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1 /* -*- C++ -*- |
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2 * |
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3 * This file is a part of LEMON, a generic C++ optimization library |
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4 * |
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5 * Copyright (C) 2003-2007 |
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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 #ifndef LEMON_PLANARITY_H |
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19 #define LEMON_PLANARITY_H |
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20 |
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21 /// \ingroup graph_prop |
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22 /// \file |
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23 /// \brief Planarity checking, embedding |
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24 |
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25 #include <vector> |
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26 #include <list> |
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27 |
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28 #include <lemon/dfs.h> |
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29 #include <lemon/radix_sort.h> |
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30 #include <lemon/maps.h> |
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31 #include <lemon/path.h> |
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32 |
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33 |
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34 namespace lemon { |
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35 |
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36 namespace _planarity_bits { |
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37 |
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38 template <typename UGraph> |
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39 struct PlanarityVisitor : DfsVisitor<UGraph> { |
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40 |
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41 typedef typename UGraph::Node Node; |
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42 typedef typename UGraph::Edge Edge; |
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43 |
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44 typedef typename UGraph::template NodeMap<Edge> PredMap; |
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45 |
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46 typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
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47 |
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48 typedef typename UGraph::template NodeMap<int> OrderMap; |
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49 typedef std::vector<Node> OrderList; |
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50 |
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51 typedef typename UGraph::template NodeMap<int> LowMap; |
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52 typedef typename UGraph::template NodeMap<int> AncestorMap; |
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53 |
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54 PlanarityVisitor(const UGraph& ugraph, |
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55 PredMap& pred_map, TreeMap& tree_map, |
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56 OrderMap& order_map, OrderList& order_list, |
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57 AncestorMap& ancestor_map, LowMap& low_map) |
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58 : _ugraph(ugraph), _pred_map(pred_map), _tree_map(tree_map), |
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59 _order_map(order_map), _order_list(order_list), |
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60 _ancestor_map(ancestor_map), _low_map(low_map) {} |
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61 |
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62 void reach(const Node& node) { |
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63 _order_map[node] = _order_list.size(); |
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64 _low_map[node] = _order_list.size(); |
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65 _ancestor_map[node] = _order_list.size(); |
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66 _order_list.push_back(node); |
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67 } |
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68 |
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69 void discover(const Edge& edge) { |
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70 Node source = _ugraph.source(edge); |
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71 Node target = _ugraph.target(edge); |
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72 |
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73 _tree_map[edge] = true; |
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74 _pred_map[target] = edge; |
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75 } |
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76 |
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77 void examine(const Edge& edge) { |
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78 Node source = _ugraph.source(edge); |
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79 Node target = _ugraph.target(edge); |
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80 |
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81 if (_order_map[target] < _order_map[source] && !_tree_map[edge]) { |
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82 if (_low_map[source] > _order_map[target]) { |
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83 _low_map[source] = _order_map[target]; |
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84 } |
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85 if (_ancestor_map[source] > _order_map[target]) { |
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86 _ancestor_map[source] = _order_map[target]; |
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87 } |
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88 } |
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89 } |
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90 |
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91 void backtrack(const Edge& edge) { |
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92 Node source = _ugraph.source(edge); |
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93 Node target = _ugraph.target(edge); |
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94 |
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95 if (_low_map[source] > _low_map[target]) { |
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96 _low_map[source] = _low_map[target]; |
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97 } |
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98 } |
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99 |
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100 const UGraph& _ugraph; |
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101 PredMap& _pred_map; |
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102 TreeMap& _tree_map; |
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103 OrderMap& _order_map; |
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104 OrderList& _order_list; |
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105 AncestorMap& _ancestor_map; |
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106 LowMap& _low_map; |
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107 }; |
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108 |
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109 template <typename UGraph, bool embedding = true> |
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110 struct NodeDataNode { |
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111 int prev, next; |
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112 int visited; |
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113 typename UGraph::Edge first; |
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114 bool inverted; |
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115 }; |
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116 |
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117 template <typename UGraph> |
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118 struct NodeDataNode<UGraph, false> { |
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119 int prev, next; |
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120 int visited; |
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121 }; |
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122 |
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123 template <typename UGraph> |
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124 struct ChildListNode { |
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125 typedef typename UGraph::Node Node; |
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126 Node first; |
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127 Node prev, next; |
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128 }; |
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129 |
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130 template <typename UGraph> |
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131 struct EdgeListNode { |
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132 typename UGraph::Edge prev, next; |
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133 }; |
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134 |
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135 } |
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136 |
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137 /// \ingroup graph_prop |
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138 /// |
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139 /// \brief Planarity checking of an undirected simple graph |
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140 /// |
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141 /// This class implements the Boyer-Myrvold algorithm for planar |
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142 /// checking of an undirected graph. This class is a simplified |
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143 /// version of the PlanarEmbedding algorithm class, and it does |
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144 /// provide neither embedding nor kuratowski subdivisons. |
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145 template <typename UGraph> |
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146 class PlanarityChecking { |
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147 private: |
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148 |
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149 UGRAPH_TYPEDEFS(typename UGraph) |
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150 |
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151 const UGraph& _ugraph; |
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152 |
