2755 lines
84 KiB
C++
Executable File
2755 lines
84 KiB
C++
Executable File
/* -*- mode: C++; indent-tabs-mode: nil; -*-
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*
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* This file is a part of LEMON, a generic C++ optimization library.
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*
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* Copyright (C) 2003-2013
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* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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* (Egervary Research Group on Combinatorial Optimization, EGRES).
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*
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* Permission to use, modify and distribute this software is granted
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* provided that this copyright notice appears in all copies. For
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* precise terms see the accompanying LICENSE file.
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*
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* This software is provided "AS IS" with no warranty of any kind,
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* express or implied, and with no claim as to its suitability for any
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* purpose.
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*
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*/
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#ifndef LEMON_PLANARITY_H
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#define LEMON_PLANARITY_H
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/// \ingroup planar
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/// \file
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/// \brief Planarity checking, embedding, drawing and coloring
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#include <vector>
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#include <list>
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#include <lemon/dfs.h>
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#include <lemon/bfs.h>
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#include <lemon/radix_sort.h>
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#include <lemon/maps.h>
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#include <lemon/path.h>
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#include <lemon/bucket_heap.h>
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#include <lemon/adaptors.h>
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#include <lemon/edge_set.h>
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#include <lemon/color.h>
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#include <lemon/dim2.h>
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namespace lemon {
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namespace _planarity_bits {
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template <typename Graph>
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struct PlanarityVisitor : DfsVisitor<Graph> {
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TEMPLATE_GRAPH_TYPEDEFS(Graph);
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typedef typename Graph::template NodeMap<Arc> PredMap;
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typedef typename Graph::template EdgeMap<bool> TreeMap;
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typedef typename Graph::template NodeMap<int> OrderMap;
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typedef std::vector<Node> OrderList;
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typedef typename Graph::template NodeMap<int> LowMap;
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typedef typename Graph::template NodeMap<int> AncestorMap;
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PlanarityVisitor(const Graph& graph,
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PredMap& pred_map, TreeMap& tree_map,
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OrderMap& order_map, OrderList& order_list,
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AncestorMap& ancestor_map, LowMap& low_map)
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: _graph(graph), _pred_map(pred_map), _tree_map(tree_map),
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_order_map(order_map), _order_list(order_list),
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_ancestor_map(ancestor_map), _low_map(low_map) {}
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void reach(const Node& node) {
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_order_map[node] = _order_list.size();
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_low_map[node] = _order_list.size();
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_ancestor_map[node] = _order_list.size();
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_order_list.push_back(node);
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}
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void discover(const Arc& arc) {
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Node target = _graph.target(arc);
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_tree_map[arc] = true;
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_pred_map[target] = arc;
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}
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void examine(const Arc& arc) {
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Node source = _graph.source(arc);
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Node target = _graph.target(arc);
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if (_order_map[target] < _order_map[source] && !_tree_map[arc]) {
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if (_low_map[source] > _order_map[target]) {
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_low_map[source] = _order_map[target];
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}
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if (_ancestor_map[source] > _order_map[target]) {
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_ancestor_map[source] = _order_map[target];
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}
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}
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}
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void backtrack(const Arc& arc) {
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Node source = _graph.source(arc);
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Node target = _graph.target(arc);
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if (_low_map[source] > _low_map[target]) {
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_low_map[source] = _low_map[target];
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}
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}
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const Graph& _graph;
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PredMap& _pred_map;
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TreeMap& _tree_map;
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OrderMap& _order_map;
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OrderList& _order_list;
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AncestorMap& _ancestor_map;
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LowMap& _low_map;
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};
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template <typename Graph, bool embedding = true>
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struct NodeDataNode {
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int prev, next;
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int visited;
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typename Graph::Arc first;
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bool inverted;
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};
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template <typename Graph>
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struct NodeDataNode<Graph, false> {
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int prev, next;
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int visited;
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};
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template <typename Graph>
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struct ChildListNode {
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typedef typename Graph::Node Node;
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Node first;
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Node prev, next;
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};
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template <typename Graph>
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struct ArcListNode {
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typename Graph::Arc prev, next;
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};
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template <typename Graph>
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class PlanarityChecking {
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private:
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TEMPLATE_GRAPH_TYPEDEFS(Graph);
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const Graph& _graph;
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private:
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typedef typename Graph::template NodeMap<Arc> PredMap;
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typedef typename Graph::template EdgeMap<bool> TreeMap;
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typedef typename Graph::template NodeMap<int> OrderMap;
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typedef std::vector<Node> OrderList;
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typedef typename Graph::template NodeMap<int> LowMap;
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typedef typename Graph::template NodeMap<int> AncestorMap;
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typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode;
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typedef std::vector<NodeDataNode> NodeData;
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typedef _planarity_bits::ChildListNode<Graph> ChildListNode;
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typedef typename Graph::template NodeMap<ChildListNode> ChildLists;
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typedef typename Graph::template NodeMap<std::list<int> > MergeRoots;
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typedef typename Graph::template NodeMap<bool> EmbedArc;
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public:
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PlanarityChecking(const Graph& graph) : _graph(graph) {}
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bool run() {
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typedef _planarity_bits::PlanarityVisitor<Graph> Visitor;
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PredMap pred_map(_graph, INVALID);
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TreeMap tree_map(_graph, false);
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OrderMap order_map(_graph, -1);
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OrderList order_list;
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AncestorMap ancestor_map(_graph, -1);
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LowMap low_map(_graph, -1);
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Visitor visitor(_graph, pred_map, tree_map,
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order_map, order_list, ancestor_map, low_map);
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DfsVisit<Graph, Visitor> visit(_graph, visitor);
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visit.run();
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ChildLists child_lists(_graph);
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createChildLists(tree_map, order_map, low_map, child_lists);
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NodeData node_data(2 * order_list.size());
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EmbedArc embed_arc(_graph, false);
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MergeRoots merge_roots(_graph);
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for (int i = order_list.size() - 1; i >= 0; --i) {
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Node node = order_list[i];
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Node source = node;
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for (OutArcIt e(_graph, node); e != INVALID; ++e) {
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Node target = _graph.target(e);
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if (order_map[source] < order_map[target] && tree_map[e]) {
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initFace(target, node_data, order_map, order_list);
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}
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}
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for (OutArcIt e(_graph, node); e != INVALID; ++e) {
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Node target = _graph.target(e);
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if (order_map[source] < order_map[target] && !tree_map[e]) {
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embed_arc[target] = true;
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walkUp(target, source, i, pred_map, low_map,
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order_map, order_list, node_data, merge_roots);
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}
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}
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for (typename MergeRoots::Value::iterator it =
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merge_roots[node].begin();
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it != merge_roots[node].end(); ++it) {
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int rn = *it;
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walkDown(rn, i, node_data, order_list, child_lists,
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ancestor_map, low_map, embed_arc, merge_roots);
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}
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merge_roots[node].clear();
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for (OutArcIt e(_graph, node); e != INVALID; ++e) {
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Node target = _graph.target(e);
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if (order_map[source] < order_map[target] && !tree_map[e]) {
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if (embed_arc[target]) {
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return false;
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}
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}
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}
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}
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return true;
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}
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private:
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void createChildLists(const TreeMap& tree_map, const OrderMap& order_map,
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const LowMap& low_map, ChildLists& child_lists) {
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for (NodeIt n(_graph); n != INVALID; ++n) {
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Node source = n;
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std::vector<Node> targets;
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for (OutArcIt e(_graph, n); e != INVALID; ++e) {
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Node target = _graph.target(e);
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if (order_map[source] < order_map[target] && tree_map[e]) {
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targets.push_back(target);
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}
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}
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if (targets.size() == 0) {
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child_lists[source].first = INVALID;
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} else if (targets.size() == 1) {
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child_lists[source].first = targets[0];
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child_lists[targets[0]].prev = INVALID;
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child_lists[targets[0]].next = INVALID;
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} else {
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radixSort(targets.begin(), targets.end(), mapToFunctor(low_map));
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for (int i = 1; i < int(targets.size()); ++i) {
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child_lists[targets[i]].prev = targets[i - 1];
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child_lists[targets[i - 1]].next = targets[i];
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}
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child_lists[targets.back()].next = INVALID;
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child_lists[targets.front()].prev = INVALID;
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child_lists[source].first = targets.front();
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}
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}
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}
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void walkUp(const Node& node, Node root, int rorder,
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const PredMap& pred_map, const LowMap& low_map,
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const OrderMap& order_map, const OrderList& order_list,
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NodeData& node_data, MergeRoots& merge_roots) {
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int na, nb;
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bool da, db;
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na = nb = order_map[node];
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da = true; db = false;
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while (true) {
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if (node_data[na].visited == rorder) break;
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if (node_data[nb].visited == rorder) break;
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node_data[na].visited = rorder;
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node_data[nb].visited = rorder;
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int rn = -1;
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if (na >= int(order_list.size())) {
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rn = na;
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} else if (nb >= int(order_list.size())) {
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rn = nb;
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}
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if (rn == -1) {
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int nn;
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nn = da ? node_data[na].prev : node_data[na].next;
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da = node_data[nn].prev != na;
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na = nn;
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nn = db ? node_data[nb].prev : node_data[nb].next;
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db = node_data[nn].prev != nb;
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nb = nn;
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} else {
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Node rep = order_list[rn - order_list.size()];
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Node parent = _graph.source(pred_map[rep]);
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if (low_map[rep] < rorder) {
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merge_roots[parent].push_back(rn);
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} else {
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merge_roots[parent].push_front(rn);
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}
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if (parent != root) {
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na = nb = order_map[parent];
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da = true; db = false;
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} else {
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break;
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}
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}
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}
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}
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void walkDown(int rn, int rorder, NodeData& node_data,
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OrderList& order_list, ChildLists& child_lists,
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AncestorMap& ancestor_map, LowMap& low_map,
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EmbedArc& embed_arc, MergeRoots& merge_roots) {
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std::vector<std::pair<int, bool> > merge_stack;
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for (int di = 0; di < 2; ++di) {
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bool rd = di == 0;
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int pn = rn;
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int n = rd ? node_data[rn].next : node_data[rn].prev;
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while (n != rn) {
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Node node = order_list[n];
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if (embed_arc[node]) {
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// Merging components on the critical path
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while (!merge_stack.empty()) {
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// Component root
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int cn = merge_stack.back().first;
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bool cd = merge_stack.back().second;
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merge_stack.pop_back();
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// Parent of component
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int dn = merge_stack.back().first;
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bool dd = merge_stack.back().second;
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merge_stack.pop_back();
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Node parent = order_list[dn];
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// Erasing from merge_roots
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merge_roots[parent].pop_front();
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Node child = order_list[cn - order_list.size()];
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// Erasing from child_lists
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if (child_lists[child].prev != INVALID) {
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child_lists[child_lists[child].prev].next =
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child_lists[child].next;
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} else {
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child_lists[parent].first = child_lists[child].next;
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}
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if (child_lists[child].next != INVALID) {
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child_lists[child_lists[child].next].prev =
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child_lists[child].prev;
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}
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// Merging external faces
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{
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int en = cn;
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cn = cd ? node_data[cn].prev : node_data[cn].next;
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cd = node_data[cn].next == en;
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}
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if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn;
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if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn;
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}
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bool d = pn == node_data[n].prev;
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if (node_data[n].prev == node_data[n].next &&
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node_data[n].inverted) {
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d = !d;
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}
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// Embedding arc into external face
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if (rd) node_data[rn].next = n; else node_data[rn].prev = n;
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if (d) node_data[n].prev = rn; else node_data[n].next = rn;
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pn = rn;
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embed_arc[order_list[n]] = false;
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}
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if (!merge_roots[node].empty()) {
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bool d = pn == node_data[n].prev;
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merge_stack.push_back(std::make_pair(n, d));
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int rn = merge_roots[node].front();
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int xn = node_data[rn].next;
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Node xnode = order_list[xn];
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int yn = node_data[rn].prev;
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Node ynode = order_list[yn];
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bool rd;
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if (!external(xnode, rorder, child_lists,
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ancestor_map, low_map)) {
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rd = true;
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} else if (!external(ynode, rorder, child_lists,
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ancestor_map, low_map)) {
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rd = false;
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} else if (pertinent(xnode, embed_arc, merge_roots)) {
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rd = true;
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} else {
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rd = false;
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}
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merge_stack.push_back(std::make_pair(rn, rd));
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pn = rn;
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n = rd ? xn : yn;
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} else if (!external(node, rorder, child_lists,
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ancestor_map, low_map)) {
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int nn = (node_data[n].next != pn ?
