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 planar |
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22 | /// \file |
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23 | /// \brief Planarity checking, embedding, drawing and coloring |
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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/bfs.h> |
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30 | #include <lemon/radix_sort.h> |
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31 | #include <lemon/maps.h> |
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32 | #include <lemon/path.h> |
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33 | #include <lemon/iterable_maps.h> |
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34 | #include <lemon/edge_set.h> |
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35 | #include <lemon/bucket_heap.h> |
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36 | #include <lemon/ugraph_adaptor.h> |
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37 | #include <lemon/color.h> |
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38 | |
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39 | |
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40 | namespace lemon { |
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41 | |
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42 | namespace _planarity_bits { |
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43 | |
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44 | template <typename UGraph> |
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45 | struct PlanarityVisitor : DfsVisitor<UGraph> { |
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46 | |
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47 | typedef typename UGraph::Node Node; |
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48 | typedef typename UGraph::Edge Edge; |
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49 | |
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50 | typedef typename UGraph::template NodeMap<Edge> PredMap; |
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51 | |
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52 | typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
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53 | |
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54 | typedef typename UGraph::template NodeMap<int> OrderMap; |
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55 | typedef std::vector<Node> OrderList; |
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56 | |
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57 | typedef typename UGraph::template NodeMap<int> LowMap; |
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58 | typedef typename UGraph::template NodeMap<int> AncestorMap; |
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59 | |
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60 | PlanarityVisitor(const UGraph& ugraph, |
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61 | PredMap& pred_map, TreeMap& tree_map, |
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62 | OrderMap& order_map, OrderList& order_list, |
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63 | AncestorMap& ancestor_map, LowMap& low_map) |
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64 | : _ugraph(ugraph), _pred_map(pred_map), _tree_map(tree_map), |
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65 | _order_map(order_map), _order_list(order_list), |
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66 | _ancestor_map(ancestor_map), _low_map(low_map) {} |
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67 | |
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68 | void reach(const Node& node) { |
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69 | _order_map[node] = _order_list.size(); |
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70 | _low_map[node] = _order_list.size(); |
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71 | _ancestor_map[node] = _order_list.size(); |
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72 | _order_list.push_back(node); |
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73 | } |
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74 | |
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75 | void discover(const Edge& edge) { |
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76 | Node source = _ugraph.source(edge); |
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77 | Node target = _ugraph.target(edge); |
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78 | |
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79 | _tree_map[edge] = true; |
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80 | _pred_map[target] = edge; |
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81 | } |
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82 | |
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83 | void examine(const Edge& edge) { |
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84 | Node source = _ugraph.source(edge); |
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85 | Node target = _ugraph.target(edge); |
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86 | |
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87 | if (_order_map[target] < _order_map[source] && !_tree_map[edge]) { |
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88 | if (_low_map[source] > _order_map[target]) { |
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89 | _low_map[source] = _order_map[target]; |
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90 | } |
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91 | if (_ancestor_map[source] > _order_map[target]) { |
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92 | _ancestor_map[source] = _order_map[target]; |
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93 | } |
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94 | } |
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95 | } |
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96 | |
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97 | void backtrack(const Edge& edge) { |
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98 | Node source = _ugraph.source(edge); |
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99 | Node target = _ugraph.target(edge); |
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100 | |
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101 | if (_low_map[source] > _low_map[target]) { |
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102 | _low_map[source] = _low_map[target]; |
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103 | } |
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104 | } |
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105 | |
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106 | const UGraph& _ugraph; |
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107 | PredMap& _pred_map; |
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108 | TreeMap& _tree_map; |
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109 | OrderMap& _order_map; |
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110 | OrderList& _order_list; |
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111 | AncestorMap& _ancestor_map; |
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112 | LowMap& _low_map; |
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113 | }; |
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114 | |
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115 | template <typename UGraph, bool embedding = true> |
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116 | struct NodeDataNode { |
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117 | int prev, next; |
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118 | int visited; |
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119 | typename UGraph::Edge first; |
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120 | bool inverted; |
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121 | }; |
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122 | |
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123 | template <typename UGraph> |
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124 | struct NodeDataNode<UGraph, false> { |
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125 | int prev, next; |
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126 | int visited; |
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127 | }; |
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128 | |
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129 | template <typename UGraph> |
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130 | struct ChildListNode { |
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131 | typedef typename UGraph::Node Node; |
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132 | Node first; |
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133 | Node prev, next; |
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134 | }; |
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135 | |
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136 | template <typename UGraph> |
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137 | struct EdgeListNode { |
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138 | typename UGraph::Edge prev, next; |
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139 | }; |
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140 | |
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141 | } |
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142 | |
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143 | /// \ingroup planar |
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144 | /// |
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145 | /// \brief Planarity checking of an undirected simple graph |
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146 | /// |
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147 | /// This class implements the Boyer-Myrvold algorithm for planarity |
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148 | /// checking of an undirected graph. This class is a simplified |
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149 | /// version of the PlanarEmbedding algorithm class, and it does |
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150 | /// provide neither embedding nor kuratowski subdivisons. |
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151 | template <typename UGraph> |
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152 | class PlanarityChecking { |
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153 | private: |
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154 | |
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155 | UGRAPH_TYPEDEFS(typename UGraph); |
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156 | |
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157 | const UGraph& _ugraph; |
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158 | |
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159 | private: |
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160 | |
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161 | typedef typename UGraph::template NodeMap<Edge> PredMap; |
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162 | |
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163 | typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
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164 | |
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165 | typedef typename UGraph::template NodeMap<int> OrderMap; |
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166 | typedef std::vector<Node> OrderList; |
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167 | |
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168 | typedef typename UGraph::template NodeMap<int> LowMap; |
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169 | typedef typename UGraph::template NodeMap<int> AncestorMap; |
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170 | |
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171 | typedef _planarity_bits::NodeDataNode<UGraph> NodeDataNode; |
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172 | typedef std::vector<NodeDataNode> NodeData; |
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173 | |
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174 | typedef _planarity_bits::ChildListNode<UGraph> ChildListNode; |
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175 | typedef typename UGraph::template NodeMap<ChildListNode> ChildLists; |
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176 | |
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177 | typedef typename UGraph::template NodeMap<std::list<int> > MergeRoots; |
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178 | |
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179 | typedef typename UGraph::template NodeMap<bool> EmbedEdge; |
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180 | |
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181 | public: |
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182 | |
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183 | /// \brief Constructor |
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184 | /// |
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185 | /// \warining The graph should be simple, i.e. parallel and loop edge |
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186 | /// free. |
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187 | PlanarityChecking(const UGraph& ugraph) : _ugraph(ugraph) {} |
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188 | |
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189 | /// \brief Runs the algorithm. |
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190 | /// |
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191 | /// Runs the algorithm. |
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192 | /// \return %True when the graph is planar. |
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193 | bool run() { |
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194 | typedef _planarity_bits::PlanarityVisitor<UGraph> Visitor; |
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195 | |
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196 | PredMap pred_map(_ugraph, INVALID); |
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197 | TreeMap tree_map(_ugraph, false); |
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198 | |
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199 | OrderMap order_map(_ugraph, -1); |
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200 | OrderList order_list; |
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201 | |
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202 | AncestorMap ancestor_map(_ugraph, -1); |
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203 | LowMap low_map(_ugraph, -1); |
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204 | |
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205 | Visitor visitor(_ugraph, pred_map, tree_map, |
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206 | order_map, order_list, ancestor_map, low_map); |
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207 | DfsVisit<UGraph, Visitor> visit(_ugraph, visitor); |
