1.1 --- a/lemon/Makefile.am Mon Aug 31 20:27:38 2009 +0200
1.2 +++ b/lemon/Makefile.am Wed Sep 09 15:32:03 2009 +0200
1.3 @@ -104,6 +104,7 @@
1.4 lemon/network_simplex.h \
1.5 lemon/pairing_heap.h \
1.6 lemon/path.h \
1.7 + lemon/planarity.h \
1.8 lemon/preflow.h \
1.9 lemon/radix_heap.h \
1.10 lemon/radix_sort.h \
2.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
2.2 +++ b/lemon/planarity.h Wed Sep 09 15:32:03 2009 +0200
2.3 @@ -0,0 +1,2737 @@
2.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
2.5 + *
2.6 + * This file is a part of LEMON, a generic C++ optimization library.
2.7 + *
2.8 + * Copyright (C) 2003-2009
2.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
2.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
2.11 + *
2.12 + * Permission to use, modify and distribute this software is granted
2.13 + * provided that this copyright notice appears in all copies. For
2.14 + * precise terms see the accompanying LICENSE file.
2.15 + *
2.16 + * This software is provided "AS IS" with no warranty of any kind,
2.17 + * express or implied, and with no claim as to its suitability for any
2.18 + * purpose.
2.19 + *
2.20 + */
2.21 +
2.22 +#ifndef LEMON_PLANARITY_H
2.23 +#define LEMON_PLANARITY_H
2.24 +
2.25 +/// \ingroup planar
2.26 +/// \file
2.27 +/// \brief Planarity checking, embedding, drawing and coloring
2.28 +
2.29 +#include <vector>
2.30 +#include <list>
2.31 +
2.32 +#include <lemon/dfs.h>
2.33 +#include <lemon/bfs.h>
2.34 +#include <lemon/radix_sort.h>
2.35 +#include <lemon/maps.h>
2.36 +#include <lemon/path.h>
2.37 +#include <lemon/bucket_heap.h>
2.38 +#include <lemon/adaptors.h>
2.39 +#include <lemon/edge_set.h>
2.40 +#include <lemon/color.h>
2.41 +#include <lemon/dim2.h>
2.42 +
2.43 +namespace lemon {
2.44 +
2.45 + namespace _planarity_bits {
2.46 +
2.47 + template <typename Graph>
2.48 + struct PlanarityVisitor : DfsVisitor<Graph> {
2.49 +
2.50 + TEMPLATE_GRAPH_TYPEDEFS(Graph);
2.51 +
2.52 + typedef typename Graph::template NodeMap<Arc> PredMap;
2.53 +
2.54 + typedef typename Graph::template EdgeMap<bool> TreeMap;
2.55 +
2.56 + typedef typename Graph::template NodeMap<int> OrderMap;
2.57 + typedef std::vector<Node> OrderList;
2.58 +
2.59 + typedef typename Graph::template NodeMap<int> LowMap;
2.60 + typedef typename Graph::template NodeMap<int> AncestorMap;
2.61 +
2.62 + PlanarityVisitor(const Graph& graph,
2.63 + PredMap& pred_map, TreeMap& tree_map,
2.64 + OrderMap& order_map, OrderList& order_list,
2.65 + AncestorMap& ancestor_map, LowMap& low_map)
2.66 + : _graph(graph), _pred_map(pred_map), _tree_map(tree_map),
2.67 + _order_map(order_map), _order_list(order_list),
2.68 + _ancestor_map(ancestor_map), _low_map(low_map) {}
2.69 +
2.70 + void reach(const Node& node) {
2.71 + _order_map[node] = _order_list.size();
2.72 + _low_map[node] = _order_list.size();
2.73 + _ancestor_map[node] = _order_list.size();
2.74 + _order_list.push_back(node);
2.75 + }
2.76 +
2.77 + void discover(const Arc& arc) {
2.78 + Node source = _graph.source(arc);
2.79 + Node target = _graph.target(arc);
2.80 +
2.81 + _tree_map[arc] = true;
2.82 + _pred_map[target] = arc;
2.83 + }
2.84 +
2.85 + void examine(const Arc& arc) {
2.86 + Node source = _graph.source(arc);
2.87 + Node target = _graph.target(arc);
2.88 +
2.89 + if (_order_map[target] < _order_map[source] && !_tree_map[arc]) {
2.90 + if (_low_map[source] > _order_map[target]) {
2.91 + _low_map[source] = _order_map[target];
2.92 + }
2.93 + if (_ancestor_map[source] > _order_map[target]) {
2.94 + _ancestor_map[source] = _order_map[target];
2.95 + }
2.96 + }
2.97 + }
2.98 +
2.99 + void backtrack(const Arc& arc) {
2.100 + Node source = _graph.source(arc);
2.101 + Node target = _graph.target(arc);
2.102 +
2.103 + if (_low_map[source] > _low_map[target]) {
2.104 + _low_map[source] = _low_map[target];
2.105 + }
2.106 + }
2.107 +
2.108 + const Graph& _graph;
2.109 + PredMap& _pred_map;
2.110 + TreeMap& _tree_map;
2.111 + OrderMap& _order_map;
2.112 + OrderList& _order_list;
2.113 + AncestorMap& _ancestor_map;
2.114 + LowMap& _low_map;
2.115 + };
2.116 +
2.117 + template <typename Graph, bool embedding = true>
2.118 + struct NodeDataNode {
2.119 + int prev, next;
2.120 + int visited;
2.121 + typename Graph::Arc first;
2.122 + bool inverted;
2.123 + };
2.124 +
2.125 + template <typename Graph>
2.126 + struct NodeDataNode<Graph, false> {
2.127 + int prev, next;
2.128 + int visited;
2.129 + };
2.130 +
2.131 + template <typename Graph>
2.132 + struct ChildListNode {
2.133 + typedef typename Graph::Node Node;
2.134 + Node first;
2.135 + Node prev, next;
2.136 + };
2.137 +
2.138 + template <typename Graph>
2.139 + struct ArcListNode {
2.140 + typename Graph::Arc prev, next;
2.141 + };
2.142 +
2.143 + }
2.144 +
2.145 + /// \ingroup planar
2.146 + ///
2.147 + /// \brief Planarity checking of an undirected simple graph
2.148 + ///
2.149 + /// This class implements the Boyer-Myrvold algorithm for planarity
2.150 + /// checking of an undirected graph. This class is a simplified
2.151 + /// version of the PlanarEmbedding algorithm class because neither
2.152 + /// the embedding nor the kuratowski subdivisons are not computed.
2.153 + template <typename Graph>
2.154 + class PlanarityChecking {
2.155 + private:
2.156 +
2.157 + TEMPLATE_GRAPH_TYPEDEFS(Graph);
2.158 +
2.159 + const Graph& _graph;
2.160 +
2.161 + private:
2.162 +
2.163 + typedef typename Graph::template NodeMap<Arc> PredMap;
2.164 +
2.165 + typedef typename Graph::template EdgeMap<bool> TreeMap;
2.166 +
2.167 + typedef typename Graph::template NodeMap<int> OrderMap;
2.168 + typedef std::vector<Node> OrderList;
2.169 +
2.170 + typedef typename Graph::template NodeMap<int> LowMap;
2.171 + typedef typename Graph::template NodeMap<int> AncestorMap;
2.172 +
2.173 + typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode;
2.174 + typedef std::vector<NodeDataNode> NodeData;
2.175 +
2.176 + typedef _planarity_bits::ChildListNode<Graph> ChildListNode;
2.177 + typedef typename Graph::template NodeMap<ChildListNode> ChildLists;
2.178 +
2.179 + typedef typename Graph::template NodeMap<std::list<int> > MergeRoots;
2.180 +
2.181 + typedef typename Graph::template NodeMap<bool> EmbedArc;
2.182 +
2.183 + public:
2.184 +
2.185 + /// \brief Constructor
2.186 + ///
2.187 + /// \note The graph should be simple, i.e. parallel and loop arc
2.188 + /// free.
