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_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 FullDigraph and FullGraph 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 directed full graph class. |
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152 | /// |
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153 | /// FullDigraph is a simple and fast implmenetation of directed full |
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154 | /// (complete) graphs. It contains an arc from each node to each node |
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155 | /// (including a loop for each node), therefore the number of arcs |
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156 | /// is the square of the number of nodes. |
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157 | /// This class is completely static and it needs constant memory space. |
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158 | /// Thus you can neither add nor delete nodes or arcs, however |
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159 | /// the structure can be resized using resize(). |
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160 | /// |
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161 | /// This type fully conforms to the \ref concepts::Digraph "Digraph concept". |
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162 | /// Most of its member functions and nested classes are documented |
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163 | /// only in the concept class. |
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164 | /// |
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165 | /// This class provides constant time counting for nodes and arcs. |
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166 | /// |
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167 | /// \note FullDigraph and FullGraph classes are very similar, |
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168 | /// but there are two differences. While this class conforms only |
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169 | /// to the \ref concepts::Digraph "Digraph" concept, FullGraph |
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170 | /// conforms to the \ref concepts::Graph "Graph" concept, |
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171 | /// moreover FullGraph does not contain a loop for each |
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172 | /// node as this class does. |
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173 | /// |
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174 | /// \sa FullGraph |
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175 | class FullDigraph : public ExtendedFullDigraphBase { |
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176 | typedef ExtendedFullDigraphBase Parent; |
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177 | |
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178 | public: |
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179 | |
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180 | /// \brief Default constructor. |
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181 | /// |
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182 | /// Default constructor. The number of nodes and arcs will be zero. |
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183 | FullDigraph() { construct(0); } |
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184 | |
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185 | /// \brief Constructor |
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186 | /// |
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187 | /// Constructor. |
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188 | /// \param n The number of the nodes. |
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189 | FullDigraph(int n) { construct(n); } |
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190 | |
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191 | /// \brief Resizes the digraph |
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192 | /// |
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193 | /// This function resizes the digraph. It fully destroys and |
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194 | /// rebuilds the structure, therefore the maps of the digraph will be |
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195 | /// reallocated automatically and the previous values will be lost. |
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196 | void resize(int n) { |
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197 | Parent::notifier(Arc()).clear(); |
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198 | Parent::notifier(Node()).clear(); |
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199 | construct(n); |
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200 | Parent::notifier(Node()).build(); |
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201 | Parent::notifier(Arc()).build(); |
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202 | } |
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203 | |
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204 | /// \brief Returns the node with the given index. |
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205 | /// |
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206 | /// Returns the node with the given index. Since this structure is |
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207 | /// completely static, the nodes can be indexed with integers from |
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208 | /// the range <tt>[0..nodeNum()-1]</tt>. |
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209 | /// The index of a node is the same as its ID. |
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210 | /// \sa index() |
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211 | Node operator()(int ix) const { return Parent::operator()(ix); } |
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212 | |
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213 | /// \brief Returns the index of the given node. |
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214 | /// |
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215 | /// Returns the index of the given node. Since this structure is |
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216 | /// completely static, the nodes can be indexed with integers from |
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217 | /// the range <tt>[0..nodeNum()-1]</tt>. |
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218 | /// The index of a node is the same as its ID. |
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219 | /// \sa operator()() |
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220 | static int index(const Node& node) { return Parent::index(node); } |
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221 | |
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222 | /// \brief Returns the arc connecting the given nodes. |
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223 | /// |
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224 | /// Returns the arc connecting the given nodes. |
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225 | Arc arc(Node u, Node v) const { |
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226 | return Parent::arc(u, v); |
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227 | } |
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228 | |
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229 | /// \brief Number of nodes. |
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230 | int nodeNum() const { return Parent::nodeNum(); } |
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231 | /// \brief Number of arcs. |
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232 | int arcNum() const { return Parent::arcNum(); } |
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233 | }; |
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234 | |
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235 | |
