1 | /* -*- C++ -*- |
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2 | * lemon/grid_graph.h - Part of LEMON, a generic C++ optimization library |
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3 | * |
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4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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6 | * |
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7 | * Permission to use, modify and distribute this software is granted |
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8 | * provided that this copyright notice appears in all copies. For |
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9 | * precise terms see the accompanying LICENSE file. |
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10 | * |
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11 | * This software is provided "AS IS" with no warranty of any kind, |
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12 | * express or implied, and with no claim as to its suitability for any |
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13 | * purpose. |
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14 | * |
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15 | */ |
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16 | |
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17 | #ifndef GRID_GRAPH_H |
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18 | #define GRID_GRAPH_H |
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19 | |
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20 | #include <iostream> |
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21 | #include <lemon/invalid.h> |
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22 | #include <lemon/utility.h> |
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23 | |
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24 | #include <lemon/bits/iterable_graph_extender.h> |
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25 | #include <lemon/bits/alteration_notifier.h> |
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26 | #include <lemon/bits/static_map.h> |
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27 | |
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28 | #include <lemon/bits/undir_graph_extender.h> |
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29 | |
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30 | #include <lemon/xy.h> |
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31 | |
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32 | ///\ingroup graphs |
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33 | ///\file |
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34 | ///\brief GridGraph class. |
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35 | |
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36 | namespace lemon { |
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37 | |
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38 | /// \brief Base graph for GridGraph. |
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39 | /// |
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40 | /// Base graph for grid graph. It describes some member functions |
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41 | /// which can be used in the GridGraph. |
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42 | /// |
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43 | /// \warning Always use the GridGraph instead of this. |
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44 | /// \see GridGraph |
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45 | class GridGraphBase { |
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46 | |
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47 | public: |
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48 | |
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49 | typedef GridGraphBase Graph; |
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50 | |
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51 | class Node; |
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52 | class Edge; |
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53 | |
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54 | public: |
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55 | |
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56 | GridGraphBase() {} |
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57 | |
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58 | protected: |
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59 | |
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60 | /// \brief Creates a grid graph with the given size. |
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61 | /// |
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62 | /// Creates a grid graph with the given size. |
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63 | void construct(int width, int height) { |
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64 | _height = height; _width = width; |
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65 | _nodeNum = height * width; _edgeNum = 2 * _nodeNum - width - height; |
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66 | _edgeLimit = _nodeNum - width; |
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67 | } |
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68 | |
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69 | /// \brief Gives back the edge goes down from the node. |
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70 | /// |
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71 | /// Gives back the edge goes down from the node. If there is not |
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72 | /// outgoing edge then it gives back INVALID. |
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73 | Edge _down(Node n) const { |
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74 | if (n.id < _nodeNum - _width) { |
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75 | return Edge(n.id); |
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76 | } else { |
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77 | return INVALID; |
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78 | } |
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79 | } |
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80 | |
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81 | /// \brief Gives back the edge comes from up into the node. |
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82 | /// |
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83 | /// Gives back the edge comes from up into the node. If there is not |
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84 | /// incoming edge then it gives back INVALID. |
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85 | Edge _up(Node n) const { |
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86 | if (n.id >= _width) { |
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87 | return Edge(n.id - _width); |
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88 | } else { |
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89 | return INVALID; |
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90 | } |
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91 | } |
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92 | |
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93 | /// \brief Gives back the edge goes right from the node. |
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94 | /// |
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95 | /// Gives back the edge goes right from the node. If there is not |
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96 | /// outgoing edge then it gives back INVALID. |
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97 | Edge _right(Node n) const { |
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98 | if (n.id % _width < _width - 1) { |
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99 | return _edgeLimit + n.id % _width + (n.id / _width) * (_width - 1); |
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100 | } else { |
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101 | return INVALID; |
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102 | } |
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103 | } |
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104 | |
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105 | /// \brief Gives back the edge comes from left into the node. |
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106 | /// |
