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_FULL_GRAPH_H |
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20 | #define LEMON_FULL_GRAPH_H |
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21 | |
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22 | #include <lemon/core.h> |
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23 | #include <lemon/bits/graph_extender.h> |
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24 | |
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25 | ///\ingroup graphs |
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26 | ///\file |
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27 | ///\brief FullGraph and FullDigraph classes. |
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28 | |
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29 | namespace lemon { |
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30 | |
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31 | class FullDigraphBase { |
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32 | public: |
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33 | |
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34 | typedef FullDigraphBase Digraph; |
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35 | |
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36 | class Node; |
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37 | class Arc; |
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38 | |
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39 | protected: |
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40 | |
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41 | int _node_num; |
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42 | int _arc_num; |
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43 | |
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44 | FullDigraphBase() {} |
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45 | |
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46 | void construct(int n) { _node_num = n; _arc_num = n * n; } |
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47 | |
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48 | public: |
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49 | |
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50 | typedef True NodeNumTag; |
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51 | typedef True ArcNumTag; |
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52 | |
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53 | Node operator()(int ix) const { return Node(ix); } |
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54 | static int index(const Node& node) { return node._id; } |
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55 | |
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56 | Arc arc(const Node& s, const Node& t) const { |
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57 | return Arc(s._id * _node_num + t._id); |
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58 | } |
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59 | |
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60 | int nodeNum() const { return _node_num; } |
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61 | int arcNum() const { return _arc_num; } |
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62 | |
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63 | int maxNodeId() const { return _node_num - 1; } |
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64 | int maxArcId() const { return _arc_num - 1; } |
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65 | |
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66 | Node source(Arc arc) const { return arc._id / _node_num; } |
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67 | Node target(Arc arc) const { return arc._id % _node_num; } |
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68 | |
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69 | static int id(Node node) { return node._id; } |
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70 | static int id(Arc arc) { return arc._id; } |
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71 | |
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72 | static Node nodeFromId(int id) { return Node(id);} |
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73 | static Arc arcFromId(int id) { return Arc(id);} |
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74 | |
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75 | typedef True FindArcTag; |
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76 | |
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77 | Arc findArc(Node s, Node t, Arc prev = INVALID) const { |
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78 | return prev == INVALID ? arc(s, t) : INVALID; |
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79 | } |
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80 | |
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81 | class Node { |
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82 | friend class FullDigraphBase; |
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83 | |
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84 | protected: |
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85 | int _id; |
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86 | Node(int id) : _id(id) {} |
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87 | public: |
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88 | Node() {} |
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89 | Node (Invalid) : _id(-1) {} |
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90 | bool operator==(const Node node) const {return _id == node._id;} |
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91 | bool operator!=(const Node node) const {return _id != node._id;} |
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92 | bool operator<(const Node node) const {return _id < node._id;} |
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93 | }; |
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94 | |
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95 | class Arc { |
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96 | friend class FullDigraphBase; |
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97 | |
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98 | protected: |
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99 | int _id; // _node_num * source + target; |
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100 | |
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101 | Arc(int id) : _id(id) {} |
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102 | |
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103 | public: |
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104 | Arc() { } |
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105 | Arc (Invalid) { _id = -1; } |
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106 | bool operator==(const Arc arc) const {return _id == arc._id;} |
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107 | bool operator!=(const Arc arc) const {return _id != arc._id;} |
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108 | bool operator<(const Arc arc) const {return _id < arc._id;} |
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109 | }; |
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110 | |
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111 | void first(Node& node) const { |
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112 | node._id = _node_num - 1; |
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113 | } |
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114 | |
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115 | static void next(Node& node) { |
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116 | --node._id; |
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117 | } |
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118 | |
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119 | void first(Arc& arc) const { |
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120 | arc._id = _arc_num - 1; |
