[861] | 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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[956] | 5 | * Copyright (C) 2003-2010 |
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[861] | 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 source = _graph.source(arc); |
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| 76 | Node target = _graph.target(arc); |
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| 77 | |
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| 78 | _tree_map[arc] = true; |
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| 79 | _pred_map[target] = arc; |
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| 80 | } |
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| 81 | |
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| 82 | void examine(const Arc& arc) { |
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| 83 | Node source = _graph.source(arc); |
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| 84 | Node target = _graph.target(arc); |
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| 85 | |
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| 86 | if (_order_map[target] < _order_map[source] && !_tree_map[arc]) { |
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| 87 | if (_low_map[source] > _order_map[target]) { |
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| 88 | _low_map[source] = _order_map[target]; |
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| 89 | } |
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| 90 | if (_ancestor_map[source] > _order_map[target]) { |
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| 91 | _ancestor_map[source] = _order_map[target]; |
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| 92 | } |
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| 93 | } |
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| 94 | } |
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| 95 | |
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| 96 | void backtrack(const Arc& arc) { |
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| 97 | Node source = _graph.source(arc); |
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| 98 | Node target = _graph.target(arc); |
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| 99 | |
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| 100 | if (_low_map[source] > _low_map[target]) { |
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| 101 | _low_map[source] = _low_map[target]; |
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| 102 | } |
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| 103 | } |
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| 104 | |
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| 105 | const Graph& _graph; |
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| 106 | PredMap& _pred_map; |
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| 107 | TreeMap& _tree_map; |
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| 108 | OrderMap& _order_map; |
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| 109 | OrderList& _order_list; |
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| 110 | AncestorMap& _ancestor_map; |
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| 111 | LowMap& _low_map; |
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| 112 | }; |
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| 113 | |
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| 114 | template <typename Graph, bool embedding = true> |
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| 115 | struct NodeDataNode { |
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| 116 | int prev, next; |
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| 117 | int visited; |
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| 118 | typename Graph::Arc first; |
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| 119 | bool inverted; |
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| 120 | }; |
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| 121 | |
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| 122 | template <typename Graph> |
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| 123 | struct NodeDataNode<Graph, false> { |
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| 124 | int prev, next; |
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| 125 | int visited; |
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| 126 | }; |
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| 127 | |
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| 128 | template <typename Graph> |
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| 129 | struct ChildListNode { |
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| 130 | typedef typename Graph::Node Node; |
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| 131 | Node first; |
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| 132 | Node prev, next; |
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| 133 | }; |
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| 134 | |
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| 135 | template <typename Graph> |
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| 136 | struct ArcListNode { |
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| 137 | typename Graph::Arc prev, next; |
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| 138 | }; |
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| 139 | |
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[862] | 140 | template <typename Graph> |
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| 141 | class PlanarityChecking { |
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| 142 | private: |
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[956] | 143 | |
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[862] | 144 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
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| 145 | |
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| 146 | const Graph& _graph; |
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| 147 | |
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| 148 | private: |
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[956] | 149 | |
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[862] | 150 | typedef typename Graph::template NodeMap<Arc> PredMap; |
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[956] | 151 | |
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[862] | 152 | typedef typename Graph::template EdgeMap<bool> TreeMap; |
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[956] | 153 | |
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[862] | 154 | typedef typename Graph::template NodeMap<int> OrderMap; |
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| 155 | typedef std::vector<Node> OrderList; |
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| 156 | |
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| 157 | typedef typename Graph::template NodeMap<int> LowMap; |
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| 158 | typedef typename Graph::template NodeMap<int> AncestorMap; |
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| 159 | |
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| 160 | typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode; |
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| 161 | typedef std::vector<NodeDataNode> NodeData; |
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| 162 | |
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| 163 | typedef _planarity_bits::ChildListNode<Graph> ChildListNode; |
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| 164 | typedef typename Graph::template NodeMap<ChildListNode> ChildLists; |
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| 165 | |
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| 166 | typedef typename Graph::template NodeMap<std::list<int> > MergeRoots; |
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| 167 | |
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| 168 | typedef typename Graph::template NodeMap<bool> EmbedArc; |
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| 169 | |
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| 170 | public: |
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| 171 | |
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| 172 | PlanarityChecking(const Graph& graph) : _graph(graph) {} |
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| 173 | |
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| 174 | bool run() { |
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| 175 | typedef _planarity_bits::PlanarityVisitor<Graph> Visitor; |
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| 176 | |
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| 177 | PredMap pred_map(_graph, INVALID); |
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| 178 | TreeMap tree_map(_graph, false); |
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| 179 | |
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| 180 | OrderMap order_map(_graph, -1); |
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| 181 | OrderList order_list; |
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| 182 | |
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| 183 | AncestorMap ancestor_map(_graph, -1); |
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| 184 | LowMap low_map(_graph, -1); |
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| 185 | |
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| 186 | Visitor visitor(_graph, pred_map, tree_map, |
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| 187 | order_map, order_list, ancestor_map, low_map); |
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| 188 | DfsVisit<Graph, Visitor> visit(_graph, visitor); |
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| 189 | visit.run(); |
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| 190 | |
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| 191 | ChildLists child_lists(_graph); |
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| 192 | createChildLists(tree_map, order_map, low_map, child_lists); |
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| 193 | |
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| 194 | NodeData node_data(2 * order_list.size()); |
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| 195 | |
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| 196 | EmbedArc embed_arc(_graph, false); |
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| 197 | |
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| 198 | MergeRoots merge_roots(_graph); |
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| 199 | |
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| 200 | for (int i = order_list.size() - 1; i >= 0; --i) { |
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| 201 | |
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| 202 | Node node = order_list[i]; |
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| 203 | |
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| 204 | Node source = node; |
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| 205 | for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
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| 206 | Node target = _graph.target(e); |
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| 207 | |
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| 208 | if (order_map[source] < order_map[target] && tree_map[e]) { |
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| 209 | initFace(target, node_data, order_map, order_list); |
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| 210 | } |
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| 211 | } |
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| 212 | |
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| 213 | for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
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| 214 | Node target = _graph.target(e); |
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| 215 | |
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| 216 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
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| 217 | embed_arc[target] = true; |
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| 218 | walkUp(target, source, i, pred_map, low_map, |
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| 219 | order_map, order_list, node_data, merge_roots); |
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| 220 | } |
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| 221 | } |
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| 222 | |
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| 223 | for (typename MergeRoots::Value::iterator it = |
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[956] | 224 | merge_roots[node].begin(); |
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[862] | 225 | it != merge_roots[node].end(); ++it) { |
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| 226 | int rn = *it; |
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| 227 | walkDown(rn, i, node_data, order_list, child_lists, |
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| 228 | ancestor_map, low_map, embed_arc, merge_roots); |
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| 229 | } |
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| 230 | merge_roots[node].clear(); |
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| 231 | |
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| 232 | for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
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| 233 | Node target = _graph.target(e); |
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| 234 | |
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| 235 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
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| 236 | if (embed_arc[target]) { |
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| 237 | return false; |
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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 | |
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| 243 | return true; |
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| 244 | } |
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| 245 | |
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| 246 | private: |
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| 247 | |
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| 248 | void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
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| 249 | const LowMap& low_map, ChildLists& child_lists) { |
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| 250 | |
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| 251 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 252 | Node source = n; |
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| 253 | |
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| 254 | std::vector<Node> targets; |
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| 255 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
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| 256 | Node target = _graph.target(e); |
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| 257 | |
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| 258 | if (order_map[source] < order_map[target] && tree_map[e]) { |
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| 259 | targets.push_back(target); |
