1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library. |
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4 | * |
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5 | * Copyright (C) 2003-2010 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_PLANARITY_H |
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20 | #define LEMON_PLANARITY_H |
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21 | |
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22 | /// \ingroup planar |
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23 | /// \file |
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24 | /// \brief Planarity checking, embedding, drawing and coloring |
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25 | |
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26 | #include <vector> |
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27 | #include <list> |
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28 | |
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29 | #include <lemon/dfs.h> |
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30 | #include <lemon/bfs.h> |
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31 | #include <lemon/radix_sort.h> |
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32 | #include <lemon/maps.h> |
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33 | #include <lemon/path.h> |
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34 | #include <lemon/bucket_heap.h> |
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35 | #include <lemon/adaptors.h> |
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36 | #include <lemon/edge_set.h> |
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37 | #include <lemon/color.h> |
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38 | #include <lemon/dim2.h> |
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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 Graph> |
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45 | struct PlanarityVisitor : DfsVisitor<Graph> { |
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46 | |
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47 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
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48 | |
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49 | typedef typename Graph::template NodeMap<Arc> PredMap; |
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50 | |
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51 | typedef typename Graph::template EdgeMap<bool> TreeMap; |
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52 | |
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53 | typedef typename Graph::template NodeMap<int> OrderMap; |
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54 | typedef std::vector<Node> OrderList; |
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55 | |
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56 | typedef typename Graph::template NodeMap<int> LowMap; |
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57 | typedef typename Graph::template NodeMap<int> AncestorMap; |
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58 | |
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59 | PlanarityVisitor(const Graph& graph, |
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60 | PredMap& pred_map, TreeMap& tree_map, |
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61 | OrderMap& order_map, OrderList& order_list, |
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62 | AncestorMap& ancestor_map, LowMap& low_map) |
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63 | : _graph(graph), _pred_map(pred_map), _tree_map(tree_map), |
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64 | _order_map(order_map), _order_list(order_list), |
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65 | _ancestor_map(ancestor_map), _low_map(low_map) {} |
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66 | |
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67 | void reach(const Node& node) { |
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68 | _order_map[node] = _order_list.size(); |
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69 | _low_map[node] = _order_list.size(); |
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70 | _ancestor_map[node] = _order_list.size(); |
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71 | _order_list.push_back(node); |
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72 | } |
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73 | |
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74 | void discover(const Arc& arc) { |
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75 | Node target = _graph.target(arc); |
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76 | |
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77 | _tree_map[arc] = true; |
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78 | _pred_map[target] = arc; |
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79 | } |
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80 | |
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81 | void examine(const Arc& arc) { |
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82 | Node source = _graph.source(arc); |
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83 | Node target = _graph.target(arc); |
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84 | |
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85 | if (_order_map[target] < _order_map[source] && !_tree_map[arc]) { |
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86 | if (_low_map[source] > _order_map[target]) { |
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87 | _low_map[source] = _order_map[target]; |
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88 | } |
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89 | if (_ancestor_map[source] > _order_map[target]) { |
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90 | _ancestor_map[source] = _order_map[target]; |
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91 | } |
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92 | } |
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93 | } |
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94 | |
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95 | void backtrack(const Arc& arc) { |
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96 | Node source = _graph.source(arc); |
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97 | Node target = _graph.target(arc); |
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98 | |
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99 | if (_low_map[source] > _low_map[target]) { |
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100 | _low_map[source] = _low_map[target]; |
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101 | } |
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102 | } |
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103 | |
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104 | const Graph& _graph; |
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105 | PredMap& _pred_map; |
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106 | TreeMap& _tree_map; |
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107 | OrderMap& _order_map; |
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108 | OrderList& _order_list; |
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109 | AncestorMap& _ancestor_map; |
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110 | LowMap& _low_map; |
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111 | }; |
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112 | |
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113 | template <typename Graph, bool embedding = true> |
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114 | struct NodeDataNode { |
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115 | int prev, next; |
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116 | int visited; |
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117 | typename Graph::Arc first; |
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118 | bool inverted; |
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119 | }; |
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120 | |
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121 | template <typename Graph> |
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122 | struct NodeDataNode<Graph, false> { |
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123 | int prev, next; |
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124 | int visited; |
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125 | }; |
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126 | |
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127 | template <typename Graph> |
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128 | struct ChildListNode { |
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129 | typedef typename Graph::Node Node; |
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130 | Node first; |
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131 | Node prev, next; |
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132 | }; |
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133 | |
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134 | template <typename Graph> |
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135 | struct ArcListNode { |
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136 | typename Graph::Arc prev, next; |
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137 | }; |
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138 | |
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139 | template <typename Graph> |
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140 | class PlanarityChecking { |
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141 | private: |
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142 | |
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143 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
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144 | |
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145 | const Graph& _graph; |
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146 | |
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147 | private: |
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148 | |
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149 | typedef typename Graph::template NodeMap<Arc> PredMap; |
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150 | |
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151 | typedef typename Graph::template EdgeMap<bool> TreeMap; |
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152 | |
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153 | typedef typename Graph::template NodeMap<int> OrderMap; |
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154 | typedef std::vector<Node> OrderList; |
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155 | |
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156 | typedef typename Graph::template NodeMap<int> LowMap; |
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157 | typedef typename Graph::template NodeMap<int> AncestorMap; |
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158 | |
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159 | typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode; |
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160 | typedef std::vector<NodeDataNode> NodeData; |
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161 | |
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162 | typedef _planarity_bits::ChildListNode<Graph> ChildListNode; |
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163 | typedef typename Graph::template NodeMap<ChildListNode> ChildLists; |
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164 | |
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165 | typedef typename Graph::template NodeMap<std::list<int> > MergeRoots; |
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166 | |
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167 | typedef typename Graph::template NodeMap<bool> EmbedArc; |
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168 | |
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169 | public: |
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170 | |
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171 | PlanarityChecking(const Graph& graph) : _graph(graph) {} |
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172 | |
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173 | bool run() { |
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174 | typedef _planarity_bits::PlanarityVisitor<Graph> Visitor; |
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175 | |
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176 | PredMap pred_map(_graph, INVALID); |
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177 | TreeMap tree_map(_graph, false); |
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178 | |
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179 | OrderMap order_map(_graph, -1); |
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180 | OrderList order_list; |
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181 | |
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182 | AncestorMap ancestor_map(_graph, -1); |
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183 | LowMap low_map(_graph, -1); |
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184 | |
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185 | Visitor visitor(_graph, pred_map, tree_map, |
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186 | order_map, order_list, ancestor_map, low_map); |
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187 | DfsVisit<Graph, Visitor> visit(_graph, visitor); |
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188 | visit.run(); |
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189 | |
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190 | ChildLists child_lists(_graph); |
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191 | createChildLists(tree_map, order_map, low_map, child_lists); |
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192 | |
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193 | NodeData node_data(2 * order_list.size()); |
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194 | |
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195 | EmbedArc embed_arc(_graph, false); |
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196 | |
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197 | MergeRoots merge_roots(_graph); |
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198 | |
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199 | for (int i = order_list.size() - 1; i >= 0; --i) { |
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200 | |
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201 | Node node = order_list[i]; |
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202 | |
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203 | Node source = node; |
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204 | for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
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205 | Node target = _graph.target(e); |
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206 | |
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207 | if (order_map[source] < order_map[target] && tree_map[e]) { |