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107 | /// Gives back the edge comes left up into the node. If there is not |
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108 | /// incoming edge then it gives back INVALID. |
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109 | Edge _left(Node n) const { |
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110 | if (n.id % _width > 0) { |
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111 | return _edgeLimit + n.id % _width + (n.id / _width) * (_width - 1) - 1; |
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112 | } else { |
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113 | return INVALID; |
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114 | } |
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115 | } |
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116 | |
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117 | |
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118 | public: |
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119 | |
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120 | /// \brief The node on the given position. |
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121 | /// |
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122 | /// Gives back the node on the given position. |
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123 | Node operator()(int i, int j) const { |
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124 | return Node(i + j * _width); |
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125 | } |
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126 | |
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127 | /// \brief Gives back the row index of the node. |
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128 | /// |
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129 | /// Gives back the row index of the node. |
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130 | int row(Node n) const { |
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131 | return n.id / _width; |
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132 | } |
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133 | |
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134 | /// \brief Gives back the coloumn index of the node. |
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135 | /// |
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136 | /// Gives back the coloumn index of the node. |
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137 | int col(Node n) const { |
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138 | return n.id % _width; |
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139 | } |
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140 | |
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141 | /// \brief Gives back the width of the graph. |
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142 | /// |
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143 | /// Gives back the width of the graph. |
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144 | int width() const { |
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145 | return _width; |
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146 | } |
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147 | |
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148 | /// \brief Gives back the height of the graph. |
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149 | /// |
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150 | /// Gives back the height of the graph. |
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151 | int height() const { |
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152 | return _height; |
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153 | } |
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154 | |
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155 | typedef True NodeNumTag; |
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156 | typedef True EdgeNumTag; |
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157 | |
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158 | ///Number of nodes. |
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159 | int nodeNum() const { return _nodeNum; } |
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160 | ///Number of edges. |
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161 | int edgeNum() const { return _edgeNum; } |
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162 | |
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163 | /// Maximum node ID. |
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164 | |
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165 | /// Maximum node ID. |
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166 | ///\sa id(Node) |
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167 | int maxId(Node = INVALID) const { return nodeNum() - 1; } |
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168 | /// Maximum edge ID. |
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169 | |
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170 | /// Maximum edge ID. |
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171 | ///\sa id(Edge) |
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172 | int maxId(Edge = INVALID) const { return edgeNum() - 1; } |
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173 | |
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174 | /// \brief Gives back the source node of an edge. |
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175 | /// |
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176 | /// Gives back the source node of an edge. |
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177 | Node source(Edge e) const { |
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178 | if (e.id < _edgeLimit) { |
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179 | return e.id; |
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180 | } else { |
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181 | return (e.id - _edgeLimit) % (_width - 1) + |
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182 | (e.id - _edgeLimit) / (_width - 1) * _width; |
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183 | } |
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184 | } |
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185 | |
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186 | /// \brief Gives back the target node of an edge. |
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187 | /// |
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188 | /// Gives back the target node of an edge. |
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189 | Node target(Edge e) const { |
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190 | if (e.id < _edgeLimit) { |
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191 | return e.id + _width; |
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192 | } else { |
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193 | return (e.id - _edgeLimit) % (_width - 1) + |
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194 | (e.id - _edgeLimit) / (_width - 1) * _width + 1; |
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195 | } |
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196 | } |
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197 | |
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198 | /// Node ID. |
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199 | |
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200 | /// The ID of a valid Node is a nonnegative integer not greater than |
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201 | /// \ref maxNodeId(). The range of the ID's is not surely continuous |
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202 | /// and the greatest node ID can be actually less then \ref maxNodeId(). |
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203 | /// |
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204 | /// The ID of the \ref INVALID node is -1. |
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205 | ///\return The ID of the node \c v. |
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206 | |
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207 | static int id(Node v) { return v.id; } |
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208 | /// Edge ID. |
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209 | |
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210 | /// The ID of a valid Edge is a nonnegative integer not greater than |