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| 260 | } |
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| 261 | } |
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| 262 | |
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| 263 | if (targets.size() == 0) { |
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| 264 | child_lists[source].first = INVALID; |
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| 265 | } else if (targets.size() == 1) { |
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| 266 | child_lists[source].first = targets[0]; |
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| 267 | child_lists[targets[0]].prev = INVALID; |
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| 268 | child_lists[targets[0]].next = INVALID; |
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| 269 | } else { |
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| 270 | radixSort(targets.begin(), targets.end(), mapToFunctor(low_map)); |
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| 271 | for (int i = 1; i < int(targets.size()); ++i) { |
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| 272 | child_lists[targets[i]].prev = targets[i - 1]; |
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| 273 | child_lists[targets[i - 1]].next = targets[i]; |
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| 274 | } |
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| 275 | child_lists[targets.back()].next = INVALID; |
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| 276 | child_lists[targets.front()].prev = INVALID; |
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| 277 | child_lists[source].first = targets.front(); |
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| 278 | } |
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| 279 | } |
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| 280 | } |
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| 281 | |
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| 282 | void walkUp(const Node& node, Node root, int rorder, |
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| 283 | const PredMap& pred_map, const LowMap& low_map, |
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| 284 | const OrderMap& order_map, const OrderList& order_list, |
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| 285 | NodeData& node_data, MergeRoots& merge_roots) { |
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| 286 | |
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| 287 | int na, nb; |
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| 288 | bool da, db; |
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| 289 | |
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| 290 | na = nb = order_map[node]; |
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| 291 | da = true; db = false; |
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| 292 | |
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| 293 | while (true) { |
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| 294 | |
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| 295 | if (node_data[na].visited == rorder) break; |
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| 296 | if (node_data[nb].visited == rorder) break; |
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| 297 | |
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| 298 | node_data[na].visited = rorder; |
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| 299 | node_data[nb].visited = rorder; |
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| 300 | |
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| 301 | int rn = -1; |
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| 302 | |
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| 303 | if (na >= int(order_list.size())) { |
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| 304 | rn = na; |
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| 305 | } else if (nb >= int(order_list.size())) { |
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| 306 | rn = nb; |
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| 307 | } |
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| 308 | |
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| 309 | if (rn == -1) { |
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| 310 | int nn; |
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| 311 | |
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| 312 | nn = da ? node_data[na].prev : node_data[na].next; |
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| 313 | da = node_data[nn].prev != na; |
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| 314 | na = nn; |
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| 315 | |
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| 316 | nn = db ? node_data[nb].prev : node_data[nb].next; |
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| 317 | db = node_data[nn].prev != nb; |
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| 318 | nb = nn; |
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| 319 | |
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| 320 | } else { |
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| 321 | |
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| 322 | Node rep = order_list[rn - order_list.size()]; |
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| 323 | Node parent = _graph.source(pred_map[rep]); |
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| 324 | |
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| 325 | if (low_map[rep] < rorder) { |
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| 326 | merge_roots[parent].push_back(rn); |
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| 327 | } else { |
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| 328 | merge_roots[parent].push_front(rn); |
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| 329 | } |
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| 330 | |
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| 331 | if (parent != root) { |
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| 332 | na = nb = order_map[parent]; |
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| 333 | da = true; db = false; |
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| 334 | } else { |
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| 335 | break; |
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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 | |
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| 341 | void walkDown(int rn, int rorder, NodeData& node_data, |
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| 342 | OrderList& order_list, ChildLists& child_lists, |
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| 343 | AncestorMap& ancestor_map, LowMap& low_map, |
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| 344 | EmbedArc& embed_arc, MergeRoots& merge_roots) { |
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| 345 | |
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| 346 | std::vector<std::pair<int, bool> > merge_stack; |
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| 347 | |
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| 348 | for (int di = 0; di < 2; ++di) { |
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| 349 | bool rd = di == 0; |
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| 350 | int pn = rn; |
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| 351 | int n = rd ? node_data[rn].next : node_data[rn].prev; |
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| 352 | |
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| 353 | while (n != rn) { |
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| 354 | |
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| 355 | Node node = order_list[n]; |
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| 356 | |
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| 357 | if (embed_arc[node]) { |
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| 358 | |
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| 359 | // Merging components on the critical path |
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| 360 | while (!merge_stack.empty()) { |
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| 361 | |
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| 362 | // Component root |
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| 363 | int cn = merge_stack.back().first; |
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| 364 | bool cd = merge_stack.back().second; |
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| 365 | merge_stack.pop_back(); |
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| 366 | |
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| 367 | // Parent of component |
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| 368 | int dn = merge_stack.back().first; |
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| 369 | bool dd = merge_stack.back().second; |
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| 370 | merge_stack.pop_back(); |
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| 371 | |
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| 372 | Node parent = order_list[dn]; |
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| 373 | |
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| 374 | // Erasing from merge_roots |
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| 375 | merge_roots[parent].pop_front(); |
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| 376 | |
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| 377 | Node child = order_list[cn - order_list.size()]; |
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| 378 | |
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| 379 | // Erasing from child_lists |
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| 380 | if (child_lists[child].prev != INVALID) { |
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| 381 | child_lists[child_lists[child].prev].next = |
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| 382 | child_lists[child].next; |
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| 383 | } else { |
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| 384 | child_lists[parent].first = child_lists[child].next; |
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| 385 | } |
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| 386 | |
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| 387 | if (child_lists[child].next != INVALID) { |
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| 388 | child_lists[child_lists[child].next].prev = |
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| 389 | child_lists[child].prev; |
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| 390 | } |
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| 391 | |
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| 392 | // Merging external faces |
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| 393 | { |
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| 394 | int en = cn; |
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| 395 | cn = cd ? node_data[cn].prev : node_data[cn].next; |
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| 396 | cd = node_data[cn].next == en; |
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| 397 | |
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| 398 | } |
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| 399 | |
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| 400 | if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
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| 401 | if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
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| 402 | |
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| 403 | } |
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| 404 | |
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| 405 | bool d = pn == node_data[n].prev; |
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| 406 | |
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| 407 | if (node_data[n].prev == node_data[n].next && |
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| 408 | node_data[n].inverted) { |
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| 409 | d = !d; |
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| 410 | } |
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| 411 | |
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| 412 | // Embedding arc into external face |
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| 413 | if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
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| 414 | if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
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| 415 | pn = rn; |
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| 416 | |
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| 417 | embed_arc[order_list[n]] = false; |
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| 418 | } |
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| 419 | |
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| 420 | if (!merge_roots[node].empty()) { |
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| 421 | |
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| 422 | bool d = pn == node_data[n].prev; |
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| 423 | |
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| 424 | merge_stack.push_back(std::make_pair(n, d)); |
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| 425 | |
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| 426 | int rn = merge_roots[node].front(); |
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| 427 | |
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| 428 | int xn = node_data[rn].next; |
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| 429 | Node xnode = order_list[xn]; |
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| 430 | |
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| 431 | int yn = node_data[rn].prev; |
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| 432 | Node ynode = order_list[yn]; |
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| 433 | |
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| 434 | bool rd; |
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[956] | 435 | if (!external(xnode, rorder, child_lists, |
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[862] | 436 | ancestor_map, low_map)) { |
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| 437 | rd = true; |
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| 438 | } else if (!external(ynode, rorder, child_lists, |
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| 439 | ancestor_map, low_map)) { |
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| 440 | rd = false; |
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| 441 | } else if (pertinent(xnode, embed_arc, merge_roots)) { |
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| 442 | rd = true; |
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| 443 | } else { |
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| 444 | rd = false; |
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| 445 | } |
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| 446 | |
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| 447 | merge_stack.push_back(std::make_pair(rn, rd)); |
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| 448 | |
