lemon/planarity.h
changeset 822 f903263902f6
parent 797 30cb42e3e43a
child 828 5fd7fafc4470
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/lemon/planarity.h	Mon Dec 14 06:07:52 2009 +0100
     1.3 @@ -0,0 +1,2737 @@
     1.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
     1.5 + *
     1.6 + * This file is a part of LEMON, a generic C++ optimization library.
     1.7 + *
     1.8 + * Copyright (C) 2003-2009
     1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
    1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
    1.11 + *
    1.12 + * Permission to use, modify and distribute this software is granted
    1.13 + * provided that this copyright notice appears in all copies. For
    1.14 + * precise terms see the accompanying LICENSE file.
    1.15 + *
    1.16 + * This software is provided "AS IS" with no warranty of any kind,
    1.17 + * express or implied, and with no claim as to its suitability for any
    1.18 + * purpose.
    1.19 + *
    1.20 + */
    1.21 +
    1.22 +#ifndef LEMON_PLANARITY_H
    1.23 +#define LEMON_PLANARITY_H
    1.24 +
    1.25 +/// \ingroup planar
    1.26 +/// \file
    1.27 +/// \brief Planarity checking, embedding, drawing and coloring
    1.28 +
    1.29 +#include <vector>
    1.30 +#include <list>
    1.31 +
    1.32 +#include <lemon/dfs.h>
    1.33 +#include <lemon/bfs.h>
    1.34 +#include <lemon/radix_sort.h>
    1.35 +#include <lemon/maps.h>
    1.36 +#include <lemon/path.h>
    1.37 +#include <lemon/bucket_heap.h>
    1.38 +#include <lemon/adaptors.h>
    1.39 +#include <lemon/edge_set.h>
    1.40 +#include <lemon/color.h>
    1.41 +#include <lemon/dim2.h>
    1.42 +
    1.43 +namespace lemon {
    1.44 +
    1.45 +  namespace _planarity_bits {
    1.46 +
    1.47 +    template <typename Graph>
    1.48 +    struct PlanarityVisitor : DfsVisitor<Graph> {
    1.49 +
    1.50 +      TEMPLATE_GRAPH_TYPEDEFS(Graph);
    1.51 +
    1.52 +      typedef typename Graph::template NodeMap<Arc> PredMap;
    1.53 +
    1.54 +      typedef typename Graph::template EdgeMap<bool> TreeMap;
    1.55 +
    1.56 +      typedef typename Graph::template NodeMap<int> OrderMap;
    1.57 +      typedef std::vector<Node> OrderList;
    1.58 +
    1.59 +      typedef typename Graph::template NodeMap<int> LowMap;
    1.60 +      typedef typename Graph::template NodeMap<int> AncestorMap;
    1.61 +
    1.62 +      PlanarityVisitor(const Graph& graph,
    1.63 +                       PredMap& pred_map, TreeMap& tree_map,
    1.64 +                       OrderMap& order_map, OrderList& order_list,
    1.65 +                       AncestorMap& ancestor_map, LowMap& low_map)
    1.66 +        : _graph(graph), _pred_map(pred_map), _tree_map(tree_map),
    1.67 +          _order_map(order_map), _order_list(order_list),
    1.68 +          _ancestor_map(ancestor_map), _low_map(low_map) {}
    1.69 +
    1.70 +      void reach(const Node& node) {
    1.71 +        _order_map[node] = _order_list.size();
    1.72 +        _low_map[node] = _order_list.size();
    1.73 +        _ancestor_map[node] = _order_list.size();
    1.74 +        _order_list.push_back(node);
    1.75 +      }
    1.76 +
    1.77 +      void discover(const Arc& arc) {
    1.78 +        Node source = _graph.source(arc);
    1.79 +        Node target = _graph.target(arc);
    1.80 +
    1.81 +        _tree_map[arc] = true;
    1.82 +        _pred_map[target] = arc;
    1.83 +      }
    1.84 +
    1.85 +      void examine(const Arc& arc) {
    1.86 +        Node source = _graph.source(arc);
    1.87 +        Node target = _graph.target(arc);
    1.88 +
    1.89 +        if (_order_map[target] < _order_map[source] && !_tree_map[arc]) {
    1.90 +          if (_low_map[source] > _order_map[target]) {
    1.91 +            _low_map[source] = _order_map[target];
    1.92 +          }
    1.93 +          if (_ancestor_map[source] > _order_map[target]) {
    1.94 +            _ancestor_map[source] = _order_map[target];
    1.95 +          }
    1.96 +        }
    1.97 +      }
    1.98 +
    1.99 +      void backtrack(const Arc& arc) {
   1.100 +        Node source = _graph.source(arc);
   1.101 +        Node target = _graph.target(arc);
   1.102 +
   1.103 +        if (_low_map[source] > _low_map[target]) {
   1.104 +          _low_map[source] = _low_map[target];
   1.105 +        }
   1.106 +      }
   1.107 +
   1.108 +      const Graph& _graph;
   1.109 +      PredMap& _pred_map;
   1.110 +      TreeMap& _tree_map;
   1.111 +      OrderMap& _order_map;
   1.112 +      OrderList& _order_list;
   1.113 +      AncestorMap& _ancestor_map;
   1.114 +      LowMap& _low_map;
   1.115 +    };
   1.116 +
   1.117 +    template <typename Graph, bool embedding = true>
   1.118 +    struct NodeDataNode {
   1.119 +      int prev, next;
   1.120 +      int visited;
   1.121 +      typename Graph::Arc first;
   1.122 +      bool inverted;
   1.123 +    };
   1.124 +
   1.125 +    template <typename Graph>
   1.126 +    struct NodeDataNode<Graph, false> {
   1.127 +      int prev, next;
   1.128 +      int visited;
   1.129 +    };
   1.130 +
   1.131 +    template <typename Graph>
   1.132 +    struct ChildListNode {
   1.133 +      typedef typename Graph::Node Node;
   1.134 +      Node first;
   1.135 +      Node prev, next;
   1.136 +    };
   1.137 +
   1.138 +    template <typename Graph>
   1.139 +    struct ArcListNode {
   1.140 +      typename Graph::Arc prev, next;
   1.141 +    };
   1.142 +
   1.143 +    template <typename Graph>
   1.144 +    class PlanarityChecking {
   1.145 +    private:
   1.146 +      
   1.147 +      TEMPLATE_GRAPH_TYPEDEFS(Graph);
   1.148 +
   1.149 +      const Graph& _graph;
   1.150 +
   1.151 +    private:
   1.152 +      
   1.153 +      typedef typename Graph::template NodeMap<Arc> PredMap;
   1.154 +      
   1.155 +      typedef typename Graph::template EdgeMap<bool> TreeMap;
   1.156 +      
   1.157 +      typedef typename Graph::template NodeMap<int> OrderMap;
   1.158 +      typedef std::vector<Node> OrderList;
   1.159 +
   1.160 +      typedef typename Graph::template NodeMap<int> LowMap;
   1.161 +      typedef typename Graph::template NodeMap<int> AncestorMap;
   1.162 +
   1.163 +      typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode;
   1.164 +      typedef std::vector<NodeDataNode> NodeData;
   1.165 +
   1.166 +      typedef _planarity_bits::ChildListNode<Graph> ChildListNode;
   1.167 +      typedef typename Graph::template NodeMap<ChildListNode> ChildLists;
   1.168 +
   1.169 +      typedef typename Graph::template NodeMap<std::list<int> > MergeRoots;
   1.170 +
   1.171 +      typedef typename Graph::template NodeMap<bool> EmbedArc;
   1.172 +
   1.173 +    public:
   1.174 +
   1.175 +      PlanarityChecking(const Graph& graph) : _graph(graph) {}
   1.176 +
   1.177 +      bool run() {
   1.178 +        typedef _planarity_bits::PlanarityVisitor<Graph> Visitor;
   1.179 +
   1.180 +        PredMap pred_map(_graph, INVALID);
   1.181 +        TreeMap tree_map(_graph, false);
   1.182 +
   1.183 +        OrderMap order_map(_graph, -1);
   1.184 +        OrderList order_list;
   1.185 +
   1.186 +        AncestorMap ancestor_map(_graph, -1);
   1.187 +        LowMap low_map(_graph, -1);
   1.188 +
   1.189 +        Visitor visitor(_graph, pred_map, tree_map,
   1.190 +                        order_map, order_list, ancestor_map, low_map);
   1.191 +        DfsVisit<Graph, Visitor> visit(_graph, visitor);
   1.192 +        visit.run();
   1.193 +
   1.194 +        ChildLists child_lists(_graph);
   1.195 +        createChildLists(tree_map, order_map, low_map, child_lists);
   1.196 +
   1.197 +        NodeData node_data(2 * order_list.size());
   1.198 +
   1.199 +        EmbedArc embed_arc(_graph, false);
   1.200 +
   1.201 +        MergeRoots merge_roots(_graph);
   1.202 +
   1.203 +        for (int i = order_list.size() - 1; i >= 0; --i) {
   1.204 +
   1.205 +          Node node = order_list[i];
   1.206 +
   1.207 +          Node source = node;
   1.208 +          for (OutArcIt e(_graph, node); e != INVALID; ++e) {
   1.209 +            Node target = _graph.target(e);
   1.210 +
   1.211 +            if (order_map[source] < order_map[target] && tree_map[e]) {
   1.212 +              initFace(target, node_data, order_map, order_list);
   1.213 +            }
   1.214 +          }
   1.215 +
   1.216 +          for (OutArcIt e(_graph, node); e != INVALID; ++e) {
   1.217 +            Node target = _graph.target(e);
   1.218 +
   1.219 +            if (order_map[source] < order_map[target] && !tree_map[e]) {
   1.220 +              embed_arc[target] = true;
   1.221 +              walkUp(target, source, i, pred_map, low_map,
   1.222 +                     order_map, order_list, node_data, merge_roots);
   1.223 +            }
   1.224 +          }
   1.225 +
   1.226 +          for (typename MergeRoots::Value::iterator it =
   1.227 +                 merge_roots[node].begin(); 
   1.228 +               it != merge_roots[node].end(); ++it) {
   1.229 +            int rn = *it;
   1.230 +            walkDown(rn, i, node_data, order_list, child_lists,
   1.231 +                     ancestor_map, low_map, embed_arc, merge_roots);
   1.232 +          }
   1.233 +          merge_roots[node].clear();
   1.234 +
   1.235 +          for (OutArcIt e(_graph, node); e != INVALID; ++e) {
   1.236 +            Node target = _graph.target(e);
   1.237 +
   1.238 +            if (order_map[source] < order_map[target] && !tree_map[e]) {
   1.239 +              if (embed_arc[target]) {
   1.240 +                return false;
   1.241 +              }
   1.242 +            }
   1.243 +          }
   1.244 +        }
   1.245 +
   1.246 +        return true;
   1.247 +      }
   1.248 +
   1.249 +    private:
   1.250 +
   1.251 +      void createChildLists(const TreeMap& tree_map, const OrderMap& order_map,
   1.252 +                            const LowMap& low_map, ChildLists& child_lists) {
   1.253 +
   1.254 +        for (NodeIt n(_graph); n != INVALID; ++n) {
   1.255 +          Node source = n;
   1.256 +
   1.257 +          std::vector<Node> targets;
   1.258 +          for (OutArcIt e(_graph, n); e != INVALID; ++e) {
   1.259 +            Node target = _graph.target(e);
   1.260 +
   1.261 +            if (order_map[source] < order_map[target] && tree_map[e]) {
   1.262 +              targets.push_back(target);
   1.263 +            }
   1.264 +          }
   1.265 +
   1.266 +          if (targets.size() == 0) {
   1.267 +            child_lists[source].first = INVALID;
   1.268 +          } else if (targets.size() == 1) {
   1.269 +            child_lists[source].first = targets[0];
   1.270 +            child_lists[targets[0]].prev = INVALID;
   1.271 +            child_lists[targets[0]].next = INVALID;
   1.272 +          } else {
   1.273 +            radixSort(targets.begin(), targets.end(), mapToFunctor(low_map));
   1.274 +            for (int i = 1; i < int(targets.size()); ++i) {
   1.275 +              child_lists[targets[i]].prev = targets[i - 1];
   1.276 +              child_lists[targets[i - 1]].next = targets[i];
   1.277 +            }
   1.278 +            child_lists[targets.back()].next = INVALID;
   1.279 +            child_lists[targets.front()].prev = INVALID;
   1.280 +            child_lists[source].first = targets.front();
   1.281 +          }
   1.282 +        }
   1.283 +      }
   1.284 +
   1.285 +      void walkUp(const Node& node, Node root, int rorder,
   1.286 +                  const PredMap& pred_map, const LowMap& low_map,
   1.287 +                  const OrderMap& order_map, const OrderList& order_list,
   1.288 +                  NodeData& node_data, MergeRoots& merge_roots) {
   1.289 +
   1.290 +        int na, nb;
   1.291 +        bool da, db;
   1.292 +
   1.293 +        na = nb = order_map[node];
   1.294 +        da = true; db = false;
   1.295 +
   1.296 +        while (true) {
   1.297 +
   1.298 +          if (node_data[na].visited == rorder) break;
   1.299 +          if (node_data[nb].visited == rorder) break;
   1.300 +
   1.301 +          node_data[na].visited = rorder;
   1.302 +          node_data[nb].visited = rorder;
   1.303 +
   1.304 +          int rn = -1;
   1.305 +
   1.306 +          if (na >= int(order_list.size())) {
   1.307 +            rn = na;
   1.308 +          } else if (nb >= int(order_list.size())) {
   1.309 +            rn = nb;
   1.310 +          }
   1.311 +
   1.312 +          if (rn == -1) {
   1.313 +            int nn;
   1.314 +
   1.315 +            nn = da ? node_data[na].prev : node_data[na].next;
   1.316 +            da = node_data[nn].prev != na;
   1.317 +            na = nn;
   1.318 +
   1.319 +            nn = db ? node_data[nb].prev : node_data[nb].next;
   1.320 +            db = node_data[nn].prev != nb;
   1.321 +            nb = nn;
   1.322 +
   1.323 +          } else {
   1.324 +
   1.325 +            Node rep = order_list[rn - order_list.size()];
   1.326 +            Node parent = _graph.source(pred_map[rep]);
   1.327 +
   1.328 +            if (low_map[rep] < rorder) {
   1.329 +              merge_roots[parent].push_back(rn);
   1.330 +            } else {
   1.331 +              merge_roots[parent].push_front(rn);
   1.332 +            }
   1.333 +
   1.334 +            if (parent != root) {
   1.335 +              na = nb = order_map[parent];
   1.336 +              da = true; db = false;
   1.337 +            } else {
   1.338 +              break;
   1.339 +            }
   1.340 +          }
   1.341 +        }
   1.342 +      }
   1.343 +
   1.344 +      void walkDown(int rn, int rorder, NodeData& node_data,
   1.345 +                    OrderList& order_list, ChildLists& child_lists,
   1.346 +                    AncestorMap& ancestor_map, LowMap& low_map,
   1.347 +                    EmbedArc& embed_arc, MergeRoots& merge_roots) {
   1.348 +
   1.349 +        std::vector<std::pair<int, bool> > merge_stack;
   1.350 +
   1.351 +        for (int di = 0; di < 2; ++di) {
   1.352 +          bool rd = di == 0;
   1.353 +          int pn = rn;
   1.354 +          int n = rd ? node_data[rn].next : node_data[rn].prev;
   1.355 +
   1.356 +          while (n != rn) {
   1.357 +
   1.358 +            Node node = order_list[n];
   1.359 +
   1.360 +            if (embed_arc[node]) {
   1.361 +
   1.362 +              // Merging components on the critical path
   1.363 +              while (!merge_stack.empty()) {
   1.364 +
   1.365 +                // Component root
   1.366 +                int cn = merge_stack.back().first;
   1.367 +                bool cd = merge_stack.back().second;
   1.368 +                merge_stack.pop_back();
   1.369 +
   1.370 +                // Parent of component
   1.371 +                int dn = merge_stack.back().first;
   1.372 +                bool dd = merge_stack.back().second;
   1.373 +                merge_stack.pop_back();
   1.374 +
   1.375 +                Node parent = order_list[dn];
   1.376 +
   1.377 +                // Erasing from merge_roots
   1.378 +                merge_roots[parent].pop_front();
   1.379 +
   1.380 +                Node child = order_list[cn - order_list.size()];
   1.381 +
   1.382 +                // Erasing from child_lists
   1.383 +                if (child_lists[child].prev != INVALID) {
   1.384 +                  child_lists[child_lists[child].prev].next =
   1.385 +                    child_lists[child].next;
   1.386 +                } else {
   1.387 +                  child_lists[parent].first = child_lists[child].next;
   1.388 +                }
   1.389 +
   1.390 +                if (child_lists[child].next != INVALID) {
   1.391 +                  child_lists[child_lists[child].next].prev =
   1.392 +                    child_lists[child].prev;
   1.393 +                }
   1.394 +
   1.395 +                // Merging external faces
   1.396 +                {
   1.397 +                  int en = cn;
   1.398 +                  cn = cd ? node_data[cn].prev : node_data[cn].next;
   1.399 +                  cd = node_data[cn].next == en;
   1.400 +
   1.401 +                }
   1.402 +
   1.403 +                if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn;
   1.404 +                if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn;
   1.405 +
   1.406 +              }
   1.407 +
   1.408 +              bool d = pn == node_data[n].prev;
   1.409 +
   1.410 +              if (node_data[n].prev == node_data[n].next &&
   1.411 +                  node_data[n].inverted) {
   1.412 +                d = !d;
   1.413 +              }
   1.414 +
   1.415 +              // Embedding arc into external face
   1.416 +              if (rd) node_data[rn].next = n; else node_data[rn].prev = n;
   1.417 +              if (d) node_data[n].prev = rn; else node_data[n].next = rn;
   1.418 +              pn = rn;
   1.419 +
   1.420 +              embed_arc[order_list[n]] = false;
   1.421 +            }
   1.422 +
   1.423 +            if (!merge_roots[node].empty()) {
   1.424 +
   1.425 +              bool d = pn == node_data[n].prev;
   1.426 +
   1.427 +              merge_stack.push_back(std::make_pair(n, d));
   1.428 +
   1.429 +              int rn = merge_roots[node].front();
   1.430 +
   1.431 +              int xn = node_data[rn].next;
   1.432 +              Node xnode = order_list[xn];
   1.433 +
   1.434 +              int yn = node_data[rn].prev;
   1.435 +              Node ynode = order_list[yn];
   1.436 +
   1.437 +              bool rd;
   1.438 +              if (!external(xnode, rorder, child_lists, 
   1.439 +                            ancestor_map, low_map)) {
   1.440 +                rd = true;
   1.441 +              } else if (!external(ynode, rorder, child_lists,
   1.442 +                                   ancestor_map, low_map)) {
   1.443 +                rd = false;
   1.444 +              } else if (pertinent(xnode, embed_arc, merge_roots)) {
   1.445 +                rd = true;
   1.446 +              } else {
   1.447 +                rd = false;
   1.448 +              }
   1.449 +
   1.450 +              merge_stack.push_back(std::make_pair(rn, rd));
   1.451 +
   1.452 +              pn = rn;
   1.453 +              n = rd ? xn : yn;
   1.454 +
   1.455 +            } else if (!external(node, rorder, child_lists,
   1.456 +                                 ancestor_map, low_map)) {
   1.457 +              int nn = (node_data[n].next != pn ?