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208 | initFace(target, node_data, order_map, order_list); |
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209 | } |
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210 | } |
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211 | |
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212 | for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
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213 | Node target = _graph.target(e); |
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214 | |
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215 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
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216 | embed_arc[target] = true; |
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217 | walkUp(target, source, i, pred_map, low_map, |
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218 | order_map, order_list, node_data, merge_roots); |
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219 | } |
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220 | } |
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221 | |
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222 | for (typename MergeRoots::Value::iterator it = |
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223 | merge_roots[node].begin(); |
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224 | it != merge_roots[node].end(); ++it) { |
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225 | int rn = *it; |
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226 | walkDown(rn, i, node_data, order_list, child_lists, |
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227 | ancestor_map, low_map, embed_arc, merge_roots); |
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228 | } |
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229 | merge_roots[node].clear(); |
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230 | |
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231 | for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
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232 | Node target = _graph.target(e); |
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233 | |
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234 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
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235 | if (embed_arc[target]) { |
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236 | return false; |
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237 | } |
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238 | } |
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239 | } |
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240 | } |
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241 | |
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242 | return true; |
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243 | } |
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244 | |
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245 | private: |
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246 | |
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247 | void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
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248 | const LowMap& low_map, ChildLists& child_lists) { |
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249 | |
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250 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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251 | Node source = n; |
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252 | |
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253 | std::vector<Node> targets; |
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254 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
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255 | Node target = _graph.target(e); |
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256 | |
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257 | if (order_map[source] < order_map[target] && tree_map[e]) { |
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258 | targets.push_back(target); |
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259 | } |
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260 | } |
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261 | |
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262 | if (targets.size() == 0) { |
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263 | child_lists[source].first = INVALID; |
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264 | } else if (targets.size() == 1) { |
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265 | child_lists[source].first = targets[0]; |
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266 | child_lists[targets[0]].prev = INVALID; |
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267 | child_lists[targets[0]].next = INVALID; |
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268 | } else { |
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269 | radixSort(targets.begin(), targets.end(), mapToFunctor(low_map)); |
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270 | for (int i = 1; i < int(targets.size()); ++i) { |
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271 | child_lists[targets[i]].prev = targets[i - 1]; |
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272 | child_lists[targets[i - 1]].next = targets[i]; |
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273 | } |
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274 | child_lists[targets.back()].next = INVALID; |
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275 | child_lists[targets.front()].prev = INVALID; |
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276 | child_lists[source].first = targets.front(); |
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277 | } |
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278 | } |
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279 | } |
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280 | |
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281 | void walkUp(const Node& node, Node root, int rorder, |
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282 | const PredMap& pred_map, const LowMap& low_map, |
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283 | const OrderMap& order_map, const OrderList& order_list, |
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284 | NodeData& node_data, MergeRoots& merge_roots) { |
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285 | |
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286 | int na, nb; |
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287 | bool da, db; |
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288 | |
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289 | na = nb = order_map[node]; |
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290 | da = true; db = false; |
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291 | |
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292 | while (true) { |
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293 | |
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294 | if (node_data[na].visited == rorder) break; |
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295 | if (node_data[nb].visited == rorder) break; |
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296 | |
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297 | node_data[na].visited = rorder; |
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298 | node_data[nb].visited = rorder; |
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299 | |
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300 | int rn = -1; |
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301 | |
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302 | if (na >= int(order_list.size())) { |
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303 | rn = na; |
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304 | } else if (nb >= int(order_list.size())) { |
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305 | rn = nb; |
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306 | } |
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307 | |
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308 | if (rn == -1) { |
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309 | int nn; |
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310 | |
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311 | nn = da ? node_data[na].prev : node_data[na].next; |
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312 | da = node_data[nn].prev != na; |
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313 | na = nn; |
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314 | |
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315 | nn = db ? node_data[nb].prev : node_data[nb].next; |
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316 | db = node_data[nn].prev != nb; |
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317 | nb = nn; |
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318 | |
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319 | } else { |
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320 | |
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321 | Node rep = order_list[rn - order_list.size()]; |
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322 | Node parent = _graph.source(pred_map[rep]); |
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323 | |
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324 | if (low_map[rep] < rorder) { |
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325 | merge_roots[parent].push_back(rn); |
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326 | } else { |
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327 | merge_roots[parent].push_front(rn); |
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328 | } |
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329 | |
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330 | if (parent != root) { |
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331 | na = nb = order_map[parent]; |
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332 | da = true; db = false; |
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333 | } else { |
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334 | break; |
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335 | } |
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336 | } |
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337 | } |
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338 | } |
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339 | |
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340 | void walkDown(int rn, int rorder, NodeData& node_data, |
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341 | OrderList& order_list, ChildLists& child_lists, |
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342 | AncestorMap& ancestor_map, LowMap& low_map, |
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343 | EmbedArc& embed_arc, MergeRoots& merge_roots) { |
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344 | |
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345 | std::vector<std::pair<int, bool> > merge_stack; |
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346 | |
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347 | for (int di = 0; di < 2; ++di) { |
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348 | bool rd = di == 0; |
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349 | int pn = rn; |
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350 | int n = rd ? node_data[rn].next : node_data[rn].prev; |
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351 | |
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352 | while (n != rn) { |
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353 | |
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354 | Node node = order_list[n]; |
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355 | |
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356 | if (embed_arc[node]) { |
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357 | |
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358 | // Merging components on the critical path |
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359 | while (!merge_stack.empty()) { |
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360 | |
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361 | // Component root |
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362 | int cn = merge_stack.back().first; |
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363 | bool cd = merge_stack.back().second; |
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364 | merge_stack.pop_back(); |
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365 | |
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366 | // Parent of component |
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367 | int dn = merge_stack.back().first; |
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368 | bool dd = merge_stack.back().second; |
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369 | merge_stack.pop_back(); |
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370 | |
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371 | Node parent = order_list[dn]; |
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372 | |
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373 | // Erasing from merge_roots |
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374 | merge_roots[parent].pop_front(); |
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375 | |
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376 | Node child = order_list[cn - order_list.size()]; |
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377 | |
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378 | // Erasing from child_lists |
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379 | if (child_lists[child].prev != INVALID) { |
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380 | child_lists[child_lists[child].prev].next = |
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381 | child_lists[child].next; |
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382 | } else { |
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383 | child_lists[parent].first = child_lists[child].next; |
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384 | } |
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385 | |
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386 | if (child_lists[child].next != INVALID) { |
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387 | child_lists[child_lists[child].next].prev = |
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388 | child_lists[child].prev; |
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389 | } |
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390 | |
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391 | // Merging external faces |
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392 | { |
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393 | int en = cn; |
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394 | cn = cd ? node_data[cn].prev : node_data[cn].next; |
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395 | cd = node_data[cn].next == en; |
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396 | |
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397 | } |
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398 | |