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236 | class FullGraphBase { |
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237 | public: |
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238 | |
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239 | typedef FullGraphBase Graph; |
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240 | |
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241 | class Node; |
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242 | class Arc; |
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243 | class Edge; |
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244 | |
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245 | protected: |
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246 | |
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247 | int _node_num; |
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248 | int _edge_num; |
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249 | |
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250 | FullGraphBase() {} |
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251 | |
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252 | void construct(int n) { _node_num = n; _edge_num = n * (n - 1) / 2; } |
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253 | |
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254 | int _uid(int e) const { |
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255 | int u = e / _node_num; |
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256 | int v = e % _node_num; |
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257 | return u < v ? u : _node_num - 2 - u; |
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258 | } |
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259 | |
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260 | int _vid(int e) const { |
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261 | int u = e / _node_num; |
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262 | int v = e % _node_num; |
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263 | return u < v ? v : _node_num - 1 - v; |
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264 | } |
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265 | |
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266 | void _uvid(int e, int& u, int& v) const { |
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267 | u = e / _node_num; |
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268 | v = e % _node_num; |
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269 | if (u >= v) { |
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270 | u = _node_num - 2 - u; |
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271 | v = _node_num - 1 - v; |
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272 | } |
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273 | } |
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274 | |
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275 | void _stid(int a, int& s, int& t) const { |
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276 | if ((a & 1) == 1) { |
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277 | _uvid(a >> 1, s, t); |
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278 | } else { |
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279 | _uvid(a >> 1, t, s); |
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280 | } |
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281 | } |
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282 | |
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283 | int _eid(int u, int v) const { |
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284 | if (u < (_node_num - 1) / 2) { |
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285 | return u * _node_num + v; |
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286 | } else { |
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287 | return (_node_num - 1 - u) * _node_num - v - 1; |
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288 | } |
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289 | } |
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290 | |
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291 | public: |
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292 | |
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293 | Node operator()(int ix) const { return Node(ix); } |
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294 | static int index(const Node& node) { return node._id; } |
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295 | |
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296 | Edge edge(const Node& u, const Node& v) const { |
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297 | if (u._id < v._id) { |
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298 | return Edge(_eid(u._id, v._id)); |
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299 | } else if (u._id != v._id) { |
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300 | return Edge(_eid(v._id, u._id)); |
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301 | } else { |
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302 | return INVALID; |
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303 | } |
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304 | } |
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305 | |
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306 | Arc arc(const Node& s, const Node& t) const { |
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307 | if (s._id < t._id) { |
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308 | return Arc((_eid(s._id, t._id) << 1) | 1); |
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309 | } else if (s._id != t._id) { |
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310 | return Arc(_eid(t._id, s._id) << 1); |
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311 | } else { |
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312 | return INVALID; |
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313 | } |
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314 | } |
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315 | |
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316 | typedef True NodeNumTag; |
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317 | typedef True ArcNumTag; |
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318 | typedef True EdgeNumTag; |
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319 | |
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320 | int nodeNum() const { return _node_num; } |
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321 | int arcNum() const { return 2 * _edge_num; } |
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322 | int edgeNum() const { return _edge_num; } |
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323 | |
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324 | static int id(Node node) { return node._id; } |
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325 | static int id(Arc arc) { return arc._id; } |
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326 | static int id(Edge edge) { return edge._id; } |
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327 | |
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328 | int maxNodeId() const { return _node_num-1; } |
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329 | int maxArcId() const { return 2 * _edge_num-1; } |
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330 | int maxEdgeId() const { return _edge_num-1; } |
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331 | |
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332 | static Node nodeFromId(int id) { return Node(id);} |
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333 | static Arc arcFromId(int id) { return Arc(id);} |
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334 | static Edge edgeFromId(int id) { return Edge(id);} |
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335 | |
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336 | Node u(Edge edge) const { |