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153 private: |
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154 |
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155 typedef typename UGraph::template NodeMap<Edge> PredMap; |
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156 |
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157 typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
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158 |
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159 typedef typename UGraph::template NodeMap<int> OrderMap; |
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160 typedef std::vector<Node> OrderList; |
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161 |
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162 typedef typename UGraph::template NodeMap<int> LowMap; |
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163 typedef typename UGraph::template NodeMap<int> AncestorMap; |
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164 |
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165 typedef _planarity_bits::NodeDataNode<UGraph> NodeDataNode; |
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166 typedef std::vector<NodeDataNode> NodeData; |
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167 |
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168 typedef _planarity_bits::ChildListNode<UGraph> ChildListNode; |
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169 typedef typename UGraph::template NodeMap<ChildListNode> ChildLists; |
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170 |
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171 typedef typename UGraph::template NodeMap<std::list<int> > MergeRoots; |
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172 |
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173 typedef typename UGraph::template NodeMap<bool> EmbedEdge; |
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174 |
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175 public: |
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176 |
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177 /// \brief Constructor |
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178 /// |
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179 /// \warining The graph should be simple, i.e. parallel and loop edge |
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180 /// free. |
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181 PlanarityChecking(const UGraph& ugraph) : _ugraph(ugraph) {} |
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182 |
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183 /// \brief Runs the algorithm. |
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184 /// |
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185 /// Runs the algorithm. |
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186 /// \param kuratowski If the parameter is false, then the |
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187 /// algorithm does not calculate the isolate Kuratowski |
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188 /// subdivisions. |
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189 /// \return %True when the graph is planar. |
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190 bool run(bool kuratowski = true) { |
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191 typedef _planarity_bits::PlanarityVisitor<UGraph> Visitor; |
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192 |
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193 PredMap pred_map(_ugraph, INVALID); |
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194 TreeMap tree_map(_ugraph, false); |
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195 |
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196 OrderMap order_map(_ugraph, -1); |
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197 OrderList order_list; |
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198 |
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199 AncestorMap ancestor_map(_ugraph, -1); |
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200 LowMap low_map(_ugraph, -1); |
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201 |
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202 Visitor visitor(_ugraph, pred_map, tree_map, |
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203 order_map, order_list, ancestor_map, low_map); |
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204 DfsVisit<UGraph, Visitor> visit(_ugraph, visitor); |
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205 visit.run(); |
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206 |
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207 ChildLists child_lists(_ugraph); |
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208 createChildLists(tree_map, order_map, low_map, child_lists); |
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209 |
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210 NodeData node_data(2 * order_list.size()); |
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211 |
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212 EmbedEdge embed_edge(_ugraph, false); |
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213 |
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214 MergeRoots merge_roots(_ugraph); |
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215 |
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216 for (int i = order_list.size() - 1; i >= 0; --i) { |
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217 |
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218 Node node = order_list[i]; |
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219 |
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220 Node source = node; |
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221 for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
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222 Node target = _ugraph.target(e); |
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223 |
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224 if (order_map[source] < order_map[target] && tree_map[e]) { |
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225 initFace(target, node_data, pred_map, order_map, order_list); |
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226 } |
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227 } |
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228 |
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229 for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
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230 Node target = _ugraph.target(e); |
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231 |
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232 if (order_map[source] < order_map[target] && !tree_map[e]) { |
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233 embed_edge[target] = true; |
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234 walkUp(target, source, i, pred_map, low_map, |
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235 order_map, order_list, node_data, merge_roots); |
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236 } |
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237 } |
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238 |
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239 for (typename MergeRoots::Value::iterator it = |
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240 merge_roots[node].begin(); it != merge_roots[node].end(); ++it) { |
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241 int rn = *it; |
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242 walkDown(rn, i, node_data, order_list, child_lists, |
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243 ancestor_map, low_map, embed_edge, merge_roots); |
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244 } |
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245 merge_roots[node].clear(); |
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246 |
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247 for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
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248 Node target = _ugraph.target(e); |
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249 |
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250 if (order_map[source] < order_map[target] && !tree_map[e]) { |
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251 if (embed_edge[target]) { |
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252 return false; |
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253 } |
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254 } |
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255 } |
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256 } |
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257 |
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258 return true; |
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259 } |
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260 |
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261 private: |
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262 |
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263 void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
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264 const LowMap& low_map, ChildLists& child_lists) { |
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265 |
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266 for (NodeIt n(_ugraph); n != INVALID; ++n) { |
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267 Node source = n; |
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268 |
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269 std::vector<Node> targets; |
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270 for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
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271 Node target = _ugraph.target(e); |
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272 |
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273 if (order_map[source] < order_map[target] && tree_map[e]) { |
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274 targets.push_back(target); |
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275 } |
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276 } |
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277 |
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278 if (targets.size() == 0) { |
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279 child_lists[source].first = INVALID; |
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280 } else if (targets.size() == 1) { |
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281 child_lists[source].first = targets[0]; |
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282 child_lists[targets[0]].prev = INVALID; |
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283 child_lists[targets[0]].next = INVALID; |
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284 } else { |
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285 radixSort(targets.begin(), targets.end(), mapFunctor(low_map)); |
