[2480] | 1 | /* -*- C++ -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2007 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | #ifndef LEMON_PLANARITY_H |
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| 19 | #define LEMON_PLANARITY_H |
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| 20 | |
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| 21 | /// \ingroup graph_prop |
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| 22 | /// \file |
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| 23 | /// \brief Planarity checking, embedding |
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| 24 | |
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| 25 | #include <vector> |
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| 26 | #include <list> |
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| 27 | |
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| 28 | #include <lemon/dfs.h> |
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| 29 | #include <lemon/radix_sort.h> |
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| 30 | #include <lemon/maps.h> |
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| 31 | #include <lemon/path.h> |
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| 32 | |
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| 33 | |
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| 34 | namespace lemon { |
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| 35 | |
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| 36 | namespace _planarity_bits { |
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| 37 | |
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| 38 | template <typename UGraph> |
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| 39 | struct PlanarityVisitor : DfsVisitor<UGraph> { |
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| 40 | |
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| 41 | typedef typename UGraph::Node Node; |
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| 42 | typedef typename UGraph::Edge Edge; |
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| 43 | |
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| 44 | typedef typename UGraph::template NodeMap<Edge> PredMap; |
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| 45 | |
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| 46 | typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
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| 47 | |
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| 48 | typedef typename UGraph::template NodeMap<int> OrderMap; |
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| 49 | typedef std::vector<Node> OrderList; |
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| 50 | |
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| 51 | typedef typename UGraph::template NodeMap<int> LowMap; |
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| 52 | typedef typename UGraph::template NodeMap<int> AncestorMap; |
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| 53 | |
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| 54 | PlanarityVisitor(const UGraph& ugraph, |
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| 55 | PredMap& pred_map, TreeMap& tree_map, |
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| 56 | OrderMap& order_map, OrderList& order_list, |
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| 57 | AncestorMap& ancestor_map, LowMap& low_map) |
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| 58 | : _ugraph(ugraph), _pred_map(pred_map), _tree_map(tree_map), |
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| 59 | _order_map(order_map), _order_list(order_list), |
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| 60 | _ancestor_map(ancestor_map), _low_map(low_map) {} |
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| 61 | |
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| 62 | void reach(const Node& node) { |
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| 63 | _order_map[node] = _order_list.size(); |
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| 64 | _low_map[node] = _order_list.size(); |
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| 65 | _ancestor_map[node] = _order_list.size(); |
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| 66 | _order_list.push_back(node); |
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| 67 | } |
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| 68 | |
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| 69 | void discover(const Edge& edge) { |
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| 70 | Node source = _ugraph.source(edge); |
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| 71 | Node target = _ugraph.target(edge); |
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| 72 | |
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| 73 | _tree_map[edge] = true; |
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| 74 | _pred_map[target] = edge; |
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| 75 | } |
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| 76 | |
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| 77 | void examine(const Edge& edge) { |
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| 78 | Node source = _ugraph.source(edge); |
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| 79 | Node target = _ugraph.target(edge); |
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| 80 | |
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| 81 | if (_order_map[target] < _order_map[source] && !_tree_map[edge]) { |
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| 82 | if (_low_map[source] > _order_map[target]) { |
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| 83 | _low_map[source] = _order_map[target]; |
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| 84 | } |
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| 85 | if (_ancestor_map[source] > _order_map[target]) { |
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| 86 | _ancestor_map[source] = _order_map[target]; |
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| 87 | } |
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| 88 | } |
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| 89 | } |
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| 90 | |
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| 91 | void backtrack(const Edge& edge) { |
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| 92 | Node source = _ugraph.source(edge); |
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| 93 | Node target = _ugraph.target(edge); |
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| 94 | |
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| 95 | if (_low_map[source] > _low_map[target]) { |
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| 96 | _low_map[source] = _low_map[target]; |
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| 97 | } |
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| 98 | } |
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| 99 | |
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| 100 | const UGraph& _ugraph; |
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| 101 | PredMap& _pred_map; |
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| 102 | TreeMap& _tree_map; |
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| 103 | OrderMap& _order_map; |
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| 104 | OrderList& _order_list; |
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| 105 | AncestorMap& _ancestor_map; |
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| 106 | LowMap& _low_map; |
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| 107 | }; |
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| 108 | |
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| 109 | template <typename UGraph, bool embedding = true> |
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| 110 | struct NodeDataNode { |
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| 111 | int prev, next; |
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| 112 | int visited; |
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| 113 | typename UGraph::Edge first; |
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| 114 | bool inverted; |
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| 115 | }; |
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| 116 | |
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| 117 | template <typename UGraph> |
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| 118 | struct NodeDataNode<UGraph, false> { |
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| 119 | int prev, next; |
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| 120 | int visited; |
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| 121 | }; |
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| 122 | |
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| 123 | template <typename UGraph> |
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| 124 | struct ChildListNode { |
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| 125 | typedef typename UGraph::Node Node; |
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| 126 | Node first; |
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| 127 | Node prev, next; |
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| 128 | }; |
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| 129 | |
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| 130 | template <typename UGraph> |
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| 131 | struct EdgeListNode { |
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| 132 | typename UGraph::Edge prev, next; |
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| 133 | }; |
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| 134 | |
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| 135 | } |
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| 136 | |
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| 137 | /// \ingroup graph_prop |
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| 138 | /// |
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| 139 | /// \brief Planarity checking of an undirected simple graph |
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| 140 | /// |
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| 141 | /// This class implements the Boyer-Myrvold algorithm for planar |
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| 142 | /// checking of an undirected graph. This class is a simplified |
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| 143 | /// version of the PlanarEmbedding algorithm class, and it does |
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| 144 | /// provide neither embedding nor kuratowski subdivisons. |
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| 145 | template <typename UGraph> |
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| 146 | class PlanarityChecking { |
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| 147 | private: |
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| 148 | |
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| 149 | UGRAPH_TYPEDEFS(typename UGraph) |
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| 150 | |
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| 151 | const UGraph& _ugraph; |
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| 152 | |
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| 153 | private: |
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| 154 | |
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| 155 | typedef typename UGraph::template NodeMap<Edge> PredMap; |
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| 156 | |
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| 157 | typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
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| 158 | |
