1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2006 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef HYPERCUBE_GRAPH_H |
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20 | #define HYPERCUBE_GRAPH_H |
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21 | |
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22 | #include <iostream> |
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23 | #include <vector> |
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24 | #include <lemon/bits/invalid.h> |
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25 | #include <lemon/bits/utility.h> |
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26 | #include <lemon/error.h> |
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27 | |
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28 | #include <lemon/bits/base_extender.h> |
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29 | #include <lemon/bits/graph_extender.h> |
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30 | |
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31 | ///\ingroup graphs |
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32 | ///\file |
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33 | ///\brief HyperCubeGraph class. |
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34 | |
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35 | namespace lemon { |
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36 | |
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37 | /// \brief Base graph for HyperCubeGraph. |
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38 | /// |
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39 | /// Base graph for hyper-cube graph. It describes some member functions |
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40 | /// which can be used in the HyperCubeGraph. |
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41 | /// |
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42 | /// \warning Always use the HyperCubeGraph instead of this. |
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43 | /// \see HyperCubeGraph |
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44 | class HyperCubeGraphBase { |
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45 | |
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46 | public: |
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47 | |
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48 | typedef HyperCubeGraphBase Graph; |
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49 | |
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50 | class Node; |
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51 | class Edge; |
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52 | |
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53 | public: |
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54 | |
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55 | HyperCubeGraphBase() {} |
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56 | |
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57 | protected: |
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58 | |
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59 | /// \brief Creates a hypercube graph with the given size. |
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60 | /// |
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61 | /// Creates a hypercube graph with the given size. |
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62 | void construct(int dim) { |
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63 | _dim = dim; |
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64 | _nodeNum = 1 << dim; |
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65 | } |
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66 | |
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67 | public: |
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68 | |
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69 | |
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70 | typedef True NodeNumTag; |
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71 | typedef True EdgeNumTag; |
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72 | |
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73 | ///Number of nodes. |
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74 | int nodeNum() const { return _nodeNum; } |
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75 | ///Number of edges. |
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76 | int edgeNum() const { return _nodeNum * _dim; } |
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77 | |
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78 | /// Maximum node ID. |
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79 | |
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80 | /// Maximum node ID. |
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81 | ///\sa id(Node) |
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82 | int maxNodeId() const { return nodeNum() - 1; } |
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83 | /// Maximum edge ID. |
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84 | |
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85 | /// Maximum edge ID. |
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86 | ///\sa id(Edge) |
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87 | int maxEdgeId() const { return edgeNum() - 1; } |
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88 | |
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89 | /// \brief Gives back the source node of an edge. |
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90 | /// |
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91 | /// Gives back the source node of an edge. |
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92 | Node source(Edge e) const { |
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93 | return e.id / _dim; |
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94 | } |
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95 | |
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96 | /// \brief Gives back the target node of an edge. |
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97 | /// |
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98 | /// Gives back the target node of an edge. |
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99 | Node target(Edge e) const { |
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100 | return (e.id / _dim) ^ ( 1 << (e.id % _dim)); |
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101 | } |
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102 | |
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103 | /// Node ID. |
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104 | |
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105 | /// The ID of a valid Node is a nonnegative integer not greater than |
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106 | /// \ref maxNodeId(). The range of the ID's is not surely continuous |
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107 | /// and the greatest node ID can be actually less then \ref maxNodeId(). |
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108 | /// |
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109 | /// The ID of the \ref INVALID node is -1. |
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110 | ///\return The ID of the node \c v. |
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111 | |
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112 | static int id(Node v) { return v.id; } |
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113 | /// Edge ID. |
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114 | |
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115 | /// The ID of a valid Edge is a nonnegative integer not greater than |
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116 | /// \ref maxEdgeId(). The range of the ID's is not surely continuous |
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117 | /// and the greatest edge ID can be actually less then \ref maxEdgeId(). |
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118 | /// |
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119 | /// The ID of the \ref INVALID edge is -1. |
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120 | ///\return The ID of the edge \c e. |
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121 | static int id(Edge e) { return e.id; } |
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122 | |
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123 | static Node nodeFromId(int id) { return Node(id);} |
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124 | |
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125 | static Edge edgeFromId(int id) { return Edge(id);} |
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126 | |
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127 | class Node { |