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286 for (int i = 1; i < int(targets.size()); ++i) { |
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287 child_lists[targets[i]].prev = targets[i - 1]; |
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288 child_lists[targets[i - 1]].next = targets[i]; |
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289 } |
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290 child_lists[targets.back()].next = INVALID; |
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291 child_lists[targets.front()].prev = INVALID; |
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292 child_lists[source].first = targets.front(); |
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293 } |
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294 } |
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295 } |
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296 |
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297 void walkUp(const Node& node, Node root, int rorder, |
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298 const PredMap& pred_map, const LowMap& low_map, |
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299 const OrderMap& order_map, const OrderList& order_list, |
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300 NodeData& node_data, MergeRoots& merge_roots) { |
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301 |
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302 int na, nb; |
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303 bool da, db; |
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304 |
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305 na = nb = order_map[node]; |
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306 da = true; db = false; |
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307 |
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308 while (true) { |
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309 |
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310 if (node_data[na].visited == rorder) break; |
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311 if (node_data[nb].visited == rorder) break; |
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312 |
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313 node_data[na].visited = rorder; |
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314 node_data[nb].visited = rorder; |
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315 |
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316 int rn = -1; |
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317 |
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318 if (na >= int(order_list.size())) { |
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319 rn = na; |
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320 } else if (nb >= int(order_list.size())) { |
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321 rn = nb; |
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322 } |
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323 |
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324 if (rn == -1) { |
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325 int nn; |
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326 |
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327 nn = da ? node_data[na].prev : node_data[na].next; |
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328 da = node_data[nn].prev != na; |
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329 na = nn; |
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330 |
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331 nn = db ? node_data[nb].prev : node_data[nb].next; |
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332 db = node_data[nn].prev != nb; |
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333 nb = nn; |
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334 |
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335 } else { |
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336 |
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337 Node rep = order_list[rn - order_list.size()]; |
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338 Node parent = _ugraph.source(pred_map[rep]); |
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339 |
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340 if (low_map[rep] < rorder) { |
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341 merge_roots[parent].push_back(rn); |
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342 } else { |
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343 merge_roots[parent].push_front(rn); |
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344 } |
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345 |
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346 if (parent != root) { |
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347 na = nb = order_map[parent]; |
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348 da = true; db = false; |
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349 } else { |
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350 break; |
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351 } |
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352 } |
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353 } |
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354 } |
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355 |
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356 void walkDown(int rn, int rorder, NodeData& node_data, |
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357 OrderList& order_list, ChildLists& child_lists, |
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358 AncestorMap& ancestor_map, LowMap& low_map, |
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359 EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
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360 |
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361 std::vector<std::pair<int, bool> > merge_stack; |
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362 |
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363 for (int di = 0; di < 2; ++di) { |
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364 bool rd = di == 0; |
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365 int pn = rn; |
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366 int n = rd ? node_data[rn].next : node_data[rn].prev; |
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367 |
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368 while (n != rn) { |
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369 |
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370 Node node = order_list[n]; |
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371 |
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372 if (embed_edge[node]) { |
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373 |
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374 // Merging components on the critical path |
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375 while (!merge_stack.empty()) { |
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376 |
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377 // Component root |
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378 int cn = merge_stack.back().first; |
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379 bool cd = merge_stack.back().second; |
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380 merge_stack.pop_back(); |
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381 |
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382 // Parent of component |
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383 int dn = merge_stack.back().first; |
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384 bool dd = merge_stack.back().second; |
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385 merge_stack.pop_back(); |
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386 |
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387 Node parent = order_list[dn]; |
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388 |
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389 // Erasing from merge_roots |
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390 merge_roots[parent].pop_front(); |
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391 |
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392 Node child = order_list[cn - order_list.size()]; |
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393 |
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394 // Erasing from child_lists |
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395 if (child_lists[child].prev != INVALID) { |
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396 child_lists[child_lists[child].prev].next = |
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397 child_lists[child].next; |
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398 } else { |
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399 child_lists[parent].first = child_lists[child].next; |
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400 } |
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401 |
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402 if (child_lists[child].next != INVALID) { |
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403 child_lists[child_lists[child].next].prev = |
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404 child_lists[child].prev; |
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405 } |
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406 |
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407 // Merging external faces |
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408 { |
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409 int en = cn; |
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410 cn = cd ? node_data[cn].prev : node_data[cn].next; |
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411 cd = node_data[cn].next == en; |
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412 |
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413 } |
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414 |
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415 if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
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416 if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
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417 |
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418 } |
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419 |
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420 bool d = pn == node_data[n].prev; |
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421 |
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422 if (node_data[n].prev == node_data[n].next && |
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423 node_data[n].inverted) { |
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424 d = !d; |
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425 } |
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426 |
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427 // Embedding edge into external face |