   1.458 +                        node_data[n].next : node_data[n].prev);
   1.459 +
   1.460 +              bool nd = n == node_data[nn].prev;
   1.461 +
   1.462 +              if (nd) node_data[nn].prev = pn;
   1.463 +              else node_data[nn].next = pn;
   1.464 +
   1.465 +              if (n == node_data[pn].prev) node_data[pn].prev = nn;
   1.466 +              else node_data[pn].next = nn;
   1.467 +
   1.468 +              node_data[nn].inverted =
   1.469 +                (node_data[nn].prev == node_data[nn].next && nd != rd);
   1.470 +
   1.471 +              n = nn;
   1.472 +            }
   1.473 +            else break;
   1.474 +
   1.475 +          }
   1.476 +
   1.477 +          if (!merge_stack.empty() || n == rn) {
   1.478 +            break;
   1.479 +          }
   1.480 +        }
   1.481 +      }
   1.482 +
   1.483 +      void initFace(const Node& node, NodeData& node_data,
   1.484 +                    const OrderMap& order_map, const OrderList& order_list) {
   1.485 +        int n = order_map[node];
   1.486 +        int rn = n + order_list.size();
   1.487 +
   1.488 +        node_data[n].next = node_data[n].prev = rn;
   1.489 +        node_data[rn].next = node_data[rn].prev = n;
   1.490 +
   1.491 +        node_data[n].visited = order_list.size();
   1.492 +        node_data[rn].visited = order_list.size();
   1.493 +
   1.494 +      }
   1.495 +
   1.496 +      bool external(const Node& node, int rorder,
   1.497 +                    ChildLists& child_lists, AncestorMap& ancestor_map,
   1.498 +                    LowMap& low_map) {
   1.499 +        Node child = child_lists[node].first;
   1.500 +
   1.501 +        if (child != INVALID) {
   1.502 +          if (low_map[child] < rorder) return true;
   1.503 +        }
   1.504 +
   1.505 +        if (ancestor_map[node] < rorder) return true;
   1.506 +
   1.507 +        return false;
   1.508 +      }
   1.509 +
   1.510 +      bool pertinent(const Node& node, const EmbedArc& embed_arc,
   1.511 +                     const MergeRoots& merge_roots) {
   1.512 +        return !merge_roots[node].empty() || embed_arc[node];
   1.513 +      }
   1.514 +
   1.515 +    };
   1.516 +
   1.517 +  }
   1.518 +
   1.519 +  /// \ingroup planar
   1.520 +  ///
   1.521 +  /// \brief Planarity checking of an undirected simple graph
   1.522 +  ///
   1.523 +  /// This function implements the Boyer-Myrvold algorithm for
   1.524 +  /// planarity checking of an undirected graph. It is a simplified
   1.525 +  /// version of the PlanarEmbedding algorithm class because neither
   1.526 +  /// the embedding nor the kuratowski subdivisons are not computed.
   1.527 +  template <typename GR>
   1.528 +  bool checkPlanarity(const GR& graph) {
   1.529 +    _planarity_bits::PlanarityChecking<GR> pc(graph);
   1.530 +    return pc.run();
   1.531 +  }
   1.532 +
   1.533 +  /// \ingroup planar
   1.534 +  ///
   1.535 +  /// \brief Planar embedding of an undirected simple graph
   1.536 +  ///
   1.537 +  /// This class implements the Boyer-Myrvold algorithm for planar
   1.538 +  /// embedding of an undirected graph. The planar embedding is an
   1.539 +  /// ordering of the outgoing edges of the nodes, which is a possible
   1.540 +  /// configuration to draw the graph in the plane. If there is not
   1.541 +  /// such ordering then the graph contains a \f$ K_5 \f$ (full graph
   1.542 +  /// with 5 nodes) or a \f$ K_{3,3} \f$ (complete bipartite graph on
   1.543 +  /// 3 ANode and 3 BNode) subdivision.
   1.544 +  ///
   1.545 +  /// The current implementation calculates either an embedding or a
   1.546 +  /// Kuratowski subdivision. The running time of the algorithm is 
   1.547 +  /// \f$ O(n) \f$.
   1.548 +  template <typename Graph>
   1.549 +  class PlanarEmbedding {
   1.550 +  private:
   1.551 +
   1.552 +    TEMPLATE_GRAPH_TYPEDEFS(Graph);
   1.553 +
   1.554 +    const Graph& _graph;
   1.555 +    typename Graph::template ArcMap<Arc> _embedding;
   1.556 +
   1.557 +    typename Graph::template EdgeMap<bool> _kuratowski;
   1.558 +
   1.559 +  private:
   1.560 +
   1.561 +    typedef typename Graph::template NodeMap<Arc> PredMap;
   1.562 +
   1.563 +    typedef typename Graph::template EdgeMap<bool> TreeMap;
   1.564 +
   1.565 +    typedef typename Graph::template NodeMap<int> OrderMap;
   1.566 +    typedef std::vector<Node> OrderList;
   1.567 +
   1.568 +    typedef typename Graph::template NodeMap<int> LowMap;
   1.569 +    typedef typename Graph::template NodeMap<int> AncestorMap;
   1.570 +
   1.571 +    typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode;
   1.572 +    typedef std::vector<NodeDataNode> NodeData;
   1.573 +
   1.574 +    typedef _planarity_bits::ChildListNode<Graph> ChildListNode;
   1.575 +    typedef typename Graph::template NodeMap<ChildListNode> ChildLists;
   1.576 +
   1.577 +    typedef typename Graph::template NodeMap<std::list<int> > MergeRoots;
   1.578 +
   1.579 +    typedef typename Graph::template NodeMap<Arc> EmbedArc;
   1.580 +
   1.581 +    typedef _planarity_bits::ArcListNode<Graph> ArcListNode;
   1.582 +    typedef typename Graph::template ArcMap<ArcListNode> ArcLists;
   1.583 +
   1.584 +    typedef typename Graph::template NodeMap<bool> FlipMap;
   1.585 +
   1.586 +    typedef typename Graph::template NodeMap<int> TypeMap;
   1.587 +
   1.588 +    enum IsolatorNodeType {
   1.589 +      HIGHX = 6, LOWX = 7,
   1.590 +      HIGHY = 8, LOWY = 9,
   1.591 +      ROOT = 10, PERTINENT = 11,
   1.592 +      INTERNAL = 12
   1.593 +    };
   1.594 +
   1.595 +  public:
   1.596 +
   1.597 +    /// \brief The map for store of embedding
   1.598 +    typedef typename Graph::template ArcMap<Arc> EmbeddingMap;
   1.599 +
   1.600 +    /// \brief Constructor
   1.601 +    ///
   1.602 +    /// \note The graph should be simple, i.e. parallel and loop arc
   1.603 +    /// free.
   1.604 +    PlanarEmbedding(const Graph& graph)
   1.605 +      : _graph(graph), _embedding(_graph), _kuratowski(graph, false) {}
   1.606 +
   1.607 +    /// \brief Runs the algorithm.
   1.608 +    ///
   1.609 +    /// Runs the algorithm.
   1.610 +    /// \param kuratowski If the parameter is false, then the
   1.611 +    /// algorithm does not compute a Kuratowski subdivision.
   1.612 +    ///\return %True when the graph is planar.
   1.613 +    bool run(bool kuratowski = true) {
   1.614 +      typedef _planarity_bits::PlanarityVisitor<Graph> Visitor;
   1.615 +
   1.616 +      PredMap pred_map(_graph, INVALID);
   1.617 +      TreeMap tree_map(_graph, false);
   1.618 +
   1.619 +      OrderMap order_map(_graph, -1);
   1.620 +      OrderList order_list;
   1.621 +
   1.622 +      AncestorMap ancestor_map(_graph, -1);
   1.623 +      LowMap low_map(_graph, -1);
   1.624 +
   1.625 +      Visitor visitor(_graph, pred_map, tree_map,
   1.626 +                      order_map, order_list, ancestor_map, low_map);
   1.627 +      DfsVisit<Graph, Visitor> visit(_graph, visitor);
   1.628 +      visit.run();
   1.629 +
   1.630 +      ChildLists child_lists(_graph);
   1.631 +      createChildLists(tree_map, order_map, low_map, child_lists);
   1.632 +
   1.633 +      NodeData node_data(2 * order_list.size());
   1.634 +
   1.635 +      EmbedArc embed_arc(_graph, INVALID);
   1.636 +
   1.637 +      MergeRoots merge_roots(_graph);
   1.638 +
   1.639 +      ArcLists arc_lists(_graph);
   1.640 +
   1.641 +      FlipMap flip_map(_graph, false);
   1.642 +
   1.643 +      for (int i = order_list.size() - 1; i >= 0; --i) {
   1.644 +
   1.645 +        Node node = order_list[i];
   1.646 +
   1.647 +        node_data[i].first = INVALID;
   1.648 +
   1.649 +        Node source = node;
   1.650 +        for (OutArcIt e(_graph, node); e != INVALID; ++e) {
   1.651 +          Node target = _graph.target(e);
   1.652 +
   1.653 +          if (order_map[source] < order_map[target] && tree_map[e]) {
   1.654 +            initFace(target, arc_lists, node_data,
   1.655 +                     pred_map, order_map, order_list);
   1.656 +          }
   1.657 +        }
   1.658 +
   1.659 +        for (OutArcIt e(_graph, node); e != INVALID; ++e) {
   1.660 +          Node target = _graph.target(e);
   1.661 +
   1.662 +          if (order_map[source] < order_map[target] && !tree_map[e]) {
   1.663 +            embed_arc[target] = e;
   1.664 +            walkUp(target, source, i, pred_map, low_map,
   1.665 +                   order_map, order_list, node_data, merge_roots);
   1.666 +          }
   1.667 +        }
   1.668 +
   1.669 +        for (typename MergeRoots::Value::iterator it =
   1.670 +               merge_roots[node].begin(); it != merge_roots[node].end(); ++it) {
   1.671 +          int rn = *it;
   1.672 +          walkDown(rn, i, node_data, arc_lists, flip_map, order_list,
   1.673 +                   child_lists, ancestor_map, low_map, embed_arc, merge_roots);
   1.674 +        }
   1.675 +        merge_roots[node].clear();
   1.676 +
   1.677 +        for (OutArcIt e(_graph, node); e != INVALID; ++e) {
   1.678 +          Node target = _graph.target(e);
   1.679 +
   1.680 +          if (order_map[source] < order_map[target] && !tree_map[e]) {
   1.681 +            if (embed_arc[target] != INVALID) {
   1.682 +              if (kuratowski) {
   1.683 +                isolateKuratowski(e, node_data, arc_lists, flip_map,
   1.684 +                                  order_map, order_list, pred_map, child_lists,
   1.685 +                                  ancestor_map, low_map,
   1.686 +                                  embed_arc, merge_roots);
   1.687 +              }
   1.688 +              return false;
   1.689 +            }
   1.690 +          }
   1.691 +        }
   1.692 +      }
   1.693 +
   1.694 +      for (int i = 0; i < int(order_list.size()); ++i) {
   1.695 +
   1.696 +        mergeRemainingFaces(order_list[i], node_data, order_list, order_map,
   1.697 +                            child_lists, arc_lists);
   1.698 +        storeEmbedding(order_list[i], node_data, order_map, pred_map,
   1.699 +                       arc_lists, flip_map);
   1.700 +      }
   1.701 +
   1.702 +      return true;
   1.703 +    }
   1.704 +
   1.705 +    /// \brief Gives back the successor of an arc
   1.706 +    ///
   1.707 +    /// Gives back the successor of an arc. This function makes
   1.708 +    /// possible to query the cyclic order of the outgoing arcs from
   1.709 +    /// a node.
   1.710 +    Arc next(const Arc& arc) const {
   1.711 +      return _embedding[arc];
   1.712 +    }
   1.713 +
   1.714 +    /// \brief Gives back the calculated embedding map
   1.715 +    ///
   1.716 +    /// The returned map contains the successor of each arc in the
   1.717 +    /// graph.
   1.718 +    const EmbeddingMap& embeddingMap() const {
   1.719 +      return _embedding;
   1.720 +    }
   1.721 +
   1.722 +    /// \brief Gives back true if the undirected arc is in the
   1.723 +    /// kuratowski subdivision
   1.724 +    ///
   1.725 +    /// Gives back true if the undirected arc is in the kuratowski
   1.726 +    /// subdivision
   1.727 +    /// \note The \c run() had to be called with true value.