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208 | visit.run(); |
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209 | |
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210 | ChildLists child_lists(_ugraph); |
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211 | createChildLists(tree_map, order_map, low_map, child_lists); |
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212 | |
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213 | NodeData node_data(2 * order_list.size()); |
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214 | |
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215 | EmbedEdge embed_edge(_ugraph, false); |
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216 | |
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217 | MergeRoots merge_roots(_ugraph); |
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218 | |
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219 | for (int i = order_list.size() - 1; i >= 0; --i) { |
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220 | |
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221 | Node node = order_list[i]; |
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222 | |
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223 | Node source = node; |
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224 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
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225 | Node target = _ugraph.target(e); |
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226 | |
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227 | if (order_map[source] < order_map[target] && tree_map[e]) { |
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228 | initFace(target, node_data, order_map, order_list); |
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229 | } |
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230 | } |
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231 | |
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232 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
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233 | Node target = _ugraph.target(e); |
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234 | |
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235 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
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236 | embed_edge[target] = true; |
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237 | walkUp(target, source, i, pred_map, low_map, |
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238 | order_map, order_list, node_data, merge_roots); |
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239 | } |
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240 | } |
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241 | |
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242 | for (typename MergeRoots::Value::iterator it = |
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243 | merge_roots[node].begin(); it != merge_roots[node].end(); ++it) { |
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244 | int rn = *it; |
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245 | walkDown(rn, i, node_data, order_list, child_lists, |
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246 | ancestor_map, low_map, embed_edge, merge_roots); |
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247 | } |
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248 | merge_roots[node].clear(); |
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249 | |
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250 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
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251 | Node target = _ugraph.target(e); |
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252 | |
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253 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
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254 | if (embed_edge[target]) { |
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255 | return false; |
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256 | } |
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257 | } |
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258 | } |
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259 | } |
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260 | |
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261 | return true; |
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262 | } |
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263 | |
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264 | private: |
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265 | |
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266 | void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
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267 | const LowMap& low_map, ChildLists& child_lists) { |
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268 | |
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269 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
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270 | Node source = n; |
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271 | |
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272 | std::vector<Node> targets; |
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273 | for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
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274 | Node target = _ugraph.target(e); |
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275 | |
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276 | if (order_map[source] < order_map[target] && tree_map[e]) { |
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277 | targets.push_back(target); |
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278 | } |
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279 | } |
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280 | |
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281 | if (targets.size() == 0) { |
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282 | child_lists[source].first = INVALID; |
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283 | } else if (targets.size() == 1) { |
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284 | child_lists[source].first = targets[0]; |
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285 | child_lists[targets[0]].prev = INVALID; |
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286 | child_lists[targets[0]].next = INVALID; |
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287 | } else { |
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288 | radixSort(targets.begin(), targets.end(), mapFunctor(low_map)); |
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289 | for (int i = 1; i < int(targets.size()); ++i) { |
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290 | child_lists[targets[i]].prev = targets[i - 1]; |
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291 | child_lists[targets[i - 1]].next = targets[i]; |
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292 | } |
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293 | child_lists[targets.back()].next = INVALID; |
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294 | child_lists[targets.front()].prev = INVALID; |
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295 | child_lists[source].first = targets.front(); |
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296 | } |
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297 | } |
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298 | } |
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299 | |
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300 | void walkUp(const Node& node, Node root, int rorder, |
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301 | const PredMap& pred_map, const LowMap& low_map, |
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302 | const OrderMap& order_map, const OrderList& order_list, |
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303 | NodeData& node_data, MergeRoots& merge_roots) { |
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304 | |
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305 | int na, nb; |
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306 | bool da, db; |
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307 | |
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308 | na = nb = order_map[node]; |
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309 | da = true; db = false; |
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310 | |
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311 | while (true) { |
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312 | |
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313 | if (node_data[na].visited == rorder) break; |
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314 | if (node_data[nb].visited == rorder) break; |
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315 | |
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316 | node_data[na].visited = rorder; |
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317 | node_data[nb].visited = rorder; |
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318 | |
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319 | int rn = -1; |
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320 | |
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321 | if (na >= int(order_list.size())) { |
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322 | rn = na; |
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323 | } else if (nb >= int(order_list.size())) { |
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324 | rn = nb; |
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325 | } |
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326 | |
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327 | if (rn == -1) { |
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328 | int nn; |
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329 | |
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330 | nn = da ? node_data[na].prev : node_data[na].next; |
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331 | da = node_data[nn].prev != na; |
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332 | na = nn; |
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333 | |
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334 | nn = db ? node_data[nb].prev : node_data[nb].next; |
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335 | db = node_data[nn].prev != nb; |
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336 | nb = nn; |
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337 | |
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338 | } else { |
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339 | |
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340 | Node rep = order_list[rn - order_list.size()]; |
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341 | Node parent = _ugraph.source(pred_map[rep]); |
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342 | |
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343 | if (low_map[rep] < rorder) { |
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344 | merge_roots[parent].push_back(rn); |
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345 | } else { |
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346 | merge_roots[parent].push_front(rn); |
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347 | } |
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348 | |
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349 | if (parent != root) { |
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350 | na = nb = order_map[parent]; |
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351 | da = true; db = false; |
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352 | } else { |
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353 | break; |
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354 | } |
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355 | } |
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356 | } |
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357 | } |
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358 | |
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359 | void walkDown(int rn, int rorder, NodeData& node_data, |
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360 | OrderList& order_list, ChildLists& child_lists, |
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361 | AncestorMap& ancestor_map, LowMap& low_map, |
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362 | EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
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363 | |
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364 | std::vector<std::pair<int, bool> > merge_stack; |
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365 | |
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366 | for (int di = 0; di < 2; ++di) { |
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367 | bool rd = di == 0; |
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368 | int pn = rn; |
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369 | int n = rd ? node_data[rn].next : node_data[rn].prev; |
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370 | |
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371 | while (n != rn) { |
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372 | |
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373 | Node node = order_list[n]; |
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374 | |
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375 | if (embed_edge[node]) { |
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376 | |
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377 | // Merging components on the critical path |
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378 | while (!merge_stack.empty()) { |
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379 | |
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380 | // Component root |
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381 | int cn = merge_stack.back().first; |
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382 | bool cd = merge_stack.back().second; |
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383 | merge_stack.pop_back(); |
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384 | |
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385 | // Parent of component |
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386 | int dn = merge_stack.back().first; |
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387 | bool dd = merge_stack.back().second; |
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388 | merge_stack.pop_back(); |
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389 | |
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390 | Node parent = order_list[dn]; |
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391 | |
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392 | // Erasing from merge_roots |
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393 | merge_roots[parent].pop_front(); |
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394 | |
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395 | Node child = order_list[cn - order_list.size()]; |