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211 | /// \ref maxEdgeId(). The range of the ID's is not surely continuous |
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212 | /// and the greatest edge ID can be actually less then \ref maxEdgeId(). |
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213 | /// |
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214 | /// The ID of the \ref INVALID edge is -1. |
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215 | ///\return The ID of the edge \c e. |
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216 | static int id(Edge e) { return e.id; } |
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217 | |
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218 | static Node fromId(int id, Node) { return Node(id);} |
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219 | |
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220 | static Edge fromId(int id, Edge) { return Edge(id);} |
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221 | |
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222 | typedef True FindEdgeTag; |
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223 | |
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224 | /// Finds an edge between two nodes. |
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225 | |
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226 | /// Finds an edge from node \c u to node \c v. |
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227 | /// |
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228 | /// If \c prev is \ref INVALID (this is the default value), then |
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229 | /// It finds the first edge from \c u to \c v. Otherwise it looks for |
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230 | /// the next edge from \c u to \c v after \c prev. |
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231 | /// \return The found edge or INVALID if there is no such an edge. |
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232 | Edge findEdge(Node u, Node v, Edge prev = INVALID) { |
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233 | if (prev != INVALID) return INVALID; |
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234 | if (v.id - u.id == _width) return Edge(u.id); |
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235 | if (v.id - u.id == 1 && u.id % _width < _width - 1) { |
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236 | return Edge(u.id / _width * (_width - 1) + |
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237 | u.id % _width + _edgeLimit); |
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238 | } |
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239 | return INVALID; |
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240 | } |
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241 | |
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242 | |
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243 | class Node { |
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244 | friend class GridGraphBase; |
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245 | |
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246 | protected: |
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247 | int id; |
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248 | Node(int _id) { id = _id;} |
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249 | public: |
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250 | Node() {} |
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251 | Node (Invalid) { id = -1; } |
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252 | bool operator==(const Node node) const {return id == node.id;} |
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253 | bool operator!=(const Node node) const {return id != node.id;} |
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254 | bool operator<(const Node node) const {return id < node.id;} |
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255 | }; |
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256 | |
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257 | |
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258 | |
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259 | class Edge { |
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260 | friend class GridGraphBase; |
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261 | |
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262 | protected: |
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263 | int id; |
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264 | |
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265 | Edge(int _id) : id(_id) {} |
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266 | |
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267 | public: |
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268 | Edge() { } |
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269 | Edge (Invalid) { id = -1; } |
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270 | bool operator==(const Edge edge) const {return id == edge.id;} |
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271 | bool operator!=(const Edge edge) const {return id != edge.id;} |
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272 | bool operator<(const Edge edge) const {return id < edge.id;} |
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273 | }; |
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274 | |
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275 | void first(Node& node) const { |
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276 | node.id = nodeNum() - 1; |
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277 | } |
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278 | |
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279 | static void next(Node& node) { |
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280 | --node.id; |
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281 | } |
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282 | |
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283 | void first(Edge& edge) const { |
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284 | edge.id = edgeNum() - 1; |
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285 | } |
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286 | |
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287 | static void next(Edge& edge) { |
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288 | --edge.id; |
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289 | } |
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290 | |
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291 | void firstOut(Edge& edge, const Node& node) const { |
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292 | if (node.id < _nodeNum - _width) { |
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293 | edge.id = node.id; |
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294 | } else if (node.id % _width < _width - 1) { |
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295 | edge.id = _edgeLimit + node.id % _width + |
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296 | (node.id / _width) * (_width - 1); |
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297 | } else { |
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298 | edge.id = -1; |
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299 | } |
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300 | } |
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301 | |
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302 | void nextOut(Edge& edge) const { |
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303 | if (edge.id >= _edgeLimit) { |
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304 | edge.id = -1; |
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305 | } else if (edge.id % _width < _width - 1) { |
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306 | edge.id = _edgeLimit + edge.id % _width + |
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307 | (edge.id / _width) * (_width - 1); |
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308 | } else { |
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309 | edge.id = -1; |
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310 | } |
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311 | } |
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312 | |
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313 | void firstIn(Edge& edge, const Node& node) const { |