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| 449 | pn = rn; |
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| 450 | n = rd ? xn : yn; |
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| 451 | |
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| 452 | } else if (!external(node, rorder, child_lists, |
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| 453 | ancestor_map, low_map)) { |
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| 454 | int nn = (node_data[n].next != pn ? |
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| 455 | node_data[n].next : node_data[n].prev); |
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| 456 | |
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| 457 | bool nd = n == node_data[nn].prev; |
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| 458 | |
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| 459 | if (nd) node_data[nn].prev = pn; |
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| 460 | else node_data[nn].next = pn; |
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| 461 | |
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| 462 | if (n == node_data[pn].prev) node_data[pn].prev = nn; |
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| 463 | else node_data[pn].next = nn; |
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| 464 | |
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| 465 | node_data[nn].inverted = |
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| 466 | (node_data[nn].prev == node_data[nn].next && nd != rd); |
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| 467 | |
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| 468 | n = nn; |
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| 469 | } |
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| 470 | else break; |
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| 471 | |
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| 472 | } |
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| 473 | |
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| 474 | if (!merge_stack.empty() || n == rn) { |
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| 475 | break; |
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| 476 | } |
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| 477 | } |
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| 478 | } |
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| 479 | |
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| 480 | void initFace(const Node& node, NodeData& node_data, |
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| 481 | const OrderMap& order_map, const OrderList& order_list) { |
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| 482 | int n = order_map[node]; |
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| 483 | int rn = n + order_list.size(); |
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| 484 | |
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| 485 | node_data[n].next = node_data[n].prev = rn; |
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| 486 | node_data[rn].next = node_data[rn].prev = n; |
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| 487 | |
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| 488 | node_data[n].visited = order_list.size(); |
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| 489 | node_data[rn].visited = order_list.size(); |
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| 490 | |
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| 491 | } |
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| 492 | |
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| 493 | bool external(const Node& node, int rorder, |
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| 494 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
| 495 | LowMap& low_map) { |
---|
| 496 | Node child = child_lists[node].first; |
---|
| 497 | |
---|
| 498 | if (child != INVALID) { |
---|
| 499 | if (low_map[child] < rorder) return true; |
---|
| 500 | } |
---|
| 501 | |
---|
| 502 | if (ancestor_map[node] < rorder) return true; |
---|
| 503 | |
---|
| 504 | return false; |
---|
| 505 | } |
---|
| 506 | |
---|
| 507 | bool pertinent(const Node& node, const EmbedArc& embed_arc, |
---|
| 508 | const MergeRoots& merge_roots) { |
---|
| 509 | return !merge_roots[node].empty() || embed_arc[node]; |
---|
| 510 | } |
---|
| 511 | |
---|
| 512 | }; |
---|
| 513 | |
---|
[861] | 514 | } |
---|
| 515 | |
---|
| 516 | /// \ingroup planar |
---|
| 517 | /// |
---|
| 518 | /// \brief Planarity checking of an undirected simple graph |
---|
| 519 | /// |
---|
[862] | 520 | /// This function implements the Boyer-Myrvold algorithm for |
---|
[896] | 521 | /// planarity checking of an undirected simple graph. It is a simplified |
---|
[861] | 522 | /// version of the PlanarEmbedding algorithm class because neither |
---|
[896] | 523 | /// the embedding nor the Kuratowski subdivisons are computed. |
---|
[862] | 524 | template <typename GR> |
---|
| 525 | bool checkPlanarity(const GR& graph) { |
---|
| 526 | _planarity_bits::PlanarityChecking<GR> pc(graph); |
---|
| 527 | return pc.run(); |
---|
| 528 | } |
---|
[861] | 529 | |
---|
| 530 | /// \ingroup planar |
---|
| 531 | /// |
---|
| 532 | /// \brief Planar embedding of an undirected simple graph |
---|
| 533 | /// |
---|
| 534 | /// This class implements the Boyer-Myrvold algorithm for planar |
---|
[896] | 535 | /// embedding of an undirected simple graph. The planar embedding is an |
---|
[861] | 536 | /// ordering of the outgoing edges of the nodes, which is a possible |
---|
| 537 | /// configuration to draw the graph in the plane. If there is not |
---|
[896] | 538 | /// such ordering then the graph contains a K<sub>5</sub> (full graph |
---|
| 539 | /// with 5 nodes) or a K<sub>3,3</sub> (complete bipartite graph on |
---|
| 540 | /// 3 Red and 3 Blue nodes) subdivision. |
---|
[861] | 541 | /// |
---|
| 542 | /// The current implementation calculates either an embedding or a |
---|
[896] | 543 | /// Kuratowski subdivision. The running time of the algorithm is O(n). |
---|
| 544 | /// |
---|
| 545 | /// \see PlanarDrawing, checkPlanarity() |
---|
[861] | 546 | template <typename Graph> |
---|
| 547 | class PlanarEmbedding { |
---|
| 548 | private: |
---|
| 549 | |
---|
| 550 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
| 551 | |
---|
| 552 | const Graph& _graph; |
---|
| 553 | typename Graph::template ArcMap<Arc> _embedding; |
---|
| 554 | |
---|
| 555 | typename Graph::template EdgeMap<bool> _kuratowski; |
---|
| 556 | |
---|
| 557 | private: |
---|
| 558 | |
---|
| 559 | typedef typename Graph::template NodeMap<Arc> PredMap; |
---|
| 560 | |
---|
| 561 | typedef typename Graph::template EdgeMap<bool> TreeMap; |
---|
| 562 | |
---|
| 563 | typedef typename Graph::template NodeMap<int> OrderMap; |
---|
| 564 | typedef std::vector<Node> OrderList; |
---|
| 565 | |
---|
| 566 | typedef typename Graph::template NodeMap<int> LowMap; |
---|
| 567 | typedef typename Graph::template NodeMap<int> AncestorMap; |
---|
| 568 | |
---|
| 569 | typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode; |
---|
| 570 | typedef std::vector<NodeDataNode> NodeData; |
---|
| 571 | |
---|
| 572 | typedef _planarity_bits::ChildListNode<Graph> ChildListNode; |
---|
| 573 | typedef typename Graph::template NodeMap<ChildListNode> ChildLists; |
---|
| 574 | |
---|
| 575 | typedef typename Graph::template NodeMap<std::list<int> > MergeRoots; |
---|
| 576 | |
---|
| 577 | typedef typename Graph::template NodeMap<Arc> EmbedArc; |
---|
| 578 | |
---|
| 579 | typedef _planarity_bits::ArcListNode<Graph> ArcListNode; |
---|
| 580 | typedef typename Graph::template ArcMap<ArcListNode> ArcLists; |
---|
| 581 | |
---|
| 582 | typedef typename Graph::template NodeMap<bool> FlipMap; |
---|
| 583 | |
---|
| 584 | typedef typename Graph::template NodeMap<int> TypeMap; |
---|
| 585 | |
---|
| 586 | enum IsolatorNodeType { |
---|
| 587 | HIGHX = 6, LOWX = 7, |
---|
| 588 | HIGHY = 8, LOWY = 9, |
---|
| 589 | ROOT = 10, PERTINENT = 11, |
---|
| 590 | INTERNAL = 12 |
---|
| 591 | }; |
---|
| 592 | |
---|
| 593 | public: |
---|
| 594 | |
---|
[896] | 595 | /// \brief The map type for storing the embedding |
---|
| 596 | /// |
---|
| 597 | /// The map type for storing the embedding. |
---|
| 598 | /// \see embeddingMap() |
---|
[861] | 599 | typedef typename Graph::template ArcMap<Arc> EmbeddingMap; |
---|
| 600 | |
---|
| 601 | /// \brief Constructor |
---|
| 602 | /// |
---|
[896] | 603 | /// Constructor. |
---|
| 604 | /// \pre The graph must be simple, i.e. it should not |
---|
| 605 | /// contain parallel or loop arcs. |
---|
[861] | 606 | PlanarEmbedding(const Graph& graph) |
---|
| 607 | : _graph(graph), _embedding(_graph), _kuratowski(graph, false) {} |
---|
| 608 | |
---|
[896] | 609 | /// \brief Run the algorithm. |
---|
[861] | 610 | /// |
---|
[896] | 611 | /// This function runs the algorithm. |
---|
| 612 | /// \param kuratowski If this parameter is set to \c false, then the |
---|
[861] | 613 | /// algorithm does not compute a Kuratowski subdivision. |
---|
[896] | 614 | /// \return \c true if the graph is planar. |
---|
[861] | 615 | bool run(bool kuratowski = true) { |
---|
| 616 | typedef _planarity_bits::PlanarityVisitor<Graph> Visitor; |
---|
| 617 | |
---|
| 618 | PredMap pred_map(_graph, INVALID); |
---|
| 619 | TreeMap tree_map(_graph, false); |
---|
| 620 | |
---|
| 621 | OrderMap order_map(_graph, -1); |
---|
| 622 | OrderList order_list; |
---|
| 623 | |
---|
| 624 | AncestorMap ancestor_map(_graph, -1); |
---|
| 625 | LowMap low_map(_graph, -1); |
---|
| 626 | |
---|
| 627 | Visitor visitor(_graph, pred_map, tree_map, |
---|
| 628 | order_map, order_list, ancestor_map, low_map); |
---|
| 629 | DfsVisit<Graph, Visitor> visit(_graph, visitor); |
---|
| 630 | visit.run(); |
---|
| 631 | |
---|
| 632 | ChildLists child_lists(_graph); |
---|
| 633 | createChildLists(tree_map, order_map, low_map, child_lists); |
---|
| 634 | |
---|
| 635 | NodeData node_data(2 * order_list.size()); |
---|
| 636 | |
---|
| 637 | EmbedArc embed_arc(_graph, INVALID); |
---|
| 638 | |
---|
| 639 | MergeRoots merge_roots(_graph); |
---|
| 640 | |
---|
| 641 | ArcLists arc_lists(_graph); |
---|
| 642 | |
---|
| 643 | FlipMap flip_map(_graph, false); |
---|
| 644 | |
---|
| 645 | for (int i = order_list.size() - 1; i >= 0; --i) { |
---|
| 646 | |
---|
| 647 | Node node = order_list[i]; |
---|
| 648 | |
---|
| 649 | node_data[i].first = INVALID; |
---|
| 650 | |
---|
| 651 | Node source = node; |
---|
| 652 | for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
---|
| 653 | Node target = _graph.target(e); |
---|
| 654 | |
---|
| 655 | if (order_map[source] < order_map[target] && tree_map[e]) { |
---|
| 656 | initFace(target, arc_lists, node_data, |
---|
| 657 | pred_map, order_map, order_list); |
---|
| 658 | } |
---|
| 659 | } |
---|
| 660 | |
---|
| 661 | for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
---|
| 662 | Node target = _graph.target(e); |
---|
| 663 | |
---|
| 664 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
---|
| 665 | embed_arc[target] = e; |
---|
| 666 | walkUp(target, source, i, pred_map, low_map, |
---|
| 667 | order_map, order_list, node_data, merge_roots); |
---|
| 668 | } |
---|
| 669 | } |
---|
| 670 | |
---|
| 671 | for (typename MergeRoots::Value::iterator it = |
---|
| 672 | merge_roots[node].begin(); it != merge_roots[node].end(); ++it) { |
---|
| 673 | int rn = *it; |
---|
| 674 | walkDown(rn, i, node_data, arc_lists, flip_map, order_list, |
---|
| 675 | child_lists, ancestor_map, low_map, embed_arc, merge_roots); |
---|
| 676 | } |
---|
| 677 | merge_roots[node].clear(); |
---|
| 678 | |
---|
| 679 | for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
---|
| 680 | Node target = _graph.target(e); |
---|
| 681 | |
---|
| 682 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
---|
| 683 | if (embed_arc[target] != INVALID) { |
---|
| 684 | if (kuratowski) { |
---|
| 685 | isolateKuratowski(e, node_data, arc_lists, flip_map, |
---|
| 686 | order_map, order_list, pred_map, child_lists, |
---|
| 687 | ancestor_map, low_map, |
---|
| 688 | embed_arc, merge_roots); |
---|
| 689 | } |
---|
| 690 | return false; |
---|
| 691 | } |
---|
| 692 | } |
---|
| 693 | } |
---|
| 694 | } |
---|
| 695 | |
---|
| 696 | for (int i = 0; i < int(order_list.size()); ++i) { |
---|
| 697 | |
---|
| 698 | mergeRemainingFaces(order_list[i], node_data, order_list, order_map, |
---|
| 699 | child_lists, arc_lists); |
---|
| 700 | storeEmbedding(order_list[i], node_data, order_map, pred_map, |
---|
| 701 | arc_lists, flip_map); |
---|
| 702 | } |
---|
| 703 | |
---|
| 704 | return true; |
---|
| 705 | } |
---|
| 706 | |
---|
[896] | 707 | /// \brief Give back the successor of an arc |
---|
[861] | 708 | /// |
---|
[896] | 709 | /// This function gives back the successor of an arc. It makes |
---|
[861] | 710 | /// possible to query the cyclic order of the outgoing arcs from |
---|
| 711 | /// a node. |
---|
| 712 | Arc next(const Arc& arc) const { |
---|
| 713 | return _embedding[arc]; |
---|
| 714 | } |
---|
| 715 | |
---|
[896] | 716 | /// \brief Give back the calculated embedding map |
---|
[861] | 717 | /// |
---|
[896] | 718 | /// This function gives back the calculated embedding map, which |
---|
| 719 | /// contains the successor of each arc in the cyclic order of the |
---|
| 720 | /// outgoing arcs of its source node. |
---|
[862] | 721 | const EmbeddingMap& embeddingMap() const { |
---|
[861] | 722 | return _embedding; |
---|
| 723 | } |
---|
| 724 | |
---|
[896] | 725 | /// \brief Give back \c true if the given edge is in the Kuratowski |
---|
| 726 | /// subdivision |
---|
[861] | 727 | /// |
---|
[896] | 728 | /// This function gives back \c true if the given edge is in the found |
---|
| 729 | /// Kuratowski subdivision. |
---|
| 730 | /// \pre The \c run() function must be called with \c true parameter |
---|
| 731 | /// before using this function. |
---|
| 732 | bool kuratowski(const Edge& edge) const { |
---|
[861] | 733 | return _kuratowski[edge]; |
---|
| 734 | } |
---|
| 735 | |
---|
| 736 | private: |
---|
| 737 | |
---|
| 738 | void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
---|
| 739 | const LowMap& low_map, ChildLists& child_lists) { |
---|
| 740 | |
---|
| 741 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 742 | Node source = n; |
---|
| 743 | |
---|
| 744 | std::vector<Node> targets; |
---|
| 745 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 746 | Node target = _graph.target(e); |
---|
| 747 | |
---|
| 748 | if (order_map[source] < order_map[target] && tree_map[e]) { |
---|
| 749 | targets.push_back(target); |
---|
| 750 | } |
---|
| 751 | } |
---|
| 752 | |
---|
| 753 | if (targets.size() == 0) { |
---|
| 754 | child_lists[source].first = INVALID; |
---|
| 755 | } else if (targets.size() == 1) { |
---|
| 756 | child_lists[source].first = targets[0]; |
---|
| 757 | child_lists[targets[0]].prev = INVALID; |
---|
| 758 | child_lists[targets[0]].next = INVALID; |
---|
| 759 | } else { |
---|
| 760 | radixSort(targets.begin(), targets.end(), mapToFunctor(low_map)); |
---|
| 761 | for (int i = 1; i < int(targets.size()); ++i) { |
---|
| 762 | child_lists[targets[i]].prev = targets[i - 1]; |
---|
| 763 | child_lists[targets[i - 1]].next = targets[i]; |
---|
| 764 | } |
---|
| 765 | child_lists[targets.back()].next = INVALID; |
---|
| 766 | child_lists[targets.front()].prev = INVALID; |
---|
| 767 | child_lists[source].first = targets.front(); |
---|
| 768 | } |
---|
| 769 | } |
---|
| 770 | } |
---|
| 771 | |
---|
| 772 | void walkUp(const Node& node, Node root, int rorder, |