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396 | |
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397 | // Erasing from child_lists |
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398 | if (child_lists[child].prev != INVALID) { |
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399 | child_lists[child_lists[child].prev].next = |
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400 | child_lists[child].next; |
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401 | } else { |
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402 | child_lists[parent].first = child_lists[child].next; |
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403 | } |
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404 | |
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405 | if (child_lists[child].next != INVALID) { |
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406 | child_lists[child_lists[child].next].prev = |
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407 | child_lists[child].prev; |
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408 | } |
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409 | |
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410 | // Merging external faces |
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411 | { |
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412 | int en = cn; |
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413 | cn = cd ? node_data[cn].prev : node_data[cn].next; |
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414 | cd = node_data[cn].next == en; |
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415 | |
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416 | } |
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417 | |
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418 | if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
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419 | if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
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420 | |
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421 | } |
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422 | |
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423 | bool d = pn == node_data[n].prev; |
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424 | |
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425 | if (node_data[n].prev == node_data[n].next && |
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426 | node_data[n].inverted) { |
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427 | d = !d; |
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428 | } |
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429 | |
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430 | // Embedding edge into external face |
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431 | if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
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432 | if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
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433 | pn = rn; |
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434 | |
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435 | embed_edge[order_list[n]] = false; |
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436 | } |
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437 | |
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438 | if (!merge_roots[node].empty()) { |
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439 | |
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440 | bool d = pn == node_data[n].prev; |
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441 | |
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442 | merge_stack.push_back(std::make_pair(n, d)); |
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443 | |
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444 | int rn = merge_roots[node].front(); |
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445 | |
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446 | int xn = node_data[rn].next; |
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447 | Node xnode = order_list[xn]; |
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448 | |
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449 | int yn = node_data[rn].prev; |
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450 | Node ynode = order_list[yn]; |
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451 | |
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452 | bool rd; |
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453 | if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) { |
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454 | rd = true; |
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455 | } else if (!external(ynode, rorder, child_lists, |
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456 | ancestor_map, low_map)) { |
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457 | rd = false; |
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458 | } else if (pertinent(xnode, embed_edge, merge_roots)) { |
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459 | rd = true; |
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460 | } else { |
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461 | rd = false; |
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462 | } |
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463 | |
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464 | merge_stack.push_back(std::make_pair(rn, rd)); |
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465 | |
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466 | pn = rn; |
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467 | n = rd ? xn : yn; |
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468 | |
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469 | } else if (!external(node, rorder, child_lists, |
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470 | ancestor_map, low_map)) { |
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471 | int nn = (node_data[n].next != pn ? |
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472 | node_data[n].next : node_data[n].prev); |
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473 | |
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474 | bool nd = n == node_data[nn].prev; |
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475 | |
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476 | if (nd) node_data[nn].prev = pn; |
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477 | else node_data[nn].next = pn; |
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478 | |
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479 | if (n == node_data[pn].prev) node_data[pn].prev = nn; |
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480 | else node_data[pn].next = nn; |
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481 | |
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482 | node_data[nn].inverted = |
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483 | (node_data[nn].prev == node_data[nn].next && nd != rd); |
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484 | |
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485 | n = nn; |
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486 | } |
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487 | else break; |
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488 | |
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489 | } |
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490 | |
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491 | if (!merge_stack.empty() || n == rn) { |
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492 | break; |
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493 | } |
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494 | } |
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495 | } |
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496 | |
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497 | void initFace(const Node& node, NodeData& node_data, |
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498 | const OrderMap& order_map, const OrderList& order_list) { |
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499 | int n = order_map[node]; |
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500 | int rn = n + order_list.size(); |
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501 | |
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502 | node_data[n].next = node_data[n].prev = rn; |
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503 | node_data[rn].next = node_data[rn].prev = n; |
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504 | |
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505 | node_data[n].visited = order_list.size(); |
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506 | node_data[rn].visited = order_list.size(); |
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507 | |
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508 | } |
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509 | |
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510 | bool external(const Node& node, int rorder, |
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511 | ChildLists& child_lists, AncestorMap& ancestor_map, |
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512 | LowMap& low_map) { |
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513 | Node child = child_lists[node].first; |
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514 | |
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515 | if (child != INVALID) { |
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516 | if (low_map[child] < rorder) return true; |
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517 | } |
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518 | |
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519 | if (ancestor_map[node] < rorder) return true; |
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520 | |
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521 | return false; |
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522 | } |
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523 | |
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524 | bool pertinent(const Node& node, const EmbedEdge& embed_edge, |
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525 | const MergeRoots& merge_roots) { |
---|
526 | return !merge_roots[node].empty() || embed_edge[node]; |
---|
527 | } |
---|
528 | |
---|
529 | }; |
---|
530 | |
---|
531 | /// \ingroup planar |
---|
532 | /// |
---|
533 | /// \brief Planar embedding of an undirected simple graph |
---|
534 | /// |
---|
535 | /// This class implements the Boyer-Myrvold algorithm for planar |
---|
536 | /// embedding of an undirected graph. The planar embeding is an |
---|
537 | /// ordering of the outgoing edges in each node, which is a possible |
---|
538 | /// configuration to draw the graph in the plane. If there is not |
---|
539 | /// such ordering then the graph contains a \f$ K_5 \f$ (full graph |
---|
540 | /// with 5 nodes) or an \f$ K_{3,3} \f$ (complete bipartite graph on |
---|
541 | /// 3 ANode and 3 BNode) subdivision. |
---|
542 | /// |
---|
543 | /// The current implementation calculates an embedding or an |
---|
544 | /// Kuratowski subdivision if the graph is not planar. The running |
---|
545 | /// time of the algorithm is \f$ O(n) \f$. |
---|
546 | template <typename UGraph> |
---|
547 | class PlanarEmbedding { |
---|
548 | private: |
---|
549 | |
---|
550 | UGRAPH_TYPEDEFS(typename UGraph); |
---|
551 | |
---|
552 | const UGraph& _ugraph; |
---|
553 | typename UGraph::template EdgeMap<Edge> _embedding; |
---|
554 | |
---|
555 | typename UGraph::template UEdgeMap<bool> _kuratowski; |
---|
556 | |
---|
557 | private: |
---|
558 | |
---|
559 | typedef typename UGraph::template NodeMap<Edge> PredMap; |
---|
560 | |
---|
561 | typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
---|
562 | |
---|
563 | typedef typename UGraph::template NodeMap<int> OrderMap; |
---|
564 | typedef std::vector<Node> OrderList; |
---|
565 | |
---|
566 | typedef typename UGraph::template NodeMap<int> LowMap; |
---|
567 | typedef typename UGraph::template NodeMap<int> AncestorMap; |
---|
568 | |
---|
569 | typedef _planarity_bits::NodeDataNode<UGraph> NodeDataNode; |
---|
570 | typedef std::vector<NodeDataNode> NodeData; |
---|
571 | |
---|
572 | typedef _planarity_bits::ChildListNode<UGraph> ChildListNode; |
---|
573 | typedef typename UGraph::template NodeMap<ChildListNode> ChildLists; |
---|
574 | |
---|
575 | typedef typename UGraph::template NodeMap<std::list<int> > MergeRoots; |
---|
576 | |
---|
577 | typedef typename UGraph::template NodeMap<Edge> EmbedEdge; |
---|
578 | |
---|
579 | typedef _planarity_bits::EdgeListNode<UGraph> EdgeListNode; |
---|
580 | typedef typename UGraph::template EdgeMap<EdgeListNode> EdgeLists; |
---|
581 | |
---|
582 | typedef typename UGraph::template NodeMap<bool> FlipMap; |
---|
583 | |
---|
584 | typedef typename UGraph::template NodeMap<int> TypeMap; |
---|
585 | |
---|
586 | enum IsolatorNodeType { |
---|
587 | HIGHX = 6, LOWX = 7, |
---|
588 | HIGHY = 8, LOWY = 9, |
---|
589 | ROOT = 10, PERTINENT = 11, |
---|
590 | INTERNAL = 12 |
---|
591 | }; |
---|
592 | |
---|
593 | public: |
---|
594 | |
---|
595 | /// \brief The map for store of embedding |
---|
596 | typedef typename UGraph::template EdgeMap<Edge> EmbeddingMap; |
---|
597 | |
---|
598 | /// \brief Constructor |
---|
599 | /// |
---|
600 | /// \warining The graph should be simple, i.e. parallel and loop edge |
---|
601 | /// free. |
---|
602 | PlanarEmbedding(const UGraph& ugraph) |
---|
603 | : _ugraph(ugraph), _embedding(_ugraph), _kuratowski(ugraph, false) {} |
---|
604 | |
---|
605 | /// \brief Runs the algorithm. |
---|
606 | /// |
---|
607 | /// Runs the algorithm. |
---|
608 | /// \param kuratowski If the parameter is false, then the |
---|
609 | /// algorithm does not calculate the isolate Kuratowski |
---|
610 | /// subdivisions. |
---|
611 | ///\return %True when the graph is planar. |
---|
612 | bool run(bool kuratowski = true) { |
---|
613 | typedef _planarity_bits::PlanarityVisitor<UGraph> Visitor; |
---|
614 | |
---|
615 | PredMap pred_map(_ugraph, INVALID); |
---|
616 | TreeMap tree_map(_ugraph, false); |
---|
617 | |
---|
618 | OrderMap order_map(_ugraph, -1); |
---|
619 | OrderList order_list; |
---|
620 | |
---|
621 | AncestorMap ancestor_map(_ugraph, -1); |
---|
622 | LowMap low_map(_ugraph, -1); |
---|
623 | |
---|
624 | Visitor visitor(_ugraph, pred_map, tree_map, |
---|
625 | order_map, order_list, ancestor_map, low_map); |
---|
626 | DfsVisit<UGraph, Visitor> visit(_ugraph, visitor); |
---|
627 | visit.run(); |
---|
628 | |
---|
629 | ChildLists child_lists(_ugraph); |
---|
630 | createChildLists(tree_map, order_map, low_map, child_lists); |
---|
631 | |
---|
632 | NodeData node_data(2 * order_list.size()); |
---|
633 | |
---|
634 | EmbedEdge embed_edge(_ugraph, INVALID); |
---|
635 | |
---|
636 | MergeRoots merge_roots(_ugraph); |
---|
637 | |
---|
638 | EdgeLists edge_lists(_ugraph); |
---|
639 | |
---|
640 | FlipMap flip_map(_ugraph, false); |
---|
641 | |
---|
642 | for (int i = order_list.size() - 1; i >= 0; --i) { |
---|
643 | |
---|
644 | Node node = order_list[i]; |
---|
645 | |
---|
646 | node_data[i].first = INVALID; |