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399 | if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
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400 | if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
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401 | |
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402 | } |
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403 | |
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404 | bool d = pn == node_data[n].prev; |
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405 | |
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406 | if (node_data[n].prev == node_data[n].next && |
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407 | node_data[n].inverted) { |
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408 | d = !d; |
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409 | } |
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410 | |
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411 | // Embedding arc into external face |
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412 | if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
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413 | if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
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414 | pn = rn; |
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415 | |
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416 | embed_arc[order_list[n]] = false; |
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417 | } |
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418 | |
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419 | if (!merge_roots[node].empty()) { |
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420 | |
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421 | bool d = pn == node_data[n].prev; |
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422 | |
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423 | merge_stack.push_back(std::make_pair(n, d)); |
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424 | |
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425 | int rn = merge_roots[node].front(); |
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426 | |
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427 | int xn = node_data[rn].next; |
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428 | Node xnode = order_list[xn]; |
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429 | |
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430 | int yn = node_data[rn].prev; |
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431 | Node ynode = order_list[yn]; |
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432 | |
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433 | bool rd; |
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434 | if (!external(xnode, rorder, child_lists, |
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435 | ancestor_map, low_map)) { |
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436 | rd = true; |
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437 | } else if (!external(ynode, rorder, child_lists, |
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438 | ancestor_map, low_map)) { |
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439 | rd = false; |
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440 | } else if (pertinent(xnode, embed_arc, merge_roots)) { |
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441 | rd = true; |
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442 | } else { |
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443 | rd = false; |
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444 | } |
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445 | |
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446 | merge_stack.push_back(std::make_pair(rn, rd)); |
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447 | |
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448 | pn = rn; |
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449 | n = rd ? xn : yn; |
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450 | |
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451 | } else if (!external(node, rorder, child_lists, |
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452 | ancestor_map, low_map)) { |
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453 | int nn = (node_data[n].next != pn ? |
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454 | node_data[n].next : node_data[n].prev); |
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455 | |
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456 | bool nd = n == node_data[nn].prev; |
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457 | |
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458 | if (nd) node_data[nn].prev = pn; |
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459 | else node_data[nn].next = pn; |
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460 | |
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461 | if (n == node_data[pn].prev) node_data[pn].prev = nn; |
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462 | else node_data[pn].next = nn; |
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463 | |
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464 | node_data[nn].inverted = |
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465 | (node_data[nn].prev == node_data[nn].next && nd != rd); |
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466 | |
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467 | n = nn; |
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468 | } |
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469 | else break; |
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470 | |
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471 | } |
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472 | |
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473 | if (!merge_stack.empty() || n == rn) { |
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474 | break; |
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475 | } |
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476 | } |
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477 | } |
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478 | |
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479 | void initFace(const Node& node, NodeData& node_data, |
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480 | const OrderMap& order_map, const OrderList& order_list) { |
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481 | int n = order_map[node]; |
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482 | int rn = n + order_list.size(); |
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483 | |
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484 | node_data[n].next = node_data[n].prev = rn; |
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485 | node_data[rn].next = node_data[rn].prev = n; |
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486 | |
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487 | node_data[n].visited = order_list.size(); |
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488 | node_data[rn].visited = order_list.size(); |
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489 | |
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490 | } |
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491 | |
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492 | bool external(const Node& node, int rorder, |
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493 | ChildLists& child_lists, AncestorMap& ancestor_map, |
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494 | LowMap& low_map) { |
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495 | Node child = child_lists[node].first; |
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496 | |
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497 | if (child != INVALID) { |
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498 | if (low_map[child] < rorder) return true; |
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499 | } |
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500 | |
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501 | if (ancestor_map[node] < rorder) return true; |
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502 | |
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503 | return false; |
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504 | } |
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505 | |
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506 | bool pertinent(const Node& node, const EmbedArc& embed_arc, |
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507 | const MergeRoots& merge_roots) { |
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508 | return !merge_roots[node].empty() || embed_arc[node]; |
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509 | } |
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510 | |
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511 | }; |
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512 | |
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513 | } |
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514 | |
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515 | /// \ingroup planar |
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516 | /// |
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517 | /// \brief Planarity checking of an undirected simple graph |
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518 | /// |
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519 | /// This function implements the Boyer-Myrvold algorithm for |
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520 | /// planarity checking of an undirected simple graph. It is a simplified |
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521 | /// version of the PlanarEmbedding algorithm class because neither |
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522 | /// the embedding nor the Kuratowski subdivisons are computed. |
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523 | template <typename GR> |
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524 | bool checkPlanarity(const GR& graph) { |
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525 | _planarity_bits::PlanarityChecking<GR> pc(graph); |
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526 | return pc.run(); |
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527 | } |
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528 | |
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529 | /// \ingroup planar |
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530 | /// |
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531 | /// \brief Planar embedding of an undirected simple graph |
---|
532 | /// |
---|
533 | /// This class implements the Boyer-Myrvold algorithm for planar |
---|
534 | /// embedding of an undirected simple graph. The planar embedding is an |
---|
535 | /// ordering of the outgoing edges of the nodes, which is a possible |
---|
536 | /// configuration to draw the graph in the plane. If there is not |
---|
537 | /// such ordering then the graph contains a K<sub>5</sub> (full graph |
---|
538 | /// with 5 nodes) or a K<sub>3,3</sub> (complete bipartite graph on |
---|
539 | /// 3 Red and 3 Blue nodes) subdivision. |
---|
540 | /// |
---|
541 | /// The current implementation calculates either an embedding or a |
---|
542 | /// Kuratowski subdivision. The running time of the algorithm is O(n). |
---|
543 | /// |
---|
544 | /// \see PlanarDrawing, checkPlanarity() |
---|
545 | template <typename Graph> |
---|
546 | class PlanarEmbedding { |
---|
547 | private: |
---|
548 | |
---|
549 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
550 | |
---|
551 | const Graph& _graph; |
---|
552 | typename Graph::template ArcMap<Arc> _embedding; |
---|
553 | |
---|
554 | typename Graph::template EdgeMap<bool> _kuratowski; |
---|
555 | |
---|
556 | private: |
---|
557 | |
---|
558 | typedef typename Graph::template NodeMap<Arc> PredMap; |
---|
559 | |
---|
560 | typedef typename Graph::template EdgeMap<bool> TreeMap; |
---|
561 | |
---|
562 | typedef typename Graph::template NodeMap<int> OrderMap; |
---|
563 | typedef std::vector<Node> OrderList; |
---|
564 | |
---|
565 | typedef typename Graph::template NodeMap<int> LowMap; |
---|
566 | typedef typename Graph::template NodeMap<int> AncestorMap; |
---|
567 | |
---|
568 | typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode; |
---|
569 | typedef std::vector<NodeDataNode> NodeData; |
---|
570 | |
---|
571 | typedef _planarity_bits::ChildListNode<Graph> ChildListNode; |
---|
572 | typedef typename Graph::template NodeMap<ChildListNode> ChildLists; |
---|
573 | |
---|
574 | typedef typename Graph::template NodeMap<std::list<int> > MergeRoots; |
---|
575 | |
---|
576 | typedef typename Graph::template NodeMap<Arc> EmbedArc; |
---|
577 | |
---|
578 | typedef _planarity_bits::ArcListNode<Graph> ArcListNode; |
---|
579 | typedef typename Graph::template ArcMap<ArcListNode> ArcLists; |
---|
580 | |
---|
581 | typedef typename Graph::template NodeMap<bool> FlipMap; |
---|
582 | |
---|
583 | typedef typename Graph::template NodeMap<int> TypeMap; |
---|
584 | |
---|
585 | enum IsolatorNodeType { |
---|
586 | HIGHX = 6, LOWX = 7, |
---|
587 | HIGHY = 8, LOWY = 9, |
---|
588 | ROOT = 10, PERTINENT = 11, |
---|
589 | INTERNAL = 12 |
---|
590 | }; |
---|
591 | |
---|
592 | public: |
---|
593 | |
---|
594 | /// \brief The map type for storing the embedding |
---|
595 | /// |
---|
596 | /// The map type for storing the embedding. |
---|
597 | /// \see embeddingMap() |
---|
598 | typedef typename Graph::template ArcMap<Arc> EmbeddingMap; |
---|
599 | |
---|
600 | /// \brief Constructor |
---|
601 | /// |
---|
602 | /// Constructor. |
---|
603 | /// \pre The graph must be simple, i.e. it should not |
---|
604 | /// contain parallel or loop arcs. |
---|
605 | PlanarEmbedding(const Graph& graph) |
---|
606 | : _graph(graph), _embedding(_graph), _kuratowski(graph, false) {} |
---|
607 | |
---|
608 | /// \brief Run the algorithm. |
---|
609 | /// |
---|
610 | /// This function runs the algorithm. |
---|
611 | /// \param kuratowski If this parameter is set to \c false, then the |
---|
612 | /// algorithm does not compute a Kuratowski subdivision. |
---|
613 | /// \return \c true if the graph is planar. |
---|
614 | bool run(bool kuratowski = true) { |
---|
615 | typedef _planarity_bits::PlanarityVisitor<Graph> Visitor; |
---|
616 | |
---|
617 | PredMap pred_map(_graph, INVALID); |
---|
618 | TreeMap tree_map(_graph, false); |
---|
619 | |
---|
620 | OrderMap order_map(_graph, -1); |
---|
621 | OrderList order_list; |
---|
622 | |
---|
623 | AncestorMap ancestor_map(_graph, -1); |
---|
624 | LowMap low_map(_graph, -1); |
---|
625 | |
---|
626 | Visitor visitor(_graph, pred_map, tree_map, |
---|
627 | order_map, order_list, ancestor_map, low_map); |
---|
628 | DfsVisit<Graph, Visitor> visit(_graph, visitor); |
---|
629 | visit.run(); |
---|
630 | |
---|
631 | ChildLists child_lists(_graph); |
---|
632 | createChildLists(tree_map, order_map, low_map, child_lists); |
---|
633 | |
---|
634 | NodeData node_data(2 * order_list.size()); |
---|
635 | |
---|
636 | EmbedArc embed_arc(_graph, INVALID); |
---|
637 | |
---|
638 | MergeRoots merge_roots(_graph); |
---|
639 | |
---|
640 | ArcLists arc_lists(_graph); |
---|
641 | |
---|
642 | FlipMap flip_map(_graph, false); |
---|
643 | |
---|
644 | for (int i = order_list.size() - 1; i >= 0; --i) { |
---|
645 | |
---|
646 | Node node = order_list[i]; |