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428 if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
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429 if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
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430 pn = rn; |
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431 |
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432 embed_edge[order_list[n]] = false; |
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433 } |
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434 |
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435 if (!merge_roots[node].empty()) { |
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436 |
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437 bool d = pn == node_data[n].prev; |
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438 |
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439 merge_stack.push_back(std::make_pair(n, d)); |
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440 |
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441 int rn = merge_roots[node].front(); |
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442 |
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443 int xn = node_data[rn].next; |
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444 Node xnode = order_list[xn]; |
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445 |
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446 int yn = node_data[rn].prev; |
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447 Node ynode = order_list[yn]; |
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448 |
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449 bool rd; |
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450 if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) { |
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451 rd = true; |
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452 } else if (!external(ynode, rorder, child_lists, |
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453 ancestor_map, low_map)) { |
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454 rd = false; |
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455 } else if (pertinent(xnode, embed_edge, merge_roots)) { |
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456 rd = true; |
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457 } else { |
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458 rd = false; |
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459 } |
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460 |
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461 merge_stack.push_back(std::make_pair(rn, rd)); |
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462 |
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463 pn = rn; |
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464 n = rd ? xn : yn; |
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465 |
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466 } else if (!external(node, rorder, child_lists, |
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467 ancestor_map, low_map)) { |
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468 int nn = (node_data[n].next != pn ? |
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469 node_data[n].next : node_data[n].prev); |
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470 |
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471 bool nd = n == node_data[nn].prev; |
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472 |
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473 if (nd) node_data[nn].prev = pn; |
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474 else node_data[nn].next = pn; |
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475 |
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476 if (n == node_data[pn].prev) node_data[pn].prev = nn; |
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477 else node_data[pn].next = nn; |
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478 |
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479 node_data[nn].inverted = |
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480 (node_data[nn].prev == node_data[nn].next && nd != rd); |
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481 |
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482 n = nn; |
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483 } |
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484 else break; |
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485 |
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486 } |
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487 |
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488 if (!merge_stack.empty() || n == rn) { |
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489 break; |
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490 } |
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491 } |
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492 } |
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493 |
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494 void initFace(const Node& node, NodeData& node_data, |
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495 const PredMap& pred_map, const OrderMap& order_map, |
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496 const OrderList& order_list) { |
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497 int n = order_map[node]; |
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498 int rn = n + order_list.size(); |
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499 |
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500 node_data[n].next = node_data[n].prev = rn; |
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501 node_data[rn].next = node_data[rn].prev = n; |
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502 |
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503 node_data[n].visited = order_list.size(); |
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504 node_data[rn].visited = order_list.size(); |
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505 |
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506 } |
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507 |
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508 bool external(const Node& node, int rorder, |
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509 ChildLists& child_lists, AncestorMap& ancestor_map, |
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510 LowMap& low_map) { |
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511 Node child = child_lists[node].first; |
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512 |
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513 if (child != INVALID) { |
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514 if (low_map[child] < rorder) return true; |
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515 } |
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516 |
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517 if (ancestor_map[node] < rorder) return true; |
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518 |
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519 return false; |
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520 } |
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521 |
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522 bool pertinent(const Node& node, const EmbedEdge& embed_edge, |
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523 const MergeRoots& merge_roots) { |
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524 return !merge_roots[node].empty() || embed_edge[node]; |
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525 } |
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526 |
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527 }; |
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528 |
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529 /// \ingroup graph_prop |
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530 /// |
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531 /// \brief Planar embedding of an undirected simple graph |
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532 /// |
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533 /// This class implements the Boyer-Myrvold algorithm for planar |
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534 /// embedding of an undirected graph. The planar embeding is an |
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535 /// ordering of the outgoing edges in each node, which is a possible |
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536 /// configuration to draw the graph in the plane. If there is not |
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537 /// such ordering then the graph contains a \f$ K_5 \f$ (full graph |
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538 /// with 5 nodes) or an \f$ K_{3,3} \f$ (complete bipartite graph on |
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539 /// 3 ANode and 3 BNode) subdivision. |
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540 /// |
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541 /// The current implementation calculates an embedding or an |
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542 /// Kuratowski subdivision if the graph is not planar. The running |
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543 /// time of the algorithm is \f$ O(n) \f$. |
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544 template <typename UGraph> |
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545 class PlanarEmbedding { |
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546 private: |
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547 |
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548 UGRAPH_TYPEDEFS(typename UGraph) |
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549 |
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550 const UGraph& _ugraph; |
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551 typename UGraph::template EdgeMap<Edge> _embedding; |
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552 |
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553 typename UGraph::template UEdgeMap<bool> _kuratowski; |
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554 |
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555 private: |
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556 |
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557 typedef typename UGraph::template NodeMap<Edge> PredMap; |
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558 |
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559 typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
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560 |
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561 typedef typename UGraph::template NodeMap<int> OrderMap; |
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562 typedef std::vector<Node> OrderList; |
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563 |
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564 typedef typename UGraph::template NodeMap<int> LowMap; |
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565 typedef typename UGraph::template NodeMap<int> AncestorMap; |