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node_data[n].next : node_data[n].prev);
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bool nd = n == node_data[nn].prev;
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if (nd) node_data[nn].prev = pn;
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else node_data[nn].next = pn;
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if (n == node_data[pn].prev) node_data[pn].prev = nn;
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else node_data[pn].next = nn;
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node_data[nn].inverted =
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(node_data[nn].prev == node_data[nn].next && nd != rd);
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n = nn;
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}
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else break;
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}
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if (!merge_stack.empty() || n == rn) {
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break;
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}
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}
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}
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void initFace(const Node& node, NodeData& node_data,
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const OrderMap& order_map, const OrderList& order_list) {
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int n = order_map[node];
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int rn = n + order_list.size();
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node_data[n].next = node_data[n].prev = rn;
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node_data[rn].next = node_data[rn].prev = n;
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node_data[n].visited = order_list.size();
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node_data[rn].visited = order_list.size();
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}
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bool external(const Node& node, int rorder,
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ChildLists& child_lists, AncestorMap& ancestor_map,
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LowMap& low_map) {
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Node child = child_lists[node].first;
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if (child != INVALID) {
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if (low_map[child] < rorder) return true;
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}
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if (ancestor_map[node] < rorder) return true;
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return false;
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}
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bool pertinent(const Node& node, const EmbedArc& embed_arc,
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const MergeRoots& merge_roots) {
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return !merge_roots[node].empty() || embed_arc[node];
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}
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};
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}
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/// \ingroup planar
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///
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/// \brief Planarity checking of an undirected simple graph
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///
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/// This function implements the Boyer-Myrvold algorithm for
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/// planarity checking of an undirected simple graph. It is a simplified
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/// version of the PlanarEmbedding algorithm class because neither
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/// the embedding nor the Kuratowski subdivisons are computed.
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template <typename GR>
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bool checkPlanarity(const GR& graph) {
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_planarity_bits::PlanarityChecking<GR> pc(graph);
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return pc.run();
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}
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|
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/// \ingroup planar
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///
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/// \brief Planar embedding of an undirected simple graph
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///
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/// This class implements the Boyer-Myrvold algorithm for planar
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/// embedding of an undirected simple graph. The planar embedding is an
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/// ordering of the outgoing edges of the nodes, which is a possible
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/// configuration to draw the graph in the plane. If there is not
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/// such ordering then the graph contains a K<sub>5</sub> (full graph
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/// with 5 nodes) or a K<sub>3,3</sub> (complete bipartite graph on
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/// 3 Red and 3 Blue nodes) subdivision.
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///
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/// The current implementation calculates either an embedding or a
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/// Kuratowski subdivision. The running time of the algorithm is O(n).
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///
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/// \see PlanarDrawing, checkPlanarity()
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template <typename Graph>
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class PlanarEmbedding {
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private:
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TEMPLATE_GRAPH_TYPEDEFS(Graph);
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const Graph& _graph;
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typename Graph::template ArcMap<Arc> _embedding;
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typename Graph::template EdgeMap<bool> _kuratowski;
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private:
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typedef typename Graph::template NodeMap<Arc> PredMap;
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typedef typename Graph::template EdgeMap<bool> TreeMap;
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typedef typename Graph::template NodeMap<int> OrderMap;
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typedef std::vector<Node> OrderList;
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typedef typename Graph::template NodeMap<int> LowMap;
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typedef typename Graph::template NodeMap<int> AncestorMap;
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typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode;
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typedef std::vector<NodeDataNode> NodeData;
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typedef _planarity_bits::ChildListNode<Graph> ChildListNode;
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typedef typename Graph::template NodeMap<ChildListNode> ChildLists;
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typedef typename Graph::template NodeMap<std::list<int> > MergeRoots;
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typedef typename Graph::template NodeMap<Arc> EmbedArc;
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typedef _planarity_bits::ArcListNode<Graph> ArcListNode;
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typedef typename Graph::template ArcMap<ArcListNode> ArcLists;
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typedef typename Graph::template NodeMap<bool> FlipMap;
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typedef typename Graph::template NodeMap<int> TypeMap;
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enum IsolatorNodeType {
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HIGHX = 6, LOWX = 7,
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HIGHY = 8, LOWY = 9,
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ROOT = 10, PERTINENT = 11,
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INTERNAL = 12
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};
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public:
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/// \brief The map type for storing the embedding
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///
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/// The map type for storing the embedding.
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/// \see embeddingMap()
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typedef typename Graph::template ArcMap<Arc> EmbeddingMap;
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/// \brief Constructor
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///
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/// Constructor.
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/// \pre The graph must be simple, i.e. it should not
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/// contain parallel or loop arcs.
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PlanarEmbedding(const Graph& graph)
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: _graph(graph), _embedding(_graph), _kuratowski(graph, false) {}
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/// \brief Run the algorithm.
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///
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/// This function runs the algorithm.
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/// \param kuratowski If this parameter is set to \c false, then the
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/// algorithm does not compute a Kuratowski subdivision.
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/// \return \c true if the graph is planar.
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bool run(bool kuratowski = true) {
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typedef _planarity_bits::PlanarityVisitor<Graph> Visitor;
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PredMap pred_map(_graph, INVALID);
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TreeMap tree_map(_graph, false);
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OrderMap order_map(_graph, -1);
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OrderList order_list;
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AncestorMap ancestor_map(_graph, -1);
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LowMap low_map(_graph, -1);
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Visitor visitor(_graph, pred_map, tree_map,
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order_map, order_list, ancestor_map, low_map);
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DfsVisit<Graph, Visitor> visit(_graph, visitor);
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visit.run();
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ChildLists child_lists(_graph);
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createChildLists(tree_map, order_map, low_map, child_lists);
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NodeData node_data(2 * order_list.size());
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EmbedArc embed_arc(_graph, INVALID);
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MergeRoots merge_roots(_graph);
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ArcLists arc_lists(_graph);
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FlipMap flip_map(_graph, false);
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for (int i = order_list.size() - 1; i >= 0; --i) {
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Node node = order_list[i];
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node_data[i].first = INVALID;
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Node source = node;
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for (OutArcIt e(_graph, node); e != INVALID; ++e) {
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Node target = _graph.target(e);
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if (order_map[source] < order_map[target] && tree_map[e]) {
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initFace(target, arc_lists, node_data,
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pred_map, order_map, order_list);
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}
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}
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for (OutArcIt e(_graph, node); e != INVALID; ++e) {
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Node target = _graph.target(e);
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if (order_map[source] < order_map[target] && !tree_map[e]) {
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embed_arc[target] = e;
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walkUp(target, source, i, pred_map, low_map,
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order_map, order_list, node_data, merge_roots);
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}
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}
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for (typename MergeRoots::Value::iterator it =
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merge_roots[node].begin(); it != merge_roots[node].end(); ++it) {
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int rn = *it;
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walkDown(rn, i, node_data, arc_lists, flip_map, order_list,
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child_lists, ancestor_map, low_map, embed_arc, merge_roots);
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}
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merge_roots[node].clear();
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for (OutArcIt e(_graph, node); e != INVALID; ++e) {
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Node target = _graph.target(e);
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if (order_map[source] < order_map[target] && !tree_map[e]) {
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if (embed_arc[target] != INVALID) {
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if (kuratowski) {
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isolateKuratowski(e, node_data, arc_lists, flip_map,
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order_map, order_list, pred_map, child_lists,
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ancestor_map, low_map,
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embed_arc, merge_roots);
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}
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return false;
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}
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}
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}
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}
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for (int i = 0; i < int(order_list.size()); ++i) {
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mergeRemainingFaces(order_list[i], node_data, order_list, order_map,
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child_lists, arc_lists);
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storeEmbedding(order_list[i], node_data, order_map, pred_map,
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arc_lists, flip_map);
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}
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return true;
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}
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/// \brief Give back the successor of an arc
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///
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/// This function gives back the successor of an arc. It makes
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/// possible to query the cyclic order of the outgoing arcs from
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/// a node.
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Arc next(const Arc& arc) const {
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return _embedding[arc];
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}
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/// \brief Give back the calculated embedding map
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///
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/// This function gives back the calculated embedding map, which
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/// contains the successor of each arc in the cyclic order of the
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/// outgoing arcs of its source node.
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const EmbeddingMap& embeddingMap() const {
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return _embedding;
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}
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/// \brief Give back \c true if the given edge is in the Kuratowski
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/// subdivision
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///
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/// This function gives back \c true if the given edge is in the found
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/// Kuratowski subdivision.
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/// \pre The \c run() function must be called with \c true parameter
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/// before using this function.