2.189 + PlanarityChecking(const Graph& graph) : _graph(graph) {}
2.190 +
2.191 + /// \brief Runs the algorithm.
2.192 + ///
2.193 + /// Runs the algorithm.
2.194 + /// \return %True when the graph is planar.
2.195 + bool run() {
2.196 + typedef _planarity_bits::PlanarityVisitor<Graph> Visitor;
2.197 +
2.198 + PredMap pred_map(_graph, INVALID);
2.199 + TreeMap tree_map(_graph, false);
2.200 +
2.201 + OrderMap order_map(_graph, -1);
2.202 + OrderList order_list;
2.203 +
2.204 + AncestorMap ancestor_map(_graph, -1);
2.205 + LowMap low_map(_graph, -1);
2.206 +
2.207 + Visitor visitor(_graph, pred_map, tree_map,
2.208 + order_map, order_list, ancestor_map, low_map);
2.209 + DfsVisit<Graph, Visitor> visit(_graph, visitor);
2.210 + visit.run();
2.211 +
2.212 + ChildLists child_lists(_graph);
2.213 + createChildLists(tree_map, order_map, low_map, child_lists);
2.214 +
2.215 + NodeData node_data(2 * order_list.size());
2.216 +
2.217 + EmbedArc embed_arc(_graph, false);
2.218 +
2.219 + MergeRoots merge_roots(_graph);
2.220 +
2.221 + for (int i = order_list.size() - 1; i >= 0; --i) {
2.222 +
2.223 + Node node = order_list[i];
2.224 +
2.225 + Node source = node;
2.226 + for (OutArcIt e(_graph, node); e != INVALID; ++e) {
2.227 + Node target = _graph.target(e);
2.228 +
2.229 + if (order_map[source] < order_map[target] && tree_map[e]) {
2.230 + initFace(target, node_data, order_map, order_list);
2.231 + }
2.232 + }
2.233 +
2.234 + for (OutArcIt e(_graph, node); e != INVALID; ++e) {
2.235 + Node target = _graph.target(e);
2.236 +
2.237 + if (order_map[source] < order_map[target] && !tree_map[e]) {
2.238 + embed_arc[target] = true;
2.239 + walkUp(target, source, i, pred_map, low_map,
2.240 + order_map, order_list, node_data, merge_roots);
2.241 + }
2.242 + }
2.243 +
2.244 + for (typename MergeRoots::Value::iterator it =
2.245 + merge_roots[node].begin(); it != merge_roots[node].end(); ++it) {
2.246 + int rn = *it;
2.247 + walkDown(rn, i, node_data, order_list, child_lists,
2.248 + ancestor_map, low_map, embed_arc, merge_roots);
2.249 + }
2.250 + merge_roots[node].clear();
2.251 +
2.252 + for (OutArcIt e(_graph, node); e != INVALID; ++e) {
2.253 + Node target = _graph.target(e);
2.254 +
2.255 + if (order_map[source] < order_map[target] && !tree_map[e]) {
2.256 + if (embed_arc[target]) {
2.257 + return false;
2.258 + }
2.259 + }
2.260 + }
2.261 + }
2.262 +
2.263 + return true;
2.264 + }
2.265 +
2.266 + private:
2.267 +
2.268 + void createChildLists(const TreeMap& tree_map, const OrderMap& order_map,
2.269 + const LowMap& low_map, ChildLists& child_lists) {
2.270 +
2.271 + for (NodeIt n(_graph); n != INVALID; ++n) {
2.272 + Node source = n;
2.273 +
2.274 + std::vector<Node> targets;
2.275 + for (OutArcIt e(_graph, n); e != INVALID; ++e) {
2.276 + Node target = _graph.target(e);
2.277 +
2.278 + if (order_map[source] < order_map[target] && tree_map[e]) {
2.279 + targets.push_back(target);
2.280 + }
2.281 + }
2.282 +
2.283 + if (targets.size() == 0) {
2.284 + child_lists[source].first = INVALID;
2.285 + } else if (targets.size() == 1) {
2.286 + child_lists[source].first = targets[0];
2.287 + child_lists[targets[0]].prev = INVALID;
2.288 + child_lists[targets[0]].next = INVALID;
2.289 + } else {
2.290 + radixSort(targets.begin(), targets.end(), mapToFunctor(low_map));
2.291 + for (int i = 1; i < int(targets.size()); ++i) {
2.292 + child_lists[targets[i]].prev = targets[i - 1];
2.293 + child_lists[targets[i - 1]].next = targets[i];
2.294 + }
2.295 + child_lists[targets.back()].next = INVALID;
2.296 + child_lists[targets.front()].prev = INVALID;
2.297 + child_lists[source].first = targets.front();
2.298 + }
2.299 + }
2.300 + }
2.301 +
2.302 + void walkUp(const Node& node, Node root, int rorder,
2.303 + const PredMap& pred_map, const LowMap& low_map,
2.304 + const OrderMap& order_map, const OrderList& order_list,
2.305 + NodeData& node_data, MergeRoots& merge_roots) {
2.306 +
2.307 + int na, nb;
2.308 + bool da, db;
2.309 +
2.310 + na = nb = order_map[node];
2.311 + da = true; db = false;
2.312 +
2.313 + while (true) {
2.314 +
2.315 + if (node_data[na].visited == rorder) break;
2.316 + if (node_data[nb].visited == rorder) break;
2.317 +
2.318 + node_data[na].visited = rorder;
2.319 + node_data[nb].visited = rorder;
2.320 +
2.321 + int rn = -1;
2.322 +
2.323 + if (na >= int(order_list.size())) {
2.324 + rn = na;
2.325 + } else if (nb >= int(order_list.size())) {
2.326 + rn = nb;
2.327 + }
2.328 +
2.329 + if (rn == -1) {
2.330 + int nn;
2.331 +
2.332 + nn = da ? node_data[na].prev : node_data[na].next;
2.333 + da = node_data[nn].prev != na;
2.334 + na = nn;
2.335 +
2.336 + nn = db ? node_data[nb].prev : node_data[nb].next;
2.337 + db = node_data[nn].prev != nb;
2.338 + nb = nn;
2.339 +
2.340 + } else {
2.341 +
2.342 + Node rep = order_list[rn - order_list.size()];
2.343 + Node parent = _graph.source(pred_map[rep]);
2.344 +
2.345 + if (low_map[rep] < rorder) {
2.346 + merge_roots[parent].push_back(rn);
2.347 + } else {
2.348 + merge_roots[parent].push_front(rn);
2.349 + }
2.350 +
2.351 + if (parent != root) {
2.352 + na = nb = order_map[parent];
2.353 + da = true; db = false;
2.354 + } else {
2.355 + break;
2.356 + }
2.357 + }
2.358 + }
2.359 + }
2.360 +
2.361 + void walkDown(int rn, int rorder, NodeData& node_data,
2.362 + OrderList& order_list, ChildLists& child_lists,
2.363 + AncestorMap& ancestor_map, LowMap& low_map,
2.364 + EmbedArc& embed_arc, MergeRoots& merge_roots) {
2.365 +
2.366 + std::vector<std::pair<int, bool> > merge_stack;
2.367 +
2.368 + for (int di = 0; di < 2; ++di) {
2.369 + bool rd = di == 0;
2.370 + int pn = rn;
2.371 + int n = rd ? node_data[rn].next : node_data[rn].prev;
2.372 +
2.373 + while (n != rn) {
2.374 +
2.375 + Node node = order_list[n];
2.376 +
2.377 + if (embed_arc[node]) {
2.378 +
2.379 + // Merging components on the critical path
2.380 + while (!merge_stack.empty()) {
2.381 +
2.382 + // Component root
2.383 + int cn = merge_stack.back().first;
2.384 + bool cd = merge_stack.back().second;
2.385 + merge_stack.pop_back();
2.386 +
2.387 + // Parent of component
2.388 + int dn = merge_stack.back().first;
2.389 + bool dd = merge_stack.back().second;
2.390 + merge_stack.pop_back();
2.391 +
2.392 + Node parent = order_list[dn];
2.393 +
2.394 + // Erasing from merge_roots
2.395 + merge_roots[parent].pop_front();
2.396 +
2.397 + Node child = order_list[cn - order_list.size()];
2.398 +
2.399 + // Erasing from child_lists