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566 |
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567 typedef _planarity_bits::NodeDataNode<UGraph> NodeDataNode; |
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568 typedef std::vector<NodeDataNode> NodeData; |
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569 |
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570 typedef _planarity_bits::ChildListNode<UGraph> ChildListNode; |
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571 typedef typename UGraph::template NodeMap<ChildListNode> ChildLists; |
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572 |
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573 typedef typename UGraph::template NodeMap<std::list<int> > MergeRoots; |
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574 |
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575 typedef typename UGraph::template NodeMap<Edge> EmbedEdge; |
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576 |
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577 typedef _planarity_bits::EdgeListNode<UGraph> EdgeListNode; |
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578 typedef typename UGraph::template EdgeMap<EdgeListNode> EdgeLists; |
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579 |
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580 typedef typename UGraph::template NodeMap<bool> FlipMap; |
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581 |
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582 typedef typename UGraph::template NodeMap<int> TypeMap; |
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583 |
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584 enum IsolatorNodeType { |
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585 HIGHX = 6, LOWX = 7, |
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586 HIGHY = 8, LOWY = 9, |
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587 ROOT = 10, PERTINENT = 11, |
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588 INTERNAL = 12 |
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589 }; |
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590 |
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591 public: |
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592 |
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593 /// \brief Constructor |
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594 /// |
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595 /// \warining The graph should be simple, i.e. parallel and loop edge |
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596 /// free. |
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597 PlanarEmbedding(const UGraph& ugraph) |
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598 : _ugraph(ugraph), _embedding(_ugraph), _kuratowski(ugraph, false) {} |
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599 |
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600 /// \brief Runs the algorithm. |
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601 /// |
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602 /// Runs the algorithm. |
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603 /// \param kuratowski If the parameter is false, then the |
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604 /// algorithm does not calculate the isolate Kuratowski |
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605 /// subdivisions. |
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606 ///\return %True when the graph is planar. |
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607 bool run(bool kuratowski = true) { |
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608 typedef _planarity_bits::PlanarityVisitor<UGraph> Visitor; |
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609 |
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610 PredMap pred_map(_ugraph, INVALID); |
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611 TreeMap tree_map(_ugraph, false); |
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612 |
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613 OrderMap order_map(_ugraph, -1); |
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614 OrderList order_list; |
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615 |
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616 AncestorMap ancestor_map(_ugraph, -1); |
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617 LowMap low_map(_ugraph, -1); |
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618 |
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619 Visitor visitor(_ugraph, pred_map, tree_map, |
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620 order_map, order_list, ancestor_map, low_map); |
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621 DfsVisit<UGraph, Visitor> visit(_ugraph, visitor); |
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622 visit.run(); |
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623 |
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624 ChildLists child_lists(_ugraph); |
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625 createChildLists(tree_map, order_map, low_map, child_lists); |
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626 |
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627 NodeData node_data(2 * order_list.size()); |
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628 |
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629 EmbedEdge embed_edge(_ugraph, INVALID); |
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630 |
|
631 MergeRoots merge_roots(_ugraph); |
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632 |
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633 EdgeLists edge_lists(_ugraph); |
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634 |
|
635 FlipMap flip_map(_ugraph, false); |
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636 |
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637 for (int i = order_list.size() - 1; i >= 0; --i) { |
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638 |
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639 Node node = order_list[i]; |
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640 |
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641 node_data[i].first = INVALID; |
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642 |
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643 Node source = node; |
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644 for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
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645 Node target = _ugraph.target(e); |
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646 |
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647 if (order_map[source] < order_map[target] && tree_map[e]) { |
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648 initFace(target, edge_lists, node_data, |
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649 pred_map, order_map, order_list); |
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650 } |
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651 } |
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652 |
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653 for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
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654 Node target = _ugraph.target(e); |
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655 |
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656 if (order_map[source] < order_map[target] && !tree_map[e]) { |
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657 embed_edge[target] = e; |
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658 walkUp(target, source, i, pred_map, low_map, |
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659 order_map, order_list, node_data, merge_roots); |
|
660 } |
|
661 } |
|
662 |
|
663 for (typename MergeRoots::Value::iterator it = |
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664 merge_roots[node].begin(); it != merge_roots[node].end(); ++it) { |
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665 int rn = *it; |
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666 walkDown(rn, i, node_data, edge_lists, flip_map, order_list, |
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667 child_lists, ancestor_map, low_map, embed_edge, merge_roots); |
|
668 } |
|
669 merge_roots[node].clear(); |
|
670 |
|
671 for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
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672 Node target = _ugraph.target(e); |
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673 |
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674 if (order_map[source] < order_map[target] && !tree_map[e]) { |
|
675 if (embed_edge[target] != INVALID) { |
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676 if (kuratowski) { |
|
677 isolateKuratowski(e, node_data, edge_lists, flip_map, |
|
678 order_map, order_list, pred_map, child_lists, |
|
679 ancestor_map, low_map, |
|
680 embed_edge, merge_roots); |
|
681 } |
|
682 return false; |
|
683 } |
|
684 } |
|
685 } |
|
686 } |
|
687 |
|
688 for (int i = 0; i < int(order_list.size()); ++i) { |
|
689 |
|
690 mergeRemainingFaces(order_list[i], node_data, order_list, order_map, |
|
691 child_lists, edge_lists); |
|
692 storeEmbedding(order_list[i], node_data, order_map, pred_map, |
|
693 edge_lists, flip_map); |
|
694 } |
|
695 |
|
696 return true; |
|
697 } |
|
698 |
|
699 /// \brief Gives back the successor of an edge |
|
700 /// |
|
701 /// Gives back the successor of an edge. This function makes |
|
702 /// possible to query the cyclic order of the outgoing edges from |
|
703 /// a node. |
|
704 Edge next(const Edge& edge) const { |
|
705 return _embedding[edge]; |
|
706 } |
|
707 |
|
708 /// \brief Gives back true when the undirected edge is in the |
|
709 /// kuratowski subdivision |
|
710 /// |
|
711 /// Gives back true when the undirected edge is in the kuratowski |
|
712 /// subdivision |
|
713 bool kuratowski(const UEdge& uedge) { |
|
714 return _kuratowski[uedge]; |
|
715 } |
|
716 |
|
717 private: |
|
718 |
|
719 void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
|
720 const LowMap& low_map, ChildLists& child_lists) { |
|
721 |
|
722 for (NodeIt n(_ugraph); n != INVALID; ++n) { |
|
723 Node source = n; |
|
724 |
|
725 std::vector<Node> targets; |
|
726 for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
|
727 Node target = _ugraph.target(e); |
|
728 |
|
729 if (order_map[source] < order_map[target] && tree_map[e]) { |
|
730 targets.push_back(target); |
|
731 } |
|
732 } |
|
733 |
|
734 if (targets.size() == 0) { |
|
735 child_lists[source].first = INVALID; |
|
736 } else if (targets.size() == 1) { |
|
737 child_lists[source].first = targets[0]; |
|
738 child_lists[targets[0]].prev = INVALID; |
|
739 child_lists[targets[0]].next = INVALID; |
|
740 } else { |
|
741 radixSort(targets.begin(), targets.end(), mapFunctor(low_map)); |
|
742 for (int i = 1; i < int(targets.size()); ++i) { |
|
743 child_lists[targets[i]].prev = targets[i - 1]; |
|
744 child_lists[targets[i - 1]].next = targets[i]; |
|
745 } |
|
746 child_lists[targets.back()].next = INVALID; |
|