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bool kuratowski(const Edge& edge) const {
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return _kuratowski[edge];
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}
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private:
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void createChildLists(const TreeMap& tree_map, const OrderMap& order_map,
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const LowMap& low_map, ChildLists& child_lists) {
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for (NodeIt n(_graph); n != INVALID; ++n) {
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Node source = n;
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std::vector<Node> targets;
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for (OutArcIt e(_graph, n); e != INVALID; ++e) {
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Node target = _graph.target(e);
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if (order_map[source] < order_map[target] && tree_map[e]) {
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targets.push_back(target);
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}
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}
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if (targets.size() == 0) {
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child_lists[source].first = INVALID;
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} else if (targets.size() == 1) {
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child_lists[source].first = targets[0];
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child_lists[targets[0]].prev = INVALID;
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child_lists[targets[0]].next = INVALID;
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} else {
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radixSort(targets.begin(), targets.end(), mapToFunctor(low_map));
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for (int i = 1; i < int(targets.size()); ++i) {
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child_lists[targets[i]].prev = targets[i - 1];
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child_lists[targets[i - 1]].next = targets[i];
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}
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child_lists[targets.back()].next = INVALID;
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child_lists[targets.front()].prev = INVALID;
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child_lists[source].first = targets.front();
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}
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}
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}
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void walkUp(const Node& node, Node root, int rorder,
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const PredMap& pred_map, const LowMap& low_map,
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const OrderMap& order_map, const OrderList& order_list,
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NodeData& node_data, MergeRoots& merge_roots) {
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int na, nb;
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bool da, db;
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na = nb = order_map[node];
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da = true; db = false;
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while (true) {
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if (node_data[na].visited == rorder) break;
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if (node_data[nb].visited == rorder) break;
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node_data[na].visited = rorder;
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node_data[nb].visited = rorder;
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int rn = -1;
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if (na >= int(order_list.size())) {
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rn = na;
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} else if (nb >= int(order_list.size())) {
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rn = nb;
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}
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if (rn == -1) {
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int nn;
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nn = da ? node_data[na].prev : node_data[na].next;
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da = node_data[nn].prev != na;
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na = nn;
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nn = db ? node_data[nb].prev : node_data[nb].next;
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db = node_data[nn].prev != nb;
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nb = nn;
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} else {
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Node rep = order_list[rn - order_list.size()];
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Node parent = _graph.source(pred_map[rep]);
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if (low_map[rep] < rorder) {
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merge_roots[parent].push_back(rn);
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} else {
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merge_roots[parent].push_front(rn);
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}
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if (parent != root) {
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na = nb = order_map[parent];
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da = true; db = false;
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} else {
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break;
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}
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}
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}
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}
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void walkDown(int rn, int rorder, NodeData& node_data,
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ArcLists& arc_lists, FlipMap& flip_map,
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OrderList& order_list, ChildLists& child_lists,
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AncestorMap& ancestor_map, LowMap& low_map,
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EmbedArc& embed_arc, MergeRoots& merge_roots) {
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std::vector<std::pair<int, bool> > merge_stack;
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for (int di = 0; di < 2; ++di) {
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bool rd = di == 0;
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int pn = rn;
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int n = rd ? node_data[rn].next : node_data[rn].prev;
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while (n != rn) {
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Node node = order_list[n];
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if (embed_arc[node] != INVALID) {
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// Merging components on the critical path
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while (!merge_stack.empty()) {
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// Component root
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int cn = merge_stack.back().first;
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bool cd = merge_stack.back().second;
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merge_stack.pop_back();
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// Parent of component
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int dn = merge_stack.back().first;
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bool dd = merge_stack.back().second;
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merge_stack.pop_back();
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Node parent = order_list[dn];
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// Erasing from merge_roots
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merge_roots[parent].pop_front();
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Node child = order_list[cn - order_list.size()];
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// Erasing from child_lists
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if (child_lists[child].prev != INVALID) {
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child_lists[child_lists[child].prev].next =
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child_lists[child].next;
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} else {
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child_lists[parent].first = child_lists[child].next;
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}
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if (child_lists[child].next != INVALID) {
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child_lists[child_lists[child].next].prev =
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child_lists[child].prev;
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}
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// Merging arcs + flipping
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Arc de = node_data[dn].first;
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Arc ce = node_data[cn].first;
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flip_map[order_list[cn - order_list.size()]] = cd != dd;
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if (cd != dd) {
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std::swap(arc_lists[ce].prev, arc_lists[ce].next);
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ce = arc_lists[ce].prev;
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std::swap(arc_lists[ce].prev, arc_lists[ce].next);
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}
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{
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Arc dne = arc_lists[de].next;
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Arc cne = arc_lists[ce].next;
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arc_lists[de].next = cne;
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arc_lists[ce].next = dne;
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arc_lists[dne].prev = ce;
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arc_lists[cne].prev = de;
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}
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if (dd) {
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node_data[dn].first = ce;
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}
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// Merging external faces
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{
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int en = cn;
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cn = cd ? node_data[cn].prev : node_data[cn].next;
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cd = node_data[cn].next == en;
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if (node_data[cn].prev == node_data[cn].next &&
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node_data[cn].inverted) {
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cd = !cd;
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}
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}
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if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn;
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if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn;
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}
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bool d = pn == node_data[n].prev;
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if (node_data[n].prev == node_data[n].next &&
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node_data[n].inverted) {
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d = !d;
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}
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// Add new arc
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{
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Arc arc = embed_arc[node];
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Arc re = node_data[rn].first;
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arc_lists[arc_lists[re].next].prev = arc;
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arc_lists[arc].next = arc_lists[re].next;
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arc_lists[arc].prev = re;
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arc_lists[re].next = arc;
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if (!rd) {
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node_data[rn].first = arc;
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}
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Arc rev = _graph.oppositeArc(arc);
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Arc e = node_data[n].first;
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arc_lists[arc_lists[e].next].prev = rev;
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arc_lists[rev].next = arc_lists[e].next;
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arc_lists[rev].prev = e;
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arc_lists[e].next = rev;
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if (d) {
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node_data[n].first = rev;
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}
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}
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// Embedding arc into external face
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if (rd) node_data[rn].next = n; else node_data[rn].prev = n;
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if (d) node_data[n].prev = rn; else node_data[n].next = rn;
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pn = rn;
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embed_arc[order_list[n]] = INVALID;
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}
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if (!merge_roots[node].empty()) {
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bool d = pn == node_data[n].prev;
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if (node_data[n].prev == node_data[n].next &&
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node_data[n].inverted) {
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d = !d;
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}
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merge_stack.push_back(std::make_pair(n, d));
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int rn = merge_roots[node].front();
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int xn = node_data[rn].next;
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Node xnode = order_list[xn];
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int yn = node_data[rn].prev;
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Node ynode = order_list[yn];
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bool rd;
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if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) {
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rd = true;
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} else if (!external(ynode, rorder, child_lists,
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ancestor_map, low_map)) {
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rd = false;
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} else if (pertinent(xnode, embed_arc, merge_roots)) {
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rd = true;
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} else {
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rd = false;
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}
|
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merge_stack.push_back(std::make_pair(rn, rd));
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pn = rn;
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n = rd ? xn : yn;
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} else if (!external(node, rorder, child_lists,
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ancestor_map, low_map)) {
|
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int nn = (node_data[n].next != pn ?
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node_data[n].next : node_data[n].prev);
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bool nd = n == node_data[nn].prev;
|
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|
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if (nd) node_data[nn].prev = pn;
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else node_data[nn].next = pn;
|
|
|
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if (n == node_data[pn].prev) node_data[pn].prev = nn;
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else node_data[pn].next = nn;
|
|
|
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node_data[nn].inverted =
|
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(node_data[nn].prev == node_data[nn].next && nd != rd);
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|
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n = nn;
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}
|
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else break;
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|
|
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}
|
|
|
|
if (!merge_stack.empty() || n == rn) {
|
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break;
|
|
}
|
|
}
|
|
}
|
|
|
|
void initFace(const Node& node, ArcLists& arc_lists,
|
|
NodeData& node_data, const PredMap& pred_map,
|
|
const OrderMap& order_map, const OrderList& order_list) {
|
|
int n = order_map[node];
|
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int rn = n + order_list.size();
|
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|
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node_data[n].next = node_data[n].prev = rn;
|
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node_data[rn].next = node_data[rn].prev = n;
|
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|
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node_data[n].visited = order_list.size();
|
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node_data[rn].visited = order_list.size();
|
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|
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node_data[n].inverted = false;
|
|
node_data[rn].inverted = false;
|
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|
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Arc arc = pred_map[node];
|
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Arc rev = _graph.oppositeArc(arc);
|
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|
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node_data[rn].first = arc;
|
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node_data[n].first = rev;
|
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|
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arc_lists[arc].prev = arc;
|
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arc_lists[arc].next = arc;
|
|
|
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arc_lists[rev].prev = rev;
|
|
arc_lists[rev].next = rev;
|
|
|
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}
|
|
|
|
void mergeRemainingFaces(const Node& node, NodeData& node_data,
|
|
OrderList& order_list, OrderMap& order_map,
|
|
ChildLists& child_lists, ArcLists& arc_lists) {
|
|
while (child_lists[node].first != INVALID) {
|
|
int dd = order_map[node];
|
|
Node child = child_lists[node].first;
|
|
int cd = order_map[child] + order_list.size();
|
|
child_lists[node].first = child_lists[child].next;
|
|
|
|
Arc de = node_data[dd].first;
|
|
Arc ce = node_data[cd].first;
|
|
|
|
if (de != INVALID) {
|
|
Arc dne = arc_lists[de].next;
|
|
Arc cne = arc_lists[ce].next;
|
|
|
|
arc_lists[de].next = cne;
|
|
arc_lists[ce].next = dne;
|
|
|
|
arc_lists[dne].prev = ce;
|
|
arc_lists[cne].prev = de;
|
|
}
|
|
|
|
node_data[dd].first = ce;
|
|
|
|
}
|
|
}
|
|
|
|
void storeEmbedding(const Node& node, NodeData& node_data,
|
|
OrderMap& order_map, PredMap& pred_map,
|
|
ArcLists& arc_lists, FlipMap& flip_map) {
|
|
|
|
if (node_data[order_map[node]].first == INVALID) return;
|
|
|
|
if (pred_map[node] != INVALID) {
|
|
Node source = _graph.source(pred_map[node]);
|
|
flip_map[node] = flip_map[node] != flip_map[source];
|
|
}
|
|
|
|
Arc first = node_data[order_map[node]].first;
|
|
Arc prev = first;
|
|
|
|
Arc arc = flip_map[node] ?
|
|
arc_lists[prev].prev : arc_lists[prev].next;
|
|
|
|
_embedding[prev] = arc;
|
|
|
|
while (arc != first) {
|
|
Arc next = arc_lists[arc].prev == prev ?