---|
| 773 | const PredMap& pred_map, const LowMap& low_map, |
---|
| 774 | const OrderMap& order_map, const OrderList& order_list, |
---|
| 775 | NodeData& node_data, MergeRoots& merge_roots) { |
---|
| 776 | |
---|
| 777 | int na, nb; |
---|
| 778 | bool da, db; |
---|
| 779 | |
---|
| 780 | na = nb = order_map[node]; |
---|
| 781 | da = true; db = false; |
---|
| 782 | |
---|
| 783 | while (true) { |
---|
| 784 | |
---|
| 785 | if (node_data[na].visited == rorder) break; |
---|
| 786 | if (node_data[nb].visited == rorder) break; |
---|
| 787 | |
---|
| 788 | node_data[na].visited = rorder; |
---|
| 789 | node_data[nb].visited = rorder; |
---|
| 790 | |
---|
| 791 | int rn = -1; |
---|
| 792 | |
---|
| 793 | if (na >= int(order_list.size())) { |
---|
| 794 | rn = na; |
---|
| 795 | } else if (nb >= int(order_list.size())) { |
---|
| 796 | rn = nb; |
---|
| 797 | } |
---|
| 798 | |
---|
| 799 | if (rn == -1) { |
---|
| 800 | int nn; |
---|
| 801 | |
---|
| 802 | nn = da ? node_data[na].prev : node_data[na].next; |
---|
| 803 | da = node_data[nn].prev != na; |
---|
| 804 | na = nn; |
---|
| 805 | |
---|
| 806 | nn = db ? node_data[nb].prev : node_data[nb].next; |
---|
| 807 | db = node_data[nn].prev != nb; |
---|
| 808 | nb = nn; |
---|
| 809 | |
---|
| 810 | } else { |
---|
| 811 | |
---|
| 812 | Node rep = order_list[rn - order_list.size()]; |
---|
| 813 | Node parent = _graph.source(pred_map[rep]); |
---|
| 814 | |
---|
| 815 | if (low_map[rep] < rorder) { |
---|
| 816 | merge_roots[parent].push_back(rn); |
---|
| 817 | } else { |
---|
| 818 | merge_roots[parent].push_front(rn); |
---|
| 819 | } |
---|
| 820 | |
---|
| 821 | if (parent != root) { |
---|
| 822 | na = nb = order_map[parent]; |
---|
| 823 | da = true; db = false; |
---|
| 824 | } else { |
---|
| 825 | break; |
---|
| 826 | } |
---|
| 827 | } |
---|
| 828 | } |
---|
| 829 | } |
---|
| 830 | |
---|
| 831 | void walkDown(int rn, int rorder, NodeData& node_data, |
---|
| 832 | ArcLists& arc_lists, FlipMap& flip_map, |
---|
| 833 | OrderList& order_list, ChildLists& child_lists, |
---|
| 834 | AncestorMap& ancestor_map, LowMap& low_map, |
---|
| 835 | EmbedArc& embed_arc, MergeRoots& merge_roots) { |
---|
| 836 | |
---|
| 837 | std::vector<std::pair<int, bool> > merge_stack; |
---|
| 838 | |
---|
| 839 | for (int di = 0; di < 2; ++di) { |
---|
| 840 | bool rd = di == 0; |
---|
| 841 | int pn = rn; |
---|
| 842 | int n = rd ? node_data[rn].next : node_data[rn].prev; |
---|
| 843 | |
---|
| 844 | while (n != rn) { |
---|
| 845 | |
---|
| 846 | Node node = order_list[n]; |
---|
| 847 | |
---|
| 848 | if (embed_arc[node] != INVALID) { |
---|
| 849 | |
---|
| 850 | // Merging components on the critical path |
---|
| 851 | while (!merge_stack.empty()) { |
---|
| 852 | |
---|
| 853 | // Component root |
---|
| 854 | int cn = merge_stack.back().first; |
---|
| 855 | bool cd = merge_stack.back().second; |
---|
| 856 | merge_stack.pop_back(); |
---|
| 857 | |
---|
| 858 | // Parent of component |
---|
| 859 | int dn = merge_stack.back().first; |
---|
| 860 | bool dd = merge_stack.back().second; |
---|
| 861 | merge_stack.pop_back(); |
---|
| 862 | |
---|
| 863 | Node parent = order_list[dn]; |
---|
| 864 | |
---|
| 865 | // Erasing from merge_roots |
---|
| 866 | merge_roots[parent].pop_front(); |
---|
| 867 | |
---|
| 868 | Node child = order_list[cn - order_list.size()]; |
---|
| 869 | |
---|
| 870 | // Erasing from child_lists |
---|
| 871 | if (child_lists[child].prev != INVALID) { |
---|
| 872 | child_lists[child_lists[child].prev].next = |
---|
| 873 | child_lists[child].next; |
---|
| 874 | } else { |
---|
| 875 | child_lists[parent].first = child_lists[child].next; |
---|
| 876 | } |
---|
| 877 | |
---|
| 878 | if (child_lists[child].next != INVALID) { |
---|
| 879 | child_lists[child_lists[child].next].prev = |
---|
| 880 | child_lists[child].prev; |
---|
| 881 | } |
---|
| 882 | |
---|
| 883 | // Merging arcs + flipping |
---|
| 884 | Arc de = node_data[dn].first; |
---|
| 885 | Arc ce = node_data[cn].first; |
---|
| 886 | |
---|
| 887 | flip_map[order_list[cn - order_list.size()]] = cd != dd; |
---|
| 888 | if (cd != dd) { |
---|
| 889 | std::swap(arc_lists[ce].prev, arc_lists[ce].next); |
---|
| 890 | ce = arc_lists[ce].prev; |
---|
| 891 | std::swap(arc_lists[ce].prev, arc_lists[ce].next); |
---|
| 892 | } |
---|
| 893 | |
---|
| 894 | { |
---|
| 895 | Arc dne = arc_lists[de].next; |
---|
| 896 | Arc cne = arc_lists[ce].next; |
---|
| 897 | |
---|
| 898 | arc_lists[de].next = cne; |
---|
| 899 | arc_lists[ce].next = dne; |
---|
| 900 | |
---|
| 901 | arc_lists[dne].prev = ce; |
---|
| 902 | arc_lists[cne].prev = de; |
---|
| 903 | } |
---|
| 904 | |
---|
| 905 | if (dd) { |
---|
| 906 | node_data[dn].first = ce; |
---|
| 907 | } |
---|
| 908 | |
---|
| 909 | // Merging external faces |
---|
| 910 | { |
---|
| 911 | int en = cn; |
---|
| 912 | cn = cd ? node_data[cn].prev : node_data[cn].next; |
---|
| 913 | cd = node_data[cn].next == en; |
---|
| 914 | |
---|
| 915 | if (node_data[cn].prev == node_data[cn].next && |
---|
| 916 | node_data[cn].inverted) { |
---|
| 917 | cd = !cd; |
---|
| 918 | } |
---|
| 919 | } |
---|
| 920 | |
---|
| 921 | if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
---|
| 922 | if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
---|
| 923 | |
---|
| 924 | } |
---|
| 925 | |
---|
| 926 | bool d = pn == node_data[n].prev; |
---|
| 927 | |
---|
| 928 | if (node_data[n].prev == node_data[n].next && |
---|
| 929 | node_data[n].inverted) { |
---|
| 930 | d = !d; |
---|
| 931 | } |
---|
| 932 | |
---|
| 933 | // Add new arc |
---|
| 934 | { |
---|
| 935 | Arc arc = embed_arc[node]; |
---|
| 936 | Arc re = node_data[rn].first; |
---|
| 937 | |
---|
| 938 | arc_lists[arc_lists[re].next].prev = arc; |
---|
| 939 | arc_lists[arc].next = arc_lists[re].next; |
---|
| 940 | arc_lists[arc].prev = re; |
---|
| 941 | arc_lists[re].next = arc; |
---|
| 942 | |
---|
| 943 | if (!rd) { |
---|
| 944 | node_data[rn].first = arc; |
---|
| 945 | } |
---|
| 946 | |
---|
| 947 | Arc rev = _graph.oppositeArc(arc); |
---|
| 948 | Arc e = node_data[n].first; |
---|
| 949 | |
---|
| 950 | arc_lists[arc_lists[e].next].prev = rev; |
---|
| 951 | arc_lists[rev].next = arc_lists[e].next; |
---|
| 952 | arc_lists[rev].prev = e; |
---|
| 953 | arc_lists[e].next = rev; |
---|
| 954 | |
---|
| 955 | if (d) { |
---|
| 956 | node_data[n].first = rev; |
---|
| 957 | } |
---|
| 958 | |
---|
| 959 | } |
---|
| 960 | |
---|
| 961 | // Embedding arc into external face |
---|
| 962 | if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
---|
| 963 | if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
---|
| 964 | pn = rn; |
---|
| 965 | |
---|
| 966 | embed_arc[order_list[n]] = INVALID; |
---|
| 967 | } |
---|
| 968 | |
---|
| 969 | if (!merge_roots[node].empty()) { |
---|
| 970 | |
---|
| 971 | bool d = pn == node_data[n].prev; |
---|
| 972 | if (node_data[n].prev == node_data[n].next && |
---|
| 973 | node_data[n].inverted) { |
---|
| 974 | d = !d; |
---|
| 975 | } |
---|
| 976 | |
---|
| 977 | merge_stack.push_back(std::make_pair(n, d)); |
---|
| 978 | |
---|
| 979 | int rn = merge_roots[node].front(); |
---|
| 980 | |
---|
| 981 | int xn = node_data[rn].next; |
---|
| 982 | Node xnode = order_list[xn]; |
---|
| 983 | |
---|
| 984 | int yn = node_data[rn].prev; |
---|
| 985 | Node ynode = order_list[yn]; |
---|
| 986 | |
---|
| 987 | bool rd; |
---|
| 988 | if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
| 989 | rd = true; |
---|
| 990 | } else if (!external(ynode, rorder, child_lists, |
---|
| 991 | ancestor_map, low_map)) { |
---|
| 992 | rd = false; |
---|
| 993 | } else if (pertinent(xnode, embed_arc, merge_roots)) { |
---|
| 994 | rd = true; |
---|
| 995 | } else { |
---|
| 996 | rd = false; |
---|
| 997 | } |
---|
| 998 | |
---|
| 999 | merge_stack.push_back(std::make_pair(rn, rd)); |
---|
| 1000 | |
---|
| 1001 | pn = rn; |
---|
| 1002 | n = rd ? xn : yn; |
---|
| 1003 | |
---|
| 1004 | } else if (!external(node, rorder, child_lists, |
---|
| 1005 | ancestor_map, low_map)) { |
---|
| 1006 | int nn = (node_data[n].next != pn ? |
---|
| 1007 | node_data[n].next : node_data[n].prev); |
---|
| 1008 | |
---|
| 1009 | bool nd = n == node_data[nn].prev; |
---|
| 1010 | |
---|
| 1011 | if (nd) node_data[nn].prev = pn; |
---|
| 1012 | else node_data[nn].next = pn; |
---|
| 1013 | |
---|
| 1014 | if (n == node_data[pn].prev) node_data[pn].prev = nn; |
---|
| 1015 | else node_data[pn].next = nn; |
---|
| 1016 | |
---|
| 1017 | node_data[nn].inverted = |
---|
| 1018 | (node_data[nn].prev == node_data[nn].next && nd != rd); |
---|
| 1019 | |
---|
| 1020 | n = nn; |
---|
| 1021 | } |
---|
| 1022 | else break; |
---|
| 1023 | |
---|
| 1024 | } |
---|
| 1025 | |
---|
| 1026 | if (!merge_stack.empty() || n == rn) { |
---|
| 1027 | break; |
---|
| 1028 | } |
---|
| 1029 | } |
---|
| 1030 | } |
---|
| 1031 | |
---|
| 1032 | void initFace(const Node& node, ArcLists& arc_lists, |
---|
| 1033 | NodeData& node_data, const PredMap& pred_map, |
---|
| 1034 | const OrderMap& order_map, const OrderList& order_list) { |
---|
| 1035 | int n = order_map[node]; |
---|
| 1036 | int rn = n + order_list.size(); |
---|
| 1037 | |
---|
| 1038 | node_data[n].next = node_data[n].prev = rn; |
---|
| 1039 | node_data[rn].next = node_data[rn].prev = n; |
---|
| 1040 | |
---|
| 1041 | node_data[n].visited = order_list.size(); |
---|
| 1042 | node_data[rn].visited = order_list.size(); |
---|
| 1043 | |
---|
| 1044 | node_data[n].inverted = false; |
---|
| 1045 | node_data[rn].inverted = false; |
---|
| 1046 | |
---|
| 1047 | Arc arc = pred_map[node]; |
---|
| 1048 | Arc rev = _graph.oppositeArc(arc); |
---|
| 1049 | |
---|
| 1050 | node_data[rn].first = arc; |
---|
| 1051 | node_data[n].first = rev; |
---|
| 1052 | |
---|
| 1053 | arc_lists[arc].prev = arc; |
---|
| 1054 | arc_lists[arc].next = arc; |
---|
| 1055 | |
---|
| 1056 | arc_lists[rev].prev = rev; |
---|
| 1057 | arc_lists[rev].next = rev; |
---|
| 1058 | |
---|
| 1059 | } |
---|
| 1060 | |
---|
| 1061 | void mergeRemainingFaces(const Node& node, NodeData& node_data, |
---|
| 1062 | OrderList& order_list, OrderMap& order_map, |
---|
| 1063 | ChildLists& child_lists, ArcLists& arc_lists) { |
---|
| 1064 | while (child_lists[node].first != INVALID) { |
---|
| 1065 | int dd = order_map[node]; |
---|
| 1066 | Node child = child_lists[node].first; |
---|
| 1067 | int cd = order_map[child] + order_list.size(); |
---|
| 1068 | child_lists[node].first = child_lists[child].next; |
---|
| 1069 | |
---|
| 1070 | Arc de = node_data[dd].first; |
---|
| 1071 | Arc ce = node_data[cd].first; |
---|
| 1072 | |
---|
| 1073 | if (de != INVALID) { |
---|
| 1074 | Arc dne = arc_lists[de].next; |
---|
| 1075 | Arc cne = arc_lists[ce].next; |
---|
| 1076 | |
---|
| 1077 | arc_lists[de].next = cne; |
---|
| 1078 | arc_lists[ce].next = dne; |
---|
| 1079 | |
---|
| 1080 | arc_lists[dne].prev = ce; |
---|
| 1081 | arc_lists[cne].prev = de; |
---|
| 1082 | } |
---|
| 1083 | |
---|
| 1084 | node_data[dd].first = ce; |
---|
| 1085 | |
---|
| 1086 | } |
---|
| 1087 | } |
---|
| 1088 | |
---|
| 1089 | void storeEmbedding(const Node& node, NodeData& node_data, |
---|
| 1090 | OrderMap& order_map, PredMap& pred_map, |
---|
| 1091 | ArcLists& arc_lists, FlipMap& flip_map) { |
---|
| 1092 | |
---|
| 1093 | if (node_data[order_map[node]].first == INVALID) return; |
---|
| 1094 | |
---|
| 1095 | if (pred_map[node] != INVALID) { |
---|
| 1096 | Node source = _graph.source(pred_map[node]); |
---|
| 1097 | flip_map[node] = flip_map[node] != flip_map[source]; |
---|
| 1098 | } |
---|
| 1099 | |
---|
| 1100 | Arc first = node_data[order_map[node]].first; |
---|
| 1101 | Arc prev = first; |
---|
| 1102 | |
---|
| 1103 | Arc arc = flip_map[node] ? |
---|
| 1104 | arc_lists[prev].prev : arc_lists[prev].next; |
---|
| 1105 | |
---|
| 1106 | _embedding[prev] = arc; |
---|
| 1107 | |
---|
| 1108 | while (arc != first) { |
---|
| 1109 | Arc next = arc_lists[arc].prev == prev ? |
---|
| 1110 | arc_lists[arc].next : arc_lists[arc].prev; |
---|
| 1111 | prev = arc; arc = next; |
---|
| 1112 | _embedding[prev] = arc; |
---|
| 1113 | } |
---|
| 1114 | } |
---|
| 1115 | |
---|
| 1116 | |
---|
| 1117 | bool external(const Node& node, int rorder, |
---|
| 1118 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
| 1119 | LowMap& low_map) { |
---|
| 1120 | Node child = child_lists[node].first; |
---|
| 1121 | |
---|
| 1122 | if (child != INVALID) { |
---|
| 1123 | if (low_map[child] < rorder) return true; |
---|
| 1124 | } |
---|
| 1125 | |
---|
| 1126 | if (ancestor_map[node] < rorder) return true; |
---|
| 1127 | |
---|
| 1128 | return false; |
---|
| 1129 | } |
---|
| 1130 | |
---|
| 1131 | bool pertinent(const Node& node, const EmbedArc& embed_arc, |
---|
| 1132 | const MergeRoots& merge_roots) { |
---|
| 1133 | return !merge_roots[node].empty() || embed_arc[node] != INVALID; |
---|
| 1134 | } |
---|
| 1135 | |
---|
| 1136 | int lowPoint(const Node& node, OrderMap& order_map, ChildLists& child_lists, |
---|
| 1137 | AncestorMap& ancestor_map, LowMap& low_map) { |
---|
| 1138 | int low_point; |
---|
| 1139 | |
---|
| 1140 | Node child = child_lists[node].first; |
---|
| 1141 | |
---|
| 1142 | if (child != INVALID) { |
---|
| 1143 | low_point = low_map[child]; |
---|
| 1144 | } else { |
---|
| 1145 | low_point = order_map[node]; |
---|
| 1146 | } |
---|
| 1147 | |
---|
| 1148 | if (low_point > ancestor_map[node]) { |
---|
| 1149 | low_point = ancestor_map[node]; |
---|
| 1150 | } |
---|
| 1151 | |
---|
| 1152 | return low_point; |
---|
| 1153 | } |
---|
| 1154 | |
---|
| 1155 | int findComponentRoot(Node root, Node node, ChildLists& child_lists, |
---|
| 1156 | OrderMap& order_map, OrderList& order_list) { |
---|
| 1157 | |
---|
| 1158 | int order = order_map[root]; |
---|
| 1159 | int norder = order_map[node]; |
---|
| 1160 | |
---|
| 1161 | Node child = child_lists[root].first; |
---|
| 1162 | while (child != INVALID) { |
---|
| 1163 | int corder = order_map[child]; |
---|
| 1164 | if (corder > order && corder < norder) { |
---|
| 1165 | order = corder; |
---|
| 1166 | } |
---|
| 1167 | child = child_lists[child].next; |
---|
| 1168 | } |
---|
| 1169 | return order + order_list.size(); |
---|
| 1170 | } |
---|
| 1171 | |
---|
| 1172 | Node findPertinent(Node node, OrderMap& order_map, NodeData& node_data, |
---|
| 1173 | EmbedArc& embed_arc, MergeRoots& merge_roots) { |
---|
| 1174 | Node wnode =_graph.target(node_data[order_map[node]].first); |
---|
| 1175 | while (!pertinent(wnode, embed_arc, merge_roots)) { |
---|
| 1176 | wnode = _graph.target(node_data[order_map[wnode]].first); |
---|
| 1177 | } |
---|
| 1178 | return wnode; |
---|
| 1179 | } |
---|
| 1180 | |
---|
| 1181 | |
---|
| 1182 | Node findExternal(Node node, int rorder, OrderMap& order_map, |
---|
| 1183 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
| 1184 | LowMap& low_map, NodeData& node_data) { |
---|
| 1185 | Node wnode =_graph.target(node_data[order_map[node]].first); |
---|
| 1186 | while (!external(wnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
| 1187 | wnode = _graph.target(node_data[order_map[wnode]].first); |
---|
| 1188 | } |
---|
| 1189 | return wnode; |
---|
| 1190 | } |
---|
| 1191 | |
---|
| 1192 | void markCommonPath(Node node, int rorder, Node& wnode, Node& znode, |
---|
| 1193 | OrderList& order_list, OrderMap& order_map, |
---|
| 1194 | NodeData& node_data, ArcLists& arc_lists, |
---|
| 1195 | EmbedArc& embed_arc, MergeRoots& merge_roots, |
---|
| 1196 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
| 1197 | LowMap& low_map) { |
---|
| 1198 | |
---|
| 1199 | Node cnode = node; |