---|
647 | |
---|
648 | node_data[i].first = INVALID; |
---|
649 | |
---|
650 | Node source = node; |
---|
651 | for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
---|
652 | Node target = _graph.target(e); |
---|
653 | |
---|
654 | if (order_map[source] < order_map[target] && tree_map[e]) { |
---|
655 | initFace(target, arc_lists, node_data, |
---|
656 | pred_map, order_map, order_list); |
---|
657 | } |
---|
658 | } |
---|
659 | |
---|
660 | for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
---|
661 | Node target = _graph.target(e); |
---|
662 | |
---|
663 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
---|
664 | embed_arc[target] = e; |
---|
665 | walkUp(target, source, i, pred_map, low_map, |
---|
666 | order_map, order_list, node_data, merge_roots); |
---|
667 | } |
---|
668 | } |
---|
669 | |
---|
670 | for (typename MergeRoots::Value::iterator it = |
---|
671 | merge_roots[node].begin(); it != merge_roots[node].end(); ++it) { |
---|
672 | int rn = *it; |
---|
673 | walkDown(rn, i, node_data, arc_lists, flip_map, order_list, |
---|
674 | child_lists, ancestor_map, low_map, embed_arc, merge_roots); |
---|
675 | } |
---|
676 | merge_roots[node].clear(); |
---|
677 | |
---|
678 | for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
---|
679 | Node target = _graph.target(e); |
---|
680 | |
---|
681 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
---|
682 | if (embed_arc[target] != INVALID) { |
---|
683 | if (kuratowski) { |
---|
684 | isolateKuratowski(e, node_data, arc_lists, flip_map, |
---|
685 | order_map, order_list, pred_map, child_lists, |
---|
686 | ancestor_map, low_map, |
---|
687 | embed_arc, merge_roots); |
---|
688 | } |
---|
689 | return false; |
---|
690 | } |
---|
691 | } |
---|
692 | } |
---|
693 | } |
---|
694 | |
---|
695 | for (int i = 0; i < int(order_list.size()); ++i) { |
---|
696 | |
---|
697 | mergeRemainingFaces(order_list[i], node_data, order_list, order_map, |
---|
698 | child_lists, arc_lists); |
---|
699 | storeEmbedding(order_list[i], node_data, order_map, pred_map, |
---|
700 | arc_lists, flip_map); |
---|
701 | } |
---|
702 | |
---|
703 | return true; |
---|
704 | } |
---|
705 | |
---|
706 | /// \brief Give back the successor of an arc |
---|
707 | /// |
---|
708 | /// This function gives back the successor of an arc. It makes |
---|
709 | /// possible to query the cyclic order of the outgoing arcs from |
---|
710 | /// a node. |
---|
711 | Arc next(const Arc& arc) const { |
---|
712 | return _embedding[arc]; |
---|
713 | } |
---|
714 | |
---|
715 | /// \brief Give back the calculated embedding map |
---|
716 | /// |
---|
717 | /// This function gives back the calculated embedding map, which |
---|
718 | /// contains the successor of each arc in the cyclic order of the |
---|
719 | /// outgoing arcs of its source node. |
---|
720 | const EmbeddingMap& embeddingMap() const { |
---|
721 | return _embedding; |
---|
722 | } |
---|
723 | |
---|
724 | /// \brief Give back \c true if the given edge is in the Kuratowski |
---|
725 | /// subdivision |
---|
726 | /// |
---|
727 | /// This function gives back \c true if the given edge is in the found |
---|
728 | /// Kuratowski subdivision. |
---|
729 | /// \pre The \c run() function must be called with \c true parameter |
---|
730 | /// before using this function. |
---|
731 | bool kuratowski(const Edge& edge) const { |
---|
732 | return _kuratowski[edge]; |
---|
733 | } |
---|
734 | |
---|
735 | private: |
---|
736 | |
---|
737 | void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
---|
738 | const LowMap& low_map, ChildLists& child_lists) { |
---|
739 | |
---|
740 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
741 | Node source = n; |
---|
742 | |
---|
743 | std::vector<Node> targets; |
---|
744 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
745 | Node target = _graph.target(e); |
---|
746 | |
---|
747 | if (order_map[source] < order_map[target] && tree_map[e]) { |
---|
748 | targets.push_back(target); |
---|
749 | } |
---|
750 | } |
---|
751 | |
---|
752 | if (targets.size() == 0) { |
---|
753 | child_lists[source].first = INVALID; |
---|
754 | } else if (targets.size() == 1) { |
---|
755 | child_lists[source].first = targets[0]; |
---|
756 | child_lists[targets[0]].prev = INVALID; |
---|
757 | child_lists[targets[0]].next = INVALID; |
---|
758 | } else { |
---|
759 | radixSort(targets.begin(), targets.end(), mapToFunctor(low_map)); |
---|
760 | for (int i = 1; i < int(targets.size()); ++i) { |
---|
761 | child_lists[targets[i]].prev = targets[i - 1]; |
---|
762 | child_lists[targets[i - 1]].next = targets[i]; |
---|
763 | } |
---|
764 | child_lists[targets.back()].next = INVALID; |
---|
765 | child_lists[targets.front()].prev = INVALID; |
---|
766 | child_lists[source].first = targets.front(); |
---|
767 | } |
---|
768 | } |
---|
769 | } |
---|
770 | |
---|
771 | void walkUp(const Node& node, Node root, int rorder, |
---|
772 | const PredMap& pred_map, const LowMap& low_map, |
---|
773 | const OrderMap& order_map, const OrderList& order_list, |
---|
774 | NodeData& node_data, MergeRoots& merge_roots) { |
---|
775 | |
---|
776 | int na, nb; |
---|
777 | bool da, db; |
---|
778 | |
---|
779 | na = nb = order_map[node]; |
---|
780 | da = true; db = false; |
---|
781 | |
---|
782 | while (true) { |
---|
783 | |
---|
784 | if (node_data[na].visited == rorder) break; |
---|
785 | if (node_data[nb].visited == rorder) break; |
---|
786 | |
---|
787 | node_data[na].visited = rorder; |
---|
788 | node_data[nb].visited = rorder; |
---|
789 | |
---|
790 | int rn = -1; |
---|
791 | |
---|
792 | if (na >= int(order_list.size())) { |
---|
793 | rn = na; |
---|
794 | } else if (nb >= int(order_list.size())) { |
---|
795 | rn = nb; |
---|
796 | } |
---|
797 | |
---|
798 | if (rn == -1) { |
---|
799 | int nn; |
---|
800 | |
---|
801 | nn = da ? node_data[na].prev : node_data[na].next; |
---|
802 | da = node_data[nn].prev != na; |
---|
803 | na = nn; |
---|
804 | |
---|
805 | nn = db ? node_data[nb].prev : node_data[nb].next; |
---|
806 | db = node_data[nn].prev != nb; |
---|
807 | nb = nn; |
---|
808 | |
---|
809 | } else { |
---|
810 | |
---|
811 | Node rep = order_list[rn - order_list.size()]; |
---|
812 | Node parent = _graph.source(pred_map[rep]); |
---|
813 | |
---|
814 | if (low_map[rep] < rorder) { |
---|
815 | merge_roots[parent].push_back(rn); |
---|
816 | } else { |
---|
817 | merge_roots[parent].push_front(rn); |
---|
818 | } |
---|
819 | |
---|
820 | if (parent != root) { |
---|
821 | na = nb = order_map[parent]; |
---|
822 | da = true; db = false; |
---|
823 | } else { |
---|
824 | break; |
---|
825 | } |
---|
826 | } |
---|
827 | } |
---|
828 | } |
---|
829 | |
---|
830 | void walkDown(int rn, int rorder, NodeData& node_data, |
---|
831 | ArcLists& arc_lists, FlipMap& flip_map, |
---|
832 | OrderList& order_list, ChildLists& child_lists, |
---|
833 | AncestorMap& ancestor_map, LowMap& low_map, |
---|
834 | EmbedArc& embed_arc, MergeRoots& merge_roots) { |
---|
835 | |
---|
836 | std::vector<std::pair<int, bool> > merge_stack; |
---|
837 | |
---|
838 | for (int di = 0; di < 2; ++di) { |
---|
839 | bool rd = di == 0; |
---|
840 | int pn = rn; |
---|
841 | int n = rd ? node_data[rn].next : node_data[rn].prev; |
---|
842 | |
---|
843 | while (n != rn) { |
---|
844 | |
---|
845 | Node node = order_list[n]; |
---|
846 | |
---|
847 | if (embed_arc[node] != INVALID) { |
---|
848 | |
---|
849 | // Merging components on the critical path |
---|
850 | while (!merge_stack.empty()) { |
---|
851 | |
---|
852 | // Component root |
---|
853 | int cn = merge_stack.back().first; |
---|
854 | bool cd = merge_stack.back().second; |
---|
855 | merge_stack.pop_back(); |
---|
856 | |
---|
857 | // Parent of component |
---|
858 | int dn = merge_stack.back().first; |
---|
859 | bool dd = merge_stack.back().second; |
---|
860 | merge_stack.pop_back(); |
---|
861 | |
---|
862 | Node parent = order_list[dn]; |
---|
863 | |
---|
864 | // Erasing from merge_roots |
---|
865 | merge_roots[parent].pop_front(); |
---|
866 | |
---|
867 | Node child = order_list[cn - order_list.size()]; |
---|
868 | |
---|
869 | // Erasing from child_lists |
---|
870 | if (child_lists[child].prev != INVALID) { |
---|
871 | child_lists[child_lists[child].prev].next = |
---|
872 | child_lists[child].next; |
---|
873 | } else { |
---|
874 | child_lists[parent].first = child_lists[child].next; |
---|
875 | } |
---|
876 | |
---|
877 | if (child_lists[child].next != INVALID) { |
---|
878 | child_lists[child_lists[child].next].prev = |
---|
879 | child_lists[child].prev; |
---|
880 | } |
---|
881 | |
---|
882 | // Merging arcs + flipping |
---|
883 | Arc de = node_data[dn].first; |
---|
884 | Arc ce = node_data[cn].first; |
---|
885 | |
---|
886 | flip_map[order_list[cn - order_list.size()]] = cd != dd; |
---|
887 | if (cd != dd) { |
---|
888 | std::swap(arc_lists[ce].prev, arc_lists[ce].next); |
---|
889 | ce = arc_lists[ce].prev; |
---|
890 | std::swap(arc_lists[ce].prev, arc_lists[ce].next); |
---|
891 | } |
---|
892 | |
---|
893 | { |
---|
894 | Arc dne = arc_lists[de].next; |
---|
895 | Arc cne = arc_lists[ce].next; |
---|
896 | |
---|
897 | arc_lists[de].next = cne; |
---|
898 | arc_lists[ce].next = dne; |
---|
899 | |
---|
900 | arc_lists[dne].prev = ce; |
---|
901 | arc_lists[cne].prev = de; |
---|
902 | } |
---|
903 | |
---|
904 | if (dd) { |
---|
905 | node_data[dn].first = ce; |
---|
906 | } |
---|
907 | |
---|
908 | // Merging external faces |
---|
909 | { |
---|
910 | int en = cn; |
---|
911 | cn = cd ? node_data[cn].prev : node_data[cn].next; |
---|
912 | cd = node_data[cn].next == en; |
---|
913 | |
---|
914 | if (node_data[cn].prev == node_data[cn].next && |
---|
915 | node_data[cn].inverted) { |
---|
916 | cd = !cd; |
---|
917 | } |
---|
918 | } |
---|
919 | |
---|
920 | if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
---|
921 | if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
---|
922 | |
---|
923 | } |
---|
924 | |
---|
925 | bool d = pn == node_data[n].prev; |
---|
926 | |
---|
927 | if (node_data[n].prev == node_data[n].next && |
---|
928 | node_data[n].inverted) { |
---|
929 | d = !d; |
---|
930 | } |
---|
931 | |
---|
932 | // Add new arc |
---|
933 | { |
---|
934 | Arc arc = embed_arc[node]; |
---|
935 | Arc re = node_data[rn].first; |
---|
936 | |
---|
937 | arc_lists[arc_lists[re].next].prev = arc; |
---|
938 | arc_lists[arc].next = arc_lists[re].next; |
---|
939 | arc_lists[arc].prev = re; |
---|
940 | arc_lists[re].next = arc; |
---|
941 | |
---|
942 | if (!rd) { |
---|
943 | node_data[rn].first = arc; |
---|
944 | } |
---|
945 | |
---|
946 | Arc rev = _graph.oppositeArc(arc); |
---|
947 | Arc e = node_data[n].first; |
---|
948 | |
---|
949 | arc_lists[arc_lists[e].next].prev = rev; |
---|
950 | arc_lists[rev].next = arc_lists[e].next; |
---|
951 | arc_lists[rev].prev = e; |
---|
952 | arc_lists[e].next = rev; |
---|
953 | |
---|
954 | if (d) { |
---|
955 | node_data[n].first = rev; |
---|
956 | } |
---|
957 | |
---|
958 | } |
---|
959 | |
---|
960 | // Embedding arc into external face |
---|
961 | if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
---|
962 | if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
---|
963 | pn = rn; |
---|
964 | |
---|
965 | embed_arc[order_list[n]] = INVALID; |
---|
966 | } |
---|
967 | |
---|
968 | if (!merge_roots[node].empty()) { |
---|
969 | |
---|
970 | bool d = pn == node_data[n].prev; |
---|
971 | if (node_data[n].prev == node_data[n].next && |
---|
972 | node_data[n].inverted) { |
---|
973 | d = !d; |
---|
974 | } |
---|
975 | |
---|
976 | merge_stack.push_back(std::make_pair(n, d)); |
---|
977 | |
---|
978 | int rn = merge_roots[node].front(); |
---|
979 | |
---|
980 | int xn = node_data[rn].next; |
---|
981 | Node xnode = order_list[xn]; |
---|
982 | |
---|
983 | int yn = node_data[rn].prev; |
---|
984 | Node ynode = order_list[yn]; |
---|
985 | |
---|
986 | bool rd; |
---|
987 | if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
988 | rd = true; |
---|
989 | } else if (!external(ynode, rorder, child_lists, |
---|
990 | ancestor_map, low_map)) { |
---|
991 | rd = false; |
---|
992 | } else if (pertinent(xnode, embed_arc, merge_roots)) { |
---|
993 | rd = true; |
---|
994 | } else { |
---|
995 | rd = false; |
---|
996 | } |
---|
997 | |
---|
998 | merge_stack.push_back(std::make_pair(rn, rd)); |
---|
999 | |
---|
1000 | pn = rn; |
---|
1001 | n = rd ? xn : yn; |
---|
1002 | |
---|
1003 | } else if (!external(node, rorder, child_lists, |
---|
1004 | ancestor_map, low_map)) { |
---|
1005 | int nn = (node_data[n].next != pn ? |
---|
1006 | node_data[n].next : node_data[n].prev); |
---|
1007 | |
---|
1008 | bool nd = n == node_data[nn].prev; |
---|
1009 | |
---|
1010 | if (nd) node_data[nn].prev = pn; |
---|
1011 | else node_data[nn].next = pn; |
---|
1012 | |
---|
1013 | if (n == node_data[pn].prev) node_data[pn].prev = nn; |
---|
1014 | else node_data[pn].next = nn; |
---|
1015 | |
---|
1016 | node_data[nn].inverted = |
---|
1017 | (node_data[nn].prev == node_data[nn].next && nd != rd); |
---|
1018 | |
---|
1019 | n = nn; |
---|
1020 | } |
---|
1021 | else break; |
---|
1022 | |
---|
1023 | } |
---|
1024 | |
---|
1025 | if (!merge_stack.empty() || n == rn) { |
---|
1026 | break; |
---|
1027 | } |
---|
1028 | } |
---|
1029 | } |
---|
1030 | |
---|
1031 | void initFace(const Node& node, ArcLists& arc_lists, |
---|
1032 | NodeData& node_data, const PredMap& pred_map, |
---|
1033 | const OrderMap& order_map, const OrderList& order_list) { |
---|
1034 | int n = order_map[node]; |
---|
1035 | int rn = n + order_list.size(); |
---|
1036 | |
---|
1037 | node_data[n].next = node_data[n].prev = rn; |
---|
1038 | node_data[rn].next = node_data[rn].prev = n; |
---|
1039 | |
---|
1040 | node_data[n].visited = order_list.size(); |
---|
1041 | node_data[rn].visited = order_list.size(); |
---|
1042 | |
---|
1043 | node_data[n].inverted = false; |
---|
1044 | node_data[rn].inverted = false; |
---|
1045 | |
---|
1046 | Arc arc = pred_map[node]; |
---|
1047 | Arc rev = _graph.oppositeArc(arc); |
---|
1048 | |
---|
1049 | node_data[rn].first = arc; |
---|
1050 | node_data[n].first = rev; |
---|
1051 | |
---|
1052 | arc_lists[arc].prev = arc; |
---|
1053 | arc_lists[arc].next = arc; |
---|
1054 | |
---|
1055 | arc_lists[rev].prev = rev; |
---|
1056 | arc_lists[rev].next = rev; |
---|
1057 | |
---|
1058 | } |
---|
1059 | |
---|
1060 | void mergeRemainingFaces(const Node& node, NodeData& node_data, |
---|
1061 | OrderList& order_list, OrderMap& order_map, |
---|
1062 | ChildLists& child_lists, ArcLists& arc_lists) { |
---|
1063 | while (child_lists[node].first != INVALID) { |
---|
1064 | int dd = order_map[node]; |
---|
1065 | Node child = child_lists[node].first; |
---|
1066 | int cd = order_map[child] + order_list.size(); |
---|
1067 | child_lists[node].first = child_lists[child].next; |
---|
1068 | |
---|
1069 | Arc de = node_data[dd].first; |
---|
1070 | Arc ce = node_data[cd].first; |
---|
1071 | |
---|
1072 | if (de != INVALID) { |
---|
1073 | Arc dne = arc_lists[de].next; |
---|
1074 | Arc cne = arc_lists[ce].next; |
---|
1075 | |
---|
1076 | arc_lists[de].next = cne; |
---|
1077 | arc_lists[ce].next = dne; |
---|
1078 | |
---|
1079 | arc_lists[dne].prev = ce; |
---|
1080 | arc_lists[cne].prev = de; |
---|
1081 | } |
---|
1082 | |
---|
1083 | node_data[dd].first = ce; |
---|
1084 | |
---|
1085 | } |
---|
1086 | } |
---|
1087 | |
---|
1088 | void storeEmbedding(const Node& node, NodeData& node_data, |
---|
1089 | OrderMap& order_map, PredMap& pred_map, |
---|
1090 | ArcLists& arc_lists, FlipMap& flip_map) { |
---|
1091 | |
---|
1092 | if (node_data[order_map[node]].first == INVALID) return; |
---|
1093 | |
---|
