1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library. |
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4 | * |
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5 | * Copyright (C) 2003-2009 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef GRID_GRAPH_H |
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20 | #define GRID_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 | #include <lemon/dim2.h> |
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25 | #include <lemon/assert.h> |
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26 | |
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27 | ///\ingroup graphs |
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28 | ///\file |
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29 | ///\brief GridGraph class. |
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30 | |
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31 | namespace lemon { |
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32 | |
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33 | class GridGraphBase { |
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34 | |
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35 | public: |
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36 | |
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37 | typedef GridGraphBase Graph; |
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38 | |
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39 | class Node; |
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40 | class Edge; |
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41 | class Arc; |
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42 | |
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43 | public: |
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44 | |
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45 | GridGraphBase() {} |
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46 | |
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47 | protected: |
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48 | |
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49 | void construct(int width, int height) { |
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50 | _width = width; _height = height; |
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51 | _node_num = width * height; |
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52 | _edge_num = 2 * _node_num - width - height; |
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53 | _edge_limit = _node_num - _width; |
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54 | } |
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55 | |
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56 | public: |
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57 | |
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58 | Node operator()(int i, int j) const { |
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59 | LEMON_DEBUG(0 <= i && i < _width && |
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60 | 0 <= j && j < _height, "Index out of range"); |
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61 | return Node(i + j * _width); |
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62 | } |
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63 | |
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64 | int col(Node n) const { |
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65 | return n._id % _width; |
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66 | } |
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67 | |
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68 | int row(Node n) const { |
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69 | return n._id / _width; |
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70 | } |
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71 | |
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72 | dim2::Point<int> pos(Node n) const { |
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73 | return dim2::Point<int>(col(n), row(n)); |
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74 | } |
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75 | |
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76 | int width() const { |
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77 | return _width; |
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78 | } |
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79 | |
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80 | int height() const { |
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81 | return _height; |
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82 | } |
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83 | |
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84 | typedef True NodeNumTag; |
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85 | typedef True EdgeNumTag; |
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86 | typedef True ArcNumTag; |
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87 | |
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88 | int nodeNum() const { return _node_num; } |
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89 | int edgeNum() const { return _edge_num; } |
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90 | int arcNum() const { return 2 * _edge_num; } |
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91 | |
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92 | Node u(Edge edge) const { |
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93 | if (edge._id < _edge_limit) { |
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94 | return edge._id; |
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95 | } else { |
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96 | return (edge._id - _edge_limit) % (_width - 1) + |
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97 | (edge._id - _edge_limit) / (_width - 1) * _width; |
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98 | } |
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99 | } |
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100 | |
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101 | Node v(Edge edge) const { |
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102 | if (edge._id < _edge_limit) { |
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103 | return edge._id + _width; |
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104 | } else { |
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105 | return (edge._id - _edge_limit) % (_width - 1) + |
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106 | (edge._id - _edge_limit) / (_width - 1) * _width + 1; |
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107 | } |
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108 | } |
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109 | |
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110 | Node source(Arc arc) const { |
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111 | return (arc._id & 1) == 1 ? u(arc) : v(arc); |
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112 | } |
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113 | |
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114 | Node target(Arc arc) const { |
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115 | return (arc._id & 1) == 1 ? v(arc) : u(arc); |
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116 | } |
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117 | |
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118 | static int id(Node node) { return node._id; } |
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119 | static int id(Edge edge) { return edge._id; } |
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120 | static int id(Arc arc) { return arc._id; } |
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121 | |
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122 | int maxNodeId() const { return _node_num - 1; } |
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123 | int maxEdgeId() const { return _edge_num - 1; } |
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124 | int maxArcId() const { return 2 * _edge_num - 1; } |
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125 | |
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126 | static Node nodeFromId(int id) { return Node(id);} |
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127 | static Edge edgeFromId(int id) { return Edge(id);} |
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128 | static Arc arcFromId(int id) { return Arc(id);} |
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129 | |
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130 | typedef True FindEdgeTag; |
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131 | typedef True FindArcTag; |
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132 | |
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133 | Edge findEdge(Node u, Node v, Edge prev = INVALID) const { |
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134 | if (prev != INVALID) return INVALID; |
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135 | if (v._id > u._id) { |
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136 | if (v._id - u._id == _width) |