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121 | } |
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122 | |
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123 | static void next(Arc& arc) { |
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124 | --arc._id; |
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125 | } |
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126 | |
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127 | void firstOut(Arc& arc, const Node& node) const { |
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128 | arc._id = (node._id + 1) * _node_num - 1; |
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129 | } |
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130 | |
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131 | void nextOut(Arc& arc) const { |
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132 | if (arc._id % _node_num == 0) arc._id = 0; |
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133 | --arc._id; |
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134 | } |
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135 | |
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136 | void firstIn(Arc& arc, const Node& node) const { |
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137 | arc._id = _arc_num + node._id - _node_num; |
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138 | } |
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139 | |
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140 | void nextIn(Arc& arc) const { |
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141 | arc._id -= _node_num; |
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142 | if (arc._id < 0) arc._id = -1; |
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143 | } |
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144 | |
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145 | }; |
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146 | |
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147 | typedef DigraphExtender<FullDigraphBase> ExtendedFullDigraphBase; |
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148 | |
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149 | /// \ingroup graphs |
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150 | /// |
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151 | /// \brief A full digraph class. |
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152 | /// |
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153 | /// This is a simple and fast directed full graph implementation. |
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154 | /// From each node go arcs to each node (including the source node), |
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155 | /// therefore the number of the arcs in the digraph is the square of |
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156 | /// the node number. This digraph type is completely static, so you |
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157 | /// can neither add nor delete either arcs or nodes, and it needs |
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158 | /// constant space in memory. |
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159 | /// |
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160 | /// This class fully conforms to the \ref concepts::Digraph |
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161 | /// "Digraph concept". |
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162 | /// |
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163 | /// The \c FullDigraph and \c FullGraph classes are very similar, |
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164 | /// but there are two differences. While this class conforms only |
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165 | /// to the \ref concepts::Digraph "Digraph" concept, the \c FullGraph |
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166 | /// class conforms to the \ref concepts::Graph "Graph" concept, |
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167 | /// moreover \c FullGraph does not contain a loop arc for each |
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168 | /// node as \c FullDigraph does. |
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169 | /// |
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170 | /// \sa FullGraph |
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171 | class FullDigraph : public ExtendedFullDigraphBase { |
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172 | typedef ExtendedFullDigraphBase Parent; |
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173 | |
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174 | public: |
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175 | |
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176 | /// \brief Constructor |
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177 | FullDigraph() { construct(0); } |
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178 | |
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179 | /// \brief Constructor |
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180 | /// |
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181 | /// Constructor. |
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182 | /// \param n The number of the nodes. |
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183 | FullDigraph(int n) { construct(n); } |
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184 | |
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185 | /// \brief Resizes the digraph |
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186 | /// |
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187 | /// Resizes the digraph. The function will fully destroy and |
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188 | /// rebuild the digraph. This cause that the maps of the digraph will |
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189 | /// reallocated automatically and the previous values will be lost. |
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190 | void resize(int n) { |
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191 | Parent::notifier(Arc()).clear(); |
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192 | Parent::notifier(Node()).clear(); |
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193 | construct(n); |
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194 | Parent::notifier(Node()).build(); |
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195 | Parent::notifier(Arc()).build(); |
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196 | } |
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197 | |
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198 | /// \brief Returns the node with the given index. |
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199 | /// |
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200 | /// Returns the node with the given index. Since it is a static |
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201 | /// digraph its nodes can be indexed with integers from the range |
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202 | /// <tt>[0..nodeNum()-1]</tt>. |
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203 | /// \sa index() |
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204 | Node operator()(int ix) const { return Parent::operator()(ix); } |
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205 | |
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206 | /// \brief Returns the index of the given node. |
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207 | /// |
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208 | /// Returns the index of the given node. Since it is a static |
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209 | /// digraph its nodes can be indexed with integers from the range |
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210 | /// <tt>[0..nodeNum()-1]</tt>. |
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211 | /// \sa operator() |
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212 | static int index(const Node& node) { return Parent::index(node); } |