---|
| 1200 | Node pred = INVALID; |
---|
| 1201 | |
---|
| 1202 | while (true) { |
---|
| 1203 | |
---|
| 1204 | bool pert = pertinent(cnode, embed_arc, merge_roots); |
---|
| 1205 | bool ext = external(cnode, rorder, child_lists, ancestor_map, low_map); |
---|
| 1206 | |
---|
| 1207 | if (pert && ext) { |
---|
| 1208 | if (!merge_roots[cnode].empty()) { |
---|
| 1209 | int cn = merge_roots[cnode].back(); |
---|
| 1210 | |
---|
| 1211 | if (low_map[order_list[cn - order_list.size()]] < rorder) { |
---|
| 1212 | Arc arc = node_data[cn].first; |
---|
| 1213 | _kuratowski.set(arc, true); |
---|
| 1214 | |
---|
| 1215 | pred = cnode; |
---|
| 1216 | cnode = _graph.target(arc); |
---|
| 1217 | |
---|
| 1218 | continue; |
---|
| 1219 | } |
---|
| 1220 | } |
---|
| 1221 | wnode = znode = cnode; |
---|
| 1222 | return; |
---|
| 1223 | |
---|
| 1224 | } else if (pert) { |
---|
| 1225 | wnode = cnode; |
---|
| 1226 | |
---|
| 1227 | while (!external(cnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
| 1228 | Arc arc = node_data[order_map[cnode]].first; |
---|
| 1229 | |
---|
| 1230 | if (_graph.target(arc) == pred) { |
---|
| 1231 | arc = arc_lists[arc].next; |
---|
| 1232 | } |
---|
| 1233 | _kuratowski.set(arc, true); |
---|
| 1234 | |
---|
| 1235 | Node next = _graph.target(arc); |
---|
| 1236 | pred = cnode; cnode = next; |
---|
| 1237 | } |
---|
| 1238 | |
---|
| 1239 | znode = cnode; |
---|
| 1240 | return; |
---|
| 1241 | |
---|
| 1242 | } else if (ext) { |
---|
| 1243 | znode = cnode; |
---|
| 1244 | |
---|
| 1245 | while (!pertinent(cnode, embed_arc, merge_roots)) { |
---|
| 1246 | Arc arc = node_data[order_map[cnode]].first; |
---|
| 1247 | |
---|
| 1248 | if (_graph.target(arc) == pred) { |
---|
| 1249 | arc = arc_lists[arc].next; |
---|
| 1250 | } |
---|
| 1251 | _kuratowski.set(arc, true); |
---|
| 1252 | |
---|
| 1253 | Node next = _graph.target(arc); |
---|
| 1254 | pred = cnode; cnode = next; |
---|
| 1255 | } |
---|
| 1256 | |
---|
| 1257 | wnode = cnode; |
---|
| 1258 | return; |
---|
| 1259 | |
---|
| 1260 | } else { |
---|
| 1261 | Arc arc = node_data[order_map[cnode]].first; |
---|
| 1262 | |
---|
| 1263 | if (_graph.target(arc) == pred) { |
---|
| 1264 | arc = arc_lists[arc].next; |
---|
| 1265 | } |
---|
| 1266 | _kuratowski.set(arc, true); |
---|
| 1267 | |
---|
| 1268 | Node next = _graph.target(arc); |
---|
| 1269 | pred = cnode; cnode = next; |
---|
| 1270 | } |
---|
| 1271 | |
---|
| 1272 | } |
---|
| 1273 | |
---|
| 1274 | } |
---|
| 1275 | |
---|
| 1276 | void orientComponent(Node root, int rn, OrderMap& order_map, |
---|
| 1277 | PredMap& pred_map, NodeData& node_data, |
---|
| 1278 | ArcLists& arc_lists, FlipMap& flip_map, |
---|
| 1279 | TypeMap& type_map) { |
---|
| 1280 | node_data[order_map[root]].first = node_data[rn].first; |
---|
| 1281 | type_map[root] = 1; |
---|
| 1282 | |
---|
| 1283 | std::vector<Node> st, qu; |
---|
| 1284 | |
---|
| 1285 | st.push_back(root); |
---|
| 1286 | while (!st.empty()) { |
---|
| 1287 | Node node = st.back(); |
---|
| 1288 | st.pop_back(); |
---|
| 1289 | qu.push_back(node); |
---|
| 1290 | |
---|
| 1291 | Arc arc = node_data[order_map[node]].first; |
---|
| 1292 | |
---|
| 1293 | if (type_map[_graph.target(arc)] == 0) { |
---|
| 1294 | st.push_back(_graph.target(arc)); |
---|
| 1295 | type_map[_graph.target(arc)] = 1; |
---|
| 1296 | } |
---|
| 1297 | |
---|
| 1298 | Arc last = arc, pred = arc; |
---|
| 1299 | arc = arc_lists[arc].next; |
---|
| 1300 | while (arc != last) { |
---|
| 1301 | |
---|
| 1302 | if (type_map[_graph.target(arc)] == 0) { |
---|
| 1303 | st.push_back(_graph.target(arc)); |
---|
| 1304 | type_map[_graph.target(arc)] = 1; |
---|
| 1305 | } |
---|
| 1306 | |
---|
| 1307 | Arc next = arc_lists[arc].next != pred ? |
---|
| 1308 | arc_lists[arc].next : arc_lists[arc].prev; |
---|
| 1309 | pred = arc; arc = next; |
---|
| 1310 | } |
---|
| 1311 | |
---|
| 1312 | } |
---|
| 1313 | |
---|
| 1314 | type_map[root] = 2; |
---|
| 1315 | flip_map[root] = false; |
---|
| 1316 | |
---|
| 1317 | for (int i = 1; i < int(qu.size()); ++i) { |
---|
| 1318 | |
---|
| 1319 | Node node = qu[i]; |
---|
| 1320 | |
---|
| 1321 | while (type_map[node] != 2) { |
---|
| 1322 | st.push_back(node); |
---|
| 1323 | type_map[node] = 2; |
---|
| 1324 | node = _graph.source(pred_map[node]); |
---|
| 1325 | } |
---|
| 1326 | |
---|
| 1327 | bool flip = flip_map[node]; |
---|
| 1328 | |
---|
| 1329 | while (!st.empty()) { |
---|
| 1330 | node = st.back(); |
---|
| 1331 | st.pop_back(); |
---|
| 1332 | |
---|
| 1333 | flip_map[node] = flip != flip_map[node]; |
---|
| 1334 | flip = flip_map[node]; |
---|
| 1335 | |
---|
| 1336 | if (flip) { |
---|
| 1337 | Arc arc = node_data[order_map[node]].first; |
---|
| 1338 | std::swap(arc_lists[arc].prev, arc_lists[arc].next); |
---|
| 1339 | arc = arc_lists[arc].prev; |
---|
| 1340 | std::swap(arc_lists[arc].prev, arc_lists[arc].next); |
---|
| 1341 | node_data[order_map[node]].first = arc; |
---|
| 1342 | } |
---|
| 1343 | } |
---|
| 1344 | } |
---|
| 1345 | |
---|
| 1346 | for (int i = 0; i < int(qu.size()); ++i) { |
---|
| 1347 | |
---|
| 1348 | Arc arc = node_data[order_map[qu[i]]].first; |
---|
| 1349 | Arc last = arc, pred = arc; |
---|
| 1350 | |
---|
| 1351 | arc = arc_lists[arc].next; |
---|
| 1352 | while (arc != last) { |
---|
| 1353 | |
---|
| 1354 | if (arc_lists[arc].next == pred) { |
---|
| 1355 | std::swap(arc_lists[arc].next, arc_lists[arc].prev); |
---|
| 1356 | } |
---|
| 1357 | pred = arc; arc = arc_lists[arc].next; |
---|
| 1358 | } |
---|
| 1359 | |
---|
| 1360 | } |
---|
| 1361 | } |
---|
| 1362 | |
---|
| 1363 | void setFaceFlags(Node root, Node wnode, Node ynode, Node xnode, |
---|
| 1364 | OrderMap& order_map, NodeData& node_data, |
---|
| 1365 | TypeMap& type_map) { |
---|
| 1366 | Node node = _graph.target(node_data[order_map[root]].first); |
---|
| 1367 | |
---|
| 1368 | while (node != ynode) { |
---|
| 1369 | type_map[node] = HIGHY; |
---|
| 1370 | node = _graph.target(node_data[order_map[node]].first); |
---|
| 1371 | } |
---|
| 1372 | |
---|
| 1373 | while (node != wnode) { |
---|
| 1374 | type_map[node] = LOWY; |
---|
| 1375 | node = _graph.target(node_data[order_map[node]].first); |
---|
| 1376 | } |
---|
| 1377 | |
---|
| 1378 | node = _graph.target(node_data[order_map[wnode]].first); |
---|
| 1379 | |
---|
| 1380 | while (node != xnode) { |
---|
| 1381 | type_map[node] = LOWX; |
---|
| 1382 | node = _graph.target(node_data[order_map[node]].first); |
---|
| 1383 | } |
---|
| 1384 | type_map[node] = LOWX; |
---|
| 1385 | |
---|
| 1386 | node = _graph.target(node_data[order_map[xnode]].first); |
---|
| 1387 | while (node != root) { |
---|
| 1388 | type_map[node] = HIGHX; |
---|
| 1389 | node = _graph.target(node_data[order_map[node]].first); |
---|
| 1390 | } |
---|
| 1391 | |
---|
| 1392 | type_map[wnode] = PERTINENT; |
---|
| 1393 | type_map[root] = ROOT; |
---|
| 1394 | } |
---|
| 1395 | |
---|
| 1396 | void findInternalPath(std::vector<Arc>& ipath, |
---|
| 1397 | Node wnode, Node root, TypeMap& type_map, |
---|
| 1398 | OrderMap& order_map, NodeData& node_data, |
---|
| 1399 | ArcLists& arc_lists) { |
---|
| 1400 | std::vector<Arc> st; |
---|
| 1401 | |
---|
| 1402 | Node node = wnode; |
---|
| 1403 | |
---|
| 1404 | while (node != root) { |
---|
| 1405 | Arc arc = arc_lists[node_data[order_map[node]].first].next; |
---|
| 1406 | st.push_back(arc); |
---|
| 1407 | node = _graph.target(arc); |
---|
| 1408 | } |
---|
| 1409 | |
---|
| 1410 | while (true) { |
---|
| 1411 | Arc arc = st.back(); |
---|
| 1412 | if (type_map[_graph.target(arc)] == LOWX || |
---|
| 1413 | type_map[_graph.target(arc)] == HIGHX) { |
---|
| 1414 | break; |
---|
| 1415 | } |
---|
| 1416 | if (type_map[_graph.target(arc)] == 2) { |
---|
| 1417 | type_map[_graph.target(arc)] = 3; |
---|
| 1418 | |
---|
| 1419 | arc = arc_lists[_graph.oppositeArc(arc)].next; |
---|
| 1420 | st.push_back(arc); |
---|
| 1421 | } else { |
---|
| 1422 | st.pop_back(); |
---|
| 1423 | arc = arc_lists[arc].next; |
---|
| 1424 | |
---|
| 1425 | while (_graph.oppositeArc(arc) == st.back()) { |
---|
| 1426 | arc = st.back(); |
---|
| 1427 | st.pop_back(); |
---|
| 1428 | arc = arc_lists[arc].next; |
---|
| 1429 | } |
---|
| 1430 | st.push_back(arc); |
---|
| 1431 | } |
---|
| 1432 | } |
---|
| 1433 | |
---|
| 1434 | for (int i = 0; i < int(st.size()); ++i) { |
---|
| 1435 | if (type_map[_graph.target(st[i])] != LOWY && |
---|
| 1436 | type_map[_graph.target(st[i])] != HIGHY) { |
---|
| 1437 | for (; i < int(st.size()); ++i) { |
---|
| 1438 | ipath.push_back(st[i]); |
---|
| 1439 | } |
---|
| 1440 | } |
---|
| 1441 | } |
---|
| 1442 | } |
---|
| 1443 | |
---|
| 1444 | void setInternalFlags(std::vector<Arc>& ipath, TypeMap& type_map) { |
---|
| 1445 | for (int i = 1; i < int(ipath.size()); ++i) { |
---|
| 1446 | type_map[_graph.source(ipath[i])] = INTERNAL; |
---|
| 1447 | } |
---|
| 1448 | } |
---|
| 1449 | |
---|
| 1450 | void findPilePath(std::vector<Arc>& ppath, |
---|
| 1451 | Node root, TypeMap& type_map, OrderMap& order_map, |
---|
| 1452 | NodeData& node_data, ArcLists& arc_lists) { |
---|
| 1453 | std::vector<Arc> st; |
---|
| 1454 | |
---|
| 1455 | st.push_back(_graph.oppositeArc(node_data[order_map[root]].first)); |
---|
| 1456 | st.push_back(node_data[order_map[root]].first); |
---|
| 1457 | |
---|
| 1458 | while (st.size() > 1) { |
---|
| 1459 | Arc arc = st.back(); |
---|
| 1460 | if (type_map[_graph.target(arc)] == INTERNAL) { |
---|
| 1461 | break; |
---|
| 1462 | } |
---|
| 1463 | if (type_map[_graph.target(arc)] == 3) { |
---|
| 1464 | type_map[_graph.target(arc)] = 4; |
---|
| 1465 | |
---|
| 1466 | arc = arc_lists[_graph.oppositeArc(arc)].next; |
---|
| 1467 | st.push_back(arc); |
---|
| 1468 | } else { |
---|
| 1469 | st.pop_back(); |
---|
| 1470 | arc = arc_lists[arc].next; |
---|
| 1471 | |
---|
| 1472 | while (!st.empty() && _graph.oppositeArc(arc) == st.back()) { |
---|
| 1473 | arc = st.back(); |
---|
| 1474 | st.pop_back(); |
---|
| 1475 | arc = arc_lists[arc].next; |
---|
| 1476 | } |
---|
| 1477 | st.push_back(arc); |
---|
| 1478 | } |
---|
| 1479 | } |
---|
| 1480 | |
---|
| 1481 | for (int i = 1; i < int(st.size()); ++i) { |
---|
| 1482 | ppath.push_back(st[i]); |
---|
| 1483 | } |
---|
| 1484 | } |
---|
| 1485 | |
---|
| 1486 | |
---|
| 1487 | int markExternalPath(Node node, OrderMap& order_map, |
---|
| 1488 | ChildLists& child_lists, PredMap& pred_map, |
---|
| 1489 | AncestorMap& ancestor_map, LowMap& low_map) { |
---|
| 1490 | int lp = lowPoint(node, order_map, child_lists, |
---|
| 1491 | ancestor_map, low_map); |
---|
| 1492 | |
---|
| 1493 | if (ancestor_map[node] != lp) { |
---|
| 1494 | node = child_lists[node].first; |
---|
| 1495 | _kuratowski[pred_map[node]] = true; |
---|
| 1496 | |
---|
| 1497 | while (ancestor_map[node] != lp) { |
---|
| 1498 | for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
---|
| 1499 | Node tnode = _graph.target(e); |
---|
| 1500 | if (order_map[tnode] > order_map[node] && low_map[tnode] == lp) { |
---|
| 1501 | node = tnode; |
---|
| 1502 | _kuratowski[e] = true; |
---|
| 1503 | break; |
---|
| 1504 | } |
---|
| 1505 | } |
---|
| 1506 | } |
---|
| 1507 | } |
---|
| 1508 | |
---|
| 1509 | for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
---|
| 1510 | if (order_map[_graph.target(e)] == lp) { |
---|
| 1511 | _kuratowski[e] = true; |
---|
| 1512 | break; |
---|
| 1513 | } |
---|
| 1514 | } |
---|
| 1515 | |
---|
| 1516 | return lp; |
---|
| 1517 | } |
---|
| 1518 | |
---|
| 1519 | void markPertinentPath(Node node, OrderMap& order_map, |
---|
| 1520 | NodeData& node_data, ArcLists& arc_lists, |
---|
| 1521 | EmbedArc& embed_arc, MergeRoots& merge_roots) { |
---|
| 1522 | while (embed_arc[node] == INVALID) { |
---|
| 1523 | int n = merge_roots[node].front(); |
---|
| 1524 | Arc arc = node_data[n].first; |
---|
| 1525 | |
---|
| 1526 | _kuratowski.set(arc, true); |
---|
| 1527 | |
---|
| 1528 | Node pred = node; |
---|
| 1529 | node = _graph.target(arc); |
---|
| 1530 | while (!pertinent(node, embed_arc, merge_roots)) { |
---|
| 1531 | arc = node_data[order_map[node]].first; |
---|
| 1532 | if (_graph.target(arc) == pred) { |
---|
| 1533 | arc = arc_lists[arc].next; |
---|
| 1534 | } |
---|
| 1535 | _kuratowski.set(arc, true); |
---|
| 1536 | pred = node; |
---|
| 1537 | node = _graph.target(arc); |
---|
| 1538 | } |
---|
| 1539 | } |
---|
| 1540 | _kuratowski.set(embed_arc[node], true); |
---|
| 1541 | } |
---|
| 1542 | |
---|
| 1543 | void markPredPath(Node node, Node snode, PredMap& pred_map) { |
---|
| 1544 | while (node != snode) { |
---|
| 1545 | _kuratowski.set(pred_map[node], true); |
---|
| 1546 | node = _graph.source(pred_map[node]); |
---|
| 1547 | } |
---|
| 1548 | } |
---|
| 1549 | |
---|
| 1550 | void markFacePath(Node ynode, Node xnode, |
---|
| 1551 | OrderMap& order_map, NodeData& node_data) { |
---|
| 1552 | Arc arc = node_data[order_map[ynode]].first; |
---|
| 1553 | Node node = _graph.target(arc); |
---|
| 1554 | _kuratowski.set(arc, true); |
---|
| 1555 | |
---|
| 1556 | while (node != xnode) { |
---|
| 1557 | arc = node_data[order_map[node]].first; |
---|
| 1558 | _kuratowski.set(arc, true); |
---|
| 1559 | node = _graph.target(arc); |
---|
| 1560 | } |
---|
| 1561 | } |
---|
| 1562 | |
---|
| 1563 | void markInternalPath(std::vector<Arc>& path) { |
---|
| 1564 | for (int i = 0; i < int(path.size()); ++i) { |
---|
| 1565 | _kuratowski.set(path[i], true); |
---|
| 1566 | } |
---|
| 1567 | } |
---|
| 1568 | |
---|
| 1569 | void markPilePath(std::vector<Arc>& path) { |
---|
| 1570 | for (int i = 0; i < int(path.size()); ++i) { |
---|
| 1571 | _kuratowski.set(path[i], true); |
---|
| 1572 | } |
---|
| 1573 | } |
---|
| 1574 | |
---|
| 1575 | void isolateKuratowski(Arc arc, NodeData& node_data, |
---|
| 1576 | ArcLists& arc_lists, FlipMap& flip_map, |
---|
| 1577 | OrderMap& order_map, OrderList& order_list, |
---|
| 1578 | PredMap& pred_map, ChildLists& child_lists, |
---|
| 1579 | AncestorMap& ancestor_map, LowMap& low_map, |
---|
| 1580 | EmbedArc& embed_arc, MergeRoots& merge_roots) { |
---|
| 1581 | |
---|
| 1582 | Node root = _graph.source(arc); |
---|
| 1583 | Node enode = _graph.target(arc); |
---|
| 1584 | |
---|
| 1585 | int rorder = order_map[root]; |
---|
| 1586 | |
---|
| 1587 | TypeMap type_map(_graph, 0); |
---|
| 1588 | |
---|
| 1589 | int rn = findComponentRoot(root, enode, child_lists, |
---|
| 1590 | order_map, order_list); |
---|
| 1591 | |
---|
| 1592 | Node xnode = order_list[node_data[rn].next]; |
---|
| 1593 | Node ynode = order_list[node_data[rn].prev]; |
---|
| 1594 | |
---|
| 1595 | // Minor-A |
---|
| 1596 | { |
---|
| 1597 | while (!merge_roots[xnode].empty() || !merge_roots[ynode].empty()) { |
---|
| 1598 | |
---|
| 1599 | if (!merge_roots[xnode].empty()) { |
---|
| 1600 | root = xnode; |
---|
| 1601 | rn = merge_roots[xnode].front(); |
---|
| 1602 | } else { |
---|
| 1603 | root = ynode; |
---|
| 1604 | rn = merge_roots[ynode].front(); |
---|
| 1605 | } |
---|
| 1606 | |
---|
| 1607 | xnode = order_list[node_data[rn].next]; |
---|
| 1608 | ynode = order_list[node_data[rn].prev]; |
---|
| 1609 | } |
---|
| 1610 | |
---|
| 1611 | if (root != _graph.source(arc)) { |
---|
| 1612 | orientComponent(root, rn, order_map, pred_map, |
---|
| 1613 | node_data, arc_lists, flip_map, type_map); |
---|
| 1614 | markFacePath(root, root, order_map, node_data); |
---|
| 1615 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
| 1616 | pred_map, ancestor_map, low_map); |
---|
| 1617 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
| 1618 | pred_map, ancestor_map, low_map); |
---|
| 1619 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