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137 | return Edge(u._id); |
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138 | if (v._id - u._id == 1 && u._id % _width < _width - 1) { |
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139 | return Edge(u._id / _width * (_width - 1) + |
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140 | u._id % _width + _edge_limit); |
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141 | } |
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142 | } else { |
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143 | if (u._id - v._id == _width) |
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144 | return Edge(v._id); |
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145 | if (u._id - v._id == 1 && v._id % _width < _width - 1) { |
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146 | return Edge(v._id / _width * (_width - 1) + |
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147 | v._id % _width + _edge_limit); |
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148 | } |
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149 | } |
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150 | return INVALID; |
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151 | } |
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152 | |
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153 | Arc findArc(Node u, Node v, Arc prev = INVALID) const { |
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154 | if (prev != INVALID) return INVALID; |
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155 | if (v._id > u._id) { |
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156 | if (v._id - u._id == _width) |
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157 | return Arc((u._id << 1) | 1); |
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158 | if (v._id - u._id == 1 && u._id % _width < _width - 1) { |
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159 | return Arc(((u._id / _width * (_width - 1) + |
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160 | u._id % _width + _edge_limit) << 1) | 1); |
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161 | } |
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162 | } else { |
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163 | if (u._id - v._id == _width) |
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164 | return Arc(v._id << 1); |
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165 | if (u._id - v._id == 1 && v._id % _width < _width - 1) { |
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166 | return Arc((v._id / _width * (_width - 1) + |
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167 | v._id % _width + _edge_limit) << 1); |
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168 | } |
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169 | } |
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170 | return INVALID; |
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171 | } |
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172 | |
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173 | class Node { |
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174 | friend class GridGraphBase; |
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175 | |
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176 | protected: |
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177 | int _id; |
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178 | Node(int id) : _id(id) {} |
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179 | public: |
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180 | Node() {} |
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181 | Node (Invalid) : _id(-1) {} |
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182 | bool operator==(const Node node) const {return _id == node._id;} |
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183 | bool operator!=(const Node node) const {return _id != node._id;} |
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184 | bool operator<(const Node node) const {return _id < node._id;} |
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185 | }; |
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186 | |
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187 | class Edge { |
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188 | friend class GridGraphBase; |
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189 | friend class Arc; |
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190 | |
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191 | protected: |
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192 | int _id; |
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193 | |
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194 | Edge(int id) : _id(id) {} |
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195 | |
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196 | public: |
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197 | Edge() {} |
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198 | Edge (Invalid) : _id(-1) {} |
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199 | bool operator==(const Edge edge) const {return _id == edge._id;} |
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200 | bool operator!=(const Edge edge) const {return _id != edge._id;} |
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201 | bool operator<(const Edge edge) const {return _id < edge._id;} |
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202 | }; |
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203 | |
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204 | class Arc { |
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205 | friend class GridGraphBase; |
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206 | |
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207 | protected: |
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208 | int _id; |
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209 | |
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210 | Arc(int id) : _id(id) {} |
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211 | |
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212 | public: |
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213 | Arc() {} |
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214 | Arc (Invalid) : _id(-1) {} |
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215 | operator Edge() const { return _id != -1 ? Edge(_id >> 1) : INVALID; } |
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216 | bool operator==(const Arc arc) const {return _id == arc._id;} |
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217 | bool operator!=(const Arc arc) const {return _id != arc._id;} |
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218 | bool operator<(const Arc arc) const {return _id < arc._id;} |
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219 | }; |
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220 | |
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221 | static bool direction(Arc arc) { |
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222 | return (arc._id & 1) == 1; |
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223 | } |
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224 | |
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225 | static Arc direct(Edge edge, bool dir) { |
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226 | return Arc((edge._id << 1) | (dir ? 1 : 0)); |
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227 | } |
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228 | |
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229 | void first(Node& node) const { |
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230 | node._id = _node_num - 1; |
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231 | } |
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232 | |
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233 | static void next(Node& node) { |
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234 | --node._id; |
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235 | } |
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236 | |
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237 | void first(Edge& edge) const { |
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238 | edge._id = _edge_num - 1; |
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239 | } |
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240 | |
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241 | static void next(Edge& edge) { |
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242 | --edge._id; |
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243 | } |
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244 | |
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245 | void first(Arc& arc) const { |
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246 | arc._id = 2 * _edge_num - 1; |
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247 | } |
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248 | |
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249 | static void next(Arc& arc) { |