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| 159 | typedef typename UGraph::template NodeMap<int> OrderMap; |
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| 160 | typedef std::vector<Node> OrderList; |
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| 161 | |
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| 162 | typedef typename UGraph::template NodeMap<int> LowMap; |
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| 163 | typedef typename UGraph::template NodeMap<int> AncestorMap; |
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| 164 | |
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| 165 | typedef _planarity_bits::NodeDataNode<UGraph> NodeDataNode; |
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| 166 | typedef std::vector<NodeDataNode> NodeData; |
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| 167 | |
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| 168 | typedef _planarity_bits::ChildListNode<UGraph> ChildListNode; |
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| 169 | typedef typename UGraph::template NodeMap<ChildListNode> ChildLists; |
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| 170 | |
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| 171 | typedef typename UGraph::template NodeMap<std::list<int> > MergeRoots; |
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| 172 | |
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| 173 | typedef typename UGraph::template NodeMap<bool> EmbedEdge; |
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| 174 | |
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| 175 | public: |
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| 176 | |
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| 177 | /// \brief Constructor |
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| 178 | /// |
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| 179 | /// \warining The graph should be simple, i.e. parallel and loop edge |
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| 180 | /// free. |
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| 181 | PlanarityChecking(const UGraph& ugraph) : _ugraph(ugraph) {} |
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| 182 | |
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| 183 | /// \brief Runs the algorithm. |
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| 184 | /// |
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| 185 | /// Runs the algorithm. |
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| 186 | /// \return %True when the graph is planar. |
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[2481] | 187 | bool run() { |
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[2480] | 188 | typedef _planarity_bits::PlanarityVisitor<UGraph> Visitor; |
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| 189 | |
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| 190 | PredMap pred_map(_ugraph, INVALID); |
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| 191 | TreeMap tree_map(_ugraph, false); |
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| 192 | |
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| 193 | OrderMap order_map(_ugraph, -1); |
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| 194 | OrderList order_list; |
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| 195 | |
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| 196 | AncestorMap ancestor_map(_ugraph, -1); |
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| 197 | LowMap low_map(_ugraph, -1); |
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| 198 | |
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| 199 | Visitor visitor(_ugraph, pred_map, tree_map, |
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| 200 | order_map, order_list, ancestor_map, low_map); |
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| 201 | DfsVisit<UGraph, Visitor> visit(_ugraph, visitor); |
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| 202 | visit.run(); |
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| 203 | |
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| 204 | ChildLists child_lists(_ugraph); |
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| 205 | createChildLists(tree_map, order_map, low_map, child_lists); |
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| 206 | |
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| 207 | NodeData node_data(2 * order_list.size()); |
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| 208 | |
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| 209 | EmbedEdge embed_edge(_ugraph, false); |
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| 210 | |
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| 211 | MergeRoots merge_roots(_ugraph); |
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| 212 | |
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| 213 | for (int i = order_list.size() - 1; i >= 0; --i) { |
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| 214 | |
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| 215 | Node node = order_list[i]; |
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| 216 | |
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| 217 | Node source = node; |
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| 218 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
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| 219 | Node target = _ugraph.target(e); |
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| 220 | |
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| 221 | if (order_map[source] < order_map[target] && tree_map[e]) { |
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[2481] | 222 | initFace(target, node_data, order_map, order_list); |
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[2480] | 223 | } |
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| 224 | } |
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| 225 | |
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| 226 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
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| 227 | Node target = _ugraph.target(e); |
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| 228 | |
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| 229 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
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| 230 | embed_edge[target] = true; |
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| 231 | walkUp(target, source, i, pred_map, low_map, |
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| 232 | order_map, order_list, node_data, merge_roots); |
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| 233 | } |
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| 234 | } |
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| 235 | |
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| 236 | for (typename MergeRoots::Value::iterator it = |
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| 237 | merge_roots[node].begin(); it != merge_roots[node].end(); ++it) { |
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| 238 | int rn = *it; |
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| 239 | walkDown(rn, i, node_data, order_list, child_lists, |
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| 240 | ancestor_map, low_map, embed_edge, merge_roots); |
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| 241 | } |
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| 242 | merge_roots[node].clear(); |
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| 243 | |
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| 244 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
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| 245 | Node target = _ugraph.target(e); |
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| 246 | |
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| 247 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
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| 248 | if (embed_edge[target]) { |
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| 249 | return false; |
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| 250 | } |
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| 251 | } |
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| 252 | } |
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| 253 | } |
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| 254 | |
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| 255 | return true; |
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| 256 | } |
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| 257 | |
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| 258 | private: |
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| 259 | |
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| 260 | void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
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| 261 | const LowMap& low_map, ChildLists& child_lists) { |
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| 262 | |
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| 263 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
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| 264 | Node source = n; |
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| 265 | |
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| 266 | std::vector<Node> targets; |
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| 267 | for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
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| 268 | Node target = _ugraph.target(e); |
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| 269 | |
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| 270 | if (order_map[source] < order_map[target] && tree_map[e]) { |
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| 271 | targets.push_back(target); |
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| 272 | } |
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| 273 | } |
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| 274 | |
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| 275 | if (targets.size() == 0) { |
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| 276 | child_lists[source].first = INVALID; |
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| 277 | } else if (targets.size() == 1) { |
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| 278 | child_lists[source].first = targets[0]; |
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| 279 | child_lists[targets[0]].prev = INVALID; |
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| 280 | child_lists[targets[0]].next = INVALID; |
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| 281 | } else { |
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| 282 | radixSort(targets.begin(), targets.end(), mapFunctor(low_map)); |
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| 283 | for (int i = 1; i < int(targets.size()); ++i) { |
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| 284 | child_lists[targets[i]].prev = targets[i - 1]; |
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| 285 | child_lists[targets[i - 1]].next = targets[i]; |
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| 286 | } |
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| 287 | child_lists[targets.back()].next = INVALID; |
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| 288 | child_lists[targets.front()].prev = INVALID; |
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| 289 | child_lists[source].first = targets.front(); |
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| 290 | } |
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| 291 | } |
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| 292 | } |
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| 293 | |