---|
647 | |
---|
648 | Node source = node; |
---|
649 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
650 | Node target = _ugraph.target(e); |
---|
651 | |
---|
652 | if (order_map[source] < order_map[target] && tree_map[e]) { |
---|
653 | initFace(target, edge_lists, node_data, |
---|
654 | pred_map, order_map, order_list); |
---|
655 | } |
---|
656 | } |
---|
657 | |
---|
658 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
659 | Node target = _ugraph.target(e); |
---|
660 | |
---|
661 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
---|
662 | embed_edge[target] = e; |
---|
663 | walkUp(target, source, i, pred_map, low_map, |
---|
664 | order_map, order_list, node_data, merge_roots); |
---|
665 | } |
---|
666 | } |
---|
667 | |
---|
668 | for (typename MergeRoots::Value::iterator it = |
---|
669 | merge_roots[node].begin(); it != merge_roots[node].end(); ++it) { |
---|
670 | int rn = *it; |
---|
671 | walkDown(rn, i, node_data, edge_lists, flip_map, order_list, |
---|
672 | child_lists, ancestor_map, low_map, embed_edge, merge_roots); |
---|
673 | } |
---|
674 | merge_roots[node].clear(); |
---|
675 | |
---|
676 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
677 | Node target = _ugraph.target(e); |
---|
678 | |
---|
679 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
---|
680 | if (embed_edge[target] != INVALID) { |
---|
681 | if (kuratowski) { |
---|
682 | isolateKuratowski(e, node_data, edge_lists, flip_map, |
---|
683 | order_map, order_list, pred_map, child_lists, |
---|
684 | ancestor_map, low_map, |
---|
685 | embed_edge, merge_roots); |
---|
686 | } |
---|
687 | return false; |
---|
688 | } |
---|
689 | } |
---|
690 | } |
---|
691 | } |
---|
692 | |
---|
693 | for (int i = 0; i < int(order_list.size()); ++i) { |
---|
694 | |
---|
695 | mergeRemainingFaces(order_list[i], node_data, order_list, order_map, |
---|
696 | child_lists, edge_lists); |
---|
697 | storeEmbedding(order_list[i], node_data, order_map, pred_map, |
---|
698 | edge_lists, flip_map); |
---|
699 | } |
---|
700 | |
---|
701 | return true; |
---|
702 | } |
---|
703 | |
---|
704 | /// \brief Gives back the successor of an edge |
---|
705 | /// |
---|
706 | /// Gives back the successor of an edge. This function makes |
---|
707 | /// possible to query the cyclic order of the outgoing edges from |
---|
708 | /// a node. |
---|
709 | Edge next(const Edge& edge) const { |
---|
710 | return _embedding[edge]; |
---|
711 | } |
---|
712 | |
---|
713 | /// \brief Gives back the calculated embedding map |
---|
714 | /// |
---|
715 | /// The returned map contains the successor of each edge in the |
---|
716 | /// graph. |
---|
717 | const EmbeddingMap& embedding() const { |
---|
718 | return _embedding; |
---|
719 | } |
---|
720 | |
---|
721 | /// \brief Gives back true when the undirected edge is in the |
---|
722 | /// kuratowski subdivision |
---|
723 | /// |
---|
724 | /// Gives back true when the undirected edge is in the kuratowski |
---|
725 | /// subdivision |
---|
726 | bool kuratowski(const UEdge& uedge) { |
---|
727 | return _kuratowski[uedge]; |
---|
728 | } |
---|
729 | |
---|
730 | private: |
---|
731 | |
---|
732 | void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
---|
733 | const LowMap& low_map, ChildLists& child_lists) { |
---|
734 | |
---|
735 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
736 | Node source = n; |
---|
737 | |
---|
738 | std::vector<Node> targets; |
---|
739 | for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
740 | Node target = _ugraph.target(e); |
---|
741 | |
---|
742 | if (order_map[source] < order_map[target] && tree_map[e]) { |
---|
743 | targets.push_back(target); |
---|
744 | } |
---|
745 | } |
---|
746 | |
---|
747 | if (targets.size() == 0) { |
---|
748 | child_lists[source].first = INVALID; |
---|
749 | } else if (targets.size() == 1) { |
---|
750 | child_lists[source].first = targets[0]; |
---|
751 | child_lists[targets[0]].prev = INVALID; |
---|
752 | child_lists[targets[0]].next = INVALID; |
---|
753 | } else { |
---|
754 | radixSort(targets.begin(), targets.end(), mapFunctor(low_map)); |
---|
755 | for (int i = 1; i < int(targets.size()); ++i) { |
---|
756 | child_lists[targets[i]].prev = targets[i - 1]; |
---|
757 | child_lists[targets[i - 1]].next = targets[i]; |
---|
758 | } |
---|
759 | child_lists[targets.back()].next = INVALID; |
---|
760 | child_lists[targets.front()].prev = INVALID; |
---|
761 | child_lists[source].first = targets.front(); |
---|
762 | } |
---|
763 | } |
---|
764 | } |
---|
765 | |
---|
766 | void walkUp(const Node& node, Node root, int rorder, |
---|
767 | const PredMap& pred_map, const LowMap& low_map, |
---|
768 | const OrderMap& order_map, const OrderList& order_list, |
---|
769 | NodeData& node_data, MergeRoots& merge_roots) { |
---|
770 | |
---|
771 | int na, nb; |
---|
772 | bool da, db; |
---|
773 | |
---|
774 | na = nb = order_map[node]; |
---|
775 | da = true; db = false; |
---|
776 | |
---|
777 | while (true) { |
---|
778 | |
---|
779 | if (node_data[na].visited == rorder) break; |
---|
780 | if (node_data[nb].visited == rorder) break; |
---|
781 | |
---|
782 | node_data[na].visited = rorder; |
---|
783 | node_data[nb].visited = rorder; |
---|
784 | |
---|
785 | int rn = -1; |
---|
786 | |
---|
787 | if (na >= int(order_list.size())) { |
---|
788 | rn = na; |
---|
789 | } else if (nb >= int(order_list.size())) { |
---|
790 | rn = nb; |
---|
791 | } |
---|
792 | |
---|
793 | if (rn == -1) { |
---|
794 | int nn; |
---|
795 | |
---|
796 | nn = da ? node_data[na].prev : node_data[na].next; |
---|
797 | da = node_data[nn].prev != na; |
---|
798 | na = nn; |
---|
799 | |
---|
800 | nn = db ? node_data[nb].prev : node_data[nb].next; |
---|
801 | db = node_data[nn].prev != nb; |
---|
802 | nb = nn; |
---|
803 | |
---|
804 | } else { |
---|
805 | |
---|
806 | Node rep = order_list[rn - order_list.size()]; |
---|
807 | Node parent = _ugraph.source(pred_map[rep]); |
---|
808 | |
---|
809 | if (low_map[rep] < rorder) { |
---|
810 | merge_roots[parent].push_back(rn); |
---|
811 | } else { |
---|
812 | merge_roots[parent].push_front(rn); |
---|
813 | } |
---|
814 | |
---|
815 | if (parent != root) { |
---|
816 | na = nb = order_map[parent]; |
---|
817 | da = true; db = false; |
---|
818 | } else { |
---|
819 | break; |
---|
820 | } |
---|
821 | } |
---|
822 | } |
---|
823 | } |
---|
824 | |
---|
825 | void walkDown(int rn, int rorder, NodeData& node_data, |
---|
826 | EdgeLists& edge_lists, FlipMap& flip_map, |
---|
827 | OrderList& order_list, ChildLists& child_lists, |
---|
828 | AncestorMap& ancestor_map, LowMap& low_map, |
---|
829 | EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
---|
830 | |
---|
831 | std::vector<std::pair<int, bool> > merge_stack; |
---|
832 | |
---|
833 | for (int di = 0; di < 2; ++di) { |
---|
834 | bool rd = di == 0; |
---|
835 | int pn = rn; |
---|
836 | int n = rd ? node_data[rn].next : node_data[rn].prev; |
---|
837 | |
---|
838 | while (n != rn) { |
---|
839 | |
---|
840 | Node node = order_list[n]; |
---|
841 | |
---|
842 | if (embed_edge[node] != INVALID) { |
---|
843 | |
---|
844 | // Merging components on the critical path |
---|
845 | while (!merge_stack.empty()) { |
---|
846 | |
---|
847 | // Component root |
---|
848 | int cn = merge_stack.back().first; |
---|
849 | bool cd = merge_stack.back().second; |
---|
850 | merge_stack.pop_back(); |
---|
851 | |
---|
852 | // Parent of component |
---|
853 | int dn = merge_stack.back().first; |
---|
854 | bool dd = merge_stack.back().second; |
---|
855 | merge_stack.pop_back(); |
---|
856 | |
---|
857 | Node parent = order_list[dn]; |
---|
858 | |
---|
859 | // Erasing from merge_roots |
---|
860 | merge_roots[parent].pop_front(); |
---|
861 | |
---|
862 | Node child = order_list[cn - order_list.size()]; |
---|
863 | |
---|
864 | // Erasing from child_lists |
---|
865 | if (child_lists[child].prev != INVALID) { |
---|
866 | child_lists[child_lists[child].prev].next = |
---|
867 | child_lists[child].next; |
---|
868 | } else { |
---|
869 | child_lists[parent].first = child_lists[child].next; |
---|
870 | } |
---|
871 | |
---|
872 | if (child_lists[child].next != INVALID) { |
---|
873 | child_lists[child_lists[child].next].prev = |
---|
874 | child_lists[child].prev; |
---|
875 | } |
---|
876 | |
---|
877 | // Merging edges + flipping |
---|
878 | Edge de = node_data[dn].first; |
---|
879 | Edge ce = node_data[cn].first; |
---|
880 | |
---|
881 | flip_map[order_list[cn - order_list.size()]] = cd != dd; |
---|
882 | if (cd != dd) { |
---|
883 | std::swap(edge_lists[ce].prev, edge_lists[ce].next); |
---|
884 | ce = edge_lists[ce].prev; |
---|
885 | std::swap(edge_lists[ce].prev, edge_lists[ce].next); |
---|
886 | } |
---|
887 | |
---|
888 | { |
---|
889 | Edge dne = edge_lists[de].next; |
---|
890 | Edge cne = edge_lists[ce].next; |
---|
891 | |
---|
892 | edge_lists[de].next = cne; |
---|
893 | edge_lists[ce].next = dne; |
---|
894 | |
---|
895 | edge_lists[dne].prev = ce; |
---|
896 | edge_lists[cne].prev = de; |
---|
897 | } |
---|
898 | |
---|
899 | if (dd) { |
---|
900 | node_data[dn].first = ce; |
---|
901 | } |
---|
902 | |
---|
903 | // Merging external faces |
---|
904 | { |
---|
905 | int en = cn; |
---|
906 | cn = cd ? node_data[cn].prev : node_data[cn].next; |
---|
907 | cd = node_data[cn].next == en; |
---|
908 | |
---|
909 | if (node_data[cn].prev == node_data[cn].next && |
---|
910 | node_data[cn].inverted) { |
---|
911 | cd = !cd; |
---|
912 | } |
---|
913 | } |
---|
914 | |
---|
915 | if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
---|
916 | if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
---|
917 | |
---|
918 | } |
---|
919 | |
---|
920 | bool d = pn == node_data[n].prev; |
---|
921 | |
---|
922 | if (node_data[n].prev == node_data[n].next && |
---|
923 | node_data[n].inverted) { |
---|
924 | d = !d; |
---|
925 | } |
---|
926 | |
---|
927 | // Add new edge |
---|
928 | { |
---|
929 | Edge edge = embed_edge[node]; |
---|
930 | Edge re = node_data[rn].first; |
---|
931 | |
---|
932 | edge_lists[edge_lists[re].next].prev = edge; |
---|
933 | edge_lists[edge].next = edge_lists[re].next; |
---|
934 | edge_lists[edge].prev = re; |
---|
935 | edge_lists[re].next = edge; |
---|
936 | |
---|
937 | if (!rd) { |
---|
938 | node_data[rn].first = edge; |
---|
939 | } |
---|
940 | |
---|
941 | Edge rev = _ugraph.oppositeEdge(edge); |
---|
942 | Edge e = node_data[n].first; |
---|
943 | |
---|
944 | edge_lists[edge_lists[e].next].prev = rev; |
---|
945 | edge_lists[rev].next = edge_lists[e].next; |
---|
946 | edge_lists[rev].prev = e; |
---|
947 | edge_lists[e].next = rev; |
---|
948 | |
---|
949 | if (d) { |
---|
950 | node_data[n].first = rev; |
---|
951 | } |
---|
952 | |
---|
953 | } |
---|
954 | |
---|
955 | // Embedding edge into external face |
---|
956 | if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
---|
957 | if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
---|
958 | pn = rn; |
---|
959 | |
---|
960 | embed_edge[order_list[n]] = INVALID; |
---|
961 | } |
---|
962 | |
---|
963 | if (!merge_roots[node].empty()) { |
---|
964 | |
---|
965 | bool d = pn == node_data[n].prev; |
---|
966 | if (node_data[n].prev == node_data[n].next && |
---|
967 | node_data[n].inverted) { |
---|
968 | d = !d; |
---|
969 | } |
---|
970 | |
---|
971 | merge_stack.push_back(std::make_pair(n, d)); |
---|
972 | |
---|
973 | int rn = merge_roots[node].front(); |
---|
974 | |
---|
975 | int xn = node_data[rn].next; |
---|
976 | Node xnode = order_list[xn]; |
---|
977 | |
---|
978 | int yn = node_data[rn].prev; |
---|
979 | Node ynode = order_list[yn]; |
---|
980 | |
---|
981 | bool rd; |
---|
982 | if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
983 | rd = true; |
---|
984 | } else if (!external(ynode, rorder, child_lists, |
---|
985 | ancestor_map, low_map)) { |
---|
986 | rd = false; |
---|
987 | } else if (pertinent(xnode, embed_edge, merge_roots)) { |
---|
988 | rd = true; |
---|
989 | } else { |
---|
990 | rd = false; |
---|
991 | } |
---|
992 | |
---|
993 | merge_stack.push_back(std::make_pair(rn, rd)); |
---|
994 | |
---|
995 | pn = rn; |
---|
996 | n = rd ? xn : yn; |
---|
997 | |
---|
998 | } else if (!external(node, rorder, child_lists, |
---|
999 | ancestor_map, low_map)) { |
---|
1000 | int nn = (node_data[n].next != pn ? |
---|
1001 | node_data[n].next : node_data[n].prev); |
---|
1002 | |
---|
1003 | bool nd = n == node_data[nn].prev; |
---|
1004 | |
---|
1005 | if (nd) node_data[nn].prev = pn; |
---|
1006 | else node_data[nn].next = pn; |
---|
1007 | |
---|
1008 | if (n == node_data[pn].prev) node_data[pn].prev = nn; |
---|
1009 | else node_data[pn].next = nn; |
---|
1010 | |
---|
1011 | node_data[nn].inverted = |
---|
1012 | (node_data[nn].prev == node_data[nn].next && nd != rd); |
---|
1013 | |
---|
1014 | n = nn; |
---|
1015 | } |
---|
1016 | else break; |
---|
1017 | |
---|
1018 | } |
---|
1019 | |
---|
1020 | if (!merge_stack.empty() || n == rn) { |
---|
1021 | break; |
---|
1022 | } |
---|
1023 | } |
---|
1024 | } |
---|
1025 | |
---|
1026 | void initFace(const Node& node, EdgeLists& edge_lists, |
---|
1027 | NodeData& node_data, const PredMap& pred_map, |
---|
1028 | const OrderMap& order_map, const OrderList& order_list) { |
---|
1029 | int n = order_map[node]; |
---|
1030 | int rn = n + order_list.size(); |
---|
1031 | |
---|
1032 | node_data[n].next = node_data[n].prev = rn; |
---|
1033 | node_data[rn].next = node_data[rn].prev = n; |
---|
1034 | |
---|
1035 | node_data[n].visited = order_list.size(); |
---|
1036 | node_data[rn].visited = order_list.size(); |
---|
1037 | |
---|
1038 | node_data[n].inverted = false; |
---|
1039 | node_data[rn].inverted = false; |
---|
1040 | |
---|
1041 | Edge edge = pred_map[node]; |
---|
1042 | Edge rev = _ugraph.oppositeEdge(edge); |
---|
1043 | |
---|
1044 | node_data[rn].first = edge; |
---|
1045 | node_data[n].first = rev; |
---|
1046 | |
---|
1047 | edge_lists[edge].prev = edge; |
---|
1048 | edge_lists[edge].next = edge; |
---|
1049 | |
---|
1050 | edge_lists[rev].prev = rev; |
---|
1051 | edge_lists[rev].next = rev; |
---|
1052 | |
---|
1053 | } |
---|
1054 | |
---|
1055 | void mergeRemainingFaces(const Node& node, NodeData& node_data, |
---|
1056 | OrderList& order_list, OrderMap& order_map, |
---|
1057 | ChildLists& child_lists, EdgeLists& edge_lists) { |
---|
1058 | while (child_lists[node].first != INVALID) { |
---|
1059 | int dd = order_map[node]; |
---|
1060 | Node child = child_lists[node].first; |
---|
1061 | int cd = order_map[child] + order_list.size(); |
---|
1062 | child_lists[node].first = child_lists[child].next; |
---|
1063 | |
---|
1064 | Edge de = node_data[dd].first; |
---|
1065 | Edge ce = node_data[cd].first; |
---|
1066 | |
---|
1067 | if (de != INVALID) { |
---|
1068 | Edge dne = edge_lists[de].next; |
---|
1069 | Edge cne = edge_lists[ce].next; |
---|
1070 | |
---|
1071 | edge_lists[de].next = cne; |
---|
1072 | edge_lists[ce].next = dne; |
---|
1073 | |
---|
1074 | edge_lists[dne].prev = ce; |
---|
1075 | edge_lists[cne].prev = de; |
---|
1076 | } |
---|
1077 | |
---|
1078 | node_data[dd].first = ce; |
---|
1079 | |
---|
1080 | } |
---|
1081 | } |
---|
1082 | |
---|
1083 | void storeEmbedding(const Node& node, NodeData& node_data, |
---|
1084 | OrderMap& order_map, PredMap& pred_map, |
---|
1085 | EdgeLists& edge_lists, FlipMap& flip_map) { |
---|
1086 | |
---|
1087 | if (node_data[order_map[node]].first == INVALID) return; |
---|
1088 | |
---|
1089 | if (pred_map[node] != INVALID) { |
---|
