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