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213 | |
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214 | /// \brief Returns the arc connecting the given nodes. |
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215 | /// |
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216 | /// Returns the arc connecting the given nodes. |
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217 | Arc arc(const Node& u, const Node& v) const { |
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218 | return Parent::arc(u, v); |
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219 | } |
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220 | |
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221 | /// \brief Number of nodes. |
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222 | int nodeNum() const { return Parent::nodeNum(); } |
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223 | /// \brief Number of arcs. |
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224 | int arcNum() const { return Parent::arcNum(); } |
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225 | }; |
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226 | |
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227 | |
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228 | class FullGraphBase { |
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229 | public: |
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230 | |
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231 | typedef FullGraphBase Graph; |
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232 | |
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233 | class Node; |
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234 | class Arc; |
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235 | class Edge; |
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236 | |
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237 | protected: |
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238 | |
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239 | int _node_num; |
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240 | int _edge_num; |
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241 | |
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242 | FullGraphBase() {} |
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243 | |
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244 | void construct(int n) { _node_num = n; _edge_num = n * (n - 1) / 2; } |
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245 | |
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246 | int _uid(int e) const { |
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247 | int u = e / _node_num; |
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248 | int v = e % _node_num; |
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249 | return u < v ? u : _node_num - 2 - u; |
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250 | } |
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251 | |
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252 | int _vid(int e) const { |
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253 | int u = e / _node_num; |
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254 | int v = e % _node_num; |
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255 | return u < v ? v : _node_num - 1 - v; |
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256 | } |
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257 | |
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258 | void _uvid(int e, int& u, int& v) const { |
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259 | u = e / _node_num; |
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260 | v = e % _node_num; |
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261 | if (u >= v) { |
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262 | u = _node_num - 2 - u; |
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263 | v = _node_num - 1 - v; |
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264 | } |
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265 | } |
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266 | |
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267 | void _stid(int a, int& s, int& t) const { |
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268 | if ((a & 1) == 1) { |
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269 | _uvid(a >> 1, s, t); |
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270 | } else { |
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271 | _uvid(a >> 1, t, s); |
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272 | } |
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273 | } |
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274 | |
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275 | int _eid(int u, int v) const { |
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276 | if (u < (_node_num - 1) / 2) { |
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277 | return u * _node_num + v; |
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278 | } else { |
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279 | return (_node_num - 1 - u) * _node_num - v - 1; |
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280 | } |
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281 | } |
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282 | |
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283 | public: |
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284 | |
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285 | Node operator()(int ix) const { return Node(ix); } |
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286 | static int index(const Node& node) { return node._id; } |
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287 | |
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288 | Edge edge(const Node& u, const Node& v) const { |
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289 | if (u._id < v._id) { |
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290 | return Edge(_eid(u._id, v._id)); |
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291 | } else if (u._id != v._id) { |
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292 | return Edge(_eid(v._id, u._id)); |
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293 | } else { |
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294 | return INVALID; |
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295 | } |
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296 | } |
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297 | |
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298 | Arc arc(const Node& s, const Node& t) const { |
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299 | if (s._id < t._id) { |
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300 | return Arc((_eid(s._id, t._id) << 1) | 1); |
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301 | } else if (s._id != t._id) { |
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302 | return Arc(_eid(t._id, s._id) << 1); |
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303 | } else { |
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304 | return INVALID; |
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305 | } |
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306 | } |
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307 | |
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308 | typedef True NodeNumTag; |
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309 | typedef True ArcNumTag; |
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310 | typedef True EdgeNumTag; |
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311 | |
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312 | int nodeNum() const { return _node_num; } |
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313 | int arcNum() const { return 2 * _edge_num; } |
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314 | int edgeNum() const { return _edge_num; } |
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315 | |
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316 | static int id(Node node) { return node._id; } |