|
|
arc_lists[arc].next : arc_lists[arc].prev;
|
|
prev = arc; arc = next;
|
|
_embedding[prev] = arc;
|
|
}
|
|
}
|
|
|
|
|
|
bool external(const Node& node, int rorder,
|
|
ChildLists& child_lists, AncestorMap& ancestor_map,
|
|
LowMap& low_map) {
|
|
Node child = child_lists[node].first;
|
|
|
|
if (child != INVALID) {
|
|
if (low_map[child] < rorder) return true;
|
|
}
|
|
|
|
if (ancestor_map[node] < rorder) return true;
|
|
|
|
return false;
|
|
}
|
|
|
|
bool pertinent(const Node& node, const EmbedArc& embed_arc,
|
|
const MergeRoots& merge_roots) {
|
|
return !merge_roots[node].empty() || embed_arc[node] != INVALID;
|
|
}
|
|
|
|
int lowPoint(const Node& node, OrderMap& order_map, ChildLists& child_lists,
|
|
AncestorMap& ancestor_map, LowMap& low_map) {
|
|
int low_point;
|
|
|
|
Node child = child_lists[node].first;
|
|
|
|
if (child != INVALID) {
|
|
low_point = low_map[child];
|
|
} else {
|
|
low_point = order_map[node];
|
|
}
|
|
|
|
if (low_point > ancestor_map[node]) {
|
|
low_point = ancestor_map[node];
|
|
}
|
|
|
|
return low_point;
|
|
}
|
|
|
|
int findComponentRoot(Node root, Node node, ChildLists& child_lists,
|
|
OrderMap& order_map, OrderList& order_list) {
|
|
|
|
int order = order_map[root];
|
|
int norder = order_map[node];
|
|
|
|
Node child = child_lists[root].first;
|
|
while (child != INVALID) {
|
|
int corder = order_map[child];
|
|
if (corder > order && corder < norder) {
|
|
order = corder;
|
|
}
|
|
child = child_lists[child].next;
|
|
}
|
|
return order + order_list.size();
|
|
}
|
|
|
|
Node findPertinent(Node node, OrderMap& order_map, NodeData& node_data,
|
|
EmbedArc& embed_arc, MergeRoots& merge_roots) {
|
|
Node wnode =_graph.target(node_data[order_map[node]].first);
|
|
while (!pertinent(wnode, embed_arc, merge_roots)) {
|
|
wnode = _graph.target(node_data[order_map[wnode]].first);
|
|
}
|
|
return wnode;
|
|
}
|
|
|
|
|
|
Node findExternal(Node node, int rorder, OrderMap& order_map,
|
|
ChildLists& child_lists, AncestorMap& ancestor_map,
|
|
LowMap& low_map, NodeData& node_data) {
|
|
Node wnode =_graph.target(node_data[order_map[node]].first);
|
|
while (!external(wnode, rorder, child_lists, ancestor_map, low_map)) {
|
|
wnode = _graph.target(node_data[order_map[wnode]].first);
|
|
}
|
|
return wnode;
|
|
}
|
|
|
|
void markCommonPath(Node node, int rorder, Node& wnode, Node& znode,
|
|
OrderList& order_list, OrderMap& order_map,
|
|
NodeData& node_data, ArcLists& arc_lists,
|
|
EmbedArc& embed_arc, MergeRoots& merge_roots,
|
|
ChildLists& child_lists, AncestorMap& ancestor_map,
|
|
LowMap& low_map) {
|
|
|
|
Node cnode = node;
|
|
Node pred = INVALID;
|
|
|
|
while (true) {
|
|
|
|
bool pert = pertinent(cnode, embed_arc, merge_roots);
|
|
bool ext = external(cnode, rorder, child_lists, ancestor_map, low_map);
|
|
|
|
if (pert && ext) {
|
|
if (!merge_roots[cnode].empty()) {
|
|
int cn = merge_roots[cnode].back();
|
|
|
|
if (low_map[order_list[cn - order_list.size()]] < rorder) {
|
|
Arc arc = node_data[cn].first;
|
|
_kuratowski.set(arc, true);
|
|
|
|
pred = cnode;
|
|
cnode = _graph.target(arc);
|
|
|
|
continue;
|
|
}
|
|
}
|
|
wnode = znode = cnode;
|
|
return;
|
|
|
|
} else if (pert) {
|
|
wnode = cnode;
|
|
|
|
while (!external(cnode, rorder, child_lists, ancestor_map, low_map)) {
|
|
Arc arc = node_data[order_map[cnode]].first;
|
|
|
|
if (_graph.target(arc) == pred) {
|
|
arc = arc_lists[arc].next;
|
|
}
|
|
_kuratowski.set(arc, true);
|
|
|
|
Node next = _graph.target(arc);
|
|
pred = cnode; cnode = next;
|
|
}
|
|
|
|
znode = cnode;
|
|
return;
|
|
|
|
} else if (ext) {
|
|
znode = cnode;
|
|
|
|
while (!pertinent(cnode, embed_arc, merge_roots)) {
|
|
Arc arc = node_data[order_map[cnode]].first;
|
|
|
|
if (_graph.target(arc) == pred) {
|
|
arc = arc_lists[arc].next;
|
|
}
|
|
_kuratowski.set(arc, true);
|
|
|
|
Node next = _graph.target(arc);
|
|
pred = cnode; cnode = next;
|
|
}
|
|
|
|
wnode = cnode;
|
|
return;
|
|
|
|
} else {
|
|
Arc arc = node_data[order_map[cnode]].first;
|
|
|
|
if (_graph.target(arc) == pred) {
|
|
arc = arc_lists[arc].next;
|
|
}
|
|
_kuratowski.set(arc, true);
|
|
|
|
Node next = _graph.target(arc);
|
|
pred = cnode; cnode = next;
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
void orientComponent(Node root, int rn, OrderMap& order_map,
|
|
PredMap& pred_map, NodeData& node_data,
|
|
ArcLists& arc_lists, FlipMap& flip_map,
|
|
TypeMap& type_map) {
|
|
node_data[order_map[root]].first = node_data[rn].first;
|
|
type_map[root] = 1;
|
|
|
|
std::vector<Node> st, qu;
|
|
|
|
st.push_back(root);
|
|
while (!st.empty()) {
|
|
Node node = st.back();
|
|
st.pop_back();
|
|
qu.push_back(node);
|
|
|
|
Arc arc = node_data[order_map[node]].first;
|
|
|
|
if (type_map[_graph.target(arc)] == 0) {
|
|
st.push_back(_graph.target(arc));
|
|
type_map[_graph.target(arc)] = 1;
|
|
}
|
|
|
|
Arc last = arc, pred = arc;
|
|
arc = arc_lists[arc].next;
|
|
while (arc != last) {
|
|
|
|
if (type_map[_graph.target(arc)] == 0) {
|
|
st.push_back(_graph.target(arc));
|
|
type_map[_graph.target(arc)] = 1;
|
|
}
|
|
|
|
Arc next = arc_lists[arc].next != pred ?
|
|
arc_lists[arc].next : arc_lists[arc].prev;
|
|
pred = arc; arc = next;
|
|
}
|
|
|
|
}
|
|
|
|
type_map[root] = 2;
|
|
flip_map[root] = false;
|
|
|
|
for (int i = 1; i < int(qu.size()); ++i) {
|
|
|
|
Node node = qu[i];
|
|
|
|
while (type_map[node] != 2) {
|
|
st.push_back(node);
|
|
type_map[node] = 2;
|
|
node = _graph.source(pred_map[node]);
|
|
}
|
|
|
|
bool flip = flip_map[node];
|
|
|
|
while (!st.empty()) {
|
|
node = st.back();
|
|
st.pop_back();
|
|
|
|
flip_map[node] = flip != flip_map[node];
|
|
flip = flip_map[node];
|
|
|
|
if (flip) {
|
|
Arc arc = node_data[order_map[node]].first;
|
|
std::swap(arc_lists[arc].prev, arc_lists[arc].next);
|
|
arc = arc_lists[arc].prev;
|
|
std::swap(arc_lists[arc].prev, arc_lists[arc].next);
|
|
node_data[order_map[node]].first = arc;
|
|
}
|
|
}
|
|
}
|
|
|
|
for (int i = 0; i < int(qu.size()); ++i) {
|
|
|
|
Arc arc = node_data[order_map[qu[i]]].first;
|
|
Arc last = arc, pred = arc;
|
|
|
|
arc = arc_lists[arc].next;
|
|
while (arc != last) {
|
|
|
|
if (arc_lists[arc].next == pred) {
|
|
std::swap(arc_lists[arc].next, arc_lists[arc].prev);
|
|
}
|
|
pred = arc; arc = arc_lists[arc].next;
|
|
}
|
|
|
|
}
|
|
}
|
|
|
|
void setFaceFlags(Node root, Node wnode, Node ynode, Node xnode,
|
|
OrderMap& order_map, NodeData& node_data,
|
|
TypeMap& type_map) {
|
|
Node node = _graph.target(node_data[order_map[root]].first);
|
|
|
|
while (node != ynode) {
|
|
type_map[node] = HIGHY;
|
|
node = _graph.target(node_data[order_map[node]].first);
|
|
}
|
|
|
|
while (node != wnode) {
|
|
type_map[node] = LOWY;
|
|
node = _graph.target(node_data[order_map[node]].first);
|
|
}
|
|
|
|
node = _graph.target(node_data[order_map[wnode]].first);
|
|
|
|
while (node != xnode) {
|
|
type_map[node] = LOWX;
|
|
node = _graph.target(node_data[order_map[node]].first);
|
|
}
|
|
type_map[node] = LOWX;
|
|
|
|
node = _graph.target(node_data[order_map[xnode]].first);
|
|
while (node != root) {
|
|
type_map[node] = HIGHX;
|
|
node = _graph.target(node_data[order_map[node]].first);
|
|
}
|
|
|
|
type_map[wnode] = PERTINENT;
|
|
type_map[root] = ROOT;
|
|
}
|
|
|
|
void findInternalPath(std::vector<Arc>& ipath,
|
|
Node wnode, Node root, TypeMap& type_map,
|
|
OrderMap& order_map, NodeData& node_data,
|
|
ArcLists& arc_lists) {
|
|
std::vector<Arc> st;
|
|
|
|
Node node = wnode;
|
|
|
|
while (node != root) {
|
|
Arc arc = arc_lists[node_data[order_map[node]].first].next;
|
|
st.push_back(arc);
|
|
node = _graph.target(arc);
|
|
}
|
|
|
|
while (true) {
|
|
Arc arc = st.back();
|
|
if (type_map[_graph.target(arc)] == LOWX ||
|
|
type_map[_graph.target(arc)] == HIGHX) {
|
|
break;
|
|
}
|
|
if (type_map[_graph.target(arc)] == 2) {
|
|
type_map[_graph.target(arc)] = 3;
|
|
|
|
arc = arc_lists[_graph.oppositeArc(arc)].next;
|
|
st.push_back(arc);
|
|
} else {
|
|
st.pop_back();
|
|
arc = arc_lists[arc].next;
|
|
|
|
while (_graph.oppositeArc(arc) == st.back()) {
|
|
arc = st.back();
|
|
st.pop_back();
|
|
arc = arc_lists[arc].next;
|
|
}
|
|
st.push_back(arc);
|
|
}
|
|
}
|
|
|
|
for (int i = 0; i < int(st.size()); ++i) {
|
|
if (type_map[_graph.target(st[i])] != LOWY &&
|
|
type_map[_graph.target(st[i])] != HIGHY) {
|
|
for (; i < int(st.size()); ++i) {
|
|
ipath.push_back(st[i]);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void setInternalFlags(std::vector<Arc>& ipath, TypeMap& type_map) {
|
|
for (int i = 1; i < int(ipath.size()); ++i) {
|
|
type_map[_graph.source(ipath[i])] = INTERNAL;
|
|
}
|
|
}
|
|
|
|
void findPilePath(std::vector<Arc>& ppath,
|
|
Node root, TypeMap& type_map, OrderMap& order_map,
|
|
NodeData& node_data, ArcLists& arc_lists) {
|
|
std::vector<Arc> st;
|
|
|
|
st.push_back(_graph.oppositeArc(node_data[order_map[root]].first));
|
|
st.push_back(node_data[order_map[root]].first);
|
|
|
|