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128 | friend class HyperCubeGraphBase; |
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129 | |
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130 | protected: |
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131 | int id; |
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132 | Node(int _id) { id = _id;} |
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133 | public: |
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134 | Node() {} |
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135 | Node (Invalid) { id = -1; } |
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136 | bool operator==(const Node node) const {return id == node.id;} |
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137 | bool operator!=(const Node node) const {return id != node.id;} |
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138 | bool operator<(const Node node) const {return id < node.id;} |
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139 | }; |
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140 | |
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141 | class Edge { |
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142 | friend class HyperCubeGraphBase; |
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143 | |
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144 | protected: |
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145 | int id; |
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146 | |
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147 | Edge(int _id) : id(_id) {} |
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148 | |
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149 | public: |
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150 | Edge() { } |
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151 | Edge (Invalid) { id = -1; } |
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152 | bool operator==(const Edge edge) const {return id == edge.id;} |
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153 | bool operator!=(const Edge edge) const {return id != edge.id;} |
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154 | bool operator<(const Edge edge) const {return id < edge.id;} |
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155 | }; |
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156 | |
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157 | void first(Node& node) const { |
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158 | node.id = nodeNum() - 1; |
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159 | } |
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160 | |
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161 | static void next(Node& node) { |
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162 | --node.id; |
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163 | } |
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164 | |
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165 | void first(Edge& edge) const { |
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166 | edge.id = edgeNum() - 1; |
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167 | } |
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168 | |
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169 | static void next(Edge& edge) { |
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170 | --edge.id; |
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171 | } |
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172 | |
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173 | void firstOut(Edge& edge, const Node& node) const { |
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174 | edge.id = node.id * _dim; |
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175 | } |
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176 | |
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177 | void nextOut(Edge& edge) const { |
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178 | ++edge.id; |
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179 | if (edge.id % _dim == 0) edge.id = -1; |
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180 | } |
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181 | |
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182 | void firstIn(Edge& edge, const Node& node) const { |
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183 | edge.id = (node.id ^ 1) * _dim; |
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184 | } |
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185 | |
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186 | void nextIn(Edge& edge) const { |
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187 | int cnt = edge.id % _dim; |
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188 | if ((cnt + 1) % _dim == 0) { |
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189 | edge.id = -1; |
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190 | } else { |
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191 | edge.id = ((edge.id / _dim) ^ ((1 << cnt) * 3)) * _dim + cnt + 1; |
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192 | } |
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193 | } |
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194 | |
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195 | /// \brief Gives back the number of the dimensions. |
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196 | /// |
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197 | /// Gives back the number of the dimensions. |
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198 | int dimension() const { |
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199 | return _dim; |
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200 | } |
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201 | |
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202 | /// \brief Returns true if the n'th bit of the node is one. |
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203 | /// |
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204 | /// Returns true if the n'th bit of the node is one. |
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205 | bool projection(Node node, int n) const { |
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206 | return (bool)(node.id & (1 << n)); |
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207 | } |
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208 | |
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209 | /// \brief The dimension id of the edge. |
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210 | /// |
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211 | /// It returns the dimension id of the edge. It can |
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212 | /// be in the ${0, 1, dim-1}$ intervall. |
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213 | int dimension(Edge edge) const { |
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214 | return edge.id % _dim; |
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215 | } |
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216 | |
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217 | /// \brief Gives back the index of the node. |
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218 | /// |
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219 | /// Gives back the index of the node. The lower bits of the |
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220 | /// integer describe the node. |
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221 | int index(Node node) const { |
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222 | return node.id; |
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223 | } |
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224 | |
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225 | /// \brief Gives back the node by its index. |
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226 | /// |
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227 | /// Gives back the node by its index. |
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228 | Node operator()(int index) const { |
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229 | return Node(index); |
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230 | } |
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231 | |
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232 | private: |
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233 | int _dim, _nodeNum; |
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234 | }; |
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235 | |
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236 | |
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237 | typedef GraphExtender<HyperCubeGraphBase> ExtendedHyperCubeGraphBase; |
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238 | |