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337 | return Node(_uid(edge._id)); |
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338 | } |
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339 | |
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340 | Node v(Edge edge) const { |
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341 | return Node(_vid(edge._id)); |
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342 | } |
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343 | |
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344 | Node source(Arc arc) const { |
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345 | return Node((arc._id & 1) == 1 ? |
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346 | _uid(arc._id >> 1) : _vid(arc._id >> 1)); |
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347 | } |
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348 | |
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349 | Node target(Arc arc) const { |
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350 | return Node((arc._id & 1) == 1 ? |
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351 | _vid(arc._id >> 1) : _uid(arc._id >> 1)); |
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352 | } |
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353 | |
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354 | typedef True FindEdgeTag; |
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355 | typedef True FindArcTag; |
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356 | |
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357 | Edge findEdge(Node u, Node v, Edge prev = INVALID) const { |
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358 | return prev != INVALID ? INVALID : edge(u, v); |
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359 | } |
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360 | |
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361 | Arc findArc(Node s, Node t, Arc prev = INVALID) const { |
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362 | return prev != INVALID ? INVALID : arc(s, t); |
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363 | } |
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364 | |
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365 | class Node { |
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366 | friend class FullGraphBase; |
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367 | |
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368 | protected: |
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369 | int _id; |
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370 | Node(int id) : _id(id) {} |
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371 | public: |
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372 | Node() {} |
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373 | Node (Invalid) { _id = -1; } |
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374 | bool operator==(const Node node) const {return _id == node._id;} |
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375 | bool operator!=(const Node node) const {return _id != node._id;} |
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376 | bool operator<(const Node node) const {return _id < node._id;} |
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377 | }; |
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378 | |
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379 | class Edge { |
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380 | friend class FullGraphBase; |
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381 | friend class Arc; |
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382 | |
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383 | protected: |
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384 | int _id; |
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385 | |
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386 | Edge(int id) : _id(id) {} |
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387 | |
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388 | public: |
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389 | Edge() { } |
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390 | Edge (Invalid) { _id = -1; } |
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391 | |
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392 | bool operator==(const Edge edge) const {return _id == edge._id;} |
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393 | bool operator!=(const Edge edge) const {return _id != edge._id;} |
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394 | bool operator<(const Edge edge) const {return _id < edge._id;} |
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395 | }; |
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396 | |
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397 | class Arc { |
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398 | friend class FullGraphBase; |
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399 | |
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400 | protected: |
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401 | int _id; |
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402 | |
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403 | Arc(int id) : _id(id) {} |
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404 | |
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405 | public: |
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406 | Arc() { } |
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407 | Arc (Invalid) { _id = -1; } |
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408 | |
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409 | operator Edge() const { return Edge(_id != -1 ? (_id >> 1) : -1); } |
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410 | |
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411 | bool operator==(const Arc arc) const {return _id == arc._id;} |
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412 | bool operator!=(const Arc arc) const {return _id != arc._id;} |
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413 | bool operator<(const Arc arc) const {return _id < arc._id;} |
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414 | }; |
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415 | |
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416 | static bool direction(Arc arc) { |
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417 | return (arc._id & 1) == 1; |
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418 | } |
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419 | |
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420 | static Arc direct(Edge edge, bool dir) { |
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421 | return Arc((edge._id << 1) | (dir ? 1 : 0)); |
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422 | } |
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423 | |
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424 | void first(Node& node) const { |
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425 | node._id = _node_num - 1; |
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426 | } |
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427 | |
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428 | static void next(Node& node) { |
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429 | --node._id; |
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430 | } |
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431 | |
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432 | void first(Arc& arc) const { |
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433 | arc._id = (_edge_num << 1) - 1; |
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434 | } |
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435 | |
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436 | static void next(Arc& arc) { |
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437 | --arc._id; |