1094 | if (pred_map[node] != INVALID) { |
---|
1095 | Node source = _graph.source(pred_map[node]); |
---|
1096 | flip_map[node] = flip_map[node] != flip_map[source]; |
---|
1097 | } |
---|
1098 | |
---|
1099 | Arc first = node_data[order_map[node]].first; |
---|
1100 | Arc prev = first; |
---|
1101 | |
---|
1102 | Arc arc = flip_map[node] ? |
---|
1103 | arc_lists[prev].prev : arc_lists[prev].next; |
---|
1104 | |
---|
1105 | _embedding[prev] = arc; |
---|
1106 | |
---|
1107 | while (arc != first) { |
---|
1108 | Arc next = arc_lists[arc].prev == prev ? |
---|
1109 | arc_lists[arc].next : arc_lists[arc].prev; |
---|
1110 | prev = arc; arc = next; |
---|
1111 | _embedding[prev] = arc; |
---|
1112 | } |
---|
1113 | } |
---|
1114 | |
---|
1115 | |
---|
1116 | bool external(const Node& node, int rorder, |
---|
1117 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
1118 | LowMap& low_map) { |
---|
1119 | Node child = child_lists[node].first; |
---|
1120 | |
---|
1121 | if (child != INVALID) { |
---|
1122 | if (low_map[child] < rorder) return true; |
---|
1123 | } |
---|
1124 | |
---|
1125 | if (ancestor_map[node] < rorder) return true; |
---|
1126 | |
---|
1127 | return false; |
---|
1128 | } |
---|
1129 | |
---|
1130 | bool pertinent(const Node& node, const EmbedArc& embed_arc, |
---|
1131 | const MergeRoots& merge_roots) { |
---|
1132 | return !merge_roots[node].empty() || embed_arc[node] != INVALID; |
---|
1133 | } |
---|
1134 | |
---|
1135 | int lowPoint(const Node& node, OrderMap& order_map, ChildLists& child_lists, |
---|
1136 | AncestorMap& ancestor_map, LowMap& low_map) { |
---|
1137 | int low_point; |
---|
1138 | |
---|
1139 | Node child = child_lists[node].first; |
---|
1140 | |
---|
1141 | if (child != INVALID) { |
---|
1142 | low_point = low_map[child]; |
---|
1143 | } else { |
---|
1144 | low_point = order_map[node]; |
---|
1145 | } |
---|
1146 | |
---|
1147 | if (low_point > ancestor_map[node]) { |
---|
1148 | low_point = ancestor_map[node]; |
---|
1149 | } |
---|
1150 | |
---|
1151 | return low_point; |
---|
1152 | } |
---|
1153 | |
---|
1154 | int findComponentRoot(Node root, Node node, ChildLists& child_lists, |
---|
1155 | OrderMap& order_map, OrderList& order_list) { |
---|
1156 | |
---|
1157 | int order = order_map[root]; |
---|
1158 | int norder = order_map[node]; |
---|
1159 | |
---|
1160 | Node child = child_lists[root].first; |
---|
1161 | while (child != INVALID) { |
---|
1162 | int corder = order_map[child]; |
---|
1163 | if (corder > order && corder < norder) { |
---|
1164 | order = corder; |
---|
1165 | } |
---|
1166 | child = child_lists[child].next; |
---|
1167 | } |
---|
1168 | return order + order_list.size(); |
---|
1169 | } |
---|
1170 | |
---|
1171 | Node findPertinent(Node node, OrderMap& order_map, NodeData& node_data, |
---|
1172 | EmbedArc& embed_arc, MergeRoots& merge_roots) { |
---|
1173 | Node wnode =_graph.target(node_data[order_map[node]].first); |
---|
1174 | while (!pertinent(wnode, embed_arc, merge_roots)) { |
---|
1175 | wnode = _graph.target(node_data[order_map[wnode]].first); |
---|
1176 | } |
---|
1177 | return wnode; |
---|
1178 | } |
---|
1179 | |
---|
1180 | |
---|
1181 | Node findExternal(Node node, int rorder, OrderMap& order_map, |
---|
1182 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
1183 | LowMap& low_map, NodeData& node_data) { |
---|
1184 | Node wnode =_graph.target(node_data[order_map[node]].first); |
---|
1185 | while (!external(wnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
1186 | wnode = _graph.target(node_data[order_map[wnode]].first); |
---|
1187 | } |
---|
1188 | return wnode; |
---|
1189 | } |
---|
1190 | |
---|
1191 | void markCommonPath(Node node, int rorder, Node& wnode, Node& znode, |
---|
1192 | OrderList& order_list, OrderMap& order_map, |
---|
1193 | NodeData& node_data, ArcLists& arc_lists, |
---|
1194 | EmbedArc& embed_arc, MergeRoots& merge_roots, |
---|
1195 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
1196 | LowMap& low_map) { |
---|
1197 | |
---|
1198 | Node cnode = node; |
---|
1199 | Node pred = INVALID; |
---|
1200 | |
---|
1201 | while (true) { |
---|
1202 | |
---|
1203 | bool pert = pertinent(cnode, embed_arc, merge_roots); |
---|
1204 | bool ext = external(cnode, rorder, child_lists, ancestor_map, low_map); |
---|
1205 | |
---|
1206 | if (pert && ext) { |
---|
1207 | if (!merge_roots[cnode].empty()) { |
---|
1208 | int cn = merge_roots[cnode].back(); |
---|
1209 | |
---|
1210 | if (low_map[order_list[cn - order_list.size()]] < rorder) { |
---|
1211 | Arc arc = node_data[cn].first; |
---|
1212 | _kuratowski.set(arc, true); |
---|
1213 | |
---|
1214 | pred = cnode; |
---|
1215 | cnode = _graph.target(arc); |
---|
1216 | |
---|
1217 | continue; |
---|
1218 | } |
---|
1219 | } |
---|
1220 | wnode = znode = cnode; |
---|
1221 | return; |
---|
1222 | |
---|
1223 | } else if (pert) { |
---|
1224 | wnode = cnode; |
---|
1225 | |
---|
1226 | while (!external(cnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
1227 | Arc arc = node_data[order_map[cnode]].first; |
---|
1228 | |
---|
1229 | if (_graph.target(arc) == pred) { |
---|
1230 | arc = arc_lists[arc].next; |
---|
1231 | } |
---|
1232 | _kuratowski.set(arc, true); |
---|
1233 | |
---|
1234 | Node next = _graph.target(arc); |
---|
1235 | pred = cnode; cnode = next; |
---|
1236 | } |
---|
1237 | |
---|
1238 | znode = cnode; |
---|
1239 | return; |
---|
1240 | |
---|
1241 | } else if (ext) { |
---|
1242 | znode = cnode; |
---|
1243 | |
---|
1244 | while (!pertinent(cnode, embed_arc, merge_roots)) { |
---|
1245 | Arc arc = node_data[order_map[cnode]].first; |
---|
1246 | |
---|
1247 | if (_graph.target(arc) == pred) { |
---|
1248 | arc = arc_lists[arc].next; |
---|
1249 | } |
---|
1250 | _kuratowski.set(arc, true); |
---|
1251 | |
---|
1252 | Node next = _graph.target(arc); |
---|
1253 | pred = cnode; cnode = next; |
---|
1254 | } |
---|
1255 | |
---|
1256 | wnode = cnode; |
---|
1257 | return; |
---|
1258 | |
---|
1259 | } else { |
---|
1260 | Arc arc = node_data[order_map[cnode]].first; |
---|
1261 | |
---|
1262 | if (_graph.target(arc) == pred) { |
---|
1263 | arc = arc_lists[arc].next; |
---|
1264 | } |
---|
1265 | _kuratowski.set(arc, true); |
---|
1266 | |
---|
1267 | Node next = _graph.target(arc); |
---|
1268 | pred = cnode; cnode = next; |
---|
1269 | } |
---|
1270 | |
---|
1271 | } |
---|
1272 | |
---|
1273 | } |
---|
1274 | |
---|
1275 | void orientComponent(Node root, int rn, OrderMap& order_map, |
---|
1276 | PredMap& pred_map, NodeData& node_data, |
---|
1277 | ArcLists& arc_lists, FlipMap& flip_map, |
---|
1278 | TypeMap& type_map) { |
---|
1279 | node_data[order_map[root]].first = node_data[rn].first; |
---|
1280 | type_map[root] = 1; |
---|
1281 | |
---|
1282 | std::vector<Node> st, qu; |
---|
1283 | |
---|
1284 | st.push_back(root); |
---|
1285 | while (!st.empty()) { |
---|
1286 | Node node = st.back(); |
---|
1287 | st.pop_back(); |
---|
1288 | qu.push_back(node); |
---|
1289 | |
---|
1290 | Arc arc = node_data[order_map[node]].first; |
---|
1291 | |
---|
1292 | if (type_map[_graph.target(arc)] == 0) { |
---|
1293 | st.push_back(_graph.target(arc)); |
---|
1294 | type_map[_graph.target(arc)] = 1; |
---|
1295 | } |
---|
1296 | |
---|
1297 | Arc last = arc, pred = arc; |
---|
1298 | arc = arc_lists[arc].next; |
---|
1299 | while (arc != last) { |
---|
1300 | |
---|
1301 | if (type_map[_graph.target(arc)] == 0) { |
---|
1302 | st.push_back(_graph.target(arc)); |
---|
1303 | type_map[_graph.target(arc)] = 1; |
---|
1304 | } |
---|
1305 | |
---|
1306 | Arc next = arc_lists[arc].next != pred ? |
---|
1307 | arc_lists[arc].next : arc_lists[arc].prev; |
---|
1308 | pred = arc; arc = next; |
---|
1309 | } |
---|
1310 | |
---|
1311 | } |
---|
1312 | |
---|
1313 | type_map[root] = 2; |
---|
1314 | flip_map[root] = false; |
---|
1315 | |
---|
1316 | for (int i = 1; i < int(qu.size()); ++i) { |
---|
1317 | |
---|
1318 | Node node = qu[i]; |
---|
1319 | |
---|
1320 | while (type_map[node] != 2) { |
---|
1321 | st.push_back(node); |
---|
1322 | type_map[node] = 2; |
---|
1323 | node = _graph.source(pred_map[node]); |
---|
1324 | } |
---|
1325 | |
---|
1326 | bool flip = flip_map[node]; |
---|
1327 | |
---|
1328 | while (!st.empty()) { |
---|
1329 | node = st.back(); |
---|
1330 | st.pop_back(); |
---|
1331 | |
---|
1332 | flip_map[node] = flip != flip_map[node]; |
---|
1333 | flip = flip_map[node]; |
---|
1334 | |
---|
1335 | if (flip) { |
---|
1336 | Arc arc = node_data[order_map[node]].first; |
---|
1337 | std::swap(arc_lists[arc].prev, arc_lists[arc].next); |
---|
1338 | arc = arc_lists[arc].prev; |
---|
1339 | std::swap(arc_lists[arc].prev, arc_lists[arc].next); |
---|
1340 | node_data[order_map[node]].first = arc; |
---|
1341 | } |
---|
1342 | } |
---|
1343 | } |
---|
1344 | |
---|
1345 | for (int i = 0; i < int(qu.size()); ++i) { |
---|
1346 | |
---|
1347 | Arc arc = node_data[order_map[qu[i]]].first; |
---|
1348 | Arc last = arc, pred = arc; |
---|
1349 | |
---|
1350 | arc = arc_lists[arc].next; |
---|
1351 | while (arc != last) { |
---|
1352 | |
---|
1353 | if (arc_lists[arc].next == pred) { |
---|
1354 | std::swap(arc_lists[arc].next, arc_lists[arc].prev); |
---|
1355 | } |
---|
1356 | pred = arc; arc = arc_lists[arc].next; |
---|
1357 | } |
---|
1358 | |
---|
1359 | } |
---|
1360 | } |
---|
1361 | |
---|
1362 | void setFaceFlags(Node root, Node wnode, Node ynode, Node xnode, |
---|
1363 | OrderMap& order_map, NodeData& node_data, |
---|
1364 | TypeMap& type_map) { |
---|
1365 | Node node = _graph.target(node_data[order_map[root]].first); |
---|
1366 | |
---|
1367 | while (node != ynode) { |
---|
1368 | type_map[node] = HIGHY; |
---|
1369 | node = _graph.target(node_data[order_map[node]].first); |
---|
1370 | } |
---|
1371 | |
---|
1372 | while (node != wnode) { |
---|
1373 | type_map[node] = LOWY; |
---|
1374 | node = _graph.target(node_data[order_map[node]].first); |
---|
1375 | } |
---|
1376 | |
---|
1377 | node = _graph.target(node_data[order_map[wnode]].first); |
---|
1378 | |
---|
1379 | while (node != xnode) { |
---|
1380 | type_map[node] = LOWX; |
---|
1381 | node = _graph.target(node_data[order_map[node]].first); |
---|
1382 | } |
---|
1383 | type_map[node] = LOWX; |
---|
1384 | |
---|
1385 | node = _graph.target(node_data[order_map[xnode]].first); |
---|
1386 | while (node != root) { |
---|
1387 | type_map[node] = HIGHX; |
---|
1388 | node = _graph.target(node_data[order_map[node]].first); |
---|
1389 | } |
---|
1390 | |
---|
1391 | type_map[wnode] = PERTINENT; |
---|
1392 | type_map[root] = ROOT; |
---|
1393 | } |
---|
1394 | |
---|
1395 | void findInternalPath(std::vector<Arc>& ipath, |
---|
1396 | Node wnode, Node root, TypeMap& type_map, |
---|
1397 | OrderMap& order_map, NodeData& node_data, |
---|
1398 | ArcLists& arc_lists) { |
---|
1399 | std::vector<Arc> st; |
---|
1400 | |
---|
1401 | Node node = wnode; |
---|
1402 | |
---|
1403 | while (node != root) { |
---|
1404 | Arc arc = arc_lists[node_data[order_map[node]].first].next; |
---|
1405 | st.push_back(arc); |
---|
1406 | node = _graph.target(arc); |
---|
1407 | } |
---|
1408 | |
---|
1409 | while (true) { |
---|
1410 | Arc arc = st.back(); |
---|
1411 | if (type_map[_graph.target(arc)] == LOWX || |
---|
1412 | type_map[_graph.target(arc)] == HIGHX) { |
---|
1413 | break; |
---|
1414 | } |
---|
1415 | if (type_map[_graph.target(arc)] == 2) { |
---|
1416 | type_map[_graph.target(arc)] = 3; |
---|
1417 | |
---|
1418 | arc = arc_lists[_graph.oppositeArc(arc)].next; |
---|
1419 | st.push_back(arc); |
---|
1420 | } else { |
---|
1421 | st.pop_back(); |
---|
1422 | arc = arc_lists[arc].next; |
---|
1423 | |
---|
1424 | while (_graph.oppositeArc(arc) == st.back()) { |
---|
1425 | arc = st.back(); |
---|
1426 | st.pop_back(); |
---|
1427 | arc = arc_lists[arc].next; |
---|
1428 | } |
---|
1429 | st.push_back(arc); |
---|
1430 | } |
---|
1431 | } |
---|
1432 | |
---|
1433 | for (int i = 0; i < int(st.size()); ++i) { |
---|
1434 | if (type_map[_graph.target(st[i])] != LOWY && |
---|
1435 | type_map[_graph.target(st[i])] != HIGHY) { |
---|
1436 | for (; i < int(st.size()); ++i) { |
---|
1437 | ipath.push_back(st[i]); |
---|
1438 | } |
---|
1439 | } |
---|
1440 | } |
---|
1441 | } |
---|
1442 | |
---|
1443 | void setInternalFlags(std::vector<Arc>& ipath, TypeMap& type_map) { |
---|
1444 | for (int i = 1; i < int(ipath.size()); ++i) { |
---|
1445 | type_map[_graph.source(ipath[i])] = INTERNAL; |
---|
1446 | } |
---|
1447 | } |
---|
1448 | |
---|
1449 | void findPilePath(std::vector<Arc>& ppath, |
---|
1450 | Node root, TypeMap& type_map, OrderMap& order_map, |
---|
1451 | NodeData& node_data, ArcLists& arc_lists) { |
---|
1452 | std::vector<Arc> st; |
---|
1453 | |
---|
1454 | st.push_back(_graph.oppositeArc(node_data[order_map[root]].first)); |
---|
1455 | st.push_back(node_data[order_map[root]].first); |
---|
1456 | |
---|
1457 | while (st.size() > 1) { |
---|
1458 | Arc arc = st.back(); |
---|
1459 | if (type_map[_graph.target(arc)] == INTERNAL) { |
---|
1460 | break; |
---|
1461 | } |
---|
1462 | if (type_map[_graph.target(arc)] == 3) { |
---|
1463 | type_map[_graph.target(arc)] = 4; |
---|
1464 | |
---|
1465 | arc = arc_lists[_graph.oppositeArc(arc)].next; |
---|
1466 | st.push_back(arc); |
---|
1467 | } else { |
---|
1468 | st.pop_back(); |
---|
1469 | arc = arc_lists[arc].next; |
---|
1470 | |
---|
1471 | while (!st.empty() && _graph.oppositeArc(arc) == st.back()) { |
---|
1472 | arc = st.back(); |
---|
1473 | st.pop_back(); |
---|
1474 | arc = arc_lists[arc].next; |
---|
1475 | } |
---|
1476 | st.push_back(arc); |
---|
1477 | } |
---|
1478 | } |
---|
1479 | |
---|
1480 | for (int i = 1; i < int(st.size()); ++i) { |
---|
1481 | ppath.push_back(st[i]); |
---|
1482 | } |
---|
1483 | } |
---|
1484 | |
---|
1485 | |
---|
1486 | int markExternalPath(Node node, OrderMap& order_map, |
---|
1487 | ChildLists& child_lists, PredMap& pred_map, |
---|
1488 | AncestorMap& ancestor_map, LowMap& low_map) { |
---|
1489 | int lp = lowPoint(node, order_map, child_lists, |
---|
1490 | ancestor_map, low_map); |
---|
1491 | |
---|
1492 | if (ancestor_map[node] != lp) { |
---|
1493 | node = child_lists[node].first; |
---|
1494 | _kuratowski[pred_map[node]] = true; |
---|
1495 | |
---|
1496 | while (ancestor_map[node] != lp) { |
---|
1497 | for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
---|
1498 | Node tnode = _graph.target(e); |
---|
1499 | if (order_map[tnode] > order_map[node] && low_map[tnode] == lp) { |
---|
1500 | node = tnode; |
---|
1501 | _kuratowski[e] = true; |
---|
1502 | break; |
---|
1503 | } |
---|
1504 | } |
---|
1505 | } |
---|
1506 | } |
---|
1507 | |
---|
1508 | for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
---|
1509 | if (order_map[_graph.target(e)] == lp) { |
---|
1510 | _kuratowski[e] = true; |
---|
1511 | break; |
---|
1512 | } |
---|
1513 | } |
---|
1514 | |
---|
1515 | return lp; |
---|
1516 | } |
---|
1517 | |
---|
1518 | void markPertinentPath(Node node, OrderMap& order_map, |
---|
1519 | NodeData& node_data, ArcLists& arc_lists, |
---|
1520 | EmbedArc& embed_arc, MergeRoots& merge_roots) { |
---|
1521 | while (embed_arc[node] == INVALID) { |
---|
1522 | int n = merge_roots[node].front(); |
---|
1523 | Arc arc = node_data[n].first; |
---|
1524 | |
---|
1525 | _kuratowski.set(arc, true); |
---|
1526 | |
---|
1527 | Node pred = node; |
---|
1528 | node = _graph.target(arc); |
---|
1529 | while (!pertinent(node, embed_arc, merge_roots)) { |
---|
1530 | arc = node_data[order_map[node]].first; |
---|
1531 | if (_graph.target(arc) == pred) { |
---|
1532 | arc = arc_lists[arc].next; |
---|
1533 | } |
---|
1534 | _kuratowski.set(arc, true); |
---|
1535 | pred = node; |
---|
1536 | node = _graph.target(arc); |
---|
1537 | } |