2.400 + if (child_lists[child].prev != INVALID) {
2.401 + child_lists[child_lists[child].prev].next =
2.402 + child_lists[child].next;
2.403 + } else {
2.404 + child_lists[parent].first = child_lists[child].next;
2.405 + }
2.406 +
2.407 + if (child_lists[child].next != INVALID) {
2.408 + child_lists[child_lists[child].next].prev =
2.409 + child_lists[child].prev;
2.410 + }
2.411 +
2.412 + // Merging external faces
2.413 + {
2.414 + int en = cn;
2.415 + cn = cd ? node_data[cn].prev : node_data[cn].next;
2.416 + cd = node_data[cn].next == en;
2.417 +
2.418 + }
2.419 +
2.420 + if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn;
2.421 + if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn;
2.422 +
2.423 + }
2.424 +
2.425 + bool d = pn == node_data[n].prev;
2.426 +
2.427 + if (node_data[n].prev == node_data[n].next &&
2.428 + node_data[n].inverted) {
2.429 + d = !d;
2.430 + }
2.431 +
2.432 + // Embedding arc into external face
2.433 + if (rd) node_data[rn].next = n; else node_data[rn].prev = n;
2.434 + if (d) node_data[n].prev = rn; else node_data[n].next = rn;
2.435 + pn = rn;
2.436 +
2.437 + embed_arc[order_list[n]] = false;
2.438 + }
2.439 +
2.440 + if (!merge_roots[node].empty()) {
2.441 +
2.442 + bool d = pn == node_data[n].prev;
2.443 +
2.444 + merge_stack.push_back(std::make_pair(n, d));
2.445 +
2.446 + int rn = merge_roots[node].front();
2.447 +
2.448 + int xn = node_data[rn].next;
2.449 + Node xnode = order_list[xn];
2.450 +
2.451 + int yn = node_data[rn].prev;
2.452 + Node ynode = order_list[yn];
2.453 +
2.454 + bool rd;
2.455 + if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) {
2.456 + rd = true;
2.457 + } else if (!external(ynode, rorder, child_lists,
2.458 + ancestor_map, low_map)) {
2.459 + rd = false;
2.460 + } else if (pertinent(xnode, embed_arc, merge_roots)) {
2.461 + rd = true;
2.462 + } else {
2.463 + rd = false;
2.464 + }
2.465 +
2.466 + merge_stack.push_back(std::make_pair(rn, rd));
2.467 +
2.468 + pn = rn;
2.469 + n = rd ? xn : yn;
2.470 +
2.471 + } else if (!external(node, rorder, child_lists,
2.472 + ancestor_map, low_map)) {
2.473 + int nn = (node_data[n].next != pn ?
2.474 + node_data[n].next : node_data[n].prev);
2.475 +
2.476 + bool nd = n == node_data[nn].prev;
2.477 +
2.478 + if (nd) node_data[nn].prev = pn;
2.479 + else node_data[nn].next = pn;
2.480 +
2.481 + if (n == node_data[pn].prev) node_data[pn].prev = nn;
2.482 + else node_data[pn].next = nn;
2.483 +
2.484 + node_data[nn].inverted =
2.485 + (node_data[nn].prev == node_data[nn].next && nd != rd);
2.486 +
2.487 + n = nn;
2.488 + }
2.489 + else break;
2.490 +
2.491 + }
2.492 +
2.493 + if (!merge_stack.empty() || n == rn) {
2.494 + break;
2.495 + }
2.496 + }
2.497 + }
2.498 +
2.499 + void initFace(const Node& node, NodeData& node_data,
2.500 + const OrderMap& order_map, const OrderList& order_list) {
2.501 + int n = order_map[node];
2.502 + int rn = n + order_list.size();
2.503 +
2.504 + node_data[n].next = node_data[n].prev = rn;
2.505 + node_data[rn].next = node_data[rn].prev = n;
2.506 +
2.507 + node_data[n].visited = order_list.size();
2.508 + node_data[rn].visited = order_list.size();
2.509 +
2.510 + }
2.511 +
2.512 + bool external(const Node& node, int rorder,
2.513 + ChildLists& child_lists, AncestorMap& ancestor_map,
2.514 + LowMap& low_map) {
2.515 + Node child = child_lists[node].first;
2.516 +
2.517 + if (child != INVALID) {
2.518 + if (low_map[child] < rorder) return true;
2.519 + }
2.520 +
2.521 + if (ancestor_map[node] < rorder) return true;
2.522 +
2.523 + return false;
2.524 + }
2.525 +
2.526 + bool pertinent(const Node& node, const EmbedArc& embed_arc,
2.527 + const MergeRoots& merge_roots) {
2.528 + return !merge_roots[node].empty() || embed_arc[node];
2.529 + }
2.530 +
2.531 + };
2.532 +
2.533 + /// \ingroup planar
2.534 + ///
2.535 + /// \brief Planar embedding of an undirected simple graph
2.536 + ///
2.537 + /// This class implements the Boyer-Myrvold algorithm for planar
2.538 + /// embedding of an undirected graph. The planar embedding is an
2.539 + /// ordering of the outgoing edges of the nodes, which is a possible
2.540 + /// configuration to draw the graph in the plane. If there is not
2.541 + /// such ordering then the graph contains a \f$ K_5 \f$ (full graph
2.542 + /// with 5 nodes) or a \f$ K_{3,3} \f$ (complete bipartite graph on
2.543 + /// 3 ANode and 3 BNode) subdivision.
2.544 + ///
2.545 + /// The current implementation calculates either an embedding or a
2.546 + /// Kuratowski subdivision. The running time of the algorithm is
2.547 + /// \f$ O(n) \f$.
2.548 + template <typename Graph>
2.549 + class PlanarEmbedding {
2.550 + private:
2.551 +
2.552 + TEMPLATE_GRAPH_TYPEDEFS(Graph);
2.553 +
2.554 + const Graph& _graph;
2.555 + typename Graph::template ArcMap<Arc> _embedding;
2.556 +
2.557 + typename Graph::template EdgeMap<bool> _kuratowski;
2.558 +
2.559 + private:
2.560 +
2.561 + typedef typename Graph::template NodeMap<Arc> PredMap;
2.562 +
2.563 + typedef typename Graph::template EdgeMap<bool> TreeMap;
2.564 +
2.565 + typedef typename Graph::template NodeMap<int> OrderMap;
2.566 + typedef std::vector<Node> OrderList;
2.567 +
2.568 + typedef typename Graph::template NodeMap<int> LowMap;
2.569 + typedef typename Graph::template NodeMap<int> AncestorMap;
2.570 +
2.571 + typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode;
2.572 + typedef std::vector<NodeDataNode> NodeData;
2.573 +
2.574 + typedef _planarity_bits::ChildListNode<Graph> ChildListNode;
2.575 + typedef typename Graph::template NodeMap<ChildListNode> ChildLists;
2.576 +
2.577 + typedef typename Graph::template NodeMap<std::list<int> > MergeRoots;
2.578 +
2.579 + typedef typename Graph::template NodeMap<Arc> EmbedArc;
2.580 +
2.581 + typedef _planarity_bits::ArcListNode<Graph> ArcListNode;
2.582 + typedef typename Graph::template ArcMap<ArcListNode> ArcLists;
2.583 +
2.584 + typedef typename Graph::template NodeMap<bool> FlipMap;
2.585 +
2.586 + typedef typename Graph::template NodeMap<int> TypeMap;
2.587 +
2.588 + enum IsolatorNodeType {
2.589 + HIGHX = 6, LOWX = 7,
2.590 + HIGHY = 8, LOWY = 9,
2.591 + ROOT = 10, PERTINENT = 11,
2.592 + INTERNAL = 12
2.593 + };
2.594 +
2.595 + public:
2.596 +
2.597 + /// \brief The map for store of embedding
2.598 + typedef typename Graph::template ArcMap<Arc> EmbeddingMap;
2.599 +
2.600 + /// \brief Constructor
2.601 + ///
2.602 + /// \note The graph should be simple, i.e. parallel and loop arc
2.603 + /// free.