while (st.size() > 1) {
|
|
Arc arc = st.back();
|
|
if (type_map[_graph.target(arc)] == INTERNAL) {
|
|
break;
|
|
}
|
|
if (type_map[_graph.target(arc)] == 3) {
|
|
type_map[_graph.target(arc)] = 4;
|
|
|
|
arc = arc_lists[_graph.oppositeArc(arc)].next;
|
|
st.push_back(arc);
|
|
} else {
|
|
st.pop_back();
|
|
arc = arc_lists[arc].next;
|
|
|
|
while (!st.empty() && _graph.oppositeArc(arc) == st.back()) {
|
|
arc = st.back();
|
|
st.pop_back();
|
|
arc = arc_lists[arc].next;
|
|
}
|
|
st.push_back(arc);
|
|
}
|
|
}
|
|
|
|
for (int i = 1; i < int(st.size()); ++i) {
|
|
ppath.push_back(st[i]);
|
|
}
|
|
}
|
|
|
|
|
|
int markExternalPath(Node node, OrderMap& order_map,
|
|
ChildLists& child_lists, PredMap& pred_map,
|
|
AncestorMap& ancestor_map, LowMap& low_map) {
|
|
int lp = lowPoint(node, order_map, child_lists,
|
|
ancestor_map, low_map);
|
|
|
|
if (ancestor_map[node] != lp) {
|
|
node = child_lists[node].first;
|
|
_kuratowski[pred_map[node]] = true;
|
|
|
|
while (ancestor_map[node] != lp) {
|
|
for (OutArcIt e(_graph, node); e != INVALID; ++e) {
|
|
Node tnode = _graph.target(e);
|
|
if (order_map[tnode] > order_map[node] && low_map[tnode] == lp) {
|
|
node = tnode;
|
|
_kuratowski[e] = true;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
for (OutArcIt e(_graph, node); e != INVALID; ++e) {
|
|
if (order_map[_graph.target(e)] == lp) {
|
|
_kuratowski[e] = true;
|
|
break;
|
|
}
|
|
}
|
|
|
|
return lp;
|
|
}
|
|
|
|
void markPertinentPath(Node node, OrderMap& order_map,
|
|
NodeData& node_data, ArcLists& arc_lists,
|
|
EmbedArc& embed_arc, MergeRoots& merge_roots) {
|
|
while (embed_arc[node] == INVALID) {
|
|
int n = merge_roots[node].front();
|
|
Arc arc = node_data[n].first;
|
|
|
|
_kuratowski.set(arc, true);
|
|
|
|
Node pred = node;
|
|
node = _graph.target(arc);
|
|
while (!pertinent(node, embed_arc, merge_roots)) {
|
|
arc = node_data[order_map[node]].first;
|
|
if (_graph.target(arc) == pred) {
|
|
arc = arc_lists[arc].next;
|
|
}
|
|
_kuratowski.set(arc, true);
|
|
pred = node;
|
|
node = _graph.target(arc);
|
|
}
|
|
}
|
|
_kuratowski.set(embed_arc[node], true);
|
|
}
|
|
|
|
void markPredPath(Node node, Node snode, PredMap& pred_map) {
|
|
while (node != snode) {
|
|
_kuratowski.set(pred_map[node], true);
|
|
node = _graph.source(pred_map[node]);
|
|
}
|
|
}
|
|
|
|
void markFacePath(Node ynode, Node xnode,
|
|
OrderMap& order_map, NodeData& node_data) {
|
|
Arc arc = node_data[order_map[ynode]].first;
|
|
Node node = _graph.target(arc);
|
|
_kuratowski.set(arc, true);
|
|
|
|
while (node != xnode) {
|
|
arc = node_data[order_map[node]].first;
|
|
_kuratowski.set(arc, true);
|
|
node = _graph.target(arc);
|
|
}
|
|
}
|
|
|
|
void markInternalPath(std::vector<Arc>& path) {
|
|
for (int i = 0; i < int(path.size()); ++i) {
|
|
_kuratowski.set(path[i], true);
|
|
}
|
|
}
|
|
|
|
void markPilePath(std::vector<Arc>& path) {
|
|
for (int i = 0; i < int(path.size()); ++i) {
|
|
_kuratowski.set(path[i], true);
|
|
}
|
|
}
|
|
|
|
void isolateKuratowski(Arc arc, NodeData& node_data,
|
|
ArcLists& arc_lists, FlipMap& flip_map,
|
|
OrderMap& order_map, OrderList& order_list,
|
|
PredMap& pred_map, ChildLists& child_lists,
|
|
AncestorMap& ancestor_map, LowMap& low_map,
|
|
EmbedArc& embed_arc, MergeRoots& merge_roots) {
|
|
|
|
Node root = _graph.source(arc);
|
|
Node enode = _graph.target(arc);
|
|
|
|
int rorder = order_map[root];
|
|
|
|
TypeMap type_map(_graph, 0);
|
|
|
|
int rn = findComponentRoot(root, enode, child_lists,
|
|
order_map, order_list);
|
|
|
|
Node xnode = order_list[node_data[rn].next];
|
|
Node ynode = order_list[node_data[rn].prev];
|
|
|
|
// Minor-A
|
|
{
|
|
while (!merge_roots[xnode].empty() || !merge_roots[ynode].empty()) {
|
|
|
|
if (!merge_roots[xnode].empty()) {
|
|
root = xnode;
|
|
rn = merge_roots[xnode].front();
|
|
} else {
|
|
root = ynode;
|
|
rn = merge_roots[ynode].front();
|
|
}
|
|
|
|
xnode = order_list[node_data[rn].next];
|
|
ynode = order_list[node_data[rn].prev];
|
|
}
|
|
|
|
if (root != _graph.source(arc)) {
|
|
orientComponent(root, rn, order_map, pred_map,
|
|
node_data, arc_lists, flip_map, type_map);
|
|
markFacePath(root, root, order_map, node_data);
|
|
int xlp = markExternalPath(xnode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
int ylp = markExternalPath(ynode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
|
|
Node lwnode = findPertinent(ynode, order_map, node_data,
|
|
embed_arc, merge_roots);
|
|
|
|
markPertinentPath(lwnode, order_map, node_data, arc_lists,
|
|
embed_arc, merge_roots);
|
|
|
|
return;
|
|
}
|
|
}
|
|
|
|
orientComponent(root, rn, order_map, pred_map,
|
|
node_data, arc_lists, flip_map, type_map);
|
|
|
|
Node wnode = findPertinent(ynode, order_map, node_data,
|
|
embed_arc, merge_roots);
|
|
setFaceFlags(root, wnode, ynode, xnode, order_map, node_data, type_map);
|
|
|
|
|
|
//Minor-B
|
|
if (!merge_roots[wnode].empty()) {
|
|
int cn = merge_roots[wnode].back();
|
|
Node rep = order_list[cn - order_list.size()];
|
|
if (low_map[rep] < rorder) {
|
|
markFacePath(root, root, order_map, node_data);
|
|
int xlp = markExternalPath(xnode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
int ylp = markExternalPath(ynode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
|
|
Node lwnode, lznode;
|
|
markCommonPath(wnode, rorder, lwnode, lznode, order_list,
|
|
order_map, node_data, arc_lists, embed_arc,
|
|
merge_roots, child_lists, ancestor_map, low_map);
|
|
|
|
markPertinentPath(lwnode, order_map, node_data, arc_lists,
|
|
embed_arc, merge_roots);
|
|
int zlp = markExternalPath(lznode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
|
|
int minlp = xlp < ylp ? xlp : ylp;
|
|
if (zlp < minlp) minlp = zlp;
|
|
|
|
int maxlp = xlp > ylp ? xlp : ylp;
|
|
if (zlp > maxlp) maxlp = zlp;
|
|
|
|
markPredPath(order_list[maxlp], order_list[minlp], pred_map);
|
|
|
|
return;
|
|
}
|
|
}
|
|
|
|
Node pxnode, pynode;
|
|
std::vector<Arc> ipath;
|
|
findInternalPath(ipath, wnode, root, type_map, order_map,
|
|
node_data, arc_lists);
|
|
setInternalFlags(ipath, type_map);
|
|
pynode = _graph.source(ipath.front());
|
|
pxnode = _graph.target(ipath.back());
|
|
|
|
wnode = findPertinent(pynode, order_map, node_data,
|
|
embed_arc, merge_roots);
|
|
|
|
// Minor-C
|
|
{
|
|
if (type_map[_graph.source(ipath.front())] == HIGHY) {
|
|
if (type_map[_graph.target(ipath.back())] == HIGHX) {
|
|
markFacePath(xnode, pxnode, order_map, node_data);
|
|
}
|
|
markFacePath(root, xnode, order_map, node_data);
|
|
markPertinentPath(wnode, order_map, node_data, arc_lists,
|
|
embed_arc, merge_roots);
|
|
markInternalPath(ipath);
|
|
int xlp = markExternalPath(xnode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
int ylp = markExternalPath(ynode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
|
|
return;
|
|
}
|
|
|
|
if (type_map[_graph.target(ipath.back())] == HIGHX) {
|
|
markFacePath(ynode, root, order_map, node_data);
|
|
markPertinentPath(wnode, order_map, node_data, arc_lists,
|
|
embed_arc, merge_roots);
|
|
markInternalPath(ipath);
|
|
int xlp = markExternalPath(xnode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
int ylp = markExternalPath(ynode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
|
|
return;
|
|
}
|
|
}
|
|
|
|
std::vector<Arc> ppath;
|
|
findPilePath(ppath, root, type_map, order_map, node_data, arc_lists);
|
|
|
|
// Minor-D
|
|
if (!ppath.empty()) {
|
|
markFacePath(ynode, xnode, order_map, node_data);
|
|
markPertinentPath(wnode, order_map, node_data, arc_lists,
|
|
embed_arc, merge_roots);
|
|
markPilePath(ppath);
|
|
markInternalPath(ipath);
|
|
int xlp = markExternalPath(xnode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
int ylp = markExternalPath(ynode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
|
|
return;
|
|
}
|
|
|
|
// Minor-E*
|
|
{
|
|
|
|
if (!external(wnode, rorder, child_lists, ancestor_map, low_map)) {
|
|
Node znode = findExternal(pynode, rorder, order_map,
|
|
child_lists, ancestor_map,
|
|
low_map, node_data);
|
|
|
|
if (type_map[znode] == LOWY) {
|
|
markFacePath(root, xnode, order_map, node_data);
|
|
markPertinentPath(wnode, order_map, node_data, arc_lists,
|
|
embed_arc, merge_roots);
|
|
markInternalPath(ipath);
|
|
int xlp = markExternalPath(xnode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
int zlp = markExternalPath(znode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
markPredPath(root, order_list[xlp < zlp ? xlp : zlp], pred_map);
|
|
} else {
|
|
markFacePath(ynode, root, order_map, node_data);
|
|
markPertinentPath(wnode, order_map, node_data, arc_lists,
|
|
embed_arc, merge_roots);
|
|
markInternalPath(ipath);
|
|
int ylp = markExternalPath(ynode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
int zlp = markExternalPath(znode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
markPredPath(root, order_list[ylp < zlp ? ylp : zlp], pred_map);
|
|
}
|
|
return;
|
|
}
|
|
|
|