   1.728 +    bool kuratowski(const Edge& edge) {
   1.729 +      return _kuratowski[edge];
   1.730 +    }
   1.731 +
   1.732 +  private:
   1.733 +
   1.734 +    void createChildLists(const TreeMap& tree_map, const OrderMap& order_map,
   1.735 +                          const LowMap& low_map, ChildLists& child_lists) {
   1.736 +
   1.737 +      for (NodeIt n(_graph); n != INVALID; ++n) {
   1.738 +        Node source = n;
   1.739 +
   1.740 +        std::vector<Node> targets;
   1.741 +        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
   1.742 +          Node target = _graph.target(e);
   1.743 +
   1.744 +          if (order_map[source] < order_map[target] && tree_map[e]) {
   1.745 +            targets.push_back(target);
   1.746 +          }
   1.747 +        }
   1.748 +
   1.749 +        if (targets.size() == 0) {
   1.750 +          child_lists[source].first = INVALID;
   1.751 +        } else if (targets.size() == 1) {
   1.752 +          child_lists[source].first = targets[0];
   1.753 +          child_lists[targets[0]].prev = INVALID;
   1.754 +          child_lists[targets[0]].next = INVALID;
   1.755 +        } else {
   1.756 +          radixSort(targets.begin(), targets.end(), mapToFunctor(low_map));
   1.757 +          for (int i = 1; i < int(targets.size()); ++i) {
   1.758 +            child_lists[targets[i]].prev = targets[i - 1];
   1.759 +            child_lists[targets[i - 1]].next = targets[i];
   1.760 +          }
   1.761 +          child_lists[targets.back()].next = INVALID;
   1.762 +          child_lists[targets.front()].prev = INVALID;
   1.763 +          child_lists[source].first = targets.front();
   1.764 +        }
   1.765 +      }
   1.766 +    }
   1.767 +
   1.768 +    void walkUp(const Node& node, Node root, int rorder,
   1.769 +                const PredMap& pred_map, const LowMap& low_map,
   1.770 +                const OrderMap& order_map, const OrderList& order_list,
   1.771 +                NodeData& node_data, MergeRoots& merge_roots) {
   1.772 +
   1.773 +      int na, nb;
   1.774 +      bool da, db;
   1.775 +
   1.776 +      na = nb = order_map[node];
   1.777 +      da = true; db = false;
   1.778 +
   1.779 +      while (true) {
   1.780 +
   1.781 +        if (node_data[na].visited == rorder) break;
   1.782 +        if (node_data[nb].visited == rorder) break;
   1.783 +
   1.784 +        node_data[na].visited = rorder;
   1.785 +        node_data[nb].visited = rorder;
   1.786 +
   1.787 +        int rn = -1;
   1.788 +
   1.789 +        if (na >= int(order_list.size())) {
   1.790 +          rn = na;
   1.791 +        } else if (nb >= int(order_list.size())) {
   1.792 +          rn = nb;
   1.793 +        }
   1.794 +
   1.795 +        if (rn == -1) {
   1.796 +          int nn;
   1.797 +
   1.798 +          nn = da ? node_data[na].prev : node_data[na].next;
   1.799 +          da = node_data[nn].prev != na;
   1.800 +          na = nn;
   1.801 +
   1.802 +          nn = db ? node_data[nb].prev : node_data[nb].next;
   1.803 +          db = node_data[nn].prev != nb;
   1.804 +          nb = nn;
   1.805 +
   1.806 +        } else {
   1.807 +
   1.808 +          Node rep = order_list[rn - order_list.size()];
   1.809 +          Node parent = _graph.source(pred_map[rep]);
   1.810 +
   1.811 +          if (low_map[rep] < rorder) {
   1.812 +            merge_roots[parent].push_back(rn);
   1.813 +          } else {
   1.814 +            merge_roots[parent].push_front(rn);
   1.815 +          }
   1.816 +
   1.817 +          if (parent != root) {
   1.818 +            na = nb = order_map[parent];
   1.819 +            da = true; db = false;
   1.820 +          } else {
   1.821 +            break;
   1.822 +          }
   1.823 +        }
   1.824 +      }
   1.825 +    }
   1.826 +
   1.827 +    void walkDown(int rn, int rorder, NodeData& node_data,
   1.828 +                  ArcLists& arc_lists, FlipMap& flip_map,
   1.829 +                  OrderList& order_list, ChildLists& child_lists,
   1.830 +                  AncestorMap& ancestor_map, LowMap& low_map,
   1.831 +                  EmbedArc& embed_arc, MergeRoots& merge_roots) {
   1.832 +
   1.833 +      std::vector<std::pair<int, bool> > merge_stack;
   1.834 +
   1.835 +      for (int di = 0; di < 2; ++di) {
   1.836 +        bool rd = di == 0;
   1.837 +        int pn = rn;
   1.838 +        int n = rd ? node_data[rn].next : node_data[rn].prev;
   1.839 +
   1.840 +        while (n != rn) {
   1.841 +
   1.842 +          Node node = order_list[n];
   1.843 +
   1.844 +          if (embed_arc[node] != INVALID) {
   1.845 +
   1.846 +            // Merging components on the critical path
   1.847 +            while (!merge_stack.empty()) {
   1.848 +
   1.849 +              // Component root
   1.850 +              int cn = merge_stack.back().first;
   1.851 +              bool cd = merge_stack.back().second;
   1.852 +              merge_stack.pop_back();
   1.853 +
   1.854 +              // Parent of component
   1.855 +              int dn = merge_stack.back().first;
   1.856 +              bool dd = merge_stack.back().second;
   1.857 +              merge_stack.pop_back();
   1.858 +
   1.859 +              Node parent = order_list[dn];
   1.860 +
   1.861 +              // Erasing from merge_roots
   1.862 +              merge_roots[parent].pop_front();
   1.863 +
   1.864 +              Node child = order_list[cn - order_list.size()];
   1.865 +
   1.866 +              // Erasing from child_lists
   1.867 +              if (child_lists[child].prev != INVALID) {
   1.868 +                child_lists[child_lists[child].prev].next =
   1.869 +                  child_lists[child].next;
   1.870 +              } else {
   1.871 +                child_lists[parent].first = child_lists[child].next;
   1.872 +              }
   1.873 +
   1.874 +              if (child_lists[child].next != INVALID) {
   1.875 +                child_lists[child_lists[child].next].prev =
   1.876 +                  child_lists[child].prev;
   1.877 +              }
   1.878 +
   1.879 +              // Merging arcs + flipping
   1.880 +              Arc de = node_data[dn].first;
   1.881 +              Arc ce = node_data[cn].first;
   1.882 +
   1.883 +              flip_map[order_list[cn - order_list.size()]] = cd != dd;
   1.884 +              if (cd != dd) {
   1.885 +                std::swap(arc_lists[ce].prev, arc_lists[ce].next);
   1.886 +                ce = arc_lists[ce].prev;
   1.887 +                std::swap(arc_lists[ce].prev, arc_lists[ce].next);
   1.888 +              }
   1.889 +
   1.890 +              {
   1.891 +                Arc dne = arc_lists[de].next;
   1.892 +                Arc cne = arc_lists[ce].next;
   1.893 +
   1.894 +                arc_lists[de].next = cne;
   1.895 +                arc_lists[ce].next = dne;
   1.896 +
   1.897 +                arc_lists[dne].prev = ce;
   1.898 +                arc_lists[cne].prev = de;
   1.899 +              }
   1.900 +
   1.901 +              if (dd) {
   1.902 +                node_data[dn].first = ce;
   1.903 +              }
   1.904 +
   1.905 +              // Merging external faces
   1.906 +              {
   1.907 +                int en = cn;
   1.908 +                cn = cd ? node_data[cn].prev : node_data[cn].next;
   1.909 +                cd = node_data[cn].next == en;
   1.910 +
   1.911 +                 if (node_data[cn].prev == node_data[cn].next &&
   1.912 +                    node_data[cn].inverted) {
   1.913 +                   cd = !cd;
   1.914 +                 }
   1.915 +              }
   1.916 +
   1.917 +              if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn;
   1.918 +              if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn;
   1.919 +
   1.920 +            }
   1.921 +
   1.922 +            bool d = pn == node_data[n].prev;
   1.923 +
   1.924 +            if (node_data[n].prev == node_data[n].next &&
   1.925 +                node_data[n].inverted) {
   1.926 +              d = !d;
   1.927 +            }
   1.928 +
   1.929 +            // Add new arc
   1.930 +            {
   1.931 +              Arc arc = embed_arc[node];
   1.932 +              Arc re = node_data[rn].first;
   1.933 +
   1.934 +              arc_lists[arc_lists[re].next].prev = arc;
   1.935 +              arc_lists[arc].next = arc_lists[re].next;
   1.936 +              arc_lists[arc].prev = re;
   1.937 +              arc_lists[re].next = arc;
   1.938 +
   1.939 +              if (!rd) {
   1.940 +                node_data[rn].first = arc;
   1.941 +              }
   1.942 +
   1.943 +              Arc rev = _graph.oppositeArc(arc);
   1.944 +              Arc e = node_data[n].first;
   1.945 +
   1.946 +              arc_lists[arc_lists[e].next].prev = rev;
   1.947 +              arc_lists[rev].next = arc_lists[e].next;
   1.948 +              arc_lists[rev].prev = e;
   1.949 +              arc_lists[e].next = rev;
   1.950 +
   1.951 +              if (d) {
   1.952 +                node_data[n].first = rev;
   1.953 +              }
   1.954 +
   1.955 +            }
   1.956 +
   1.957 +            // Embedding arc into external face
   1.958 +            if (rd) node_data[rn].next = n; else node_data[rn].prev = n;
   1.959 +            if (d) node_data[n].prev = rn; else node_data[n].next = rn;
   1.960 +            pn = rn;
   1.961 +
   1.962 +            embed_arc[order_list[n]] = INVALID;
   1.963 +          }
   1.964 +
   1.965 +          if (!merge_roots[node].empty()) {
   1.966 +
   1.967 +            bool d = pn == node_data[n].prev;
   1.968 +            if (node_data[n].prev == node_data[n].next &&
   1.969 +                node_data[n].inverted) {
   1.970 +              d = !d;
   1.971 +            }
   1.972 +
   1.973 +            merge_stack.push_back(std::make_pair(n, d));
   1.974 +
   1.975 +            int rn = merge_roots[node].front();
   1.976 +
   1.977 +            int xn = node_data[rn].next;
   1.978 +            Node xnode = order_list[xn];
   1.979 +
   1.980 +            int yn = node_data[rn].prev;
   1.981 +            Node ynode = order_list[yn];
   1.982 +
   1.983 +            bool rd;
   1.984 +            if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) {
   1.985 +              rd = true;
   1.986 +            } else if (!external(ynode, rorder, child_lists,
   1.987 +                                 ancestor_map, low_map)) {
   1.988 +              rd = false;
   1.989 +            } else if (pertinent(xnode, embed_arc, merge_roots)) {
   1.990 +              rd = true;
   1.991 +            } else {
   1.992 +              rd = false;
   1.993 +            }
   1.994 +
   1.995 +            merge_stack.push_back(std::make_pair(rn, rd));
   1.996 +
   1.997 +            pn = rn;
   1.998 +            n = rd ? xn : yn;
   1.999 +
  1.1000 +          } else if (!external(node, rorder, child_lists,
  1.1001 +                               ancestor_map, low_map)) {
  1.1002 +            int nn = (node_data[n].next != pn ?
  1.1003 +                      node_data[n].next : node_data[n].prev);
  1.1004 +
  1.1005 +            bool nd = n == node_data[nn].prev;
  1.1006 +
  1.1007 +            if (nd) node_data[nn].prev = pn;
  1.1008 +            else node_data[nn].next = pn;
  1.1009 +
  1.1010 +            if (n == node_data[pn].prev) node_data[pn].prev = nn;
  1.1011 +            else node_data[pn].next = nn;
  1.1012 +
  1.1013 +            node_data[nn].inverted =
  1.1014 +              (node_data[nn].prev == node_data[nn].next && nd != rd);
  1.1015 +
  1.1016 +            n = nn;
  1.1017 +          }
  1.1018 +          else break;
  1.1019 +
  1.1020 +        }
  1.1021 +
  1.1022 +        if (!merge_stack.empty() || n == rn) {
  1.1023 +          break;
  1.1024 +        }
  1.1025 +      }
  1.1026 +    }
  1.1027 +
  1.1028 +    void initFace(const Node& node, ArcLists& arc_lists,
  1.1029 +                  NodeData& node_data, const PredMap& pred_map,
  1.1030 +                  const OrderMap& order_map, const OrderList& order_list) {
  1.1031 +      int n = order_map[node];
  1.1032 +      int rn = n + order_list.size();
  1.1033 +
  1.1034 +      node_data[n].next = node_data[n].prev = rn;
  1.1035 +      node_data[rn].next = node_data[rn].prev = n;
  1.1036 +
  1.1037 +      node_data[n].visited = order_list.size();
  1.1038 +      node_data[rn].visited = order_list.size();
  1.1039 +
  1.1040 +      node_data[n].inverted = false;
  1.1041 +      node_data[rn].inverted = false;
  1.1042 +
  1.1043 +      Arc arc = pred_map[node];
  1.1044 +      Arc rev = _graph.oppositeArc(arc);
  1.1045 +
  1.1046 +      node_data[rn].first = arc;
  1.1047 +      node_data[n].first = rev;
  1.1048 +
  1.1049 +      arc_lists[arc].prev = arc;
  1.1050 +      arc_lists[arc].next = arc;
  1.1051 +
  1.1052 +      arc_lists[rev].prev = rev;
  1.1053 +      arc_lists[rev].next = rev;
  1.1054 +
  1.1055 +    }
  1.1056 +
  1.1057 +    void mergeRemainingFaces(const Node& node, NodeData& node_data,
  1.1058 +                             OrderList& order_list, OrderMap& order_map,
  1.1059 +                             ChildLists& child_lists, ArcLists& arc_lists) {
  1.1060 +      while (child_lists[node].first != INVALID) {
  1.1061 +        int dd = order_map[node];
  1.1062 +        Node child = child_lists[node].first;
  1.1063 +        int cd = order_map[child] + order_list.size();
  1.1064 +        child_lists[node].first = child_lists[child].next;
  1.1065 +
  1.1066 +        Arc de = node_data[dd].first;
  1.1067 +        Arc ce = node_data[cd].first;
  1.1068 +
  1.1069 +        if (de != INVALID) {
  1.1070 +          Arc dne = arc_lists[de].next;
  1.1071 +          Arc cne = arc_lists[ce].next;
  1.1072 +
  1.1073 +          arc_lists[de].next = cne;
  1.1074 +          arc_lists[ce].next = dne;
  1.1075 +
  1.1076 +          arc_lists[dne].prev = ce;
  1.1077 +          arc_lists[cne].prev = de;
  1.1078 +        }
  1.1079 +
  1.1080 +        node_data[dd].first = ce;
  1.1081 +
  1.1082 +      }
  1.1083 +    }
  1.1084 +
  1.1085 +    void storeEmbedding(const Node& node, NodeData& node_data,
  1.1086 +                        OrderMap& order_map, PredMap& pred_map,
  1.1087 +                        ArcLists& arc_lists, FlipMap& flip_map) {
  1.1088 +
  1.1089 +      if (node_data[order_map[node]].first == INVALID) return;
  1.1090 +
  1.1091 +      if (pred_map[node] != INVALID) {
  1.1092 +        Node source = _graph.source(pred_map[node]);
  1.1093 +        flip_map[node] = flip_map[node] != flip_map[source];
  1.1094 +      }
  1.1095 +
  1.1096 +      Arc first = node_data[order_map[node]].first;
  1.1097 +      Arc prev = first;
  1.1098 +
  1.1099 +      Arc arc = flip_map[node] ?