1090 | Node source = _ugraph.source(pred_map[node]); |
---|
1091 | flip_map[node] = flip_map[node] != flip_map[source]; |
---|
1092 | } |
---|
1093 | |
---|
1094 | Edge first = node_data[order_map[node]].first; |
---|
1095 | Edge prev = first; |
---|
1096 | |
---|
1097 | Edge edge = flip_map[node] ? |
---|
1098 | edge_lists[prev].prev : edge_lists[prev].next; |
---|
1099 | |
---|
1100 | _embedding[prev] = edge; |
---|
1101 | |
---|
1102 | while (edge != first) { |
---|
1103 | Edge next = edge_lists[edge].prev == prev ? |
---|
1104 | edge_lists[edge].next : edge_lists[edge].prev; |
---|
1105 | prev = edge; edge = next; |
---|
1106 | _embedding[prev] = edge; |
---|
1107 | } |
---|
1108 | } |
---|
1109 | |
---|
1110 | |
---|
1111 | bool external(const Node& node, int rorder, |
---|
1112 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
1113 | LowMap& low_map) { |
---|
1114 | Node child = child_lists[node].first; |
---|
1115 | |
---|
1116 | if (child != INVALID) { |
---|
1117 | if (low_map[child] < rorder) return true; |
---|
1118 | } |
---|
1119 | |
---|
1120 | if (ancestor_map[node] < rorder) return true; |
---|
1121 | |
---|
1122 | return false; |
---|
1123 | } |
---|
1124 | |
---|
1125 | bool pertinent(const Node& node, const EmbedEdge& embed_edge, |
---|
1126 | const MergeRoots& merge_roots) { |
---|
1127 | return !merge_roots[node].empty() || embed_edge[node] != INVALID; |
---|
1128 | } |
---|
1129 | |
---|
1130 | int lowPoint(const Node& node, OrderMap& order_map, ChildLists& child_lists, |
---|
1131 | AncestorMap& ancestor_map, LowMap& low_map) { |
---|
1132 | int low_point; |
---|
1133 | |
---|
1134 | Node child = child_lists[node].first; |
---|
1135 | |
---|
1136 | if (child != INVALID) { |
---|
1137 | low_point = low_map[child]; |
---|
1138 | } else { |
---|
1139 | low_point = order_map[node]; |
---|
1140 | } |
---|
1141 | |
---|
1142 | if (low_point > ancestor_map[node]) { |
---|
1143 | low_point = ancestor_map[node]; |
---|
1144 | } |
---|
1145 | |
---|
1146 | return low_point; |
---|
1147 | } |
---|
1148 | |
---|
1149 | int findComponentRoot(Node root, Node node, ChildLists& child_lists, |
---|
1150 | OrderMap& order_map, OrderList& order_list) { |
---|
1151 | |
---|
1152 | int order = order_map[root]; |
---|
1153 | int norder = order_map[node]; |
---|
1154 | |
---|
1155 | Node child = child_lists[root].first; |
---|
1156 | while (child != INVALID) { |
---|
1157 | int corder = order_map[child]; |
---|
1158 | if (corder > order && corder < norder) { |
---|
1159 | order = corder; |
---|
1160 | } |
---|
1161 | child = child_lists[child].next; |
---|
1162 | } |
---|
1163 | return order + order_list.size(); |
---|
1164 | } |
---|
1165 | |
---|
1166 | Node findPertinent(Node node, OrderMap& order_map, NodeData& node_data, |
---|
1167 | EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
---|
1168 | Node wnode =_ugraph.target(node_data[order_map[node]].first); |
---|
1169 | while (!pertinent(wnode, embed_edge, merge_roots)) { |
---|
1170 | wnode = _ugraph.target(node_data[order_map[wnode]].first); |
---|
1171 | } |
---|
1172 | return wnode; |
---|
1173 | } |
---|
1174 | |
---|
1175 | |
---|
1176 | Node findExternal(Node node, int rorder, OrderMap& order_map, |
---|
1177 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
1178 | LowMap& low_map, NodeData& node_data) { |
---|
1179 | Node wnode =_ugraph.target(node_data[order_map[node]].first); |
---|
1180 | while (!external(wnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
1181 | wnode = _ugraph.target(node_data[order_map[wnode]].first); |
---|
1182 | } |
---|
1183 | return wnode; |
---|
1184 | } |
---|
1185 | |
---|
1186 | void markCommonPath(Node node, int rorder, Node& wnode, Node& znode, |
---|
1187 | OrderList& order_list, OrderMap& order_map, |
---|
1188 | NodeData& node_data, EdgeLists& edge_lists, |
---|
1189 | EmbedEdge& embed_edge, MergeRoots& merge_roots, |
---|
1190 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
1191 | LowMap& low_map) { |
---|
1192 | |
---|
1193 | Node cnode = node; |
---|
1194 | Node pred = INVALID; |
---|
1195 | |
---|
1196 | while (true) { |
---|
1197 | |
---|
1198 | bool pert = pertinent(cnode, embed_edge, merge_roots); |
---|
1199 | bool ext = external(cnode, rorder, child_lists, ancestor_map, low_map); |
---|
1200 | |
---|
1201 | if (pert && ext) { |
---|
1202 | if (!merge_roots[cnode].empty()) { |
---|
1203 | int cn = merge_roots[cnode].back(); |
---|
1204 | |
---|
1205 | if (low_map[order_list[cn - order_list.size()]] < rorder) { |
---|
1206 | Edge edge = node_data[cn].first; |
---|
1207 | _kuratowski.set(edge, true); |
---|
1208 | |
---|
1209 | pred = cnode; |
---|
1210 | cnode = _ugraph.target(edge); |
---|
1211 | |
---|
1212 | continue; |
---|
1213 | } |
---|
1214 | } |
---|
1215 | wnode = znode = cnode; |
---|
1216 | return; |
---|
1217 | |
---|
1218 | } else if (pert) { |
---|
1219 | wnode = cnode; |
---|
1220 | |
---|
1221 | while (!external(cnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
1222 | Edge edge = node_data[order_map[cnode]].first; |
---|
1223 | |
---|
1224 | if (_ugraph.target(edge) == pred) { |
---|
1225 | edge = edge_lists[edge].next; |
---|
1226 | } |
---|
1227 | _kuratowski.set(edge, true); |
---|
1228 | |
---|
1229 | Node next = _ugraph.target(edge); |
---|
1230 | pred = cnode; cnode = next; |
---|
1231 | } |
---|
1232 | |
---|
1233 | znode = cnode; |
---|
1234 | return; |
---|
1235 | |
---|
1236 | } else if (ext) { |
---|
1237 | znode = cnode; |
---|
1238 | |
---|
1239 | while (!pertinent(cnode, embed_edge, merge_roots)) { |
---|
1240 | Edge edge = node_data[order_map[cnode]].first; |
---|
1241 | |
---|
1242 | if (_ugraph.target(edge) == pred) { |
---|
1243 | edge = edge_lists[edge].next; |
---|
1244 | } |
---|
1245 | _kuratowski.set(edge, true); |
---|
1246 | |
---|
1247 | Node next = _ugraph.target(edge); |
---|
1248 | pred = cnode; cnode = next; |
---|
1249 | } |
---|
1250 | |
---|
1251 | wnode = cnode; |
---|
1252 | return; |
---|
1253 | |
---|
1254 | } else { |
---|
1255 | Edge edge = node_data[order_map[cnode]].first; |
---|
1256 | |
---|
1257 | if (_ugraph.target(edge) == pred) { |
---|
1258 | edge = edge_lists[edge].next; |
---|
1259 | } |
---|
1260 | _kuratowski.set(edge, true); |
---|
1261 | |
---|
1262 | Node next = _ugraph.target(edge); |
---|
1263 | pred = cnode; cnode = next; |
---|
1264 | } |
---|
1265 | |
---|
1266 | } |
---|
1267 | |
---|
1268 | } |
---|
1269 | |
---|
1270 | void orientComponent(Node root, int rn, OrderMap& order_map, |
---|
1271 | PredMap& pred_map, NodeData& node_data, |
---|
1272 | EdgeLists& edge_lists, FlipMap& flip_map, |
---|
1273 | TypeMap& type_map) { |
---|
1274 | node_data[order_map[root]].first = node_data[rn].first; |
---|
1275 | type_map[root] = 1; |
---|
1276 | |
---|
1277 | std::vector<Node> st, qu; |
---|
1278 | |
---|
1279 | st.push_back(root); |
---|
1280 | while (!st.empty()) { |
---|
1281 | Node node = st.back(); |
---|
1282 | st.pop_back(); |
---|
1283 | qu.push_back(node); |
---|
1284 | |
---|
1285 | Edge edge = node_data[order_map[node]].first; |
---|
1286 | |
---|
1287 | if (type_map[_ugraph.target(edge)] == 0) { |
---|
1288 | st.push_back(_ugraph.target(edge)); |
---|
1289 | type_map[_ugraph.target(edge)] = 1; |
---|
1290 | } |
---|
1291 | |
---|
1292 | Edge last = edge, pred = edge; |
---|
1293 | edge = edge_lists[edge].next; |
---|
1294 | while (edge != last) { |
---|
1295 | |
---|
1296 | if (type_map[_ugraph.target(edge)] == 0) { |
---|
1297 | st.push_back(_ugraph.target(edge)); |
---|
1298 | type_map[_ugraph.target(edge)] = 1; |
---|
1299 | } |
---|
1300 | |
---|
1301 | Edge next = edge_lists[edge].next != pred ? |
---|
1302 | edge_lists[edge].next : edge_lists[edge].prev; |
---|
1303 | pred = edge; edge = next; |
---|
1304 | } |
---|
1305 | |
---|
1306 | } |
---|
1307 | |
---|
1308 | type_map[root] = 2; |
---|
1309 | flip_map[root] = false; |
---|
1310 | |
---|
1311 | for (int i = 1; i < int(qu.size()); ++i) { |
---|
1312 | |
---|
1313 | Node node = qu[i]; |
---|
1314 | |
---|
1315 | while (type_map[node] != 2) { |
---|
1316 | st.push_back(node); |
---|
1317 | type_map[node] = 2; |
---|
1318 | node = _ugraph.source(pred_map[node]); |
---|
1319 | } |
---|
1320 | |
---|
1321 | bool flip = flip_map[node]; |
---|
1322 | |
---|
1323 | while (!st.empty()) { |
---|
1324 | node = st.back(); |
---|
1325 | st.pop_back(); |
---|
1326 | |
---|
1327 | flip_map[node] = flip != flip_map[node]; |
---|
1328 | flip = flip_map[node]; |
---|
1329 | |
---|
1330 | if (flip) { |
---|
1331 | Edge edge = node_data[order_map[node]].first; |
---|
1332 | std::swap(edge_lists[edge].prev, edge_lists[edge].next); |
---|
1333 | edge = edge_lists[edge].prev; |
---|
1334 | std::swap(edge_lists[edge].prev, edge_lists[edge].next); |
---|
1335 | node_data[order_map[node]].first = edge; |
---|
1336 | } |
---|
1337 | } |
---|
1338 | } |
---|
1339 | |
---|
1340 | for (int i = 0; i < int(qu.size()); ++i) { |
---|
1341 | |
---|
1342 | Edge edge = node_data[order_map[qu[i]]].first; |
---|
1343 | Edge last = edge, pred = edge; |
---|
1344 | |
---|
1345 | edge = edge_lists[edge].next; |
---|
1346 | while (edge != last) { |
---|
1347 | |
---|
1348 | if (edge_lists[edge].next == pred) { |
---|
1349 | std::swap(edge_lists[edge].next, edge_lists[edge].prev); |
---|
1350 | } |
---|
1351 | pred = edge; edge = edge_lists[edge].next; |
---|
1352 | } |
---|
1353 | |
---|
1354 | } |
---|
1355 | } |
---|
1356 | |
---|
1357 | void setFaceFlags(Node root, Node wnode, Node ynode, Node xnode, |
---|
1358 | OrderMap& order_map, NodeData& node_data, |
---|
1359 | TypeMap& type_map) { |
---|
1360 | Node node = _ugraph.target(node_data[order_map[root]].first); |
---|
1361 | |
---|
1362 | while (node != ynode) { |
---|
1363 | type_map[node] = HIGHY; |
---|
1364 | node = _ugraph.target(node_data[order_map[node]].first); |
---|
1365 | } |
---|
1366 | |
---|
1367 | while (node != wnode) { |
---|
1368 | type_map[node] = LOWY; |
---|
1369 | node = _ugraph.target(node_data[order_map[node]].first); |
---|
1370 | } |
---|
1371 | |
---|
1372 | node = _ugraph.target(node_data[order_map[wnode]].first); |
---|
1373 | |
---|
1374 | while (node != xnode) { |
---|
1375 | type_map[node] = LOWX; |
---|
1376 | node = _ugraph.target(node_data[order_map[node]].first); |
---|
1377 | } |
---|
1378 | type_map[node] = LOWX; |
---|
1379 | |
---|
1380 | node = _ugraph.target(node_data[order_map[xnode]].first); |
---|
1381 | while (node != root) { |
---|
1382 | type_map[node] = HIGHX; |
---|
1383 | node = _ugraph.target(node_data[order_map[node]].first); |
---|
1384 | } |
---|
1385 | |
---|
1386 | type_map[wnode] = PERTINENT; |
---|
1387 | type_map[root] = ROOT; |
---|
1388 | } |
---|
1389 | |
---|
1390 | void findInternalPath(std::vector<Edge>& ipath, |
---|
1391 | Node wnode, Node root, TypeMap& type_map, |
---|
1392 | OrderMap& order_map, NodeData& node_data, |
---|
1393 | EdgeLists& edge_lists) { |
---|
1394 | std::vector<Edge> st; |
---|
1395 | |
---|
1396 | Node node = wnode; |
---|
1397 | |
---|
1398 | while (node != root) { |
---|
1399 | Edge edge = edge_lists[node_data[order_map[node]].first].next; |
---|
1400 | st.push_back(edge); |
---|
1401 | node = _ugraph.target(edge); |
---|
1402 | } |
---|
1403 | |
---|
1404 | while (true) { |
---|
1405 | Edge edge = st.back(); |
---|
1406 | if (type_map[_ugraph.target(edge)] == LOWX || |
---|
1407 | type_map[_ugraph.target(edge)] == HIGHX) { |
---|
1408 | break; |
---|
1409 | } |
---|
1410 | if (type_map[_ugraph.target(edge)] == 2) { |
---|
1411 | type_map[_ugraph.target(edge)] = 3; |
---|
1412 | |
---|
1413 | edge = edge_lists[_ugraph.oppositeEdge(edge)].next; |
---|
1414 | st.push_back(edge); |
---|
1415 | } else { |
---|
1416 | st.pop_back(); |
---|
1417 | edge = edge_lists[edge].next; |
---|
1418 | |
---|
1419 | while (_ugraph.oppositeEdge(edge) == st.back()) { |
---|
1420 | edge = st.back(); |
---|
1421 | st.pop_back(); |
---|
1422 | edge = edge_lists[edge].next; |
---|
1423 | } |
---|
1424 | st.push_back(edge); |
---|
1425 | } |
---|
1426 | } |
---|
1427 | |
---|
1428 | for (int i = 0; i < int(st.size()); ++i) { |
---|
1429 | if (type_map[_ugraph.target(st[i])] != LOWY && |
---|
1430 | type_map[_ugraph.target(st[i])] != HIGHY) { |
---|
1431 | for (; i < int(st.size()); ++i) { |
---|
1432 | ipath.push_back(st[i]); |
---|
1433 | } |
---|
1434 | } |
---|
1435 | } |
---|
1436 | } |
---|
1437 | |
---|
1438 | void setInternalFlags(std::vector<Edge>& ipath, TypeMap& type_map) { |
---|
1439 | for (int i = 1; i < int(ipath.size()); ++i) { |
---|
1440 | type_map[_ugraph.source(ipath[i])] = INTERNAL; |
---|
1441 | } |
---|
1442 | } |
---|
1443 | |
---|
1444 | void findPilePath(std::vector<Edge>& ppath, |
---|
1445 | Node root, TypeMap& type_map, OrderMap& order_map, |
---|
1446 | NodeData& node_data, EdgeLists& edge_lists) { |
---|
1447 | std::vector<Edge> st; |
---|
1448 | |
---|
1449 | st.push_back(_ugraph.oppositeEdge(node_data[order_map[root]].first)); |
---|
1450 | st.push_back(node_data[order_map[root]].first); |
---|
1451 | |
---|
1452 | while (st.size() > 1) { |
---|
1453 | Edge edge = st.back(); |
---|
1454 | if (type_map[_ugraph.target(edge)] == INTERNAL) { |
---|
1455 | break; |
---|
1456 | } |
---|
1457 | if (type_map[_ugraph.target(edge)] == 3) { |
---|
1458 | type_map[_ugraph.target(edge)] = 4; |
---|
1459 | |
---|
1460 | edge = edge_lists[_ugraph.oppositeEdge(edge)].next; |
---|
1461 | st.push_back(edge); |
---|
1462 | } else { |
---|
1463 | st.pop_back(); |
---|
1464 | edge = edge_lists[edge].next; |
---|
1465 | |
---|
1466 | while (!st.empty() && _ugraph.oppositeEdge(edge) == st.back()) { |
---|
1467 | edge = st.back(); |
---|
1468 | st.pop_back(); |
---|
1469 | edge = edge_lists[edge].next; |
---|
1470 | } |
---|
1471 | st.push_back(edge); |
---|
1472 | } |
---|
1473 | } |
---|
1474 | |
---|
1475 | for (int i = 1; i < int(st.size()); ++i) { |
---|
1476 | ppath.push_back(st[i]); |
---|
1477 | } |
---|
1478 | } |
---|
1479 | |
---|
1480 | |
---|
1481 | int markExternalPath(Node node, OrderMap& order_map, |
---|
1482 | ChildLists& child_lists, PredMap& pred_map, |
---|
1483 | AncestorMap& ancestor_map, LowMap& low_map) { |
---|
1484 | int lp = lowPoint(node, order_map, child_lists, |
---|
1485 | ancestor_map, low_map); |
---|
1486 | |
---|
1487 | if (ancestor_map[node] != lp) { |
---|
1488 | node = child_lists[node].first; |
---|
1489 | _kuratowski[pred_map[node]] = true; |
---|
1490 | |
---|
1491 | while (ancestor_map[node] != lp) { |
---|
1492 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
1493 | Node tnode = _ugraph.target(e); |
---|
1494 | if (order_map[tnode] > order_map[node] && low_map[tnode] == lp) { |
---|
1495 | node = tnode; |
---|
1496 | _kuratowski[e] = true; |
---|
1497 | break; |
---|
1498 | } |
---|
1499 | } |
---|
1500 | } |
---|
1501 | } |
---|
1502 | |
---|
1503 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
1504 | if (order_map[_ugraph.target(e)] == lp) { |
---|
1505 | _kuratowski[e] = true; |
---|
1506 | break; |
---|
1507 | } |
---|
1508 | } |
---|
1509 | |
---|
1510 | return lp; |
---|
1511 | } |
---|
1512 | |
---|
1513 | void markPertinentPath(Node node, OrderMap& order_map, |
---|
1514 | NodeData& node_data, EdgeLists& edge_lists, |
---|
1515 | EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
---|
1516 | while (embed_edge[node] == INVALID) { |
---|
1517 | int n = merge_roots[node].front(); |
---|
1518 | Edge edge = node_data[n].first; |
---|
1519 | |
---|
1520 | _kuratowski.set(edge, true); |
---|
1521 | |
---|
1522 | Node pred = node; |
---|
1523 | node = _ugraph.target(edge); |