747 child_lists[targets.front()].prev = INVALID; |
|
748 child_lists[source].first = targets.front(); |
|
749 } |
|
750 } |
|
751 } |
|
752 |
|
753 void walkUp(const Node& node, Node root, int rorder, |
|
754 const PredMap& pred_map, const LowMap& low_map, |
|
755 const OrderMap& order_map, const OrderList& order_list, |
|
756 NodeData& node_data, MergeRoots& merge_roots) { |
|
757 |
|
758 int na, nb; |
|
759 bool da, db; |
|
760 |
|
761 na = nb = order_map[node]; |
|
762 da = true; db = false; |
|
763 |
|
764 while (true) { |
|
765 |
|
766 if (node_data[na].visited == rorder) break; |
|
767 if (node_data[nb].visited == rorder) break; |
|
768 |
|
769 node_data[na].visited = rorder; |
|
770 node_data[nb].visited = rorder; |
|
771 |
|
772 int rn = -1; |
|
773 |
|
774 if (na >= int(order_list.size())) { |
|
775 rn = na; |
|
776 } else if (nb >= int(order_list.size())) { |
|
777 rn = nb; |
|
778 } |
|
779 |
|
780 if (rn == -1) { |
|
781 int nn; |
|
782 |
|
783 nn = da ? node_data[na].prev : node_data[na].next; |
|
784 da = node_data[nn].prev != na; |
|
785 na = nn; |
|
786 |
|
787 nn = db ? node_data[nb].prev : node_data[nb].next; |
|
788 db = node_data[nn].prev != nb; |
|
789 nb = nn; |
|
790 |
|
791 } else { |
|
792 |
|
793 Node rep = order_list[rn - order_list.size()]; |
|
794 Node parent = _ugraph.source(pred_map[rep]); |
|
795 |
|
796 if (low_map[rep] < rorder) { |
|
797 merge_roots[parent].push_back(rn); |
|
798 } else { |
|
799 merge_roots[parent].push_front(rn); |
|
800 } |
|
801 |
|
802 if (parent != root) { |
|
803 na = nb = order_map[parent]; |
|
804 da = true; db = false; |
|
805 } else { |
|
806 break; |
|
807 } |
|
808 } |
|
809 } |
|
810 } |
|
811 |
|
812 void walkDown(int rn, int rorder, NodeData& node_data, |
|
813 EdgeLists& edge_lists, FlipMap& flip_map, |
|
814 OrderList& order_list, ChildLists& child_lists, |
|
815 AncestorMap& ancestor_map, LowMap& low_map, |
|
816 EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
|
817 |
|
818 std::vector<std::pair<int, bool> > merge_stack; |
|
819 |
|
820 for (int di = 0; di < 2; ++di) { |
|
821 bool rd = di == 0; |
|
822 int pn = rn; |
|
823 int n = rd ? node_data[rn].next : node_data[rn].prev; |
|
824 |
|
825 while (n != rn) { |
|
826 |
|
827 Node node = order_list[n]; |
|
828 |
|
829 if (embed_edge[node] != INVALID) { |
|
830 |
|
831 // Merging components on the critical path |
|
832 while (!merge_stack.empty()) { |
|
833 |
|
834 // Component root |
|
835 int cn = merge_stack.back().first; |
|
836 bool cd = merge_stack.back().second; |
|
837 merge_stack.pop_back(); |
|
838 |
|
839 // Parent of component |
|
840 int dn = merge_stack.back().first; |
|
841 bool dd = merge_stack.back().second; |
|
842 merge_stack.pop_back(); |
|
843 |
|
844 Node parent = order_list[dn]; |
|
845 |
|
846 // Erasing from merge_roots |
|
847 merge_roots[parent].pop_front(); |
|
848 |
|
849 Node child = order_list[cn - order_list.size()]; |
|
850 |
|
851 // Erasing from child_lists |
|
852 if (child_lists[child].prev != INVALID) { |
|
853 child_lists[child_lists[child].prev].next = |
|
854 child_lists[child].next; |
|
855 } else { |
|
856 child_lists[parent].first = child_lists[child].next; |
|
857 } |
|
858 |
|
859 if (child_lists[child].next != INVALID) { |
|
860 child_lists[child_lists[child].next].prev = |
|
861 child_lists[child].prev; |
|
862 } |
|
863 |
|
864 // Merging edges + flipping |
|
865 Edge de = node_data[dn].first; |
|
866 Edge ce = node_data[cn].first; |
|
867 |
|
868 flip_map[order_list[cn - order_list.size()]] = cd != dd; |
|
869 if (cd != dd) { |
|
870 std::swap(edge_lists[ce].prev, edge_lists[ce].next); |
|
871 ce = edge_lists[ce].prev; |
|
872 std::swap(edge_lists[ce].prev, edge_lists[ce].next); |
|
873 } |
|
874 |
|
875 { |
|
876 Edge dne = edge_lists[de].next; |
|
877 Edge cne = edge_lists[ce].next; |
|
878 |
|
879 edge_lists[de].next = cne; |
|
880 edge_lists[ce].next = dne; |
|
881 |
|
882 edge_lists[dne].prev = ce; |
|
883 edge_lists[cne].prev = de; |
|
884 } |
|
885 |
|
886 if (dd) { |
|
887 node_data[dn].first = ce; |
|
888 } |
|
889 |
|
890 // Merging external faces |
|
891 { |
|
892 int en = cn; |
|
893 cn = cd ? node_data[cn].prev : node_data[cn].next; |
|
894 cd = node_data[cn].next == en; |
|
895 |
|
896 if (node_data[cn].prev == node_data[cn].next && |
|
897 node_data[cn].inverted) { |
|
898 cd = !cd; |
|
899 } |
|
900 } |
|
901 |
|
902 if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
|
903 if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
|
904 |
|
905 } |
|
906 |
|
907 bool d = pn == node_data[n].prev; |
|
908 |
|
909 if (node_data[n].prev == node_data[n].next && |
|
910 node_data[n].inverted) { |
|
911 d = !d; |
|
912 } |
|
913 |
|
914 // Add new edge |
|
915 { |
|
916 Edge edge = embed_edge[node]; |
|
917 Edge re = node_data[rn].first; |
|
918 |
|
919 edge_lists[edge_lists[re].next].prev = edge; |
|
920 edge_lists[edge].next = edge_lists[re].next; |
|
921 edge_lists[edge].prev = re; |
|
922 edge_lists[re].next = edge; |
|
923 |
|
924 if (!rd) { |
|
925 node_data[rn].first = edge; |
|
926 } |
|
927 |
|
928 Edge rev = _ugraph.oppositeEdge(edge); |
|
929 Edge e = node_data[n].first; |
|
930 |
|
931 edge_lists[edge_lists[e].next].prev = rev; |
|
932 edge_lists[rev].next = edge_lists[e].next; |
|
933 edge_lists[rev].prev = e; |
|
934 edge_lists[e].next = rev; |
|
935 |
|
936 if (d) { |
|
937 node_data[n].first = rev; |
|
938 } |
|
939 |
|
940 } |
|
941 |
|
942 // Embedding edge into external face |
|
943 if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
|
944 if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
|
945 pn = rn; |
|
946 |
|
947 embed_edge[order_list[n]] = INVALID; |
|
948 } |
|
949 |
|
950 if (!merge_roots[node].empty()) { |
|
951 |
|
952 bool d = pn == node_data[n].prev; |
|
953 if (node_data[n].prev == node_data[n].next && |
|
954 node_data[n].inverted) { |
|
955 d = !d; |
|
956 } |
|
957 |
|
958 merge_stack.push_back(std::make_pair(n, d)); |
|
959 |
|
960 int rn = merge_roots[node].front(); |
|
961 |
|
962 int xn = node_data[rn].next; |
|
963 Node xnode = order_list[xn]; |
|
964 |
|
965 int yn = node_data[rn].prev; |
|
966 Node ynode = order_list[yn]; |
|
967 |
|
968 bool rd; |
|
969 if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) { |
|
970 rd = true; |
|
971 } else if (!external(ynode, rorder, child_lists, |
|
972 ancestor_map, low_map)) { |
|
973 rd = false; |
|
974 } else if (pertinent(xnode, embed_edge, merge_roots)) { |
|
975 rd = true; |
|
976 } else { |
|
977 rd = false; |
|
978 } |
|
979 |
|
980 merge_stack.push_back(std::make_pair(rn, rd)); |
|
981 |
|
982 pn = rn; |
|
983 n = rd ? xn : yn; |
|
984 |
|
985 } else if (!external(node, rorder, child_lists, |
|
986 ancestor_map, low_map)) { |
|
987 int nn = (node_data[n].next != pn ? |
|
988 node_data[n].next : node_data[n].prev); |
|
989 |
|
990 bool nd = n == node_data[nn].prev; |
|
991 |
|
992 if (nd) node_data[nn].prev = pn; |
|
993 else node_data[nn].next = pn; |
|
994 |
|
995 if (n == node_data[pn].prev) node_data[pn].prev = nn; |
|
996 else node_data[pn].next = nn; |
|
997 |
|
998 node_data[nn].inverted = |
|
999 (node_data[nn].prev == node_data[nn].next && nd != rd); |
|
1000 |
|
1001 n = nn; |
|
1002 } |
|
1003 else break; |
|
1004 |
|
1005 } |
|
1006 |
|
1007 if (!merge_stack.empty() || n == rn) { |
|
1008 break; |
|
1009 } |
|
1010 } |
|
1011 } |
|
1012 |
|
1013 void initFace(const Node& node, EdgeLists& edge_lists, |
|
1014 NodeData& node_data, const PredMap& pred_map, |
|
1015 const OrderMap& order_map, const OrderList& order_list) { |
|
1016 int n = order_map[node]; |
|
1017 int rn = n + order_list.size(); |
|
1018 |
|
1019 node_data[n].next = node_data[n].prev = rn; |
|
1020 node_data[rn].next = node_data[rn].prev = n; |
|
1021 |
|
1022 node_data[n].visited = order_list.size(); |
|
1023 node_data[rn].visited = order_list.size(); |
|
1024 |
|
1025 node_data[n].inverted = false; |
|
1026 node_data[rn].inverted = false; |
|
1027 |
|
1028 Edge edge = pred_map[node]; |
|
1029 Edge rev = _ugraph.oppositeEdge(edge); |
|
1030 |
|
1031 node_data[rn].first = edge; |
|
1032 node_data[n].first = rev; |
|
1033 |
|
1034 edge_lists[edge].prev = edge; |
|
1035 edge_lists[edge].next = edge; |
|
1036 |
|
1037 edge_lists[rev].prev = rev; |
|
1038 edge_lists[rev].next = rev; |
|
1039 |
|
1040 } |
|
1041 |
|
1042 void mergeRemainingFaces(const Node& node, NodeData& node_data, |
|
1043 OrderList& order_list, OrderMap& order_map, |
|
1044 ChildLists& child_lists, EdgeLists& edge_lists) { |
|
1045 while (child_lists[node].first != INVALID) { |
|
1046 int dd = order_map[node]; |
|
1047 Node child = child_lists[node].first; |
|
1048 int cd = order_map[child] + order_list.size(); |
|
1049 child_lists[node].first = child_lists[child].next; |
|
1050 |
|
1051 Edge de = node_data[dd].first; |
|
1052 Edge ce = node_data[cd].first; |
|
1053 |
|
1054 if (de != INVALID) { |
|
1055 Edge dne = edge_lists[de].next; |
|
1056 Edge cne = edge_lists[ce].next; |
|
1057 |
|
1058 edge_lists[de].next = cne; |
|
1059 edge_lists[ce].next = dne; |
|
1060 |
|
1061 edge_lists[dne].prev = ce; |
|
1062 edge_lists[cne].prev = de; |
|
1063 } |
|
1064 |
|
1065 node_data[dd].first = ce; |
|
1066 |
|
1067 } |
|
1068 } |
|
1069 |
|
1070 void storeEmbedding(const Node& node, NodeData& node_data, |
|
1071 OrderMap& order_map, PredMap& pred_map, |
|
1072 EdgeLists& edge_lists, FlipMap& flip_map) { |
|
1073 |
|
1074 if (node_data[order_map[node]].first == INVALID) return; |
|
1075 |
|
1076 if (pred_map[node] != INVALID) { |
|
1077 Node source = _ugraph.source(pred_map[node]); |
|
1078 flip_map[node] = flip_map[node] != flip_map[source]; |
|
1079 } |
|
1080 |
|
1081 Edge first = node_data[order_map[node]].first; |
|
1082 Edge prev = first; |
|
1083 |
|
1084 Edge edge = flip_map[node] ? |
|
1085 edge_lists[prev].prev : edge_lists[prev].next; |
|
1086 |
|
1087 _embedding[prev] = edge; |
|
1088 |
|
1089 while (edge != first) { |
|
1090 Edge next = edge_lists[edge].prev == prev ? |
|
1091 edge_lists[edge].next : edge_lists[edge].prev; |
|
1092 prev = edge; edge = next; |
|
1093 _embedding[prev] = edge; |
|
1094 } |
|
1095 } |
|
1096 |
|
1097 |
|
1098 bool external(const Node& node, int rorder, |
|
1099 ChildLists& child_lists, AncestorMap& ancestor_map, |
|
1100 LowMap& low_map) { |
|
1101 Node child = child_lists[node].first; |
|
1102 |
|
1103 if (child != INVALID) { |
|
1104 if (low_map[child] < rorder) return true; |
|
1105 } |
|
1106 |
|
1107 if (ancestor_map[node] < rorder) return true; |
|
1108 |
|
1109 return false; |
|
1110 } |
|
1111 |
|
1112 bool pertinent(const Node& node, const EmbedEdge& embed_edge, |
|
1113 const MergeRoots& merge_roots) { |
|
1114 return !merge_roots[node].empty() || embed_edge[node] != INVALID; |
|
1115 } |
|
1116 |
|
1117 int lowPoint(const Node& node, OrderMap& order_map, ChildLists& child_lists, |
|
1118 AncestorMap& ancestor_map, LowMap& low_map) { |
|
1119 int low_point; |
|
1120 |
|
1121 Node child = child_lists[node].first; |
|
1122 |
|
1123 if (child != INVALID) { |
|
1124 low_point = low_map[child]; |
|
1125 } else { |
|
1126 low_point = order_map[node]; |
|
1127 } |
|
1128 |
|
1129 if (low_point > ancestor_map[node]) { |
|
1130 low_point = ancestor_map[node]; |
|
1131 } |
|
1132 |
|
1133 return low_point; |
|
1134 } |
|
1135 |
|
1136 int findComponentRoot(Node root, Node node, ChildLists& child_lists, |