  1.1100 +        arc_lists[prev].prev : arc_lists[prev].next;
  1.1101 +
  1.1102 +      _embedding[prev] = arc;
  1.1103 +
  1.1104 +      while (arc != first) {
  1.1105 +        Arc next = arc_lists[arc].prev == prev ?
  1.1106 +          arc_lists[arc].next : arc_lists[arc].prev;
  1.1107 +        prev = arc; arc = next;
  1.1108 +        _embedding[prev] = arc;
  1.1109 +      }
  1.1110 +    }
  1.1111 +
  1.1112 +
  1.1113 +    bool external(const Node& node, int rorder,
  1.1114 +                  ChildLists& child_lists, AncestorMap& ancestor_map,
  1.1115 +                  LowMap& low_map) {
  1.1116 +      Node child = child_lists[node].first;
  1.1117 +
  1.1118 +      if (child != INVALID) {
  1.1119 +        if (low_map[child] < rorder) return true;
  1.1120 +      }
  1.1121 +
  1.1122 +      if (ancestor_map[node] < rorder) return true;
  1.1123 +
  1.1124 +      return false;
  1.1125 +    }
  1.1126 +
  1.1127 +    bool pertinent(const Node& node, const EmbedArc& embed_arc,
  1.1128 +                   const MergeRoots& merge_roots) {
  1.1129 +      return !merge_roots[node].empty() || embed_arc[node] != INVALID;
  1.1130 +    }
  1.1131 +
  1.1132 +    int lowPoint(const Node& node, OrderMap& order_map, ChildLists& child_lists,
  1.1133 +                 AncestorMap& ancestor_map, LowMap& low_map) {
  1.1134 +      int low_point;
  1.1135 +
  1.1136 +      Node child = child_lists[node].first;
  1.1137 +
  1.1138 +      if (child != INVALID) {
  1.1139 +        low_point = low_map[child];
  1.1140 +      } else {
  1.1141 +        low_point = order_map[node];
  1.1142 +      }
  1.1143 +
  1.1144 +      if (low_point > ancestor_map[node]) {
  1.1145 +        low_point = ancestor_map[node];
  1.1146 +      }
  1.1147 +
  1.1148 +      return low_point;
  1.1149 +    }
  1.1150 +
  1.1151 +    int findComponentRoot(Node root, Node node, ChildLists& child_lists,
  1.1152 +                          OrderMap& order_map, OrderList& order_list) {
  1.1153 +
  1.1154 +      int order = order_map[root];
  1.1155 +      int norder = order_map[node];
  1.1156 +
  1.1157 +      Node child = child_lists[root].first;
  1.1158 +      while (child != INVALID) {
  1.1159 +        int corder = order_map[child];
  1.1160 +        if (corder > order && corder < norder) {
  1.1161 +          order = corder;
  1.1162 +        }
  1.1163 +        child = child_lists[child].next;
  1.1164 +      }
  1.1165 +      return order + order_list.size();
  1.1166 +    }
  1.1167 +
  1.1168 +    Node findPertinent(Node node, OrderMap& order_map, NodeData& node_data,
  1.1169 +                       EmbedArc& embed_arc, MergeRoots& merge_roots) {
  1.1170 +      Node wnode =_graph.target(node_data[order_map[node]].first);
  1.1171 +      while (!pertinent(wnode, embed_arc, merge_roots)) {
  1.1172 +        wnode = _graph.target(node_data[order_map[wnode]].first);
  1.1173 +      }
  1.1174 +      return wnode;
  1.1175 +    }
  1.1176 +
  1.1177 +
  1.1178 +    Node findExternal(Node node, int rorder, OrderMap& order_map,
  1.1179 +                      ChildLists& child_lists, AncestorMap& ancestor_map,
  1.1180 +                      LowMap& low_map, NodeData& node_data) {
  1.1181 +      Node wnode =_graph.target(node_data[order_map[node]].first);
  1.1182 +      while (!external(wnode, rorder, child_lists, ancestor_map, low_map)) {
  1.1183 +        wnode = _graph.target(node_data[order_map[wnode]].first);
  1.1184 +      }
  1.1185 +      return wnode;
  1.1186 +    }
  1.1187 +
  1.1188 +    void markCommonPath(Node node, int rorder, Node& wnode, Node& znode,
  1.1189 +                        OrderList& order_list, OrderMap& order_map,
  1.1190 +                        NodeData& node_data, ArcLists& arc_lists,
  1.1191 +                        EmbedArc& embed_arc, MergeRoots& merge_roots,
  1.1192 +                        ChildLists& child_lists, AncestorMap& ancestor_map,
  1.1193 +                        LowMap& low_map) {
  1.1194 +
  1.1195 +      Node cnode = node;
  1.1196 +      Node pred = INVALID;
  1.1197 +
  1.1198 +      while (true) {
  1.1199 +
  1.1200 +        bool pert = pertinent(cnode, embed_arc, merge_roots);
  1.1201 +        bool ext = external(cnode, rorder, child_lists, ancestor_map, low_map);
  1.1202 +
  1.1203 +        if (pert && ext) {
  1.1204 +          if (!merge_roots[cnode].empty()) {
  1.1205 +            int cn = merge_roots[cnode].back();
  1.1206 +
  1.1207 +            if (low_map[order_list[cn - order_list.size()]] < rorder) {
  1.1208 +              Arc arc = node_data[cn].first;
  1.1209 +              _kuratowski.set(arc, true);
  1.1210 +
  1.1211 +              pred = cnode;
  1.1212 +              cnode = _graph.target(arc);
  1.1213 +
  1.1214 +              continue;
  1.1215 +            }
  1.1216 +          }
  1.1217 +          wnode = znode = cnode;
  1.1218 +          return;
  1.1219 +
  1.1220 +        } else if (pert) {
  1.1221 +          wnode = cnode;
  1.1222 +
  1.1223 +          while (!external(cnode, rorder, child_lists, ancestor_map, low_map)) {
  1.1224 +            Arc arc = node_data[order_map[cnode]].first;
  1.1225 +
  1.1226 +            if (_graph.target(arc) == pred) {
  1.1227 +              arc = arc_lists[arc].next;
  1.1228 +            }
  1.1229 +            _kuratowski.set(arc, true);
  1.1230 +
  1.1231 +            Node next = _graph.target(arc);
  1.1232 +            pred = cnode; cnode = next;
  1.1233 +          }
  1.1234 +
  1.1235 +          znode = cnode;
  1.1236 +          return;
  1.1237 +
  1.1238 +        } else if (ext) {
  1.1239 +          znode = cnode;
  1.1240 +
  1.1241 +          while (!pertinent(cnode, embed_arc, merge_roots)) {
  1.1242 +            Arc arc = node_data[order_map[cnode]].first;
  1.1243 +
  1.1244 +            if (_graph.target(arc) == pred) {
  1.1245 +              arc = arc_lists[arc].next;
  1.1246 +            }
  1.1247 +            _kuratowski.set(arc, true);
  1.1248 +
  1.1249 +            Node next = _graph.target(arc);
  1.1250 +            pred = cnode; cnode = next;
  1.1251 +          }
  1.1252 +
  1.1253 +          wnode = cnode;
  1.1254 +          return;
  1.1255 +
  1.1256 +        } else {
  1.1257 +          Arc arc = node_data[order_map[cnode]].first;
  1.1258 +
  1.1259 +          if (_graph.target(arc) == pred) {
  1.1260 +            arc = arc_lists[arc].next;
  1.1261 +          }
  1.1262 +          _kuratowski.set(arc, true);
  1.1263 +
  1.1264 +          Node next = _graph.target(arc);
  1.1265 +          pred = cnode; cnode = next;
  1.1266 +        }
  1.1267 +
  1.1268 +      }
  1.1269 +
  1.1270 +    }
  1.1271 +
  1.1272 +    void orientComponent(Node root, int rn, OrderMap& order_map,
  1.1273 +                         PredMap& pred_map, NodeData& node_data,
  1.1274 +                         ArcLists& arc_lists, FlipMap& flip_map,
  1.1275 +                         TypeMap& type_map) {
  1.1276 +      node_data[order_map[root]].first = node_data[rn].first;
  1.1277 +      type_map[root] = 1;
  1.1278 +
  1.1279 +      std::vector<Node> st, qu;
  1.1280 +
  1.1281 +      st.push_back(root);
  1.1282 +      while (!st.empty()) {
  1.1283 +        Node node = st.back();
  1.1284 +        st.pop_back();
  1.1285 +        qu.push_back(node);
  1.1286 +
  1.1287 +        Arc arc = node_data[order_map[node]].first;
  1.1288 +
  1.1289 +        if (type_map[_graph.target(arc)] == 0) {
  1.1290 +          st.push_back(_graph.target(arc));
  1.1291 +          type_map[_graph.target(arc)] = 1;
  1.1292 +        }
  1.1293 +
  1.1294 +        Arc last = arc, pred = arc;
  1.1295 +        arc = arc_lists[arc].next;
  1.1296 +        while (arc != last) {
  1.1297 +
  1.1298 +          if (type_map[_graph.target(arc)] == 0) {
  1.1299 +            st.push_back(_graph.target(arc));
  1.1300 +            type_map[_graph.target(arc)] = 1;
  1.1301 +          }
  1.1302 +
  1.1303 +          Arc next = arc_lists[arc].next != pred ?
  1.1304 +            arc_lists[arc].next : arc_lists[arc].prev;
  1.1305 +          pred = arc; arc = next;
  1.1306 +        }
  1.1307 +
  1.1308 +      }
  1.1309 +
  1.1310 +      type_map[root] = 2;
  1.1311 +      flip_map[root] = false;
  1.1312 +
  1.1313 +      for (int i = 1; i < int(qu.size()); ++i) {
  1.1314 +
  1.1315 +        Node node = qu[i];
  1.1316 +
  1.1317 +        while (type_map[node] != 2) {
  1.1318 +          st.push_back(node);
  1.1319 +          type_map[node] = 2;
  1.1320 +          node = _graph.source(pred_map[node]);
  1.1321 +        }
  1.1322 +
  1.1323 +        bool flip = flip_map[node];
  1.1324 +
  1.1325 +        while (!st.empty()) {
  1.1326 +          node = st.back();
  1.1327 +          st.pop_back();
  1.1328 +
  1.1329 +          flip_map[node] = flip != flip_map[node];
  1.1330 +          flip = flip_map[node];
  1.1331 +
  1.1332 +          if (flip) {
  1.1333 +            Arc arc = node_data[order_map[node]].first;
  1.1334 +            std::swap(arc_lists[arc].prev, arc_lists[arc].next);
  1.1335 +            arc = arc_lists[arc].prev;
  1.1336 +            std::swap(arc_lists[arc].prev, arc_lists[arc].next);
  1.1337 +            node_data[order_map[node]].first = arc;
  1.1338 +          }
  1.1339 +        }
  1.1340 +      }
  1.1341 +
  1.1342 +      for (int i = 0; i < int(qu.size()); ++i) {
  1.1343 +
  1.1344 +        Arc arc = node_data[order_map[qu[i]]].first;
  1.1345 +        Arc last = arc, pred = arc;
  1.1346 +
  1.1347 +        arc = arc_lists[arc].next;
  1.1348 +        while (arc != last) {
  1.1349 +
  1.1350 +          if (arc_lists[arc].next == pred) {
  1.1351 +            std::swap(arc_lists[arc].next, arc_lists[arc].prev);
  1.1352 +          }
  1.1353 +          pred = arc; arc = arc_lists[arc].next;
  1.1354 +        }
  1.1355 +
  1.1356 +      }
  1.1357 +    }
  1.1358 +
  1.1359 +    void setFaceFlags(Node root, Node wnode, Node ynode, Node xnode,
  1.1360 +                      OrderMap& order_map, NodeData& node_data,
  1.1361 +                      TypeMap& type_map) {
  1.1362 +      Node node = _graph.target(node_data[order_map[root]].first);
  1.1363 +
  1.1364 +      while (node != ynode) {
  1.1365 +        type_map[node] = HIGHY;
  1.1366 +        node = _graph.target(node_data[order_map[node]].first);
  1.1367 +      }
  1.1368 +
  1.1369 +      while (node != wnode) {
  1.1370 +        type_map[node] = LOWY;
  1.1371 +        node = _graph.target(node_data[order_map[node]].first);
  1.1372 +      }
  1.1373 +
  1.1374 +      node = _graph.target(node_data[order_map[wnode]].first);
  1.1375 +
  1.1376 +      while (node != xnode) {
  1.1377 +        type_map[node] = LOWX;
  1.1378 +        node = _graph.target(node_data[order_map[node]].first);
  1.1379 +      }
  1.1380 +      type_map[node] = LOWX;
  1.1381 +
  1.1382 +      node = _graph.target(node_data[order_map[xnode]].first);
  1.1383 +      while (node != root) {
  1.1384 +        type_map[node] = HIGHX;
  1.1385 +        node = _graph.target(node_data[order_map[node]].first);
  1.1386 +      }
  1.1387 +
  1.1388 +      type_map[wnode] = PERTINENT;
  1.1389 +      type_map[root] = ROOT;
  1.1390 +    }
  1.1391 +
  1.1392 +    void findInternalPath(std::vector<Arc>& ipath,
  1.1393 +                          Node wnode, Node root, TypeMap& type_map,
  1.1394 +                          OrderMap& order_map, NodeData& node_data,
  1.1395 +                          ArcLists& arc_lists) {
  1.1396 +      std::vector<Arc> st;
  1.1397 +
  1.1398 +      Node node = wnode;
  1.1399 +
  1.1400 +      while (node != root) {
  1.1401 +        Arc arc = arc_lists[node_data[order_map[node]].first].next;
  1.1402 +        st.push_back(arc);
  1.1403 +        node = _graph.target(arc);
  1.1404 +      }
  1.1405 +
  1.1406 +      while (true) {
  1.1407 +        Arc arc = st.back();
  1.1408 +        if (type_map[_graph.target(arc)] == LOWX ||
  1.1409 +            type_map[_graph.target(arc)] == HIGHX) {
  1.1410 +          break;
  1.1411 +        }
  1.1412 +        if (type_map[_graph.target(arc)] == 2) {
  1.1413 +          type_map[_graph.target(arc)] = 3;
  1.1414 +
  1.1415 +          arc = arc_lists[_graph.oppositeArc(arc)].next;
  1.1416 +          st.push_back(arc);
  1.1417 +        } else {
  1.1418 +          st.pop_back();
  1.1419 +          arc = arc_lists[arc].next;
  1.1420 +
  1.1421 +          while (_graph.oppositeArc(arc) == st.back()) {
  1.1422 +            arc = st.back();
  1.1423 +            st.pop_back();
  1.1424 +            arc = arc_lists[arc].next;
  1.1425 +          }
  1.1426 +          st.push_back(arc);
  1.1427 +        }
  1.1428 +      }
  1.1429 +
  1.1430 +      for (int i = 0; i < int(st.size()); ++i) {
  1.1431 +        if (type_map[_graph.target(st[i])] != LOWY &&
  1.1432 +            type_map[_graph.target(st[i])] != HIGHY) {
  1.1433 +          for (; i < int(st.size()); ++i) {
  1.1434 +            ipath.push_back(st[i]);
  1.1435 +          }
  1.1436 +        }
  1.1437 +      }
  1.1438 +    }
  1.1439 +
  1.1440 +    void setInternalFlags(std::vector<Arc>& ipath, TypeMap& type_map) {
  1.1441 +      for (int i = 1; i < int(ipath.size()); ++i) {
  1.1442 +        type_map[_graph.source(ipath[i])] = INTERNAL;
  1.1443 +      }
  1.1444 +    }
  1.1445 +
  1.1446 +    void findPilePath(std::vector<Arc>& ppath,
  1.1447 +                      Node root, TypeMap& type_map, OrderMap& order_map,
  1.1448 +                      NodeData& node_data, ArcLists& arc_lists) {
  1.1449 +      std::vector<Arc> st;
  1.1450 +
  1.1451 +      st.push_back(_graph.oppositeArc(node_data[order_map[root]].first));
  1.1452 +      st.push_back(node_data[order_map[root]].first);
  1.1453 +