2.604 + PlanarEmbedding(const Graph& graph)
2.605 + : _graph(graph), _embedding(_graph), _kuratowski(graph, false) {}
2.606 +
2.607 + /// \brief Runs the algorithm.
2.608 + ///
2.609 + /// Runs the algorithm.
2.610 + /// \param kuratowski If the parameter is false, then the
2.611 + /// algorithm does not compute a Kuratowski subdivision.
2.612 + ///\return %True when the graph is planar.
2.613 + bool run(bool kuratowski = true) {
2.614 + typedef _planarity_bits::PlanarityVisitor<Graph> Visitor;
2.615 +
2.616 + PredMap pred_map(_graph, INVALID);
2.617 + TreeMap tree_map(_graph, false);
2.618 +
2.619 + OrderMap order_map(_graph, -1);
2.620 + OrderList order_list;
2.621 +
2.622 + AncestorMap ancestor_map(_graph, -1);
2.623 + LowMap low_map(_graph, -1);
2.624 +
2.625 + Visitor visitor(_graph, pred_map, tree_map,
2.626 + order_map, order_list, ancestor_map, low_map);
2.627 + DfsVisit<Graph, Visitor> visit(_graph, visitor);
2.628 + visit.run();
2.629 +
2.630 + ChildLists child_lists(_graph);
2.631 + createChildLists(tree_map, order_map, low_map, child_lists);
2.632 +
2.633 + NodeData node_data(2 * order_list.size());
2.634 +
2.635 + EmbedArc embed_arc(_graph, INVALID);
2.636 +
2.637 + MergeRoots merge_roots(_graph);
2.638 +
2.639 + ArcLists arc_lists(_graph);
2.640 +
2.641 + FlipMap flip_map(_graph, false);
2.642 +
2.643 + for (int i = order_list.size() - 1; i >= 0; --i) {
2.644 +
2.645 + Node node = order_list[i];
2.646 +
2.647 + node_data[i].first = INVALID;
2.648 +
2.649 + Node source = node;
2.650 + for (OutArcIt e(_graph, node); e != INVALID; ++e) {
2.651 + Node target = _graph.target(e);
2.652 +
2.653 + if (order_map[source] < order_map[target] && tree_map[e]) {
2.654 + initFace(target, arc_lists, node_data,
2.655 + pred_map, order_map, order_list);
2.656 + }
2.657 + }
2.658 +
2.659 + for (OutArcIt e(_graph, node); e != INVALID; ++e) {
2.660 + Node target = _graph.target(e);
2.661 +
2.662 + if (order_map[source] < order_map[target] && !tree_map[e]) {
2.663 + embed_arc[target] = e;
2.664 + walkUp(target, source, i, pred_map, low_map,
2.665 + order_map, order_list, node_data, merge_roots);
2.666 + }
2.667 + }
2.668 +
2.669 + for (typename MergeRoots::Value::iterator it =
2.670 + merge_roots[node].begin(); it != merge_roots[node].end(); ++it) {
2.671 + int rn = *it;
2.672 + walkDown(rn, i, node_data, arc_lists, flip_map, order_list,
2.673 + child_lists, ancestor_map, low_map, embed_arc, merge_roots);
2.674 + }
2.675 + merge_roots[node].clear();
2.676 +
2.677 + for (OutArcIt e(_graph, node); e != INVALID; ++e) {
2.678 + Node target = _graph.target(e);
2.679 +
2.680 + if (order_map[source] < order_map[target] && !tree_map[e]) {
2.681 + if (embed_arc[target] != INVALID) {
2.682 + if (kuratowski) {
2.683 + isolateKuratowski(e, node_data, arc_lists, flip_map,
2.684 + order_map, order_list, pred_map, child_lists,
2.685 + ancestor_map, low_map,
2.686 + embed_arc, merge_roots);
2.687 + }
2.688 + return false;
2.689 + }
2.690 + }
2.691 + }
2.692 + }
2.693 +
2.694 + for (int i = 0; i < int(order_list.size()); ++i) {
2.695 +
2.696 + mergeRemainingFaces(order_list[i], node_data, order_list, order_map,
2.697 + child_lists, arc_lists);
2.698 + storeEmbedding(order_list[i], node_data, order_map, pred_map,
2.699 + arc_lists, flip_map);
2.700 + }
2.701 +
2.702 + return true;
2.703 + }
2.704 +
2.705 + /// \brief Gives back the successor of an arc
2.706 + ///
2.707 + /// Gives back the successor of an arc. This function makes
2.708 + /// possible to query the cyclic order of the outgoing arcs from
2.709 + /// a node.
2.710 + Arc next(const Arc& arc) const {
2.711 + return _embedding[arc];
2.712 + }
2.713 +
2.714 + /// \brief Gives back the calculated embedding map
2.715 + ///
2.716 + /// The returned map contains the successor of each arc in the
2.717 + /// graph.
2.718 + const EmbeddingMap& embedding() const {
2.719 + return _embedding;
2.720 + }
2.721 +
2.722 + /// \brief Gives back true if the undirected arc is in the
2.723 + /// kuratowski subdivision
2.724 + ///
2.725 + /// Gives back true if the undirected arc is in the kuratowski
2.726 + /// subdivision
2.727 + /// \note The \c run() had to be called with true value.