int xlp = markExternalPath(xnode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
int ylp = markExternalPath(ynode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
int wlp = markExternalPath(wnode, order_map, child_lists,
|
|
pred_map, ancestor_map, low_map);
|
|
|
|
if (wlp > xlp && wlp > ylp) {
|
|
markFacePath(root, root, order_map, node_data);
|
|
markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
|
|
return;
|
|
}
|
|
|
|
markInternalPath(ipath);
|
|
markPertinentPath(wnode, order_map, node_data, arc_lists,
|
|
embed_arc, merge_roots);
|
|
|
|
if (xlp > ylp && xlp > wlp) {
|
|
markFacePath(root, pynode, order_map, node_data);
|
|
markFacePath(wnode, xnode, order_map, node_data);
|
|
markPredPath(root, order_list[ylp < wlp ? ylp : wlp], pred_map);
|
|
return;
|
|
}
|
|
|
|
if (ylp > xlp && ylp > wlp) {
|
|
markFacePath(pxnode, root, order_map, node_data);
|
|
markFacePath(ynode, wnode, order_map, node_data);
|
|
markPredPath(root, order_list[xlp < wlp ? xlp : wlp], pred_map);
|
|
return;
|
|
}
|
|
|
|
if (pynode != ynode) {
|
|
markFacePath(pxnode, wnode, order_map, node_data);
|
|
|
|
int minlp = xlp < ylp ? xlp : ylp;
|
|
if (wlp < minlp) minlp = wlp;
|
|
|
|
int maxlp = xlp > ylp ? xlp : ylp;
|
|
if (wlp > maxlp) maxlp = wlp;
|
|
|
|
markPredPath(order_list[maxlp], order_list[minlp], pred_map);
|
|
return;
|
|
}
|
|
|
|
if (pxnode != xnode) {
|
|
markFacePath(wnode, pynode, order_map, node_data);
|
|
|
|
int minlp = xlp < ylp ? xlp : ylp;
|
|
if (wlp < minlp) minlp = wlp;
|
|
|
|
int maxlp = xlp > ylp ? xlp : ylp;
|
|
if (wlp > maxlp) maxlp = wlp;
|
|
|
|
markPredPath(order_list[maxlp], order_list[minlp], pred_map);
|
|
return;
|
|
}
|
|
|
|
markFacePath(root, root, order_map, node_data);
|
|
int minlp = xlp < ylp ? xlp : ylp;
|
|
if (wlp < minlp) minlp = wlp;
|
|
markPredPath(root, order_list[minlp], pred_map);
|
|
return;
|
|
}
|
|
|
|
}
|
|
|
|
};
|
|
|
|
namespace _planarity_bits {
|
|
|
|
template <typename Graph, typename EmbeddingMap>
|
|
void makeConnected(Graph& graph, EmbeddingMap& embedding) {
|
|
DfsVisitor<Graph> null_visitor;
|
|
DfsVisit<Graph, DfsVisitor<Graph> > dfs(graph, null_visitor);
|
|
dfs.init();
|
|
|
|
typename Graph::Node u = INVALID;
|
|
for (typename Graph::NodeIt n(graph); n != INVALID; ++n) {
|
|
if (!dfs.reached(n)) {
|
|
dfs.addSource(n);
|
|
dfs.start();
|
|
if (u == INVALID) {
|
|
u = n;
|
|
} else {
|
|
typename Graph::Node v = n;
|
|
|
|
typename Graph::Arc ue = typename Graph::OutArcIt(graph, u);
|
|
typename Graph::Arc ve = typename Graph::OutArcIt(graph, v);
|
|
|
|
typename Graph::Arc e = graph.direct(graph.addEdge(u, v), true);
|
|
|
|
if (ue != INVALID) {
|
|
embedding[e] = embedding[ue];
|
|
embedding[ue] = e;
|
|
} else {
|
|
embedding[e] = e;
|
|
}
|
|
|
|
if (ve != INVALID) {
|
|
embedding[graph.oppositeArc(e)] = embedding[ve];
|
|
embedding[ve] = graph.oppositeArc(e);
|
|
} else {
|
|
embedding[graph.oppositeArc(e)] = graph.oppositeArc(e);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
template <typename Graph, typename EmbeddingMap>
|
|
void makeBiNodeConnected(Graph& graph, EmbeddingMap& embedding) {
|
|
typename Graph::template ArcMap<bool> processed(graph);
|
|
|
|
std::vector<typename Graph::Arc> arcs;
|
|
for (typename Graph::ArcIt e(graph); e != INVALID; ++e) {
|
|
arcs.push_back(e);
|
|
}
|
|
|
|
IterableBoolMap<Graph, typename Graph::Node> visited(graph, false);
|
|
|
|
for (int i = 0; i < int(arcs.size()); ++i) {
|
|
typename Graph::Arc pp = arcs[i];
|
|
if (processed[pp]) continue;
|
|
|
|
typename Graph::Arc e = embedding[graph.oppositeArc(pp)];
|
|
processed[e] = true;
|
|
visited.set(graph.source(e), true);
|
|
|
|
typename Graph::Arc p = e, l = e;
|
|
e = embedding[graph.oppositeArc(e)];
|
|
|
|
while (e != l) {
|
|
processed[e] = true;
|
|
|
|
if (visited[graph.source(e)]) {
|
|
|
|
typename Graph::Arc n =
|
|
graph.direct(graph.addEdge(graph.source(p),
|
|
graph.target(e)), true);
|
|
embedding[n] = p;
|
|
embedding[graph.oppositeArc(pp)] = n;
|
|
|
|
embedding[graph.oppositeArc(n)] =
|
|
embedding[graph.oppositeArc(e)];
|
|
embedding[graph.oppositeArc(e)] =
|
|
graph.oppositeArc(n);
|
|
|
|
p = n;
|
|
e = embedding[graph.oppositeArc(n)];
|
|
} else {
|
|
visited.set(graph.source(e), true);
|
|
pp = p;
|
|
p = e;
|
|
e = embedding[graph.oppositeArc(e)];
|
|
}
|
|
}
|
|
visited.setAll(false);
|
|
}
|
|
}
|
|
|
|
|
|
template <typename Graph, typename EmbeddingMap>
|
|
void makeMaxPlanar(Graph& graph, EmbeddingMap& embedding) {
|
|
|
|
typename Graph::template NodeMap<int> degree(graph);
|
|
|
|
for (typename Graph::NodeIt n(graph); n != INVALID; ++n) {
|
|
degree[n] = countIncEdges(graph, n);
|
|
}
|
|
|
|
typename Graph::template ArcMap<bool> processed(graph);
|
|
IterableBoolMap<Graph, typename Graph::Node> visited(graph, false);
|
|
|
|
std::vector<typename Graph::Arc> arcs;
|
|
for (typename Graph::ArcIt e(graph); e != INVALID; ++e) {
|
|
arcs.push_back(e);
|
|
}
|
|
|
|
for (int i = 0; i < int(arcs.size()); ++i) {
|
|
typename Graph::Arc e = arcs[i];
|
|
|
|
if (processed[e]) continue;
|
|
processed[e] = true;
|
|
|
|
typename Graph::Arc mine = e;
|
|
int mind = degree[graph.source(e)];
|
|
|
|
int face_size = 1;
|
|
|
|
typename Graph::Arc l = e;
|
|
e = embedding[graph.oppositeArc(e)];
|
|
while (l != e) {
|
|
processed[e] = true;
|
|
|
|
++face_size;
|
|
|
|
if (degree[graph.source(e)] < mind) {
|
|
mine = e;
|
|
mind = degree[graph.source(e)];
|
|
}
|
|
|
|
e = embedding[graph.oppositeArc(e)];
|
|
}
|
|
|
|
if (face_size < 4) {
|
|
continue;
|
|
}
|
|
|
|
typename Graph::Node s = graph.source(mine);
|
|
for (typename Graph::OutArcIt e(graph, s); e != INVALID; ++e) {
|
|
visited.set(graph.target(e), true);
|
|
}
|
|
|
|
typename Graph::Arc oppe = INVALID;
|
|
|
|
e = embedding[graph.oppositeArc(mine)];
|
|
e = embedding[graph.oppositeArc(e)];
|
|
while (graph.target(e) != s) {
|
|
if (visited[graph.source(e)]) {
|
|
oppe = e;
|
|
break;
|
|
}
|
|
e = embedding[graph.oppositeArc(e)];
|
|
}
|
|
visited.setAll(false);
|
|
|
|
if (oppe == INVALID) {
|
|
|
|
e = embedding[graph.oppositeArc(mine)];
|
|
typename Graph::Arc pn = mine, p = e;
|
|
|
|
e = embedding[graph.oppositeArc(e)];
|
|
while (graph.target(e) != s) {
|
|
typename Graph::Arc n =
|
|
graph.direct(graph.addEdge(s, graph.source(e)), true);
|
|
|
|
embedding[n] = pn;
|
|
embedding[graph.oppositeArc(n)] = e;
|
|
embedding[graph.oppositeArc(p)] = graph.oppositeArc(n);
|
|
|
|
pn = n;
|
|
|
|
p = e;
|
|
e = embedding[graph.oppositeArc(e)];
|
|
}
|
|
|
|
embedding[graph.oppositeArc(e)] = pn;
|
|
|
|
} else {
|
|
|
|
mine = embedding[graph.oppositeArc(mine)];
|
|
s = graph.source(mine);
|
|
oppe = embedding[graph.oppositeArc(oppe)];
|
|
typename Graph::Node t = graph.source(oppe);
|
|
|
|
typename Graph::Arc ce = graph.direct(graph.addEdge(s, t), true);
|
|
embedding[ce] = mine;
|
|
embedding[graph.oppositeArc(ce)] = oppe;
|
|
|
|
typename Graph::Arc pn = ce, p = oppe;
|
|
e = embedding[graph.oppositeArc(oppe)];
|
|
while (graph.target(e) != s) {
|
|
typename Graph::Arc n =
|
|
graph.direct(graph.addEdge(s, graph.source(e)), true);
|
|
|
|
embedding[n] = pn;
|
|
embedding[graph.oppositeArc(n)] = e;
|
|
embedding[graph.oppositeArc(p)] = graph.oppositeArc(n);
|
|
|
|
pn = n;
|
|
|
|
p = e;
|
|
e = embedding[graph.oppositeArc(e)];
|
|
|
|
}
|
|
embedding[graph.oppositeArc(e)] = pn;
|
|
|
|
pn = graph.oppositeArc(ce), p = mine;
|
|
e = embedding[graph.oppositeArc(mine)];
|
|
while (graph.target(e) != t) {
|
|
typename Graph::Arc n =
|
|
graph.direct(graph.addEdge(t, graph.source(e)), true);
|
|
|
|
embedding[n] = pn;
|
|
embedding[graph.oppositeArc(n)] = e;
|
|
embedding[graph.oppositeArc(p)] = graph.oppositeArc(n);
|
|
|
|
pn = n;
|
|
|
|
p = e;
|
|
e = embedding[graph.oppositeArc(e)];
|
|
|
|
}
|
|
embedding[graph.oppositeArc(e)] = pn;
|
|
}
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
/// \ingroup planar
|
|
///
|
|
/// \brief Schnyder's planar drawing algorithm
|
|
///
|
|
/// The planar drawing algorithm calculates positions for the nodes
|
|
/// in the plane. These coordinates satisfy that if the edges are
|
|
/// represented with straight lines, then they will not intersect
|
|
/// each other.
|
|
///
|
|
/// Scnyder's algorithm embeds the graph on an \c (n-2)x(n-2) size grid,
|
|
/// i.e. each node will be located in the \c [0..n-2]x[0..n-2] square.
|
|
/// The time complexity of the algorithm is O(n).
|
|
///
|
|
/// \see PlanarEmbedding
|
|
template <typename Graph>
|
|
class PlanarDrawing {
|
|
public:
|
|
|
|
TEMPLATE_GRAPH_TYPEDEFS(Graph);
|
|
|
|
/// \brief The point type for storing coordinates
|
|
typedef dim2::Point<int> Point;
|
|
/// \brief The map type for storing the coordinates of the nodes
|
|
typedef typename Graph::template NodeMap<Point> PointMap;
|
|
|
|
|
|
/// \brief Constructor
|
|
///
|
|
/// Constructor
|
|
/// \pre The graph must be simple, i.e. it should not
|
|
/// contain parallel or loop arcs.