  1.1454 +      while (st.size() > 1) {
  1.1455 +        Arc arc = st.back();
  1.1456 +        if (type_map[_graph.target(arc)] == INTERNAL) {
  1.1457 +          break;
  1.1458 +        }
  1.1459 +        if (type_map[_graph.target(arc)] == 3) {
  1.1460 +          type_map[_graph.target(arc)] = 4;
  1.1461 +
  1.1462 +          arc = arc_lists[_graph.oppositeArc(arc)].next;
  1.1463 +          st.push_back(arc);
  1.1464 +        } else {
  1.1465 +          st.pop_back();
  1.1466 +          arc = arc_lists[arc].next;
  1.1467 +
  1.1468 +          while (!st.empty() && _graph.oppositeArc(arc) == st.back()) {
  1.1469 +            arc = st.back();
  1.1470 +            st.pop_back();
  1.1471 +            arc = arc_lists[arc].next;
  1.1472 +          }
  1.1473 +          st.push_back(arc);
  1.1474 +        }
  1.1475 +      }
  1.1476 +
  1.1477 +      for (int i = 1; i < int(st.size()); ++i) {
  1.1478 +        ppath.push_back(st[i]);
  1.1479 +      }
  1.1480 +    }
  1.1481 +
  1.1482 +
  1.1483 +    int markExternalPath(Node node, OrderMap& order_map,
  1.1484 +                         ChildLists& child_lists, PredMap& pred_map,
  1.1485 +                         AncestorMap& ancestor_map, LowMap& low_map) {
  1.1486 +      int lp = lowPoint(node, order_map, child_lists,
  1.1487 +                        ancestor_map, low_map);
  1.1488 +
  1.1489 +      if (ancestor_map[node] != lp) {
  1.1490 +        node = child_lists[node].first;
  1.1491 +        _kuratowski[pred_map[node]] = true;
  1.1492 +
  1.1493 +        while (ancestor_map[node] != lp) {
  1.1494 +          for (OutArcIt e(_graph, node); e != INVALID; ++e) {
  1.1495 +            Node tnode = _graph.target(e);
  1.1496 +            if (order_map[tnode] > order_map[node] && low_map[tnode] == lp) {
  1.1497 +              node = tnode;
  1.1498 +              _kuratowski[e] = true;
  1.1499 +              break;
  1.1500 +            }
  1.1501 +          }
  1.1502 +        }
  1.1503 +      }
  1.1504 +
  1.1505 +      for (OutArcIt e(_graph, node); e != INVALID; ++e) {
  1.1506 +        if (order_map[_graph.target(e)] == lp) {
  1.1507 +          _kuratowski[e] = true;
  1.1508 +          break;
  1.1509 +        }
  1.1510 +      }
  1.1511 +
  1.1512 +      return lp;
  1.1513 +    }
  1.1514 +
  1.1515 +    void markPertinentPath(Node node, OrderMap& order_map,
  1.1516 +                           NodeData& node_data, ArcLists& arc_lists,
  1.1517 +                           EmbedArc& embed_arc, MergeRoots& merge_roots) {
  1.1518 +      while (embed_arc[node] == INVALID) {
  1.1519 +        int n = merge_roots[node].front();
  1.1520 +        Arc arc = node_data[n].first;
  1.1521 +
  1.1522 +        _kuratowski.set(arc, true);
  1.1523 +
  1.1524 +        Node pred = node;
  1.1525 +        node = _graph.target(arc);
  1.1526 +        while (!pertinent(node, embed_arc, merge_roots)) {
  1.1527 +          arc = node_data[order_map[node]].first;
  1.1528 +          if (_graph.target(arc) == pred) {
  1.1529 +            arc = arc_lists[arc].next;
  1.1530 +          }
  1.1531 +          _kuratowski.set(arc, true);
  1.1532 +          pred = node;
  1.1533 +          node = _graph.target(arc);
  1.1534 +        }
  1.1535 +      }
  1.1536 +      _kuratowski.set(embed_arc[node], true);
  1.1537 +    }
  1.1538 +
  1.1539 +    void markPredPath(Node node, Node snode, PredMap& pred_map) {
  1.1540 +      while (node != snode) {
  1.1541 +        _kuratowski.set(pred_map[node], true);
  1.1542 +        node = _graph.source(pred_map[node]);
  1.1543 +      }
  1.1544 +    }
  1.1545 +
  1.1546 +    void markFacePath(Node ynode, Node xnode,
  1.1547 +                      OrderMap& order_map, NodeData& node_data) {
  1.1548 +      Arc arc = node_data[order_map[ynode]].first;
  1.1549 +      Node node = _graph.target(arc);
  1.1550 +      _kuratowski.set(arc, true);
  1.1551 +
  1.1552 +      while (node != xnode) {
  1.1553 +        arc = node_data[order_map[node]].first;
  1.1554 +        _kuratowski.set(arc, true);
  1.1555 +        node = _graph.target(arc);
  1.1556 +      }
  1.1557 +    }
  1.1558 +
  1.1559 +    void markInternalPath(std::vector<Arc>& path) {
  1.1560 +      for (int i = 0; i < int(path.size()); ++i) {
  1.1561 +        _kuratowski.set(path[i], true);
  1.1562 +      }
  1.1563 +    }
  1.1564 +
  1.1565 +    void markPilePath(std::vector<Arc>& path) {
  1.1566 +      for (int i = 0; i < int(path.size()); ++i) {
  1.1567 +        _kuratowski.set(path[i], true);
  1.1568 +      }
  1.1569 +    }
  1.1570 +
  1.1571 +    void isolateKuratowski(Arc arc, NodeData& node_data,
  1.1572 +                           ArcLists& arc_lists, FlipMap& flip_map,
  1.1573 +                           OrderMap& order_map, OrderList& order_list,
  1.1574 +                           PredMap& pred_map, ChildLists& child_lists,
  1.1575 +                           AncestorMap& ancestor_map, LowMap& low_map,
  1.1576 +                           EmbedArc& embed_arc, MergeRoots& merge_roots) {
  1.1577 +
  1.1578 +      Node root = _graph.source(arc);
  1.1579 +      Node enode = _graph.target(arc);
  1.1580 +
  1.1581 +      int rorder = order_map[root];
  1.1582 +
  1.1583 +      TypeMap type_map(_graph, 0);
  1.1584 +
  1.1585 +      int rn = findComponentRoot(root, enode, child_lists,
  1.1586 +                                 order_map, order_list);
  1.1587 +
  1.1588 +      Node xnode = order_list[node_data[rn].next];
  1.1589 +      Node ynode = order_list[node_data[rn].prev];
  1.1590 +
  1.1591 +      // Minor-A
  1.1592 +      {
  1.1593 +        while (!merge_roots[xnode].empty() || !merge_roots[ynode].empty()) {
  1.1594 +
  1.1595 +          if (!merge_roots[xnode].empty()) {
  1.1596 +            root = xnode;
  1.1597 +            rn = merge_roots[xnode].front();
  1.1598 +          } else {
  1.1599 +            root = ynode;
  1.1600 +            rn = merge_roots[ynode].front();
  1.1601 +          }
  1.1602 +
  1.1603 +          xnode = order_list[node_data[rn].next];
  1.1604 +          ynode = order_list[node_data[rn].prev];
  1.1605 +        }
  1.1606 +
  1.1607 +        if (root != _graph.source(arc)) {
  1.1608 +          orientComponent(root, rn, order_map, pred_map,
  1.1609 +                          node_data, arc_lists, flip_map, type_map);
  1.1610 +          markFacePath(root, root, order_map, node_data);
  1.1611 +          int xlp = markExternalPath(xnode, order_map, child_lists,
  1.1612 +                                     pred_map, ancestor_map, low_map);
  1.1613 +          int ylp = markExternalPath(ynode, order_map, child_lists,
  1.1614 +                                     pred_map, ancestor_map, low_map);
  1.1615 +          markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
  1.1616 +          Node lwnode = findPertinent(ynode, order_map, node_data,
  1.1617 +                                      embed_arc, merge_roots);
  1.1618 +
  1.1619 +          markPertinentPath(lwnode, order_map, node_data, arc_lists,
  1.1620 +                            embed_arc, merge_roots);
  1.1621 +
  1.1622 +          return;
  1.1623 +        }
  1.1624 +      }
  1.1625 +
  1.1626 +      orientComponent(root, rn, order_map, pred_map,
  1.1627 +                      node_data, arc_lists, flip_map, type_map);
  1.1628 +
  1.1629 +      Node wnode = findPertinent(ynode, order_map, node_data,
  1.1630 +                                 embed_arc, merge_roots);
  1.1631 +      setFaceFlags(root, wnode, ynode, xnode, order_map, node_data, type_map);
  1.1632 +
  1.1633 +
  1.1634 +      //Minor-B
  1.1635 +      if (!merge_roots[wnode].empty()) {
  1.1636 +        int cn = merge_roots[wnode].back();
  1.1637 +        Node rep = order_list[cn - order_list.size()];
  1.1638 +        if (low_map[rep] < rorder) {
  1.1639 +          markFacePath(root, root, order_map, node_data);
  1.1640 +          int xlp = markExternalPath(xnode, order_map, child_lists,
  1.1641 +                                     pred_map, ancestor_map, low_map);
  1.1642 +          int ylp = markExternalPath(ynode, order_map, child_lists,
  1.1643 +                                     pred_map, ancestor_map, low_map);
  1.1644 +
  1.1645 +          Node lwnode, lznode;
  1.1646 +          markCommonPath(wnode, rorder, lwnode, lznode, order_list,
  1.1647 +                         order_map, node_data, arc_lists, embed_arc,
  1.1648 +                         merge_roots, child_lists, ancestor_map, low_map);
  1.1649 +
  1.1650 +          markPertinentPath(lwnode, order_map, node_data, arc_lists,
  1.1651 +                            embed_arc, merge_roots);
  1.1652 +          int zlp = markExternalPath(lznode, order_map, child_lists,
  1.1653 +                                     pred_map, ancestor_map, low_map);
  1.1654 +
  1.1655 +          int minlp = xlp < ylp ? xlp : ylp;
  1.1656 +          if (zlp < minlp) minlp = zlp;
  1.1657 +
  1.1658 +          int maxlp = xlp > ylp ? xlp : ylp;
  1.1659 +          if (zlp > maxlp) maxlp = zlp;
  1.1660 +
  1.1661 +          markPredPath(order_list[maxlp], order_list[minlp], pred_map);
  1.1662 +
  1.1663 +          return;
  1.1664 +        }
  1.1665 +      }
  1.1666 +
  1.1667 +      Node pxnode, pynode;
  1.1668 +      std::vector<Arc> ipath;
  1.1669 +      findInternalPath(ipath, wnode, root, type_map, order_map,
  1.1670 +                       node_data, arc_lists);
  1.1671 +      setInternalFlags(ipath, type_map);
  1.1672 +      pynode = _graph.source(ipath.front());
  1.1673 +      pxnode = _graph.target(ipath.back());
  1.1674 +
  1.1675 +      wnode = findPertinent(pynode, order_map, node_data,
  1.1676 +                            embed_arc, merge_roots);
  1.1677 +
  1.1678 +      // Minor-C
  1.1679 +      {
  1.1680 +        if (type_map[_graph.source(ipath.front())] == HIGHY) {
  1.1681 +          if (type_map[_graph.target(ipath.back())] == HIGHX) {
  1.1682 +            markFacePath(xnode, pxnode, order_map, node_data);
  1.1683 +          }
  1.1684 +          markFacePath(root, xnode, order_map, node_data);
  1.1685 +          markPertinentPath(wnode, order_map, node_data, arc_lists,
  1.1686 +                            embed_arc, merge_roots);
  1.1687 +          markInternalPath(ipath);
  1.1688 +          int xlp = markExternalPath(xnode, order_map, child_lists,
  1.1689 +                                     pred_map, ancestor_map, low_map);
  1.1690 +          int ylp = markExternalPath(ynode, order_map, child_lists,
  1.1691 +                                     pred_map, ancestor_map, low_map);
  1.1692 +          markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
  1.1693 +          return;
  1.1694 +        }
  1.1695 +
  1.1696 +        if (type_map[_graph.target(ipath.back())] == HIGHX) {
  1.1697 +          markFacePath(ynode, root, order_map, node_data);
  1.1698 +          markPertinentPath(wnode, order_map, node_data, arc_lists,
  1.1699 +                            embed_arc, merge_roots);
  1.1700 +          markInternalPath(ipath);
  1.1701 +          int xlp = markExternalPath(xnode, order_map, child_lists,
  1.1702 +                                     pred_map, ancestor_map, low_map);
  1.1703 +          int ylp = markExternalPath(ynode, order_map, child_lists,
  1.1704 +                                     pred_map, ancestor_map, low_map);
  1.1705 +          markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
  1.1706 +          return;
  1.1707 +        }
  1.1708 +      }
  1.1709 +
  1.1710 +      std::vector<Arc> ppath;
  1.1711 +      findPilePath(ppath, root, type_map, order_map, node_data, arc_lists);
  1.1712 +
  1.1713 +      // Minor-D
  1.1714 +      if (!ppath.empty()) {
  1.1715 +        markFacePath(ynode, xnode, order_map, node_data);
  1.1716 +        markPertinentPath(wnode, order_map, node_data, arc_lists,
  1.1717 +                          embed_arc, merge_roots);
  1.1718 +        markPilePath(ppath);
  1.1719 +        markInternalPath(ipath);
  1.1720 +        int xlp = markExternalPath(xnode, order_map, child_lists,
  1.1721 +                                   pred_map, ancestor_map, low_map);
  1.1722 +        int ylp = markExternalPath(ynode, order_map, child_lists,
  1.1723 +                                   pred_map, ancestor_map, low_map);
  1.1724 +        markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
  1.1725 +        return;
  1.1726 +      }
  1.1727 +
  1.1728 +      // Minor-E*
  1.1729 +      {
  1.1730 +
  1.1731 +        if (!external(wnode, rorder, child_lists, ancestor_map, low_map)) {
  1.1732 +          Node znode = findExternal(pynode, rorder, order_map,
  1.1733 +                                    child_lists, ancestor_map,
  1.1734 +                                    low_map, node_data);
  1.1735 +
  1.1736 +          if (type_map[znode] == LOWY) {
  1.1737 +            markFacePath(root, xnode, order_map, node_data);
  1.1738 +            markPertinentPath(wnode, order_map, node_data, arc_lists,
  1.1739 +                              embed_arc, merge_roots);
  1.1740 +            markInternalPath(ipath);
  1.1741 +            int xlp = markExternalPath(xnode, order_map, child_lists,
  1.1742 +                                       pred_map, ancestor_map, low_map);
  1.1743 +            int zlp = markExternalPath(znode, order_map, child_lists,
  1.1744 +                                       pred_map, ancestor_map, low_map);
  1.1745 +            markPredPath(root, order_list[xlp < zlp ? xlp : zlp], pred_map);
  1.1746 +          } else {
  1.1747 +            markFacePath(ynode, root, order_map, node_data);
  1.1748 +            markPertinentPath(wnode, order_map, node_data, arc_lists,