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| 294 | void walkUp(const Node& node, Node root, int rorder, |
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| 295 | const PredMap& pred_map, const LowMap& low_map, |
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| 296 | const OrderMap& order_map, const OrderList& order_list, |
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| 297 | NodeData& node_data, MergeRoots& merge_roots) { |
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| 298 | |
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| 299 | int na, nb; |
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| 300 | bool da, db; |
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| 301 | |
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| 302 | na = nb = order_map[node]; |
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| 303 | da = true; db = false; |
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| 304 | |
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| 305 | while (true) { |
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| 306 | |
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| 307 | if (node_data[na].visited == rorder) break; |
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| 308 | if (node_data[nb].visited == rorder) break; |
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| 309 | |
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| 310 | node_data[na].visited = rorder; |
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| 311 | node_data[nb].visited = rorder; |
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| 312 | |
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| 313 | int rn = -1; |
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| 314 | |
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| 315 | if (na >= int(order_list.size())) { |
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| 316 | rn = na; |
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| 317 | } else if (nb >= int(order_list.size())) { |
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| 318 | rn = nb; |
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| 319 | } |
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| 320 | |
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| 321 | if (rn == -1) { |
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| 322 | int nn; |
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| 323 | |
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| 324 | nn = da ? node_data[na].prev : node_data[na].next; |
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| 325 | da = node_data[nn].prev != na; |
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| 326 | na = nn; |
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| 327 | |
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| 328 | nn = db ? node_data[nb].prev : node_data[nb].next; |
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| 329 | db = node_data[nn].prev != nb; |
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| 330 | nb = nn; |
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| 331 | |
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| 332 | } else { |
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| 333 | |
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| 334 | Node rep = order_list[rn - order_list.size()]; |
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| 335 | Node parent = _ugraph.source(pred_map[rep]); |
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| 336 | |
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| 337 | if (low_map[rep] < rorder) { |
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| 338 | merge_roots[parent].push_back(rn); |
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| 339 | } else { |
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| 340 | merge_roots[parent].push_front(rn); |
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| 341 | } |
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| 342 | |
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| 343 | if (parent != root) { |
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| 344 | na = nb = order_map[parent]; |
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| 345 | da = true; db = false; |
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| 346 | } else { |
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| 347 | break; |
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| 348 | } |
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| 349 | } |
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| 350 | } |
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| 351 | } |
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| 352 | |
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| 353 | void walkDown(int rn, int rorder, NodeData& node_data, |
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| 354 | OrderList& order_list, ChildLists& child_lists, |
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| 355 | AncestorMap& ancestor_map, LowMap& low_map, |
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| 356 | EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
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| 357 | |
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| 358 | std::vector<std::pair<int, bool> > merge_stack; |
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| 359 | |
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| 360 | for (int di = 0; di < 2; ++di) { |
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| 361 | bool rd = di == 0; |
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| 362 | int pn = rn; |
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| 363 | int n = rd ? node_data[rn].next : node_data[rn].prev; |
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| 364 | |
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| 365 | while (n != rn) { |
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| 366 | |
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| 367 | Node node = order_list[n]; |
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| 368 | |
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| 369 | if (embed_edge[node]) { |
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| 370 | |
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| 371 | // Merging components on the critical path |
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| 372 | while (!merge_stack.empty()) { |
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| 373 | |
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| 374 | // Component root |
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| 375 | int cn = merge_stack.back().first; |
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| 376 | bool cd = merge_stack.back().second; |
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| 377 | merge_stack.pop_back(); |
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| 378 | |
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| 379 | // Parent of component |
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| 380 | int dn = merge_stack.back().first; |
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| 381 | bool dd = merge_stack.back().second; |
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| 382 | merge_stack.pop_back(); |
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| 383 | |
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| 384 | Node parent = order_list[dn]; |
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| 385 | |
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| 386 | // Erasing from merge_roots |
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| 387 | merge_roots[parent].pop_front(); |
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| 388 | |
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| 389 | Node child = order_list[cn - order_list.size()]; |
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| 390 | |
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| 391 | // Erasing from child_lists |
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| 392 | if (child_lists[child].prev != INVALID) { |
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| 393 | child_lists[child_lists[child].prev].next = |
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| 394 | child_lists[child].next; |
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| 395 | } else { |
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| 396 | child_lists[parent].first = child_lists[child].next; |
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| 397 | } |
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| 398 | |
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| 399 | if (child_lists[child].next != INVALID) { |
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| 400 | child_lists[child_lists[child].next].prev = |
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| 401 | child_lists[child].prev; |
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| 402 | } |
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| 403 | |
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| 404 | // Merging external faces |
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| 405 | { |
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| 406 | int en = cn; |
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| 407 | cn = cd ? node_data[cn].prev : node_data[cn].next; |
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| 408 | cd = node_data[cn].next == en; |
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| 409 | |
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| 410 | } |
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| 411 | |
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| 412 | if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
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| 413 | if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
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| 414 | |
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| 415 | } |
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| 416 | |
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| 417 | bool d = pn == node_data[n].prev; |
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| 418 | |
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| 419 | if (node_data[n].prev == node_data[n].next && |
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| 420 | node_data[n].inverted) { |
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| 421 | d = !d; |
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| 422 | } |
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| 423 | |
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| 424 | // Embedding edge into external face |
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| 425 | if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
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| 426 | if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
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| 427 | pn = rn; |
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| 428 | |
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| 429 | embed_edge[order_list[n]] = false; |
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| 430 | } |
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| 431 | |
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| 432 | if (!merge_roots[node].empty()) { |
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| 433 | |
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| 434 | bool d = pn == node_data[n].prev; |
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| 435 | |
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| 436 | merge_stack.push_back(std::make_pair(n, d)); |
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| 437 | |