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314 | if (node.id >= _width) { |
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315 | edge.id = node.id - _width; |
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316 | } else if (node.id % _width > 0) { |
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317 | edge.id = _edgeLimit + node.id % _width + |
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318 | (node.id / _width) * (_width - 1) - 1; |
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319 | } else { |
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320 | edge.id = -1; |
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321 | } |
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322 | } |
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323 | |
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324 | void nextIn(Edge& edge) const { |
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325 | if (edge.id >= _edgeLimit) { |
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326 | edge.id = -1; |
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327 | } else if (edge.id % _width > 0) { |
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328 | edge.id = _edgeLimit + edge.id % _width + |
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329 | (edge.id / _width + 1) * (_width - 1) - 1; |
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330 | } else { |
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331 | edge.id = -1; |
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332 | } |
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333 | } |
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334 | |
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335 | private: |
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336 | int _width, _height; |
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337 | int _nodeNum, _edgeNum; |
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338 | int _edgeLimit; |
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339 | }; |
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340 | |
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341 | |
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342 | typedef StaticMappableUndirGraphExtender< |
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343 | IterableUndirGraphExtender< |
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344 | AlterableUndirGraphExtender< |
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345 | UndirGraphExtender<GridGraphBase> > > > ExtendedGridGraphBase; |
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346 | |
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347 | /// \ingroup graphs |
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348 | /// |
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349 | /// \brief Grid graph class |
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350 | /// |
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351 | /// This class implements a special graph type. The nodes of the |
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352 | /// graph can be indiced by two integer \c (i,j) value where \c i |
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353 | /// is in the \c [0,height) range and j is in the [0, width) range. |
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354 | /// Two nodes are connected in the graph if the indices differ only |
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355 | /// on one position and only one is the difference. |
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356 | /// |
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357 | /// The graph can be indiced in the following way: |
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358 | /// \code |
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359 | /// GridGraph graph(h, w); |
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360 | /// GridGraph::NodeMap<int> val(graph); |
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361 | /// for (int i = 0; i < graph.height(); ++i) { |
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362 | /// for (int j = 0; j < graph.width(); ++j) { |
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363 | /// val[graph(i, j)] = i + j; |
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364 | /// } |
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365 | /// } |
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366 | /// \endcode |
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367 | /// |
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368 | /// The graph type is fully conform to the \ref concept::UndirGraph |
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369 | /// "Undirected Graph" concept. |
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370 | /// |
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371 | /// \author Balazs Dezso |
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372 | /// \see GridGraphBase |
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373 | class GridGraph : public ExtendedGridGraphBase { |
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374 | public: |
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375 | |
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376 | /// \brief Map to get the indices of the nodes as xy<int>. |
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377 | /// |
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378 | /// Map to get the indices of the nodes as xy<int>. |
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379 | class IndexMap { |
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380 | public: |
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381 | typedef True NeedCopy; |
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382 | /// \brief The key type of the map |
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383 | typedef GridGraph::Node Key; |
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384 | /// \brief The value type of the map |
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385 | typedef xy<int> Value; |
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386 | |
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387 | /// \brief Constructor |
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388 | /// |
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389 | /// Constructor |
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390 | IndexMap(const GridGraph& _graph) : graph(_graph) {} |
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391 | |
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392 | /// \brief The subscript operator |
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393 | /// |
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394 | /// The subscript operator. |
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395 | Value operator[](Key key) const { |
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396 | return xy<int>(graph.row(key), graph.col(key)); |
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397 | } |
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398 | |
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399 | private: |
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400 | const GridGraph& graph; |
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401 | }; |
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402 | |
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403 | /// \brief Map to get the row of the nodes. |
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404 | /// |
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405 | /// Map to get the row of the nodes. |
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406 | class RowMap { |
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407 | public: |
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408 | typedef True NeedCopy; |
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409 | /// \brief The key type of the map |
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410 | typedef GridGraph::Node Key; |
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411 | /// \brief The value type of the map |
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412 | typedef int Value; |
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413 | |
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414 | /// \brief Constructor |
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415 | /// |
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416 | /// Constructor |