  1.1749 +                              embed_arc, merge_roots);
  1.1750 +            markInternalPath(ipath);
  1.1751 +            int ylp = markExternalPath(ynode, order_map, child_lists,
  1.1752 +                                       pred_map, ancestor_map, low_map);
  1.1753 +            int zlp = markExternalPath(znode, order_map, child_lists,
  1.1754 +                                       pred_map, ancestor_map, low_map);
  1.1755 +            markPredPath(root, order_list[ylp < zlp ? ylp : zlp], pred_map);
  1.1756 +          }
  1.1757 +          return;
  1.1758 +        }
  1.1759 +
  1.1760 +        int xlp = markExternalPath(xnode, order_map, child_lists,
  1.1761 +                                   pred_map, ancestor_map, low_map);
  1.1762 +        int ylp = markExternalPath(ynode, order_map, child_lists,
  1.1763 +                                   pred_map, ancestor_map, low_map);
  1.1764 +        int wlp = markExternalPath(wnode, order_map, child_lists,
  1.1765 +                                   pred_map, ancestor_map, low_map);
  1.1766 +
  1.1767 +        if (wlp > xlp && wlp > ylp) {
  1.1768 +          markFacePath(root, root, order_map, node_data);
  1.1769 +          markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
  1.1770 +          return;
  1.1771 +        }
  1.1772 +
  1.1773 +        markInternalPath(ipath);
  1.1774 +        markPertinentPath(wnode, order_map, node_data, arc_lists,
  1.1775 +                          embed_arc, merge_roots);
  1.1776 +
  1.1777 +        if (xlp > ylp && xlp > wlp) {
  1.1778 +          markFacePath(root, pynode, order_map, node_data);
  1.1779 +          markFacePath(wnode, xnode, order_map, node_data);
  1.1780 +          markPredPath(root, order_list[ylp < wlp ? ylp : wlp], pred_map);
  1.1781 +          return;
  1.1782 +        }
  1.1783 +
  1.1784 +        if (ylp > xlp && ylp > wlp) {
  1.1785 +          markFacePath(pxnode, root, order_map, node_data);
  1.1786 +          markFacePath(ynode, wnode, order_map, node_data);
  1.1787 +          markPredPath(root, order_list[xlp < wlp ? xlp : wlp], pred_map);
  1.1788 +          return;
  1.1789 +        }
  1.1790 +
  1.1791 +        if (pynode != ynode) {
  1.1792 +          markFacePath(pxnode, wnode, order_map, node_data);
  1.1793 +
  1.1794 +          int minlp = xlp < ylp ? xlp : ylp;
  1.1795 +          if (wlp < minlp) minlp = wlp;
  1.1796 +
  1.1797 +          int maxlp = xlp > ylp ? xlp : ylp;
  1.1798 +          if (wlp > maxlp) maxlp = wlp;
  1.1799 +
  1.1800 +          markPredPath(order_list[maxlp], order_list[minlp], pred_map);
  1.1801 +          return;
  1.1802 +        }
  1.1803 +
  1.1804 +        if (pxnode != xnode) {
  1.1805 +          markFacePath(wnode, pynode, order_map, node_data);
  1.1806 +
  1.1807 +          int minlp = xlp < ylp ? xlp : ylp;
  1.1808 +          if (wlp < minlp) minlp = wlp;
  1.1809 +
  1.1810 +          int maxlp = xlp > ylp ? xlp : ylp;
  1.1811 +          if (wlp > maxlp) maxlp = wlp;
  1.1812 +
  1.1813 +          markPredPath(order_list[maxlp], order_list[minlp], pred_map);
  1.1814 +          return;
  1.1815 +        }
  1.1816 +
  1.1817 +        markFacePath(root, root, order_map, node_data);
  1.1818 +        int minlp = xlp < ylp ? xlp : ylp;
  1.1819 +        if (wlp < minlp) minlp = wlp;
  1.1820 +        markPredPath(root, order_list[minlp], pred_map);
  1.1821 +        return;
  1.1822 +      }
  1.1823 +
  1.1824 +    }
  1.1825 +
  1.1826 +  };
  1.1827 +
  1.1828 +  namespace _planarity_bits {
  1.1829 +
  1.1830 +    template <typename Graph, typename EmbeddingMap>
  1.1831 +    void makeConnected(Graph& graph, EmbeddingMap& embedding) {
  1.1832 +      DfsVisitor<Graph> null_visitor;
  1.1833 +      DfsVisit<Graph, DfsVisitor<Graph> > dfs(graph, null_visitor);
  1.1834 +      dfs.init();
  1.1835 +
  1.1836 +      typename Graph::Node u = INVALID;
  1.1837 +      for (typename Graph::NodeIt n(graph); n != INVALID; ++n) {
  1.1838 +        if (!dfs.reached(n)) {
  1.1839 +          dfs.addSource(n);
  1.1840 +          dfs.start();
  1.1841 +          if (u == INVALID) {
  1.1842 +            u = n;
  1.1843 +          } else {
  1.1844 +            typename Graph::Node v = n;
  1.1845 +
  1.1846 +            typename Graph::Arc ue = typename Graph::OutArcIt(graph, u);
  1.1847 +            typename Graph::Arc ve = typename Graph::OutArcIt(graph, v);
  1.1848 +
  1.1849 +            typename Graph::Arc e = graph.direct(graph.addEdge(u, v), true);
  1.1850 +
  1.1851 +            if (ue != INVALID) {
  1.1852 +              embedding[e] = embedding[ue];
  1.1853 +              embedding[ue] = e;
  1.1854 +            } else {
  1.1855 +              embedding[e] = e;
  1.1856 +            }
  1.1857 +
  1.1858 +            if (ve != INVALID) {
  1.1859 +              embedding[graph.oppositeArc(e)] = embedding[ve];
  1.1860 +              embedding[ve] = graph.oppositeArc(e);
  1.1861 +            } else {
  1.1862 +              embedding[graph.oppositeArc(e)] = graph.oppositeArc(e);
  1.1863 +            }
  1.1864 +          }
  1.1865 +        }
  1.1866 +      }
  1.1867 +    }
  1.1868 +
  1.1869 +    template <typename Graph, typename EmbeddingMap>
  1.1870 +    void makeBiNodeConnected(Graph& graph, EmbeddingMap& embedding) {
  1.1871 +      typename Graph::template ArcMap<bool> processed(graph);
  1.1872 +
  1.1873 +      std::vector<typename Graph::Arc> arcs;
  1.1874 +      for (typename Graph::ArcIt e(graph); e != INVALID; ++e) {
  1.1875 +        arcs.push_back(e);
  1.1876 +      }
  1.1877 +
  1.1878 +      IterableBoolMap<Graph, typename Graph::Node> visited(graph, false);
  1.1879 +
  1.1880 +      for (int i = 0; i < int(arcs.size()); ++i) {
  1.1881 +        typename Graph::Arc pp = arcs[i];
  1.1882 +        if (processed[pp]) continue;
  1.1883 +
  1.1884 +        typename Graph::Arc e = embedding[graph.oppositeArc(pp)];
  1.1885 +        processed[e] = true;
  1.1886 +        visited.set(graph.source(e), true);
  1.1887 +
  1.1888 +        typename Graph::Arc p = e, l = e;
  1.1889 +        e = embedding[graph.oppositeArc(e)];
  1.1890 +
  1.1891 +        while (e != l) {
  1.1892 +          processed[e] = true;
  1.1893 +
  1.1894 +          if (visited[graph.source(e)]) {
  1.1895 +
  1.1896 +            typename Graph::Arc n =
  1.1897 +              graph.direct(graph.addEdge(graph.source(p),
  1.1898 +                                           graph.target(e)), true);
  1.1899 +            embedding[n] = p;
  1.1900 +            embedding[graph.oppositeArc(pp)] = n;
  1.1901 +
  1.1902 +            embedding[graph.oppositeArc(n)] =
  1.1903 +              embedding[graph.oppositeArc(e)];
  1.1904 +            embedding[graph.oppositeArc(e)] =
  1.1905 +              graph.oppositeArc(n);
  1.1906 +
  1.1907 +            p = n;
  1.1908 +            e = embedding[graph.oppositeArc(n)];
  1.1909 +          } else {
  1.1910 +            visited.set(graph.source(e), true);
  1.1911 +            pp = p;
  1.1912 +            p = e;
  1.1913 +            e = embedding[graph.oppositeArc(e)];
  1.1914 +          }
  1.1915 +        }
  1.1916 +        visited.setAll(false);
  1.1917 +      }
  1.1918 +    }
  1.1919 +
  1.1920 +
  1.1921 +    template <typename Graph, typename EmbeddingMap>
  1.1922 +    void makeMaxPlanar(Graph& graph, EmbeddingMap& embedding) {
  1.1923 +
  1.1924 +      typename Graph::template NodeMap<int> degree(graph);
  1.1925 +
  1.1926 +      for (typename Graph::NodeIt n(graph); n != INVALID; ++n) {
  1.1927 +        degree[n] = countIncEdges(graph, n);
  1.1928 +      }
  1.1929 +
  1.1930 +      typename Graph::template ArcMap<bool> processed(graph);
  1.1931 +      IterableBoolMap<Graph, typename Graph::Node> visited(graph, false);
  1.1932 +
  1.1933 +      std::vector<typename Graph::Arc> arcs;
  1.1934 +      for (typename Graph::ArcIt e(graph); e != INVALID; ++e) {
  1.1935 +        arcs.push_back(e);
  1.1936 +      }
  1.1937 +
  1.1938 +      for (int i = 0; i < int(arcs.size()); ++i) {
  1.1939 +        typename Graph::Arc e = arcs[i];
  1.1940 +
  1.1941 +        if (processed[e]) continue;
  1.1942 +        processed[e] = true;
  1.1943 +
  1.1944 +        typename Graph::Arc mine = e;
  1.1945 +        int mind = degree[graph.source(e)];
  1.1946 +
  1.1947 +        int face_size = 1;
  1.1948 +
  1.1949 +        typename Graph::Arc l = e;
  1.1950 +        e = embedding[graph.oppositeArc(e)];
  1.1951 +        while (l != e) {
  1.1952 +          processed[e] = true;
  1.1953 +
  1.1954 +          ++face_size;
  1.1955 +
  1.1956 +          if (degree[graph.source(e)] < mind) {
  1.1957 +            mine = e;
  1.1958 +            mind = degree[graph.source(e)];
  1.1959 +          }
  1.1960 +
  1.1961 +          e = embedding[graph.oppositeArc(e)];
  1.1962 +        }
  1.1963 +
  1.1964 +        if (face_size < 4) {
  1.1965 +          continue;
  1.1966 +        }
  1.1967 +
  1.1968 +        typename Graph::Node s = graph.source(mine);
  1.1969 +        for (typename Graph::OutArcIt e(graph, s); e != INVALID; ++e) {
  1.1970 +          visited.set(graph.target(e), true);
  1.1971 +        }
  1.1972 +
  1.1973 +        typename Graph::Arc oppe = INVALID;
  1.1974 +
  1.1975 +        e = embedding[graph.oppositeArc(mine)];
  1.1976 +        e = embedding[graph.oppositeArc(e)];
  1.1977 +        while (graph.target(e) != s) {
  1.1978 +          if (visited[graph.source(e)]) {
  1.1979 +            oppe = e;
  1.1980 +            break;
  1.1981 +          }
  1.1982 +          e = embedding[graph.oppositeArc(e)];
  1.1983 +        }
  1.1984 +        visited.setAll(false);
  1.1985 +
  1.1986 +        if (oppe == INVALID) {
  1.1987 +
  1.1988 +          e = embedding[graph.oppositeArc(mine)];
  1.1989 +          typename Graph::Arc pn = mine, p = e;
  1.1990 +
  1.1991 +          e = embedding[graph.oppositeArc(e)];
  1.1992 +          while (graph.target(e) != s) {
  1.1993 +            typename Graph::Arc n =
  1.1994 +              graph.direct(graph.addEdge(s, graph.source(e)), true);
  1.1995 +
  1.1996 +            embedding[n] = pn;
  1.1997 +            embedding[graph.oppositeArc(n)] = e;
  1.1998 +            embedding[graph.oppositeArc(p)] = graph.oppositeArc(n);
  1.1999 +
  1.2000 +            pn = n;
  1.2001 +
  1.2002 +            p = e;
  1.2003 +            e = embedding[graph.oppositeArc(e)];
  1.2004 +          }
  1.2005 +
  1.2006 +          embedding[graph.oppositeArc(e)] = pn;
  1.2007 +
  1.2008 +        } else {
  1.2009 +
  1.2010 +          mine = embedding[graph.oppositeArc(mine)];
  1.2011 +          s = graph.source(mine);
  1.2012 +          oppe = embedding[graph.oppositeArc(oppe)];
  1.2013 +          typename Graph::Node t = graph.source(oppe);
  1.2014 +
  1.2015 +          typename Graph::Arc ce = graph.direct(graph.addEdge(s, t), true);
  1.2016 +          embedding[ce] = mine;
  1.2017 +          embedding[graph.oppositeArc(ce)] = oppe;
  1.2018 +
  1.2019 +          typename Graph::Arc pn = ce, p = oppe;
  1.2020 +          e = embedding[graph.oppositeArc(oppe)];
  1.2021 +          while (graph.target(e) != s) {
  1.2022 +            typename Graph::Arc n =
  1.2023 +              graph.direct(graph.addEdge(s, graph.source(e)), true);
  1.2024 +
  1.2025 +            embedding[n] = pn;
  1.2026 +            embedding[graph.oppositeArc(n)] = e;
  1.2027 +            embedding[graph.oppositeArc(p)] = graph.oppositeArc(n);
  1.2028 +
  1.2029 +            pn = n;
  1.2030 +
  1.2031 +            p = e;
  1.2032 +            e = embedding[graph.oppositeArc(e)];
  1.2033 +
  1.2034 +          }
  1.2035 +          embedding[graph.oppositeArc(e)] = pn;
  1.2036 +
  1.2037 +          pn = graph.oppositeArc(ce), p = mine;
  1.2038 +          e = embedding[graph.oppositeArc(mine)];
  1.2039 +          while (graph.target(e) != t) {
  1.2040 +            typename Graph::Arc n =
  1.2041 +              graph.direct(graph.addEdge(t, graph.source(e)), true);
  1.2042 +
  1.2043 +            embedding[n] = pn;
  1.2044 +            embedding[graph.oppositeArc(n)] = e;
  1.2045 +            embedding[graph.oppositeArc(p)] = graph.oppositeArc(n);
  1.2046 +
  1.2047 +            pn = n;
  1.2048 +
  1.2049 +            p = e;
  1.2050 +            e = embedding[graph.oppositeArc(e)];
  1.2051 +
  1.2052 +          }
  1.2053 +          embedding[graph.oppositeArc(e)] = pn;
  1.2054 +        }
  1.2055 +      }
  1.2056 +    }
  1.2057 +
  1.2058 +  }
  1.2059 +
  1.2060 +  /// \ingroup planar
  1.2061 +  ///
  1.2062 +  /// \brief Schnyder's planar drawing algorithm
  1.2063 +  ///
  1.2064 +  /// The planar drawing algorithm calculates positions for the nodes
  1.2065 +  /// in the plane which coordinates satisfy that if the arcs are
  1.2066 +  /// represented with straight lines then they will not intersect
  1.2067 +  /// each other.
  1.2068 +  ///
  1.2069 +  /// Scnyder's algorithm embeds the graph on \c (n-2,n-2) size grid,
  1.2070 +  /// i.e. each node will be located in the \c [0,n-2]x[0,n-2] square.
  1.2071 +  /// The time complexity of the algorithm is O(n).
  1.2072 +  template <typename Graph>
  1.2073 +  class PlanarDrawing {
  1.2074 +  public:
  1.2075 +
  1.2076 +    TEMPLATE_GRAPH_TYPEDEFS(Graph);
  1.2077 +
  1.2078 +    /// \brief The point type for store coordinates
  1.2079 +    typedef dim2::Point<int> Point;
  1.2080 +    /// \brief The map type for store coordinates
  1.2081 +    typedef typename Graph::template NodeMap<Point> PointMap;
  1.2082 +
  1.2083 +
  1.2084 +    /// \brief Constructor
  1.2085 +    ///
  1.2086 +    /// Constructor
  1.2087 +    /// \pre The graph should be simple, i.e. loop and parallel arc free.