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438 | } |
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439 | |
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440 | void first(Edge& edge) const { |
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441 | edge._id = _edge_num - 1; |
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442 | } |
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443 | |
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444 | static void next(Edge& edge) { |
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445 | --edge._id; |
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446 | } |
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447 | |
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448 | void firstOut(Arc& arc, const Node& node) const { |
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449 | int s = node._id, t = _node_num - 1; |
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450 | if (s < t) { |
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451 | arc._id = (_eid(s, t) << 1) | 1; |
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452 | } else { |
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453 | --t; |
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454 | arc._id = (t != -1 ? (_eid(t, s) << 1) : -1); |
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455 | } |
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456 | } |
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457 | |
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458 | void nextOut(Arc& arc) const { |
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459 | int s, t; |
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460 | _stid(arc._id, s, t); |
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461 | --t; |
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462 | if (s < t) { |
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463 | arc._id = (_eid(s, t) << 1) | 1; |
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464 | } else { |
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465 | if (s == t) --t; |
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466 | arc._id = (t != -1 ? (_eid(t, s) << 1) : -1); |
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467 | } |
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468 | } |
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469 | |
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470 | void firstIn(Arc& arc, const Node& node) const { |
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471 | int s = _node_num - 1, t = node._id; |
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472 | if (s > t) { |
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473 | arc._id = (_eid(t, s) << 1); |
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474 | } else { |
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475 | --s; |
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476 | arc._id = (s != -1 ? (_eid(s, t) << 1) | 1 : -1); |
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477 | } |
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478 | } |
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479 | |
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480 | void nextIn(Arc& arc) const { |
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481 | int s, t; |
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482 | _stid(arc._id, s, t); |
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483 | --s; |
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484 | if (s > t) { |
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485 | arc._id = (_eid(t, s) << 1); |
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486 | } else { |
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487 | if (s == t) --s; |
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488 | arc._id = (s != -1 ? (_eid(s, t) << 1) | 1 : -1); |
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489 | } |
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490 | } |
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491 | |
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492 | void firstInc(Edge& edge, bool& dir, const Node& node) const { |
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493 | int u = node._id, v = _node_num - 1; |
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494 | if (u < v) { |
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495 | edge._id = _eid(u, v); |
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496 | dir = true; |
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497 | } else { |
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498 | --v; |
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499 | edge._id = (v != -1 ? _eid(v, u) : -1); |
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500 | dir = false; |
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501 | } |
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502 | } |
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503 | |
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504 | void nextInc(Edge& edge, bool& dir) const { |
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505 | int u, v; |
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506 | if (dir) { |
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507 | _uvid(edge._id, u, v); |
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508 | --v; |
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509 | if (u < v) { |
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510 | edge._id = _eid(u, v); |
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511 | } else { |
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512 | --v; |
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513 | edge._id = (v != -1 ? _eid(v, u) : -1); |
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514 | dir = false; |
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515 | } |
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516 | } else { |
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517 | _uvid(edge._id, v, u); |
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518 | --v; |
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519 | edge._id = (v != -1 ? _eid(v, u) : -1); |
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520 | } |
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521 | } |
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522 | |
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523 | }; |
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524 | |
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525 | typedef GraphExtender<FullGraphBase> ExtendedFullGraphBase; |
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526 | |
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527 | /// \ingroup graphs |
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528 | /// |
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529 | /// \brief An undirected full graph class. |
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530 | /// |
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531 | /// FullGraph is a simple and fast implmenetation of undirected full |
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532 | /// (complete) graphs. It contains an edge between every distinct pair |
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533 | /// of nodes, therefore the number of edges is <tt>n(n-1)/2</tt>. |
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534 | /// This class is completely static and it needs constant memory space. |
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535 | /// Thus you can neither add nor delete nodes or edges, however |
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536 | /// the structure can be resized using resize(). |
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537 | /// |
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538 | /// This type fully conforms to the \ref concepts::Graph "Graph concept". |
