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) 2003-2006 |
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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/invalid.h> |
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20 | #include<lemon/topology.h> |
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21 | #include <list> |
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22 | |
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23 | /// \ingroup topology |
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24 | /// \file |
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25 | /// \brief Euler tour |
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26 | /// |
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27 | ///This file provides an Euler tour iterator and ways to check |
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28 | ///if a graph is euler. |
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29 | |
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30 | |
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31 | namespace lemon { |
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32 | |
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33 | ///Euler iterator for directed graphs. |
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34 | |
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35 | /// \ingroup topology |
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36 | ///This iterator converts to the \c Edge type of the graph and using |
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37 | ///operator ++ it provides an Euler tour of a \e directed |
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38 | ///graph (if there exists). |
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39 | /// |
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40 | ///For example |
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41 | ///if the given graph if Euler (i.e it has only one nontrivial component |
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42 | ///and the in-degree is equal to the out-degree for all nodes), |
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43 | ///the following code will put the edges of \c g |
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44 | ///to the vector \c et according to an |
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45 | ///Euler tour of \c g. |
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46 | ///\code |
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47 | /// std::vector<ListGraph::Edge> et; |
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48 | /// for(EulerIt<ListGraph> e(g),e!=INVALID;++e) |
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49 | /// et.push_back(e); |
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50 | ///\endcode |
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51 | ///If \c g is not Euler then the resulted tour will not be full or closed. |
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52 | ///\sa UEulerIt |
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53 | ///\todo Test required |
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54 | template<class Graph> |
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55 | class EulerIt |
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56 | { |
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57 | typedef typename Graph::Node Node; |
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58 | typedef typename Graph::NodeIt NodeIt; |
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59 | typedef typename Graph::Edge Edge; |
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60 | typedef typename Graph::EdgeIt EdgeIt; |
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61 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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62 | typedef typename Graph::InEdgeIt InEdgeIt; |
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63 | |
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64 | const Graph &g; |
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65 | typename Graph::NodeMap<OutEdgeIt> nedge; |
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66 | std::list<Edge> euler; |
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67 | |
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68 | public: |
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69 | |
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70 | ///Constructor |
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71 | |
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72 | ///\param _g A directed graph. |
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73 | ///\param start The starting point of the tour. If it is not given |
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74 | /// the tour will start from the first node. |
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75 | EulerIt(const Graph &_g,typename Graph::Node start=INVALID) |
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76 | : g(_g), nedge(g) |
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77 | { |
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78 | if(start==INVALID) start=NodeIt(g); |
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79 | for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutEdgeIt(g,n); |
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80 | while(nedge[start]!=INVALID) { |
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81 | euler.push_back(nedge[start]); |
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82 | Node next=g.target(nedge[start]); |
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83 | ++nedge[start]; |
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84 | start=next; |
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85 | } |
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86 | } |
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87 | |
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88 | ///Edge Conversion |
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89 | operator Edge() { return euler.empty()?INVALID:euler.front(); } |
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90 | bool operator==(Invalid) { return euler.empty(); } |
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91 | bool operator!=(Invalid) { return !euler.empty(); } |
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92 | |
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93 | ///Next edge of the tour |
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94 | EulerIt &operator++() { |
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95 | Node s=g.target(euler.front()); |
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96 | euler.pop_front(); |
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97 | //This produces a warning.Strange. |
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98 | //std::list<Edge>::iterator next=euler.begin(); |
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99 | typename std::list<Edge>::iterator next=euler.begin(); |
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100 | while(nedge[s]!=INVALID) { |
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101 | euler.insert(next,nedge[s]); |
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102 | Node n=g.target(nedge[s]); |
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103 | ++nedge[s]; |
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104 | s=n; |
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105 | } |
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106 | return *this; |
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107 | } |
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108 | ///Postfix incrementation |
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109 | |
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110 | ///\warning This incrementation |
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111 | ///returns an \c Edge, not an \ref EulerIt, as one may |
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112 | ///expect. |
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113 | Edge operator++(int) |
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114 | { |
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115 | Edge e=*this; |
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116 | ++(*this); |
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117 | return e; |
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118 | } |
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119 | }; |
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120 | |
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121 | ///Euler iterator for undirected graphs. |
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122 | |
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123 | /// \ingroup topology |
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124 | ///This iterator converts to the \c Edge (or \cUEdge) |
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125 | ///type of the graph and using |
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126 | ///operator ++ it provides an Euler tour of an \undirected |
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127 | ///graph (if there exists). |
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128 | /// |
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129 | ///For example |
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130 | ///if the given graph if Euler (i.e it has only one nontrivial component |
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131 | ///and the degree of each node is even), |
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132 | ///the following code will print the edge IDs according to an |
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133 | ///Euler tour of \c g. |
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134 | ///\code |
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135 | /// for(UEulerIt<ListUGraph> e(g),e!=INVALID;++e) { |
