the number of incident edges is even |
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220 | ///for each node. <em>Therefore, there are graphs which are not Euler, but |
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221 | ///still have an Euler tour</em>. |
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222 | ///\todo Test required |
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223 | template<class Graph> |
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224 | #ifdef DOXYGEN |
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225 | bool |
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226 | #else |
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227 | typename enable_if<typename Graph::UndirTag,bool>::type |
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228 | euler(const Graph &g) |
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229 | { |
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230 | for(typename Graph::NodeIt n(g);n!=INVALID;++n) |
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231 | if(countIncEdges(g,n)%2) return false; |
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232 | return connected(g); |
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233 | } |
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234 | template<class Graph> |
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235 | typename disable_if<typename Graph::UndirTag,bool>::type |
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236 | #endif |
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237 | euler(const Graph &g) |
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238 | { |
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239 | for(typename Graph::NodeIt n(g);n!=INVALID;++n) |
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240 | if(countInEdges(g,n)!=countOutEdges(g,n)) return false; |
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241 | return connected(g); |
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242 | } |
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243 | |
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244 | } |
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