2.728 + bool kuratowski(const Edge& edge) {
2.729 + return _kuratowski[edge];
2.730 + }
2.731 +
2.732 + private:
2.733 +
2.734 + void createChildLists(const TreeMap& tree_map, const OrderMap& order_map,
2.735 + const LowMap& low_map, ChildLists& child_lists) {
2.736 +
2.737 + for (NodeIt n(_graph); n != INVALID; ++n) {
2.738 + Node source = n;
2.739 +
2.740 + std::vector<Node> targets;
2.741 + for (OutArcIt e(_graph, n); e != INVALID; ++e) {
2.742 + Node target = _graph.target(e);
2.743 +
2.744 + if (order_map[source] < order_map[target] && tree_map[e]) {
2.745 + targets.push_back(target);
2.746 + }
2.747 + }
2.748 +
2.749 + if (targets.size() == 0) {
2.750 + child_lists[source].first = INVALID;
2.751 + } else if (targets.size() == 1) {
2.752 + child_lists[source].first = targets[0];
2.753 + child_lists[targets[0]].prev = INVALID;
2.754 + child_lists[targets[0]].next = INVALID;
2.755 + } else {
2.756 + radixSort(targets.begin(), targets.end(), mapToFunctor(low_map));
2.757 + for (int i = 1; i < int(targets.size()); ++i) {
2.758 + child_lists[targets[i]].prev = targets[i - 1];
2.759 + child_lists[targets[i - 1]].next = targets[i];
2.760 + }
2.761 + child_lists[targets.back()].next = INVALID;
2.762 + child_lists[targets.front()].prev = INVALID;
2.763 + child_lists[source].first = targets.front();
2.764 + }
2.765 + }
2.766 + }
2.767 +
2.768 + void walkUp(const Node& node, Node root, int rorder,
2.769 + const PredMap& pred_map, const LowMap& low_map,
2.770 + const OrderMap& order_map, const OrderList& order_list,
2.771 + NodeData& node_data, MergeRoots& merge_roots) {
2.772 +
2.773 + int na, nb;
2.774 + bool da, db;
2.775 +
2.776 + na = nb = order_map[node];
2.777 + da = true; db = false;
2.778 +
2.779 + while (true) {
2.780 +
2.781 + if (node_data[na].visited == rorder) break;
2.782 + if (node_data[nb].visited == rorder) break;
2.783 +
2.784 + node_data[na].visited = rorder;
2.785 + node_data[nb].visited = rorder;
2.786 +
2.787 + int rn = -1;
2.788 +
2.789 + if (na >= int(order_list.size())) {
2.790 + rn = na;
2.791 + } else if (nb >= int(order_list.size())) {
2.792 + rn = nb;
2.793 + }
2.794 +
2.795 + if (rn == -1) {
2.796 + int nn;
2.797 +
2.798 + nn = da ? node_data[na].prev : node_data[na].next;
2.799 + da = node_data[nn].prev != na;
2.800 + na = nn;
2.801 +
2.802 + nn = db ? node_data[nb].prev : node_data[nb].next;
2.803 + db = node_data[nn].prev != nb;
2.804 + nb = nn;
2.805 +
2.806 + } else {
2.807 +
2.808 + Node rep = order_list[rn - order_list.size()];
2.809 + Node parent = _graph.source(pred_map[rep]);
2.810 +
2.811 + if (low_map[rep] < rorder) {
2.812 + merge_roots[parent].push_back(rn);
2.813 + } else {
2.814 + merge_roots[parent].push_front(rn);
2.815 + }
2.816 +
2.817 + if (parent != root) {
2.818 + na = nb = order_map[parent];
2.819 + da = true; db = false;
2.820 + } else {
2.821 + break;
2.822 + }
2.823 + }
2.824 + }
2.825 + }
2.826 +
2.827 + void walkDown(int rn, int rorder, NodeData& node_data,
2.828 + ArcLists& arc_lists, FlipMap& flip_map,
2.829 + OrderList& order_list, ChildLists& child_lists,
2.830 + AncestorMap& ancestor_map, LowMap& low_map,
2.831 + EmbedArc& embed_arc, MergeRoots& merge_roots) {
2.832 +
2.833 + std::vector<std::pair<int, bool> > merge_stack;
2.834 +
2.835 + for (int di = 0; di < 2; ++di) {
2.836 + bool rd = di == 0;
2.837 + int pn = rn;
2.838 + int n = rd ? node_data[rn].next : node_data[rn].prev;
2.839 +
2.840 + while (n != rn) {
2.841 +
2.842 + Node node = order_list[n];
2.843 +
2.844 + if (embed_arc[node] != INVALID) {
2.845 +
2.846 + // Merging components on the critical path
2.847 + while (!merge_stack.empty()) {
2.848 +
2.849 + // Component root
2.850 + int cn = merge_stack.back().first;
2.851 + bool cd = merge_stack.back().second;
2.852 + merge_stack.pop_back();
2.853 +
2.854 + // Parent of component
2.855 + int dn = merge_stack.back().first;
2.856 + bool dd = merge_stack.back().second;
2.857 + merge_stack.pop_back();
2.858 +
2.859 + Node parent = order_list[dn];
2.860 +
2.861 + // Erasing from merge_roots
2.862 + merge_roots[parent].pop_front();
2.863 +
2.864 + Node child = order_list[cn - order_list.size()];
2.865 +
2.866 + // Erasing from child_lists
2.867 + if (child_lists[child].prev != INVALID) {
2.868 + child_lists[child_lists[child].prev].next =
2.869 + child_lists[child].next;
2.870 + } else {
2.871 + child_lists[parent].first = child_lists[child].next;
2.872 + }
2.873 +
2.874 + if (child_lists[child].next != INVALID) {
2.875 + child_lists[child_lists[child].next].prev =
2.876 + child_lists[child].prev;
2.877 + }
2.878 +
2.879 + // Merging arcs + flipping
2.880 + Arc de = node_data[dn].first;
2.881 + Arc ce = node_data[cn].first;
2.882 +
2.883 + flip_map[order_list[cn - order_list.size()]] = cd != dd;
2.884 + if (cd != dd) {
2.885 + std::swap(arc_lists[ce].prev, arc_lists[ce].next);
2.886 + ce = arc_lists[ce].prev;
2.887 + std::swap(arc_lists[ce].prev, arc_lists[ce].next);
2.888 + }
2.889 +
2.890 + {
2.891 + Arc dne = arc_lists[de].next;
2.892 + Arc cne = arc_lists[ce].next;
2.893 +
2.894 + arc_lists[de].next = cne;
2.895 + arc_lists[ce].next = dne;
2.896 +
2.897 + arc_lists[dne].prev = ce;
2.898 + arc_lists[cne].prev = de;
2.899 + }
2.900 +
2.901 + if (dd) {
2.902 + node_data[dn].first = ce;
2.903 + }
2.904 +
2.905 + // Merging external faces
2.906 + {
2.907 + int en = cn;
2.908 + cn = cd ? node_data[cn].prev : node_data[cn].next;
2.909 + cd = node_data[cn].next == en;
2.910 +
2.911 + if (node_data[cn].prev == node_data[cn].next &&
2.912 + node_data[cn].inverted) {
2.913 + cd = !cd;
2.914 + }
2.915 + }
2.916 +
2.917 + if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn;
2.918 + if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn;
2.919 +
2.920 + }
2.921 +
2.922 + bool d = pn == node_data[n].prev;
2.923 +
2.924 + if (node_data[n].prev == node_data[n].next &&
2.925 + node_data[n].inverted) {
2.926 + d = !d;
2.927 + }
2.928 +
2.929 + // Add new arc
2.930 + {
2.931 + Arc arc = embed_arc[node];
2.932 + Arc re = node_data[rn].first;
2.933 +
2.934 + arc_lists[arc_lists[re].next].prev = arc;
2.935 + arc_lists[arc].next = arc_lists[re].next;
2.936 + arc_lists[arc].prev = re;
2.937 + arc_lists[re].next = arc;
2.938 +
2.939 + if (!rd) {
2.940 + node_data[rn].first = arc;
2.941 + }
2.942 +
2.943 + Arc rev = _graph.oppositeArc(arc);
2.944 + Arc e = node_data[n].first;
2.945 +
2.946 + arc_lists[arc_lists[e].next].prev = rev;
2.947 + arc_lists[rev].next = arc_lists[e].next;
2.948 + arc_lists[rev].prev = e;
2.949 + arc_lists[e].next = rev;
2.950 +
2.951 + if (d) {
2.952 + node_data[n].first = rev;
2.953 + }
2.954 +
2.955 + }
2.956 +
2.957 + // Embedding arc into external face
2.958 + if (rd) node_data[rn].next = n; else node_data[rn].prev = n;
2.959 + if (d) node_data[n].prev = rn; else node_data[n].next = rn;
2.960 + pn = rn;
2.961 +
2.962 + embed_arc[order_list[n]] = INVALID;
2.963 + }
2.964 +
2.965 + if (!merge_roots[node].empty()) {
2.966 +
2.967 + bool d = pn == node_data[n].prev;
2.968 + if (node_data[n].prev == node_data[n].next &&
2.969 + node_data[n].inverted) {
2.970 + d = !d;
2.971 + }
2.972 +
2.973 + merge_stack.push_back(std::make_pair(n, d));
2.974 +
2.975 + int rn = merge_roots[node].front();
2.976 +
2.977 + int xn = node_data[rn].next;
2.978 + Node xnode = order_list[xn];
2.979 +
2.980 + int yn = node_data[rn].prev;
2.981 + Node ynode = order_list[yn];
2.982 +
2.983 + bool rd;
2.984 + if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) {
2.985 + rd = true;
2.986 + } else if (!external(ynode, rorder, child_lists,
2.987 + ancestor_map, low_map)) {
2.988 + rd = false;
2.989 + } else if (pertinent(xnode, embed_arc, merge_roots)) {
2.990 + rd = true;
2.991 + } else {
2.992 + rd = false;
2.993 + }
2.994 +
2.995 + merge_stack.push_back(std::make_pair(rn, rd));
2.996 +
2.997 + pn = rn;
2.998 + n = rd ? xn : yn;
2.999 +
2.1000 + } else if (!external(node, rorder, child_lists,
2.1001 + ancestor_map, low_map)) {
2.1002 + int nn = (node_data[n].next != pn ?