| 1620 | Node lwnode = findPertinent(ynode, order_map, node_data, |
---|
| 1621 | embed_arc, merge_roots); |
---|
| 1622 | |
---|
| 1623 | markPertinentPath(lwnode, order_map, node_data, arc_lists, |
---|
| 1624 | embed_arc, merge_roots); |
---|
| 1625 | |
---|
| 1626 | return; |
---|
| 1627 | } |
---|
| 1628 | } |
---|
| 1629 | |
---|
| 1630 | orientComponent(root, rn, order_map, pred_map, |
---|
| 1631 | node_data, arc_lists, flip_map, type_map); |
---|
| 1632 | |
---|
| 1633 | Node wnode = findPertinent(ynode, order_map, node_data, |
---|
| 1634 | embed_arc, merge_roots); |
---|
| 1635 | setFaceFlags(root, wnode, ynode, xnode, order_map, node_data, type_map); |
---|
| 1636 | |
---|
| 1637 | |
---|
| 1638 | //Minor-B |
---|
| 1639 | if (!merge_roots[wnode].empty()) { |
---|
| 1640 | int cn = merge_roots[wnode].back(); |
---|
| 1641 | Node rep = order_list[cn - order_list.size()]; |
---|
| 1642 | if (low_map[rep] < rorder) { |
---|
| 1643 | markFacePath(root, root, order_map, node_data); |
---|
| 1644 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
| 1645 | pred_map, ancestor_map, low_map); |
---|
| 1646 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
| 1647 | pred_map, ancestor_map, low_map); |
---|
| 1648 | |
---|
| 1649 | Node lwnode, lznode; |
---|
| 1650 | markCommonPath(wnode, rorder, lwnode, lznode, order_list, |
---|
| 1651 | order_map, node_data, arc_lists, embed_arc, |
---|
| 1652 | merge_roots, child_lists, ancestor_map, low_map); |
---|
| 1653 | |
---|
| 1654 | markPertinentPath(lwnode, order_map, node_data, arc_lists, |
---|
| 1655 | embed_arc, merge_roots); |
---|
| 1656 | int zlp = markExternalPath(lznode, order_map, child_lists, |
---|
| 1657 | pred_map, ancestor_map, low_map); |
---|
| 1658 | |
---|
| 1659 | int minlp = xlp < ylp ? xlp : ylp; |
---|
| 1660 | if (zlp < minlp) minlp = zlp; |
---|
| 1661 | |
---|
| 1662 | int maxlp = xlp > ylp ? xlp : ylp; |
---|
| 1663 | if (zlp > maxlp) maxlp = zlp; |
---|
| 1664 | |
---|
| 1665 | markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
---|
| 1666 | |
---|
| 1667 | return; |
---|
| 1668 | } |
---|
| 1669 | } |
---|
| 1670 | |
---|
| 1671 | Node pxnode, pynode; |
---|
| 1672 | std::vector<Arc> ipath; |
---|
| 1673 | findInternalPath(ipath, wnode, root, type_map, order_map, |
---|
| 1674 | node_data, arc_lists); |
---|
| 1675 | setInternalFlags(ipath, type_map); |
---|
| 1676 | pynode = _graph.source(ipath.front()); |
---|
| 1677 | pxnode = _graph.target(ipath.back()); |
---|
| 1678 | |
---|
| 1679 | wnode = findPertinent(pynode, order_map, node_data, |
---|
| 1680 | embed_arc, merge_roots); |
---|
| 1681 | |
---|
| 1682 | // Minor-C |
---|
| 1683 | { |
---|
| 1684 | if (type_map[_graph.source(ipath.front())] == HIGHY) { |
---|
| 1685 | if (type_map[_graph.target(ipath.back())] == HIGHX) { |
---|
| 1686 | markFacePath(xnode, pxnode, order_map, node_data); |
---|
| 1687 | } |
---|
| 1688 | markFacePath(root, xnode, order_map, node_data); |
---|
| 1689 | markPertinentPath(wnode, order_map, node_data, arc_lists, |
---|
| 1690 | embed_arc, merge_roots); |
---|
| 1691 | markInternalPath(ipath); |
---|
| 1692 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
| 1693 | pred_map, ancestor_map, low_map); |
---|
| 1694 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
| 1695 | pred_map, ancestor_map, low_map); |
---|
| 1696 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
| 1697 | return; |
---|
| 1698 | } |
---|
| 1699 | |
---|
| 1700 | if (type_map[_graph.target(ipath.back())] == HIGHX) { |
---|
| 1701 | markFacePath(ynode, root, order_map, node_data); |
---|
| 1702 | markPertinentPath(wnode, order_map, node_data, arc_lists, |
---|
| 1703 | embed_arc, merge_roots); |
---|
| 1704 | markInternalPath(ipath); |
---|
| 1705 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
| 1706 | pred_map, ancestor_map, low_map); |
---|
| 1707 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
| 1708 | pred_map, ancestor_map, low_map); |
---|
| 1709 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
| 1710 | return; |
---|
| 1711 | } |
---|
| 1712 | } |
---|
| 1713 | |
---|
| 1714 | std::vector<Arc> ppath; |
---|
| 1715 | findPilePath(ppath, root, type_map, order_map, node_data, arc_lists); |
---|
| 1716 | |
---|
| 1717 | // Minor-D |
---|
| 1718 | if (!ppath.empty()) { |
---|
| 1719 | markFacePath(ynode, xnode, order_map, node_data); |
---|
| 1720 | markPertinentPath(wnode, order_map, node_data, arc_lists, |
---|
| 1721 | embed_arc, merge_roots); |
---|
| 1722 | markPilePath(ppath); |
---|
| 1723 | markInternalPath(ipath); |
---|
| 1724 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
| 1725 | pred_map, ancestor_map, low_map); |
---|
| 1726 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
| 1727 | pred_map, ancestor_map, low_map); |
---|
| 1728 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
| 1729 | return; |
---|
| 1730 | } |
---|
| 1731 | |
---|
| 1732 | // Minor-E* |
---|
| 1733 | { |
---|
| 1734 | |
---|
| 1735 | if (!external(wnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
| 1736 | Node znode = findExternal(pynode, rorder, order_map, |
---|
| 1737 | child_lists, ancestor_map, |
---|
| 1738 | low_map, node_data); |
---|
| 1739 | |
---|
| 1740 | if (type_map[znode] == LOWY) { |
---|
| 1741 | markFacePath(root, xnode, order_map, node_data); |
---|
| 1742 | markPertinentPath(wnode, order_map, node_data, arc_lists, |
---|
| 1743 | embed_arc, merge_roots); |
---|
| 1744 | markInternalPath(ipath); |
---|
| 1745 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
| 1746 | pred_map, ancestor_map, low_map); |
---|
| 1747 | int zlp = markExternalPath(znode, order_map, child_lists, |
---|
| 1748 | pred_map, ancestor_map, low_map); |
---|
| 1749 | markPredPath(root, order_list[xlp < zlp ? xlp : zlp], pred_map); |
---|
| 1750 | } else { |
---|
| 1751 | markFacePath(ynode, root, order_map, node_data); |
---|
| 1752 | markPertinentPath(wnode, order_map, node_data, arc_lists, |
---|
| 1753 | embed_arc, merge_roots); |
---|
| 1754 | markInternalPath(ipath); |
---|
| 1755 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
| 1756 | pred_map, ancestor_map, low_map); |
---|
| 1757 | int zlp = markExternalPath(znode, order_map, child_lists, |
---|
| 1758 | pred_map, ancestor_map, low_map); |
---|
| 1759 | markPredPath(root, order_list[ylp < zlp ? ylp : zlp], pred_map); |
---|
| 1760 | } |
---|
| 1761 | return; |
---|
| 1762 | } |
---|
| 1763 | |
---|
| 1764 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
| 1765 | pred_map, ancestor_map, low_map); |
---|
| 1766 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
| 1767 | pred_map, ancestor_map, low_map); |
---|
| 1768 | int wlp = markExternalPath(wnode, order_map, child_lists, |
---|
| 1769 | pred_map, ancestor_map, low_map); |
---|
| 1770 | |
---|
| 1771 | if (wlp > xlp && wlp > ylp) { |
---|
| 1772 | markFacePath(root, root, order_map, node_data); |
---|
| 1773 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
| 1774 | return; |
---|
| 1775 | } |
---|
| 1776 | |
---|
| 1777 | markInternalPath(ipath); |
---|
| 1778 | markPertinentPath(wnode, order_map, node_data, arc_lists, |
---|
| 1779 | embed_arc, merge_roots); |
---|
| 1780 | |
---|
| 1781 | if (xlp > ylp && xlp > wlp) { |
---|
| 1782 | markFacePath(root, pynode, order_map, node_data); |
---|
| 1783 | markFacePath(wnode, xnode, order_map, node_data); |
---|
| 1784 | markPredPath(root, order_list[ylp < wlp ? ylp : wlp], pred_map); |
---|
| 1785 | return; |
---|
| 1786 | } |
---|
| 1787 | |
---|
| 1788 | if (ylp > xlp && ylp > wlp) { |
---|
| 1789 | markFacePath(pxnode, root, order_map, node_data); |
---|
| 1790 | markFacePath(ynode, wnode, order_map, node_data); |
---|
| 1791 | markPredPath(root, order_list[xlp < wlp ? xlp : wlp], pred_map); |
---|
| 1792 | return; |
---|
| 1793 | } |
---|
| 1794 | |
---|
| 1795 | if (pynode != ynode) { |
---|
| 1796 | markFacePath(pxnode, wnode, order_map, node_data); |
---|
| 1797 | |
---|
| 1798 | int minlp = xlp < ylp ? xlp : ylp; |
---|
| 1799 | if (wlp < minlp) minlp = wlp; |
---|
| 1800 | |
---|
| 1801 | int maxlp = xlp > ylp ? xlp : ylp; |
---|
| 1802 | if (wlp > maxlp) maxlp = wlp; |
---|
| 1803 | |
---|
| 1804 | markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
---|
| 1805 | return; |
---|
| 1806 | } |
---|
| 1807 | |
---|
| 1808 | if (pxnode != xnode) { |
---|
| 1809 | markFacePath(wnode, pynode, order_map, node_data); |
---|
| 1810 | |
---|
| 1811 | int minlp = xlp < ylp ? xlp : ylp; |
---|
| 1812 | if (wlp < minlp) minlp = wlp; |
---|
| 1813 | |
---|
| 1814 | int maxlp = xlp > ylp ? xlp : ylp; |
---|
| 1815 | if (wlp > maxlp) maxlp = wlp; |
---|
| 1816 | |
---|
| 1817 | markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
---|
| 1818 | return; |
---|
| 1819 | } |
---|
| 1820 | |
---|
| 1821 | markFacePath(root, root, order_map, node_data); |
---|
| 1822 | int minlp = xlp < ylp ? xlp : ylp; |
---|
| 1823 | if (wlp < minlp) minlp = wlp; |
---|
| 1824 | markPredPath(root, order_list[minlp], pred_map); |
---|
| 1825 | return; |
---|
| 1826 | } |
---|
| 1827 | |
---|
| 1828 | } |
---|
| 1829 | |
---|
| 1830 | }; |
---|
| 1831 | |
---|
| 1832 | namespace _planarity_bits { |
---|
| 1833 | |
---|
| 1834 | template <typename Graph, typename EmbeddingMap> |
---|
| 1835 | void makeConnected(Graph& graph, EmbeddingMap& embedding) { |
---|
| 1836 | DfsVisitor<Graph> null_visitor; |
---|
| 1837 | DfsVisit<Graph, DfsVisitor<Graph> > dfs(graph, null_visitor); |
---|
| 1838 | dfs.init(); |
---|
| 1839 | |
---|
| 1840 | typename Graph::Node u = INVALID; |
---|
| 1841 | for (typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
---|
| 1842 | if (!dfs.reached(n)) { |
---|
| 1843 | dfs.addSource(n); |
---|
| 1844 | dfs.start(); |
---|
| 1845 | if (u == INVALID) { |
---|
| 1846 | u = n; |
---|
| 1847 | } else { |
---|
| 1848 | typename Graph::Node v = n; |
---|
| 1849 | |
---|
| 1850 | typename Graph::Arc ue = typename Graph::OutArcIt(graph, u); |
---|
| 1851 | typename Graph::Arc ve = typename Graph::OutArcIt(graph, v); |
---|
| 1852 | |
---|
| 1853 | typename Graph::Arc e = graph.direct(graph.addEdge(u, v), true); |
---|
| 1854 | |
---|
| 1855 | if (ue != INVALID) { |
---|
| 1856 | embedding[e] = embedding[ue]; |
---|
| 1857 | embedding[ue] = e; |
---|
| 1858 | } else { |
---|
| 1859 | embedding[e] = e; |
---|
| 1860 | } |
---|
| 1861 | |
---|
| 1862 | if (ve != INVALID) { |
---|
| 1863 | embedding[graph.oppositeArc(e)] = embedding[ve]; |
---|
| 1864 | embedding[ve] = graph.oppositeArc(e); |
---|
| 1865 | } else { |
---|
| 1866 | embedding[graph.oppositeArc(e)] = graph.oppositeArc(e); |
---|
| 1867 | } |
---|
| 1868 | } |
---|
| 1869 | } |
---|
| 1870 | } |
---|
| 1871 | } |
---|
| 1872 | |
---|
| 1873 | template <typename Graph, typename EmbeddingMap> |
---|
| 1874 | void makeBiNodeConnected(Graph& graph, EmbeddingMap& embedding) { |
---|
| 1875 | typename Graph::template ArcMap<bool> processed(graph); |
---|
| 1876 | |
---|
| 1877 | std::vector<typename Graph::Arc> arcs; |
---|
| 1878 | for (typename Graph::ArcIt e(graph); e != INVALID; ++e) { |
---|
| 1879 | arcs.push_back(e); |
---|
| 1880 | } |
---|
| 1881 | |
---|
| 1882 | IterableBoolMap<Graph, typename Graph::Node> visited(graph, false); |
---|
| 1883 | |
---|
| 1884 | for (int i = 0; i < int(arcs.size()); ++i) { |
---|
| 1885 | typename Graph::Arc pp = arcs[i]; |
---|
| 1886 | if (processed[pp]) continue; |
---|
| 1887 | |
---|
| 1888 | typename Graph::Arc e = embedding[graph.oppositeArc(pp)]; |
---|
| 1889 | processed[e] = true; |
---|
| 1890 | visited.set(graph.source(e), true); |
---|
| 1891 | |
---|
| 1892 | typename Graph::Arc p = e, l = e; |
---|
| 1893 | e = embedding[graph.oppositeArc(e)]; |
---|
| 1894 | |
---|
| 1895 | while (e != l) { |
---|
| 1896 | processed[e] = true; |
---|
| 1897 | |
---|
| 1898 | if (visited[graph.source(e)]) { |
---|
| 1899 | |
---|
| 1900 | typename Graph::Arc n = |
---|
| 1901 | graph.direct(graph.addEdge(graph.source(p), |
---|
| 1902 | graph.target(e)), true); |
---|
| 1903 | embedding[n] = p; |
---|
| 1904 | embedding[graph.oppositeArc(pp)] = n; |
---|
| 1905 | |
---|
| 1906 | embedding[graph.oppositeArc(n)] = |
---|
| 1907 | embedding[graph.oppositeArc(e)]; |
---|
| 1908 | embedding[graph.oppositeArc(e)] = |
---|
| 1909 | graph.oppositeArc(n); |
---|
| 1910 | |
---|
| 1911 | p = n; |
---|
| 1912 | e = embedding[graph.oppositeArc(n)]; |
---|
| 1913 | } else { |
---|
| 1914 | visited.set(graph.source(e), true); |
---|
| 1915 | pp = p; |
---|
| 1916 | p = e; |
---|
| 1917 | e = embedding[graph.oppositeArc(e)]; |
---|
| 1918 | } |
---|
| 1919 | } |
---|
| 1920 | visited.setAll(false); |
---|
| 1921 | } |
---|
| 1922 | } |
---|
| 1923 | |
---|
| 1924 | |
---|
| 1925 | template <typename Graph, typename EmbeddingMap> |
---|
| 1926 | void makeMaxPlanar(Graph& graph, EmbeddingMap& embedding) { |
---|
| 1927 | |
---|
| 1928 | typename Graph::template NodeMap<int> degree(graph); |
---|
| 1929 | |
---|
| 1930 | for (typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
---|
| 1931 | degree[n] = countIncEdges(graph, n); |
---|
| 1932 | } |
---|
| 1933 | |
---|
| 1934 | typename Graph::template ArcMap<bool> processed(graph); |
---|
| 1935 | IterableBoolMap<Graph, typename Graph::Node> visited(graph, false); |
---|
| 1936 | |
---|
| 1937 | std::vector<typename Graph::Arc> arcs; |
---|
| 1938 | for (typename Graph::ArcIt e(graph); e != INVALID; ++e) { |
---|
| 1939 | arcs.push_back(e); |
---|
| 1940 | } |
---|
| 1941 | |
---|
| 1942 | for (int i = 0; i < int(arcs.size()); ++i) { |
---|
| 1943 | typename Graph::Arc e = arcs[i]; |
---|
| 1944 | |
---|
| 1945 | if (processed[e]) continue; |
---|
| 1946 | processed[e] = true; |
---|
| 1947 | |
---|
| 1948 | typename Graph::Arc mine = e; |
---|
| 1949 | int mind = degree[graph.source(e)]; |
---|
| 1950 | |
---|
| 1951 | int face_size = 1; |
---|
| 1952 | |
---|
| 1953 | typename Graph::Arc l = e; |
---|
| 1954 | e = embedding[graph.oppositeArc(e)]; |
---|
| 1955 | while (l != e) { |
---|
| 1956 | processed[e] = true; |
---|
| 1957 | |
---|
| 1958 | ++face_size; |
---|
| 1959 | |
---|
| 1960 | if (degree[graph.source(e)] < mind) { |
---|
| 1961 | mine = e; |
---|
| 1962 | mind = degree[graph.source(e)]; |
---|
| 1963 | } |
---|
| 1964 | |
---|
| 1965 | e = embedding[graph.oppositeArc(e)]; |
---|
| 1966 | } |
---|
| 1967 | |
---|
| 1968 | if (face_size < 4) { |
---|
| 1969 | continue; |
---|
| 1970 | } |
---|
| 1971 | |
---|
| 1972 | typename Graph::Node s = graph.source(mine); |
---|
| 1973 | for (typename Graph::OutArcIt e(graph, s); e != INVALID; ++e) { |
---|
| 1974 | visited.set(graph.target(e), true); |
---|
| 1975 | } |
---|
| 1976 | |
---|
| 1977 | typename Graph::Arc oppe = INVALID; |
---|
| 1978 | |
---|
| 1979 | e = embedding[graph.oppositeArc(mine)]; |
---|
| 1980 | e = embedding[graph.oppositeArc(e)]; |
---|
| 1981 | while (graph.target(e) != s) { |
---|
| 1982 | if (visited[graph.source(e)]) { |
---|
| 1983 | oppe = e; |
---|
| 1984 | break; |
---|
| 1985 | } |
---|
| 1986 | e = embedding[graph.oppositeArc(e)]; |
---|
| 1987 | } |
---|
| 1988 | visited.setAll(false); |
---|
| 1989 | |
---|
| 1990 | if (oppe == INVALID) { |
---|
| 1991 | |
---|
| 1992 | e = embedding[graph.oppositeArc(mine)]; |
---|
| 1993 | typename Graph::Arc pn = mine, p = e; |
---|
| 1994 | |
---|
| 1995 | e = embedding[graph.oppositeArc(e)]; |
---|
| 1996 | while (graph.target(e) != s) { |
---|
| 1997 | typename Graph::Arc n = |
---|
| 1998 | graph.direct(graph.addEdge(s, graph.source(e)), true); |
---|
| 1999 | |
---|
| 2000 | embedding[n] = pn; |
---|
| 2001 | embedding[graph.oppositeArc(n)] = e; |
---|
| 2002 | embedding[graph.oppositeArc(p)] = graph.oppositeArc(n); |
---|