---|
1524 | while (!pertinent(node, embed_edge, merge_roots)) { |
---|
1525 | edge = node_data[order_map[node]].first; |
---|
1526 | if (_ugraph.target(edge) == pred) { |
---|
1527 | edge = edge_lists[edge].next; |
---|
1528 | } |
---|
1529 | _kuratowski.set(edge, true); |
---|
1530 | pred = node; |
---|
1531 | node = _ugraph.target(edge); |
---|
1532 | } |
---|
1533 | } |
---|
1534 | _kuratowski.set(embed_edge[node], true); |
---|
1535 | } |
---|
1536 | |
---|
1537 | void markPredPath(Node node, Node snode, PredMap& pred_map) { |
---|
1538 | while (node != snode) { |
---|
1539 | _kuratowski.set(pred_map[node], true); |
---|
1540 | node = _ugraph.source(pred_map[node]); |
---|
1541 | } |
---|
1542 | } |
---|
1543 | |
---|
1544 | void markFacePath(Node ynode, Node xnode, |
---|
1545 | OrderMap& order_map, NodeData& node_data) { |
---|
1546 | Edge edge = node_data[order_map[ynode]].first; |
---|
1547 | Node node = _ugraph.target(edge); |
---|
1548 | _kuratowski.set(edge, true); |
---|
1549 | |
---|
1550 | while (node != xnode) { |
---|
1551 | edge = node_data[order_map[node]].first; |
---|
1552 | _kuratowski.set(edge, true); |
---|
1553 | node = _ugraph.target(edge); |
---|
1554 | } |
---|
1555 | } |
---|
1556 | |
---|
1557 | void markInternalPath(std::vector<Edge>& path) { |
---|
1558 | for (int i = 0; i < int(path.size()); ++i) { |
---|
1559 | _kuratowski.set(path[i], true); |
---|
1560 | } |
---|
1561 | } |
---|
1562 | |
---|
1563 | void markPilePath(std::vector<Edge>& path) { |
---|
1564 | for (int i = 0; i < int(path.size()); ++i) { |
---|
1565 | _kuratowski.set(path[i], true); |
---|
1566 | } |
---|
1567 | } |
---|
1568 | |
---|
1569 | void isolateKuratowski(Edge edge, NodeData& node_data, |
---|
1570 | EdgeLists& edge_lists, FlipMap& flip_map, |
---|
1571 | OrderMap& order_map, OrderList& order_list, |
---|
1572 | PredMap& pred_map, ChildLists& child_lists, |
---|
1573 | AncestorMap& ancestor_map, LowMap& low_map, |
---|
1574 | EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
---|
1575 | |
---|
1576 | Node root = _ugraph.source(edge); |
---|
1577 | Node enode = _ugraph.target(edge); |
---|
1578 | |
---|
1579 | int rorder = order_map[root]; |
---|
1580 | |
---|
1581 | TypeMap type_map(_ugraph, 0); |
---|
1582 | |
---|
1583 | int rn = findComponentRoot(root, enode, child_lists, |
---|
1584 | order_map, order_list); |
---|
1585 | |
---|
1586 | Node xnode = order_list[node_data[rn].next]; |
---|
1587 | Node ynode = order_list[node_data[rn].prev]; |
---|
1588 | |
---|
1589 | // Minor-A |
---|
1590 | { |
---|
1591 | while (!merge_roots[xnode].empty() || !merge_roots[ynode].empty()) { |
---|
1592 | |
---|
1593 | if (!merge_roots[xnode].empty()) { |
---|
1594 | root = xnode; |
---|
1595 | rn = merge_roots[xnode].front(); |
---|
1596 | } else { |
---|
1597 | root = ynode; |
---|
1598 | rn = merge_roots[ynode].front(); |
---|
1599 | } |
---|
1600 | |
---|
1601 | xnode = order_list[node_data[rn].next]; |
---|
1602 | ynode = order_list[node_data[rn].prev]; |
---|
1603 | } |
---|
1604 | |
---|
1605 | if (root != _ugraph.source(edge)) { |
---|
1606 | orientComponent(root, rn, order_map, pred_map, |
---|
1607 | node_data, edge_lists, flip_map, type_map); |
---|
1608 | markFacePath(root, root, order_map, node_data); |
---|
1609 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1610 | pred_map, ancestor_map, low_map); |
---|
1611 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1612 | pred_map, ancestor_map, low_map); |
---|
1613 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
1614 | Node lwnode = findPertinent(ynode, order_map, node_data, |
---|
1615 | embed_edge, merge_roots); |
---|
1616 | |
---|
1617 | markPertinentPath(lwnode, order_map, node_data, edge_lists, |
---|
1618 | embed_edge, merge_roots); |
---|
1619 | |
---|
1620 | return; |
---|
1621 | } |
---|
1622 | } |
---|
1623 | |
---|
1624 | orientComponent(root, rn, order_map, pred_map, |
---|
1625 | node_data, edge_lists, flip_map, type_map); |
---|
1626 | |
---|
1627 | Node wnode = findPertinent(ynode, order_map, node_data, |
---|
1628 | embed_edge, merge_roots); |
---|
1629 | setFaceFlags(root, wnode, ynode, xnode, order_map, node_data, type_map); |
---|
1630 | |
---|
1631 | |
---|
1632 | //Minor-B |
---|
1633 | if (!merge_roots[wnode].empty()) { |
---|
1634 | int cn = merge_roots[wnode].back(); |
---|
1635 | Node rep = order_list[cn - order_list.size()]; |
---|
1636 | if (low_map[rep] < rorder) { |
---|
1637 | markFacePath(root, root, order_map, node_data); |
---|
1638 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1639 | pred_map, ancestor_map, low_map); |
---|
1640 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1641 | pred_map, ancestor_map, low_map); |
---|
1642 | |
---|
1643 | Node lwnode, lznode; |
---|
1644 | markCommonPath(wnode, rorder, lwnode, lznode, order_list, |
---|
1645 | order_map, node_data, edge_lists, embed_edge, |
---|
1646 | merge_roots, child_lists, ancestor_map, low_map); |
---|
1647 | |
---|
1648 | markPertinentPath(lwnode, order_map, node_data, edge_lists, |
---|
1649 | embed_edge, merge_roots); |
---|
1650 | int zlp = markExternalPath(lznode, order_map, child_lists, |
---|
1651 | pred_map, ancestor_map, low_map); |
---|
1652 | |
---|
1653 | int minlp = xlp < ylp ? xlp : ylp; |
---|
1654 | if (zlp < minlp) minlp = zlp; |
---|
1655 | |
---|
1656 | int maxlp = xlp > ylp ? xlp : ylp; |
---|
1657 | if (zlp > maxlp) maxlp = zlp; |
---|
1658 | |
---|
1659 | markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
---|
1660 | |
---|
1661 | return; |
---|
1662 | } |
---|
1663 | } |
---|
1664 | |
---|
1665 | Node pxnode, pynode; |
---|
1666 | std::vector<Edge> ipath; |
---|
1667 | findInternalPath(ipath, wnode, root, type_map, order_map, |
---|
1668 | node_data, edge_lists); |
---|
1669 | setInternalFlags(ipath, type_map); |
---|
1670 | pynode = _ugraph.source(ipath.front()); |
---|
1671 | pxnode = _ugraph.target(ipath.back()); |
---|
1672 | |
---|
1673 | wnode = findPertinent(pynode, order_map, node_data, |
---|
1674 | embed_edge, merge_roots); |
---|
1675 | |
---|
1676 | // Minor-C |
---|
1677 | { |
---|
1678 | if (type_map[_ugraph.source(ipath.front())] == HIGHY) { |
---|
1679 | if (type_map[_ugraph.target(ipath.back())] == HIGHX) { |
---|
1680 | markFacePath(xnode, pxnode, order_map, node_data); |
---|
1681 | } |
---|
1682 | markFacePath(root, xnode, 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 | if (type_map[_ugraph.target(ipath.back())] == HIGHX) { |
---|
1695 | markFacePath(ynode, root, order_map, node_data); |
---|
1696 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
1697 | embed_edge, merge_roots); |
---|
1698 | markInternalPath(ipath); |
---|
1699 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1700 | pred_map, ancestor_map, low_map); |
---|
1701 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1702 | pred_map, ancestor_map, low_map); |
---|
1703 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
1704 | return; |
---|
1705 | } |
---|
1706 | } |
---|
1707 | |
---|
1708 | std::vector<Edge> ppath; |
---|
1709 | findPilePath(ppath, root, type_map, order_map, node_data, edge_lists); |
---|
1710 | |
---|
1711 | // Minor-D |
---|
1712 | if (!ppath.empty()) { |
---|
1713 | markFacePath(ynode, xnode, order_map, node_data); |
---|
1714 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
1715 | embed_edge, merge_roots); |
---|
1716 | markPilePath(ppath); |
---|
1717 | markInternalPath(ipath); |
---|
1718 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1719 | pred_map, ancestor_map, low_map); |
---|
1720 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1721 | pred_map, ancestor_map, low_map); |
---|
1722 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
1723 | return; |
---|
1724 | } |
---|
1725 | |
---|
1726 | // Minor-E* |
---|
1727 | { |
---|
1728 | |
---|
1729 | if (!external(wnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
1730 | Node znode = findExternal(pynode, rorder, order_map, |
---|
1731 | child_lists, ancestor_map, |
---|
1732 | low_map, node_data); |
---|
1733 | |
---|
1734 | if (type_map[znode] == LOWY) { |
---|
1735 | markFacePath(root, xnode, order_map, node_data); |
---|
1736 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
1737 | embed_edge, merge_roots); |
---|
1738 | markInternalPath(ipath); |
---|
1739 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1740 | pred_map, ancestor_map, low_map); |
---|
1741 | int zlp = markExternalPath(znode, order_map, child_lists, |
---|
1742 | pred_map, ancestor_map, low_map); |
---|
1743 | markPredPath(root, order_list[xlp < zlp ? xlp : zlp], pred_map); |
---|
1744 | } else { |
---|
1745 | markFacePath(ynode, root, order_map, node_data); |
---|
1746 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
1747 | embed_edge, merge_roots); |
---|
1748 | markInternalPath(ipath); |
---|
1749 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1750 | pred_map, ancestor_map, low_map); |
---|
1751 | int zlp = markExternalPath(znode, order_map, child_lists, |
---|
1752 | pred_map, ancestor_map, low_map); |
---|
1753 | markPredPath(root, order_list[ylp < zlp ? ylp : zlp], pred_map); |
---|
1754 | } |
---|
1755 | return; |
---|
1756 | } |
---|
1757 | |
---|
1758 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1759 | pred_map, ancestor_map, low_map); |
---|
1760 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1761 | pred_map, ancestor_map, low_map); |
---|
1762 | int wlp = markExternalPath(wnode, order_map, child_lists, |
---|
1763 | pred_map, ancestor_map, low_map); |
---|
1764 | |
---|
1765 | if (wlp > xlp && wlp > ylp) { |
---|
1766 | markFacePath(root, root, order_map, node_data); |
---|
1767 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
1768 | return; |
---|
1769 | } |
---|
1770 | |
---|
1771 | markInternalPath(ipath); |
---|
1772 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
1773 | embed_edge, merge_roots); |
---|
1774 | |
---|
1775 | if (xlp > ylp && xlp > wlp) { |
---|
1776 | markFacePath(root, pynode, order_map, node_data); |
---|
1777 | markFacePath(wnode, xnode, order_map, node_data); |
---|
1778 | markPredPath(root, order_list[ylp < wlp ? ylp : wlp], pred_map); |
---|
1779 | return; |
---|
1780 | } |
---|
1781 | |
---|
1782 | if (ylp > xlp && ylp > wlp) { |
---|
1783 | markFacePath(pxnode, root, order_map, node_data); |
---|
1784 | markFacePath(ynode, wnode, order_map, node_data); |
---|
1785 | markPredPath(root, order_list[xlp < wlp ? xlp : wlp], pred_map); |
---|
1786 | return; |
---|
1787 | } |
---|
1788 | |
---|
1789 | if (pynode != ynode) { |
---|
1790 | markFacePath(pxnode, wnode, 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 | if (pxnode != xnode) { |
---|
1803 | markFacePath(wnode, pynode, order_map, node_data); |
---|
1804 | |
---|
1805 | int minlp = xlp < ylp ? xlp : ylp; |
---|
1806 | if (wlp < minlp) minlp = wlp; |
---|
1807 | |
---|
1808 | int maxlp = xlp > ylp ? xlp : ylp; |
---|
1809 | if (wlp > maxlp) maxlp = wlp; |
---|
1810 | |
---|
1811 | markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
---|
1812 | return; |
---|
1813 | } |
---|
1814 | |
---|
1815 | markFacePath(root, root, order_map, node_data); |
---|
1816 | int minlp = xlp < ylp ? xlp : ylp; |
---|
1817 | if (wlp < minlp) minlp = wlp; |
---|
1818 | markPredPath(root, order_list[minlp], pred_map); |
---|
1819 | return; |
---|
1820 | } |
---|
1821 | |
---|
1822 | } |
---|
1823 | |
---|
1824 | }; |
---|
1825 | |
---|
1826 | namespace _planarity_bits { |
---|
1827 | |
---|
1828 | template <typename UGraph, typename EmbeddingMap> |
---|
1829 | void makeConnected(UGraph& ugraph, EmbeddingMap& embedding) { |
---|
1830 | DfsVisitor<UGraph> null_visitor; |
---|
1831 | DfsVisit<UGraph, DfsVisitor<UGraph> > dfs(ugraph, null_visitor); |
---|
1832 | dfs.init(); |
---|
1833 | |
---|
1834 | typename UGraph::Node u = INVALID; |
---|
1835 | for (typename UGraph::NodeIt n(ugraph); n != INVALID; ++n) { |
---|
1836 | if (!dfs.reached(n)) { |
---|
1837 | dfs.addSource(n); |
---|
1838 | dfs.start(); |
---|
1839 | if (u == INVALID) { |
---|
1840 | u = n; |
---|
1841 | } else { |
---|
1842 | typename UGraph::Node v = n; |
---|
1843 | |
---|
1844 | typename UGraph::Edge ue = typename UGraph::OutEdgeIt(ugraph, u); |
---|
1845 | typename UGraph::Edge ve = typename UGraph::OutEdgeIt(ugraph, v); |
---|
1846 | |
---|
1847 | typename UGraph::Edge e = ugraph.direct(ugraph.addEdge(u, v), true); |
---|
1848 | |
---|
1849 | if (ue != INVALID) { |
---|
1850 | embedding[e] = embedding[ue]; |
---|
1851 | embedding[ue] = e; |
---|
1852 | } else { |
---|
1853 | embedding[e] = e; |
---|
1854 | } |
---|
1855 | |
---|
1856 | if (ve != INVALID) { |
---|
1857 | embedding[ugraph.oppositeEdge(e)] = embedding[ve]; |
---|
1858 | embedding[ve] = ugraph.oppositeEdge(e); |
---|
1859 | } else { |
---|
1860 | embedding[ugraph.oppositeEdge(e)] = ugraph.oppositeEdge(e); |
---|
1861 | } |
---|
1862 | } |
---|
1863 | } |
---|
1864 | } |
---|
1865 | } |
---|
1866 | |
---|
1867 | template <typename UGraph, typename EmbeddingMap> |
---|
1868 | void makeBiNodeConnected(UGraph& ugraph, EmbeddingMap& embedding) { |
---|
1869 | typename UGraph::template EdgeMap<bool> processed(ugraph); |
---|
1870 | |
---|
1871 | std::vector<typename UGraph::Edge> edges; |
---|
1872 | for (typename UGraph::EdgeIt e(ugraph); e != INVALID; ++e) { |
---|
1873 | edges.push_back(e); |
---|
1874 | } |
---|
1875 | |
---|
1876 | IterableBoolMap<UGraph, typename UGraph::Node> visited(ugraph, false); |
---|
1877 | |
---|
1878 | for (int i = 0; i < int(edges.size()); ++i) { |
---|
1879 | typename UGraph::Edge pp = edges[i]; |
---|
1880 | if (processed[pp]) continue; |
---|
1881 | |
---|
1882 | typename UGraph::Edge e = embedding[ugraph.oppositeEdge(pp)]; |
---|
1883 | processed[e] = true; |
---|
1884 | visited.set(ugraph.source(e), true); |
---|
1885 | |
---|
1886 | typename UGraph::Edge p = e, l = e; |
---|
1887 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
1888 | |
---|
1889 | while (e != l) { |
---|
1890 | processed[e] = true; |
---|
1891 | |
---|
1892 | if (visited[ugraph.source(e)]) { |
---|
1893 | |
---|
1894 | typename UGraph::Edge n = |
---|
1895 | ugraph.direct(ugraph.addEdge(ugraph.source(p), |
---|
1896 | ugraph.target(e)), true); |
---|
1897 | embedding[n] = p; |
---|
1898 | embedding[ugraph.oppositeEdge(pp)] = n; |
---|
1899 | |
---|
1900 | embedding[ugraph.oppositeEdge(n)] = |
---|
1901 | embedding[ugraph.oppositeEdge(e)]; |
---|
1902 | embedding[ugraph.oppositeEdge(e)] = |
---|
1903 | ugraph.oppositeEdge(n); |
---|
1904 | |
---|
1905 | p = n; |
---|
1906 | e = embedding[ugraph.oppositeEdge(n)]; |
---|
1907 | } else { |
---|
1908 | visited.set(ugraph.source(e), true); |
---|
1909 | pp = p; |
---|
1910 | p = e; |
---|
1911 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
1912 | } |
---|
1913 | } |
---|
1914 | visited.setAll(false); |
---|
1915 | } |
---|
1916 | } |
---|
1917 | |
---|
1918 | |
---|
1919 | template <typename UGraph, typename EmbeddingMap> |
---|
1920 | void makeMaxPlanar(UGraph& ugraph, EmbeddingMap& embedding) { |
---|
1921 | |
---|
1922 | typename UGraph::template NodeMap<int> degree(ugraph); |
---|
1923 | |
---|
1924 | for (typename UGraph::NodeIt n(ugraph); n != INVALID; ++n) { |
---|
1925 | degree[n] = countIncEdges(ugraph, n); |
---|
1926 | } |
---|
1927 | |
---|
1928 | typename UGraph::template EdgeMap<bool> processed(ugraph); |
---|
1929 | IterableBoolMap<UGraph, typename UGraph::Node> visited(ugraph, false); |
---|
1930 | |
---|
1931 | std::vector<typename UGraph::Edge> edges; |
---|