|
|
PlanarDrawing(const Graph& graph)
|
|
: _graph(graph), _point_map(graph) {}
|
|
|
|
private:
|
|
|
|
template <typename AuxGraph, typename AuxEmbeddingMap>
|
|
void drawing(const AuxGraph& graph,
|
|
const AuxEmbeddingMap& next,
|
|
PointMap& point_map) {
|
|
TEMPLATE_GRAPH_TYPEDEFS(AuxGraph);
|
|
|
|
typename AuxGraph::template ArcMap<Arc> prev(graph);
|
|
|
|
for (NodeIt n(graph); n != INVALID; ++n) {
|
|
Arc e = OutArcIt(graph, n);
|
|
|
|
Arc p = e, l = e;
|
|
|
|
e = next[e];
|
|
while (e != l) {
|
|
prev[e] = p;
|
|
p = e;
|
|
e = next[e];
|
|
}
|
|
prev[e] = p;
|
|
}
|
|
|
|
Node anode, bnode, cnode;
|
|
|
|
{
|
|
Arc e = ArcIt(graph);
|
|
anode = graph.source(e);
|
|
bnode = graph.target(e);
|
|
cnode = graph.target(next[graph.oppositeArc(e)]);
|
|
}
|
|
|
|
IterableBoolMap<AuxGraph, Node> proper(graph, false);
|
|
typename AuxGraph::template NodeMap<int> conn(graph, -1);
|
|
|
|
conn[anode] = conn[bnode] = -2;
|
|
{
|
|
for (OutArcIt e(graph, anode); e != INVALID; ++e) {
|
|
Node m = graph.target(e);
|
|
if (conn[m] == -1) {
|
|
conn[m] = 1;
|
|
}
|
|
}
|
|
conn[cnode] = 2;
|
|
|
|
for (OutArcIt e(graph, bnode); e != INVALID; ++e) {
|
|
Node m = graph.target(e);
|
|
if (conn[m] == -1) {
|
|
conn[m] = 1;
|
|
} else if (conn[m] != -2) {
|
|
conn[m] += 1;
|
|
Arc pe = graph.oppositeArc(e);
|
|
if (conn[graph.target(next[pe])] == -2) {
|
|
conn[m] -= 1;
|
|
}
|
|
if (conn[graph.target(prev[pe])] == -2) {
|
|
conn[m] -= 1;
|
|
}
|
|
|
|
proper.set(m, conn[m] == 1);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
typename AuxGraph::template ArcMap<int> angle(graph, -1);
|
|
|
|
while (proper.trueNum() != 0) {
|
|
Node n = typename IterableBoolMap<AuxGraph, Node>::TrueIt(proper);
|
|
proper.set(n, false);
|
|
conn[n] = -2;
|
|
|
|
for (OutArcIt e(graph, n); e != INVALID; ++e) {
|
|
Node m = graph.target(e);
|
|
if (conn[m] == -1) {
|
|
conn[m] = 1;
|
|
} else if (conn[m] != -2) {
|
|
conn[m] += 1;
|
|
Arc pe = graph.oppositeArc(e);
|
|
if (conn[graph.target(next[pe])] == -2) {
|
|
conn[m] -= 1;
|
|
}
|
|
if (conn[graph.target(prev[pe])] == -2) {
|
|
conn[m] -= 1;
|
|
}
|
|
|
|
proper.set(m, conn[m] == 1);
|
|
}
|
|
}
|
|
|
|
{
|
|
Arc e = OutArcIt(graph, n);
|
|
Arc p = e, l = e;
|
|
|
|
e = next[e];
|
|
while (e != l) {
|
|
|
|
if (conn[graph.target(e)] == -2 && conn[graph.target(p)] == -2) {
|
|
Arc f = e;
|
|
angle[f] = 0;
|
|
f = next[graph.oppositeArc(f)];
|
|
angle[f] = 1;
|
|
f = next[graph.oppositeArc(f)];
|
|
angle[f] = 2;
|
|
}
|
|
|
|
p = e;
|
|
e = next[e];
|
|
}
|
|
|
|
if (conn[graph.target(e)] == -2 && conn[graph.target(p)] == -2) {
|
|
Arc f = e;
|
|
angle[f] = 0;
|
|
f = next[graph.oppositeArc(f)];
|
|
angle[f] = 1;
|
|
f = next[graph.oppositeArc(f)];
|
|
angle[f] = 2;
|
|
}
|
|
}
|
|
}
|
|
|
|
typename AuxGraph::template NodeMap<Node> apred(graph, INVALID);
|
|
typename AuxGraph::template NodeMap<Node> bpred(graph, INVALID);
|
|
typename AuxGraph::template NodeMap<Node> cpred(graph, INVALID);
|
|
|
|
typename AuxGraph::template NodeMap<int> apredid(graph, -1);
|
|
typename AuxGraph::template NodeMap<int> bpredid(graph, -1);
|
|
typename AuxGraph::template NodeMap<int> cpredid(graph, -1);
|
|
|
|
for (ArcIt e(graph); e != INVALID; ++e) {
|
|
if (angle[e] == angle[next[e]]) {
|
|
switch (angle[e]) {
|
|
case 2:
|
|
apred[graph.target(e)] = graph.source(e);
|
|
apredid[graph.target(e)] = graph.id(graph.source(e));
|
|
break;
|
|
case 1:
|
|
bpred[graph.target(e)] = graph.source(e);
|
|
bpredid[graph.target(e)] = graph.id(graph.source(e));
|
|
break;
|
|
case 0:
|
|
cpred[graph.target(e)] = graph.source(e);
|
|
cpredid[graph.target(e)] = graph.id(graph.source(e));
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
|
|
cpred[anode] = INVALID;
|
|
cpred[bnode] = INVALID;
|
|
|
|
std::vector<Node> aorder, border, corder;
|
|
|
|
{
|
|
typename AuxGraph::template NodeMap<bool> processed(graph, false);
|
|
std::vector<Node> st;
|
|
for (NodeIt n(graph); n != INVALID; ++n) {
|
|
if (!processed[n] && n != bnode && n != cnode) {
|
|
st.push_back(n);
|
|
processed[n] = true;
|
|
Node m = apred[n];
|
|
while (m != INVALID && !processed[m]) {
|
|
st.push_back(m);
|
|
processed[m] = true;
|
|
m = apred[m];
|
|
}
|
|
while (!st.empty()) {
|
|
aorder.push_back(st.back());
|
|
st.pop_back();
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
{
|
|
typename AuxGraph::template NodeMap<bool> processed(graph, false);
|
|
std::vector<Node> st;
|
|
for (NodeIt n(graph); n != INVALID; ++n) {
|
|
if (!processed[n] && n != cnode && n != anode) {
|
|
st.push_back(n);
|
|
processed[n] = true;
|
|
Node m = bpred[n];
|
|
while (m != INVALID && !processed[m]) {
|
|
st.push_back(m);
|
|
processed[m] = true;
|
|
m = bpred[m];
|
|
}
|
|
while (!st.empty()) {
|
|
border.push_back(st.back());
|
|
st.pop_back();
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
{
|
|
typename AuxGraph::template NodeMap<bool> processed(graph, false);
|
|
std::vector<Node> st;
|
|
for (NodeIt n(graph); n != INVALID; ++n) {
|
|
if (!processed[n] && n != anode && n != bnode) {
|
|
st.push_back(n);
|
|
processed[n] = true;
|
|
Node m = cpred[n];
|
|
while (m != INVALID && !processed[m]) {
|
|
st.push_back(m);
|
|
processed[m] = true;
|
|
m = cpred[m];
|
|
}
|
|
while (!st.empty()) {
|
|
corder.push_back(st.back());
|
|
st.pop_back();
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
typename AuxGraph::template NodeMap<int> atree(graph, 0);
|
|
for (int i = aorder.size() - 1; i >= 0; --i) {
|
|
Node n = aorder[i];
|
|
atree[n] = 1;
|
|
for (OutArcIt e(graph, n); e != INVALID; ++e) {
|
|
if (apred[graph.target(e)] == n) {
|
|
atree[n] += atree[graph.target(e)];
|
|
}
|
|
}
|
|
}
|
|
|
|
typename AuxGraph::template NodeMap<int> btree(graph, 0);
|
|
for (int i = border.size() - 1; i >= 0; --i) {
|
|
Node n = border[i];
|
|
btree[n] = 1;
|
|
for (OutArcIt e(graph, n); e != INVALID; ++e) {
|
|
if (bpred[graph.target(e)] == n) {
|
|
btree[n] += btree[graph.target(e)];
|
|
}
|
|
}
|
|
}
|
|
|
|
typename AuxGraph::template NodeMap<int> apath(graph, 0);
|
|
apath[bnode] = apath[cnode] = 1;
|
|
typename AuxGraph::template NodeMap<int> apath_btree(graph, 0);
|
|
apath_btree[bnode] = btree[bnode];
|
|
for (int i = 1; i < int(aorder.size()); ++i) {
|
|
Node n = aorder[i];
|
|
apath[n] = apath[apred[n]] + 1;
|
|
apath_btree[n] = btree[n] + apath_btree[apred[n]];
|
|
}
|
|
|
|
typename AuxGraph::template NodeMap<int> bpath_atree(graph, 0);
|
|
bpath_atree[anode] = atree[anode];
|
|
for (int i = 1; i < int(border.size()); ++i) {
|
|
Node n = border[i];
|
|
bpath_atree[n] = atree[n] + bpath_atree[bpred[n]];
|
|
}
|
|
|
|
typename AuxGraph::template NodeMap<int> cpath(graph, 0);
|
|
cpath[anode] = cpath[bnode] = 1;
|
|
typename AuxGraph::template NodeMap<int> cpath_atree(graph, 0);
|
|
cpath_atree[anode] = atree[anode];
|
|
typename AuxGraph::template NodeMap<int> cpath_btree(graph, 0);
|
|
cpath_btree[bnode] = btree[bnode];
|
|
for (int i = 1; i < int(corder.size()); ++i) {
|
|
Node n = corder[i];
|
|
cpath[n] = cpath[cpred[n]] + 1;
|
|
cpath_atree[n] = atree[n] + cpath_atree[cpred[n]];
|
|
cpath_btree[n] = btree[n] + cpath_btree[cpred[n]];
|
|
}
|
|
|
|
typename AuxGraph::template NodeMap<int> third(graph);
|
|
for (NodeIt n(graph); n != INVALID; ++n) {
|
|
point_map[n].x =
|
|
bpath_atree[n] + cpath_atree[n] - atree[n] - cpath[n] + 1;
|
|
point_map[n].y =
|
|
cpath_btree[n] + apath_btree[n] - btree[n] - apath[n] + 1;
|
|
}
|
|
|
|
}
|
|
|
|
public:
|
|
|
|
/// \brief Calculate the node positions
|
|
///
|
|
/// This function calculates the node positions on the plane.
|
|
/// \return \c true if the graph is planar.
|
|
bool run() {
|
|
PlanarEmbedding<Graph> pe(_graph);
|
|
if (!pe.run()) return false;
|
|
|
|
run(pe);
|
|
return true;
|
|
}
|
|
|
|
/// \brief Calculate the node positions according to a
|
|
/// combinatorical embedding
|
|
///
|
|
/// This function calculates the node positions on the plane.
|
|
/// The given \c embedding map should contain a valid combinatorical
|
|
/// embedding, i.e. a valid cyclic order of the arcs.
|
|
/// It can be computed using PlanarEmbedding.
|
|
template <typename EmbeddingMap>
|
|
void run(const EmbeddingMap& embedding) {
|
|
typedef SmartEdgeSet<Graph> AuxGraph;
|
|
|
|
if (3 * countNodes(_graph) - 6 == countEdges(_graph)) {
|
|
drawing(_graph, embedding, _point_map);
|
|
return;
|
|
}
|
|
|
|
AuxGraph aux_graph(_graph);
|
|
typename AuxGraph::template ArcMap<typename AuxGraph::Arc>
|
|
aux_embedding(aux_graph);
|
|
|
|
{
|
|
|
|
typename Graph::template EdgeMap<typename AuxGraph::Edge>
|
|
ref(_graph);
|
|
|
|
for (EdgeIt e(_graph); e != INVALID; ++e) {
|
|
ref[e] = aux_graph.addEdge(_graph.u(e), _graph.v(e));
|
|
}
|
|
|
|
for (EdgeIt e(_graph); e != INVALID; ++e) {
|
|
Arc ee = embedding[_graph.direct(e, true)];
|
|
aux_embedding[aux_graph.direct(ref[e], true)] =
|
|
aux_graph.direct(ref[ee], _graph.direction(ee));
|
|
ee = embedding[_graph.direct(e, false)];
|
|
aux_embedding[aux_graph.direct(ref[e], false)] =
|
|
aux_graph.direct(ref[ee], _graph.direction(ee));
|
|
}
|
|
}
|
|
_planarity_bits::makeConnected(aux_graph, aux_embedding);
|
|
_planarity_bits::makeBiNodeConnected(aux_graph, aux_embedding);
|
|
_planarity_bits::makeMaxPlanar(aux_graph, aux_embedding);
|
|
drawing(aux_graph, aux_embedding, _point_map);
|
|
}
|
|
|
|
/// \brief The coordinate of the given node
|
|
///
|
|
/// This function returns the coordinate of the given node.