2.1003 + node_data[n].next : node_data[n].prev);
2.1004 +
2.1005 + bool nd = n == node_data[nn].prev;
2.1006 +
2.1007 + if (nd) node_data[nn].prev = pn;
2.1008 + else node_data[nn].next = pn;
2.1009 +
2.1010 + if (n == node_data[pn].prev) node_data[pn].prev = nn;
2.1011 + else node_data[pn].next = nn;
2.1012 +
2.1013 + node_data[nn].inverted =
2.1014 + (node_data[nn].prev == node_data[nn].next && nd != rd);
2.1015 +
2.1016 + n = nn;
2.1017 + }
2.1018 + else break;
2.1019 +
2.1020 + }
2.1021 +
2.1022 + if (!merge_stack.empty() || n == rn) {
2.1023 + break;
2.1024 + }
2.1025 + }
2.1026 + }
2.1027 +
2.1028 + void initFace(const Node& node, ArcLists& arc_lists,
2.1029 + NodeData& node_data, const PredMap& pred_map,
2.1030 + const OrderMap& order_map, const OrderList& order_list) {
2.1031 + int n = order_map[node];
2.1032 + int rn = n + order_list.size();
2.1033 +
2.1034 + node_data[n].next = node_data[n].prev = rn;
2.1035 + node_data[rn].next = node_data[rn].prev = n;
2.1036 +
2.1037 + node_data[n].visited = order_list.size();
2.1038 + node_data[rn].visited = order_list.size();
2.1039 +
2.1040 + node_data[n].inverted = false;
2.1041 + node_data[rn].inverted = false;
2.1042 +
2.1043 + Arc arc = pred_map[node];
2.1044 + Arc rev = _graph.oppositeArc(arc);
2.1045 +
2.1046 + node_data[rn].first = arc;
2.1047 + node_data[n].first = rev;
2.1048 +
2.1049 + arc_lists[arc].prev = arc;
2.1050 + arc_lists[arc].next = arc;
2.1051 +
2.1052 + arc_lists[rev].prev = rev;
2.1053 + arc_lists[rev].next = rev;
2.1054 +
2.1055 + }
2.1056 +
2.1057 + void mergeRemainingFaces(const Node& node, NodeData& node_data,
2.1058 + OrderList& order_list, OrderMap& order_map,
2.1059 + ChildLists& child_lists, ArcLists& arc_lists) {
2.1060 + while (child_lists[node].first != INVALID) {
2.1061 + int dd = order_map[node];
2.1062 + Node child = child_lists[node].first;
2.1063 + int cd = order_map[child] + order_list.size();
2.1064 + child_lists[node].first = child_lists[child].next;
2.1065 +
2.1066 + Arc de = node_data[dd].first;
2.1067 + Arc ce = node_data[cd].first;
2.1068 +
2.1069 + if (de != INVALID) {
2.1070 + Arc dne = arc_lists[de].next;
2.1071 + Arc cne = arc_lists[ce].next;
2.1072 +
2.1073 + arc_lists[de].next = cne;
2.1074 + arc_lists[ce].next = dne;
2.1075 +
2.1076 + arc_lists[dne].prev = ce;
2.1077 + arc_lists[cne].prev = de;
2.1078 + }
2.1079 +
2.1080 + node_data[dd].first = ce;
2.1081 +
2.1082 + }
2.1083 + }
2.1084 +
2.1085 + void storeEmbedding(const Node& node, NodeData& node_data,
2.1086 + OrderMap& order_map, PredMap& pred_map,
2.1087 + ArcLists& arc_lists, FlipMap& flip_map) {
2.1088 +
2.1089 + if (node_data[order_map[node]].first == INVALID) return;
2.1090 +
2.1091 + if (pred_map[node] != INVALID) {
2.1092 + Node source = _graph.source(pred_map[node]);
2.1093 + flip_map[node] = flip_map[node] != flip_map[source];
2.1094 + }
2.1095 +
2.1096 + Arc first = node_data[order_map[node]].first;
2.1097 + Arc prev = first;
2.1098 +
2.1099 + Arc arc = flip_map[node] ?
2.1100 + arc_lists[prev].prev : arc_lists[prev].next;
2.1101 +
2.1102 + _embedding[prev] = arc;
2.1103 +
2.1104 + while (arc != first) {
2.1105 + Arc next = arc_lists[arc].prev == prev ?