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239 | /// \ingroup graphs |
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240 | /// |
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241 | /// \brief HyperCube graph class |
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242 | /// |
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243 | /// This class implements a special graph type. The nodes of the |
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244 | /// graph can be indiced with integers with at most \c dim binary length. |
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245 | /// Two nodes are connected in the graph if the indices differ only |
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246 | /// on one position in the binary form. |
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247 | /// |
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248 | /// \note The type of the \c ids is chosen to \c int because efficiency |
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249 | /// reasons. This way the maximal dimension of this implementation |
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250 | /// is 26. |
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251 | /// |
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252 | /// The graph type is fully conform to the \ref concept::Graph |
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253 | /// concept but it does not conform to the \ref concept::UGraph. |
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254 | /// |
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255 | /// \see HyperCubeGraphBase |
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256 | /// \author Balazs Dezso |
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257 | class HyperCubeGraph : public ExtendedHyperCubeGraphBase { |
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258 | public: |
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259 | |
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260 | /// \brief Construct a graph with \c dim dimension. |
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261 | /// |
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262 | /// Construct a graph with \c dim dimension. |
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263 | HyperCubeGraph(int dim) { construct(dim); } |
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264 | |
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265 | /// \brief Linear combination map. |
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266 | /// |
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267 | /// It makes possible to give back a linear combination |
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268 | /// for each node. This function works like the \c std::accumulate |
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269 | /// so it accumulates the \c bf binary function with the \c fv |
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270 | /// first value. The map accumulates only on that dimensions where |
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271 | /// the node's index is one. The accumulated values should be |
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272 | /// given by the \c begin and \c end iterators and this range's length |
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273 | /// should be the dimension number of the graph. |
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274 | /// |
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275 | ///\code |
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276 | /// const int DIM = 3; |
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277 | /// HyperCubeGraph graph(DIM); |
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278 | /// xy<double> base[DIM]; |
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279 | /// for (int k = 0; k < DIM; ++k) { |
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280 | /// base[k].x = rand() / (RAND_MAX + 1.0); |
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281 | /// base[k].y = rand() / (RAND_MAX + 1.0); |
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282 | /// } |
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283 | /// HyperCubeGraph::HyperMap<xy<double> > |
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284 | /// pos(graph, base, base + DIM, xy<double>(0.0, 0.0)); |
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285 | ///\endcode |
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286 | /// |
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287 | /// \see HyperCubeGraph |
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288 | template <typename T, typename BF = std::plus<T> > |
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289 | class HyperMap { |
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290 | public: |
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291 | |
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292 | typedef Node Key; |
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293 | typedef T Value; |
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294 | |
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295 | |
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296 | /// \brief Constructor for HyperMap. |
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297 | /// |
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298 | /// Construct a HyperMap for the given graph. The accumulated values |
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299 | /// should be given by the \c begin and \c end iterators and this |
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300 | /// range's length should be the dimension number of the graph. |
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301 | /// |
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302 | /// This function accumulates the \c bf binary function with |
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303 | /// the \c fv first value. The map accumulates only on that dimensions |
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304 | /// where the node's index is one. |
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305 | template <typename It> |
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306 | HyperMap(const Graph& graph, It begin, It end, |
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307 | T fv = 0.0, const BF& bf = BF()) |
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308 | : _graph(graph), _values(begin, end), _first_value(fv), _bin_func(bf) { |
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309 | LEMON_ASSERT(_values.size() == graph.dimension(), |
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310 | "Wrong size of dimension"); |
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311 | } |
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312 | |
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313 | /// \brief Gives back the partial accumulated value. |
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314 | /// |
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315 | /// Gives back the partial accumulated value. |
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316 | Value operator[](Key k) const { |
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317 | Value val = _first_value; |
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318 | int id = _graph.index(k); |
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319 | int n = 0; |
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320 | while (id != 0) { |
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321 | if (id & 1) { |
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322 | val = _bin_func(val, _values[n]); |
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323 | } |
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324 | id >>= 1; |
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325 | ++n; |
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326 | } |
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327 | return val; |
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328 | } |
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329 | |
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330 | private: |
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331 | const Graph& _graph; |
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332 | std::vector<T> _values; |
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333 | T _first_value; |
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334 | BF _bin_func; |
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335 | }; |
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336 | }; |
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337 | } |
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338 | #endif |
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339 | |
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