|
|
Point operator[](const Node& node) const {
|
|
return _point_map[node];
|
|
}
|
|
|
|
/// \brief Return the grid embedding in a node map
|
|
///
|
|
/// This function returns the grid embedding in a node map of
|
|
/// \c dim2::Point<int> coordinates.
|
|
const PointMap& coords() const {
|
|
return _point_map;
|
|
}
|
|
|
|
private:
|
|
|
|
const Graph& _graph;
|
|
PointMap _point_map;
|
|
|
|
};
|
|
|
|
namespace _planarity_bits {
|
|
|
|
template <typename ColorMap>
|
|
class KempeFilter {
|
|
public:
|
|
typedef typename ColorMap::Key Key;
|
|
typedef bool Value;
|
|
|
|
KempeFilter(const ColorMap& color_map,
|
|
const typename ColorMap::Value& first,
|
|
const typename ColorMap::Value& second)
|
|
: _color_map(color_map), _first(first), _second(second) {}
|
|
|
|
Value operator[](const Key& key) const {
|
|
return _color_map[key] == _first || _color_map[key] == _second;
|
|
}
|
|
|
|
private:
|
|
const ColorMap& _color_map;
|
|
typename ColorMap::Value _first, _second;
|
|
};
|
|
}
|
|
|
|
/// \ingroup planar
|
|
///
|
|
/// \brief Coloring planar graphs
|
|
///
|
|
/// The graph coloring problem is the coloring of the graph nodes
|
|
/// so that there are no adjacent nodes with the same color. The
|
|
/// planar graphs can always be colored with four colors, which is
|
|
/// proved by Appel and Haken. Their proofs provide a quadratic
|
|
/// time algorithm for four coloring, but it could not be used to
|
|
/// implement an efficient algorithm. The five and six coloring can be
|
|
/// made in linear time, but in this class, the five coloring has
|
|
/// quadratic worst case time complexity. The two coloring (if
|
|
/// possible) is solvable with a graph search algorithm and it is
|
|
/// implemented in \ref bipartitePartitions() function in LEMON. To
|
|
/// decide whether a planar graph is three colorable is NP-complete.
|
|
///
|
|
/// This class contains member functions for calculate colorings
|
|
/// with five and six colors. The six coloring algorithm is a simple
|
|
/// greedy coloring on the backward minimum outgoing order of nodes.
|
|
/// This order can be computed by selecting the node with least
|
|
/// outgoing arcs to unprocessed nodes in each phase. This order
|
|
/// guarantees that when a node is chosen for coloring it has at
|
|
/// most five already colored adjacents. The five coloring algorithm
|
|
/// use the same method, but if the greedy approach fails to color
|
|
/// with five colors, i.e. the node has five already different
|
|
/// colored neighbours, it swaps the colors in one of the connected
|
|
/// two colored sets with the Kempe recoloring method.
|
|
template <typename Graph>
|
|
class PlanarColoring {
|
|
public:
|
|
|
|
TEMPLATE_GRAPH_TYPEDEFS(Graph);
|
|
|
|
/// \brief The map type for storing color indices
|
|
typedef typename Graph::template NodeMap<int> IndexMap;
|
|
/// \brief The map type for storing colors
|
|
///
|
|
/// The map type for storing colors.
|
|
/// \see Palette, Color
|
|
typedef ComposeMap<Palette, IndexMap> ColorMap;
|
|
|
|
/// \brief Constructor
|
|
///
|
|
/// Constructor.
|
|
/// \pre The graph must be simple, i.e. it should not
|
|
/// contain parallel or loop arcs.
|
|
PlanarColoring(const Graph& graph)
|
|
: _graph(graph), _color_map(graph), _palette(0) {
|
|
_palette.add(Color(1,0,0));
|
|
_palette.add(Color(0,1,0));
|
|
_palette.add(Color(0,0,1));
|
|
_palette.add(Color(1,1,0));
|
|
_palette.add(Color(1,0,1));
|
|
_palette.add(Color(0,1,1));
|
|
}
|
|
|
|
/// \brief Return the node map of color indices
|
|
///
|
|
/// This function returns the node map of color indices. The values are
|
|
/// in the range \c [0..4] or \c [0..5] according to the coloring method.
|
|
IndexMap colorIndexMap() const {
|
|
return _color_map;
|
|
}
|
|
|
|
/// \brief Return the node map of colors
|
|
///
|
|
/// This function returns the node map of colors. The values are among
|
|
/// five or six distinct \ref lemon::Color "colors".
|
|
ColorMap colorMap() const {
|
|
return composeMap(_palette, _color_map);
|
|
}
|
|
|
|
/// \brief Return the color index of the node
|
|
///
|
|
/// This function returns the color index of the given node. The value is
|
|
/// in the range \c [0..4] or \c [0..5] according to the coloring method.
|
|
int colorIndex(const Node& node) const {
|
|
return _color_map[node];
|
|
}
|
|
|
|
/// \brief Return the color of the node
|
|
///
|
|
/// This function returns the color of the given node. The value is among
|
|
/// five or six distinct \ref lemon::Color "colors".
|
|
Color color(const Node& node) const {
|
|
return _palette[_color_map[node]];
|
|
}
|
|
|
|
|
|
/// \brief Calculate a coloring with at most six colors
|
|
///
|
|
/// This function calculates a coloring with at most six colors. The time
|
|
/// complexity of this variant is linear in the size of the graph.
|
|
/// \return \c true if the algorithm could color the graph with six colors.
|
|
/// If the algorithm fails, then the graph is not planar.
|
|
/// \note This function can return \c true if the graph is not
|
|
/// planar, but it can be colored with at most six colors.
|
|
bool runSixColoring() {
|
|
|
|
typename Graph::template NodeMap<int> heap_index(_graph, -1);
|
|
BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index);
|
|
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
_color_map[n] = -2;
|
|
heap.push(n, countOutArcs(_graph, n));
|
|
}
|
|
|
|
std::vector<Node> order;
|
|
|
|
while (!heap.empty()) {
|
|
Node n = heap.top();
|
|
heap.pop();
|
|
_color_map[n] = -1;
|
|
order.push_back(n);
|
|
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
|
|
Node t = _graph.runningNode(e);
|
|
if (_color_map[t] == -2) {
|
|
heap.decrease(t, heap[t] - 1);
|
|
}
|
|
}
|
|
}
|
|
|
|
for (int i = order.size() - 1; i >= 0; --i) {
|
|
std::vector<bool> forbidden(6, false);
|
|
for (OutArcIt e(_graph, order[i]); e != INVALID; ++e) {
|
|
Node t = _graph.runningNode(e);
|
|
if (_color_map[t] != -1) {
|
|
forbidden[_color_map[t]] = true;
|
|
}
|
|
}
|
|
for (int k = 0; k < 6; ++k) {
|
|
if (!forbidden[k]) {
|
|
_color_map[order[i]] = k;
|
|
break;
|
|
}
|
|
}
|
|
if (_color_map[order[i]] == -1) {
|
|
return false;
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
|
|
private:
|
|
|
|
bool recolor(const Node& u, const Node& v) {
|
|
int ucolor = _color_map[u];
|
|
int vcolor = _color_map[v];
|
|
typedef _planarity_bits::KempeFilter<IndexMap> KempeFilter;
|
|
KempeFilter filter(_color_map, ucolor, vcolor);
|
|
|
|
typedef FilterNodes<const Graph, const KempeFilter> KempeGraph;
|
|
KempeGraph kempe_graph(_graph, filter);
|
|
|
|
std::vector<Node> comp;
|
|
Bfs<KempeGraph> bfs(kempe_graph);
|
|
bfs.init();
|
|
bfs.addSource(u);
|
|
while (!bfs.emptyQueue()) {
|
|
Node n = bfs.nextNode();
|
|
if (n == v) return false;
|
|
comp.push_back(n);
|
|
bfs.processNextNode();
|
|
}
|
|
|
|
int scolor = ucolor + vcolor;
|
|
for (int i = 0; i < static_cast<int>(comp.size()); ++i) {
|
|
_color_map[comp[i]] = scolor - _color_map[comp[i]];
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
template <typename EmbeddingMap>
|
|
void kempeRecoloring(const Node& node, const EmbeddingMap& embedding) {
|
|
std::vector<Node> nodes;
|
|
nodes.reserve(4);
|
|
|
|
for (Arc e = OutArcIt(_graph, node); e != INVALID; e = embedding[e]) {
|
|
Node t = _graph.target(e);
|
|
if (_color_map[t] != -1) {
|
|
nodes.push_back(t);
|
|
if (nodes.size() == 4) break;
|
|
}
|
|
}
|
|
|
|
int color = _color_map[nodes[0]];
|
|
if (recolor(nodes[0], nodes[2])) {
|
|
_color_map[node] = color;
|
|
} else {
|
|
color = _color_map[nodes[1]];
|
|
recolor(nodes[1], nodes[3]);
|
|
_color_map[node] = color;
|
|
}
|
|
}
|
|
|
|
public:
|
|
|
|
/// \brief Calculate a coloring with at most five colors
|
|
///
|
|
/// This function calculates a coloring with at most five
|
|
/// colors. The worst case time complexity of this variant is
|
|
/// quadratic in the size of the graph.
|
|
/// \param embedding This map should contain a valid combinatorical
|
|
/// embedding, i.e. a valid cyclic order of the arcs.
|
|
/// It can be computed using PlanarEmbedding.
|
|
template <typename EmbeddingMap>
|
|
void runFiveColoring(const EmbeddingMap& embedding) {
|
|
|
|
typename Graph::template NodeMap<int> heap_index(_graph, -1);
|
|
BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index);
|
|
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
_color_map[n] = -2;
|
|
heap.push(n, countOutArcs(_graph, n));
|
|
}
|
|
|
|
std::vector<Node> order;
|
|
|
|
while (!heap.empty()) {
|
|
Node n = heap.top();
|
|
heap.pop();
|
|
_color_map[n] = -1;
|
|
order.push_back(n);
|
|
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
|
|
Node t = _graph.runningNode(e);
|
|
if (_color_map[t] == -2) {
|
|
heap.decrease(t, heap[t] - 1);
|
|
}
|
|
}
|
|
}
|
|
|
|
for (int i = order.size() - 1; i >= 0; --i) {
|
|
std::vector<bool> forbidden(5, false);
|
|
for (OutArcIt e(_graph, order[i]); e != INVALID; ++e) {
|
|
Node t = _graph.runningNode(e);
|
|
if (_color_map[t] != -1) {
|
|
forbidden[_color_map[t]] = true;
|
|
}
|
|
}
|
|
for (int k = 0; k < 5; ++k) {
|
|
if (!forbidden[k]) {
|
|
_color_map[order[i]] = k;
|
|
break;
|
|
}
|
|
}
|
|
if (_color_map[order[i]] == -1) {
|
|
kempeRecoloring(order[i], embedding);
|
|
}
|
|
}
|
|
}
|
|
|
|
/// \brief Calculate a coloring with at most five colors
|
|
///
|
|
/// This function calculates a coloring with at most five
|
|
/// colors. The worst case time complexity of this variant is
|
|
/// quadratic in the size of the graph.
|
|
/// \return \c true if the graph is planar.
|
|
bool runFiveColoring() {
|
|
PlanarEmbedding<Graph> pe(_graph);
|
|
if (!pe.run()) return false;
|
|
|
|
runFiveColoring(pe.embeddingMap());
|
|
return true;
|
|
}
|
|
|
|
private:
|
|
|
|
const Graph& _graph;
|
|
IndexMap _color_map;
|
|
Palette _palette;
|
|
};
|
|
|
|
}
|
|
|
|
#endif
|