---|
1538 | } |
---|
1539 | _kuratowski.set(embed_arc[node], true); |
---|
1540 | } |
---|
1541 | |
---|
1542 | void markPredPath(Node node, Node snode, PredMap& pred_map) { |
---|
1543 | while (node != snode) { |
---|
1544 | _kuratowski.set(pred_map[node], true); |
---|
1545 | node = _graph.source(pred_map[node]); |
---|
1546 | } |
---|
1547 | } |
---|
1548 | |
---|
1549 | void markFacePath(Node ynode, Node xnode, |
---|
1550 | OrderMap& order_map, NodeData& node_data) { |
---|
1551 | Arc arc = node_data[order_map[ynode]].first; |
---|
1552 | Node node = _graph.target(arc); |
---|
1553 | _kuratowski.set(arc, true); |
---|
1554 | |
---|
1555 | while (node != xnode) { |
---|
1556 | arc = node_data[order_map[node]].first; |
---|
1557 | _kuratowski.set(arc, true); |
---|
1558 | node = _graph.target(arc); |
---|
1559 | } |
---|
1560 | } |
---|
1561 | |
---|
1562 | void markInternalPath(std::vector<Arc>& path) { |
---|
1563 | for (int i = 0; i < int(path.size()); ++i) { |
---|
1564 | _kuratowski.set(path[i], true); |
---|
1565 | } |
---|
1566 | } |
---|
1567 | |
---|
1568 | void markPilePath(std::vector<Arc>& path) { |
---|
1569 | for (int i = 0; i < int(path.size()); ++i) { |
---|
1570 | _kuratowski.set(path[i], true); |
---|
1571 | } |
---|
1572 | } |
---|
1573 | |
---|
1574 | void isolateKuratowski(Arc arc, NodeData& node_data, |
---|
1575 | ArcLists& arc_lists, FlipMap& flip_map, |
---|
1576 | OrderMap& order_map, OrderList& order_list, |
---|
1577 | PredMap& pred_map, ChildLists& child_lists, |
---|
1578 | AncestorMap& ancestor_map, LowMap& low_map, |
---|
1579 | EmbedArc& embed_arc, MergeRoots& merge_roots) { |
---|
1580 | |
---|
1581 | Node root = _graph.source(arc); |
---|
1582 | Node enode = _graph.target(arc); |
---|
1583 | |
---|
1584 | int rorder = order_map[root]; |
---|
1585 | |
---|
1586 | TypeMap type_map(_graph, 0); |
---|
1587 | |
---|
1588 | int rn = findComponentRoot(root, enode, child_lists, |
---|
1589 | order_map, order_list); |
---|
1590 | |
---|
1591 | Node xnode = order_list[node_data[rn].next]; |
---|
1592 | Node ynode = order_list[node_data[rn].prev]; |
---|
1593 | |
---|
1594 | // Minor-A |
---|
1595 | { |
---|
1596 | while (!merge_roots[xnode].empty() || !merge_roots[ynode].empty()) { |
---|
1597 | |
---|
1598 | if (!merge_roots[xnode].empty()) { |
---|
1599 | root = xnode; |
---|
1600 | rn = merge_roots[xnode].front(); |
---|
1601 | } else { |
---|
1602 | root = ynode; |
---|
1603 | rn = merge_roots[ynode].front(); |
---|
1604 | } |
---|
1605 | |
---|
1606 | xnode = order_list[node_data[rn].next]; |
---|
1607 | ynode = order_list[node_data[rn].prev]; |
---|
1608 | } |
---|
1609 | |
---|
1610 | if (root != _graph.source(arc)) { |
---|
1611 | orientComponent(root, rn, order_map, pred_map, |
---|
1612 | node_data, arc_lists, flip_map, type_map); |
---|
1613 | markFacePath(root, root, order_map, node_data); |
---|
1614 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1615 | pred_map, ancestor_map, low_map); |
---|
1616 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1617 | pred_map, ancestor_map, low_map); |
---|
1618 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
1619 | Node lwnode = findPertinent(ynode, order_map, node_data, |
---|
1620 | embed_arc, merge_roots); |
---|
1621 | |
---|
1622 | markPertinentPath(lwnode, order_map, node_data, arc_lists, |
---|
1623 | embed_arc, merge_roots); |
---|
1624 | |
---|
1625 | return; |
---|
1626 | } |
---|
1627 | } |
---|
1628 | |
---|
1629 | orientComponent(root, rn, order_map, pred_map, |
---|
1630 | node_data, arc_lists, flip_map, type_map); |
---|
1631 | |
---|
1632 | Node wnode = findPertinent(ynode, order_map, node_data, |
---|
1633 | embed_arc, merge_roots); |
---|
1634 | setFaceFlags(root, wnode, ynode, xnode, order_map, node_data, type_map); |
---|
1635 | |
---|
1636 | |
---|
1637 | //Minor-B |
---|
1638 | if (!merge_roots[wnode].empty()) { |
---|
1639 | int cn = merge_roots[wnode].back(); |
---|
1640 | Node rep = order_list[cn - order_list.size()]; |
---|
1641 | if (low_map[rep] < rorder) { |
---|
1642 | markFacePath(root, root, order_map, node_data); |
---|
1643 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1644 | pred_map, ancestor_map, low_map); |
---|
1645 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1646 | pred_map, ancestor_map, low_map); |
---|
1647 | |
---|
1648 | Node lwnode, lznode; |
---|
1649 | markCommonPath(wnode, rorder, lwnode, lznode, order_list, |
---|
1650 | order_map, node_data, arc_lists, embed_arc, |
---|
1651 | merge_roots, child_lists, ancestor_map, low_map); |
---|
1652 | |
---|
1653 | markPertinentPath(lwnode, order_map, node_data, arc_lists, |
---|
1654 | embed_arc, merge_roots); |
---|
1655 | int zlp = markExternalPath(lznode, order_map, child_lists, |
---|
1656 | pred_map, ancestor_map, low_map); |
---|
1657 | |
---|
1658 | int minlp = xlp < ylp ? xlp : ylp; |
---|
1659 | if (zlp < minlp) minlp = zlp; |
---|
1660 | |
---|
1661 | int maxlp = xlp > ylp ? xlp : ylp; |
---|
1662 | if (zlp > maxlp) maxlp = zlp; |
---|
1663 | |
---|
1664 | markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
---|
1665 | |
---|
1666 | return; |
---|
1667 | } |
---|
1668 | } |
---|
1669 | |
---|
1670 | Node pxnode, pynode; |
---|
1671 | std::vector<Arc> ipath; |
---|
1672 | findInternalPath(ipath, wnode, root, type_map, order_map, |
---|
1673 | node_data, arc_lists); |
---|
1674 | setInternalFlags(ipath, type_map); |
---|
1675 | pynode = _graph.source(ipath.front()); |
---|
1676 | pxnode = _graph.target(ipath.back()); |
---|
1677 | |
---|
1678 | wnode = findPertinent(pynode, order_map, node_data, |
---|
1679 | embed_arc, merge_roots); |
---|
1680 | |
---|
1681 | // Minor-C |
---|
1682 | { |
---|
1683 | if (type_map[_graph.source(ipath.front())] == HIGHY) { |
---|
1684 | if (type_map[_graph.target(ipath.back())] == HIGHX) { |
---|
1685 | markFacePath(xnode, pxnode, order_map, node_data); |
---|
1686 | } |
---|
1687 | markFacePath(root, xnode, order_map, node_data); |
---|
1688 | markPertinentPath(wnode, order_map, node_data, arc_lists, |
---|
1689 | embed_arc, merge_roots); |
---|
1690 | markInternalPath(ipath); |
---|
1691 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1692 | pred_map, ancestor_map, low_map); |
---|
1693 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1694 | pred_map, ancestor_map, low_map); |
---|
1695 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
1696 | return; |
---|
1697 | } |
---|
1698 | |
---|
1699 | if (type_map[_graph.target(ipath.back())] == HIGHX) { |
---|
1700 | markFacePath(ynode, root, order_map, node_data); |
---|
1701 | markPertinentPath(wnode, order_map, node_data, arc_lists, |
---|
1702 | embed_arc, merge_roots); |
---|
1703 | markInternalPath(ipath); |
---|
1704 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1705 | pred_map, ancestor_map, low_map); |
---|
1706 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1707 | pred_map, ancestor_map, low_map); |
---|
1708 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
1709 | return; |
---|
1710 | } |
---|
1711 | } |
---|
1712 | |
---|
1713 | std::vector<Arc> ppath; |
---|
1714 | findPilePath(ppath, root, type_map, order_map, node_data, arc_lists); |
---|
1715 | |
---|
1716 | // Minor-D |
---|
1717 | if (!ppath.empty()) { |
---|
1718 | markFacePath(ynode, xnode, order_map, node_data); |
---|
1719 | markPertinentPath(wnode, order_map, node_data, arc_lists, |
---|
1720 | embed_arc, merge_roots); |
---|
1721 | markPilePath(ppath); |
---|
1722 | markInternalPath(ipath); |
---|
1723 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1724 | pred_map, ancestor_map, low_map); |
---|
1725 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1726 | pred_map, ancestor_map, low_map); |
---|
1727 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
1728 | return; |
---|
1729 | } |
---|
1730 | |
---|
1731 | // Minor-E* |
---|
1732 | { |
---|
1733 | |
---|
1734 | if (!external(wnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
1735 | Node znode = findExternal(pynode, rorder, order_map, |
---|
1736 | child_lists, ancestor_map, |
---|
1737 | low_map, node_data); |
---|
1738 | |
---|
1739 | if (type_map[znode] == LOWY) { |
---|
1740 | markFacePath(root, xnode, order_map, node_data); |
---|
1741 | markPertinentPath(wnode, order_map, node_data, arc_lists, |
---|
1742 | embed_arc, merge_roots); |
---|
1743 | markInternalPath(ipath); |
---|
1744 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1745 | pred_map, ancestor_map, low_map); |
---|
1746 | int zlp = markExternalPath(znode, order_map, child_lists, |
---|
1747 | pred_map, ancestor_map, low_map); |
---|
1748 | markPredPath(root, order_list[xlp < zlp ? xlp : zlp], pred_map); |
---|
1749 | } else { |
---|
1750 | markFacePath(ynode, root, order_map, node_data); |
---|
1751 | markPertinentPath(wnode, order_map, node_data, arc_lists, |
---|
1752 | embed_arc, merge_roots); |
---|
1753 | markInternalPath(ipath); |
---|
1754 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1755 | pred_map, ancestor_map, low_map); |
---|
1756 | int zlp = markExternalPath(znode, order_map, child_lists, |
---|
1757 | pred_map, ancestor_map, low_map); |
---|
1758 | markPredPath(root, order_list[ylp < zlp ? ylp : zlp], pred_map); |
---|
1759 | } |
---|
1760 | return; |
---|
1761 | } |
---|
1762 | |
---|
1763 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1764 | pred_map, ancestor_map, low_map); |
---|
1765 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1766 | pred_map, ancestor_map, low_map); |
---|
1767 | int wlp = markExternalPath(wnode, order_map, child_lists, |
---|
1768 | pred_map, ancestor_map, low_map); |
---|
1769 | |
---|
1770 | if (wlp > xlp && wlp > ylp) { |
---|
1771 | markFacePath(root, root, order_map, node_data); |
---|
1772 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
1773 | return; |
---|
1774 | } |
---|
1775 | |
---|
1776 | markInternalPath(ipath); |
---|
1777 | markPertinentPath(wnode, order_map, node_data, arc_lists, |
---|
1778 | embed_arc, merge_roots); |
---|
1779 | |
---|
1780 | if (xlp > ylp && xlp > wlp) { |
---|
1781 | markFacePath(root, pynode, order_map, node_data); |
---|
1782 | markFacePath(wnode, xnode, order_map, node_data); |
---|
1783 | markPredPath(root, order_list[ylp < wlp ? ylp : wlp], pred_map); |
---|
1784 | return; |
---|
1785 | } |
---|
1786 | |
---|
1787 | if (ylp > xlp && ylp > wlp) { |
---|
1788 | markFacePath(pxnode, root, order_map, node_data); |
---|
1789 | markFacePath(ynode, wnode, order_map, node_data); |
---|
1790 | markPredPath(root, order_list[xlp < wlp ? xlp : wlp], pred_map); |
---|
1791 | return; |
---|
1792 | } |
---|
1793 | |
---|
1794 | if (pynode != ynode) { |
---|
1795 | markFacePath(pxnode, wnode, order_map, node_data); |
---|
1796 | |
---|
1797 | int minlp = xlp < ylp ? xlp : ylp; |
---|
1798 | if (wlp < minlp) minlp = wlp; |
---|
1799 | |
---|
1800 | int maxlp = xlp > ylp ? xlp : ylp; |
---|
1801 | if (wlp > maxlp) maxlp = wlp; |
---|
1802 | |
---|
1803 | markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
---|
1804 | return; |
---|
1805 | } |
---|
1806 | |
---|
1807 | if (pxnode != xnode) { |
---|
1808 | markFacePath(wnode, pynode, order_map, node_data); |
---|
1809 | |
---|
1810 | int minlp = xlp < ylp ? xlp : ylp; |
---|
1811 | if (wlp < minlp) minlp = wlp; |
---|
1812 | |
---|
1813 | int maxlp = xlp > ylp ? xlp : ylp; |
---|
1814 | if (wlp > maxlp) maxlp = wlp; |
---|
1815 | |
---|
1816 | markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
---|
1817 | return; |
---|
1818 | } |
---|
1819 | |
---|
1820 | markFacePath(root, root, order_map, node_data); |
---|
1821 | int minlp = xlp < ylp ? xlp : ylp; |
---|
1822 | if (wlp < minlp) minlp = wlp; |
---|
1823 | markPredPath(root, order_list[minlp], pred_map); |
---|
1824 | return; |
---|
1825 | } |
---|
1826 | |
---|
1827 | } |
---|
1828 | |
---|
1829 | }; |
---|
1830 | |
---|
1831 | namespace _planarity_bits { |
---|
1832 | |
---|
1833 | template <typename Graph, typename EmbeddingMap> |
---|
1834 | void makeConnected(Graph& graph, EmbeddingMap& embedding) { |
---|
1835 | DfsVisitor<Graph> null_visitor; |
---|
1836 | DfsVisit<Graph, DfsVisitor<Graph> > dfs(graph, null_visitor); |
---|
1837 | dfs.init(); |
---|
1838 | |
---|
1839 | typename Graph::Node u = INVALID; |
---|
1840 | for (typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
---|
1841 | if (!dfs.reached(n)) { |
---|
1842 | dfs.addSource(n); |
---|
1843 | dfs.start(); |
---|
1844 | if (u == INVALID) { |
---|
1845 | u = n; |
---|
1846 | } else { |
---|
1847 | typename Graph::Node v = n; |
---|
1848 | |
---|
1849 | typename Graph::Arc ue = typename Graph::OutArcIt(graph, u); |
---|
1850 | typename Graph::Arc ve = typename Graph::OutArcIt(graph, v); |
---|
1851 | |
---|
1852 | typename Graph::Arc e = graph.direct(graph.addEdge(u, v), true); |
---|
1853 | |
---|
1854 | if (ue != INVALID) { |
---|
1855 | embedding[e] = embedding[ue]; |
---|
1856 | embedding[ue] = e; |
---|
1857 | } else { |
---|
1858 | embedding[e] = e; |
---|
1859 | } |
---|
1860 | |
---|
1861 | if (ve != INVALID) { |
---|
1862 | embedding[graph.oppositeArc(e)] = embedding[ve]; |
---|
1863 | embedding[ve] = graph.oppositeArc(e); |
---|
1864 | } else { |
---|
1865 | embedding[graph.oppositeArc(e)] = graph.oppositeArc(e); |
---|
1866 | } |
---|
1867 | } |
---|
1868 | } |
---|
1869 | } |
---|
1870 | } |
---|
1871 | |
---|
1872 | template <typename Graph, typename EmbeddingMap> |
---|
1873 | void makeBiNodeConnected(Graph& graph, EmbeddingMap& embedding) { |
---|
1874 | typename Graph::template ArcMap<bool> processed(graph); |
---|
1875 | |
---|
1876 | std::vector<typename Graph::Arc> arcs; |
---|
1877 | for (typename Graph::ArcIt e(graph); e != INVALID; ++e) { |
---|
1878 | arcs.push_back(e); |
---|
1879 | } |
---|
1880 | |
---|
1881 | IterableBoolMap<Graph, typename Graph::Node> visited(graph, false); |
---|
1882 | |
---|
1883 | for (int i = 0; i < int(arcs.size()); ++i) { |
---|
1884 | typename Graph::Arc pp = arcs[i]; |
---|
1885 | if (processed[pp]) continue; |
---|
1886 | |
---|
1887 | typename Graph::Arc e = embedding[graph.oppositeArc(pp)]; |
---|
1888 | processed[e] = true; |
---|
1889 | visited.set(graph.source(e), true); |
---|
1890 | |
---|
1891 | typename Graph::Arc p = e, l = e; |
---|
1892 | e = embedding[graph.oppositeArc(e)]; |
---|
1893 | |
---|
1894 | while (e != l) { |
---|
1895 | processed[e] = true; |
---|
1896 | |
---|
1897 | if (visited[graph.source(e)]) { |
---|
1898 | |
---|
1899 | typename Graph::Arc n = |
---|
1900 | graph.direct(graph.addEdge(graph.source(p), |
---|
1901 | graph.target(e)), true); |
---|
1902 | embedding[n] = p; |
---|
1903 | embedding[graph.oppositeArc(pp)] = n; |
---|
1904 | |
---|
1905 | embedding[graph.oppositeArc(n)] = |
---|
1906 | embedding[graph.oppositeArc(e)]; |
---|
1907 | embedding[graph.oppositeArc(e)] = |
---|
1908 | graph.oppositeArc(n); |
---|
1909 | |
---|
1910 | p = n; |
---|
1911 | e = embedding[graph.oppositeArc(n)]; |
---|
1912 | } else { |
---|
1913 | visited.set(graph.source(e), true); |
---|
1914 | pp = p; |
---|
1915 | p = e; |
---|
1916 | e = embedding[graph.oppositeArc(e)]; |
---|
1917 | } |
---|
1918 | } |
---|
1919 | visited.setAll(false); |
---|
1920 | } |
---|
1921 | } |
---|
1922 | |
---|
1923 | |
---|
1924 | template <typename Graph, typename EmbeddingMap> |
---|
1925 | void makeMaxPlanar(Graph& graph, EmbeddingMap& embedding) { |
---|
1926 | |
---|
1927 | typename Graph::template NodeMap<int> degree(graph); |
---|
1928 | |
---|
1929 | for (typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
---|
1930 | degree[n] = countIncEdges(graph, n); |
---|
1931 | } |
---|
1932 | |
---|
1933 | typename Graph::template ArcMap<bool> processed(graph); |
---|
