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) 2003-2010 |
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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_properties |
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28 | /// \file |
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29 | /// \brief Euler tour iterators and a function for checking the \e Eulerian |
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30 | /// property. |
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31 | /// |
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32 | ///This file provides Euler tour iterators and a function to check |
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33 | ///if a (di)graph is \e Eulerian. |
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34 | |
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35 | namespace lemon { |
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36 | |
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37 | ///Euler tour iterator for digraphs. |
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38 | |
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39 | /// \ingroup graph_properties |
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40 | ///This iterator provides an Euler tour (Eulerian circuit) of a \e directed |
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41 | ///graph (if there exists) and it converts to the \c Arc type of the digraph. |
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42 | /// |
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43 | ///For example, if the given digraph has an Euler tour (i.e it has only one |
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44 | ///non-trivial component and the in-degree is equal to the out-degree |
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45 | ///for all nodes), then the following code will put the arcs of \c g |
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46 | ///to the vector \c et according to an Euler tour of \c g. |
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47 | ///\code |
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48 | /// std::vector<ListDigraph::Arc> et; |
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49 | /// for(DiEulerIt<ListDigraph> e(g); e!=INVALID; ++e) |
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50 | /// et.push_back(e); |
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51 | ///\endcode |
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52 | ///If \c g has no Euler tour, then the resulted walk will not be closed |
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53 | ///or not contain all arcs. |
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54 | ///\sa EulerIt |
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55 | template<typename GR> |
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56 | class DiEulerIt |
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57 | { |
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58 | typedef typename GR::Node Node; |
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59 | typedef typename GR::NodeIt NodeIt; |
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60 | typedef typename GR::Arc Arc; |
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61 | typedef typename GR::ArcIt ArcIt; |
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62 | typedef typename GR::OutArcIt OutArcIt; |
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63 | typedef typename GR::InArcIt InArcIt; |
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64 | |
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65 | const GR &g; |
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66 | typename GR::template NodeMap<OutArcIt> narc; |
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67 | std::list<Arc> euler; |
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68 | |
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69 | public: |
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70 | |
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71 | ///Constructor |
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72 | |
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73 | ///Constructor. |
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74 | ///\param gr A digraph. |
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75 | ///\param start The starting point of the tour. If it is not given, |
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76 | ///the tour will start from the first node that has an outgoing arc. |
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77 | DiEulerIt(const GR &gr, typename GR::Node start = INVALID) |
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78 | : g(gr), narc(g) |
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79 | { |
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80 | if (start==INVALID) { |
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81 | NodeIt n(g); |
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82 | while (n!=INVALID && OutArcIt(g,n)==INVALID) ++n; |
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83 | start=n; |
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84 | } |
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85 | if (start!=INVALID) { |
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86 | for (NodeIt n(g); n!=INVALID; ++n) narc[n]=OutArcIt(g,n); |
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87 | while (narc[start]!=INVALID) { |
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88 | euler.push_back(narc[start]); |
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89 | Node next=g.target(narc[start]); |
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90 | ++narc[start]; |
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91 | start=next; |
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92 | } |
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93 | } |
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94 | } |
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95 | |
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96 | ///Arc conversion |
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97 | operator Arc() { return euler.empty()?INVALID:euler.front(); } |
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98 | ///Compare with \c INVALID |
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99 | bool operator==(Invalid) { return euler.empty(); } |
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100 | ///Compare with \c INVALID |
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101 | bool operator!=(Invalid) { return !euler.empty(); } |
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102 | |
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103 | ///Next arc of the tour |
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104 | |
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105 | ///Next arc of the tour |
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106 | /// |
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107 | DiEulerIt &operator++() { |
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108 | Node s=g.target(euler.front()); |
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109 | euler.pop_front(); |
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110 | typename std::list<Arc>::iterator next=euler.begin(); |
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111 | while(narc[s]!=INVALID) { |
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112 | euler.insert(next,narc[s]); |
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113 | Node n=g.target(narc[s]); |
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114 | ++narc[s]; |
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115 | s=n; |
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116 | } |
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117 | return *this; |
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118 | } |
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119 | ///Postfix incrementation |
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120 | |
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121 | /// Postfix incrementation. |
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122 | /// |
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123 | ///\warning This incrementation |
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124 | ///returns an \c Arc, not a \ref DiEulerIt, as one may |
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125 | ///expect. |
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126 | Arc operator++(int) |
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127 | { |
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128 | Arc e=*this; |
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129 | ++(*this); |
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130 | return e; |
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131 | } |
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132 | }; |
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133 | |
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134 | ///Euler tour iterator for graphs. |
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135 | |
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136 | /// \ingroup graph_properties |
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137 | ///This iterator provides an Euler tour (Eulerian circuit) of an |
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138 | ///\e undirected graph (if there exists) and it converts to the \c Arc |
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139 | ///and \c Edge types of the graph. |
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140 | /// |
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141 | ///For example, if the given graph has an Euler tour (i.e it has only one |
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142 | ///non-trivial component and the degree of each node is even), |
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143 | ///the following code will print the arc IDs according to an |
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144 | ///Euler tour of \c g. |
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145 | ///\code |
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146 | /// for(EulerIt<ListGraph> e(g); e!=INVALID; ++e) { |
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147 | /// std::cout << g.id(Edge(e)) << std::eol; |
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148 | /// } |
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149 | ///\endcode |
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150 | ///Although this iterator is for undirected graphs, it still returns |
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151 | ///arcs in order to indicate the direction of the tour. |
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152 | ///(But arcs convert to edges, of course.) |
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153 | /// |
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154 | ///If \c g has no Euler tour, then the resulted walk will not be closed |
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155 | ///or not contain all edges. |