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| 438 | int rn = merge_roots[node].front(); |
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| 439 | |
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| 440 | int xn = node_data[rn].next; |
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| 441 | Node xnode = order_list[xn]; |
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| 442 | |
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| 443 | int yn = node_data[rn].prev; |
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| 444 | Node ynode = order_list[yn]; |
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| 445 | |
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| 446 | bool rd; |
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| 447 | if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) { |
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| 448 | rd = true; |
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| 449 | } else if (!external(ynode, rorder, child_lists, |
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| 450 | ancestor_map, low_map)) { |
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| 451 | rd = false; |
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| 452 | } else if (pertinent(xnode, embed_edge, merge_roots)) { |
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| 453 | rd = true; |
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| 454 | } else { |
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| 455 | rd = false; |
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| 456 | } |
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| 457 | |
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| 458 | merge_stack.push_back(std::make_pair(rn, rd)); |
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| 459 | |
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| 460 | pn = rn; |
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| 461 | n = rd ? xn : yn; |
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| 462 | |
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| 463 | } else if (!external(node, rorder, child_lists, |
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| 464 | ancestor_map, low_map)) { |
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| 465 | int nn = (node_data[n].next != pn ? |
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| 466 | node_data[n].next : node_data[n].prev); |
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| 467 | |
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| 468 | bool nd = n == node_data[nn].prev; |
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| 469 | |
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| 470 | if (nd) node_data[nn].prev = pn; |
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| 471 | else node_data[nn].next = pn; |
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| 472 | |
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| 473 | if (n == node_data[pn].prev) node_data[pn].prev = nn; |
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| 474 | else node_data[pn].next = nn; |
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| 475 | |
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| 476 | node_data[nn].inverted = |
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| 477 | (node_data[nn].prev == node_data[nn].next && nd != rd); |
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| 478 | |
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| 479 | n = nn; |
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| 480 | } |
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| 481 | else break; |
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| 482 | |
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| 483 | } |
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| 484 | |
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| 485 | if (!merge_stack.empty() || n == rn) { |
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| 486 | break; |
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| 487 | } |
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| 488 | } |
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| 489 | } |
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| 490 | |
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| 491 | void initFace(const Node& node, NodeData& node_data, |
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[2481] | 492 | const OrderMap& order_map, const OrderList& order_list) { |
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[2480] | 493 | int n = order_map[node]; |
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| 494 | int rn = n + order_list.size(); |
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| 495 | |
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| 496 | node_data[n].next = node_data[n].prev = rn; |
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| 497 | node_data[rn].next = node_data[rn].prev = n; |
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| 498 | |
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| 499 | node_data[n].visited = order_list.size(); |
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| 500 | node_data[rn].visited = order_list.size(); |
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| 501 | |
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| 502 | } |
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| 503 | |
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| 504 | bool external(const Node& node, int rorder, |
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| 505 | ChildLists& child_lists, AncestorMap& ancestor_map, |
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| 506 | LowMap& low_map) { |
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| 507 | Node child = child_lists[node].first; |
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| 508 | |
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| 509 | if (child != INVALID) { |
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| 510 | if (low_map[child] < rorder) return true; |
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| 511 | } |
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| 512 | |
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| 513 | if (ancestor_map[node] < rorder) return true; |
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| 514 | |
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| 515 | return false; |
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| 516 | } |
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| 517 | |
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| 518 | bool pertinent(const Node& node, const EmbedEdge& embed_edge, |
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| 519 | const MergeRoots& merge_roots) { |
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| 520 | return !merge_roots[node].empty() || embed_edge[node]; |
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| 521 | } |
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| 522 | |
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| 523 | }; |
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| 524 | |
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| 525 | /// \ingroup graph_prop |
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| 526 | /// |
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| 527 | /// \brief Planar embedding of an undirected simple graph |
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| 528 | /// |
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| 529 | /// This class implements the Boyer-Myrvold algorithm for planar |
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| 530 | /// embedding of an undirected graph. The planar embeding is an |
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| 531 | /// ordering of the outgoing edges in each node, which is a possible |
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| 532 | /// configuration to draw the graph in the plane. If there is not |
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| 533 | /// such ordering then the graph contains a \f$ K_5 \f$ (full graph |
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| 534 | /// with 5 nodes) or an \f$ K_{3,3} \f$ (complete bipartite graph on |
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| 535 | /// 3 ANode and 3 BNode) subdivision. |
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| 536 | /// |
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| 537 | /// The current implementation calculates an embedding or an |
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| 538 | /// Kuratowski subdivision if the graph is not planar. The running |
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| 539 | /// time of the algorithm is \f$ O(n) \f$. |
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| 540 | template <typename UGraph> |
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| 541 | class PlanarEmbedding { |
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| 542 | private: |
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| 543 | |
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| 544 | UGRAPH_TYPEDEFS(typename UGraph) |
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| 545 | |
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| 546 | const UGraph& _ugraph; |
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| 547 | typename UGraph::template EdgeMap<Edge> _embedding; |
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| 548 | |
---|
| 549 | typename UGraph::template UEdgeMap<bool> _kuratowski; |
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| 550 | |
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| 551 | private: |
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| 552 | |
---|
| 553 | typedef typename UGraph::template NodeMap<Edge> PredMap; |
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| 554 | |
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| 555 | typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
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| 556 | |
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| 557 | typedef typename UGraph::template NodeMap<int> OrderMap; |
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| 558 | typedef std::vector<Node> OrderList; |
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| 559 | |
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| 560 | typedef typename UGraph::template NodeMap<int> LowMap; |
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| 561 | typedef typename UGraph::template NodeMap<int> AncestorMap; |
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| 562 | |
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| 563 | typedef _planarity_bits::NodeDataNode<UGraph> NodeDataNode; |
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| 564 | typedef std::vector<NodeDataNode> NodeData; |
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| 565 | |
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| 566 | typedef _planarity_bits::ChildListNode<UGraph> ChildListNode; |
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| 567 | typedef typename UGraph::template NodeMap<ChildListNode> ChildLists; |
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| 568 | |
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| 569 | typedef typename UGraph::template NodeMap<std::list<int> > MergeRoots; |
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| 570 | |
---|
| 571 | typedef typename UGraph::template NodeMap<Edge> EmbedEdge; |
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| 572 | |
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| 573 | typedef _planarity_bits::EdgeListNode<UGraph> EdgeListNode; |
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| 574 | typedef typename UGraph::template EdgeMap<EdgeListNode> EdgeLists; |
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| 575 | |
---|