| 2003 | |
---|
| 2004 | pn = n; |
---|
| 2005 | |
---|
| 2006 | p = e; |
---|
| 2007 | e = embedding[graph.oppositeArc(e)]; |
---|
| 2008 | } |
---|
| 2009 | |
---|
| 2010 | embedding[graph.oppositeArc(e)] = pn; |
---|
| 2011 | |
---|
| 2012 | } else { |
---|
| 2013 | |
---|
| 2014 | mine = embedding[graph.oppositeArc(mine)]; |
---|
| 2015 | s = graph.source(mine); |
---|
| 2016 | oppe = embedding[graph.oppositeArc(oppe)]; |
---|
| 2017 | typename Graph::Node t = graph.source(oppe); |
---|
| 2018 | |
---|
| 2019 | typename Graph::Arc ce = graph.direct(graph.addEdge(s, t), true); |
---|
| 2020 | embedding[ce] = mine; |
---|
| 2021 | embedding[graph.oppositeArc(ce)] = oppe; |
---|
| 2022 | |
---|
| 2023 | typename Graph::Arc pn = ce, p = oppe; |
---|
| 2024 | e = embedding[graph.oppositeArc(oppe)]; |
---|
| 2025 | while (graph.target(e) != s) { |
---|
| 2026 | typename Graph::Arc n = |
---|
| 2027 | graph.direct(graph.addEdge(s, graph.source(e)), true); |
---|
| 2028 | |
---|
| 2029 | embedding[n] = pn; |
---|
| 2030 | embedding[graph.oppositeArc(n)] = e; |
---|
| 2031 | embedding[graph.oppositeArc(p)] = graph.oppositeArc(n); |
---|
| 2032 | |
---|
| 2033 | pn = n; |
---|
| 2034 | |
---|
| 2035 | p = e; |
---|
| 2036 | e = embedding[graph.oppositeArc(e)]; |
---|
| 2037 | |
---|
| 2038 | } |
---|
| 2039 | embedding[graph.oppositeArc(e)] = pn; |
---|
| 2040 | |
---|
| 2041 | pn = graph.oppositeArc(ce), p = mine; |
---|
| 2042 | e = embedding[graph.oppositeArc(mine)]; |
---|
| 2043 | while (graph.target(e) != t) { |
---|
| 2044 | typename Graph::Arc n = |
---|
| 2045 | graph.direct(graph.addEdge(t, graph.source(e)), true); |
---|
| 2046 | |
---|
| 2047 | embedding[n] = pn; |
---|
| 2048 | embedding[graph.oppositeArc(n)] = e; |
---|
| 2049 | embedding[graph.oppositeArc(p)] = graph.oppositeArc(n); |
---|
| 2050 | |
---|
| 2051 | pn = n; |
---|
| 2052 | |
---|
| 2053 | p = e; |
---|
| 2054 | e = embedding[graph.oppositeArc(e)]; |
---|
| 2055 | |
---|
| 2056 | } |
---|
| 2057 | embedding[graph.oppositeArc(e)] = pn; |
---|
| 2058 | } |
---|
| 2059 | } |
---|
| 2060 | } |
---|
| 2061 | |
---|
| 2062 | } |
---|
| 2063 | |
---|
| 2064 | /// \ingroup planar |
---|
| 2065 | /// |
---|
| 2066 | /// \brief Schnyder's planar drawing algorithm |
---|
| 2067 | /// |
---|
| 2068 | /// The planar drawing algorithm calculates positions for the nodes |
---|
[896] | 2069 | /// in the plane. These coordinates satisfy that if the edges are |
---|
| 2070 | /// represented with straight lines, then they will not intersect |
---|
[861] | 2071 | /// each other. |
---|
| 2072 | /// |
---|
[896] | 2073 | /// Scnyder's algorithm embeds the graph on an \c (n-2)x(n-2) size grid, |
---|
| 2074 | /// i.e. each node will be located in the \c [0..n-2]x[0..n-2] square. |
---|
[861] | 2075 | /// The time complexity of the algorithm is O(n). |
---|
[896] | 2076 | /// |
---|
| 2077 | /// \see PlanarEmbedding |
---|
[861] | 2078 | template <typename Graph> |
---|
| 2079 | class PlanarDrawing { |
---|
| 2080 | public: |
---|
| 2081 | |
---|
| 2082 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
| 2083 | |
---|
[896] | 2084 | /// \brief The point type for storing coordinates |
---|
[861] | 2085 | typedef dim2::Point<int> Point; |
---|
[896] | 2086 | /// \brief The map type for storing the coordinates of the nodes |
---|
[861] | 2087 | typedef typename Graph::template NodeMap<Point> PointMap; |
---|
| 2088 | |
---|
| 2089 | |
---|
| 2090 | /// \brief Constructor |
---|
| 2091 | /// |
---|
| 2092 | /// Constructor |
---|
[896] | 2093 | /// \pre The graph must be simple, i.e. it should not |
---|
| 2094 | /// contain parallel or loop arcs. |
---|
[861] | 2095 | PlanarDrawing(const Graph& graph) |
---|
| 2096 | : _graph(graph), _point_map(graph) {} |
---|
| 2097 | |
---|
| 2098 | private: |
---|
| 2099 | |
---|
| 2100 | template <typename AuxGraph, typename AuxEmbeddingMap> |
---|
| 2101 | void drawing(const AuxGraph& graph, |
---|
| 2102 | const AuxEmbeddingMap& next, |
---|
| 2103 | PointMap& point_map) { |
---|
| 2104 | TEMPLATE_GRAPH_TYPEDEFS(AuxGraph); |
---|
| 2105 | |
---|
| 2106 | typename AuxGraph::template ArcMap<Arc> prev(graph); |
---|
| 2107 | |
---|
| 2108 | for (NodeIt n(graph); n != INVALID; ++n) { |
---|
| 2109 | Arc e = OutArcIt(graph, n); |
---|
| 2110 | |
---|
| 2111 | Arc p = e, l = e; |
---|
| 2112 | |
---|
| 2113 | e = next[e]; |
---|
| 2114 | while (e != l) { |
---|
| 2115 | prev[e] = p; |
---|
| 2116 | p = e; |
---|
| 2117 | e = next[e]; |
---|
| 2118 | } |
---|
| 2119 | prev[e] = p; |
---|
| 2120 | } |
---|
| 2121 | |
---|
| 2122 | Node anode, bnode, cnode; |
---|
| 2123 | |
---|
| 2124 | { |
---|
| 2125 | Arc e = ArcIt(graph); |
---|
| 2126 | anode = graph.source(e); |
---|
| 2127 | bnode = graph.target(e); |
---|
| 2128 | cnode = graph.target(next[graph.oppositeArc(e)]); |
---|
| 2129 | } |
---|
| 2130 | |
---|
| 2131 | IterableBoolMap<AuxGraph, Node> proper(graph, false); |
---|
| 2132 | typename AuxGraph::template NodeMap<int> conn(graph, -1); |
---|
| 2133 | |
---|
| 2134 | conn[anode] = conn[bnode] = -2; |
---|
| 2135 | { |
---|
| 2136 | for (OutArcIt e(graph, anode); e != INVALID; ++e) { |
---|
| 2137 | Node m = graph.target(e); |
---|
| 2138 | if (conn[m] == -1) { |
---|
| 2139 | conn[m] = 1; |
---|
| 2140 | } |
---|
| 2141 | } |
---|
| 2142 | conn[cnode] = 2; |
---|
| 2143 | |
---|
| 2144 | for (OutArcIt e(graph, bnode); e != INVALID; ++e) { |
---|
| 2145 | Node m = graph.target(e); |
---|
| 2146 | if (conn[m] == -1) { |
---|
| 2147 | conn[m] = 1; |
---|
| 2148 | } else if (conn[m] != -2) { |
---|
| 2149 | conn[m] += 1; |
---|
| 2150 | Arc pe = graph.oppositeArc(e); |
---|
| 2151 | if (conn[graph.target(next[pe])] == -2) { |
---|
| 2152 | conn[m] -= 1; |
---|
| 2153 | } |
---|
| 2154 | if (conn[graph.target(prev[pe])] == -2) { |
---|
| 2155 | conn[m] -= 1; |
---|
| 2156 | } |
---|
| 2157 | |
---|
| 2158 | proper.set(m, conn[m] == 1); |
---|
| 2159 | } |
---|
| 2160 | } |
---|
| 2161 | } |
---|
| 2162 | |
---|
| 2163 | |
---|
| 2164 | typename AuxGraph::template ArcMap<int> angle(graph, -1); |
---|
| 2165 | |
---|
| 2166 | while (proper.trueNum() != 0) { |
---|
| 2167 | Node n = typename IterableBoolMap<AuxGraph, Node>::TrueIt(proper); |
---|
| 2168 | proper.set(n, false); |
---|
| 2169 | conn[n] = -2; |
---|
| 2170 | |
---|
| 2171 | for (OutArcIt e(graph, n); e != INVALID; ++e) { |
---|
| 2172 | Node m = graph.target(e); |
---|
| 2173 | if (conn[m] == -1) { |
---|
| 2174 | conn[m] = 1; |
---|
| 2175 | } else if (conn[m] != -2) { |
---|
| 2176 | conn[m] += 1; |
---|
| 2177 | Arc pe = graph.oppositeArc(e); |
---|
| 2178 | if (conn[graph.target(next[pe])] == -2) { |
---|
| 2179 | conn[m] -= 1; |
---|
| 2180 | } |
---|
| 2181 | if (conn[graph.target(prev[pe])] == -2) { |
---|
| 2182 | conn[m] -= 1; |
---|
| 2183 | } |
---|
| 2184 | |
---|
| 2185 | proper.set(m, conn[m] == 1); |
---|
| 2186 | } |
---|
| 2187 | } |
---|
| 2188 | |
---|
| 2189 | { |
---|
| 2190 | Arc e = OutArcIt(graph, n); |
---|
| 2191 | Arc p = e, l = e; |
---|
| 2192 | |
---|
| 2193 | e = next[e]; |
---|
| 2194 | while (e != l) { |
---|
| 2195 | |
---|
| 2196 | if (conn[graph.target(e)] == -2 && conn[graph.target(p)] == -2) { |
---|
| 2197 | Arc f = e; |
---|
| 2198 | angle[f] = 0; |
---|
| 2199 | f = next[graph.oppositeArc(f)]; |
---|
| 2200 | angle[f] = 1; |
---|
| 2201 | f = next[graph.oppositeArc(f)]; |
---|
| 2202 | angle[f] = 2; |
---|
| 2203 | } |
---|
| 2204 | |
---|
| 2205 | p = e; |
---|
| 2206 | e = next[e]; |
---|
| 2207 | } |
---|
| 2208 | |
---|
| 2209 | if (conn[graph.target(e)] == -2 && conn[graph.target(p)] == -2) { |
---|
| 2210 | Arc f = e; |
---|
| 2211 | angle[f] = 0; |
---|
| 2212 | f = next[graph.oppositeArc(f)]; |
---|
| 2213 | angle[f] = 1; |
---|
| 2214 | f = next[graph.oppositeArc(f)]; |
---|
| 2215 | angle[f] = 2; |
---|
| 2216 | } |
---|
| 2217 | } |
---|
| 2218 | } |
---|
| 2219 | |
---|
| 2220 | typename AuxGraph::template NodeMap<Node> apred(graph, INVALID); |
---|
| 2221 | typename AuxGraph::template NodeMap<Node> bpred(graph, INVALID); |
---|
| 2222 | typename AuxGraph::template NodeMap<Node> cpred(graph, INVALID); |
---|
| 2223 | |
---|
| 2224 | typename AuxGraph::template NodeMap<int> apredid(graph, -1); |
---|
| 2225 | typename AuxGraph::template NodeMap<int> bpredid(graph, -1); |
---|
| 2226 | typename AuxGraph::template NodeMap<int> cpredid(graph, -1); |
---|
| 2227 | |
---|
| 2228 | for (ArcIt e(graph); e != INVALID; ++e) { |
---|
| 2229 | if (angle[e] == angle[next[e]]) { |
---|
| 2230 | switch (angle[e]) { |
---|
| 2231 | case 2: |
---|
| 2232 | apred[graph.target(e)] = graph.source(e); |
---|
| 2233 | apredid[graph.target(e)] = graph.id(graph.source(e)); |
---|
| 2234 | break; |
---|
| 2235 | case 1: |
---|
| 2236 | bpred[graph.target(e)] = graph.source(e); |
---|
| 2237 | bpredid[graph.target(e)] = graph.id(graph.source(e)); |
---|
| 2238 | break; |
---|
| 2239 | case 0: |
---|
| 2240 | cpred[graph.target(e)] = graph.source(e); |
---|
| 2241 | cpredid[graph.target(e)] = graph.id(graph.source(e)); |
---|
| 2242 | break; |
---|
| 2243 | } |
---|
| 2244 | } |
---|
| 2245 | } |
---|
| 2246 | |
---|
| 2247 | cpred[anode] = INVALID; |
---|
| 2248 | cpred[bnode] = INVALID; |
---|
| 2249 | |
---|
| 2250 | std::vector<Node> aorder, border, corder; |
---|
| 2251 | |
---|
| 2252 | { |
---|
| 2253 | typename AuxGraph::template NodeMap<bool> processed(graph, false); |
---|
| 2254 | std::vector<Node> st; |
---|
| 2255 | for (NodeIt n(graph); n != INVALID; ++n) { |
---|
| 2256 | if (!processed[n] && n != bnode && n != cnode) { |
---|
| 2257 | st.push_back(n); |
---|
| 2258 | processed[n] = true; |
---|
| 2259 | Node m = apred[n]; |
---|
| 2260 | while (m != INVALID && !processed[m]) { |
---|
| 2261 | st.push_back(m); |
---|
| 2262 | processed[m] = true; |
---|
| 2263 | m = apred[m]; |
---|
| 2264 | } |
---|
| 2265 | while (!st.empty()) { |
---|
| 2266 | aorder.push_back(st.back()); |
---|
| 2267 | st.pop_back(); |
---|
| 2268 | } |
---|
| 2269 | } |
---|
| 2270 | } |
---|
| 2271 | } |
---|
| 2272 | |
---|
| 2273 | { |
---|
| 2274 | typename AuxGraph::template NodeMap<bool> processed(graph, false); |
---|
| 2275 | std::vector<Node> st; |
---|
| 2276 | for (NodeIt n(graph); n != INVALID; ++n) { |
---|
| 2277 | if (!processed[n] && n != cnode && n != anode) { |
---|
| 2278 | st.push_back(n); |
---|
| 2279 | processed[n] = true; |
---|
| 2280 | Node m = bpred[n]; |
---|
| 2281 | while (m != INVALID && !processed[m]) { |
---|
| 2282 | st.push_back(m); |
---|
| 2283 | processed[m] = true; |
---|
| 2284 | m = bpred[m]; |
---|
| 2285 | } |
---|
| 2286 | while (!st.empty()) { |
---|
| 2287 | border.push_back(st.back()); |
---|
| 2288 | st.pop_back(); |
---|
| 2289 | } |
---|
| 2290 | } |
---|
| 2291 | } |
---|
| 2292 | } |
---|
| 2293 | |
---|
| 2294 | { |
---|
| 2295 | typename AuxGraph::template NodeMap<bool> processed(graph, false); |
---|
| 2296 | std::vector<Node> st; |
---|
| 2297 | for (NodeIt n(graph); n != INVALID; ++n) { |
---|
| 2298 | if (!processed[n] && n != anode && n != bnode) { |
---|
| 2299 | st.push_back(n); |
---|
| 2300 | processed[n] = true; |
---|
| 2301 | Node m = cpred[n]; |
---|
| 2302 | while (m != INVALID && !processed[m]) { |
---|
| 2303 | st.push_back(m); |
---|
| 2304 | processed[m] = true; |
---|
| 2305 | m = cpred[m]; |
---|
| 2306 | } |
---|
| 2307 | while (!st.empty()) { |
---|
| 2308 | corder.push_back(st.back()); |
---|
| 2309 | st.pop_back(); |
---|
| 2310 | } |
---|
| 2311 | } |
---|
| 2312 | } |
---|
| 2313 | } |
---|
| 2314 | |
---|
| 2315 | typename AuxGraph::template NodeMap<int> atree(graph, 0); |
---|
| 2316 | for (int i = aorder.size() - 1; i >= 0; --i) { |
---|
| 2317 | Node n = aorder[i]; |
---|
| 2318 | atree[n] = 1; |
---|
| 2319 | for (OutArcIt e(graph, n); e != INVALID; ++e) { |
---|
| 2320 | if (apred[graph.target(e)] == n) { |
---|
| 2321 | atree[n] += atree[graph.target(e)]; |
---|
| 2322 | } |
---|
| 2323 | } |
---|
| 2324 | } |
---|
| 2325 | |
---|
| 2326 | typename AuxGraph::template NodeMap<int> btree(graph, 0); |
---|
| 2327 | for (int i = border.size() - 1; i >= 0; --i) { |
---|
| 2328 | Node n = border[i]; |
---|
| 2329 | btree[n] = 1; |
---|
| 2330 | for (OutArcIt e(graph, n); e != INVALID; ++e) { |
---|
| 2331 | if (bpred[graph.target(e)] == n) { |
---|
| 2332 | btree[n] += btree[graph.target(e)]; |
---|
| 2333 | } |
---|
| 2334 | } |
---|
| 2335 | } |
---|
| 2336 | |
---|
| 2337 | typename AuxGraph::template NodeMap<int> apath(graph, 0); |
---|
| 2338 | apath[bnode] = apath[cnode] = 1; |
---|
| 2339 | typename AuxGraph::template NodeMap<int> apath_btree(graph, 0); |
---|
| 2340 | apath_btree[bnode] = btree[bnode]; |
---|
| 2341 | for (int i = 1; i < int(aorder.size()); ++i) { |
---|
| 2342 | Node n = aorder[i]; |
---|
| 2343 | apath[n] = apath[apred[n]] + 1; |
---|
| 2344 | apath_btree[n] = btree[n] + apath_btree[apred[n]]; |
---|
| 2345 | } |
---|
| 2346 | |
---|
| 2347 | typename AuxGraph::template NodeMap<int> bpath_atree(graph, 0); |
---|
| 2348 | bpath_atree[anode] = atree[anode]; |
---|
| 2349 | for (int i = 1; i < int(border.size()); ++i) { |
---|
| 2350 | Node n = border[i]; |
---|
| 2351 | bpath_atree[n] = atree[n] + bpath_atree[bpred[n]]; |
---|
| 2352 | } |
---|
| 2353 | |
---|
| 2354 | typename AuxGraph::template NodeMap<int> cpath(graph, 0); |
---|
| 2355 | cpath[anode] = cpath[bnode] = 1; |
---|
| 2356 | typename AuxGraph::template NodeMap<int> cpath_atree(graph, 0); |
---|
| 2357 | cpath_atree[anode] = atree[anode]; |
---|
| 2358 | typename AuxGraph::template NodeMap<int> cpath_btree(graph, 0); |
---|
| 2359 | cpath_btree[bnode] = btree[bnode]; |
---|
| 2360 | for (int i = 1; i < int(corder.size()); ++i) { |
---|
| 2361 | Node n = corder[i]; |
---|
| 2362 | cpath[n] = cpath[cpred[n]] + 1; |
---|
| 2363 | cpath_atree[n] = atree[n] + cpath_atree[cpred[n]]; |
---|
| 2364 | cpath_btree[n] = btree[n] + cpath_btree[cpred[n]]; |
---|
| 2365 | } |
---|
| 2366 | |
---|
| 2367 | typename AuxGraph::template NodeMap<int> third(graph); |
---|
| 2368 | for (NodeIt n(graph); n != INVALID; ++n) { |
---|
| 2369 | point_map[n].x = |
---|
| 2370 | bpath_atree[n] + cpath_atree[n] - atree[n] - cpath[n] + 1; |
---|
| 2371 | point_map[n].y = |
---|
| 2372 | cpath_btree[n] + apath_btree[n] - btree[n] - apath[n] + 1; |
---|
| 2373 | } |
---|
| 2374 | |
---|
| 2375 | } |
---|
| 2376 | |
---|
| 2377 | public: |
---|
| 2378 | |
---|
[896] | 2379 | /// \brief Calculate the node positions |
---|
[861] | 2380 | /// |
---|
[896] | 2381 | /// This function calculates the node positions on the plane. |
---|
| 2382 | /// \return \c true if the graph is planar. |
---|
[861] | 2383 | bool run() { |
---|
| 2384 | PlanarEmbedding<Graph> pe(_graph); |
---|
| 2385 | if (!pe.run()) return false; |
---|
| 2386 | |
---|
| 2387 | run(pe); |
---|
| 2388 | return true; |
---|
| 2389 | } |
---|
| 2390 | |
---|
[896] | 2391 | /// \brief Calculate the node positions according to a |
---|
[861] | 2392 | /// combinatorical embedding |
---|
| 2393 | /// |
---|
[896] | 2394 | /// This function calculates the node positions on the plane. |
---|
| 2395 | /// The given \c embedding map should contain a valid combinatorical |
---|
| 2396 | /// embedding, i.e. a valid cyclic order of the arcs. |
---|
| 2397 | /// It can be computed using PlanarEmbedding. |
---|
[861] | 2398 | template <typename EmbeddingMap> |
---|
| 2399 | void run(const EmbeddingMap& embedding) { |
---|
| 2400 | typedef SmartEdgeSet<Graph> AuxGraph; |
---|
| 2401 | |
---|
| 2402 | if (3 * countNodes(_graph) - 6 == countEdges(_graph)) { |
---|
| 2403 | drawing(_graph, embedding, _point_map); |
---|
| 2404 | return; |
---|
| 2405 | } |
---|
| 2406 | |
---|