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417 | RowMap(const GridGraph& _graph) : graph(_graph) {} |
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418 | |
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419 | /// \brief The subscript operator |
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420 | /// |
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421 | /// The subscript operator. |
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422 | Value operator[](Key key) const { |
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423 | return graph.row(key); |
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424 | } |
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425 | |
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426 | private: |
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427 | const GridGraph& graph; |
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428 | }; |
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429 | |
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430 | /// \brief Map to get the column of the nodes. |
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431 | /// |
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432 | /// Map to get the column of the nodes. |
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433 | class ColMap { |
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434 | public: |
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435 | typedef True NeedCopy; |
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436 | /// \brief The key type of the map |
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437 | typedef GridGraph::Node Key; |
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438 | /// \brief The value type of the map |
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439 | typedef int Value; |
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440 | |
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441 | /// \brief Constructor |
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442 | /// |
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443 | /// Constructor |
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444 | ColMap(const GridGraph& _graph) : graph(_graph) {} |
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445 | |
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446 | /// \brief The subscript operator |
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447 | /// |
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448 | /// The subscript operator. |
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449 | Value operator[](Key key) const { |
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450 | return graph.col(key); |
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451 | } |
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452 | |
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453 | private: |
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454 | const GridGraph& graph; |
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455 | }; |
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456 | |
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457 | GridGraph(int n, int m) { construct(n, m); } |
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458 | |
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459 | /// \brief Gives back the edge goes down from the node. |
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460 | /// |
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461 | /// Gives back the edge goes down from the node. If there is not |
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462 | /// outgoing edge then it gives back INVALID. |
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463 | Edge down(Node n) const { |
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464 | UndirEdge ue = _down(n); |
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465 | return ue != INVALID ? direct(ue, true) : INVALID; |
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466 | } |
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467 | |
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468 | /// \brief Gives back the edge goes up from the node. |
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469 | /// |
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470 | /// Gives back the edge goes up from the node. If there is not |
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471 | /// outgoing edge then it gives back INVALID. |
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472 | Edge up(Node n) const { |
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473 | UndirEdge ue = _up(n); |
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474 | return ue != INVALID ? direct(ue, false) : INVALID; |
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475 | } |
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476 | |
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477 | /// \brief Gives back the edge goes right from the node. |
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478 | /// |
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479 | /// Gives back the edge goes right from the node. If there is not |
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480 | /// outgoing edge then it gives back INVALID. |
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481 | Edge right(Node n) const { |
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482 | UndirEdge ue = _right(n); |
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483 | return ue != INVALID ? direct(ue, true) : INVALID; |
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484 | } |
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485 | |
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486 | /// \brief Gives back the edge goes left from the node. |
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487 | /// |
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488 | /// Gives back the edge goes left from the node. If there is not |
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489 | /// outgoing edge then it gives back INVALID. |
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490 | Edge left(Node n) const { |
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491 | UndirEdge ue = _left(n); |
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492 | return ue != INVALID ? direct(ue, false) : INVALID; |
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493 | } |
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494 | |
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495 | }; |
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496 | |
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497 | /// \brief Index map of the grid graph |
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498 | /// |
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499 | /// Just returns an IndexMap for the grid graph. |
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500 | GridGraph::IndexMap indexMap(const GridGraph& graph) { |
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501 | return GridGraph::IndexMap(graph); |
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502 | } |
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503 | |
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504 | /// \brief Row map of the grid graph |
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505 | /// |
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506 | /// Just returns an RowMap for the grid graph. |
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507 | GridGraph::RowMap rowMap(const GridGraph& graph) { |
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508 | return GridGraph::RowMap(graph); |
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509 | } |
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510 | |
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511 | /// \brief Coloumn map of the grid graph |
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512 | /// |
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513 | /// Just returns an ColMap for the grid graph. |
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514 | GridGraph::ColMap colMap(const GridGraph& graph) { |
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515 | return GridGraph::ColMap(graph); |
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516 | } |
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517 | } |
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518 | #endif |
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