| 576 | typedef typename UGraph::template NodeMap<bool> FlipMap; |
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| 577 | |
---|
| 578 | typedef typename UGraph::template NodeMap<int> TypeMap; |
---|
| 579 | |
---|
| 580 | enum IsolatorNodeType { |
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| 581 | HIGHX = 6, LOWX = 7, |
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| 582 | HIGHY = 8, LOWY = 9, |
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| 583 | ROOT = 10, PERTINENT = 11, |
---|
| 584 | INTERNAL = 12 |
---|
| 585 | }; |
---|
| 586 | |
---|
| 587 | public: |
---|
| 588 | |
---|
| 589 | /// \brief Constructor |
---|
| 590 | /// |
---|
| 591 | /// \warining The graph should be simple, i.e. parallel and loop edge |
---|
| 592 | /// free. |
---|
| 593 | PlanarEmbedding(const UGraph& ugraph) |
---|
| 594 | : _ugraph(ugraph), _embedding(_ugraph), _kuratowski(ugraph, false) {} |
---|
| 595 | |
---|
| 596 | /// \brief Runs the algorithm. |
---|
| 597 | /// |
---|
| 598 | /// Runs the algorithm. |
---|
| 599 | /// \param kuratowski If the parameter is false, then the |
---|
| 600 | /// algorithm does not calculate the isolate Kuratowski |
---|
| 601 | /// subdivisions. |
---|
| 602 | ///\return %True when the graph is planar. |
---|
| 603 | bool run(bool kuratowski = true) { |
---|
| 604 | typedef _planarity_bits::PlanarityVisitor<UGraph> Visitor; |
---|
| 605 | |
---|
| 606 | PredMap pred_map(_ugraph, INVALID); |
---|
| 607 | TreeMap tree_map(_ugraph, false); |
---|
| 608 | |
---|
| 609 | OrderMap order_map(_ugraph, -1); |
---|
| 610 | OrderList order_list; |
---|
| 611 | |
---|
| 612 | AncestorMap ancestor_map(_ugraph, -1); |
---|
| 613 | LowMap low_map(_ugraph, -1); |
---|
| 614 | |
---|
| 615 | Visitor visitor(_ugraph, pred_map, tree_map, |
---|
| 616 | order_map, order_list, ancestor_map, low_map); |
---|
| 617 | DfsVisit<UGraph, Visitor> visit(_ugraph, visitor); |
---|
| 618 | visit.run(); |
---|
| 619 | |
---|
| 620 | ChildLists child_lists(_ugraph); |
---|
| 621 | createChildLists(tree_map, order_map, low_map, child_lists); |
---|
| 622 | |
---|
| 623 | NodeData node_data(2 * order_list.size()); |
---|
| 624 | |
---|
| 625 | EmbedEdge embed_edge(_ugraph, INVALID); |
---|
| 626 | |
---|
| 627 | MergeRoots merge_roots(_ugraph); |
---|
| 628 | |
---|
| 629 | EdgeLists edge_lists(_ugraph); |
---|
| 630 | |
---|
| 631 | FlipMap flip_map(_ugraph, false); |
---|
| 632 | |
---|
| 633 | for (int i = order_list.size() - 1; i >= 0; --i) { |
---|
| 634 | |
---|
| 635 | Node node = order_list[i]; |
---|
| 636 | |
---|
| 637 | node_data[i].first = INVALID; |
---|
| 638 | |
---|
| 639 | Node source = node; |
---|
| 640 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
| 641 | Node target = _ugraph.target(e); |
---|
| 642 | |
---|
| 643 | if (order_map[source] < order_map[target] && tree_map[e]) { |
---|
| 644 | initFace(target, edge_lists, node_data, |
---|
| 645 | pred_map, order_map, order_list); |
---|
| 646 | } |
---|
| 647 | } |
---|
| 648 | |
---|
| 649 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
| 650 | Node target = _ugraph.target(e); |
---|
| 651 | |
---|
| 652 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
---|
| 653 | embed_edge[target] = e; |
---|
| 654 | walkUp(target, source, i, pred_map, low_map, |
---|
| 655 | order_map, order_list, node_data, merge_roots); |
---|
| 656 | } |
---|
| 657 | } |
---|
| 658 | |
---|
| 659 | for (typename MergeRoots::Value::iterator it = |
---|
| 660 | merge_roots[node].begin(); it != merge_roots[node].end(); ++it) { |
---|
| 661 | int rn = *it; |
---|
| 662 | walkDown(rn, i, node_data, edge_lists, flip_map, order_list, |
---|
| 663 | child_lists, ancestor_map, low_map, embed_edge, merge_roots); |
---|
| 664 | } |
---|
| 665 | merge_roots[node].clear(); |
---|
| 666 | |
---|
| 667 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
| 668 | Node target = _ugraph.target(e); |
---|
| 669 | |
---|
| 670 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
---|
| 671 | if (embed_edge[target] != INVALID) { |
---|
| 672 | if (kuratowski) { |
---|
| 673 | isolateKuratowski(e, node_data, edge_lists, flip_map, |
---|
| 674 | order_map, order_list, pred_map, child_lists, |
---|
| 675 | ancestor_map, low_map, |
---|
| 676 | embed_edge, merge_roots); |
---|
| 677 | } |
---|
| 678 | return false; |
---|
| 679 | } |
---|
| 680 | } |
---|
| 681 | } |
---|
| 682 | } |
---|
| 683 | |
---|
| 684 | for (int i = 0; i < int(order_list.size()); ++i) { |
---|
| 685 | |
---|
| 686 | mergeRemainingFaces(order_list[i], node_data, order_list, order_map, |
---|
| 687 | child_lists, edge_lists); |
---|
| 688 | storeEmbedding(order_list[i], node_data, order_map, pred_map, |
---|
| 689 | edge_lists, flip_map); |
---|
| 690 | } |
---|
| 691 | |
---|
| 692 | return true; |
---|
| 693 | } |
---|
| 694 | |
---|
| 695 | /// \brief Gives back the successor of an edge |
---|
| 696 | /// |
---|
| 697 | /// Gives back the successor of an edge. This function makes |
---|
| 698 | /// possible to query the cyclic order of the outgoing edges from |
---|
| 699 | /// a node. |
---|
| 700 | Edge next(const Edge& edge) const { |
---|
| 701 | return _embedding[edge]; |
---|
| 702 | } |
---|
| 703 | |
---|
| 704 | /// \brief Gives back true when the undirected edge is in the |
---|
| 705 | /// kuratowski subdivision |
---|
| 706 | /// |
---|
| 707 | /// Gives back true when the undirected edge is in the kuratowski |
---|
| 708 | /// subdivision |
---|
| 709 | bool kuratowski(const UEdge& uedge) { |
---|
| 710 | return _kuratowski[uedge]; |
---|
| 711 | } |
---|
| 712 | |
---|
| 713 | private: |
---|
| 714 | |
---|
| 715 | void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
---|
| 716 | const LowMap& low_map, ChildLists& child_lists) { |
---|
| 717 | |
---|
| 718 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
| 719 | Node source = n; |
---|
| 720 | |
---|
| 721 | std::vector<Node> targets; |
---|
| 722 | for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
| 723 | Node target = _ugraph.target(e); |
---|
| 724 | |
---|
| 725 | if (order_map[source] < order_map[target] && tree_map[e]) { |
---|
| 726 | targets.push_back(target); |
---|
| 727 | } |
---|
| 728 | } |
---|
| 729 | |
---|
| 730 | if (targets.size() == 0) { |
---|
| 731 | child_lists[source].first = INVALID; |
---|
| 732 | } else if (targets.size() == 1) { |
---|
| 733 | child_lists[source].first = targets[0]; |
---|
| 734 | child_lists[targets[0]].prev = INVALID; |
---|
| 735 | child_lists[targets[0]].next = INVALID; |
---|
| 736 | } else { |
---|
| 737 | radixSort(targets.begin(), targets.end(), mapFunctor(low_map)); |
---|
| 738 | for (int i = 1; i < int(targets.size()); ++i) { |
---|
| 739 | child_lists[targets[i]].prev = targets[i - 1]; |
---|
| 740 | child_lists[targets[i - 1]].next = targets[i]; |
---|
| 741 | } |
---|
| 742 | child_lists[targets.back()].next = INVALID; |
---|
| 743 | child_lists[targets.front()].prev = INVALID; |
---|
| 744 | child_lists[source].first = targets.front(); |
---|
| 745 | } |
---|
| 746 | } |
---|
| 747 | } |
---|
| 748 | |
---|
| 749 | void walkUp(const Node& node, Node root, int rorder, |
---|
| 750 | const PredMap& pred_map, const LowMap& low_map, |
---|
| 751 | const OrderMap& order_map, const OrderList& order_list, |
---|
| 752 | NodeData& node_data, MergeRoots& merge_roots) { |
---|
| 753 | |
---|
| 754 | int na, nb; |
---|
| 755 | bool da, db; |
---|
| 756 | |
---|
| 757 | na = nb = order_map[node]; |
---|
| 758 | da = true; db = false; |
---|
| 759 | |
---|
| 760 | while (true) { |
---|
| 761 | |
---|
| 762 | if (node_data[na].visited == rorder) break; |
---|
| 763 | if (node_data[nb].visited == rorder) break; |
---|
| 764 | |
---|
| 765 | node_data[na].visited = rorder; |
---|
| 766 | node_data[nb].visited = rorder; |
---|
| 767 | |
---|
| 768 | int rn = -1; |
---|
| 769 | |
---|
| 770 | if (na >= int(order_list.size())) { |
---|
| 771 | rn = na; |
---|
| 772 | } else if (nb >= int(order_list.size())) { |
---|
| 773 | rn = nb; |
---|
| 774 | } |
---|
| 775 | |
---|
| 776 | if (rn == -1) { |
---|
| 777 | int nn; |
---|
| 778 | |
---|
| 779 | nn = da ? node_data[na].prev : node_data[na].next; |
---|
| 780 | da = node_data[nn].prev != na; |
---|
| 781 | na = nn; |
---|
| 782 | |
---|
| 783 | nn = db ? node_data[nb].prev : node_data[nb].next; |
---|
| 784 | db = node_data[nn].prev != nb; |
---|
| 785 | nb = nn; |
---|
| 786 | |
---|
| 787 | } else { |
---|
| 788 | |
---|
| 789 | Node rep = order_list[rn - order_list.size()]; |
---|
| 790 | Node parent = _ugraph.source(pred_map[rep]); |
---|
| 791 | |
---|
| 792 | if (low_map[rep] < rorder) { |
---|
| 793 | merge_roots[parent].push_back(rn); |
---|
| 794 | } else { |
---|
| 795 | merge_roots[parent].push_front(rn); |
---|
| 796 | } |
---|
| 797 | |
---|
| 798 | if (parent != root) { |
---|
| 799 | na = nb = order_map[parent]; |
---|
| 800 | da = true; db = false; |
---|
| 801 | } else { |
---|
| 802 | break; |
---|
| 803 | } |
---|
| 804 | } |
---|
| 805 | } |
---|
| 806 | } |
---|
| 807 | |
---|
| 808 | void walkDown(int rn, int rorder, NodeData& node_data, |
---|
| 809 | EdgeLists& edge_lists, FlipMap& flip_map, |
---|
| 810 | OrderList& order_list, ChildLists& child_lists, |
---|
| 811 | AncestorMap& ancestor_map, LowMap& low_map, |
---|
| 812 | EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
---|
| 813 | |
---|
| 814 | std::vector<std::pair<int, bool> > merge_stack; |
---|
| 815 | |
---|
| 816 | for (int di = 0; di < 2; ++di) { |
---|
| 817 | bool rd = di == 0; |
---|
| 818 | int pn = rn; |
---|
| 819 | int n = rd ? node_data[rn].next : node_data[rn].prev; |
---|
| 820 | |
---|
| 821 | while (n != rn) { |
---|
| 822 | |
---|
| 823 | Node node = order_list[n]; |
---|
| 824 | |
---|
| 825 | if (embed_edge[node] != INVALID) { |
---|
| 826 | |
---|
| 827 | // Merging components on the critical path |
---|
| 828 | while (!merge_stack.empty()) { |
---|
| 829 | |
---|
| 830 | // Component root |
---|
| 831 | int cn = merge_stack.back().first; |
---|
| 832 | bool cd = merge_stack.back().second; |
---|
| 833 | merge_stack.pop_back(); |
---|
| 834 | |
---|
| 835 | // Parent of component |
---|
| 836 | int dn = merge_stack.back().first; |
---|
| 837 | bool dd = merge_stack.back().second; |
---|
| 838 | merge_stack.pop_back(); |
---|
| 839 | |
---|
| 840 | Node parent = order_list[dn]; |
---|
| 841 | |
---|
| 842 | // Erasing from merge_roots |
---|
| 843 | merge_roots[parent].pop_front(); |
---|
| 844 | |
---|
| 845 | Node child = order_list[cn - order_list.size()]; |
---|
| 846 | |
---|
| 847 | // Erasing from child_lists |
---|
| 848 | if (child_lists[child].prev != INVALID) { |
---|
| 849 | child_lists[child_lists[child].prev].next = |
---|
| 850 | child_lists[child].next; |
---|
| 851 | } else { |
---|
| 852 | child_lists[parent].first = child_lists[child].next; |
---|
| 853 | } |
---|
| 854 | |
---|
| 855 | if (child_lists[child].next != INVALID) { |
---|
| 856 | child_lists[child_lists[child].next].prev = |
---|
| 857 | child_lists[child].prev; |
---|
| 858 | } |
---|
| 859 | |
---|
| 860 | // Merging edges + flipping |
---|
| 861 | Edge de = node_data[dn].first; |
---|
| 862 | Edge ce = node_data[cn].first; |
---|
| 863 | |
---|
| 864 | flip_map[order_list[cn - order_list.size()]] = cd != dd; |
---|
| 865 | if (cd != dd) { |
---|
| 866 | std::swap(edge_lists[ce].prev, edge_lists[ce].next); |
---|
| 867 | ce = edge_lists[ce].prev; |
---|
| 868 | std::swap(edge_lists[ce].prev, edge_lists[ce].next); |
---|
| 869 | } |
---|
| 870 | |
---|
| 871 | { |
---|
| 872 | Edge dne = edge_lists[de].next; |
---|
| 873 | Edge cne = edge_lists[ce].next; |
---|
| 874 | |
---|
| 875 | edge_lists[de].next = cne; |
---|
| 876 | edge_lists[ce].next = dne; |
---|
| 877 | |
---|
| 878 | edge_lists[dne].prev = ce; |
---|
| 879 | edge_lists[cne].prev = de; |
---|
| 880 | } |
---|
| 881 | |
---|
| 882 | if (dd) { |
---|
| 883 | node_data[dn].first = ce; |
---|
| 884 | } |
---|
| 885 | |
---|
| 886 | // Merging external faces |