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539 | /// Most of its member functions and nested classes are documented |
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540 | /// only in the concept class. |
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541 | /// |
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542 | /// This class provides constant time counting for nodes, edges and arcs. |
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543 | /// |
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544 | /// \note FullDigraph and FullGraph classes are very similar, |
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545 | /// but there are two differences. While FullDigraph |
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546 | /// conforms only to the \ref concepts::Digraph "Digraph" concept, |
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547 | /// this class conforms to the \ref concepts::Graph "Graph" concept, |
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548 | /// moreover this class does not contain a loop for each |
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549 | /// node as FullDigraph does. |
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550 | /// |
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551 | /// \sa FullDigraph |
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552 | class FullGraph : public ExtendedFullGraphBase { |
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553 | typedef ExtendedFullGraphBase Parent; |
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554 | |
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555 | public: |
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556 | |
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557 | /// \brief Default constructor. |
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558 | /// |
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559 | /// Default constructor. The number of nodes and edges will be zero. |
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560 | FullGraph() { construct(0); } |
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561 | |
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562 | /// \brief Constructor |
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563 | /// |
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564 | /// Constructor. |
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565 | /// \param n The number of the nodes. |
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566 | FullGraph(int n) { construct(n); } |
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567 | |
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568 | /// \brief Resizes the graph |
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569 | /// |
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570 | /// This function resizes the graph. It fully destroys and |
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571 | /// rebuilds the structure, therefore the maps of the graph will be |
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572 | /// reallocated automatically and the previous values will be lost. |
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573 | void resize(int n) { |
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574 | Parent::notifier(Arc()).clear(); |
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575 | Parent::notifier(Edge()).clear(); |
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576 | Parent::notifier(Node()).clear(); |
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577 | construct(n); |
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578 | Parent::notifier(Node()).build(); |
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579 | Parent::notifier(Edge()).build(); |
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580 | Parent::notifier(Arc()).build(); |
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581 | } |
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582 | |
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583 | /// \brief Returns the node with the given index. |
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584 | /// |
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585 | /// Returns the node with the given index. Since this structure is |
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586 | /// completely static, the nodes can be indexed with integers from |
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587 | /// the range <tt>[0..nodeNum()-1]</tt>. |
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588 | /// The index of a node is the same as its ID. |
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589 | /// \sa index() |
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590 | Node operator()(int ix) const { return Parent::operator()(ix); } |
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591 | |
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592 | /// \brief Returns the index of the given node. |
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593 | /// |
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594 | /// Returns the index of the given node. Since this structure is |
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595 | /// completely static, the nodes can be indexed with integers from |
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596 | /// the range <tt>[0..nodeNum()-1]</tt>. |
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597 | /// The index of a node is the same as its ID. |
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598 | /// \sa operator()() |
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599 | static int index(const Node& node) { return Parent::index(node); } |
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600 | |
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601 | /// \brief Returns the arc connecting the given nodes. |
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602 | /// |
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603 | /// Returns the arc connecting the given nodes. |
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604 | Arc arc(Node s, Node t) const { |
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605 | return Parent::arc(s, t); |
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606 | } |
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607 | |
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608 | /// \brief Returns the edge connecting the given nodes. |
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609 | /// |
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610 | /// Returns the edge connecting the given nodes. |
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611 | Edge edge(Node u, Node v) const { |
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612 | return Parent::edge(u, v); |
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613 | } |
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614 | |
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615 | /// \brief Number of nodes. |
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616 | int nodeNum() const { return Parent::nodeNum(); } |
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617 | /// \brief Number of arcs. |
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618 | int arcNum() const { return Parent::arcNum(); } |
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619 | /// \brief Number of edges. |
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620 | int edgeNum() const { return Parent::edgeNum(); } |
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621 | |
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622 | }; |
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623 | |
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624 | |
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625 | } //namespace lemon |
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626 | |
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627 | |
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628 | #endif //LEMON_FULL_GRAPH_H |
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