1934 | IterableBoolMap<Graph, typename Graph::Node> visited(graph, false); |
---|
1935 | |
---|
1936 | std::vector<typename Graph::Arc> arcs; |
---|
1937 | for (typename Graph::ArcIt e(graph); e != INVALID; ++e) { |
---|
1938 | arcs.push_back(e); |
---|
1939 | } |
---|
1940 | |
---|
1941 | for (int i = 0; i < int(arcs.size()); ++i) { |
---|
1942 | typename Graph::Arc e = arcs[i]; |
---|
1943 | |
---|
1944 | if (processed[e]) continue; |
---|
1945 | processed[e] = true; |
---|
1946 | |
---|
1947 | typename Graph::Arc mine = e; |
---|
1948 | int mind = degree[graph.source(e)]; |
---|
1949 | |
---|
1950 | int face_size = 1; |
---|
1951 | |
---|
1952 | typename Graph::Arc l = e; |
---|
1953 | e = embedding[graph.oppositeArc(e)]; |
---|
1954 | while (l != e) { |
---|
1955 | processed[e] = true; |
---|
1956 | |
---|
1957 | ++face_size; |
---|
1958 | |
---|
1959 | if (degree[graph.source(e)] < mind) { |
---|
1960 | mine = e; |
---|
1961 | mind = degree[graph.source(e)]; |
---|
1962 | } |
---|
1963 | |
---|
1964 | e = embedding[graph.oppositeArc(e)]; |
---|
1965 | } |
---|
1966 | |
---|
1967 | if (face_size < 4) { |
---|
1968 | continue; |
---|
1969 | } |
---|
1970 | |
---|
1971 | typename Graph::Node s = graph.source(mine); |
---|
1972 | for (typename Graph::OutArcIt e(graph, s); e != INVALID; ++e) { |
---|
1973 | visited.set(graph.target(e), true); |
---|
1974 | } |
---|
1975 | |
---|
1976 | typename Graph::Arc oppe = INVALID; |
---|
1977 | |
---|
1978 | e = embedding[graph.oppositeArc(mine)]; |
---|
1979 | e = embedding[graph.oppositeArc(e)]; |
---|
1980 | while (graph.target(e) != s) { |
---|
1981 | if (visited[graph.source(e)]) { |
---|
1982 | oppe = e; |
---|
1983 | break; |
---|
1984 | } |
---|
1985 | e = embedding[graph.oppositeArc(e)]; |
---|
1986 | } |
---|
1987 | visited.setAll(false); |
---|
1988 | |
---|
1989 | if (oppe == INVALID) { |
---|
1990 | |
---|
1991 | e = embedding[graph.oppositeArc(mine)]; |
---|
1992 | typename Graph::Arc pn = mine, p = e; |
---|
1993 | |
---|
1994 | e = embedding[graph.oppositeArc(e)]; |
---|
1995 | while (graph.target(e) != s) { |
---|
1996 | typename Graph::Arc n = |
---|
1997 | graph.direct(graph.addEdge(s, graph.source(e)), true); |
---|
1998 | |
---|
1999 | embedding[n] = pn; |
---|
2000 | embedding[graph.oppositeArc(n)] = e; |
---|
2001 | embedding[graph.oppositeArc(p)] = graph.oppositeArc(n); |
---|
2002 | |
---|
2003 | pn = n; |
---|
2004 | |
---|
2005 | p = e; |
---|
2006 | e = embedding[graph.oppositeArc(e)]; |
---|
2007 | } |
---|
2008 | |
---|
2009 | embedding[graph.oppositeArc(e)] = pn; |
---|
2010 | |
---|
2011 | } else { |
---|
2012 | |
---|
2013 | mine = embedding[graph.oppositeArc(mine)]; |
---|
2014 | s = graph.source(mine); |
---|
2015 | oppe = embedding[graph.oppositeArc(oppe)]; |
---|
2016 | typename Graph::Node t = graph.source(oppe); |
---|
2017 | |
---|
2018 | typename Graph::Arc ce = graph.direct(graph.addEdge(s, t), true); |
---|
2019 | embedding[ce] = mine; |
---|
2020 | embedding[graph.oppositeArc(ce)] = oppe; |
---|
2021 | |
---|
2022 | typename Graph::Arc pn = ce, p = oppe; |
---|
2023 | e = embedding[graph.oppositeArc(oppe)]; |
---|
2024 | while (graph.target(e) != s) { |
---|
2025 | typename Graph::Arc n = |
---|
2026 | graph.direct(graph.addEdge(s, graph.source(e)), true); |
---|
2027 | |
---|
2028 | embedding[n] = pn; |
---|
2029 | embedding[graph.oppositeArc(n)] = e; |
---|
2030 | embedding[graph.oppositeArc(p)] = graph.oppositeArc(n); |
---|
2031 | |
---|
2032 | pn = n; |
---|
2033 | |
---|
2034 | p = e; |
---|
2035 | e = embedding[graph.oppositeArc(e)]; |
---|
2036 | |
---|
2037 | } |
---|
2038 | embedding[graph.oppositeArc(e)] = pn; |
---|
2039 | |
---|
2040 | pn = graph.oppositeArc(ce), p = mine; |
---|
2041 | e = embedding[graph.oppositeArc(mine)]; |
---|
2042 | while (graph.target(e) != t) { |
---|
2043 | typename Graph::Arc n = |
---|
2044 | graph.direct(graph.addEdge(t, graph.source(e)), true); |
---|
2045 | |
---|
2046 | embedding[n] = pn; |
---|
2047 | embedding[graph.oppositeArc(n)] = e; |
---|
2048 | embedding[graph.oppositeArc(p)] = graph.oppositeArc(n); |
---|
2049 | |
---|
2050 | pn = n; |
---|
2051 | |
---|
2052 | p = e; |
---|
2053 | e = embedding[graph.oppositeArc(e)]; |
---|
2054 | |
---|
2055 | } |
---|
2056 | embedding[graph.oppositeArc(e)] = pn; |
---|
2057 | } |
---|
2058 | } |
---|
2059 | } |
---|
2060 | |
---|
2061 | } |
---|
2062 | |
---|
2063 | /// \ingroup planar |
---|
2064 | /// |
---|
2065 | /// \brief Schnyder's planar drawing algorithm |
---|
2066 | /// |
---|
2067 | /// The planar drawing algorithm calculates positions for the nodes |
---|
2068 | /// in the plane. These coordinates satisfy that if the edges are |
---|
2069 | /// represented with straight lines, then they will not intersect |
---|
2070 | /// each other. |
---|
2071 | /// |
---|
2072 | /// Scnyder's algorithm embeds the graph on an \c (n-2)x(n-2) size grid, |
---|
2073 | /// i.e. each node will be located in the \c [0..n-2]x[0..n-2] square. |
---|
2074 | /// The time complexity of the algorithm is O(n). |
---|
2075 | /// |
---|
2076 | /// \see PlanarEmbedding |
---|
2077 | template <typename Graph> |
---|
2078 | class PlanarDrawing { |
---|
2079 | public: |
---|
2080 | |
---|
2081 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
2082 | |
---|
2083 | /// \brief The point type for storing coordinates |
---|
2084 | typedef dim2::Point<int> Point; |
---|
2085 | /// \brief The map type for storing the coordinates of the nodes |
---|
2086 | typedef typename Graph::template NodeMap<Point> PointMap; |
---|
2087 | |
---|
2088 | |
---|
2089 | /// \brief Constructor |
---|
2090 | /// |
---|
2091 | /// Constructor |
---|
2092 | /// \pre The graph must be simple, i.e. it should not |
---|
2093 | /// contain parallel or loop arcs. |
---|
2094 | PlanarDrawing(const Graph& graph) |
---|
2095 | : _graph(graph), _point_map(graph) {} |
---|
2096 | |
---|
2097 | private: |
---|
2098 | |
---|
2099 | template <typename AuxGraph, typename AuxEmbeddingMap> |
---|
2100 | void drawing(const AuxGraph& graph, |
---|
2101 | const AuxEmbeddingMap& next, |
---|
2102 | PointMap& point_map) { |
---|
2103 | TEMPLATE_GRAPH_TYPEDEFS(AuxGraph); |
---|
2104 | |
---|
2105 | typename AuxGraph::template ArcMap<Arc> prev(graph); |
---|
2106 | |
---|
2107 | for (NodeIt n(graph); n != INVALID; ++n) { |
---|
2108 | Arc e = OutArcIt(graph, n); |
---|
2109 | |
---|
2110 | Arc p = e, l = e; |
---|
2111 | |
---|
2112 | e = next[e]; |
---|
2113 | while (e != l) { |
---|
2114 | prev[e] = p; |
---|
2115 | p = e; |
---|
2116 | e = next[e]; |
---|
2117 | } |
---|
2118 | prev[e] = p; |
---|
2119 | } |
---|
2120 | |
---|
2121 | Node anode, bnode, cnode; |
---|
2122 | |
---|
2123 | { |
---|
2124 | Arc e = ArcIt(graph); |
---|
2125 | anode = graph.source(e); |
---|
2126 | bnode = graph.target(e); |
---|
2127 | cnode = graph.target(next[graph.oppositeArc(e)]); |
---|
2128 | } |
---|
2129 | |
---|
2130 | IterableBoolMap<AuxGraph, Node> proper(graph, false); |
---|
2131 | typename AuxGraph::template NodeMap<int> conn(graph, -1); |
---|
2132 | |
---|
2133 | conn[anode] = conn[bnode] = -2; |
---|
2134 | { |
---|
2135 | for (OutArcIt e(graph, anode); e != INVALID; ++e) { |
---|
2136 | Node m = graph.target(e); |
---|
2137 | if (conn[m] == -1) { |
---|
2138 | conn[m] = 1; |
---|
2139 | } |
---|
2140 | } |
---|
2141 | conn[cnode] = 2; |
---|
2142 | |
---|
2143 | for (OutArcIt e(graph, bnode); e != INVALID; ++e) { |
---|
2144 | Node m = graph.target(e); |
---|
2145 | if (conn[m] == -1) { |
---|
2146 | conn[m] = 1; |
---|
2147 | } else if (conn[m] != -2) { |
---|
2148 | conn[m] += 1; |
---|
2149 | Arc pe = graph.oppositeArc(e); |
---|
2150 | if (conn[graph.target(next[pe])] == -2) { |
---|
2151 | conn[m] -= 1; |
---|
2152 | } |
---|
2153 | if (conn[graph.target(prev[pe])] == -2) { |
---|
2154 | conn[m] -= 1; |
---|
2155 | } |
---|
2156 | |
---|
2157 | proper.set(m, conn[m] == 1); |
---|
2158 | } |
---|
2159 | } |
---|
2160 | } |
---|
2161 | |
---|
2162 | |
---|
2163 | typename AuxGraph::template ArcMap<int> angle(graph, -1); |
---|
2164 | |
---|
2165 | while (proper.trueNum() != 0) { |
---|
2166 | Node n = typename IterableBoolMap<AuxGraph, Node>::TrueIt(proper); |
---|
2167 | proper.set(n, false); |
---|
2168 | conn[n] = -2; |
---|
2169 | |
---|
2170 | for (OutArcIt e(graph, n); e != INVALID; ++e) { |
---|
2171 | Node m = graph.target(e); |
---|
2172 | if (conn[m] == -1) { |
---|
2173 | conn[m] = 1; |
---|
2174 | } else if (conn[m] != -2) { |
---|
2175 | conn[m] += 1; |
---|
2176 | Arc pe = graph.oppositeArc(e); |
---|
2177 | if (conn[graph.target(next[pe])] == -2) { |
---|
2178 | conn[m] -= 1; |
---|
2179 | } |
---|
2180 | if (conn[graph.target(prev[pe])] == -2) { |
---|
2181 | conn[m] -= 1; |
---|
2182 | } |
---|
2183 | |
---|
2184 | proper.set(m, conn[m] == 1); |
---|
2185 | } |
---|
2186 | } |
---|
2187 | |
---|
2188 | { |
---|
2189 | Arc e = OutArcIt(graph, n); |
---|
2190 | Arc p = e, l = e; |
---|
2191 | |
---|
2192 | e = next[e]; |
---|
2193 | while (e != l) { |
---|
2194 | |
---|
2195 | if (conn[graph.target(e)] == -2 && conn[graph.target(p)] == -2) { |
---|
2196 | Arc f = e; |
---|
2197 | angle[f] = 0; |
---|
2198 | f = next[graph.oppositeArc(f)]; |
---|
2199 | angle[f] = 1; |
---|
2200 | f = next[graph.oppositeArc(f)]; |
---|
2201 | angle[f] = 2; |
---|
2202 | } |
---|
2203 | |
---|
2204 | p = e; |
---|
2205 | e = next[e]; |
---|
2206 | } |
---|
2207 | |
---|
2208 | if (conn[graph.target(e)] == -2 && conn[graph.target(p)] == -2) { |
---|
2209 | Arc f = e; |
---|
2210 | angle[f] = 0; |
---|
2211 | f = next[graph.oppositeArc(f)]; |
---|
2212 | angle[f] = 1; |
---|
2213 | f = next[graph.oppositeArc(f)]; |
---|
2214 | angle[f] = 2; |
---|
2215 | } |
---|
2216 | } |
---|
2217 | } |
---|
2218 | |
---|
2219 | typename AuxGraph::template NodeMap<Node> apred(graph, INVALID); |
---|
2220 | typename AuxGraph::template NodeMap<Node> bpred(graph, INVALID); |
---|
2221 | typename AuxGraph::template NodeMap<Node> cpred(graph, INVALID); |
---|
2222 | |
---|
2223 | typename AuxGraph::template NodeMap<int> apredid(graph, -1); |
---|
2224 | typename AuxGraph::template NodeMap<int> bpredid(graph, -1); |
---|
2225 | typename AuxGraph::template NodeMap<int> cpredid(graph, -1); |
---|
2226 | |
---|
2227 | for (ArcIt e(graph); e != INVALID; ++e) { |
---|
2228 | if (angle[e] == angle[next[e]]) { |
---|
2229 | switch (angle[e]) { |
---|
2230 | case 2: |
---|
2231 | apred[graph.target(e)] = graph.source(e); |
---|
2232 | apredid[graph.target(e)] = graph.id(graph.source(e)); |
---|
2233 | break; |
---|
2234 | case 1: |
---|
2235 | bpred[graph.target(e)] = graph.source(e); |
---|
2236 | bpredid[graph.target(e)] = graph.id(graph.source(e)); |
---|
2237 | break; |
---|
2238 | case 0: |
---|
2239 | cpred[graph.target(e)] = graph.source(e); |
---|
2240 | cpredid[graph.target(e)] = graph.id(graph.source(e)); |
---|
2241 | break; |
---|
2242 | } |
---|
2243 | } |
---|
2244 | } |
---|
2245 | |
---|
2246 | cpred[anode] = INVALID; |
---|
2247 | cpred[bnode] = INVALID; |
---|
2248 | |
---|
2249 | std::vector<Node> aorder, border, corder; |
---|
2250 | |
---|
2251 | { |
---|
2252 | typename AuxGraph::template NodeMap<bool> processed(graph, false); |
---|
2253 | std::vector<Node> st; |
---|
2254 | for (NodeIt n(graph); n != INVALID; ++n) { |
---|
2255 | if (!processed[n] && n != bnode && n != cnode) { |
---|
2256 | st.push_back(n); |
---|
2257 | processed[n] = true; |
---|
2258 | Node m = apred[n]; |
---|
2259 | while (m != INVALID && !processed[m]) { |
---|
2260 | st.push_back(m); |
---|
2261 | processed[m] = true; |
---|
2262 | m = apred[m]; |
---|
2263 | } |
---|
2264 | while (!st.empty()) { |
---|
2265 | aorder.push_back(st.back()); |
---|
2266 | st.pop_back(); |
---|
2267 | } |
---|
2268 | } |
---|
2269 | } |
---|
2270 | } |
---|
2271 | |
---|
2272 | { |
---|
2273 | typename AuxGraph::template NodeMap<bool> processed(graph, false); |
---|
2274 | std::vector<Node> st; |
---|
2275 | for (NodeIt n(graph); n != INVALID; ++n) { |
---|
2276 | if (!processed[n] && n != cnode && n != anode) { |
---|
2277 | st.push_back(n); |
---|
2278 | processed[n] = true; |
---|
2279 | Node m = bpred[n]; |
---|
2280 | while (m != INVALID && !processed[m]) { |
---|
2281 | st.push_back(m); |
---|
2282 | processed[m] = true; |
---|
2283 | m = bpred[m]; |
---|
2284 | } |
---|
2285 | while (!st.empty()) { |
---|
2286 | border.push_back(st.back()); |
---|
2287 | st.pop_back(); |
---|
2288 | } |
---|
2289 | } |
---|
2290 | } |
---|
2291 | } |
---|
2292 | |
---|
2293 | { |
---|
2294 | typename AuxGraph::template NodeMap<bool> processed(graph, false); |
---|
2295 | std::vector<Node> st; |
---|
2296 | for (NodeIt n(graph); n != INVALID; ++n) { |
---|
2297 | if (!processed[n] && n != anode && n != bnode) { |
---|
2298 | st.push_back(n); |
---|
2299 | processed[n] = true; |
---|
2300 | Node m = cpred[n]; |
---|
2301 | while (m != INVALID && !processed[m]) { |
---|
2302 | st.push_back(m); |
---|
2303 | processed[m] = true; |
---|
2304 | m = cpred[m]; |
---|
2305 | } |
---|
2306 | while (!st.empty()) { |
---|
2307 | corder.push_back(st.back()); |
---|
2308 | st.pop_back(); |
---|
2309 | } |
---|
2310 | } |
---|
2311 | } |
---|
2312 | } |
---|
2313 | |
---|
2314 | typename AuxGraph::template NodeMap<int> atree(graph, 0); |
---|
2315 | for (int i = aorder.size() - 1; i >= 0; --i) { |
---|
2316 | Node n = aorder[i]; |
---|
2317 | atree[n] = 1; |
---|
2318 | for (OutArcIt e(graph, n); e != INVALID; ++e) { |
---|
2319 | if (apred[graph.target(e)] == n) { |
---|
2320 | atree[n] += atree[graph.target(e)]; |
---|
2321 | } |
---|
2322 | } |
---|
2323 | } |
---|
2324 | |
---|
2325 | typename AuxGraph::template NodeMap<int> btree(graph, 0); |
---|
2326 | for (int i = border.size() - 1; i >= 0; --i) { |
---|
2327 | Node n = border[i]; |
---|
2328 | btree[n] = 1; |
---|
2329 | for (OutArcIt e(graph, n); e != INVALID; ++e) { |
---|
2330 | if (bpred[graph.target(e)] == n) { |
---|
2331 | btree[n] += btree[graph.target(e)]; |
---|
2332 | } |
---|
2333 | } |
---|
2334 | } |
---|
2335 | |
---|
2336 | typename AuxGraph::template NodeMap<int> apath(graph, 0); |
---|
2337 | apath[bnode] = apath[cnode] = 1; |
---|
2338 | typename AuxGraph::template NodeMap<int> apath_btree(graph, 0); |
---|
2339 | apath_btree[bnode] = btree[bnode]; |
---|
2340 | for (int i = 1; i < int(aorder.size()); ++i) { |
---|
2341 | Node n = aorder[i]; |
---|
2342 | apath[n] = apath[apred[n]] + 1; |
---|
2343 | apath_btree[n] = btree[n] + apath_btree[apred[n]]; |
---|
2344 | } |
---|
2345 | |
---|
2346 | typename AuxGraph::template NodeMap<int> bpath_atree(graph, 0); |
---|
2347 | bpath_atree[anode] = atree[anode]; |
---|
2348 | for (int i = 1; i < int(border.size()); ++i) { |
---|
2349 | Node n = border[i]; |
---|
2350 | bpath_atree[n] = atree[n] + bpath_atree[bpred[n]]; |
---|
2351 | } |
---|
2352 | |
---|
2353 | typename AuxGraph::template NodeMap<int> cpath(graph, 0); |
---|
2354 | cpath[anode] = cpath[bnode] = 1; |
---|
2355 | typename AuxGraph::template NodeMap<int> cpath_atree(graph, 0); |
---|
2356 | cpath_atree[anode] = atree[anode]; |
---|
2357 | typename AuxGraph::template NodeMap<int> cpath_btree(graph, 0); |
---|
2358 | cpath_btree[bnode] = btree[bnode]; |
---|
2359 | for (int i = 1; i < int(corder.size()); ++i) { |
---|
2360 | Node n = corder[i]; |
---|
2361 | cpath[n] = cpath[cpred[n]] + 1; |
---|
2362 | cpath_atree[n] = atree[n] + cpath_atree[cpred[n]]; |
---|
2363 | cpath_btree[n] = btree[n] + cpath_btree[cpred[n]]; |
---|
2364 | } |
---|
2365 | |
---|
2366 | typename AuxGraph::template NodeMap<int> third(graph); |
---|
2367 | for (NodeIt n(graph); n != INVALID; ++n) { |
---|
2368 | point_map[n].x = |
---|
2369 | bpath_atree[n] + cpath_atree[n] - atree[n] - cpath[n] + 1; |
---|