  1.2088 +    PlanarDrawing(const Graph& graph)
  1.2089 +      : _graph(graph), _point_map(graph) {}
  1.2090 +
  1.2091 +  private:
  1.2092 +
  1.2093 +    template <typename AuxGraph, typename AuxEmbeddingMap>
  1.2094 +    void drawing(const AuxGraph& graph,
  1.2095 +                 const AuxEmbeddingMap& next,
  1.2096 +                 PointMap& point_map) {
  1.2097 +      TEMPLATE_GRAPH_TYPEDEFS(AuxGraph);
  1.2098 +
  1.2099 +      typename AuxGraph::template ArcMap<Arc> prev(graph);
  1.2100 +
  1.2101 +      for (NodeIt n(graph); n != INVALID; ++n) {
  1.2102 +        Arc e = OutArcIt(graph, n);
  1.2103 +
  1.2104 +        Arc p = e, l = e;
  1.2105 +
  1.2106 +        e = next[e];
  1.2107 +        while (e != l) {
  1.2108 +          prev[e] = p;
  1.2109 +          p = e;
  1.2110 +          e = next[e];
  1.2111 +        }
  1.2112 +        prev[e] = p;
  1.2113 +      }
  1.2114 +
  1.2115 +      Node anode, bnode, cnode;
  1.2116 +
  1.2117 +      {
  1.2118 +        Arc e = ArcIt(graph);
  1.2119 +        anode = graph.source(e);
  1.2120 +        bnode = graph.target(e);
  1.2121 +        cnode = graph.target(next[graph.oppositeArc(e)]);
  1.2122 +      }
  1.2123 +
  1.2124 +      IterableBoolMap<AuxGraph, Node> proper(graph, false);
  1.2125 +      typename AuxGraph::template NodeMap<int> conn(graph, -1);
  1.2126 +
  1.2127 +      conn[anode] = conn[bnode] = -2;
  1.2128 +      {
  1.2129 +        for (OutArcIt e(graph, anode); e != INVALID; ++e) {
  1.2130 +          Node m = graph.target(e);
  1.2131 +          if (conn[m] == -1) {
  1.2132 +            conn[m] = 1;
  1.2133 +          }
  1.2134 +        }
  1.2135 +        conn[cnode] = 2;
  1.2136 +
  1.2137 +        for (OutArcIt e(graph, bnode); e != INVALID; ++e) {
  1.2138 +          Node m = graph.target(e);
  1.2139 +          if (conn[m] == -1) {
  1.2140 +            conn[m] = 1;
  1.2141 +          } else if (conn[m] != -2) {
  1.2142 +            conn[m] += 1;
  1.2143 +            Arc pe = graph.oppositeArc(e);
  1.2144 +            if (conn[graph.target(next[pe])] == -2) {
  1.2145 +              conn[m] -= 1;
  1.2146 +            }
  1.2147 +            if (conn[graph.target(prev[pe])] == -2) {
  1.2148 +              conn[m] -= 1;
  1.2149 +            }
  1.2150 +
  1.2151 +            proper.set(m, conn[m] == 1);
  1.2152 +          }
  1.2153 +        }
  1.2154 +      }
  1.2155 +
  1.2156 +
  1.2157 +      typename AuxGraph::template ArcMap<int> angle(graph, -1);
  1.2158 +
  1.2159 +      while (proper.trueNum() != 0) {
  1.2160 +        Node n = typename IterableBoolMap<AuxGraph, Node>::TrueIt(proper);
  1.2161 +        proper.set(n, false);
  1.2162 +        conn[n] = -2;
  1.2163 +
  1.2164 +        for (OutArcIt e(graph, n); e != INVALID; ++e) {
  1.2165 +          Node m = graph.target(e);
  1.2166 +          if (conn[m] == -1) {
  1.2167 +            conn[m] = 1;
  1.2168 +          } else if (conn[m] != -2) {
  1.2169 +            conn[m] += 1;
  1.2170 +            Arc pe = graph.oppositeArc(e);
  1.2171 +            if (conn[graph.target(next[pe])] == -2) {
  1.2172 +              conn[m] -= 1;
  1.2173 +            }
  1.2174 +            if (conn[graph.target(prev[pe])] == -2) {
  1.2175 +              conn[m] -= 1;
  1.2176 +            }
  1.2177 +
  1.2178 +            proper.set(m, conn[m] == 1);
  1.2179 +          }
  1.2180 +        }
  1.2181 +
  1.2182 +        {
  1.2183 +          Arc e = OutArcIt(graph, n);
  1.2184 +          Arc p = e, l = e;
  1.2185 +
  1.2186 +          e = next[e];
  1.2187 +          while (e != l) {
  1.2188 +
  1.2189 +            if (conn[graph.target(e)] == -2 && conn[graph.target(p)] == -2) {
  1.2190 +              Arc f = e;
  1.2191 +              angle[f] = 0;
  1.2192 +              f = next[graph.oppositeArc(f)];
  1.2193 +              angle[f] = 1;
  1.2194 +              f = next[graph.oppositeArc(f)];
  1.2195 +              angle[f] = 2;
  1.2196 +            }
  1.2197 +
  1.2198 +            p = e;
  1.2199 +            e = next[e];
  1.2200 +          }
  1.2201 +
  1.2202 +          if (conn[graph.target(e)] == -2 && conn[graph.target(p)] == -2) {
  1.2203 +            Arc f = e;
  1.2204 +            angle[f] = 0;
  1.2205 +            f = next[graph.oppositeArc(f)];
  1.2206 +            angle[f] = 1;
  1.2207 +            f = next[graph.oppositeArc(f)];
  1.2208 +            angle[f] = 2;
  1.2209 +          }
  1.2210 +        }
  1.2211 +      }
  1.2212 +
  1.2213 +      typename AuxGraph::template NodeMap<Node> apred(graph, INVALID);
  1.2214 +      typename AuxGraph::template NodeMap<Node> bpred(graph, INVALID);
  1.2215 +      typename AuxGraph::template NodeMap<Node> cpred(graph, INVALID);
  1.2216 +
  1.2217 +      typename AuxGraph::template NodeMap<int> apredid(graph, -1);
  1.2218 +      typename AuxGraph::template NodeMap<int> bpredid(graph, -1);
  1.2219 +      typename AuxGraph::template NodeMap<int> cpredid(graph, -1);
  1.2220 +
  1.2221 +      for (ArcIt e(graph); e != INVALID; ++e) {
  1.2222 +        if (angle[e] == angle[next[e]]) {
  1.2223 +          switch (angle[e]) {
  1.2224 +          case 2:
  1.2225 +            apred[graph.target(e)] = graph.source(e);
  1.2226 +            apredid[graph.target(e)] = graph.id(graph.source(e));
  1.2227 +            break;
  1.2228 +          case 1:
  1.2229 +            bpred[graph.target(e)] = graph.source(e);
  1.2230 +            bpredid[graph.target(e)] = graph.id(graph.source(e));
  1.2231 +            break;
  1.2232 +          case 0:
  1.2233 +            cpred[graph.target(e)] = graph.source(e);
  1.2234 +            cpredid[graph.target(e)] = graph.id(graph.source(e));
  1.2235 +            break;
  1.2236 +          }
  1.2237 +        }
  1.2238 +      }
  1.2239 +
  1.2240 +      cpred[anode] = INVALID;
  1.2241 +      cpred[bnode] = INVALID;
  1.2242 +
  1.2243 +      std::vector<Node> aorder, border, corder;
  1.2244 +
  1.2245 +      {
  1.2246 +        typename AuxGraph::template NodeMap<bool> processed(graph, false);
  1.2247 +        std::vector<Node> st;
  1.2248 +        for (NodeIt n(graph); n != INVALID; ++n) {
  1.2249 +          if (!processed[n] && n != bnode && n != cnode) {
  1.2250 +            st.push_back(n);
  1.2251 +            processed[n] = true;
  1.2252 +            Node m = apred[n];
  1.2253 +            while (m != INVALID && !processed[m]) {
  1.2254 +              st.push_back(m);
  1.2255 +              processed[m] = true;
  1.2256 +              m = apred[m];
  1.2257 +            }
  1.2258 +            while (!st.empty()) {
  1.2259 +              aorder.push_back(st.back());
  1.2260 +              st.pop_back();
  1.2261 +            }
  1.2262 +          }
  1.2263 +        }
  1.2264 +      }
  1.2265 +
  1.2266 +      {
  1.2267 +        typename AuxGraph::template NodeMap<bool> processed(graph, false);
  1.2268 +        std::vector<Node> st;
  1.2269 +        for (NodeIt n(graph); n != INVALID; ++n) {
  1.2270 +          if (!processed[n] && n != cnode && n != anode) {
  1.2271 +            st.push_back(n);
  1.2272 +            processed[n] = true;
  1.2273 +            Node m = bpred[n];
  1.2274 +            while (m != INVALID && !processed[m]) {
  1.2275 +              st.push_back(m);
  1.2276 +              processed[m] = true;
  1.2277 +              m = bpred[m];
  1.2278 +            }
  1.2279 +            while (!st.empty()) {
  1.2280 +              border.push_back(st.back());
  1.2281 +              st.pop_back();
  1.2282 +            }
  1.2283 +          }
  1.2284 +        }
  1.2285 +      }
  1.2286 +
  1.2287 +      {
  1.2288 +        typename AuxGraph::template NodeMap<bool> processed(graph, false);
  1.2289 +        std::vector<Node> st;
  1.2290 +        for (NodeIt n(graph); n != INVALID; ++n) {
  1.2291 +          if (!processed[n] && n != anode && n != bnode) {
  1.2292 +            st.push_back(n);
  1.2293 +            processed[n] = true;
  1.2294 +            Node m = cpred[n];
  1.2295 +            while (m != INVALID && !processed[m]) {
  1.2296 +              st.push_back(m);
  1.2297 +              processed[m] = true;
  1.2298 +              m = cpred[m];
  1.2299 +            }
  1.2300 +            while (!st.empty()) {
  1.2301 +              corder.push_back(st.back());
  1.2302 +              st.pop_back();
  1.2303 +            }
  1.2304 +          }
  1.2305 +        }
  1.2306 +      }
  1.2307 +
  1.2308 +      typename AuxGraph::template NodeMap<int> atree(graph, 0);
  1.2309 +      for (int i = aorder.size() - 1; i >= 0; --i) {
  1.2310 +        Node n = aorder[i];
  1.2311 +        atree[n] = 1;
  1.2312 +        for (OutArcIt e(graph, n); e != INVALID; ++e) {
  1.2313 +          if (apred[graph.target(e)] == n) {
  1.2314 +            atree[n] += atree[graph.target(e)];
  1.2315 +          }
  1.2316 +        }
  1.2317 +      }
  1.2318 +
  1.2319 +      typename AuxGraph::template NodeMap<int> btree(graph, 0);
  1.2320 +      for (int i = border.size() - 1; i >= 0; --i) {
  1.2321 +        Node n = border[i];
  1.2322 +        btree[n] = 1;
  1.2323 +        for (OutArcIt e(graph, n); e != INVALID; ++e) {
  1.2324 +          if (bpred[graph.target(e)] == n) {
  1.2325 +            btree[n] += btree[graph.target(e)];
  1.2326 +          }
  1.2327 +        }
  1.2328 +      }
  1.2329 +
  1.2330 +      typename AuxGraph::template NodeMap<int> apath(graph, 0);
  1.2331 +      apath[bnode] = apath[cnode] = 1;
  1.2332 +      typename AuxGraph::template NodeMap<int> apath_btree(graph, 0);
  1.2333 +      apath_btree[bnode] = btree[bnode];
  1.2334 +      for (int i = 1; i < int(aorder.size()); ++i) {
  1.2335 +        Node n = aorder[i];
  1.2336 +        apath[n] = apath[apred[n]] + 1;
  1.2337 +        apath_btree[n] = btree[n] + apath_btree[apred[n]];
  1.2338 +      }
  1.2339 +
  1.2340 +      typename AuxGraph::template NodeMap<int> bpath_atree(graph, 0);
  1.2341 +      bpath_atree[anode] = atree[anode];
  1.2342 +      for (int i = 1; i < int(border.size()); ++i) {
  1.2343 +        Node n = border[i];
  1.2344 +        bpath_atree[n] = atree[n] + bpath_atree[bpred[n]];
  1.2345 +      }
  1.2346 +
  1.2347 +      typename AuxGraph::template NodeMap<int> cpath(graph, 0);
  1.2348 +      cpath[anode] = cpath[bnode] = 1;
  1.2349 +      typename AuxGraph::template NodeMap<int> cpath_atree(graph, 0);
  1.2350 +      cpath_atree[anode] = atree[anode];
  1.2351 +      typename AuxGraph::template NodeMap<int> cpath_btree(graph, 0);
  1.2352 +      cpath_btree[bnode] = btree[bnode];
  1.2353 +      for (int i = 1; i < int(corder.size()); ++i) {
  1.2354 +        Node n = corder[i];
  1.2355 +        cpath[n] = cpath[cpred[n]] + 1;
  1.2356 +        cpath_atree[n] = atree[n] + cpath_atree[cpred[n]];
  1.2357 +        cpath_btree[n] = btree[n] + cpath_btree[cpred[n]];
  1.2358 +      }
  1.2359 +
  1.2360 +      typename AuxGraph::template NodeMap<int> third(graph);
  1.2361 +      for (NodeIt n(graph); n != INVALID; ++n) {
  1.2362 +        point_map[n].x =
  1.2363 +          bpath_atree[n] + cpath_atree[n] - atree[n] - cpath[n] + 1;
  1.2364 +        point_map[n].y =
  1.2365 +          cpath_btree[n] + apath_btree[n] - btree[n] - apath[n] + 1;
  1.2366 +      }
  1.2367 +
  1.2368 +    }
  1.2369 +
  1.2370 +  public:
  1.2371 +
  1.2372 +    /// \brief Calculates the node positions
  1.2373 +    ///
  1.2374 +    /// This function calculates the node positions.
  1.2375 +    /// \return %True if the graph is planar.
  1.2376 +    bool run() {
  1.2377 +      PlanarEmbedding<Graph> pe(_graph);
  1.2378 +      if (!pe.run()) return false;
  1.2379 +
  1.2380 +      run(pe);
  1.2381 +      return true;
  1.2382 +    }
  1.2383 +
  1.2384 +    /// \brief Calculates the node positions according to a
  1.2385 +    /// combinatorical embedding
  1.2386 +    ///
  1.2387 +    /// This function calculates the node locations. The \c embedding
  1.2388 +    /// parameter should contain a valid combinatorical embedding, i.e.
  1.2389 +    /// a valid cyclic order of the arcs.