2.1106 + arc_lists[arc].next : arc_lists[arc].prev;
2.1107 + prev = arc; arc = next;
2.1108 + _embedding[prev] = arc;
2.1109 + }
2.1110 + }
2.1111 +
2.1112 +
2.1113 + bool external(const Node& node, int rorder,
2.1114 + ChildLists& child_lists, AncestorMap& ancestor_map,
2.1115 + LowMap& low_map) {
2.1116 + Node child = child_lists[node].first;
2.1117 +
2.1118 + if (child != INVALID) {
2.1119 + if (low_map[child] < rorder) return true;
2.1120 + }
2.1121 +
2.1122 + if (ancestor_map[node] < rorder) return true;
2.1123 +
2.1124 + return false;
2.1125 + }
2.1126 +
2.1127 + bool pertinent(const Node& node, const EmbedArc& embed_arc,
2.1128 + const MergeRoots& merge_roots) {
2.1129 + return !merge_roots[node].empty() || embed_arc[node] != INVALID;
2.1130 + }
2.1131 +
2.1132 + int lowPoint(const Node& node, OrderMap& order_map, ChildLists& child_lists,
2.1133 + AncestorMap& ancestor_map, LowMap& low_map) {
2.1134 + int low_point;
2.1135 +
2.1136 + Node child = child_lists[node].first;
2.1137 +
2.1138 + if (child != INVALID) {
2.1139 + low_point = low_map[child];
2.1140 + } else {
2.1141 + low_point = order_map[node];
2.1142 + }
2.1143 +
2.1144 + if (low_point > ancestor_map[node]) {
2.1145 + low_point = ancestor_map[node];
2.1146 + }
2.1147 +
2.1148 + return low_point;
2.1149 + }
2.1150 +
2.1151 + int findComponentRoot(Node root, Node node, ChildLists& child_lists,
2.1152 + OrderMap& order_map, OrderList& order_list) {
2.1153 +
2.1154 + int order = order_map[root];
2.1155 + int norder = order_map[node];
2.1156 +
2.1157 + Node child = child_lists[root].first;
2.1158 + while (child != INVALID) {
2.1159 + int corder = order_map[child];
2.1160 + if (corder > order && corder < norder) {
2.1161 + order = corder;
2.1162 + }
2.1163 + child = child_lists[child].next;
2.1164 + }
2.1165 + return order + order_list.size();
2.1166 + }
2.1167 +
2.1168 + Node findPertinent(Node node, OrderMap& order_map, NodeData& node_data,
2.1169 + EmbedArc& embed_arc, MergeRoots& merge_roots) {
2.1170 + Node wnode =_graph.target(node_data[order_map[node]].first);
2.1171 + while (!pertinent(wnode, embed_arc, merge_roots)) {
2.1172 + wnode = _graph.target(node_data[order_map[wnode]].first);
2.1173 + }
2.1174 + return wnode;
2.1175 + }
2.1176 +
2.1177 +
2.1178 + Node findExternal(Node node, int rorder, OrderMap& order_map,
2.1179 + ChildLists& child_lists, AncestorMap& ancestor_map,
2.1180 + LowMap& low_map, NodeData& node_data) {
2.1181 + Node wnode =_graph.target(node_data[order_map[node]].first);
2.1182 + while (!external(wnode, rorder, child_lists, ancestor_map, low_map)) {
2.1183 + wnode = _graph.target(node_data[order_map[wnode]].first);
2.1184 + }
2.1185 + return wnode;
2.1186 + }
2.1187 +
2.1188 + void markCommonPath(Node node, int rorder, Node& wnode, Node& znode,
2.1189 + OrderList& order_list, OrderMap& order_map,
2.1190 + NodeData& node_data, ArcLists& arc_lists,
2.1191 + EmbedArc& embed_arc, MergeRoots& merge_roots,
2.1192 + ChildLists& child_lists, AncestorMap& ancestor_map,
2.1193 + LowMap& low_map) {
2.1194 +
2.1195 + Node cnode = node;
2.1196 + Node pred = INVALID;
2.1197 +
2.1198 + while (true) {
2.1199 +
2.1200 + bool pert = pertinent(cnode, embed_arc, merge_roots);
2.1201 + bool ext = external(cnode, rorder, child_lists, ancestor_map, low_map);
2.1202 +
2.1203 + if (pert && ext) {
2.1204 + if (!merge_roots[cnode].empty()) {
2.1205 + int cn = merge_roots[cnode].back();
2.1206 +
2.1207 + if (low_map[order_list[cn - order_list.size()]] < rorder) {
2.1208 + Arc arc = node_data[cn].first;
2.1209 + _kuratowski.set(arc, true);
2.1210 +
2.1211 + pred = cnode;
2.1212 + cnode = _graph.target(arc);
2.1213 +
2.1214 + continue;
2.1215 + }
2.1216 + }
2.1217 + wnode = znode = cnode;
2.1218 + return;
2.1219 +
2.1220 + } else if (pert) {
2.1221 + wnode = cnode;
2.1222 +
2.1223 + while (!external(cnode, rorder, child_lists, ancestor_map, low_map)) {
2.1224 + Arc arc = node_data[order_map[cnode]].first;
2.1225 +
2.1226 + if (_graph.target(arc) == pred) {
2.1227 + arc = arc_lists[arc].next;
2.1228 + }
2.1229 + _kuratowski.set(arc, true);
2.1230 +
2.1231 + Node next = _graph.target(arc);
2.1232 + pred = cnode; cnode = next;
2.1233 + }
2.1234 +
2.1235 + znode = cnode;
2.1236 + return;
2.1237 +
2.1238 + } else if (ext) {
2.1239 + znode = cnode;
2.1240 +
2.1241 + while (!pertinent(cnode, embed_arc, merge_roots)) {
2.1242 + Arc arc = node_data[order_map[cnode]].first;
2.1243 +
2.1244 + if (_graph.target(arc) == pred) {
2.1245 + arc = arc_lists[arc].next;
2.1246 + }
2.1247 + _kuratowski.set(arc, true);
2.1248 +
2.1249 + Node next = _graph.target(arc);
2.1250 + pred = cnode; cnode = next;
2.1251 + }
2.1252 +
2.1253 + wnode = cnode;
2.1254 + return;
2.1255 +
2.1256 + } else {
2.1257 + Arc arc = node_data[order_map[cnode]].first;
2.1258 +
2.1259 + if (_graph.target(arc) == pred) {
2.1260 + arc = arc_lists[arc].next;
2.1261 + }
2.1262 + _kuratowski.set(arc, true);
2.1263 +
2.1264 + Node next = _graph.target(arc);
2.1265 + pred = cnode; cnode = next;
2.1266 + }
2.1267 +
2.1268 + }
2.1269 +
2.1270 + }
2.1271 +
2.1272 + void orientComponent(Node root, int rn, OrderMap& order_map,
2.1273 + PredMap& pred_map, NodeData& node_data,
2.1274 + ArcLists& arc_lists, FlipMap& flip_map,
2.1275 + TypeMap& type_map) {
2.1276 + node_data[order_map[root]].first = node_data[rn].first;
2.1277 + type_map[root] = 1;
2.1278 +
2.1279 + std::vector<Node> st, qu;
2.1280 +
2.1281 + st.push_back(root);
2.1282 + while (!st.empty()) {
2.1283 + Node node = st.back();
2.1284 + st.pop_back();
2.1285 + qu.push_back(node);
2.1286 +
2.1287 + Arc arc = node_data[order_map[node]].first;
2.1288 +
2.1289 + if (type_map[_graph.target(arc)] == 0) {
2.1290 + st.push_back(_graph.target(arc));
2.1291 + type_map[_graph.target(arc)] = 1;
2.1292 + }
2.1293 +
2.1294 + Arc last = arc, pred = arc;
2.1295 + arc = arc_lists[arc].next;
2.1296 + while (arc != last) {
2.1297 +
2.1298 + if (type_map[_graph.target(arc)] == 0) {
2.1299 + st.push_back(_graph.target(arc));
2.1300 + type_map[_graph.target(arc)] = 1;
2.1301 + }
2.1302 +
2.1303 + Arc next = arc_lists[arc].next != pred ?