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317 | static int id(Arc arc) { return arc._id; } |
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318 | static int id(Edge edge) { return edge._id; } |
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319 | |
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320 | int maxNodeId() const { return _node_num-1; } |
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321 | int maxArcId() const { return 2 * _edge_num-1; } |
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322 | int maxEdgeId() const { return _edge_num-1; } |
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323 | |
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324 | static Node nodeFromId(int id) { return Node(id);} |
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325 | static Arc arcFromId(int id) { return Arc(id);} |
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326 | static Edge edgeFromId(int id) { return Edge(id);} |
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327 | |
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328 | Node u(Edge edge) const { |
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329 | return Node(_uid(edge._id)); |
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330 | } |
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331 | |
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332 | Node v(Edge edge) const { |
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333 | return Node(_vid(edge._id)); |
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334 | } |
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335 | |
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336 | Node source(Arc arc) const { |
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337 | return Node((arc._id & 1) == 1 ? |
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338 | _uid(arc._id >> 1) : _vid(arc._id >> 1)); |
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339 | } |
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340 | |
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341 | Node target(Arc arc) const { |
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342 | return Node((arc._id & 1) == 1 ? |
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343 | _vid(arc._id >> 1) : _uid(arc._id >> 1)); |
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344 | } |
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345 | |
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346 | typedef True FindEdgeTag; |
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347 | typedef True FindArcTag; |
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348 | |
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349 | Edge findEdge(Node u, Node v, Edge prev = INVALID) const { |
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350 | return prev != INVALID ? INVALID : edge(u, v); |
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351 | } |
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352 | |
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353 | Arc findArc(Node s, Node t, Arc prev = INVALID) const { |
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354 | return prev != INVALID ? INVALID : arc(s, t); |
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355 | } |
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356 | |
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357 | class Node { |
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358 | friend class FullGraphBase; |
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359 | |
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360 | protected: |
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361 | int _id; |
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362 | Node(int id) : _id(id) {} |
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363 | public: |
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364 | Node() {} |
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365 | Node (Invalid) { _id = -1; } |
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366 | bool operator==(const Node node) const {return _id == node._id;} |
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367 | bool operator!=(const Node node) const {return _id != node._id;} |
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368 | bool operator<(const Node node) const {return _id < node._id;} |
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369 | }; |
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370 | |
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371 | class Edge { |
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372 | friend class FullGraphBase; |
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373 | friend class Arc; |
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374 | |
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375 | protected: |
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376 | int _id; |
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377 | |
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378 | Edge(int id) : _id(id) {} |
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379 | |
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380 | public: |
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381 | Edge() { } |
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382 | Edge (Invalid) { _id = -1; } |
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383 | |
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384 | bool operator==(const Edge edge) const {return _id == edge._id;} |
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385 | bool operator!=(const Edge edge) const {return _id != edge._id;} |
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386 | bool operator<(const Edge edge) const {return _id < edge._id;} |
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387 | }; |
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388 | |
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389 | class Arc { |
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390 | friend class FullGraphBase; |
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391 | |
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392 | protected: |
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393 | int _id; |
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394 | |
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395 | Arc(int id) : _id(id) {} |
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396 | |
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397 | public: |
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398 | Arc() { } |
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399 | Arc (Invalid) { _id = -1; } |
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400 | |
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401 | operator Edge() const { return Edge(_id != -1 ? (_id >> 1) : -1); } |
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402 | |
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403 | bool operator==(const Arc arc) const {return _id == arc._id;} |
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404 | bool operator!=(const Arc arc) const {return _id != arc._id;} |
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405 | bool operator<(const Arc arc) const {return _id < arc._id;} |
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406 | }; |
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407 | |
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408 | static bool direction(Arc arc) { |
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409 | return (arc._id & 1) == 1; |
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410 | } |
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411 | |
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412 | static Arc direct(Edge edge, bool dir) { |
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413 | return Arc((edge._id << 1) | (dir ? 1 : 0)); |
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414 | } |
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415 | |