---|
| 887 | { |
---|
| 888 | int en = cn; |
---|
| 889 | cn = cd ? node_data[cn].prev : node_data[cn].next; |
---|
| 890 | cd = node_data[cn].next == en; |
---|
| 891 | |
---|
| 892 | if (node_data[cn].prev == node_data[cn].next && |
---|
| 893 | node_data[cn].inverted) { |
---|
| 894 | cd = !cd; |
---|
| 895 | } |
---|
| 896 | } |
---|
| 897 | |
---|
| 898 | if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
---|
| 899 | if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
---|
| 900 | |
---|
| 901 | } |
---|
| 902 | |
---|
| 903 | bool d = pn == node_data[n].prev; |
---|
| 904 | |
---|
| 905 | if (node_data[n].prev == node_data[n].next && |
---|
| 906 | node_data[n].inverted) { |
---|
| 907 | d = !d; |
---|
| 908 | } |
---|
| 909 | |
---|
| 910 | // Add new edge |
---|
| 911 | { |
---|
| 912 | Edge edge = embed_edge[node]; |
---|
| 913 | Edge re = node_data[rn].first; |
---|
| 914 | |
---|
| 915 | edge_lists[edge_lists[re].next].prev = edge; |
---|
| 916 | edge_lists[edge].next = edge_lists[re].next; |
---|
| 917 | edge_lists[edge].prev = re; |
---|
| 918 | edge_lists[re].next = edge; |
---|
| 919 | |
---|
| 920 | if (!rd) { |
---|
| 921 | node_data[rn].first = edge; |
---|
| 922 | } |
---|
| 923 | |
---|
| 924 | Edge rev = _ugraph.oppositeEdge(edge); |
---|
| 925 | Edge e = node_data[n].first; |
---|
| 926 | |
---|
| 927 | edge_lists[edge_lists[e].next].prev = rev; |
---|
| 928 | edge_lists[rev].next = edge_lists[e].next; |
---|
| 929 | edge_lists[rev].prev = e; |
---|
| 930 | edge_lists[e].next = rev; |
---|
| 931 | |
---|
| 932 | if (d) { |
---|
| 933 | node_data[n].first = rev; |
---|
| 934 | } |
---|
| 935 | |
---|
| 936 | } |
---|
| 937 | |
---|
| 938 | // Embedding edge into external face |
---|
| 939 | if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
---|
| 940 | if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
---|
| 941 | pn = rn; |
---|
| 942 | |
---|
| 943 | embed_edge[order_list[n]] = INVALID; |
---|
| 944 | } |
---|
| 945 | |
---|
| 946 | if (!merge_roots[node].empty()) { |
---|
| 947 | |
---|
| 948 | bool d = pn == node_data[n].prev; |
---|
| 949 | if (node_data[n].prev == node_data[n].next && |
---|
| 950 | node_data[n].inverted) { |
---|
| 951 | d = !d; |
---|
| 952 | } |
---|
| 953 | |
---|
| 954 | merge_stack.push_back(std::make_pair(n, d)); |
---|
| 955 | |
---|
| 956 | int rn = merge_roots[node].front(); |
---|
| 957 | |
---|
| 958 | int xn = node_data[rn].next; |
---|
| 959 | Node xnode = order_list[xn]; |
---|
| 960 | |
---|
| 961 | int yn = node_data[rn].prev; |
---|
| 962 | Node ynode = order_list[yn]; |
---|
| 963 | |
---|
| 964 | bool rd; |
---|
| 965 | if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
| 966 | rd = true; |
---|
| 967 | } else if (!external(ynode, rorder, child_lists, |
---|
| 968 | ancestor_map, low_map)) { |
---|
| 969 | rd = false; |
---|
| 970 | } else if (pertinent(xnode, embed_edge, merge_roots)) { |
---|
| 971 | rd = true; |
---|
| 972 | } else { |
---|
| 973 | rd = false; |
---|
| 974 | } |
---|
| 975 | |
---|
| 976 | merge_stack.push_back(std::make_pair(rn, rd)); |
---|
| 977 | |
---|
| 978 | pn = rn; |
---|
| 979 | n = rd ? xn : yn; |
---|
| 980 | |
---|
| 981 | } else if (!external(node, rorder, child_lists, |
---|
| 982 | ancestor_map, low_map)) { |
---|
| 983 | int nn = (node_data[n].next != pn ? |
---|
| 984 | node_data[n].next : node_data[n].prev); |
---|
| 985 | |
---|
| 986 | bool nd = n == node_data[nn].prev; |
---|
| 987 | |
---|
| 988 | if (nd) node_data[nn].prev = pn; |
---|
| 989 | else node_data[nn].next = pn; |
---|
| 990 | |
---|
| 991 | if (n == node_data[pn].prev) node_data[pn].prev = nn; |
---|
| 992 | else node_data[pn].next = nn; |
---|
| 993 | |
---|
| 994 | node_data[nn].inverted = |
---|
| 995 | (node_data[nn].prev == node_data[nn].next && nd != rd); |
---|
| 996 | |
---|
| 997 | n = nn; |
---|
| 998 | } |
---|
| 999 | else break; |
---|
| 1000 | |
---|
| 1001 | } |
---|
| 1002 | |
---|
| 1003 | if (!merge_stack.empty() || n == rn) { |
---|
| 1004 | break; |
---|
| 1005 | } |
---|
| 1006 | } |
---|
| 1007 | } |
---|
| 1008 | |
---|
| 1009 | void initFace(const Node& node, EdgeLists& edge_lists, |
---|
| 1010 | NodeData& node_data, const PredMap& pred_map, |
---|
| 1011 | const OrderMap& order_map, const OrderList& order_list) { |
---|
| 1012 | int n = order_map[node]; |
---|
| 1013 | int rn = n + order_list.size(); |
---|
| 1014 | |
---|
| 1015 | node_data[n].next = node_data[n].prev = rn; |
---|
| 1016 | node_data[rn].next = node_data[rn].prev = n; |
---|
| 1017 | |
---|
| 1018 | node_data[n].visited = order_list.size(); |
---|
| 1019 | node_data[rn].visited = order_list.size(); |
---|
| 1020 | |
---|
| 1021 | node_data[n].inverted = false; |
---|
| 1022 | node_data[rn].inverted = false; |
---|
| 1023 | |
---|
| 1024 | Edge edge = pred_map[node]; |
---|
| 1025 | Edge rev = _ugraph.oppositeEdge(edge); |
---|
| 1026 | |
---|
| 1027 | node_data[rn].first = edge; |
---|
| 1028 | node_data[n].first = rev; |
---|
| 1029 | |
---|
| 1030 | edge_lists[edge].prev = edge; |
---|
| 1031 | edge_lists[edge].next = edge; |
---|
| 1032 | |
---|
| 1033 | edge_lists[rev].prev = rev; |
---|
| 1034 | edge_lists[rev].next = rev; |
---|
| 1035 | |
---|
| 1036 | } |
---|
| 1037 | |
---|
| 1038 | void mergeRemainingFaces(const Node& node, NodeData& node_data, |
---|
| 1039 | OrderList& order_list, OrderMap& order_map, |
---|
| 1040 | ChildLists& child_lists, EdgeLists& edge_lists) { |
---|
| 1041 | while (child_lists[node].first != INVALID) { |
---|
| 1042 | int dd = order_map[node]; |
---|
| 1043 | Node child = child_lists[node].first; |
---|
| 1044 | int cd = order_map[child] + order_list.size(); |
---|
| 1045 | child_lists[node].first = child_lists[child].next; |
---|
| 1046 | |
---|
| 1047 | Edge de = node_data[dd].first; |
---|
| 1048 | Edge ce = node_data[cd].first; |
---|
| 1049 | |
---|
| 1050 | if (de != INVALID) { |
---|
| 1051 | Edge dne = edge_lists[de].next; |
---|
| 1052 | Edge cne = edge_lists[ce].next; |
---|
| 1053 | |
---|
| 1054 | edge_lists[de].next = cne; |
---|
| 1055 | edge_lists[ce].next = dne; |
---|
| 1056 | |
---|
| 1057 | edge_lists[dne].prev = ce; |
---|
| 1058 | edge_lists[cne].prev = de; |
---|
| 1059 | } |
---|
| 1060 | |
---|
| 1061 | node_data[dd].first = ce; |
---|
| 1062 | |
---|
| 1063 | } |
---|
| 1064 | } |
---|
| 1065 | |
---|
| 1066 | void storeEmbedding(const Node& node, NodeData& node_data, |
---|
| 1067 | OrderMap& order_map, PredMap& pred_map, |
---|
| 1068 | EdgeLists& edge_lists, FlipMap& flip_map) { |
---|
| 1069 | |
---|
| 1070 | if (node_data[order_map[node]].first == INVALID) return; |
---|
| 1071 | |
---|
| 1072 | if (pred_map[node] != INVALID) { |
---|
| 1073 | Node source = _ugraph.source(pred_map[node]); |
---|
| 1074 | flip_map[node] = flip_map[node] != flip_map[source]; |
---|
| 1075 | } |
---|
| 1076 | |
---|
| 1077 | Edge first = node_data[order_map[node]].first; |
---|
| 1078 | Edge prev = first; |
---|
| 1079 | |
---|
| 1080 | Edge edge = flip_map[node] ? |
---|
| 1081 | edge_lists[prev].prev : edge_lists[prev].next; |
---|
| 1082 | |
---|
| 1083 | _embedding[prev] = edge; |
---|
| 1084 | |
---|
| 1085 | while (edge != first) { |
---|
| 1086 | Edge next = edge_lists[edge].prev == prev ? |
---|
| 1087 | edge_lists[edge].next : edge_lists[edge].prev; |
---|
| 1088 | prev = edge; edge = next; |
---|
| 1089 | _embedding[prev] = edge; |
---|
| 1090 | } |
---|
| 1091 | } |
---|
| 1092 | |
---|
| 1093 | |
---|
| 1094 | bool external(const Node& node, int rorder, |
---|
| 1095 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
| 1096 | LowMap& low_map) { |
---|
| 1097 | Node child = child_lists[node].first; |
---|
| 1098 | |
---|
| 1099 | if (child != INVALID) { |
---|
| 1100 | if (low_map[child] < rorder) return true; |
---|
| 1101 | } |
---|
| 1102 | |
---|
| 1103 | if (ancestor_map[node] < rorder) return true; |
---|
| 1104 | |
---|
| 1105 | return false; |
---|
| 1106 | } |
---|
| 1107 | |
---|
| 1108 | bool pertinent(const Node& node, const EmbedEdge& embed_edge, |
---|
| 1109 | const MergeRoots& merge_roots) { |
---|
| 1110 | return !merge_roots[node].empty() || embed_edge[node] != INVALID; |
---|
| 1111 | } |
---|
| 1112 | |
---|
| 1113 | int lowPoint(const Node& node, OrderMap& order_map, ChildLists& child_lists, |
---|
| 1114 | AncestorMap& ancestor_map, LowMap& low_map) { |
---|
| 1115 | int low_point; |
---|
| 1116 | |
---|
| 1117 | Node child = child_lists[node].first; |
---|
| 1118 | |
---|
| 1119 | if (child != INVALID) { |
---|
| 1120 | low_point = low_map[child]; |
---|
| 1121 | } else { |
---|
| 1122 | low_point = order_map[node]; |
---|
| 1123 | } |
---|
| 1124 | |
---|
| 1125 | if (low_point > ancestor_map[node]) { |
---|
| 1126 | low_point = ancestor_map[node]; |
---|
| 1127 | } |
---|
| 1128 | |
---|
| 1129 | return low_point; |
---|
| 1130 | } |
---|
| 1131 | |
---|
| 1132 | int findComponentRoot(Node root, Node node, ChildLists& child_lists, |
---|
| 1133 | OrderMap& order_map, OrderList& order_list) { |
---|
| 1134 | |
---|
| 1135 | int order = order_map[root]; |
---|
| 1136 | int norder = order_map[node]; |
---|
| 1137 | |
---|
| 1138 | Node child = child_lists[root].first; |
---|
| 1139 | while (child != INVALID) { |
---|
| 1140 | int corder = order_map[child]; |
---|
| 1141 | if (corder > order && corder < norder) { |
---|
| 1142 | order = corder; |
---|
| 1143 | } |
---|
| 1144 | child = child_lists[child].next; |
---|
| 1145 | } |
---|
| 1146 | return order + order_list.size(); |
---|
| 1147 | } |
---|
| 1148 | |
---|
| 1149 | Node findPertinent(Node node, OrderMap& order_map, NodeData& node_data, |
---|
| 1150 | EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
---|
| 1151 | Node wnode =_ugraph.target(node_data[order_map[node]].first); |
---|
| 1152 | while (!pertinent(wnode, embed_edge, merge_roots)) { |
---|
| 1153 | wnode = _ugraph.target(node_data[order_map[wnode]].first); |
---|
| 1154 | } |
---|
| 1155 | return wnode; |
---|
| 1156 | } |
---|
| 1157 | |
---|
| 1158 | |
---|
| 1159 | Node findExternal(Node node, int rorder, OrderMap& order_map, |
---|
| 1160 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
| 1161 | LowMap& low_map, NodeData& node_data) { |
---|
| 1162 | Node wnode =_ugraph.target(node_data[order_map[node]].first); |
---|
| 1163 | while (!external(wnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
| 1164 | wnode = _ugraph.target(node_data[order_map[wnode]].first); |
---|
| 1165 | } |
---|
| 1166 | return wnode; |
---|
| 1167 | } |
---|
| 1168 | |
---|
| 1169 | void markCommonPath(Node node, int rorder, Node& wnode, Node& znode, |
---|
| 1170 | OrderList& order_list, OrderMap& order_map, |
---|
| 1171 | NodeData& node_data, EdgeLists& edge_lists, |
---|
| 1172 | EmbedEdge& embed_edge, MergeRoots& merge_roots, |
---|
| 1173 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
| 1174 | LowMap& low_map) { |
---|
| 1175 | |
---|
| 1176 | Node cnode = node; |
---|
| 1177 | Node pred = INVALID; |
---|
| 1178 | |
---|
| 1179 | while (true) { |
---|
| 1180 | |
---|
| 1181 | bool pert = pertinent(cnode, embed_edge, merge_roots); |
---|
| 1182 | bool ext = external(cnode, rorder, child_lists, ancestor_map, low_map); |
---|
| 1183 | |
---|
| 1184 | if (pert && ext) { |
---|
| 1185 | if (!merge_roots[cnode].empty()) { |
---|
| 1186 | int cn = merge_roots[cnode].back(); |
---|
| 1187 | |
---|
| 1188 | if (low_map[order_list[cn - order_list.size()]] < rorder) { |
---|
| 1189 | Edge edge = node_data[cn].first; |
---|
| 1190 | _kuratowski.set(edge, true); |
---|
| 1191 | |
---|
| 1192 | pred = cnode; |
---|
| 1193 | cnode = _ugraph.target(edge); |
---|
| 1194 | |
---|
| 1195 | continue; |
---|
| 1196 | } |
---|
| 1197 | } |
---|
| 1198 | wnode = znode = cnode; |
---|
| 1199 | return; |
---|
| 1200 | |
---|
| 1201 | } else if (pert) { |
---|
| 1202 | wnode = cnode; |
---|
| 1203 | |
---|
| 1204 | while (!external(cnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
| 1205 | Edge edge = node_data[order_map[cnode]].first; |