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250 | --arc._id; |
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251 | } |
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252 | |
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253 | void firstOut(Arc& arc, const Node& node) const { |
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254 | if (node._id % _width < _width - 1) { |
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255 | arc._id = (_edge_limit + node._id % _width + |
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256 | (node._id / _width) * (_width - 1)) << 1 | 1; |
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257 | return; |
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258 | } |
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259 | if (node._id < _node_num - _width) { |
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260 | arc._id = node._id << 1 | 1; |
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261 | return; |
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262 | } |
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263 | if (node._id % _width > 0) { |
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264 | arc._id = (_edge_limit + node._id % _width + |
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265 | (node._id / _width) * (_width - 1) - 1) << 1; |
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266 | return; |
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267 | } |
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268 | if (node._id >= _width) { |
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269 | arc._id = (node._id - _width) << 1; |
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270 | return; |
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271 | } |
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272 | arc._id = -1; |
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273 | } |
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274 | |
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275 | void nextOut(Arc& arc) const { |
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276 | int nid = arc._id >> 1; |
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277 | if ((arc._id & 1) == 1) { |
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278 | if (nid >= _edge_limit) { |
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279 | nid = (nid - _edge_limit) % (_width - 1) + |
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280 | (nid - _edge_limit) / (_width - 1) * _width; |
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281 | if (nid < _node_num - _width) { |
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282 | arc._id = nid << 1 | 1; |
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283 | return; |
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284 | } |
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285 | } |
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286 | if (nid % _width > 0) { |
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287 | arc._id = (_edge_limit + nid % _width + |
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288 | (nid / _width) * (_width - 1) - 1) << 1; |
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289 | return; |
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290 | } |
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291 | if (nid >= _width) { |
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292 | arc._id = (nid - _width) << 1; |
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293 | return; |
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294 | } |
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295 | } else { |
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296 | if (nid >= _edge_limit) { |
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297 | nid = (nid - _edge_limit) % (_width - 1) + |
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298 | (nid - _edge_limit) / (_width - 1) * _width + 1; |
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299 | if (nid >= _width) { |
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300 | arc._id = (nid - _width) << 1; |
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301 | return; |
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302 | } |
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303 | } |
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304 | } |
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305 | arc._id = -1; |
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306 | } |
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307 | |
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308 | void firstIn(Arc& arc, const Node& node) const { |
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309 | if (node._id % _width < _width - 1) { |
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310 | arc._id = (_edge_limit + node._id % _width + |
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311 | (node._id / _width) * (_width - 1)) << 1; |
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312 | return; |
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313 | } |
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314 | if (node._id < _node_num - _width) { |
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315 | arc._id = node._id << 1; |
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316 | return; |
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317 | } |
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318 | if (node._id % _width > 0) { |
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319 | arc._id = (_edge_limit + node._id % _width + |
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320 | (node._id / _width) * (_width - 1) - 1) << 1 | 1; |
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321 | return; |
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322 | } |
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323 | if (node._id >= _width) { |
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324 | arc._id = (node._id - _width) << 1 | 1; |
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325 | return; |
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326 | } |
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327 | arc._id = -1; |
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328 | } |
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329 | |
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330 | void nextIn(Arc& arc) const { |
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331 | int nid = arc._id >> 1; |
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332 | if ((arc._id & 1) == 0) { |
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333 | if (nid >= _edge_limit) { |
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334 | nid = (nid - _edge_limit) % (_width - 1) + |
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335 | (nid - _edge_limit) / (_width - 1) * _width; |
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336 | if (nid < _node_num - _width) { |
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337 | arc._id = nid << 1; |
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338 | return; |
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339 | } |
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340 | } |
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341 | if (nid % _width > 0) { |
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342 | arc._id = (_edge_limit + nid % _width + |
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343 | (nid / _width) * (_width - 1) - 1) << 1 | 1; |
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344 | return; |
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345 | } |
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346 | if (nid >= _width) { |
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347 | arc._id = (nid - _width) << 1 | 1; |
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348 | return; |
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349 | } |
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350 | } else { |
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351 | if (nid >= _edge_limit) { |
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352 | nid = (nid - _edge_limit) % (_width - 1) + |
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353 | (nid - _edge_limit) / (_width - 1) * _width + 1; |
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354 | if (nid >= _width) { |
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355 | arc._id = (nid - _width) << 1 | 1; |
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356 | return; |
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357 | } |
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358 | } |
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359 | } |
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360 | arc._id = -1; |
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361 | } |
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362 | |
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363 | void firstInc(Edge& edge, bool& dir, const Node& node) const { |
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364 | if (node._id % _width < _width - 1) { |