|
1137 OrderMap& order_map, OrderList& order_list) { |
|
1138 |
|
1139 int order = order_map[root]; |
|
1140 int norder = order_map[node]; |
|
1141 |
|
1142 Node child = child_lists[root].first; |
|
1143 while (child != INVALID) { |
|
1144 int corder = order_map[child]; |
|
1145 if (corder > order && corder < norder) { |
|
1146 order = corder; |
|
1147 } |
|
1148 child = child_lists[child].next; |
|
1149 } |
|
1150 return order + order_list.size(); |
|
1151 } |
|
1152 |
|
1153 Node findPertinent(Node node, OrderMap& order_map, NodeData& node_data, |
|
1154 EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
|
1155 Node wnode =_ugraph.target(node_data[order_map[node]].first); |
|
1156 while (!pertinent(wnode, embed_edge, merge_roots)) { |
|
1157 wnode = _ugraph.target(node_data[order_map[wnode]].first); |
|
1158 } |
|
1159 return wnode; |
|
1160 } |
|
1161 |
|
1162 |
|
1163 Node findExternal(Node node, int rorder, OrderMap& order_map, |
|
1164 ChildLists& child_lists, AncestorMap& ancestor_map, |
|
1165 LowMap& low_map, NodeData& node_data) { |
|
1166 Node wnode =_ugraph.target(node_data[order_map[node]].first); |
|
1167 while (!external(wnode, rorder, child_lists, ancestor_map, low_map)) { |
|
1168 wnode = _ugraph.target(node_data[order_map[wnode]].first); |
|
1169 } |
|
1170 return wnode; |
|
1171 } |
|
1172 |
|
1173 void markCommonPath(Node node, int rorder, Node& wnode, Node& znode, |
|
1174 OrderList& order_list, OrderMap& order_map, |
|
1175 NodeData& node_data, EdgeLists& edge_lists, |
|
1176 EmbedEdge& embed_edge, MergeRoots& merge_roots, |
|
1177 ChildLists& child_lists, AncestorMap& ancestor_map, |
|
1178 LowMap& low_map) { |
|
1179 |
|
1180 Node cnode = node; |
|
1181 Node pred = INVALID; |
|
1182 |
|
1183 while (true) { |
|
1184 |
|
1185 bool pert = pertinent(cnode, embed_edge, merge_roots); |
|
1186 bool ext = external(cnode, rorder, child_lists, ancestor_map, low_map); |
|
1187 |
|
1188 if (pert && ext) { |
|
1189 if (!merge_roots[cnode].empty()) { |
|
1190 int cn = merge_roots[cnode].back(); |
|
1191 |
|
1192 if (low_map[order_list[cn - order_list.size()]] < rorder) { |
|
1193 Edge edge = node_data[cn].first; |
|
1194 _kuratowski.set(edge, true); |
|
1195 |
|
1196 pred = cnode; |
|
1197 cnode = _ugraph.target(edge); |
|
1198 |
|
1199 continue; |
|
1200 } |
|
1201 } |
|
1202 wnode = znode = cnode; |
|
1203 return; |
|
1204 |
|
1205 } else if (pert) { |
|
1206 wnode = cnode; |
|
1207 |
|
1208 while (!external(cnode, rorder, child_lists, ancestor_map, low_map)) { |
|
1209 Edge edge = node_data[order_map[cnode]].first; |
|
1210 |
|
1211 if (_ugraph.target(edge) == pred) { |
|
1212 edge = edge_lists[edge].next; |
|
1213 } |
|
1214 _kuratowski.set(edge, true); |
|
1215 |
|
1216 Node next = _ugraph.target(edge); |
|
1217 pred = cnode; cnode = next; |
|
1218 } |
|
1219 |
|
1220 znode = cnode; |
|
1221 return; |
|
1222 |
|
1223 } else if (ext) { |
|
1224 znode = cnode; |
|
1225 |
|
1226 while (!pertinent(cnode, embed_edge, merge_roots)) { |
|
1227 Edge edge = node_data[order_map[cnode]].first; |
|
1228 |
|
1229 if (_ugraph.target(edge) == pred) { |
|
1230 edge = edge_lists[edge].next; |
|
1231 } |
|
1232 _kuratowski.set(edge, true); |
|
1233 |
|
1234 Node next = _ugraph.target(edge); |
|
1235 pred = cnode; cnode = next; |
|
1236 } |
|
1237 |
|
1238 wnode = cnode; |
|
1239 return; |
|
1240 |
|
1241 } else { |
|
1242 Edge edge = node_data[order_map[cnode]].first; |
|
1243 |
|
1244 if (_ugraph.target(edge) == pred) { |
|
1245 edge = edge_lists[edge].next; |
|
1246 } |
|
1247 _kuratowski.set(edge, true); |
|
1248 |
|
1249 Node next = _ugraph.target(edge); |
|
1250 pred = cnode; cnode = next; |
|
1251 } |
|
1252 |
|
1253 } |
|
1254 |
|
1255 } |
|
1256 |
|
1257 void orientComponent(Node root, int rn, OrderMap& order_map, |
|
1258 PredMap& pred_map, NodeData& node_data, |
|
1259 EdgeLists& edge_lists, FlipMap& flip_map, |
|
1260 TypeMap& type_map) { |
|
1261 node_data[order_map[root]].first = node_data[rn].first; |
|
1262 type_map[root] = 1; |
|
1263 |
|
1264 std::vector<Node> st, qu; |
|
1265 |
|
1266 st.push_back(root); |
|
1267 while (!st.empty()) { |
|
1268 Node node = st.back(); |
|
1269 st.pop_back(); |
|
1270 qu.push_back(node); |
|
1271 |
|
1272 Edge edge = node_data[order_map[node]].first; |
|
1273 |
|
1274 if (type_map[_ugraph.target(edge)] == 0) { |
|
1275 st.push_back(_ugraph.target(edge)); |
|
1276 type_map[_ugraph.target(edge)] = 1; |
|
1277 } |
|
1278 |
|
1279 Edge last = edge, pred = edge; |
|
1280 edge = edge_lists[edge].next; |
|
1281 while (edge != last) { |
|
1282 |
|
1283 if (type_map[_ugraph.target(edge)] == 0) { |
|
1284 st.push_back(_ugraph.target(edge)); |
|
1285 type_map[_ugraph.target(edge)] = 1; |
|
1286 } |
|
1287 |
|
1288 Edge next = edge_lists[edge].next != pred ? |
|
1289 edge_lists[edge].next : edge_lists[edge].prev; |
|
1290 pred = edge; edge = next; |
|
1291 } |
|
1292 |
|
1293 } |
|
1294 |
|
1295 type_map[root] = 2; |
|
1296 flip_map[root] = false; |
|
1297 |
|
1298 for (int i = 1; i < int(qu.size()); ++i) { |
|
1299 |
|
1300 Node node = qu[i]; |
|
1301 |
|
1302 while (type_map[node] != 2) { |
|
1303 st.push_back(node); |
|
1304 type_map[node] = 2; |
|
1305 node = _ugraph.source(pred_map[node]); |
|
1306 } |
|
1307 |
|
1308 bool flip = flip_map[node]; |
|
1309 |
|
1310 while (!st.empty()) { |
|
1311 node = st.back(); |
|
1312 st.pop_back(); |
|
1313 |
|
1314 flip_map[node] = flip != flip_map[node]; |
|
1315 flip = flip_map[node]; |
|
1316 |
|
1317 if (flip) { |
|
1318 Edge edge = node_data[order_map[node]].first; |
|
1319 std::swap(edge_lists[edge].prev, edge_lists[edge].next); |
|
1320 edge = edge_lists[edge].prev; |
|
1321 std::swap(edge_lists[edge].prev, edge_lists[edge].next); |
|
1322 node_data[order_map[node]].first = edge; |
|
1323 } |
|
1324 } |
|
1325 } |
|
1326 |
|
1327 for (int i = 0; i < int(qu.size()); ++i) { |
|
1328 |
|
1329 Edge edge = node_data[order_map[qu[i]]].first; |
|
1330 Edge last = edge, pred = edge; |
|
1331 |
|
1332 edge = edge_lists[edge].next; |
|
1333 while (edge != last) { |
|
1334 |
|
1335 if (edge_lists[edge].next == pred) { |
|
1336 std::swap(edge_lists[edge].next, edge_lists[edge].prev); |
|
1337 } |
|
1338 pred = edge; edge = edge_lists[edge].next; |
|
1339 } |
|
1340 |
|
1341 } |
|
1342 } |
|
1343 |
|
1344 void setFaceFlags(Node root, Node wnode, Node ynode, Node xnode, |
|
1345 OrderMap& order_map, NodeData& node_data, |
|
1346 TypeMap& type_map) { |
|
1347 Node node = _ugraph.target(node_data[order_map[root]].first); |
|
1348 |
|
1349 while (node != ynode) { |
|
1350 type_map[node] = HIGHY; |
|
1351 node = _ugraph.target(node_data[order_map[node]].first); |
|
1352 } |
|
1353 |
|
1354 while (node != wnode) { |
|
1355 type_map[node] = LOWY; |
|
1356 node = _ugraph.target(node_data[order_map[node]].first); |
|
1357 } |
|
1358 |
|
1359 node = _ugraph.target(node_data[order_map[wnode]].first); |
|
1360 |
|
1361 while (node != xnode) { |
|
1362 type_map[node] = LOWX; |
|
1363 node = _ugraph.target(node_data[order_map[node]].first); |
|
1364 } |
|
1365 type_map[node] = LOWX; |
|
1366 |
|
1367 node = _ugraph.target(node_data[order_map[xnode]].first); |
|
1368 while (node != root) { |
|
1369 type_map[node] = HIGHX; |
|
1370 node = _ugraph.target(node_data[order_map[node]].first); |
|
1371 } |
|
1372 |
|
1373 type_map[wnode] = PERTINENT; |
|
1374 type_map[root] = ROOT; |
|
1375 } |
|
1376 |
|
1377 void findInternalPath(std::vector<Edge>& ipath, |
|
1378 Node wnode, Node root, TypeMap& type_map, |
|
1379 OrderMap& order_map, NodeData& node_data, |
|
1380 EdgeLists& edge_lists) { |
|
1381 std::vector<Edge> st; |
|
1382 |
|
1383 Node node = wnode; |
|
1384 |
|
1385 while (node != root) { |
|
1386 Edge edge = edge_lists[node_data[order_map[node]].first].next; |
|
1387 st.push_back(edge); |
|
1388 node = _ugraph.target(edge); |
|
1389 } |
|
1390 |
|
1391 while (true) { |
|
1392 Edge edge = st.back(); |
|
1393 if (type_map[_ugraph.target(edge)] == LOWX || |
|
1394 type_map[_ugraph.target(edge)] == HIGHX) { |
|
1395 break; |
|
1396 } |
|
1397 if (type_map[_ugraph.target(edge)] == 2) { |
|
1398 type_map[_ugraph.target(edge)] = 3; |
|
1399 |
|
1400 edge = edge_lists[_ugraph.oppositeEdge(edge)].next; |
|
1401 st.push_back(edge); |
|
1402 } else { |
|
1403 st.pop_back(); |
|
1404 edge = edge_lists[edge].next; |
|
1405 |
|
1406 while (_ugraph.oppositeEdge(edge) == st.back()) { |
|
1407 edge = st.back(); |
|
1408 st.pop_back(); |
|
1409 edge = edge_lists[edge].next; |
|
1410 } |
|
1411 st.push_back(edge); |
|
1412 } |
|
1413 } |
|
1414 |
|
1415 for (int i = 0; i < int(st.size()); ++i) { |
|
1416 if (type_map[_ugraph.target(st[i])] != LOWY && |
|
1417 type_map[_ugraph.target(st[i])] != HIGHY) { |
|
1418 for (; i < int(st.size()); ++i) { |
|
1419 ipath.push_back(st[i]); |
|
1420 } |
|
1421 } |
|
1422 } |
|
1423 } |
|
1424 |
|
1425 void setInternalFlags(std::vector<Edge>& ipath, TypeMap& type_map) { |
|
1426 for (int i = 1; i < int(ipath.size()); ++i) { |
|
1427 type_map[_ugraph.source(ipath[i])] = INTERNAL; |
|
1428 } |
|
1429 } |
|
1430 |
|
1431 void findPilePath(std::vector<Edge>& ppath, |
|
1432 Node root, TypeMap& type_map, OrderMap& order_map, |
|
1433 NodeData& node_data, EdgeLists& edge_lists) { |
|
1434 std::vector<Edge> st; |
|
1435 |
|
1436 st.push_back(_ugraph.oppositeEdge(node_data[order_map[root]].first)); |
|
1437 st.push_back(node_data[order_map[root]].first); |
|
1438 |
|
1439 while (st.size() > 1) { |
|
1440 Edge edge = st.back(); |
|
1441 if (type_map[_ugraph.target(edge)] == INTERNAL) { |
|
1442 break; |
|
1443 } |
|
1444 if (type_map[_ugraph.target(edge)] == 3) { |
|
1445 type_map[_ugraph.target(edge)] = 4; |
|
1446 |
|
1447 edge = edge_lists[_ugraph.oppositeEdge(edge)].next; |
|
1448 st.push_back(edge); |
|
1449 } else { |
|
1450 st.pop_back(); |
|
1451 edge = edge_lists[edge].next; |
|
1452 |
|
1453 while (!st.empty() && _ugraph.oppositeEdge(edge) == st.back()) { |
|
1454 edge = st.back(); |
|
1455 st.pop_back(); |
|
1456 edge = edge_lists[edge].next; |
|
1457 } |
|
1458 st.push_back(edge); |
|
1459 } |
|
1460 } |
|
1461 |
|
1462 for (int i = 1; i < int(st.size()); ++i) { |
|
1463 ppath.push_back(st[i]); |
|
1464 } |
|
1465 } |
|
1466 |
|
1467 |
|
1468 int markExternalPath(Node node, OrderMap& order_map, |
|
1469 ChildLists& child_lists, PredMap& pred_map, |
|
1470 AncestorMap& ancestor_map, LowMap& low_map) { |
|
1471 int lp = lowPoint(node, order_map, child_lists, |
|
1472 ancestor_map, low_map); |
|
1473 |
|
1474 if (ancestor_map[node] != lp) { |
|
1475 node = child_lists[node].first; |
|
1476 _kuratowski[pred_map[node]] = true; |
|
1477 |
|
1478 while (ancestor_map[node] != lp) { |
|
1479 for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
|
1480 Node tnode = _ugraph.target(e); |
|
1481 if (order_map[tnode] > order_map[node] && low_map[tnode] == lp) { |
|
1482 node = tnode; |
|
1483 _kuratowski[e] = true; |
|
1484 break; |
|
1485 } |
|
1486 } |
|
1487 } |
|
1488 } |
|
1489 |
|
1490 for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
|
1491 if (order_map[_ugraph.target(e)] == lp) { |
|
1492 _kuratowski[e] = true; |
|
1493 break; |
|
1494 } |
|
1495 } |
|
1496 |
|
1497 return lp; |
|
1498 } |
|
1499 |
|
1500 void markPertinentPath(Node node, OrderMap& order_map, |
|
1501 NodeData& node_data, EdgeLists& edge_lists, |
|
1502 EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