1932 | for (typename UGraph::EdgeIt e(ugraph); e != INVALID; ++e) { |
---|
1933 | edges.push_back(e); |
---|
1934 | } |
---|
1935 | |
---|
1936 | for (int i = 0; i < int(edges.size()); ++i) { |
---|
1937 | typename UGraph::Edge e = edges[i]; |
---|
1938 | |
---|
1939 | if (processed[e]) continue; |
---|
1940 | processed[e] = true; |
---|
1941 | |
---|
1942 | typename UGraph::Edge mine = e; |
---|
1943 | int mind = degree[ugraph.source(e)]; |
---|
1944 | |
---|
1945 | int face_size = 1; |
---|
1946 | |
---|
1947 | typename UGraph::Edge l = e; |
---|
1948 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
1949 | while (l != e) { |
---|
1950 | processed[e] = true; |
---|
1951 | |
---|
1952 | ++face_size; |
---|
1953 | |
---|
1954 | if (degree[ugraph.source(e)] < mind) { |
---|
1955 | mine = e; |
---|
1956 | mind = degree[ugraph.source(e)]; |
---|
1957 | } |
---|
1958 | |
---|
1959 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
1960 | } |
---|
1961 | |
---|
1962 | if (face_size < 4) { |
---|
1963 | continue; |
---|
1964 | } |
---|
1965 | |
---|
1966 | typename UGraph::Node s = ugraph.source(mine); |
---|
1967 | for (typename UGraph::OutEdgeIt e(ugraph, s); e != INVALID; ++e) { |
---|
1968 | visited.set(ugraph.target(e), true); |
---|
1969 | } |
---|
1970 | |
---|
1971 | typename UGraph::Edge oppe = INVALID; |
---|
1972 | |
---|
1973 | e = embedding[ugraph.oppositeEdge(mine)]; |
---|
1974 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
1975 | while (ugraph.target(e) != s) { |
---|
1976 | if (visited[ugraph.source(e)]) { |
---|
1977 | oppe = e; |
---|
1978 | break; |
---|
1979 | } |
---|
1980 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
1981 | } |
---|
1982 | visited.setAll(false); |
---|
1983 | |
---|
1984 | if (oppe == INVALID) { |
---|
1985 | |
---|
1986 | e = embedding[ugraph.oppositeEdge(mine)]; |
---|
1987 | typename UGraph::Edge pn = mine, p = e; |
---|
1988 | |
---|
1989 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
1990 | while (ugraph.target(e) != s) { |
---|
1991 | typename UGraph::Edge n = |
---|
1992 | ugraph.direct(ugraph.addEdge(s, ugraph.source(e)), true); |
---|
1993 | |
---|
1994 | embedding[n] = pn; |
---|
1995 | embedding[ugraph.oppositeEdge(n)] = e; |
---|
1996 | embedding[ugraph.oppositeEdge(p)] = ugraph.oppositeEdge(n); |
---|
1997 | |
---|
1998 | pn = n; |
---|
1999 | |
---|
2000 | p = e; |
---|
2001 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
2002 | } |
---|
2003 | |
---|
2004 | embedding[ugraph.oppositeEdge(e)] = pn; |
---|
2005 | |
---|
2006 | } else { |
---|
2007 | |
---|
2008 | mine = embedding[ugraph.oppositeEdge(mine)]; |
---|
2009 | s = ugraph.source(mine); |
---|
2010 | oppe = embedding[ugraph.oppositeEdge(oppe)]; |
---|
2011 | typename UGraph::Node t = ugraph.source(oppe); |
---|
2012 | |
---|
2013 | typename UGraph::Edge ce = ugraph.direct(ugraph.addEdge(s, t), true); |
---|
2014 | embedding[ce] = mine; |
---|
2015 | embedding[ugraph.oppositeEdge(ce)] = oppe; |
---|
2016 | |
---|
2017 | typename UGraph::Edge pn = ce, p = oppe; |
---|
2018 | e = embedding[ugraph.oppositeEdge(oppe)]; |
---|
2019 | while (ugraph.target(e) != s) { |
---|
2020 | typename UGraph::Edge n = |
---|
2021 | ugraph.direct(ugraph.addEdge(s, ugraph.source(e)), true); |
---|
2022 | |
---|
2023 | embedding[n] = pn; |
---|
2024 | embedding[ugraph.oppositeEdge(n)] = e; |
---|
2025 | embedding[ugraph.oppositeEdge(p)] = ugraph.oppositeEdge(n); |
---|
2026 | |
---|
2027 | pn = n; |
---|
2028 | |
---|
2029 | p = e; |
---|
2030 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
2031 | |
---|
2032 | } |
---|
2033 | embedding[ugraph.oppositeEdge(e)] = pn; |
---|
2034 | |
---|
2035 | pn = ugraph.oppositeEdge(ce), p = mine; |
---|
2036 | e = embedding[ugraph.oppositeEdge(mine)]; |
---|
2037 | while (ugraph.target(e) != t) { |
---|
2038 | typename UGraph::Edge n = |
---|
2039 | ugraph.direct(ugraph.addEdge(t, ugraph.source(e)), true); |
---|
2040 | |
---|
2041 | embedding[n] = pn; |
---|
2042 | embedding[ugraph.oppositeEdge(n)] = e; |
---|
2043 | embedding[ugraph.oppositeEdge(p)] = ugraph.oppositeEdge(n); |
---|
2044 | |
---|
2045 | pn = n; |
---|
2046 | |
---|
2047 | p = e; |
---|
2048 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
2049 | |
---|
2050 | } |
---|
2051 | embedding[ugraph.oppositeEdge(e)] = pn; |
---|
2052 | } |
---|
2053 | } |
---|
2054 | } |
---|
2055 | |
---|
2056 | } |
---|
2057 | |
---|
2058 | /// \ingroup planar |
---|
2059 | /// |
---|
2060 | /// \brief Schnyder's planar drawing algorithms |
---|
2061 | /// |
---|
2062 | /// The planar drawing algorithm calculates location for each node |
---|
2063 | /// in the plane, which coordinates satisfies that if each edge is |
---|
2064 | /// represented with a straight line then the edges will not |
---|
2065 | /// intersect each other. |
---|
2066 | /// |
---|
2067 | /// Scnyder's algorithm embeds the graph on \c (n-2,n-2) size grid, |
---|
2068 | /// ie. each node will be located in the \c [0,n-2]x[0,n-2] square. |
---|
2069 | /// The time complexity of the algorithm is O(n). |
---|
2070 | template <typename UGraph> |
---|
2071 | class PlanarDrawing { |
---|
2072 | public: |
---|
2073 | |
---|
2074 | UGRAPH_TYPEDEFS(typename UGraph); |
---|
2075 | |
---|
2076 | /// \brief The point type for store coordinates |
---|
2077 | typedef dim2::Point<int> Point; |
---|
2078 | /// \brief The map type for store coordinates |
---|
2079 | typedef typename UGraph::template NodeMap<Point> PointMap; |
---|
2080 | |
---|
2081 | |
---|
2082 | /// \brief Constructor |
---|
2083 | /// |
---|
2084 | /// Constructor |
---|
2085 | /// \pre The ugraph should be simple, ie. loop and parallel edge free. |
---|
2086 | PlanarDrawing(const UGraph& ugraph) |
---|
2087 | : _ugraph(ugraph), _point_map(ugraph) {} |
---|
2088 | |
---|
2089 | private: |
---|
2090 | |
---|
2091 | template <typename AuxUGraph, typename AuxEmbeddingMap> |
---|
2092 | void drawing(const AuxUGraph& ugraph, |
---|
2093 | const AuxEmbeddingMap& next, |
---|
2094 | PointMap& point_map) { |
---|
2095 | UGRAPH_TYPEDEFS(typename AuxUGraph); |
---|
2096 | |
---|
2097 | typename AuxUGraph::template EdgeMap<Edge> prev(ugraph); |
---|
2098 | |
---|
2099 | for (NodeIt n(ugraph); n != INVALID; ++n) { |
---|
2100 | Edge e = OutEdgeIt(ugraph, n); |
---|
2101 | |
---|
2102 | Edge p = e, l = e; |
---|
2103 | |
---|
2104 | e = next[e]; |
---|
2105 | while (e != l) { |
---|
2106 | prev[e] = p; |
---|
2107 | p = e; |
---|
2108 | e = next[e]; |
---|
2109 | } |
---|
2110 | prev[e] = p; |
---|
2111 | } |
---|
2112 | |
---|
2113 | Node anode, bnode, cnode; |
---|
2114 | |
---|
2115 | { |
---|
2116 | Edge e = EdgeIt(ugraph); |
---|
2117 | anode = ugraph.source(e); |
---|
2118 | bnode = ugraph.target(e); |
---|
2119 | cnode = ugraph.target(next[ugraph.oppositeEdge(e)]); |
---|
2120 | } |
---|
2121 | |
---|
2122 | IterableBoolMap<AuxUGraph, Node> proper(ugraph, false); |
---|
2123 | typename AuxUGraph::template NodeMap<int> conn(ugraph, -1); |
---|
2124 | |
---|
2125 | conn[anode] = conn[bnode] = -2; |
---|
2126 | { |
---|
2127 | for (OutEdgeIt e(ugraph, anode); e != INVALID; ++e) { |
---|
2128 | Node m = ugraph.target(e); |
---|
2129 | if (conn[m] == -1) { |
---|
2130 | conn[m] = 1; |
---|
2131 | } |
---|
2132 | } |
---|
2133 | conn[cnode] = 2; |
---|
2134 | |
---|
2135 | for (OutEdgeIt e(ugraph, bnode); e != INVALID; ++e) { |
---|
2136 | Node m = ugraph.target(e); |
---|
2137 | if (conn[m] == -1) { |
---|
2138 | conn[m] = 1; |
---|
2139 | } else if (conn[m] != -2) { |
---|
2140 | conn[m] += 1; |
---|
2141 | Edge pe = ugraph.oppositeEdge(e); |
---|
2142 | if (conn[ugraph.target(next[pe])] == -2) { |
---|
2143 | conn[m] -= 1; |
---|
2144 | } |
---|
2145 | if (conn[ugraph.target(prev[pe])] == -2) { |
---|
2146 | conn[m] -= 1; |
---|
2147 | } |
---|
2148 | |
---|
2149 | proper.set(m, conn[m] == 1); |
---|
2150 | } |
---|
2151 | } |
---|
2152 | } |
---|
2153 | |
---|
2154 | |
---|
2155 | typename AuxUGraph::template EdgeMap<int> angle(ugraph, -1); |
---|
2156 | |
---|
2157 | while (proper.trueNum() != 0) { |
---|
2158 | Node n = typename IterableBoolMap<AuxUGraph, Node>::TrueIt(proper); |
---|
2159 | proper.set(n, false); |
---|
2160 | conn[n] = -2; |
---|
2161 | |
---|
2162 | for (OutEdgeIt e(ugraph, n); e != INVALID; ++e) { |
---|
2163 | Node m = ugraph.target(e); |
---|
2164 | if (conn[m] == -1) { |
---|
2165 | conn[m] = 1; |
---|
2166 | } else if (conn[m] != -2) { |
---|
2167 | conn[m] += 1; |
---|
2168 | Edge pe = ugraph.oppositeEdge(e); |
---|
2169 | if (conn[ugraph.target(next[pe])] == -2) { |
---|
2170 | conn[m] -= 1; |
---|
2171 | } |
---|
2172 | if (conn[ugraph.target(prev[pe])] == -2) { |
---|
2173 | conn[m] -= 1; |
---|
2174 | } |
---|
2175 | |
---|
2176 | proper.set(m, conn[m] == 1); |
---|
2177 | } |
---|
2178 | } |
---|
2179 | |
---|
2180 | { |
---|
2181 | Edge e = OutEdgeIt(ugraph, n); |
---|
2182 | Edge p = e, l = e; |
---|
2183 | |
---|
2184 | e = next[e]; |
---|
2185 | while (e != l) { |
---|
2186 | |
---|
2187 | if (conn[ugraph.target(e)] == -2 && conn[ugraph.target(p)] == -2) { |
---|
2188 | Edge f = e; |
---|
2189 | angle[f] = 0; |
---|
2190 | f = next[ugraph.oppositeEdge(f)]; |
---|
2191 | angle[f] = 1; |
---|
2192 | f = next[ugraph.oppositeEdge(f)]; |
---|
2193 | angle[f] = 2; |
---|
2194 | } |
---|
2195 | |
---|
2196 | p = e; |
---|
2197 | e = next[e]; |
---|
2198 | } |
---|
2199 | |
---|
2200 | if (conn[ugraph.target(e)] == -2 && conn[ugraph.target(p)] == -2) { |
---|
2201 | Edge f = e; |
---|
2202 | angle[f] = 0; |
---|
2203 | f = next[ugraph.oppositeEdge(f)]; |
---|
2204 | angle[f] = 1; |
---|
2205 | f = next[ugraph.oppositeEdge(f)]; |
---|
2206 | angle[f] = 2; |
---|
2207 | } |
---|
2208 | } |
---|
2209 | } |
---|
2210 | |
---|
2211 | typename AuxUGraph::template NodeMap<Node> apred(ugraph, INVALID); |
---|
2212 | typename AuxUGraph::template NodeMap<Node> bpred(ugraph, INVALID); |
---|
2213 | typename AuxUGraph::template NodeMap<Node> cpred(ugraph, INVALID); |
---|
2214 | |
---|
2215 | typename AuxUGraph::template NodeMap<int> apredid(ugraph, -1); |
---|
2216 | typename AuxUGraph::template NodeMap<int> bpredid(ugraph, -1); |
---|
2217 | typename AuxUGraph::template NodeMap<int> cpredid(ugraph, -1); |
---|
2218 | |
---|
2219 | for (EdgeIt e(ugraph); e != INVALID; ++e) { |
---|
2220 | if (angle[e] == angle[next[e]]) { |
---|
2221 | switch (angle[e]) { |
---|
2222 | case 2: |
---|
2223 | apred[ugraph.target(e)] = ugraph.source(e); |
---|
2224 | apredid[ugraph.target(e)] = ugraph.id(ugraph.source(e)); |
---|
2225 | break; |
---|
2226 | case 1: |
---|
2227 | bpred[ugraph.target(e)] = ugraph.source(e); |
---|
2228 | bpredid[ugraph.target(e)] = ugraph.id(ugraph.source(e)); |
---|
2229 | break; |
---|
2230 | case 0: |
---|
2231 | cpred[ugraph.target(e)] = ugraph.source(e); |
---|
2232 | cpredid[ugraph.target(e)] = ugraph.id(ugraph.source(e)); |
---|
2233 | break; |
---|
2234 | } |
---|
2235 | } |
---|
2236 | } |
---|
2237 | |
---|
2238 | cpred[anode] = INVALID; |
---|
2239 | cpred[bnode] = INVALID; |
---|
2240 | |
---|
2241 | std::vector<Node> aorder, border, corder; |
---|
2242 | |
---|
2243 | { |
---|
2244 | typename AuxUGraph::template NodeMap<bool> processed(ugraph, false); |
---|
2245 | std::vector<Node> st; |
---|
2246 | for (NodeIt n(ugraph); n != INVALID; ++n) { |
---|
2247 | if (!processed[n] && n != bnode && n != cnode) { |
---|
2248 | st.push_back(n); |
---|
2249 | processed[n] = true; |
---|
2250 | Node m = apred[n]; |
---|
2251 | while (m != INVALID && !processed[m]) { |
---|
2252 | st.push_back(m); |
---|
2253 | processed[m] = true; |
---|
2254 | m = apred[m]; |
---|
2255 | } |
---|
2256 | while (!st.empty()) { |
---|
2257 | aorder.push_back(st.back()); |
---|
2258 | st.pop_back(); |
---|
2259 | } |
---|
2260 | } |
---|
2261 | } |
---|
2262 | } |
---|
2263 | |
---|
2264 | { |
---|
2265 | typename AuxUGraph::template NodeMap<bool> processed(ugraph, false); |
---|
2266 | std::vector<Node> st; |
---|
2267 | for (NodeIt n(ugraph); n != INVALID; ++n) { |
---|
2268 | if (!processed[n] && n != cnode && n != anode) { |
---|
2269 | st.push_back(n); |
---|
2270 | processed[n] = true; |
---|
2271 | Node m = bpred[n]; |
---|
2272 | while (m != INVALID && !processed[m]) { |
---|
2273 | st.push_back(m); |
---|
2274 | processed[m] = true; |
---|
2275 | m = bpred[m]; |
---|
2276 | } |
---|
2277 | while (!st.empty()) { |
---|
2278 | border.push_back(st.back()); |
---|
2279 | st.pop_back(); |
---|
2280 | } |
---|
2281 | } |
---|
2282 | } |
---|
2283 | } |
---|
2284 | |
---|
2285 | { |
---|
2286 | typename AuxUGraph::template NodeMap<bool> processed(ugraph, false); |
---|
2287 | std::vector<Node> st; |
---|
2288 | for (NodeIt n(ugraph); n != INVALID; ++n) { |
---|
2289 | if (!processed[n] && n != anode && n != bnode) { |
---|
2290 | st.push_back(n); |
---|
2291 | processed[n] = true; |
---|
2292 | Node m = cpred[n]; |
---|
2293 | while (m != INVALID && !processed[m]) { |
---|
2294 | st.push_back(m); |
---|
2295 | processed[m] = true; |
---|
2296 | m = cpred[m]; |
---|
2297 | } |
---|
2298 | while (!st.empty()) { |
---|
2299 | corder.push_back(st.back()); |
---|
2300 | st.pop_back(); |
---|
2301 | } |
---|
2302 | } |
---|
2303 | } |
---|
2304 | } |
---|
2305 | |
---|
2306 | typename AuxUGraph::template NodeMap<int> atree(ugraph, 0); |
---|
2307 | for (int i = aorder.size() - 1; i >= 0; --i) { |
---|
2308 | Node n = aorder[i]; |
---|
2309 | atree[n] = 1; |
---|
2310 | for (OutEdgeIt e(ugraph, n); e != INVALID; ++e) { |
---|
2311 | if (apred[ugraph.target(e)] == n) { |
---|
2312 | atree[n] += atree[ugraph.target(e)]; |
---|
2313 | } |
---|
2314 | } |
---|
2315 | } |
---|
2316 | |
---|
2317 | typename AuxUGraph::template NodeMap<int> btree(ugraph, 0); |
---|
2318 | for (int i = border.size() - 1; i >= 0; --i) { |
---|
2319 | Node n = border[i]; |
---|
2320 | btree[n] = 1; |
---|
2321 | for (OutEdgeIt e(ugraph, n); e != INVALID; ++e) { |
---|
2322 | if (bpred[ugraph.target(e)] == n) { |
---|
2323 | btree[n] += btree[ugraph.target(e)]; |
---|
2324 | } |
---|
2325 | } |
---|
2326 | } |
---|
2327 | |
---|
2328 | typename AuxUGraph::template NodeMap<int> apath(ugraph, 0); |
---|
2329 | apath[bnode] = apath[cnode] = 1; |
---|
2330 | typename AuxUGraph::template NodeMap<int> apath_btree(ugraph, 0); |
---|
2331 | apath_btree[bnode] = btree[bnode]; |
---|
2332 | for (int i = 1; i < int(aorder.size()); ++i) { |
---|
2333 | Node n = aorder[i]; |
---|
2334 | apath[n] = apath[apred[n]] + 1; |
---|
2335 | apath_btree[n] = btree[n] + apath_btree[apred[n]]; |
---|
2336 | } |
---|
2337 | |
---|
2338 | typename AuxUGraph::template NodeMap<int> bpath_atree(ugraph, 0); |
---|
2339 | bpath_atree[anode] = atree[anode]; |
---|
2340 | for (int i = 1; i < int(border.size()); ++i) { |
---|
2341 | Node n = border[i]; |
---|
2342 | bpath_atree[n] = atree[n] + bpath_atree[bpred[n]]; |
---|
2343 | } |
---|
2344 | |
---|
2345 | typename AuxUGraph::template NodeMap<int> cpath(ugraph, 0); |
---|
2346 | cpath[anode] = cpath[bnode] = 1; |
---|
2347 | typename AuxUGraph::template NodeMap<int> cpath_atree(ugraph, 0); |
---|
2348 | cpath_atree[anode] = atree[anode]; |
---|
2349 | typename AuxUGraph::template NodeMap<int> cpath_btree(ugraph, 0); |
---|
2350 | cpath_btree[bnode] = btree[bnode]; |
---|
2351 | for (int i = 1; i < int(corder.size()); ++i) { |
---|
2352 | Node n = corder[i]; |
---|
2353 | cpath[n] = cpath[cpred[n]] + 1; |
---|
2354 | cpath_atree[n] = atree[n] + cpath_atree[cpred[n]]; |
---|
2355 | cpath_btree[n] = btree[n] + cpath_btree[cpred[n]]; |
---|
2356 | } |
---|
2357 | |
---|