2370 | point_map[n].y = |
---|
2371 | cpath_btree[n] + apath_btree[n] - btree[n] - apath[n] + 1; |
---|
2372 | } |
---|
2373 | |
---|
2374 | } |
---|
2375 | |
---|
2376 | public: |
---|
2377 | |
---|
2378 | /// \brief Calculate the node positions |
---|
2379 | /// |
---|
2380 | /// This function calculates the node positions on the plane. |
---|
2381 | /// \return \c true if the graph is planar. |
---|
2382 | bool run() { |
---|
2383 | PlanarEmbedding<Graph> pe(_graph); |
---|
2384 | if (!pe.run()) return false; |
---|
2385 | |
---|
2386 | run(pe); |
---|
2387 | return true; |
---|
2388 | } |
---|
2389 | |
---|
2390 | /// \brief Calculate the node positions according to a |
---|
2391 | /// combinatorical embedding |
---|
2392 | /// |
---|
2393 | /// This function calculates the node positions on the plane. |
---|
2394 | /// The given \c embedding map should contain a valid combinatorical |
---|
2395 | /// embedding, i.e. a valid cyclic order of the arcs. |
---|
2396 | /// It can be computed using PlanarEmbedding. |
---|
2397 | template <typename EmbeddingMap> |
---|
2398 | void run(const EmbeddingMap& embedding) { |
---|
2399 | typedef SmartEdgeSet<Graph> AuxGraph; |
---|
2400 | |
---|
2401 | if (3 * countNodes(_graph) - 6 == countEdges(_graph)) { |
---|
2402 | drawing(_graph, embedding, _point_map); |
---|
2403 | return; |
---|
2404 | } |
---|
2405 | |
---|
2406 | AuxGraph aux_graph(_graph); |
---|
2407 | typename AuxGraph::template ArcMap<typename AuxGraph::Arc> |
---|
2408 | aux_embedding(aux_graph); |
---|
2409 | |
---|
2410 | { |
---|
2411 | |
---|
2412 | typename Graph::template EdgeMap<typename AuxGraph::Edge> |
---|
2413 | ref(_graph); |
---|
2414 | |
---|
2415 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
2416 | ref[e] = aux_graph.addEdge(_graph.u(e), _graph.v(e)); |
---|
2417 | } |
---|
2418 | |
---|
2419 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
2420 | Arc ee = embedding[_graph.direct(e, true)]; |
---|
2421 | aux_embedding[aux_graph.direct(ref[e], true)] = |
---|
2422 | aux_graph.direct(ref[ee], _graph.direction(ee)); |
---|
2423 | ee = embedding[_graph.direct(e, false)]; |
---|
2424 | aux_embedding[aux_graph.direct(ref[e], false)] = |
---|
2425 | aux_graph.direct(ref[ee], _graph.direction(ee)); |
---|
2426 | } |
---|
2427 | } |
---|
2428 | _planarity_bits::makeConnected(aux_graph, aux_embedding); |
---|
2429 | _planarity_bits::makeBiNodeConnected(aux_graph, aux_embedding); |
---|
2430 | _planarity_bits::makeMaxPlanar(aux_graph, aux_embedding); |
---|
2431 | drawing(aux_graph, aux_embedding, _point_map); |
---|
2432 | } |
---|
2433 | |
---|
2434 | /// \brief The coordinate of the given node |
---|
2435 | /// |
---|
2436 | /// This function returns the coordinate of the given node. |
---|
2437 | Point operator[](const Node& node) const { |
---|
2438 | return _point_map[node]; |
---|
2439 | } |
---|
2440 | |
---|
2441 | /// \brief Return the grid embedding in a node map |
---|
2442 | /// |
---|
2443 | /// This function returns the grid embedding in a node map of |
---|
2444 | /// \c dim2::Point<int> coordinates. |
---|
2445 | const PointMap& coords() const { |
---|
2446 | return _point_map; |
---|
2447 | } |
---|
2448 | |
---|
2449 | private: |
---|
2450 | |
---|
2451 | const Graph& _graph; |
---|
2452 | PointMap _point_map; |
---|
2453 | |
---|
2454 | }; |
---|
2455 | |
---|
2456 | namespace _planarity_bits { |
---|
2457 | |
---|
2458 | template <typename ColorMap> |
---|
2459 | class KempeFilter { |
---|
2460 | public: |
---|
2461 | typedef typename ColorMap::Key Key; |
---|
2462 | typedef bool Value; |
---|
2463 | |
---|
2464 | KempeFilter(const ColorMap& color_map, |
---|
2465 | const typename ColorMap::Value& first, |
---|
2466 | const typename ColorMap::Value& second) |
---|
2467 | : _color_map(color_map), _first(first), _second(second) {} |
---|
2468 | |
---|
2469 | Value operator[](const Key& key) const { |
---|
2470 | return _color_map[key] == _first || _color_map[key] == _second; |
---|
2471 | } |
---|
2472 | |
---|
2473 | private: |
---|
2474 | const ColorMap& _color_map; |
---|
2475 | typename ColorMap::Value _first, _second; |
---|
2476 | }; |
---|
2477 | } |
---|
2478 | |
---|
2479 | /// \ingroup planar |
---|
2480 | /// |
---|
2481 | /// \brief Coloring planar graphs |
---|
2482 | /// |
---|
2483 | /// The graph coloring problem is the coloring of the graph nodes |
---|
2484 | /// so that there are no adjacent nodes with the same color. The |
---|
2485 | /// planar graphs can always be colored with four colors, which is |
---|
2486 | /// proved by Appel and Haken. Their proofs provide a quadratic |
---|
2487 | /// time algorithm for four coloring, but it could not be used to |
---|
2488 | /// implement an efficient algorithm. The five and six coloring can be |
---|
2489 | /// made in linear time, but in this class, the five coloring has |
---|
2490 | /// quadratic worst case time complexity. The two coloring (if |
---|
2491 | /// possible) is solvable with a graph search algorithm and it is |
---|
2492 | /// implemented in \ref bipartitePartitions() function in LEMON. To |
---|
2493 | /// decide whether a planar graph is three colorable is NP-complete. |
---|
2494 | /// |
---|
2495 | /// This class contains member functions for calculate colorings |
---|
2496 | /// with five and six colors. The six coloring algorithm is a simple |
---|
2497 | /// greedy coloring on the backward minimum outgoing order of nodes. |
---|
2498 | /// This order can be computed by selecting the node with least |
---|
2499 | /// outgoing arcs to unprocessed nodes in each phase. This order |
---|
2500 | /// guarantees that when a node is chosen for coloring it has at |
---|
2501 | /// most five already colored adjacents. The five coloring algorithm |
---|
2502 | /// use the same method, but if the greedy approach fails to color |
---|
2503 | /// with five colors, i.e. the node has five already different |
---|
2504 | /// colored neighbours, it swaps the colors in one of the connected |
---|
2505 | /// two colored sets with the Kempe recoloring method. |
---|
2506 | template <typename Graph> |
---|
2507 | class PlanarColoring { |
---|
2508 | public: |
---|
2509 | |
---|
2510 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
2511 | |
---|
2512 | /// \brief The map type for storing color indices |
---|
2513 | typedef typename Graph::template NodeMap<int> IndexMap; |
---|
2514 | /// \brief The map type for storing colors |
---|
2515 | /// |
---|
2516 | /// The map type for storing colors. |
---|
2517 | /// \see Palette, Color |
---|
2518 | typedef ComposeMap<Palette, IndexMap> ColorMap; |
---|
2519 | |
---|
2520 | /// \brief Constructor |
---|
2521 | /// |
---|
2522 | /// Constructor. |
---|
2523 | /// \pre The graph must be simple, i.e. it should not |
---|
2524 | /// contain parallel or loop arcs. |
---|
2525 | PlanarColoring(const Graph& graph) |
---|
2526 | : _graph(graph), _color_map(graph), _palette(0) { |
---|
2527 | _palette.add(Color(1,0,0)); |
---|
2528 | _palette.add(Color(0,1,0)); |
---|
2529 | _palette.add(Color(0,0,1)); |
---|
2530 | _palette.add(Color(1,1,0)); |
---|
2531 | _palette.add(Color(1,0,1)); |
---|
2532 | _palette.add(Color(0,1,1)); |
---|
2533 | } |
---|
2534 | |
---|
2535 | /// \brief Return the node map of color indices |
---|
2536 | /// |
---|
2537 | /// This function returns the node map of color indices. The values are |
---|
2538 | /// in the range \c [0..4] or \c [0..5] according to the coloring method. |
---|
2539 | IndexMap colorIndexMap() const { |
---|
2540 | return _color_map; |
---|
2541 | } |
---|
2542 | |
---|
2543 | /// \brief Return the node map of colors |
---|
2544 | /// |
---|
2545 | /// This function returns the node map of colors. The values are among |
---|
2546 | /// five or six distinct \ref lemon::Color "colors". |
---|
2547 | ColorMap colorMap() const { |
---|
2548 | return composeMap(_palette, _color_map); |
---|
2549 | } |
---|
2550 | |
---|
2551 | /// \brief Return the color index of the node |
---|
2552 | /// |
---|
2553 | /// This function returns the color index of the given node. The value is |
---|
2554 | /// in the range \c [0..4] or \c [0..5] according to the coloring method. |
---|
2555 | int colorIndex(const Node& node) const { |
---|
2556 | return _color_map[node]; |
---|
2557 | } |
---|
2558 | |
---|
2559 | /// \brief Return the color of the node |
---|
2560 | /// |
---|
2561 | /// This function returns the color of the given node. The value is among |
---|
2562 | /// five or six distinct \ref lemon::Color "colors". |
---|
2563 | Color color(const Node& node) const { |
---|
2564 | return _palette[_color_map[node]]; |
---|
2565 | } |
---|
2566 | |
---|
2567 | |
---|
2568 | /// \brief Calculate a coloring with at most six colors |
---|
2569 | /// |
---|
2570 | /// This function calculates a coloring with at most six colors. The time |
---|
2571 | /// complexity of this variant is linear in the size of the graph. |
---|
2572 | /// \return \c true if the algorithm could color the graph with six colors. |
---|
2573 | /// If the algorithm fails, then the graph is not planar. |
---|
2574 | /// \note This function can return \c true if the graph is not |
---|
2575 | /// planar, but it can be colored with at most six colors. |
---|
2576 | bool runSixColoring() { |
---|
2577 | |
---|
2578 | typename Graph::template NodeMap<int> heap_index(_graph, -1); |
---|
2579 | BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index); |
---|
2580 | |
---|
2581 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
2582 | _color_map[n] = -2; |
---|
2583 | heap.push(n, countOutArcs(_graph, n)); |
---|
2584 | } |
---|
2585 | |
---|
2586 | std::vector<Node> order; |
---|
2587 | |
---|
2588 | while (!heap.empty()) { |
---|
2589 | Node n = heap.top(); |
---|
2590 | heap.pop(); |
---|
2591 | _color_map[n] = -1; |
---|
2592 | order.push_back(n); |
---|
2593 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
2594 | Node t = _graph.runningNode(e); |
---|
2595 | if (_color_map[t] == -2) { |
---|
2596 | heap.decrease(t, heap[t] - 1); |
---|
2597 | } |
---|
2598 | } |
---|
2599 | } |
---|
2600 | |
---|
2601 | for (int i = order.size() - 1; i >= 0; --i) { |
---|
2602 | std::vector<bool> forbidden(6, false); |
---|
2603 | for (OutArcIt e(_graph, order[i]); e != INVALID; ++e) { |
---|
2604 | Node t = _graph.runningNode(e); |
---|
2605 | if (_color_map[t] != -1) { |
---|
2606 | forbidden[_color_map[t]] = true; |
---|
2607 | } |
---|
2608 | } |
---|
2609 | for (int k = 0; k < 6; ++k) { |
---|
2610 | if (!forbidden[k]) { |
---|
2611 | _color_map[order[i]] = k; |
---|
2612 | break; |
---|
2613 | } |
---|
2614 | } |
---|
2615 | if (_color_map[order[i]] == -1) { |
---|
2616 | return false; |
---|
2617 | } |
---|
2618 | } |
---|
2619 | return true; |
---|
2620 | } |
---|
2621 | |
---|
2622 | private: |
---|
2623 | |
---|
2624 | bool recolor(const Node& u, const Node& v) { |
---|
2625 | int ucolor = _color_map[u]; |
---|
2626 | int vcolor = _color_map[v]; |
---|
2627 | typedef _planarity_bits::KempeFilter<IndexMap> KempeFilter; |
---|
2628 | KempeFilter filter(_color_map, ucolor, vcolor); |
---|
2629 | |
---|
2630 | typedef FilterNodes<const Graph, const KempeFilter> KempeGraph; |
---|
2631 | KempeGraph kempe_graph(_graph, filter); |
---|
2632 | |
---|
2633 | std::vector<Node> comp; |
---|
2634 | Bfs<KempeGraph> bfs(kempe_graph); |
---|
2635 | bfs.init(); |
---|
2636 | bfs.addSource(u); |
---|
2637 | while (!bfs.emptyQueue()) { |
---|
2638 | Node n = bfs.nextNode(); |
---|
2639 | if (n == v) return false; |
---|
2640 | comp.push_back(n); |
---|
2641 | bfs.processNextNode(); |
---|
2642 | } |
---|
2643 | |
---|
2644 | int scolor = ucolor + vcolor; |
---|
2645 | for (int i = 0; i < static_cast<int>(comp.size()); ++i) { |
---|
2646 | _color_map[comp[i]] = scolor - _color_map[comp[i]]; |
---|
2647 | } |
---|
2648 | |
---|
2649 | return true; |
---|
2650 | } |
---|
2651 | |
---|
2652 | template <typename EmbeddingMap> |
---|
2653 | void kempeRecoloring(const Node& node, const EmbeddingMap& embedding) { |
---|
2654 | std::vector<Node> nodes; |
---|
2655 | nodes.reserve(4); |
---|
2656 | |
---|
2657 | for (Arc e = OutArcIt(_graph, node); e != INVALID; e = embedding[e]) { |
---|
2658 | Node t = _graph.target(e); |
---|
2659 | if (_color_map[t] != -1) { |
---|
2660 | nodes.push_back(t); |
---|
2661 | if (nodes.size() == 4) break; |
---|
2662 | } |
---|
2663 | } |
---|
2664 | |
---|
2665 | int color = _color_map[nodes[0]]; |
---|
2666 | if (recolor(nodes[0], nodes[2])) { |
---|
2667 | _color_map[node] = color; |
---|
2668 | } else { |
---|
2669 | color = _color_map[nodes[1]]; |
---|
2670 | recolor(nodes[1], nodes[3]); |
---|
2671 | _color_map[node] = color; |
---|
2672 | } |
---|
2673 | } |
---|
2674 | |
---|
2675 | public: |
---|
2676 | |
---|
2677 | /// \brief Calculate a coloring with at most five colors |
---|
2678 | /// |
---|
2679 | /// This function calculates a coloring with at most five |
---|
2680 | /// colors. The worst case time complexity of this variant is |
---|
2681 | /// quadratic in the size of the graph. |
---|
2682 | /// \param embedding This map should contain a valid combinatorical |
---|
2683 | /// embedding, i.e. a valid cyclic order of the arcs. |
---|
2684 | /// It can be computed using PlanarEmbedding. |
---|
2685 | template <typename EmbeddingMap> |
---|
2686 | void runFiveColoring(const EmbeddingMap& embedding) { |
---|
2687 | |
---|
2688 | typename Graph::template NodeMap<int> heap_index(_graph, -1); |
---|
2689 | BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index); |
---|
2690 | |
---|
2691 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
2692 | _color_map[n] = -2; |
---|
2693 | heap.push(n, countOutArcs(_graph, n)); |
---|
2694 | } |
---|
2695 | |
---|
2696 | std::vector<Node> order; |
---|
2697 | |
---|
2698 | while (!heap.empty()) { |
---|
2699 | Node n = heap.top(); |
---|
2700 | heap.pop(); |
---|
2701 | _color_map[n] = -1; |
---|
2702 | order.push_back(n); |
---|
2703 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
2704 | Node t = _graph.runningNode(e); |
---|
2705 | if (_color_map[t] == -2) { |
---|
2706 | heap.decrease(t, heap[t] - 1); |
---|
2707 | } |
---|
2708 | } |
---|
2709 | } |
---|
2710 | |
---|
2711 | for (int i = order.size() - 1; i >= 0; --i) { |
---|
2712 | std::vector<bool> forbidden(5, false); |
---|
2713 | for (OutArcIt e(_graph, order[i]); e != INVALID; ++e) { |
---|
2714 | Node t = _graph.runningNode(e); |
---|
2715 | if (_color_map[t] != -1) { |
---|
2716 | forbidden[_color_map[t]] = true; |
---|
2717 | } |
---|
2718 | } |
---|
2719 | for (int k = 0; k < 5; ++k) { |
---|
2720 | if (!forbidden[k]) { |
---|
2721 | _color_map[order[i]] = k; |
---|
2722 | break; |
---|
2723 | } |
---|
2724 | } |
---|
2725 | if (_color_map[order[i]] == -1) { |
---|
2726 | kempeRecoloring(order[i], embedding); |
---|
2727 | } |
---|
2728 | } |
---|
2729 | } |
---|
2730 | |
---|
2731 | /// \brief Calculate a coloring with at most five colors |
---|
2732 | /// |
---|
2733 | /// This function calculates a coloring with at most five |
---|
2734 | /// colors. The worst case time complexity of this variant is |
---|
2735 | /// quadratic in the size of the graph. |
---|
2736 | /// \return \c true if the graph is planar. |
---|
2737 | bool runFiveColoring() { |
---|
2738 | PlanarEmbedding<Graph> pe(_graph); |
---|
2739 | if (!pe.run()) return false; |
---|
2740 | |
---|
2741 | runFiveColoring(pe.embeddingMap()); |
---|
2742 | return true; |
---|
2743 | } |
---|
2744 | |
---|
2745 | private: |
---|
2746 | |
---|
2747 | const Graph& _graph; |
---|
2748 | IndexMap _color_map; |
---|
2749 | Palette _palette; |
---|
2750 | }; |
---|
2751 | |
---|
2752 | } |
---|
2753 | |
---|
2754 | #endif |
---|