  1.2390 +    template <typename EmbeddingMap>
  1.2391 +    void run(const EmbeddingMap& embedding) {
  1.2392 +      typedef SmartEdgeSet<Graph> AuxGraph;
  1.2393 +
  1.2394 +      if (3 * countNodes(_graph) - 6 == countEdges(_graph)) {
  1.2395 +        drawing(_graph, embedding, _point_map);
  1.2396 +        return;
  1.2397 +      }
  1.2398 +
  1.2399 +      AuxGraph aux_graph(_graph);
  1.2400 +      typename AuxGraph::template ArcMap<typename AuxGraph::Arc>
  1.2401 +        aux_embedding(aux_graph);
  1.2402 +
  1.2403 +      {
  1.2404 +
  1.2405 +        typename Graph::template EdgeMap<typename AuxGraph::Edge>
  1.2406 +          ref(_graph);
  1.2407 +
  1.2408 +        for (EdgeIt e(_graph); e != INVALID; ++e) {
  1.2409 +          ref[e] = aux_graph.addEdge(_graph.u(e), _graph.v(e));
  1.2410 +        }
  1.2411 +
  1.2412 +        for (EdgeIt e(_graph); e != INVALID; ++e) {
  1.2413 +          Arc ee = embedding[_graph.direct(e, true)];
  1.2414 +          aux_embedding[aux_graph.direct(ref[e], true)] =
  1.2415 +            aux_graph.direct(ref[ee], _graph.direction(ee));
  1.2416 +          ee = embedding[_graph.direct(e, false)];
  1.2417 +          aux_embedding[aux_graph.direct(ref[e], false)] =
  1.2418 +            aux_graph.direct(ref[ee], _graph.direction(ee));
  1.2419 +        }
  1.2420 +      }
  1.2421 +      _planarity_bits::makeConnected(aux_graph, aux_embedding);
  1.2422 +      _planarity_bits::makeBiNodeConnected(aux_graph, aux_embedding);
  1.2423 +      _planarity_bits::makeMaxPlanar(aux_graph, aux_embedding);
  1.2424 +      drawing(aux_graph, aux_embedding, _point_map);
  1.2425 +    }
  1.2426 +
  1.2427 +    /// \brief The coordinate of the given node
  1.2428 +    ///
  1.2429 +    /// The coordinate of the given node.
  1.2430 +    Point operator[](const Node& node) const {
  1.2431 +      return _point_map[node];
  1.2432 +    }
  1.2433 +
  1.2434 +    /// \brief Returns the grid embedding in a \e NodeMap.
  1.2435 +    ///
  1.2436 +    /// Returns the grid embedding in a \e NodeMap of \c dim2::Point<int> .
  1.2437 +    const PointMap& coords() const {
  1.2438 +      return _point_map;
  1.2439 +    }
  1.2440 +
  1.2441 +  private:
  1.2442 +
  1.2443 +    const Graph& _graph;
  1.2444 +    PointMap _point_map;
  1.2445 +
  1.2446 +  };
  1.2447 +
  1.2448 +  namespace _planarity_bits {
  1.2449 +
  1.2450 +    template <typename ColorMap>
  1.2451 +    class KempeFilter {
  1.2452 +    public:
  1.2453 +      typedef typename ColorMap::Key Key;
  1.2454 +      typedef bool Value;
  1.2455 +
  1.2456 +      KempeFilter(const ColorMap& color_map,
  1.2457 +                  const typename ColorMap::Value& first,
  1.2458 +                  const typename ColorMap::Value& second)
  1.2459 +        : _color_map(color_map), _first(first), _second(second) {}
  1.2460 +
  1.2461 +      Value operator[](const Key& key) const {
  1.2462 +        return _color_map[key] == _first || _color_map[key] == _second;
  1.2463 +      }
  1.2464 +
  1.2465 +    private:
  1.2466 +      const ColorMap& _color_map;
  1.2467 +      typename ColorMap::Value _first, _second;
  1.2468 +    };
  1.2469 +  }
  1.2470 +
  1.2471 +  /// \ingroup planar
  1.2472 +  ///
  1.2473 +  /// \brief Coloring planar graphs
  1.2474 +  ///
  1.2475 +  /// The graph coloring problem is the coloring of the graph nodes
  1.2476 +  /// that there are not adjacent nodes with the same color. The
  1.2477 +  /// planar graphs can be always colored with four colors, it is
  1.2478 +  /// proved by Appel and Haken and their proofs provide a quadratic
  1.2479 +  /// time algorithm for four coloring, but it could not be used to
  1.2480 +  /// implement efficient algorithm. The five and six coloring can be
  1.2481 +  /// made in linear time, but in this class the five coloring has
  1.2482 +  /// quadratic worst case time complexity. The two coloring (if
  1.2483 +  /// possible) is solvable with a graph search algorithm and it is
  1.2484 +  /// implemented in \ref bipartitePartitions() function in LEMON. To
  1.2485 +  /// decide whether the planar graph is three colorable is
  1.2486 +  /// NP-complete.
  1.2487 +  ///
  1.2488 +  /// This class contains member functions for calculate colorings
  1.2489 +  /// with five and six colors. The six coloring algorithm is a simple
  1.2490 +  /// greedy coloring on the backward minimum outgoing order of nodes.
  1.2491 +  /// This order can be computed as in each phase the node with least
  1.2492 +  /// outgoing arcs to unprocessed nodes is chosen. This order
  1.2493 +  /// guarantees that when a node is chosen for coloring it has at
  1.2494 +  /// most five already colored adjacents. The five coloring algorithm
  1.2495 +  /// use the same method, but if the greedy approach fails to color
  1.2496 +  /// with five colors, i.e. the node has five already different
  1.2497 +  /// colored neighbours, it swaps the colors in one of the connected
  1.2498 +  /// two colored sets with the Kempe recoloring method.
  1.2499 +  template <typename Graph>
  1.2500 +  class PlanarColoring {
  1.2501 +  public:
  1.2502 +
  1.2503 +    TEMPLATE_GRAPH_TYPEDEFS(Graph);
  1.2504 +
  1.2505 +    /// \brief The map type for store color indexes
  1.2506 +    typedef typename Graph::template NodeMap<int> IndexMap;
  1.2507 +    /// \brief The map type for store colors
  1.2508 +    typedef ComposeMap<Palette, IndexMap> ColorMap;
  1.2509 +
  1.2510 +    /// \brief Constructor
  1.2511 +    ///
  1.2512 +    /// Constructor
  1.2513 +    /// \pre The graph should be simple, i.e. loop and parallel arc free.
  1.2514 +    PlanarColoring(const Graph& graph)
  1.2515 +      : _graph(graph), _color_map(graph), _palette(0) {
  1.2516 +      _palette.add(Color(1,0,0));
  1.2517 +      _palette.add(Color(0,1,0));
  1.2518 +      _palette.add(Color(0,0,1));
  1.2519 +      _palette.add(Color(1,1,0));
  1.2520 +      _palette.add(Color(1,0,1));
  1.2521 +      _palette.add(Color(0,1,1));
  1.2522 +    }
  1.2523 +
  1.2524 +    /// \brief Returns the \e NodeMap of color indexes
  1.2525 +    ///
  1.2526 +    /// Returns the \e NodeMap of color indexes. The values are in the
  1.2527 +    /// range \c [0..4] or \c [0..5] according to the coloring method.
  1.2528 +    IndexMap colorIndexMap() const {
  1.2529 +      return _color_map;
  1.2530 +    }
  1.2531 +
  1.2532 +    /// \brief Returns the \e NodeMap of colors
  1.2533 +    ///
  1.2534 +    /// Returns the \e NodeMap of colors. The values are five or six
  1.2535 +    /// distinct \ref lemon::Color "colors".
  1.2536 +    ColorMap colorMap() const {
  1.2537 +      return composeMap(_palette, _color_map);
  1.2538 +    }
  1.2539 +
  1.2540 +    /// \brief Returns the color index of the node
  1.2541 +    ///
  1.2542 +    /// Returns the color index of the node. The values are in the
  1.2543 +    /// range \c [0..4] or \c [0..5] according to the coloring method.
  1.2544 +    int colorIndex(const Node& node) const {
  1.2545 +      return _color_map[node];
  1.2546 +    }
  1.2547 +
  1.2548 +    /// \brief Returns the color of the node
  1.2549 +    ///
  1.2550 +    /// Returns the color of the node. The values are five or six
  1.2551 +    /// distinct \ref lemon::Color "colors".
  1.2552 +    Color color(const Node& node) const {
  1.2553 +      return _palette[_color_map[node]];
  1.2554 +    }
  1.2555 +
  1.2556 +
  1.2557 +    /// \brief Calculates a coloring with at most six colors
  1.2558 +    ///
  1.2559 +    /// This function calculates a coloring with at most six colors. The time
  1.2560 +    /// complexity of this variant is linear in the size of the graph.
  1.2561 +    /// \return %True when the algorithm could color the graph with six color.
  1.2562 +    /// If the algorithm fails, then the graph could not be planar.
  1.2563 +    /// \note This function can return true if the graph is not
  1.2564 +    /// planar but it can be colored with 6 colors.
  1.2565 +    bool runSixColoring() {
  1.2566 +
  1.2567 +      typename Graph::template NodeMap<int> heap_index(_graph, -1);
  1.2568 +      BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index);
  1.2569 +
  1.2570 +      for (NodeIt n(_graph); n != INVALID; ++n) {
  1.2571 +        _color_map[n] = -2;
  1.2572 +        heap.push(n, countOutArcs(_graph, n));
  1.2573 +      }
  1.2574 +
  1.2575 +      std::vector<Node> order;
  1.2576 +
  1.2577 +      while (!heap.empty()) {
  1.2578 +        Node n = heap.top();
  1.2579 +        heap.pop();
  1.2580 +        _color_map[n] = -1;
  1.2581 +        order.push_back(n);
  1.2582 +        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
  1.2583 +          Node t = _graph.runningNode(e);
  1.2584 +          if (_color_map[t] == -2) {
  1.2585 +            heap.decrease(t, heap[t] - 1);
  1.2586 +          }
  1.2587 +        }
  1.2588 +      }
  1.2589 +
  1.2590 +      for (int i = order.size() - 1; i >= 0; --i) {
  1.2591 +        std::vector<bool> forbidden(6, false);
  1.2592 +        for (OutArcIt e(_graph, order[i]); e != INVALID; ++e) {
  1.2593 +          Node t = _graph.runningNode(e);
  1.2594 +          if (_color_map[t] != -1) {
  1.2595 +            forbidden[_color_map[t]] = true;
  1.2596 +          }
  1.2597 +        }
  1.2598 +               for (int k = 0; k < 6; ++k) {
  1.2599 +          if (!forbidden[k]) {
  1.2600 +            _color_map[order[i]] = k;
  1.2601 +            break;
  1.2602 +          }
  1.2603 +        }
  1.2604 +        if (_color_map[order[i]] == -1) {
  1.2605 +          return false;
  1.2606 +        }
  1.2607 +      }
  1.2608 +      return true;
  1.2609 +    }
  1.2610 +
  1.2611 +  private:
  1.2612 +
  1.2613 +    bool recolor(const Node& u, const Node& v) {
  1.2614 +      int ucolor = _color_map[u];
  1.2615 +      int vcolor = _color_map[v];
  1.2616 +      typedef _planarity_bits::KempeFilter<IndexMap> KempeFilter;
  1.2617 +      KempeFilter filter(_color_map, ucolor, vcolor);
  1.2618 +
  1.2619 +      typedef FilterNodes<const Graph, const KempeFilter> KempeGraph;
  1.2620 +      KempeGraph kempe_graph(_graph, filter);
  1.2621 +
  1.2622 +      std::vector<Node> comp;
  1.2623 +      Bfs<KempeGraph> bfs(kempe_graph);
  1.2624 +      bfs.init();
  1.2625 +      bfs.addSource(u);
  1.2626 +      while (!bfs.emptyQueue()) {
  1.2627 +        Node n = bfs.nextNode();
  1.2628 +        if (n == v) return false;
  1.2629 +        comp.push_back(n);
  1.2630 +        bfs.processNextNode();
  1.2631 +      }
  1.2632 +
  1.2633 +      int scolor = ucolor + vcolor;
  1.2634 +      for (int i = 0; i < static_cast<int>(comp.size()); ++i) {
  1.2635 +        _color_map[comp[i]] = scolor - _color_map[comp[i]];
  1.2636 +      }
  1.2637 +
  1.2638 +      return true;
  1.2639 +    }
  1.2640 +
  1.2641 +    template <typename EmbeddingMap>
  1.2642 +    void kempeRecoloring(const Node& node, const EmbeddingMap& embedding) {
  1.2643 +      std::vector<Node> nodes;
  1.2644 +      nodes.reserve(4);
  1.2645 +
  1.2646 +      for (Arc e = OutArcIt(_graph, node); e != INVALID; e = embedding[e]) {
  1.2647 +        Node t = _graph.target(e);
  1.2648 +        if (_color_map[t] != -1) {
  1.2649 +          nodes.push_back(t);
  1.2650 +          if (nodes.size() == 4) break;
  1.2651 +        }
  1.2652 +      }
  1.2653 +
  1.2654 +      int color = _color_map[nodes[0]];
  1.2655 +      if (recolor(nodes[0], nodes[2])) {
  1.2656 +        _color_map[node] = color;
  1.2657 +      } else {
  1.2658 +        color = _color_map[nodes[1]];
  1.2659 +        recolor(nodes[1], nodes[3]);
  1.2660 +        _color_map[node] = color;
  1.2661 +      }
  1.2662 +    }
  1.2663 +
  1.2664 +  public:
  1.2665 +
  1.2666 +    /// \brief Calculates a coloring with at most five colors
  1.2667 +    ///
  1.2668 +    /// This function calculates a coloring with at most five
  1.2669 +    /// colors. The worst case time complexity of this variant is
  1.2670 +    /// quadratic in the size of the graph.
  1.2671 +    template <typename EmbeddingMap>
  1.2672 +    void runFiveColoring(const EmbeddingMap& embedding) {
  1.2673 +
  1.2674 +      typename Graph::template NodeMap<int> heap_index(_graph, -1);
  1.2675 +      BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index);
  1.2676 +
  1.2677 +      for (NodeIt n(_graph); n != INVALID; ++n) {
  1.2678 +        _color_map[n] = -2;
  1.2679 +        heap.push(n, countOutArcs(_graph, n));
  1.2680 +      }
  1.2681 +
  1.2682 +      std::vector<Node> order;
  1.2683 +
  1.2684 +      while (!heap.empty()) {
  1.2685 +        Node n = heap.top();
  1.2686 +        heap.pop();
  1.2687 +        _color_map[n] = -1;
  1.2688 +        order.push_back(n);
  1.2689 +        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
  1.2690 +          Node t = _graph.runningNode(e);
  1.2691 +          if (_color_map[t] == -2) {
  1.2692 +            heap.decrease(t, heap[t] - 1);
  1.2693 +          }
  1.2694 +        }
  1.2695 +      }
  1.2696 +
  1.2697 +      for (int i = order.size() - 1; i >= 0; --i) {
  1.2698 +        std::vector<bool> forbidden(5, false);
  1.2699 +        for (OutArcIt e(_graph, order[i]); e != INVALID; ++e) {
  1.2700 +          Node t = _graph.runningNode(e);
  1.2701 +          if (_color_map[t] != -1) {
  1.2702 +            forbidden[_color_map[t]] = true;
  1.2703 +          }
  1.2704 +        }
  1.2705 +        for (int k = 0; k < 5; ++k) {
  1.2706 +          if (!forbidden[k]) {
  1.2707 +            _color_map[order[i]] = k;
  1.2708 +            break;
  1.2709 +          }
  1.2710 +        }
  1.2711 +        if (_color_map[order[i]] == -1) {
  1.2712 +          kempeRecoloring(order[i], embedding);
  1.2713 +        }
  1.2714 +      }
  1.2715 +    }
  1.2716 +
  1.2717 +    /// \brief Calculates a coloring with at most five colors
  1.2718 +    ///
  1.2719 +    /// This function calculates a coloring with at most five
  1.2720 +    /// colors. The worst case time complexity of this variant is
  1.2721 +    /// quadratic in the size of the graph.
  1.2722 +    /// \return %True when the graph is planar.
  1.2723 +    bool runFiveColoring() {
  1.2724 +      PlanarEmbedding<Graph> pe(_graph);
  1.2725 +      if (!pe.run()) return false;
  1.2726 +
  1.2727 +      runFiveColoring(pe.embeddingMap());
  1.2728 +      return true;
  1.2729 +    }
  1.2730 +
  1.2731 +  private:
  1.2732 +
  1.2733 +    const Graph& _graph;
  1.2734 +    IndexMap _color_map;
  1.2735 +    Palette _palette;
  1.2736 +  };
  1.2737 +
  1.2738 +}
  1.2739 +
  1.2740 +#endif