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156 | template<typename GR> |
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157 | class EulerIt |
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158 | { |
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159 | typedef typename GR::Node Node; |
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160 | typedef typename GR::NodeIt NodeIt; |
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161 | typedef typename GR::Arc Arc; |
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162 | typedef typename GR::Edge Edge; |
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163 | typedef typename GR::ArcIt ArcIt; |
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164 | typedef typename GR::OutArcIt OutArcIt; |
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165 | typedef typename GR::InArcIt InArcIt; |
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166 | |
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167 | const GR &g; |
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168 | typename GR::template NodeMap<OutArcIt> narc; |
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169 | typename GR::template EdgeMap<bool> visited; |
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170 | std::list<Arc> euler; |
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171 | |
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172 | public: |
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173 | |
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174 | ///Constructor |
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175 | |
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176 | ///Constructor. |
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177 | ///\param gr A graph. |
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178 | ///\param start The starting point of the tour. If it is not given, |
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179 | ///the tour will start from the first node that has an incident edge. |
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180 | EulerIt(const GR &gr, typename GR::Node start = INVALID) |
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181 | : g(gr), narc(g), visited(g, false) |
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182 | { |
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183 | if (start==INVALID) { |
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184 | NodeIt n(g); |
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185 | while (n!=INVALID && OutArcIt(g,n)==INVALID) ++n; |
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186 | start=n; |
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187 | } |
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188 | if (start!=INVALID) { |
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189 | for (NodeIt n(g); n!=INVALID; ++n) narc[n]=OutArcIt(g,n); |
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190 | while(narc[start]!=INVALID) { |
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191 | euler.push_back(narc[start]); |
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192 | visited[narc[start]]=true; |
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193 | Node next=g.target(narc[start]); |
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194 | ++narc[start]; |
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195 | start=next; |
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196 | while(narc[start]!=INVALID && visited[narc[start]]) ++narc[start]; |
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197 | } |
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198 | } |
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199 | } |
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200 | |
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201 | ///Arc conversion |
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202 | operator Arc() const { return euler.empty()?INVALID:euler.front(); } |
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203 | ///Edge conversion |
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204 | operator Edge() const { return euler.empty()?INVALID:euler.front(); } |
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205 | ///Compare with \c INVALID |
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206 | bool operator==(Invalid) const { return euler.empty(); } |
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207 | ///Compare with \c INVALID |
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208 | bool operator!=(Invalid) const { return !euler.empty(); } |
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209 | |
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210 | ///Next arc of the tour |
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211 | |
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212 | ///Next arc of the tour |
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213 | /// |
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214 | EulerIt &operator++() { |
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215 | Node s=g.target(euler.front()); |
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216 | euler.pop_front(); |
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217 | typename std::list<Arc>::iterator next=euler.begin(); |
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218 | while(narc[s]!=INVALID) { |
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219 | while(narc[s]!=INVALID && visited[narc[s]]) ++narc[s]; |
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220 | if(narc[s]==INVALID) break; |
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221 | else { |
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222 | euler.insert(next,narc[s]); |
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223 | visited[narc[s]]=true; |
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224 | Node n=g.target(narc[s]); |
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225 | ++narc[s]; |
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226 | s=n; |
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227 | } |
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228 | } |
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229 | return *this; |
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230 | } |
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231 | |
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232 | ///Postfix incrementation |
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233 | |
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234 | /// Postfix incrementation. |
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235 | /// |
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236 | ///\warning This incrementation returns an \c Arc (which converts to |
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237 | ///an \c Edge), not an \ref EulerIt, as one may expect. |
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238 | Arc operator++(int) |
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239 | { |
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240 | Arc e=*this; |
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241 | ++(*this); |
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242 | return e; |
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243 | } |
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244 | }; |
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245 | |
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246 | |
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247 | ///Check if the given graph is Eulerian |
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248 | |
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249 | /// \ingroup graph_properties |
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250 | ///This function checks if the given graph is Eulerian. |
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251 | ///It works for both directed and undirected graphs. |
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252 | /// |
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253 | ///By definition, a digraph is called \e Eulerian if |
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254 | ///and only if it is connected and the number of incoming and outgoing |
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255 | ///arcs are the same for each node. |
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256 | ///Similarly, an undirected graph is called \e Eulerian if |
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257 | ///and only if it is connected and the number of incident edges is even |
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258 | ///for each node. |
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259 | /// |
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260 | ///\note There are (di)graphs that are not Eulerian, but still have an |
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261 | /// Euler tour, since they may contain isolated nodes. |
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262 | /// |
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263 | ///\sa DiEulerIt, EulerIt |
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264 | template<typename GR> |
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265 | #ifdef DOXYGEN |
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266 | bool |
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267 | #else |
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268 | typename enable_if<UndirectedTagIndicator<GR>,bool>::type |
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269 | eulerian(const GR &g) |
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270 | { |
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271 | for(typename GR::NodeIt n(g);n!=INVALID;++n) |
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272 | if(countIncEdges(g,n)%2) return false; |
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273 | return connected(g); |
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274 | } |
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275 | template<class GR> |
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276 | typename disable_if<UndirectedTagIndicator<GR>,bool>::type |
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277 | #endif |
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278 | eulerian(const GR &g) |
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279 | { |
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280 | for(typename GR::NodeIt n(g);n!=INVALID;++n) |
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281 | if(countInArcs(g,n)!=countOutArcs(g,n)) return false; |
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282 | return connected(undirector(g)); |
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283 | } |
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284 | |
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285 | } |
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286 | |
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287 | #endif |
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