| 2407 | AuxGraph aux_graph(_graph); |
---|
| 2408 | typename AuxGraph::template ArcMap<typename AuxGraph::Arc> |
---|
| 2409 | aux_embedding(aux_graph); |
---|
| 2410 | |
---|
| 2411 | { |
---|
| 2412 | |
---|
| 2413 | typename Graph::template EdgeMap<typename AuxGraph::Edge> |
---|
| 2414 | ref(_graph); |
---|
| 2415 | |
---|
| 2416 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 2417 | ref[e] = aux_graph.addEdge(_graph.u(e), _graph.v(e)); |
---|
| 2418 | } |
---|
| 2419 | |
---|
| 2420 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 2421 | Arc ee = embedding[_graph.direct(e, true)]; |
---|
| 2422 | aux_embedding[aux_graph.direct(ref[e], true)] = |
---|
| 2423 | aux_graph.direct(ref[ee], _graph.direction(ee)); |
---|
| 2424 | ee = embedding[_graph.direct(e, false)]; |
---|
| 2425 | aux_embedding[aux_graph.direct(ref[e], false)] = |
---|
| 2426 | aux_graph.direct(ref[ee], _graph.direction(ee)); |
---|
| 2427 | } |
---|
| 2428 | } |
---|
| 2429 | _planarity_bits::makeConnected(aux_graph, aux_embedding); |
---|
| 2430 | _planarity_bits::makeBiNodeConnected(aux_graph, aux_embedding); |
---|
| 2431 | _planarity_bits::makeMaxPlanar(aux_graph, aux_embedding); |
---|
| 2432 | drawing(aux_graph, aux_embedding, _point_map); |
---|
| 2433 | } |
---|
| 2434 | |
---|
| 2435 | /// \brief The coordinate of the given node |
---|
| 2436 | /// |
---|
[896] | 2437 | /// This function returns the coordinate of the given node. |
---|
[861] | 2438 | Point operator[](const Node& node) const { |
---|
| 2439 | return _point_map[node]; |
---|
| 2440 | } |
---|
| 2441 | |
---|
[896] | 2442 | /// \brief Return the grid embedding in a node map |
---|
[861] | 2443 | /// |
---|
[896] | 2444 | /// This function returns the grid embedding in a node map of |
---|
| 2445 | /// \c dim2::Point<int> coordinates. |
---|
[861] | 2446 | const PointMap& coords() const { |
---|
| 2447 | return _point_map; |
---|
| 2448 | } |
---|
| 2449 | |
---|
| 2450 | private: |
---|
| 2451 | |
---|
| 2452 | const Graph& _graph; |
---|
| 2453 | PointMap _point_map; |
---|
| 2454 | |
---|
| 2455 | }; |
---|
| 2456 | |
---|
| 2457 | namespace _planarity_bits { |
---|
| 2458 | |
---|
| 2459 | template <typename ColorMap> |
---|
| 2460 | class KempeFilter { |
---|
| 2461 | public: |
---|
| 2462 | typedef typename ColorMap::Key Key; |
---|
| 2463 | typedef bool Value; |
---|
| 2464 | |
---|
| 2465 | KempeFilter(const ColorMap& color_map, |
---|
| 2466 | const typename ColorMap::Value& first, |
---|
| 2467 | const typename ColorMap::Value& second) |
---|
| 2468 | : _color_map(color_map), _first(first), _second(second) {} |
---|
| 2469 | |
---|
| 2470 | Value operator[](const Key& key) const { |
---|
| 2471 | return _color_map[key] == _first || _color_map[key] == _second; |
---|
| 2472 | } |
---|
| 2473 | |
---|
| 2474 | private: |
---|
| 2475 | const ColorMap& _color_map; |
---|
| 2476 | typename ColorMap::Value _first, _second; |
---|
| 2477 | }; |
---|
| 2478 | } |
---|
| 2479 | |
---|
| 2480 | /// \ingroup planar |
---|
| 2481 | /// |
---|
| 2482 | /// \brief Coloring planar graphs |
---|
| 2483 | /// |
---|
| 2484 | /// The graph coloring problem is the coloring of the graph nodes |
---|
[896] | 2485 | /// so that there are no adjacent nodes with the same color. The |
---|
| 2486 | /// planar graphs can always be colored with four colors, which is |
---|
| 2487 | /// proved by Appel and Haken. Their proofs provide a quadratic |
---|
[861] | 2488 | /// time algorithm for four coloring, but it could not be used to |
---|
[896] | 2489 | /// implement an efficient algorithm. The five and six coloring can be |
---|
| 2490 | /// made in linear time, but in this class, the five coloring has |
---|
[861] | 2491 | /// quadratic worst case time complexity. The two coloring (if |
---|
| 2492 | /// possible) is solvable with a graph search algorithm and it is |
---|
| 2493 | /// implemented in \ref bipartitePartitions() function in LEMON. To |
---|
[896] | 2494 | /// decide whether a planar graph is three colorable is NP-complete. |
---|
[861] | 2495 | /// |
---|
| 2496 | /// This class contains member functions for calculate colorings |
---|
| 2497 | /// with five and six colors. The six coloring algorithm is a simple |
---|
| 2498 | /// greedy coloring on the backward minimum outgoing order of nodes. |
---|
[896] | 2499 | /// This order can be computed by selecting the node with least |
---|
| 2500 | /// outgoing arcs to unprocessed nodes in each phase. This order |
---|
[861] | 2501 | /// guarantees that when a node is chosen for coloring it has at |
---|
| 2502 | /// most five already colored adjacents. The five coloring algorithm |
---|
| 2503 | /// use the same method, but if the greedy approach fails to color |
---|
| 2504 | /// with five colors, i.e. the node has five already different |
---|
| 2505 | /// colored neighbours, it swaps the colors in one of the connected |
---|
| 2506 | /// two colored sets with the Kempe recoloring method. |
---|
| 2507 | template <typename Graph> |
---|
| 2508 | class PlanarColoring { |
---|
| 2509 | public: |
---|
| 2510 | |
---|
| 2511 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
| 2512 | |
---|
[896] | 2513 | /// \brief The map type for storing color indices |
---|
[861] | 2514 | typedef typename Graph::template NodeMap<int> IndexMap; |
---|
[896] | 2515 | /// \brief The map type for storing colors |
---|
| 2516 | /// |
---|
| 2517 | /// The map type for storing colors. |
---|
| 2518 | /// \see Palette, Color |
---|
[861] | 2519 | typedef ComposeMap<Palette, IndexMap> ColorMap; |
---|
| 2520 | |
---|
| 2521 | /// \brief Constructor |
---|
| 2522 | /// |
---|
[896] | 2523 | /// Constructor. |
---|
| 2524 | /// \pre The graph must be simple, i.e. it should not |
---|
| 2525 | /// contain parallel or loop arcs. |
---|
[861] | 2526 | PlanarColoring(const Graph& graph) |
---|
| 2527 | : _graph(graph), _color_map(graph), _palette(0) { |
---|
| 2528 | _palette.add(Color(1,0,0)); |
---|
| 2529 | _palette.add(Color(0,1,0)); |
---|
| 2530 | _palette.add(Color(0,0,1)); |
---|
| 2531 | _palette.add(Color(1,1,0)); |
---|
| 2532 | _palette.add(Color(1,0,1)); |
---|
| 2533 | _palette.add(Color(0,1,1)); |
---|
| 2534 | } |
---|
| 2535 | |
---|
[896] | 2536 | /// \brief Return the node map of color indices |
---|
[861] | 2537 | /// |
---|
[896] | 2538 | /// This function returns the node map of color indices. The values are |
---|
| 2539 | /// in the range \c [0..4] or \c [0..5] according to the coloring method. |
---|
[861] | 2540 | IndexMap colorIndexMap() const { |
---|
| 2541 | return _color_map; |
---|
| 2542 | } |
---|
| 2543 | |
---|
[896] | 2544 | /// \brief Return the node map of colors |
---|
[861] | 2545 | /// |
---|
[896] | 2546 | /// This function returns the node map of colors. The values are among |
---|
| 2547 | /// five or six distinct \ref lemon::Color "colors". |
---|
[861] | 2548 | ColorMap colorMap() const { |
---|
| 2549 | return composeMap(_palette, _color_map); |
---|
| 2550 | } |
---|
| 2551 | |
---|
[896] | 2552 | /// \brief Return the color index of the node |
---|
[861] | 2553 | /// |
---|
[896] | 2554 | /// This function returns the color index of the given node. The value is |
---|
| 2555 | /// in the range \c [0..4] or \c [0..5] according to the coloring method. |
---|
[861] | 2556 | int colorIndex(const Node& node) const { |
---|
| 2557 | return _color_map[node]; |
---|
| 2558 | } |
---|
| 2559 | |
---|
[896] | 2560 | /// \brief Return the color of the node |
---|
[861] | 2561 | /// |
---|
[896] | 2562 | /// This function returns the color of the given node. The value is among |
---|
| 2563 | /// five or six distinct \ref lemon::Color "colors". |
---|
[861] | 2564 | Color color(const Node& node) const { |
---|
| 2565 | return _palette[_color_map[node]]; |
---|
| 2566 | } |
---|
| 2567 | |
---|
| 2568 | |
---|
[896] | 2569 | /// \brief Calculate a coloring with at most six colors |
---|
[861] | 2570 | /// |
---|
| 2571 | /// This function calculates a coloring with at most six colors. The time |
---|
| 2572 | /// complexity of this variant is linear in the size of the graph. |
---|
[896] | 2573 | /// \return \c true if the algorithm could color the graph with six colors. |
---|
| 2574 | /// If the algorithm fails, then the graph is not planar. |
---|
| 2575 | /// \note This function can return \c true if the graph is not |
---|
| 2576 | /// planar, but it can be colored with at most six colors. |
---|
[861] | 2577 | bool runSixColoring() { |
---|
| 2578 | |
---|
| 2579 | typename Graph::template NodeMap<int> heap_index(_graph, -1); |
---|
| 2580 | BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index); |
---|
| 2581 | |
---|
| 2582 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 2583 | _color_map[n] = -2; |
---|
| 2584 | heap.push(n, countOutArcs(_graph, n)); |
---|
| 2585 | } |
---|
| 2586 | |
---|
| 2587 | std::vector<Node> order; |
---|
| 2588 | |
---|
| 2589 | while (!heap.empty()) { |
---|
| 2590 | Node n = heap.top(); |
---|
| 2591 | heap.pop(); |
---|
| 2592 | _color_map[n] = -1; |
---|
| 2593 | order.push_back(n); |
---|
| 2594 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 2595 | Node t = _graph.runningNode(e); |
---|
| 2596 | if (_color_map[t] == -2) { |
---|
| 2597 | heap.decrease(t, heap[t] - 1); |
---|
| 2598 | } |
---|
| 2599 | } |
---|
| 2600 | } |
---|
| 2601 | |
---|
| 2602 | for (int i = order.size() - 1; i >= 0; --i) { |
---|
| 2603 | std::vector<bool> forbidden(6, false); |
---|
| 2604 | for (OutArcIt e(_graph, order[i]); e != INVALID; ++e) { |
---|
| 2605 | Node t = _graph.runningNode(e); |
---|
| 2606 | if (_color_map[t] != -1) { |
---|
| 2607 | forbidden[_color_map[t]] = true; |
---|
| 2608 | } |
---|
| 2609 | } |
---|
| 2610 | for (int k = 0; k < 6; ++k) { |
---|
| 2611 | if (!forbidden[k]) { |
---|
| 2612 | _color_map[order[i]] = k; |
---|
| 2613 | break; |
---|
| 2614 | } |
---|
| 2615 | } |
---|
| 2616 | if (_color_map[order[i]] == -1) { |
---|
| 2617 | return false; |
---|
| 2618 | } |
---|
| 2619 | } |
---|
| 2620 | return true; |
---|
| 2621 | } |
---|
| 2622 | |
---|
| 2623 | private: |
---|
| 2624 | |
---|
| 2625 | bool recolor(const Node& u, const Node& v) { |
---|
| 2626 | int ucolor = _color_map[u]; |
---|
| 2627 | int vcolor = _color_map[v]; |
---|
| 2628 | typedef _planarity_bits::KempeFilter<IndexMap> KempeFilter; |
---|
| 2629 | KempeFilter filter(_color_map, ucolor, vcolor); |
---|
| 2630 | |
---|
| 2631 | typedef FilterNodes<const Graph, const KempeFilter> KempeGraph; |
---|
| 2632 | KempeGraph kempe_graph(_graph, filter); |
---|
| 2633 | |
---|
| 2634 | std::vector<Node> comp; |
---|
| 2635 | Bfs<KempeGraph> bfs(kempe_graph); |
---|
| 2636 | bfs.init(); |
---|
| 2637 | bfs.addSource(u); |
---|
| 2638 | while (!bfs.emptyQueue()) { |
---|
| 2639 | Node n = bfs.nextNode(); |
---|
| 2640 | if (n == v) return false; |
---|
| 2641 | comp.push_back(n); |
---|
| 2642 | bfs.processNextNode(); |
---|
| 2643 | } |
---|
| 2644 | |
---|
| 2645 | int scolor = ucolor + vcolor; |
---|
| 2646 | for (int i = 0; i < static_cast<int>(comp.size()); ++i) { |
---|
| 2647 | _color_map[comp[i]] = scolor - _color_map[comp[i]]; |
---|
| 2648 | } |
---|
| 2649 | |
---|
| 2650 | return true; |
---|
| 2651 | } |
---|
| 2652 | |
---|
| 2653 | template <typename EmbeddingMap> |
---|
| 2654 | void kempeRecoloring(const Node& node, const EmbeddingMap& embedding) { |
---|
| 2655 | std::vector<Node> nodes; |
---|
| 2656 | nodes.reserve(4); |
---|
| 2657 | |
---|
| 2658 | for (Arc e = OutArcIt(_graph, node); e != INVALID; e = embedding[e]) { |
---|
| 2659 | Node t = _graph.target(e); |
---|
| 2660 | if (_color_map[t] != -1) { |
---|
| 2661 | nodes.push_back(t); |
---|
| 2662 | if (nodes.size() == 4) break; |
---|
| 2663 | } |
---|
| 2664 | } |
---|
| 2665 | |
---|
| 2666 | int color = _color_map[nodes[0]]; |
---|
| 2667 | if (recolor(nodes[0], nodes[2])) { |
---|
| 2668 | _color_map[node] = color; |
---|
| 2669 | } else { |
---|
| 2670 | color = _color_map[nodes[1]]; |
---|
| 2671 | recolor(nodes[1], nodes[3]); |
---|
| 2672 | _color_map[node] = color; |
---|
| 2673 | } |
---|
| 2674 | } |
---|
| 2675 | |
---|
| 2676 | public: |
---|
| 2677 | |
---|
[896] | 2678 | /// \brief Calculate a coloring with at most five colors |
---|
[861] | 2679 | /// |
---|
| 2680 | /// This function calculates a coloring with at most five |
---|
| 2681 | /// colors. The worst case time complexity of this variant is |
---|
| 2682 | /// quadratic in the size of the graph. |
---|
[896] | 2683 | /// \param embedding This map should contain a valid combinatorical |
---|
| 2684 | /// embedding, i.e. a valid cyclic order of the arcs. |
---|
| 2685 | /// It can be computed using PlanarEmbedding. |
---|
[861] | 2686 | template <typename EmbeddingMap> |
---|
| 2687 | void runFiveColoring(const EmbeddingMap& embedding) { |
---|
| 2688 | |
---|
| 2689 | typename Graph::template NodeMap<int> heap_index(_graph, -1); |
---|
| 2690 | BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index); |
---|
| 2691 | |
---|
| 2692 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 2693 | _color_map[n] = -2; |
---|
| 2694 | heap.push(n, countOutArcs(_graph, n)); |
---|
| 2695 | } |
---|
| 2696 | |
---|
| 2697 | std::vector<Node> order; |
---|
| 2698 | |
---|
| 2699 | while (!heap.empty()) { |
---|
| 2700 | Node n = heap.top(); |
---|
| 2701 | heap.pop(); |
---|
| 2702 | _color_map[n] = -1; |
---|
| 2703 | order.push_back(n); |
---|
| 2704 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 2705 | Node t = _graph.runningNode(e); |
---|
| 2706 | if (_color_map[t] == -2) { |
---|
| 2707 | heap.decrease(t, heap[t] - 1); |
---|
| 2708 | } |
---|
| 2709 | } |
---|
| 2710 | } |
---|
| 2711 | |
---|
| 2712 | for (int i = order.size() - 1; i >= 0; --i) { |
---|
| 2713 | std::vector<bool> forbidden(5, false); |
---|
| 2714 | for (OutArcIt e(_graph, order[i]); e != INVALID; ++e) { |
---|
| 2715 | Node t = _graph.runningNode(e); |
---|
| 2716 | if (_color_map[t] != -1) { |
---|
| 2717 | forbidden[_color_map[t]] = true; |
---|
| 2718 | } |
---|
| 2719 | } |
---|
| 2720 | for (int k = 0; k < 5; ++k) { |
---|
| 2721 | if (!forbidden[k]) { |
---|
| 2722 | _color_map[order[i]] = k; |
---|
| 2723 | break; |
---|
| 2724 | } |
---|
| 2725 | } |
---|
| 2726 | if (_color_map[order[i]] == -1) { |
---|
| 2727 | kempeRecoloring(order[i], embedding); |
---|
| 2728 | } |
---|
| 2729 | } |
---|
| 2730 | } |
---|
| 2731 | |
---|
[896] | 2732 | /// \brief Calculate a coloring with at most five colors |
---|
[861] | 2733 | /// |
---|
| 2734 | /// This function calculates a coloring with at most five |
---|
| 2735 | /// colors. The worst case time complexity of this variant is |
---|
| 2736 | /// quadratic in the size of the graph. |
---|
[896] | 2737 | /// \return \c true if the graph is planar. |
---|
[861] | 2738 | bool runFiveColoring() { |
---|
| 2739 | PlanarEmbedding<Graph> pe(_graph); |
---|
| 2740 | if (!pe.run()) return false; |
---|
| 2741 | |
---|
| 2742 | runFiveColoring(pe.embeddingMap()); |
---|
| 2743 | return true; |
---|
| 2744 | } |
---|
| 2745 | |
---|
| 2746 | private: |
---|
| 2747 | |
---|
| 2748 | const Graph& _graph; |
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| 2749 | IndexMap _color_map; |
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| 2750 | Palette _palette; |
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| 2751 | }; |
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| 2752 | |
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| 2753 | } |
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| 2754 | |
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| 2755 | #endif |
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