2358 | typename AuxUGraph::template NodeMap<int> third(ugraph); |
---|
2359 | for (NodeIt n(ugraph); n != INVALID; ++n) { |
---|
2360 | point_map[n].x = |
---|
2361 | bpath_atree[n] + cpath_atree[n] - atree[n] - cpath[n] + 1; |
---|
2362 | point_map[n].y = |
---|
2363 | cpath_btree[n] + apath_btree[n] - btree[n] - apath[n] + 1; |
---|
2364 | } |
---|
2365 | |
---|
2366 | } |
---|
2367 | |
---|
2368 | public: |
---|
2369 | |
---|
2370 | /// \brief Calculates the node locations |
---|
2371 | /// |
---|
2372 | /// This function calculates the node locations. |
---|
2373 | bool run() { |
---|
2374 | PlanarEmbedding<UGraph> pe(_ugraph); |
---|
2375 | if (!pe.run()) return false; |
---|
2376 | |
---|
2377 | run(pe); |
---|
2378 | return true; |
---|
2379 | } |
---|
2380 | |
---|
2381 | /// \brief Calculates the node locations according to a |
---|
2382 | /// combinatorical embedding |
---|
2383 | /// |
---|
2384 | /// This function calculates the node locations. The \c embedding |
---|
2385 | /// parameter should contain a valid combinatorical embedding, ie. |
---|
2386 | /// a valid cyclic order of the edges. |
---|
2387 | template <typename EmbeddingMap> |
---|
2388 | void run(const EmbeddingMap& embedding) { |
---|
2389 | typedef SmartUEdgeSet<UGraph> AuxUGraph; |
---|
2390 | |
---|
2391 | if (3 * countNodes(_ugraph) - 6 == countUEdges(_ugraph)) { |
---|
2392 | drawing(_ugraph, embedding, _point_map); |
---|
2393 | return; |
---|
2394 | } |
---|
2395 | |
---|
2396 | AuxUGraph aux_ugraph(_ugraph); |
---|
2397 | typename AuxUGraph::template EdgeMap<typename AuxUGraph::Edge> |
---|
2398 | aux_embedding(aux_ugraph); |
---|
2399 | |
---|
2400 | { |
---|
2401 | |
---|
2402 | typename UGraph::template UEdgeMap<typename AuxUGraph::UEdge> |
---|
2403 | ref(_ugraph); |
---|
2404 | |
---|
2405 | for (UEdgeIt e(_ugraph); e != INVALID; ++e) { |
---|
2406 | ref[e] = aux_ugraph.addEdge(_ugraph.source(e), _ugraph.target(e)); |
---|
2407 | } |
---|
2408 | |
---|
2409 | for (UEdgeIt e(_ugraph); e != INVALID; ++e) { |
---|
2410 | Edge ee = embedding[_ugraph.direct(e, true)]; |
---|
2411 | aux_embedding[aux_ugraph.direct(ref[e], true)] = |
---|
2412 | aux_ugraph.direct(ref[ee], _ugraph.direction(ee)); |
---|
2413 | ee = embedding[_ugraph.direct(e, false)]; |
---|
2414 | aux_embedding[aux_ugraph.direct(ref[e], false)] = |
---|
2415 | aux_ugraph.direct(ref[ee], _ugraph.direction(ee)); |
---|
2416 | } |
---|
2417 | } |
---|
2418 | _planarity_bits::makeConnected(aux_ugraph, aux_embedding); |
---|
2419 | _planarity_bits::makeBiNodeConnected(aux_ugraph, aux_embedding); |
---|
2420 | _planarity_bits::makeMaxPlanar(aux_ugraph, aux_embedding); |
---|
2421 | drawing(aux_ugraph, aux_embedding, _point_map); |
---|
2422 | } |
---|
2423 | |
---|
2424 | /// \brief The coordinate of the given node |
---|
2425 | /// |
---|
2426 | /// The coordinate of the given node. |
---|
2427 | Point operator[](const Node& node) { |
---|
2428 | return _point_map[node]; |
---|
2429 | } |
---|
2430 | |
---|
2431 | /// \brief Returns the grid embedding in a \e NodeMap. |
---|
2432 | /// |
---|
2433 | /// Returns the grid embedding in a \e NodeMap of \c dim2::Point<int> . |
---|
2434 | const PointMap& coords() const { |
---|
2435 | return _point_map; |
---|
2436 | } |
---|
2437 | |
---|
2438 | private: |
---|
2439 | |
---|
2440 | const UGraph& _ugraph; |
---|
2441 | PointMap _point_map; |
---|
2442 | |
---|
2443 | }; |
---|
2444 | |
---|
2445 | namespace _planarity_bits { |
---|
2446 | |
---|
2447 | template <typename ColorMap> |
---|
2448 | class KempeFilter { |
---|
2449 | public: |
---|
2450 | typedef typename ColorMap::Key Key; |
---|
2451 | typedef bool Value; |
---|
2452 | |
---|
2453 | KempeFilter(const ColorMap& color_map, |
---|
2454 | const typename ColorMap::Value& first, |
---|
2455 | const typename ColorMap::Value& second) |
---|
2456 | : _color_map(color_map), _first(first), _second(second) {} |
---|
2457 | |
---|
2458 | Value operator[](const Key& key) const { |
---|
2459 | return _color_map[key] == _first || _color_map[key] == _second; |
---|
2460 | } |
---|
2461 | |
---|
2462 | private: |
---|
2463 | const ColorMap& _color_map; |
---|
2464 | typename ColorMap::Value _first, _second; |
---|
2465 | }; |
---|
2466 | } |
---|
2467 | |
---|
2468 | /// \ingroup planar |
---|
2469 | /// |
---|
2470 | /// \brief Coloring planar graphs |
---|
2471 | /// |
---|
2472 | /// The graph coloring problem is the coloring of the graph nodes |
---|
2473 | /// such way that there are not adjacent nodes with the same |
---|
2474 | /// color. The planar graphs can be always colored with four colors, |
---|
2475 | /// it is proved by Appel and Haken and their proofs provide a |
---|
2476 | /// quadratic time algorithm for four coloring, but it could not be |
---|
2477 | /// used to implement efficient algorithm. The five and six coloring |
---|
2478 | /// can be made in linear time, but in this class the five coloring |
---|
2479 | /// has quadratic worst case time complexity. The two coloring (if |
---|
2480 | /// possible) is solvable with a graph search algorithm and it is |
---|
2481 | /// implemented in \ref bipartitePartitions() function in Lemon. To |
---|
2482 | /// decide whether the planar graph is three colorable is |
---|
2483 | /// NP-complete. |
---|
2484 | /// |
---|
2485 | /// This class contains member functions for calculate colorings |
---|
2486 | /// with five and six colors. The six coloring algorithm is a simple |
---|
2487 | /// greedy coloring on the backward minimum outgoing order of nodes. |
---|
2488 | /// This order can be computed such way, that in each phase the node |
---|
2489 | /// with least outgoing edges to unprocessed nodes is choosen. This |
---|
2490 | /// order guarantees that at the time of coloring of a node it has |
---|
2491 | /// at most five already colored adjacents. The five coloring |
---|
2492 | /// algorithm works in the same way, but if the greedy approach |
---|
2493 | /// fails to color with five color, ie. the node has five already |
---|
2494 | /// different colored neighbours, it swaps the colors in one |
---|
2495 | /// connected two colored set with the Kempe recoloring method. |
---|
2496 | template <typename UGraph> |
---|
2497 | class PlanarColoring { |
---|
2498 | public: |
---|
2499 | |
---|
2500 | UGRAPH_TYPEDEFS(typename UGraph); |
---|
2501 | |
---|
2502 | /// \brief The map type for store color indexes |
---|
2503 | typedef typename UGraph::template NodeMap<int> IndexMap; |
---|
2504 | /// \brief The map type for store colors |
---|
2505 | typedef ComposeMap<Palette, IndexMap> ColorMap; |
---|
2506 | |
---|
2507 | /// \brief Constructor |
---|
2508 | /// |
---|
2509 | /// Constructor |
---|
2510 | /// \pre The ugraph should be simple, ie. loop and parallel edge free. |
---|
2511 | PlanarColoring(const UGraph& ugraph) |
---|
2512 | : _ugraph(ugraph), _color_map(ugraph), _palette(0) { |
---|
2513 | _palette.add(Color(1,0,0)); |
---|
2514 | _palette.add(Color(0,1,0)); |
---|
2515 | _palette.add(Color(0,0,1)); |
---|
2516 | _palette.add(Color(1,1,0)); |
---|
2517 | _palette.add(Color(1,0,1)); |
---|
2518 | _palette.add(Color(0,1,1)); |
---|
2519 | } |
---|
2520 | |
---|
2521 | /// \brief Returns the \e NodeMap of color indexes |
---|
2522 | /// |
---|
2523 | /// Returns the \e NodeMap of color indexes. The values are in the |
---|
2524 | /// range \c [0..4] or \c [0..5] according to the five coloring or |
---|
2525 | /// six coloring. |
---|
2526 | IndexMap colorIndexMap() const { |
---|
2527 | return _color_map; |
---|
2528 | } |
---|
2529 | |
---|
2530 | /// \brief Returns the \e NodeMap of colors |
---|
2531 | /// |
---|
2532 | /// Returns the \e NodeMap of colors. The values are five or six |
---|
2533 | /// distinct \ref lemon::Color "colors". |
---|
2534 | ColorMap colorMap() const { |
---|
2535 | return composeMap(_palette, _color_map); |
---|
2536 | } |
---|
2537 | |
---|
2538 | /// \brief Returns the color index of the node |
---|
2539 | /// |
---|
2540 | /// Returns the color index of the node. The values are in the |
---|
2541 | /// range \c [0..4] or \c [0..5] according to the five coloring or |
---|
2542 | /// six coloring. |
---|
2543 | int colorIndex(const Node& node) const { |
---|
2544 | return _color_map[node]; |
---|
2545 | } |
---|
2546 | |
---|
2547 | /// \brief Returns the color of the node |
---|
2548 | /// |
---|
2549 | /// Returns the color of the node. The values are five or six |
---|
2550 | /// distinct \ref lemon::Color "colors". |
---|
2551 | int color(const Node& node) const { |
---|
2552 | return _palette[_color_map[node]]; |
---|
2553 | } |
---|
2554 | |
---|
2555 | |
---|
2556 | /// \brief Calculates a coloring with at most six colors |
---|
2557 | /// |
---|
2558 | /// This function calculates a coloring with at most six colors. The time |
---|
2559 | /// complexity of this variant is linear in the size of the graph. |
---|
2560 | /// \return %True when the algorithm could color the graph with six color. |
---|
2561 | /// If the algorithm fails, then the graph could not be planar. |
---|
2562 | bool runSixColoring() { |
---|
2563 | |
---|
2564 | typename UGraph::template NodeMap<int> heap_index(_ugraph, -1); |
---|
2565 | BucketHeap<typename UGraph::template NodeMap<int> > heap(heap_index); |
---|
2566 | |
---|
2567 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
2568 | _color_map[n] = -2; |
---|
2569 | heap.push(n, countOutEdges(_ugraph, n)); |
---|
2570 | } |
---|
2571 | |
---|
2572 | std::vector<Node> order; |
---|
2573 | |
---|
2574 | while (!heap.empty()) { |
---|
2575 | Node n = heap.top(); |
---|
2576 | heap.pop(); |
---|
2577 | _color_map[n] = -1; |
---|
2578 | order.push_back(n); |
---|
2579 | for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
2580 | Node t = _ugraph.runningNode(e); |
---|
2581 | if (_color_map[t] == -2) { |
---|
2582 | heap.decrease(t, heap[t] - 1); |
---|
2583 | } |
---|
2584 | } |
---|
2585 | } |
---|
2586 | |
---|
2587 | for (int i = order.size() - 1; i >= 0; --i) { |
---|
2588 | std::vector<bool> forbidden(6, false); |
---|
2589 | for (OutEdgeIt e(_ugraph, order[i]); e != INVALID; ++e) { |
---|
2590 | Node t = _ugraph.runningNode(e); |
---|
2591 | if (_color_map[t] != -1) { |
---|
2592 | forbidden[_color_map[t]] = true; |
---|
2593 | } |
---|
2594 | } |
---|
2595 | for (int k = 0; k < 6; ++k) { |
---|
2596 | if (!forbidden[k]) { |
---|
2597 | _color_map[order[i]] = k; |
---|
2598 | break; |
---|
2599 | } |
---|
2600 | } |
---|
2601 | if (_color_map[order[i]] == -1) { |
---|
2602 | return false; |
---|
2603 | } |
---|
2604 | } |
---|
2605 | return true; |
---|
2606 | } |
---|
2607 | |
---|
2608 | private: |
---|
2609 | |
---|
2610 | bool recolor(const Node& u, const Node& v) { |
---|
2611 | int ucolor = _color_map[u]; |
---|
2612 | int vcolor = _color_map[v]; |
---|
2613 | typedef _planarity_bits::KempeFilter<IndexMap> KempeFilter; |
---|
2614 | KempeFilter filter(_color_map, ucolor, vcolor); |
---|
2615 | |
---|
2616 | typedef NodeSubUGraphAdaptor<const UGraph, const KempeFilter> KempeUGraph; |
---|
2617 | KempeUGraph kempe_ugraph(_ugraph, filter); |
---|
2618 | |
---|
2619 | std::vector<Node> comp; |
---|
2620 | Bfs<KempeUGraph> bfs(kempe_ugraph); |
---|
2621 | bfs.init(); |
---|
2622 | bfs.addSource(u); |
---|
2623 | while (!bfs.emptyQueue()) { |
---|
2624 | Node n = bfs.nextNode(); |
---|
2625 | if (n == v) return false; |
---|
2626 | comp.push_back(n); |
---|
2627 | bfs.processNextNode(); |
---|
2628 | } |
---|
2629 | |
---|
2630 | int scolor = ucolor + vcolor; |
---|
2631 | for (int i = 0; i < static_cast<int>(comp.size()); ++i) { |
---|
2632 | _color_map[comp[i]] = scolor - _color_map[comp[i]]; |
---|
2633 | } |
---|
2634 | |
---|
2635 | return true; |
---|
2636 | } |
---|
2637 | |
---|
2638 | template <typename EmbeddingMap> |
---|
2639 | void kempeRecoloring(const Node& node, const EmbeddingMap& embedding) { |
---|
2640 | std::vector<Node> nodes; |
---|
2641 | nodes.reserve(4); |
---|
2642 | |
---|
2643 | for (Edge e = OutEdgeIt(_ugraph, node); e != INVALID; e = embedding[e]) { |
---|
2644 | Node t = _ugraph.target(e); |
---|
2645 | if (_color_map[t] != -1) { |
---|
2646 | nodes.push_back(t); |
---|
2647 | if (nodes.size() == 4) break; |
---|
2648 | } |
---|
2649 | } |
---|
2650 | |
---|
2651 | int color = _color_map[nodes[0]]; |
---|
2652 | if (recolor(nodes[0], nodes[2])) { |
---|
2653 | _color_map[node] = color; |
---|
2654 | } else { |
---|
2655 | color = _color_map[nodes[1]]; |
---|
2656 | recolor(nodes[1], nodes[3]); |
---|
2657 | _color_map[node] = color; |
---|
2658 | } |
---|
2659 | } |
---|
2660 | |
---|
2661 | public: |
---|
2662 | |
---|
2663 | /// \brief Calculates a coloring with at most five colors |
---|
2664 | /// |
---|
2665 | /// This function calculates a coloring with at most five |
---|
2666 | /// colors. The wirst case time complexity of this variant is |
---|
2667 | /// quadratic in the size of the graph. |
---|
2668 | template <typename EmbeddingMap> |
---|
2669 | void runFiveColoring(const EmbeddingMap& embedding) { |
---|
2670 | |
---|
2671 | typename UGraph::template NodeMap<int> heap_index(_ugraph, -1); |
---|
2672 | BucketHeap<typename UGraph::template NodeMap<int> > heap(heap_index); |
---|
2673 | |
---|
2674 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
2675 | _color_map[n] = -2; |
---|
2676 | heap.push(n, countOutEdges(_ugraph, n)); |
---|
2677 | } |
---|
2678 | |
---|
2679 | std::vector<Node> order; |
---|
2680 | |
---|
2681 | while (!heap.empty()) { |
---|
2682 | Node n = heap.top(); |
---|
2683 | heap.pop(); |
---|
2684 | _color_map[n] = -1; |
---|
2685 | order.push_back(n); |
---|
2686 | for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
2687 | Node t = _ugraph.runningNode(e); |
---|
2688 | if (_color_map[t] == -2) { |
---|
2689 | heap.decrease(t, heap[t] - 1); |
---|
2690 | } |
---|
2691 | } |
---|
2692 | } |
---|
2693 | |
---|
2694 | for (int i = order.size() - 1; i >= 0; --i) { |
---|
2695 | std::vector<bool> forbidden(5, false); |
---|
2696 | for (OutEdgeIt e(_ugraph, order[i]); e != INVALID; ++e) { |
---|
2697 | Node t = _ugraph.runningNode(e); |
---|
2698 | if (_color_map[t] != -1) { |
---|
2699 | forbidden[_color_map[t]] = true; |
---|
2700 | } |
---|
2701 | } |
---|
2702 | for (int k = 0; k < 5; ++k) { |
---|
2703 | if (!forbidden[k]) { |
---|
2704 | _color_map[order[i]] = k; |
---|
2705 | break; |
---|
2706 | } |
---|
2707 | } |
---|
2708 | if (_color_map[order[i]] == -1) { |
---|
2709 | kempeRecoloring(order[i], embedding); |
---|
2710 | } |
---|
2711 | } |
---|
2712 | } |
---|
2713 | |
---|
2714 | /// \brief Calculates a coloring with at most five colors |
---|
2715 | /// |
---|
2716 | /// This function calculates a coloring with at most five |
---|
2717 | /// colors. The worst case time complexity of this variant is |
---|
2718 | /// quadratic in the size of the graph, but it most cases it does |
---|
2719 | /// not have to use Kempe recoloring method, in this case it is |
---|
2720 | /// equivalent with the runSixColoring() algorithm. |
---|
2721 | /// \return %True when the graph is planar. |
---|
2722 | bool runFiveColoring() { |
---|
2723 | PlanarEmbedding<UGraph> pe(_ugraph); |
---|
2724 | if (!pe.run()) return false; |
---|
2725 | |
---|
2726 | runFiveColoring(pe.embeddingMap()); |
---|
2727 | return true; |
---|
2728 | } |
---|
2729 | |
---|
2730 | private: |
---|
2731 | |
---|
2732 | const UGraph& _ugraph; |
---|
2733 | IndexMap _color_map; |
---|
2734 | Palette _palette; |
---|
2735 | }; |
---|
2736 | |
---|
2737 | } |
---|
2738 | |
---|
2739 | #endif |
---|