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365 | edge._id = _edge_limit + node._id % _width + |
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366 | (node._id / _width) * (_width - 1); |
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367 | dir = true; |
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368 | return; |
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369 | } |
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370 | if (node._id < _node_num - _width) { |
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371 | edge._id = node._id; |
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372 | dir = true; |
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373 | return; |
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374 | } |
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375 | if (node._id % _width > 0) { |
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376 | edge._id = _edge_limit + node._id % _width + |
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377 | (node._id / _width) * (_width - 1) - 1; |
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378 | dir = false; |
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379 | return; |
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380 | } |
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381 | if (node._id >= _width) { |
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382 | edge._id = node._id - _width; |
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383 | dir = false; |
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384 | return; |
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385 | } |
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386 | edge._id = -1; |
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387 | dir = true; |
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388 | } |
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389 | |
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390 | void nextInc(Edge& edge, bool& dir) const { |
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391 | int nid = edge._id; |
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392 | if (dir) { |
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393 | if (nid >= _edge_limit) { |
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394 | nid = (nid - _edge_limit) % (_width - 1) + |
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395 | (nid - _edge_limit) / (_width - 1) * _width; |
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396 | if (nid < _node_num - _width) { |
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397 | edge._id = nid; |
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398 | return; |
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399 | } |
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400 | } |
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401 | if (nid % _width > 0) { |
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402 | edge._id = _edge_limit + nid % _width + |
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403 | (nid / _width) * (_width - 1) - 1; |
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404 | dir = false; |
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405 | return; |
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406 | } |
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407 | if (nid >= _width) { |
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408 | edge._id = nid - _width; |
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409 | dir = false; |
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410 | return; |
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411 | } |
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412 | } else { |
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413 | if (nid >= _edge_limit) { |
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414 | nid = (nid - _edge_limit) % (_width - 1) + |
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415 | (nid - _edge_limit) / (_width - 1) * _width + 1; |
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416 | if (nid >= _width) { |
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417 | edge._id = nid - _width; |
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418 | return; |
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419 | } |
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420 | } |
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421 | } |
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422 | edge._id = -1; |
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423 | dir = true; |
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424 | } |
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425 | |
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426 | Arc right(Node n) const { |
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427 | if (n._id % _width < _width - 1) { |
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428 | return Arc(((_edge_limit + n._id % _width + |
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429 | (n._id / _width) * (_width - 1)) << 1) | 1); |
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430 | } else { |
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431 | return INVALID; |
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432 | } |
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433 | } |
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434 | |
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435 | Arc left(Node n) const { |
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436 | if (n._id % _width > 0) { |
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437 | return Arc((_edge_limit + n._id % _width + |
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438 | (n._id / _width) * (_width - 1) - 1) << 1); |
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439 | } else { |
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440 | return INVALID; |
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441 | } |
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442 | } |
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443 | |
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444 | Arc up(Node n) const { |
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445 | if (n._id < _edge_limit) { |
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446 | return Arc((n._id << 1) | 1); |
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447 | } else { |
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448 | return INVALID; |
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449 | } |
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450 | } |
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451 | |
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452 | Arc down(Node n) const { |
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453 | if (n._id >= _width) { |
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454 | return Arc((n._id - _width) << 1); |
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455 | } else { |
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456 | return INVALID; |
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457 | } |
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458 | } |
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459 | |
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460 | private: |
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461 | int _width, _height; |
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462 | int _node_num, _edge_num; |
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463 | int _edge_limit; |
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464 | }; |
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465 | |
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466 | |
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467 | typedef GraphExtender<GridGraphBase> ExtendedGridGraphBase; |
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468 | |
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469 | /// \ingroup graphs |
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470 | /// |
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471 | /// \brief Grid graph class |
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472 | /// |
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473 | /// GridGraph implements a special graph type. The nodes of the |
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474 | /// graph can be indexed by two integer values \c (i,j) where \c i is |
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475 | /// in the range <tt>[0..width()-1]</tt> and j is in the range |
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476 | /// <tt>[0..height()-1]</tt>. Two nodes are connected in the graph if |
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477 | /// the indices differ exactly on one position and the difference is |
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478 | /// also exactly one. The nodes of the graph can be obtained by position |
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479 | /// using the \c operator()() function and the indices of the nodes can |