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136 | /// std::cout << g.id(UEdge(e)) << std::eol; |
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137 | /// } |
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138 | ///\endcode |
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139 | ///Although the iterator provides an Euler tour of an undirected graph, |
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140 | ///in order to indicate the direction of the tour, UEulerIt |
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141 | ///returns directed edges (that convert to the undirected ones, of course). |
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142 | /// |
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143 | ///If \c g is not Euler then the resulted tour will not be full or closed. |
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144 | ///\sa EulerIt |
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145 | ///\todo Test required |
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146 | template<class Graph> |
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147 | class UEulerIt |
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148 | { |
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149 | typedef typename Graph::Node Node; |
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150 | typedef typename Graph::NodeIt NodeIt; |
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151 | typedef typename Graph::Edge Edge; |
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152 | typedef typename Graph::EdgeIt EdgeIt; |
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153 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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154 | typedef typename Graph::InEdgeIt InEdgeIt; |
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155 | |
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156 | const Graph &g; |
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157 | typename Graph::NodeMap<OutEdgeIt> nedge; |
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158 | typename Graph::UEdgeMap<bool> visited; |
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159 | std::list<Edge> euler; |
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160 | |
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161 | public: |
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162 | |
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163 | ///Constructor |
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164 | |
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165 | ///\param _g An undirected graph. |
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166 | ///\param start The starting point of the tour. If it is not given |
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167 | /// the tour will start from the first node. |
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168 | UEulerIt(const Graph &_g,typename Graph::Node start=INVALID) |
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169 | : g(_g), nedge(g), visited(g,false) |
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170 | { |
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171 | if(start==INVALID) start=NodeIt(g); |
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172 | for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutEdgeIt(g,n); |
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173 | while(nedge[start]!=INVALID) { |
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174 | euler.push_back(nedge[start]); |
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175 | Node next=g.target(nedge[start]); |
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176 | ++nedge[start]; |
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177 | start=next; while(nedge[start]!=INVALID && visited[nedge[start]]) ++nedge[start]; |
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178 | } |
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179 | } |
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180 | |
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181 | ///Edge Conversion |
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182 | operator Edge() { return euler.empty()?INVALID:euler.front(); } |
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183 | bool operator==(Invalid) { return euler.empty(); } |
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184 | bool operator!=(Invalid) { return !euler.empty(); } |
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185 | |
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186 | ///Next edge of the tour |
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187 | UEulerIt &operator++() { |
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188 | Node s=g.target(euler.front()); |
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189 | euler.pop_front(); |
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190 | typename std::list<Edge>::iterator next=euler.begin(); |
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191 | |
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192 | while(nedge[s]!=INVALID) { |
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193 | while(nedge[s]!=INVALID && visited[nedge[s]]) ++nedge[s]; |
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194 | if(nedge[s]==INVALID) break; |
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195 | else { |
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196 | euler.insert(next,nedge[s]); |
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197 | Node n=g.target(nedge[s]); |
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198 | ++nedge[s]; |
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199 | s=n; |
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200 | } |
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201 | } |
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202 | return *this; |
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203 | } |
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204 | |
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205 | ///Postfix incrementation |
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206 | |
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207 | ///\warning This incrementation |
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208 | ///returns an \c Edge, not an \ref UEulerIt, as one may |
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209 | ///expect. |
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210 | Edge operator++(int) |
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211 | { |
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212 | Edge e=*this; |
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213 | ++(*this); |
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214 | return e; |
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215 | } |
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216 | }; |
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217 | |
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218 | |
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219 | ///Checks if the graph is Euler |
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220 | |
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221 | /// \ingroup topology |
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222 | ///Checks if the graph is Euler. It works for both directed and |
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223 | ///undirected graphs. |
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224 | ///\note By definition, a directed graph is called \e Euler if |
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225 | ///and only if connected and the number of it is incoming and outgoing edges |
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226 | ///are the same for each node. |
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227 | ///Similarly, an undirected graph is called \e Euler if |
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228 | ///and only if it is connected and the number of incident edges is even |
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229 | ///for each node. <em>Therefore, there are graphs which are not Euler, but |
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230 | ///still have an Euler tour</em>. |
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231 | ///\todo Test required |
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232 | template<class Graph> |
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233 | #ifdef DOXYGEN |
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234 | bool |
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235 | #else |
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236 | typename enable_if<UndirectedTagIndicator<Graph>,bool>::type |
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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(countIncEdges(g,n)%2) return false; |
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241 | return connected(g); |
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242 | } |
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243 | template<class Graph> |
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244 | typename disable_if<UndirectedTagIndicator<Graph>,bool>::type |
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245 | #endif |
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246 | euler(const Graph &g) |
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247 | { |
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248 | for(typename Graph::NodeIt n(g);n!=INVALID;++n) |
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249 | if(countInEdges(g,n)!=countOutEdges(g,n)) return false; |
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250 | return connected(g); |
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251 | } |
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252 | |
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253 | } |
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