|
1503 while (embed_edge[node] == INVALID) { |
|
1504 int n = merge_roots[node].front(); |
|
1505 Edge edge = node_data[n].first; |
|
1506 |
|
1507 _kuratowski.set(edge, true); |
|
1508 |
|
1509 Node pred = node; |
|
1510 node = _ugraph.target(edge); |
|
1511 while (!pertinent(node, embed_edge, merge_roots)) { |
|
1512 edge = node_data[order_map[node]].first; |
|
1513 if (_ugraph.target(edge) == pred) { |
|
1514 edge = edge_lists[edge].next; |
|
1515 } |
|
1516 _kuratowski.set(edge, true); |
|
1517 pred = node; |
|
1518 node = _ugraph.target(edge); |
|
1519 } |
|
1520 } |
|
1521 _kuratowski.set(embed_edge[node], true); |
|
1522 } |
|
1523 |
|
1524 void markPredPath(Node node, Node snode, PredMap& pred_map) { |
|
1525 while (node != snode) { |
|
1526 _kuratowski.set(pred_map[node], true); |
|
1527 node = _ugraph.source(pred_map[node]); |
|
1528 } |
|
1529 } |
|
1530 |
|
1531 void markFacePath(Node ynode, Node xnode, |
|
1532 OrderMap& order_map, NodeData& node_data) { |
|
1533 Edge edge = node_data[order_map[ynode]].first; |
|
1534 Node node = _ugraph.target(edge); |
|
1535 _kuratowski.set(edge, true); |
|
1536 |
|
1537 while (node != xnode) { |
|
1538 edge = node_data[order_map[node]].first; |
|
1539 _kuratowski.set(edge, true); |
|
1540 node = _ugraph.target(edge); |
|
1541 } |
|
1542 } |
|
1543 |
|
1544 void markInternalPath(std::vector<Edge>& path) { |
|
1545 for (int i = 0; i < int(path.size()); ++i) { |
|
1546 _kuratowski.set(path[i], true); |
|
1547 } |
|
1548 } |
|
1549 |
|
1550 void markPilePath(std::vector<Edge>& path) { |
|
1551 for (int i = 0; i < int(path.size()); ++i) { |
|
1552 _kuratowski.set(path[i], true); |
|
1553 } |
|
1554 } |
|
1555 |
|
1556 void isolateKuratowski(Edge edge, NodeData& node_data, |
|
1557 EdgeLists& edge_lists, FlipMap& flip_map, |
|
1558 OrderMap& order_map, OrderList& order_list, |
|
1559 PredMap& pred_map, ChildLists& child_lists, |
|
1560 AncestorMap& ancestor_map, LowMap& low_map, |
|
1561 EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
|
1562 |
|
1563 Node root = _ugraph.source(edge); |
|
1564 Node enode = _ugraph.target(edge); |
|
1565 |
|
1566 int rorder = order_map[root]; |
|
1567 |
|
1568 TypeMap type_map(_ugraph, 0); |
|
1569 |
|
1570 int rn = findComponentRoot(root, enode, child_lists, |
|
1571 order_map, order_list); |
|
1572 |
|
1573 Node xnode = order_list[node_data[rn].next]; |
|
1574 Node ynode = order_list[node_data[rn].prev]; |
|
1575 |
|
1576 // Minor-A |
|
1577 { |
|
1578 while (!merge_roots[xnode].empty() || !merge_roots[ynode].empty()) { |
|
1579 |
|
1580 if (!merge_roots[xnode].empty()) { |
|
1581 root = xnode; |
|
1582 rn = merge_roots[xnode].front(); |
|
1583 } else { |
|
1584 root = ynode; |
|
1585 rn = merge_roots[ynode].front(); |
|
1586 } |
|
1587 |
|
1588 xnode = order_list[node_data[rn].next]; |
|
1589 ynode = order_list[node_data[rn].prev]; |
|
1590 } |
|
1591 |
|
1592 if (root != _ugraph.source(edge)) { |
|
1593 orientComponent(root, rn, order_map, pred_map, |
|
1594 node_data, edge_lists, flip_map, type_map); |
|
1595 markFacePath(root, root, order_map, node_data); |
|
1596 int xlp = markExternalPath(xnode, order_map, child_lists, |
|
1597 pred_map, ancestor_map, low_map); |
|
1598 int ylp = markExternalPath(ynode, order_map, child_lists, |
|
1599 pred_map, ancestor_map, low_map); |
|
1600 markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
|
1601 Node lwnode = findPertinent(ynode, order_map, node_data, |
|
1602 embed_edge, merge_roots); |
|
1603 |
|
1604 markPertinentPath(lwnode, order_map, node_data, edge_lists, |
|
1605 embed_edge, merge_roots); |
|
1606 |
|
1607 return; |
|
1608 } |
|
1609 } |
|
1610 |
|
1611 orientComponent(root, rn, order_map, pred_map, |
|
1612 node_data, edge_lists, flip_map, type_map); |
|
1613 |
|
1614 Node wnode = findPertinent(ynode, order_map, node_data, |
|
1615 embed_edge, merge_roots); |
|
1616 setFaceFlags(root, wnode, ynode, xnode, order_map, node_data, type_map); |
|
1617 |
|
1618 |
|
1619 //Minor-B |
|
1620 if (!merge_roots[wnode].empty()) { |
|
1621 int cn = merge_roots[wnode].back(); |
|
1622 Node rep = order_list[cn - order_list.size()]; |
|
1623 if (low_map[rep] < rorder) { |
|
1624 markFacePath(root, root, order_map, node_data); |
|
1625 int xlp = markExternalPath(xnode, order_map, child_lists, |
|
1626 pred_map, ancestor_map, low_map); |
|
1627 int ylp = markExternalPath(ynode, order_map, child_lists, |
|
1628 pred_map, ancestor_map, low_map); |
|
1629 |
|
1630 Node lwnode, lznode; |
|
1631 markCommonPath(wnode, rorder, lwnode, lznode, order_list, |
|
1632 order_map, node_data, edge_lists, embed_edge, |
|
1633 merge_roots, child_lists, ancestor_map, low_map); |
|
1634 |
|
1635 markPertinentPath(lwnode, order_map, node_data, edge_lists, |
|
1636 embed_edge, merge_roots); |
|
1637 int zlp = markExternalPath(lznode, order_map, child_lists, |
|
1638 pred_map, ancestor_map, low_map); |
|
1639 |
|
1640 int minlp = xlp < ylp ? xlp : ylp; |
|
1641 if (zlp < minlp) minlp = zlp; |
|
1642 |
|
1643 int maxlp = xlp > ylp ? xlp : ylp; |
|
1644 if (zlp > maxlp) maxlp = zlp; |
|
1645 |
|
1646 markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
|
1647 |
|
1648 return; |
|
1649 } |
|
1650 } |
|
1651 |
|
1652 Node pxnode, pynode; |
|
1653 std::vector<Edge> ipath; |
|
1654 findInternalPath(ipath, wnode, root, type_map, order_map, |
|
1655 node_data, edge_lists); |
|
1656 setInternalFlags(ipath, type_map); |
|
1657 pynode = _ugraph.source(ipath.front()); |
|
1658 pxnode = _ugraph.target(ipath.back()); |
|
1659 |
|
1660 wnode = findPertinent(pynode, order_map, node_data, |
|
1661 embed_edge, merge_roots); |
|
1662 |
|
1663 // Minor-C |
|
1664 { |
|
1665 if (type_map[_ugraph.source(ipath.front())] == HIGHY) { |
|
1666 if (type_map[_ugraph.target(ipath.back())] == HIGHX) { |
|
1667 markFacePath(xnode, pxnode, order_map, node_data); |
|
1668 } |
|
1669 markFacePath(root, xnode, order_map, node_data); |
|
1670 markPertinentPath(wnode, order_map, node_data, edge_lists, |
|
1671 embed_edge, merge_roots); |
|
1672 markInternalPath(ipath); |
|
1673 int xlp = markExternalPath(xnode, order_map, child_lists, |
|
1674 pred_map, ancestor_map, low_map); |
|
1675 int ylp = markExternalPath(ynode, order_map, child_lists, |
|
1676 pred_map, ancestor_map, low_map); |
|
1677 markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
|
1678 return; |
|
1679 } |
|
1680 |
|
1681 if (type_map[_ugraph.target(ipath.back())] == HIGHX) { |
|
1682 markFacePath(ynode, root, order_map, node_data); |
|
1683 markPertinentPath(wnode, order_map, node_data, edge_lists, |
|
1684 embed_edge, merge_roots); |
|
1685 markInternalPath(ipath); |
|
1686 int xlp = markExternalPath(xnode, order_map, child_lists, |
|
1687 pred_map, ancestor_map, low_map); |
|
1688 int ylp = markExternalPath(ynode, order_map, child_lists, |
|
1689 pred_map, ancestor_map, low_map); |
|
1690 markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
|
1691 return; |
|
1692 } |
|
1693 } |
|
1694 |
|
1695 std::vector<Edge> ppath; |
|
1696 findPilePath(ppath, root, type_map, order_map, node_data, edge_lists); |
|
1697 |
|
1698 // Minor-D |
|
1699 if (!ppath.empty()) { |
|
1700 markFacePath(ynode, xnode, order_map, node_data); |
|
1701 markPertinentPath(wnode, order_map, node_data, edge_lists, |
|
1702 embed_edge, merge_roots); |
|
1703 markPilePath(ppath); |
|
1704 markInternalPath(ipath); |
|
1705 int xlp = markExternalPath(xnode, order_map, child_lists, |
|
1706 pred_map, ancestor_map, low_map); |
|
1707 int ylp = markExternalPath(ynode, order_map, child_lists, |
|
1708 pred_map, ancestor_map, low_map); |
|
1709 markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
|
1710 return; |
|
1711 } |
|
1712 |
|
1713 // Minor-E* |
|
1714 { |
|
1715 |
|
1716 if (!external(wnode, rorder, child_lists, ancestor_map, low_map)) { |
|
1717 Node znode = findExternal(pynode, rorder, order_map, |
|
1718 child_lists, ancestor_map, |
|
1719 low_map, node_data); |
|
1720 |
|
1721 if (type_map[znode] == LOWY) { |
|
1722 markFacePath(root, xnode, order_map, node_data); |
|
1723 markPertinentPath(wnode, order_map, node_data, edge_lists, |
|
1724 embed_edge, merge_roots); |
|
1725 markInternalPath(ipath); |
|
1726 int xlp = markExternalPath(xnode, order_map, child_lists, |
|
1727 pred_map, ancestor_map, low_map); |
|
1728 int zlp = markExternalPath(znode, order_map, child_lists, |
|
1729 pred_map, ancestor_map, low_map); |
|
1730 markPredPath(root, order_list[xlp < zlp ? xlp : zlp], pred_map); |
|
1731 } else { |
|
1732 markFacePath(ynode, root, order_map, node_data); |
|
1733 markPertinentPath(wnode, order_map, node_data, edge_lists, |
|
1734 embed_edge, merge_roots); |
|
1735 markInternalPath(ipath); |
|
1736 int ylp = markExternalPath(ynode, order_map, child_lists, |
|
1737 pred_map, ancestor_map, low_map); |
|
1738 int zlp = markExternalPath(znode, order_map, child_lists, |
|
1739 pred_map, ancestor_map, low_map); |
|
1740 markPredPath(root, order_list[ylp < zlp ? ylp : zlp], pred_map); |
|
1741 } |
|
1742 return; |
|
1743 } |
|
1744 |
|
1745 int xlp = markExternalPath(xnode, order_map, child_lists, |
|
1746 pred_map, ancestor_map, low_map); |
|
1747 int ylp = markExternalPath(ynode, order_map, child_lists, |
|
1748 pred_map, ancestor_map, low_map); |
|
1749 int wlp = markExternalPath(wnode, order_map, child_lists, |
|
1750 pred_map, ancestor_map, low_map); |
|
1751 |
|
1752 if (wlp > xlp && wlp > ylp) { |
|
1753 markFacePath(root, root, order_map, node_data); |
|
1754 markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
|
1755 return; |
|
1756 } |
|
1757 |
|
1758 markInternalPath(ipath); |
|
1759 markPertinentPath(wnode, order_map, node_data, edge_lists, |
|
1760 embed_edge, merge_roots); |
|
1761 |
|
1762 if (xlp > ylp && xlp > wlp) { |
|
1763 markFacePath(root, pynode, order_map, node_data); |
|
1764 markFacePath(wnode, xnode, order_map, node_data); |
|
1765 markPredPath(root, order_list[ylp < wlp ? ylp : wlp], pred_map); |
|
1766 return; |
|
1767 } |
|
1768 |
|
1769 if (ylp > xlp && ylp > wlp) { |
|
1770 markFacePath(pxnode, root, order_map, node_data); |
|
1771 markFacePath(ynode, wnode, order_map, node_data); |
|
1772 markPredPath(root, order_list[xlp < wlp ? xlp : wlp], pred_map); |
|
1773 return; |
|
1774 } |
|
1775 |
|
1776 if (pynode != ynode) { |
|
1777 markFacePath(pxnode, wnode, order_map, node_data); |
|
1778 |
|
1779 int minlp = xlp < ylp ? xlp : ylp; |
|
1780 if (wlp < minlp) minlp = wlp; |
|
1781 |
|
1782 int maxlp = xlp > ylp ? xlp : ylp; |
|
1783 if (wlp > maxlp) maxlp = wlp; |
|
1784 |
|
1785 markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
|
1786 return; |
|
1787 } |
|
1788 |
|
1789 if (pxnode != xnode) { |
|
1790 markFacePath(wnode, pynode, order_map, node_data); |
|
1791 |
|
1792 int minlp = xlp < ylp ? xlp : ylp; |
|
1793 if (wlp < minlp) minlp = wlp; |
|
1794 |
|
1795 int maxlp = xlp > ylp ? xlp : ylp; |
|
1796 if (wlp > maxlp) maxlp = wlp; |
|
1797 |
|
1798 markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
|
1799 return; |
|
1800 } |
|
1801 |
|
1802 markFacePath(root, root, order_map, node_data); |
|
1803 int minlp = xlp < ylp ? xlp : ylp; |
|
1804 if (wlp < minlp) minlp = wlp; |
|
1805 markPredPath(root, order_list[minlp], pred_map); |
|
1806 return; |
|
1807 } |
|
1808 |
|
1809 } |
|
1810 |
|
1811 }; |
|
1812 |
|
1813 } |
|
1814 |
|
1815 #endif |