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416 | void first(Node& node) const { |
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417 | node._id = _node_num - 1; |
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418 | } |
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419 | |
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420 | static void next(Node& node) { |
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421 | --node._id; |
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422 | } |
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423 | |
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424 | void first(Arc& arc) const { |
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425 | arc._id = (_edge_num << 1) - 1; |
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426 | } |
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427 | |
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428 | static void next(Arc& arc) { |
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429 | --arc._id; |
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430 | } |
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431 | |
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432 | void first(Edge& edge) const { |
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433 | edge._id = _edge_num - 1; |
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434 | } |
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435 | |
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436 | static void next(Edge& edge) { |
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437 | --edge._id; |
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438 | } |
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439 | |
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440 | void firstOut(Arc& arc, const Node& node) const { |
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441 | int s = node._id, t = _node_num - 1; |
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442 | if (s < t) { |
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443 | arc._id = (_eid(s, t) << 1) | 1; |
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444 | } else { |
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445 | --t; |
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446 | arc._id = (t != -1 ? (_eid(t, s) << 1) : -1); |
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447 | } |
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448 | } |
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449 | |
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450 | void nextOut(Arc& arc) const { |
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451 | int s, t; |
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452 | _stid(arc._id, s, t); |
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453 | --t; |
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454 | if (s < t) { |
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455 | arc._id = (_eid(s, t) << 1) | 1; |
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456 | } else { |
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457 | if (s == t) --t; |
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458 | arc._id = (t != -1 ? (_eid(t, s) << 1) : -1); |
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459 | } |
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460 | } |
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461 | |
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462 | void firstIn(Arc& arc, const Node& node) const { |
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463 | int s = _node_num - 1, t = node._id; |
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464 | if (s > t) { |
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465 | arc._id = (_eid(t, s) << 1); |
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466 | } else { |
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467 | --s; |
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468 | arc._id = (s != -1 ? (_eid(s, t) << 1) | 1 : -1); |
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469 | } |
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470 | } |
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471 | |
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472 | void nextIn(Arc& arc) const { |
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473 | int s, t; |
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474 | _stid(arc._id, s, t); |
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475 | --s; |
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476 | if (s > t) { |
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477 | arc._id = (_eid(t, s) << 1); |
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478 | } else { |
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479 | if (s == t) --s; |
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480 | arc._id = (s != -1 ? (_eid(s, t) << 1) | 1 : -1); |
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481 | } |
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482 | } |
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483 | |
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484 | void firstInc(Edge& edge, bool& dir, const Node& node) const { |
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485 | int u = node._id, v = _node_num - 1; |
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486 | if (u < v) { |
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487 | edge._id = _eid(u, v); |
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488 | dir = true; |
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489 | } else { |
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490 | --v; |
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491 | edge._id = (v != -1 ? _eid(v, u) : -1); |
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492 | dir = false; |
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493 | } |
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494 | } |
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495 | |
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496 | void nextInc(Edge& edge, bool& dir) const { |
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497 | int u, v; |
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498 | if (dir) { |
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499 | _uvid(edge._id, u, v); |
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500 | --v; |
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501 | if (u < v) { |
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502 | edge._id = _eid(u, v); |
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503 | } else { |
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504 | --v; |
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505 | edge._id = (v != -1 ? _eid(v, u) : -1); |
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506 | dir = false; |
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507 | } |
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508 | } else { |
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509 | _uvid(edge._id, v, u); |
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510 | --v; |
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511 | edge._id = (v != -1 ? _eid(v, u) : -1); |
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512 | } |
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513 | } |
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514 | |
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515 | }; |
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516 | |
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517 | typedef GraphExtender<FullGraphBase> ExtendedFullGraphBase; |
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518 | |
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519 | /// \ingroup graphs |
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520 | /// |
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521 | /// \brief An undirected full graph class. |
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522 | /// |