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480 | /// be obtained using \c pos(), \c col() and \c row() members. The outgoing |
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481 | /// arcs can be retrieved with the \c right(), \c up(), \c left() |
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482 | /// and \c down() functions, where the bottom-left corner is the |
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483 | /// origin. |
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484 | /// |
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485 | /// This class is completely static and it needs constant memory space. |
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486 | /// Thus you can neither add nor delete nodes or edges, however |
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487 | /// the structure can be resized using resize(). |
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488 | /// |
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489 | /// \image html grid_graph.png |
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490 | /// \image latex grid_graph.eps "Grid graph" width=\textwidth |
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491 | /// |
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492 | /// A short example about the basic usage: |
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493 | ///\code |
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494 | /// GridGraph graph(rows, cols); |
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495 | /// GridGraph::NodeMap<int> val(graph); |
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496 | /// for (int i = 0; i < graph.width(); ++i) { |
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497 | /// for (int j = 0; j < graph.height(); ++j) { |
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498 | /// val[graph(i, j)] = i + j; |
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499 | /// } |
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500 | /// } |
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501 | ///\endcode |
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502 | /// |
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503 | /// This type fully conforms to the \ref concepts::Graph "Graph concept". |
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504 | /// Most of its member functions and nested classes are documented |
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505 | /// only in the concept class. |
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506 | /// |
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507 | /// This class provides constant time counting for nodes, edges and arcs. |
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508 | class GridGraph : public ExtendedGridGraphBase { |
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509 | typedef ExtendedGridGraphBase Parent; |
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510 | |
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511 | public: |
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512 | |
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513 | /// \brief Map to get the indices of the nodes as \ref dim2::Point |
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514 | /// "dim2::Point<int>". |
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515 | /// |
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516 | /// Map to get the indices of the nodes as \ref dim2::Point |
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517 | /// "dim2::Point<int>". |
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518 | class IndexMap { |
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519 | public: |
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520 | /// \brief The key type of the map |
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521 | typedef GridGraph::Node Key; |
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522 | /// \brief The value type of the map |
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523 | typedef dim2::Point<int> Value; |
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524 | |
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525 | /// \brief Constructor |
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526 | IndexMap(const GridGraph& graph) : _graph(graph) {} |
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527 | |
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528 | /// \brief The subscript operator |
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529 | Value operator[](Key key) const { |
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530 | return _graph.pos(key); |
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531 | } |
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532 | |
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533 | private: |
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534 | const GridGraph& _graph; |
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535 | }; |
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536 | |
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537 | /// \brief Map to get the column of the nodes. |
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538 | /// |
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539 | /// Map to get the column of the nodes. |
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540 | class ColMap { |
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541 | public: |
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542 | /// \brief The key type of the map |
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543 | typedef GridGraph::Node Key; |
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544 | /// \brief The value type of the map |
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545 | typedef int Value; |
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546 | |
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547 | /// \brief Constructor |
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548 | ColMap(const GridGraph& graph) : _graph(graph) {} |
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549 | |
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550 | /// \brief The subscript operator |
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551 | Value operator[](Key key) const { |
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552 | return _graph.col(key); |
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553 | } |
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554 | |
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555 | private: |
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556 | const GridGraph& _graph; |
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557 | }; |
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558 | |
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559 | /// \brief Map to get the row of the nodes. |
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560 | /// |
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561 | /// Map to get the row of the nodes. |
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562 | class RowMap { |
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563 | public: |
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564 | /// \brief The key type of the map |
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565 | typedef GridGraph::Node Key; |
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566 | /// \brief The value type of the map |
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567 | typedef int Value; |
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568 | |
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569 | /// \brief Constructor |
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570 | RowMap(const GridGraph& graph) : _graph(graph) {} |
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571 | |
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572 | /// \brief The subscript operator |
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573 | Value operator[](Key key) const { |
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574 | return _graph.row(key); |
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575 | } |
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576 | |
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577 | private: |
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578 | const GridGraph& _graph; |
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579 | }; |
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580 | |
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581 | /// \brief Constructor |
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582 | /// |
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583 | /// Construct a grid graph with the given size. |
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584 | GridGraph(int width, int height) { construct(width, height); } |
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585 | |
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586 | /// \brief Resizes the graph |
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587 | /// |
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588 | /// This function resizes the graph. It fully destroys and |