---|
| 1206 | |
---|
| 1207 | if (_ugraph.target(edge) == pred) { |
---|
| 1208 | edge = edge_lists[edge].next; |
---|
| 1209 | } |
---|
| 1210 | _kuratowski.set(edge, true); |
---|
| 1211 | |
---|
| 1212 | Node next = _ugraph.target(edge); |
---|
| 1213 | pred = cnode; cnode = next; |
---|
| 1214 | } |
---|
| 1215 | |
---|
| 1216 | znode = cnode; |
---|
| 1217 | return; |
---|
| 1218 | |
---|
| 1219 | } else if (ext) { |
---|
| 1220 | znode = cnode; |
---|
| 1221 | |
---|
| 1222 | while (!pertinent(cnode, embed_edge, merge_roots)) { |
---|
| 1223 | Edge edge = node_data[order_map[cnode]].first; |
---|
| 1224 | |
---|
| 1225 | if (_ugraph.target(edge) == pred) { |
---|
| 1226 | edge = edge_lists[edge].next; |
---|
| 1227 | } |
---|
| 1228 | _kuratowski.set(edge, true); |
---|
| 1229 | |
---|
| 1230 | Node next = _ugraph.target(edge); |
---|
| 1231 | pred = cnode; cnode = next; |
---|
| 1232 | } |
---|
| 1233 | |
---|
| 1234 | wnode = cnode; |
---|
| 1235 | return; |
---|
| 1236 | |
---|
| 1237 | } else { |
---|
| 1238 | Edge edge = node_data[order_map[cnode]].first; |
---|
| 1239 | |
---|
| 1240 | if (_ugraph.target(edge) == pred) { |
---|
| 1241 | edge = edge_lists[edge].next; |
---|
| 1242 | } |
---|
| 1243 | _kuratowski.set(edge, true); |
---|
| 1244 | |
---|
| 1245 | Node next = _ugraph.target(edge); |
---|
| 1246 | pred = cnode; cnode = next; |
---|
| 1247 | } |
---|
| 1248 | |
---|
| 1249 | } |
---|
| 1250 | |
---|
| 1251 | } |
---|
| 1252 | |
---|
| 1253 | void orientComponent(Node root, int rn, OrderMap& order_map, |
---|
| 1254 | PredMap& pred_map, NodeData& node_data, |
---|
| 1255 | EdgeLists& edge_lists, FlipMap& flip_map, |
---|
| 1256 | TypeMap& type_map) { |
---|
| 1257 | node_data[order_map[root]].first = node_data[rn].first; |
---|
| 1258 | type_map[root] = 1; |
---|
| 1259 | |
---|
| 1260 | std::vector<Node> st, qu; |
---|
| 1261 | |
---|
| 1262 | st.push_back(root); |
---|
| 1263 | while (!st.empty()) { |
---|
| 1264 | Node node = st.back(); |
---|
| 1265 | st.pop_back(); |
---|
| 1266 | qu.push_back(node); |
---|
| 1267 | |
---|
| 1268 | Edge edge = node_data[order_map[node]].first; |
---|
| 1269 | |
---|
| 1270 | if (type_map[_ugraph.target(edge)] == 0) { |
---|
| 1271 | st.push_back(_ugraph.target(edge)); |
---|
| 1272 | type_map[_ugraph.target(edge)] = 1; |
---|
| 1273 | } |
---|
| 1274 | |
---|
| 1275 | Edge last = edge, pred = edge; |
---|
| 1276 | edge = edge_lists[edge].next; |
---|
| 1277 | while (edge != last) { |
---|
| 1278 | |
---|
| 1279 | if (type_map[_ugraph.target(edge)] == 0) { |
---|
| 1280 | st.push_back(_ugraph.target(edge)); |
---|
| 1281 | type_map[_ugraph.target(edge)] = 1; |
---|
| 1282 | } |
---|
| 1283 | |
---|
| 1284 | Edge next = edge_lists[edge].next != pred ? |
---|
| 1285 | edge_lists[edge].next : edge_lists[edge].prev; |
---|
| 1286 | pred = edge; edge = next; |
---|
| 1287 | } |
---|
| 1288 | |
---|
| 1289 | } |
---|
| 1290 | |
---|
| 1291 | type_map[root] = 2; |
---|
| 1292 | flip_map[root] = false; |
---|
| 1293 | |
---|
| 1294 | for (int i = 1; i < int(qu.size()); ++i) { |
---|
| 1295 | |
---|
| 1296 | Node node = qu[i]; |
---|
| 1297 | |
---|
| 1298 | while (type_map[node] != 2) { |
---|
| 1299 | st.push_back(node); |
---|
| 1300 | type_map[node] = 2; |
---|
| 1301 | node = _ugraph.source(pred_map[node]); |
---|
| 1302 | } |
---|
| 1303 | |
---|
| 1304 | bool flip = flip_map[node]; |
---|
| 1305 | |
---|
| 1306 | while (!st.empty()) { |
---|
| 1307 | node = st.back(); |
---|
| 1308 | st.pop_back(); |
---|
| 1309 | |
---|
| 1310 | flip_map[node] = flip != flip_map[node]; |
---|
| 1311 | flip = flip_map[node]; |
---|
| 1312 | |
---|
| 1313 | if (flip) { |
---|
| 1314 | Edge edge = node_data[order_map[node]].first; |
---|
| 1315 | std::swap(edge_lists[edge].prev, edge_lists[edge].next); |
---|
| 1316 | edge = edge_lists[edge].prev; |
---|
| 1317 | std::swap(edge_lists[edge].prev, edge_lists[edge].next); |
---|
| 1318 | node_data[order_map[node]].first = edge; |
---|
| 1319 | } |
---|
| 1320 | } |
---|
| 1321 | } |
---|
| 1322 | |
---|
| 1323 | for (int i = 0; i < int(qu.size()); ++i) { |
---|
| 1324 | |
---|
| 1325 | Edge edge = node_data[order_map[qu[i]]].first; |
---|
| 1326 | Edge last = edge, pred = edge; |
---|
| 1327 | |
---|
| 1328 | edge = edge_lists[edge].next; |
---|
| 1329 | while (edge != last) { |
---|
| 1330 | |
---|
| 1331 | if (edge_lists[edge].next == pred) { |
---|
| 1332 | std::swap(edge_lists[edge].next, edge_lists[edge].prev); |
---|
| 1333 | } |
---|
| 1334 | pred = edge; edge = edge_lists[edge].next; |
---|
| 1335 | } |
---|
| 1336 | |
---|
| 1337 | } |
---|
| 1338 | } |
---|
| 1339 | |
---|
| 1340 | void setFaceFlags(Node root, Node wnode, Node ynode, Node xnode, |
---|
| 1341 | OrderMap& order_map, NodeData& node_data, |
---|
| 1342 | TypeMap& type_map) { |
---|
| 1343 | Node node = _ugraph.target(node_data[order_map[root]].first); |
---|
| 1344 | |
---|
| 1345 | while (node != ynode) { |
---|
| 1346 | type_map[node] = HIGHY; |
---|
| 1347 | node = _ugraph.target(node_data[order_map[node]].first); |
---|
| 1348 | } |
---|
| 1349 | |
---|
| 1350 | while (node != wnode) { |
---|
| 1351 | type_map[node] = LOWY; |
---|
| 1352 | node = _ugraph.target(node_data[order_map[node]].first); |
---|
| 1353 | } |
---|
| 1354 | |
---|
| 1355 | node = _ugraph.target(node_data[order_map[wnode]].first); |
---|
| 1356 | |
---|
| 1357 | while (node != xnode) { |
---|
| 1358 | type_map[node] = LOWX; |
---|
| 1359 | node = _ugraph.target(node_data[order_map[node]].first); |
---|
| 1360 | } |
---|
| 1361 | type_map[node] = LOWX; |
---|
| 1362 | |
---|
| 1363 | node = _ugraph.target(node_data[order_map[xnode]].first); |
---|
| 1364 | while (node != root) { |
---|
| 1365 | type_map[node] = HIGHX; |
---|
| 1366 | node = _ugraph.target(node_data[order_map[node]].first); |
---|
| 1367 | } |
---|
| 1368 | |
---|
| 1369 | type_map[wnode] = PERTINENT; |
---|
| 1370 | type_map[root] = ROOT; |
---|
| 1371 | } |
---|
| 1372 | |
---|
| 1373 | void findInternalPath(std::vector<Edge>& ipath, |
---|
| 1374 | Node wnode, Node root, TypeMap& type_map, |
---|
| 1375 | OrderMap& order_map, NodeData& node_data, |
---|
| 1376 | EdgeLists& edge_lists) { |
---|
| 1377 | std::vector<Edge> st; |
---|
| 1378 | |
---|
| 1379 | Node node = wnode; |
---|
| 1380 | |
---|
| 1381 | while (node != root) { |
---|
| 1382 | Edge edge = edge_lists[node_data[order_map[node]].first].next; |
---|
| 1383 | st.push_back(edge); |
---|
| 1384 | node = _ugraph.target(edge); |
---|
| 1385 | } |
---|
| 1386 | |
---|
| 1387 | while (true) { |
---|
| 1388 | Edge edge = st.back(); |
---|
| 1389 | if (type_map[_ugraph.target(edge)] == LOWX || |
---|
| 1390 | type_map[_ugraph.target(edge)] == HIGHX) { |
---|
| 1391 | break; |
---|
| 1392 | } |
---|
| 1393 | if (type_map[_ugraph.target(edge)] == 2) { |
---|
| 1394 | type_map[_ugraph.target(edge)] = 3; |
---|
| 1395 | |
---|
| 1396 | edge = edge_lists[_ugraph.oppositeEdge(edge)].next; |
---|
| 1397 | st.push_back(edge); |
---|
| 1398 | } else { |
---|
| 1399 | st.pop_back(); |
---|
| 1400 | edge = edge_lists[edge].next; |
---|
| 1401 | |
---|
| 1402 | while (_ugraph.oppositeEdge(edge) == st.back()) { |
---|
| 1403 | edge = st.back(); |
---|
| 1404 | st.pop_back(); |
---|
| 1405 | edge = edge_lists[edge].next; |
---|
| 1406 | } |
---|
| 1407 | st.push_back(edge); |
---|
| 1408 | } |
---|
| 1409 | } |
---|
| 1410 | |
---|
| 1411 | for (int i = 0; i < int(st.size()); ++i) { |
---|
| 1412 | if (type_map[_ugraph.target(st[i])] != LOWY && |
---|
| 1413 | type_map[_ugraph.target(st[i])] != HIGHY) { |
---|
| 1414 | for (; i < int(st.size()); ++i) { |
---|
| 1415 | ipath.push_back(st[i]); |
---|
| 1416 | } |
---|
| 1417 | } |
---|
| 1418 | } |
---|
| 1419 | } |
---|
| 1420 | |
---|
| 1421 | void setInternalFlags(std::vector<Edge>& ipath, TypeMap& type_map) { |
---|
| 1422 | for (int i = 1; i < int(ipath.size()); ++i) { |
---|
| 1423 | type_map[_ugraph.source(ipath[i])] = INTERNAL; |
---|
| 1424 | } |
---|
| 1425 | } |
---|
| 1426 | |
---|
| 1427 | void findPilePath(std::vector<Edge>& ppath, |
---|
| 1428 | Node root, TypeMap& type_map, OrderMap& order_map, |
---|
| 1429 | NodeData& node_data, EdgeLists& edge_lists) { |
---|
| 1430 | std::vector<Edge> st; |
---|
| 1431 | |
---|
| 1432 | st.push_back(_ugraph.oppositeEdge(node_data[order_map[root]].first)); |
---|
| 1433 | st.push_back(node_data[order_map[root]].first); |
---|
| 1434 | |
---|
| 1435 | while (st.size() > 1) { |
---|
| 1436 | Edge edge = st.back(); |
---|
| 1437 | if (type_map[_ugraph.target(edge)] == INTERNAL) { |
---|
| 1438 | break; |
---|
| 1439 | } |
---|
| 1440 | if (type_map[_ugraph.target(edge)] == 3) { |
---|
| 1441 | type_map[_ugraph.target(edge)] = 4; |
---|
| 1442 | |
---|
| 1443 | edge = edge_lists[_ugraph.oppositeEdge(edge)].next; |
---|
| 1444 | st.push_back(edge); |
---|
| 1445 | } else { |
---|
| 1446 | st.pop_back(); |
---|
| 1447 | edge = edge_lists[edge].next; |
---|
| 1448 | |
---|
| 1449 | while (!st.empty() && _ugraph.oppositeEdge(edge) == st.back()) { |
---|
| 1450 | edge = st.back(); |
---|
| 1451 | st.pop_back(); |
---|
| 1452 | edge = edge_lists[edge].next; |
---|
| 1453 | } |
---|
| 1454 | st.push_back(edge); |
---|
| 1455 | } |
---|
| 1456 | } |
---|
| 1457 | |
---|
| 1458 | for (int i = 1; i < int(st.size()); ++i) { |
---|
| 1459 | ppath.push_back(st[i]); |
---|
| 1460 | } |
---|
| 1461 | } |
---|
| 1462 | |
---|
| 1463 | |
---|
| 1464 | int markExternalPath(Node node, OrderMap& order_map, |
---|
| 1465 | ChildLists& child_lists, PredMap& pred_map, |
---|
| 1466 | AncestorMap& ancestor_map, LowMap& low_map) { |
---|
| 1467 | int lp = lowPoint(node, order_map, child_lists, |
---|
| 1468 | ancestor_map, low_map); |
---|
| 1469 | |
---|
| 1470 | if (ancestor_map[node] != lp) { |
---|
| 1471 | node = child_lists[node].first; |
---|
| 1472 | _kuratowski[pred_map[node]] = true; |
---|
| 1473 | |
---|
| 1474 | while (ancestor_map[node] != lp) { |
---|
| 1475 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
| 1476 | Node tnode = _ugraph.target(e); |
---|
| 1477 | if (order_map[tnode] > order_map[node] && low_map[tnode] == lp) { |
---|
| 1478 | node = tnode; |
---|
| 1479 | _kuratowski[e] = true; |
---|
| 1480 | break; |
---|
| 1481 | } |
---|
| 1482 | } |
---|
| 1483 | } |
---|
| 1484 | } |
---|
| 1485 | |
---|
| 1486 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
| 1487 | if (order_map[_ugraph.target(e)] == lp) { |
---|
| 1488 | _kuratowski[e] = true; |
---|
| 1489 | break; |
---|
| 1490 | } |
---|
| 1491 | } |
---|
| 1492 | |
---|
| 1493 | return lp; |
---|
| 1494 | } |
---|
| 1495 | |
---|
| 1496 | void markPertinentPath(Node node, OrderMap& order_map, |
---|
| 1497 | NodeData& node_data, EdgeLists& edge_lists, |
---|
| 1498 | EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
---|
| 1499 | while (embed_edge[node] == INVALID) { |
---|
| 1500 | int n = merge_roots[node].front(); |
---|
| 1501 | Edge edge = node_data[n].first; |
---|
| 1502 | |
---|
| 1503 | _kuratowski.set(edge, true); |
---|
| 1504 | |
---|
| 1505 | Node pred = node; |
---|
| 1506 | node = _ugraph.target(edge); |
---|
| 1507 | while (!pertinent(node, embed_edge, merge_roots)) { |
---|
| 1508 | edge = node_data[order_map[node]].first; |
---|
| 1509 | if (_ugraph.target(edge) == pred) { |
---|
| 1510 | edge = edge_lists[edge].next; |
---|
| 1511 | } |
---|
| 1512 | _kuratowski.set(edge, true); |
---|
| 1513 | pred = node; |
---|
| 1514 | node = _ugraph.target(edge); |
---|
| 1515 | } |
---|
| 1516 | } |
---|
| 1517 | _kuratowski.set(embed_edge[node], true); |
---|
| 1518 | } |
---|
| 1519 | |
---|
| 1520 | void markPredPath(Node node, Node snode, PredMap& pred_map) { |
---|
| 1521 | while (node != snode) { |
---|
| 1522 | _kuratowski.set(pred_map[node], true); |
---|
| 1523 | node = _ugraph.source(pred_map[node]); |
---|
| 1524 | } |
---|
| 1525 | } |
---|
| 1526 | |
---|
| 1527 | void markFacePath(Node ynode, Node xnode, |
---|
| 1528 | OrderMap& order_map, NodeData& node_data) { |