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523 | /// This is a simple and fast undirected full graph |
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524 | /// implementation. From each node go edge to each other node, |
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525 | /// therefore the number of edges in the graph is \f$n(n-1)/2\f$. |
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526 | /// This graph type is completely static, so you can neither |
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527 | /// add nor delete either edges or nodes, and it needs constant |
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528 | /// space in memory. |
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529 | /// |
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530 | /// This class fully conforms to the \ref concepts::Graph "Graph concept". |
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531 | /// |
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532 | /// The \c FullGraph and \c FullDigraph classes are very similar, |
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533 | /// but there are two differences. While the \c FullDigraph class |
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534 | /// conforms only to the \ref concepts::Digraph "Digraph" concept, |
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535 | /// this class conforms to the \ref concepts::Graph "Graph" concept, |
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536 | /// moreover \c FullGraph does not contain a loop arc for each |
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537 | /// node as \c FullDigraph does. |
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538 | /// |
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539 | /// \sa FullDigraph |
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540 | class FullGraph : public ExtendedFullGraphBase { |
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541 | typedef ExtendedFullGraphBase Parent; |
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542 | |
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543 | public: |
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544 | |
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545 | /// \brief Constructor |
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546 | FullGraph() { construct(0); } |
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547 | |
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548 | /// \brief Constructor |
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549 | /// |
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550 | /// Constructor. |
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551 | /// \param n The number of the nodes. |
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552 | FullGraph(int n) { construct(n); } |
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553 | |
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554 | /// \brief Resizes the graph |
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555 | /// |
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556 | /// Resizes the graph. The function will fully destroy and |
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557 | /// rebuild the graph. This cause that the maps of the graph will |
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558 | /// reallocated automatically and the previous values will be lost. |
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559 | void resize(int n) { |
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560 | Parent::notifier(Arc()).clear(); |
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561 | Parent::notifier(Edge()).clear(); |
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562 | Parent::notifier(Node()).clear(); |
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563 | construct(n); |
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564 | Parent::notifier(Node()).build(); |
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565 | Parent::notifier(Edge()).build(); |
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566 | Parent::notifier(Arc()).build(); |
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567 | } |
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568 | |
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569 | /// \brief Returns the node with the given index. |
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570 | /// |
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571 | /// Returns the node with the given index. Since it is a static |
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572 | /// graph its nodes can be indexed with integers from the range |
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573 | /// <tt>[0..nodeNum()-1]</tt>. |
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574 | /// \sa index() |
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575 | Node operator()(int ix) const { return Parent::operator()(ix); } |
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576 | |
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577 | /// \brief Returns the index of the given node. |
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578 | /// |
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579 | /// Returns the index of the given node. Since it is a static |
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580 | /// graph its nodes can be indexed with integers from the range |
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581 | /// <tt>[0..nodeNum()-1]</tt>. |
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582 | /// \sa operator() |
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583 | static int index(const Node& node) { return Parent::index(node); } |
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584 | |
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585 | /// \brief Returns the arc connecting the given nodes. |
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586 | /// |
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587 | /// Returns the arc connecting the given nodes. |
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588 | Arc arc(const Node& s, const Node& t) const { |
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589 | return Parent::arc(s, t); |
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590 | } |
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591 | |
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592 | /// \brief Returns the edge connects the given nodes. |
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593 | /// |
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594 | /// Returns the edge connects the given nodes. |
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595 | Edge edge(const Node& u, const Node& v) const { |
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596 | return Parent::edge(u, v); |
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597 | } |
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598 | |
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599 | /// \brief Number of nodes. |
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600 | int nodeNum() const { return Parent::nodeNum(); } |
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601 | /// \brief Number of arcs. |
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602 | int arcNum() const { return Parent::arcNum(); } |
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603 | /// \brief Number of edges. |
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604 | int edgeNum() const { return Parent::edgeNum(); } |
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605 | |
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606 | }; |
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607 | |
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608 | |
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609 | } //namespace lemon |
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610 | |
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611 | |
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612 | #endif //LEMON_FULL_GRAPH_H |
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