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589 | /// rebuilds the structure, therefore the maps of the graph will be |
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590 | /// reallocated automatically and the previous values will be lost. |
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591 | void resize(int width, int height) { |
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592 | Parent::notifier(Arc()).clear(); |
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593 | Parent::notifier(Edge()).clear(); |
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594 | Parent::notifier(Node()).clear(); |
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595 | construct(width, height); |
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596 | Parent::notifier(Node()).build(); |
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597 | Parent::notifier(Edge()).build(); |
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598 | Parent::notifier(Arc()).build(); |
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599 | } |
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600 | |
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601 | /// \brief The node on the given position. |
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602 | /// |
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603 | /// Gives back the node on the given position. |
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604 | Node operator()(int i, int j) const { |
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605 | return Parent::operator()(i, j); |
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606 | } |
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607 | |
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608 | /// \brief The column index of the node. |
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609 | /// |
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610 | /// Gives back the column index of the node. |
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611 | int col(Node n) const { |
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612 | return Parent::col(n); |
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613 | } |
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614 | |
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615 | /// \brief The row index of the node. |
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616 | /// |
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617 | /// Gives back the row index of the node. |
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618 | int row(Node n) const { |
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619 | return Parent::row(n); |
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620 | } |
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621 | |
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622 | /// \brief The position of the node. |
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623 | /// |
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624 | /// Gives back the position of the node, ie. the <tt>(col,row)</tt> pair. |
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625 | dim2::Point<int> pos(Node n) const { |
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626 | return Parent::pos(n); |
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627 | } |
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628 | |
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629 | /// \brief The number of the columns. |
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630 | /// |
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631 | /// Gives back the number of the columns. |
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632 | int width() const { |
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633 | return Parent::width(); |
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634 | } |
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635 | |
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636 | /// \brief The number of the rows. |
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637 | /// |
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638 | /// Gives back the number of the rows. |
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639 | int height() const { |
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640 | return Parent::height(); |
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641 | } |
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642 | |
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643 | /// \brief The arc goes right from the node. |
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644 | /// |
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645 | /// Gives back the arc goes right from the node. If there is not |
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646 | /// outgoing arc then it gives back INVALID. |
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647 | Arc right(Node n) const { |
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648 | return Parent::right(n); |
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649 | } |
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650 | |
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651 | /// \brief The arc goes left from the node. |
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652 | /// |
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653 | /// Gives back the arc goes left from the node. If there is not |
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654 | /// outgoing arc then it gives back INVALID. |
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655 | Arc left(Node n) const { |
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656 | return Parent::left(n); |
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657 | } |
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658 | |
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659 | /// \brief The arc goes up from the node. |
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660 | /// |
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661 | /// Gives back the arc goes up from the node. If there is not |
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662 | /// outgoing arc then it gives back INVALID. |
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663 | Arc up(Node n) const { |
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664 | return Parent::up(n); |
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665 | } |
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666 | |
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667 | /// \brief The arc goes down from the node. |
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668 | /// |
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669 | /// Gives back the arc goes down from the node. If there is not |
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670 | /// outgoing arc then it gives back INVALID. |
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671 | Arc down(Node n) const { |
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672 | return Parent::down(n); |
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673 | } |
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674 | |
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675 | /// \brief Index map of the grid graph |
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676 | /// |
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677 | /// Just returns an IndexMap for the grid graph. |
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678 | IndexMap indexMap() const { |
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679 | return IndexMap(*this); |
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680 | } |
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681 | |
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682 | /// \brief Row map of the grid graph |
---|
683 | /// |
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684 | /// Just returns a RowMap for the grid graph. |
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685 | RowMap rowMap() const { |
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686 | return RowMap(*this); |
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687 | } |
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688 | |
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689 | /// \brief Column map of the grid graph |
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690 | /// |
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691 | /// Just returns a ColMap for the grid graph. |
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692 | ColMap colMap() const { |
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693 | return ColMap(*this); |
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694 | } |
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695 | |
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696 | }; |
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697 | |
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698 | } |
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699 | #endif |
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