---|
| 1529 | Edge edge = node_data[order_map[ynode]].first; |
---|
| 1530 | Node node = _ugraph.target(edge); |
---|
| 1531 | _kuratowski.set(edge, true); |
---|
| 1532 | |
---|
| 1533 | while (node != xnode) { |
---|
| 1534 | edge = node_data[order_map[node]].first; |
---|
| 1535 | _kuratowski.set(edge, true); |
---|
| 1536 | node = _ugraph.target(edge); |
---|
| 1537 | } |
---|
| 1538 | } |
---|
| 1539 | |
---|
| 1540 | void markInternalPath(std::vector<Edge>& path) { |
---|
| 1541 | for (int i = 0; i < int(path.size()); ++i) { |
---|
| 1542 | _kuratowski.set(path[i], true); |
---|
| 1543 | } |
---|
| 1544 | } |
---|
| 1545 | |
---|
| 1546 | void markPilePath(std::vector<Edge>& path) { |
---|
| 1547 | for (int i = 0; i < int(path.size()); ++i) { |
---|
| 1548 | _kuratowski.set(path[i], true); |
---|
| 1549 | } |
---|
| 1550 | } |
---|
| 1551 | |
---|
| 1552 | void isolateKuratowski(Edge edge, NodeData& node_data, |
---|
| 1553 | EdgeLists& edge_lists, FlipMap& flip_map, |
---|
| 1554 | OrderMap& order_map, OrderList& order_list, |
---|
| 1555 | PredMap& pred_map, ChildLists& child_lists, |
---|
| 1556 | AncestorMap& ancestor_map, LowMap& low_map, |
---|
| 1557 | EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
---|
| 1558 | |
---|
| 1559 | Node root = _ugraph.source(edge); |
---|
| 1560 | Node enode = _ugraph.target(edge); |
---|
| 1561 | |
---|
| 1562 | int rorder = order_map[root]; |
---|
| 1563 | |
---|
| 1564 | TypeMap type_map(_ugraph, 0); |
---|
| 1565 | |
---|
| 1566 | int rn = findComponentRoot(root, enode, child_lists, |
---|
| 1567 | order_map, order_list); |
---|
| 1568 | |
---|
| 1569 | Node xnode = order_list[node_data[rn].next]; |
---|
| 1570 | Node ynode = order_list[node_data[rn].prev]; |
---|
| 1571 | |
---|
| 1572 | // Minor-A |
---|
| 1573 | { |
---|
| 1574 | while (!merge_roots[xnode].empty() || !merge_roots[ynode].empty()) { |
---|
| 1575 | |
---|
| 1576 | if (!merge_roots[xnode].empty()) { |
---|
| 1577 | root = xnode; |
---|
| 1578 | rn = merge_roots[xnode].front(); |
---|
| 1579 | } else { |
---|
| 1580 | root = ynode; |
---|
| 1581 | rn = merge_roots[ynode].front(); |
---|
| 1582 | } |
---|
| 1583 | |
---|
| 1584 | xnode = order_list[node_data[rn].next]; |
---|
| 1585 | ynode = order_list[node_data[rn].prev]; |
---|
| 1586 | } |
---|
| 1587 | |
---|
| 1588 | if (root != _ugraph.source(edge)) { |
---|
| 1589 | orientComponent(root, rn, order_map, pred_map, |
---|
| 1590 | node_data, edge_lists, flip_map, type_map); |
---|
| 1591 | markFacePath(root, root, order_map, node_data); |
---|
| 1592 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
| 1593 | pred_map, ancestor_map, low_map); |
---|
| 1594 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
| 1595 | pred_map, ancestor_map, low_map); |
---|
| 1596 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
| 1597 | Node lwnode = findPertinent(ynode, order_map, node_data, |
---|
| 1598 | embed_edge, merge_roots); |
---|
| 1599 | |
---|
| 1600 | markPertinentPath(lwnode, order_map, node_data, edge_lists, |
---|
| 1601 | embed_edge, merge_roots); |
---|
| 1602 | |
---|
| 1603 | return; |
---|
| 1604 | } |
---|
| 1605 | } |
---|
| 1606 | |
---|
| 1607 | orientComponent(root, rn, order_map, pred_map, |
---|
| 1608 | node_data, edge_lists, flip_map, type_map); |
---|
| 1609 | |
---|
| 1610 | Node wnode = findPertinent(ynode, order_map, node_data, |
---|
| 1611 | embed_edge, merge_roots); |
---|
| 1612 | setFaceFlags(root, wnode, ynode, xnode, order_map, node_data, type_map); |
---|
| 1613 | |
---|
| 1614 | |
---|
| 1615 | //Minor-B |
---|
| 1616 | if (!merge_roots[wnode].empty()) { |
---|
| 1617 | int cn = merge_roots[wnode].back(); |
---|
| 1618 | Node rep = order_list[cn - order_list.size()]; |
---|
| 1619 | if (low_map[rep] < rorder) { |
---|
| 1620 | markFacePath(root, root, order_map, node_data); |
---|
| 1621 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
| 1622 | pred_map, ancestor_map, low_map); |
---|
| 1623 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
| 1624 | pred_map, ancestor_map, low_map); |
---|
| 1625 | |
---|
| 1626 | Node lwnode, lznode; |
---|
| 1627 | markCommonPath(wnode, rorder, lwnode, lznode, order_list, |
---|
| 1628 | order_map, node_data, edge_lists, embed_edge, |
---|
| 1629 | merge_roots, child_lists, ancestor_map, low_map); |
---|
| 1630 | |
---|
| 1631 | markPertinentPath(lwnode, order_map, node_data, edge_lists, |
---|
| 1632 | embed_edge, merge_roots); |
---|
| 1633 | int zlp = markExternalPath(lznode, order_map, child_lists, |
---|
| 1634 | pred_map, ancestor_map, low_map); |
---|
| 1635 | |
---|
| 1636 | int minlp = xlp < ylp ? xlp : ylp; |
---|
| 1637 | if (zlp < minlp) minlp = zlp; |
---|
| 1638 | |
---|
| 1639 | int maxlp = xlp > ylp ? xlp : ylp; |
---|
| 1640 | if (zlp > maxlp) maxlp = zlp; |
---|
| 1641 | |
---|
| 1642 | markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
---|
| 1643 | |
---|
| 1644 | return; |
---|
| 1645 | } |
---|
| 1646 | } |
---|
| 1647 | |
---|
| 1648 | Node pxnode, pynode; |
---|
| 1649 | std::vector<Edge> ipath; |
---|
| 1650 | findInternalPath(ipath, wnode, root, type_map, order_map, |
---|
| 1651 | node_data, edge_lists); |
---|
| 1652 | setInternalFlags(ipath, type_map); |
---|
| 1653 | pynode = _ugraph.source(ipath.front()); |
---|
| 1654 | pxnode = _ugraph.target(ipath.back()); |
---|
| 1655 | |
---|
| 1656 | wnode = findPertinent(pynode, order_map, node_data, |
---|
| 1657 | embed_edge, merge_roots); |
---|
| 1658 | |
---|
| 1659 | // Minor-C |
---|
| 1660 | { |
---|
| 1661 | if (type_map[_ugraph.source(ipath.front())] == HIGHY) { |
---|
| 1662 | if (type_map[_ugraph.target(ipath.back())] == HIGHX) { |
---|
| 1663 | markFacePath(xnode, pxnode, order_map, node_data); |
---|
| 1664 | } |
---|
| 1665 | markFacePath(root, xnode, order_map, node_data); |
---|
| 1666 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
| 1667 | embed_edge, merge_roots); |
---|
| 1668 | markInternalPath(ipath); |
---|
| 1669 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
| 1670 | pred_map, ancestor_map, low_map); |
---|
| 1671 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
| 1672 | pred_map, ancestor_map, low_map); |
---|
| 1673 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
| 1674 | return; |
---|
| 1675 | } |
---|
| 1676 | |
---|
| 1677 | if (type_map[_ugraph.target(ipath.back())] == HIGHX) { |
---|
| 1678 | markFacePath(ynode, root, order_map, node_data); |
---|
| 1679 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
| 1680 | embed_edge, merge_roots); |
---|
| 1681 | markInternalPath(ipath); |
---|
| 1682 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
| 1683 | pred_map, ancestor_map, low_map); |
---|
| 1684 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
| 1685 | pred_map, ancestor_map, low_map); |
---|
| 1686 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
| 1687 | return; |
---|
| 1688 | } |
---|
| 1689 | } |
---|
| 1690 | |
---|
| 1691 | std::vector<Edge> ppath; |
---|
| 1692 | findPilePath(ppath, root, type_map, order_map, node_data, edge_lists); |
---|
| 1693 | |
---|
| 1694 | // Minor-D |
---|
| 1695 | if (!ppath.empty()) { |
---|
| 1696 | markFacePath(ynode, xnode, order_map, node_data); |
---|
| 1697 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
| 1698 | embed_edge, merge_roots); |
---|
| 1699 | markPilePath(ppath); |
---|
| 1700 | markInternalPath(ipath); |
---|
| 1701 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
| 1702 | pred_map, ancestor_map, low_map); |
---|
| 1703 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
| 1704 | pred_map, ancestor_map, low_map); |
---|
| 1705 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
| 1706 | return; |
---|
| 1707 | } |
---|
| 1708 | |
---|
| 1709 | // Minor-E* |
---|
| 1710 | { |
---|
| 1711 | |
---|
| 1712 | if (!external(wnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
| 1713 | Node znode = findExternal(pynode, rorder, order_map, |
---|
| 1714 | child_lists, ancestor_map, |
---|
| 1715 | low_map, node_data); |
---|
| 1716 | |
---|
| 1717 | if (type_map[znode] == LOWY) { |
---|
| 1718 | markFacePath(root, xnode, order_map, node_data); |
---|
| 1719 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
| 1720 | embed_edge, merge_roots); |
---|
| 1721 | markInternalPath(ipath); |
---|
| 1722 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
| 1723 | pred_map, ancestor_map, low_map); |
---|
| 1724 | int zlp = markExternalPath(znode, order_map, child_lists, |
---|
| 1725 | pred_map, ancestor_map, low_map); |
---|
| 1726 | markPredPath(root, order_list[xlp < zlp ? xlp : zlp], pred_map); |
---|
| 1727 | } else { |
---|
| 1728 | markFacePath(ynode, root, order_map, node_data); |
---|
| 1729 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
| 1730 | embed_edge, merge_roots); |
---|
| 1731 | markInternalPath(ipath); |
---|
| 1732 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
| 1733 | pred_map, ancestor_map, low_map); |
---|
| 1734 | int zlp = markExternalPath(znode, order_map, child_lists, |
---|
| 1735 | pred_map, ancestor_map, low_map); |
---|
| 1736 | markPredPath(root, order_list[ylp < zlp ? ylp : zlp], pred_map); |
---|
| 1737 | } |
---|
| 1738 | return; |
---|
| 1739 | } |
---|
| 1740 | |
---|
| 1741 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
| 1742 | pred_map, ancestor_map, low_map); |
---|
| 1743 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
| 1744 | pred_map, ancestor_map, low_map); |
---|
| 1745 | int wlp = markExternalPath(wnode, order_map, child_lists, |
---|
| 1746 | pred_map, ancestor_map, low_map); |
---|
| 1747 | |
---|
| 1748 | if (wlp > xlp && wlp > ylp) { |
---|
| 1749 | markFacePath(root, root, order_map, node_data); |
---|
| 1750 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
| 1751 | return; |
---|
| 1752 | } |
---|
| 1753 | |
---|
| 1754 | markInternalPath(ipath); |
---|
| 1755 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
| 1756 | embed_edge, merge_roots); |
---|
| 1757 | |
---|
| 1758 | if (xlp > ylp && xlp > wlp) { |
---|
| 1759 | markFacePath(root, pynode, order_map, node_data); |
---|
| 1760 | markFacePath(wnode, xnode, order_map, node_data); |
---|
| 1761 | markPredPath(root, order_list[ylp < wlp ? ylp : wlp], pred_map); |
---|
| 1762 | return; |
---|
| 1763 | } |
---|
| 1764 | |
---|
| 1765 | if (ylp > xlp && ylp > wlp) { |
---|
| 1766 | markFacePath(pxnode, root, order_map, node_data); |
---|
| 1767 | markFacePath(ynode, wnode, order_map, node_data); |
---|
| 1768 | markPredPath(root, order_list[xlp < wlp ? xlp : wlp], pred_map); |
---|
| 1769 | return; |
---|
| 1770 | } |
---|
| 1771 | |
---|
| 1772 | if (pynode != ynode) { |
---|
| 1773 | markFacePath(pxnode, wnode, order_map, node_data); |
---|
| 1774 | |
---|
| 1775 | int minlp = xlp < ylp ? xlp : ylp; |
---|
| 1776 | if (wlp < minlp) minlp = wlp; |
---|
| 1777 | |
---|
| 1778 | int maxlp = xlp > ylp ? xlp : ylp; |
---|
| 1779 | if (wlp > maxlp) maxlp = wlp; |
---|
| 1780 | |
---|
| 1781 | markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
---|
| 1782 | return; |
---|
| 1783 | } |
---|
| 1784 | |
---|
| 1785 | if (pxnode != xnode) { |
---|
| 1786 | markFacePath(wnode, pynode, order_map, node_data); |
---|
| 1787 | |
---|
| 1788 | int minlp = xlp < ylp ? xlp : ylp; |
---|
| 1789 | if (wlp < minlp) minlp = wlp; |
---|
| 1790 | |
---|
| 1791 | int maxlp = xlp > ylp ? xlp : ylp; |
---|
| 1792 | if (wlp > maxlp) maxlp = wlp; |
---|
| 1793 | |
---|
| 1794 | markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
---|
| 1795 | return; |
---|
| 1796 | } |
---|
| 1797 | |
---|
| 1798 | markFacePath(root, root, order_map, node_data); |
---|
| 1799 | int minlp = xlp < ylp ? xlp : ylp; |
---|
| 1800 | if (wlp < minlp) minlp = wlp; |
---|
| 1801 | markPredPath(root, order_list[minlp], pred_map); |
---|
| 1802 | return; |
---|
| 1803 | } |
---|
| 1804 | |
---|
| 1805 | } |
---|
| 1806 | |
---|
| 1807 | }; |
---|
| 1808 | |
---|
| 1809 | } |
---|
| 1810 | |
---|
| 1811 | #endif |
---|