2.1304 + arc_lists[arc].next : arc_lists[arc].prev;
2.1305 + pred = arc; arc = next;
2.1306 + }
2.1307 +
2.1308 + }
2.1309 +
2.1310 + type_map[root] = 2;
2.1311 + flip_map[root] = false;
2.1312 +
2.1313 + for (int i = 1; i < int(qu.size()); ++i) {
2.1314 +
2.1315 + Node node = qu[i];
2.1316 +
2.1317 + while (type_map[node] != 2) {
2.1318 + st.push_back(node);
2.1319 + type_map[node] = 2;
2.1320 + node = _graph.source(pred_map[node]);
2.1321 + }
2.1322 +
2.1323 + bool flip = flip_map[node];
2.1324 +
2.1325 + while (!st.empty()) {
2.1326 + node = st.back();
2.1327 + st.pop_back();
2.1328 +
2.1329 + flip_map[node] = flip != flip_map[node];
2.1330 + flip = flip_map[node];
2.1331 +
2.1332 + if (flip) {
2.1333 + Arc arc = node_data[order_map[node]].first;
2.1334 + std::swap(arc_lists[arc].prev, arc_lists[arc].next);
2.1335 + arc = arc_lists[arc].prev;
2.1336 + std::swap(arc_lists[arc].prev, arc_lists[arc].next);
2.1337 + node_data[order_map[node]].first = arc;
2.1338 + }
2.1339 + }
2.1340 + }
2.1341 +
2.1342 + for (int i = 0; i < int(qu.size()); ++i) {
2.1343 +
2.1344 + Arc arc = node_data[order_map[qu[i]]].first;
2.1345 + Arc last = arc, pred = arc;
2.1346 +
2.1347 + arc = arc_lists[arc].next;
2.1348 + while (arc != last) {
2.1349 +
2.1350 + if (arc_lists[arc].next == pred) {
2.1351 + std::swap(arc_lists[arc].next, arc_lists[arc].prev);
2.1352 + }
2.1353 + pred = arc; arc = arc_lists[arc].next;
2.1354 + }
2.1355 +
2.1356 + }
2.1357 + }
2.1358 +
2.1359 + void setFaceFlags(Node root, Node wnode, Node ynode, Node xnode,
2.1360 + OrderMap& order_map, NodeData& node_data,
2.1361 + TypeMap& type_map) {
2.1362 + Node node = _graph.target(node_data[order_map[root]].first);
2.1363 +
2.1364 + while (node != ynode) {
2.1365 + type_map[node] = HIGHY;
2.1366 + node = _graph.target(node_data[order_map[node]].first);
2.1367 + }
2.1368 +
2.1369 + while (node != wnode) {
2.1370 + type_map[node] = LOWY;
2.1371 + node = _graph.target(node_data[order_map[node]].first);
2.1372 + }
2.1373 +
2.1374 + node = _graph.target(node_data[order_map[wnode]].first);
2.1375 +
2.1376 + while (node != xnode) {
2.1377 + type_map[node] = LOWX;
2.1378 + node = _graph.target(node_data[order_map[node]].first);
2.1379 + }
2.1380 + type_map[node] = LOWX;
2.1381 +
2.1382 + node = _graph.target(node_data[order_map[xnode]].first);
2.1383 + while (node != root) {
2.1384 + type_map[node] = HIGHX;
2.1385 + node = _graph.target(node_data[order_map[node]].first);
2.1386 + }
2.1387 +
2.1388 + type_map[wnode] = PERTINENT;
2.1389 + type_map[root] = ROOT;
2.1390 + }
2.1391 +
2.1392 + void findInternalPath(std::vector<Arc>& ipath,
2.1393 + Node wnode, Node root, TypeMap& type_map,
2.1394 + OrderMap& order_map, NodeData& node_data,
2.1395 + ArcLists& arc_lists) {
2.1396 + std::vector<Arc> st;
2.1397 +
2.1398 + Node node = wnode;
2.1399 +
2.1400 + while (node != root) {
2.1401 + Arc arc = arc_lists[node_data[order_map[node]].first].next;
2.1402 + st.push_back(arc);
2.1403 + node = _graph.target(arc);
2.1404 + }
2.1405 +
2.1406 + while (true) {
2.1407 + Arc arc = st.back();
2.1408 + if (type_map[_graph.target(arc)] == LOWX ||
2.1409 + type_map[_graph.target(arc)] == HIGHX) {
2.1410 + break;
2.1411 + }
2.1412 + if (type_map[_graph.target(arc)] == 2) {
2.1413 + type_map[_graph.target(arc)] = 3;
2.1414 +
2.1415 + arc = arc_lists[_graph.oppositeArc(arc)].next;
2.1416 + st.push_back(arc);
2.1417 + } else {
2.1418 + st.pop_back();
2.1419 + arc = arc_lists[arc].next;
2.1420 +
2.1421 + while (_graph.oppositeArc(arc) == st.back()) {
2.1422 + arc = st.back();
2.1423 + st.pop_back();
2.1424 + arc = arc_lists[arc].next;
2.1425 + }
2.1426 + st.push_back(arc);
2.1427 + }
2.1428 + }
2.1429 +
2.1430 + for (int i = 0; i < int(st.size()); ++i) {
2.1431 + if (type_map[_graph.target(st[i])] != LOWY &&
2.1432 + type_map[_graph.target(st[i])] != HIGHY) {
2.1433 + for (; i < int(st.size()); ++i) {
2.1434 + ipath.push_back(st[i]);
2.1435 + }
2.1436 + }
2.1437 + }
2.1438 + }
2.1439 +
2.1440 + void setInternalFlags(std::vector<Arc>& ipath, TypeMap& type_map) {
2.1441 + for (int i = 1; i < int(ipath.size()); ++i) {
2.1442 + type_map[_graph.source(ipath[i])] = INTERNAL;
2.1443 + }
2.1444 + }
2.1445 +
2.1446 + void findPilePath(std::vector<Arc>& ppath,
2.1447 + Node root, TypeMap& type_map, OrderMap& order_map,
2.1448 + NodeData& node_data, ArcLists& arc_lists) {
2.1449 + std::vector<Arc> st;
2.1450 +
2.1451 + st.push_back(_graph.oppositeArc(node_data[order_map[root]].first));
2.1452 + st.push_back(node_data[order_map[root]].first);
2.1453 +
2.1454 + while (st.size() > 1) {
2.1455 + Arc arc = st.back();
2.1456 + if (type_map[_graph.target(arc)] == INTERNAL) {
2.1457 + break;
2.1458 + }
2.1459 + if (type_map[_graph.target(arc)] == 3) {
2.1460 + type_map[_graph.target(arc)] = 4;
2.1461 +
2.1462 + arc = arc_lists[_graph.oppositeArc(arc)].next;
2.1463 + st.push_back(arc);
2.1464 + } else {
2.1465 + st.pop_back();
2.1466 + arc = arc_lists[arc].next;
2.1467 +
2.1468 + while (!st.empty() && _graph.oppositeArc(arc) == st.back()) {
2.1469 + arc = st.back();
2.1470 + st.pop_back();
2.1471 + arc = arc_lists[arc].next;
2.1472 + }
2.1473 + st.push_back(arc);
2.1474 + }
2.1475 + }
2.1476 +
2.1477 + for (int i = 1; i < int(st.size()); ++i) {
2.1478 + ppath.push_back(st[i]);
2.1479 + }
2.1480 + }
2.1481 +
2.1482 +
2.1483 + int markExternalPath(Node node, OrderMap& order_map,
2.1484 + ChildLists& child_lists, PredMap& pred_map,
2.1485 + AncestorMap& ancestor_map, LowMap& low_map) {
2.1486 + int lp = lowPoint(node, order_map, child_lists,
2.1487 + ancestor_map, low_map);
2.1488 +
2.1489 + if (ancestor_map[node] != lp) {
2.1490 + node = child_lists[node].first;
2.1491 + _kuratowski[pred_map[node]] = true;
2.1492 +
2.1493 + while (ancestor_map[node] != lp) {
2.1494 + for (OutArcIt e(_graph, node); e != INVALID; ++e) {
2.1495 + Node tnode = _graph.target(e);
2.1496 + if (order_map[tnode] > order_map[node] && low_map[tnode] == lp) {
2.1497 + node = tnode;
2.1498 + _kuratowski[e] = true;
2.1499 + break;
2.1500 + }
2.1501 + }
2.1502 + }
2.1503 + }
2.1504 +
2.1505 + for (OutArcIt e(_graph, node); e != INVALID; ++e) {
2.1506 + if (order_map[_graph.target(e)] == lp) {
2.1507 + _kuratowski[e] = true;
2.1508 + break;
2.1509 + }
2.1510 + }
2.1511 +
2.1512 + return lp;
2.1513 + }
2.1514 +
2.1515 + void markPertinentPath(Node node, OrderMap& order_map,
2.1516 + NodeData& node_data, ArcLists& arc_lists,
2.1517 + EmbedArc& embed_arc, MergeRoots& merge_roots) {
2.1518 + while (embed_arc[node] == INVALID) {
2.1519 + int n = merge_roots[node].front();
2.1520 + Arc arc = node_data[n].first;
2.1521 +
2.1522 + _kuratowski.set(arc, true);
2.1523 +
2.1524 + Node pred = node;
2.1525 + node = _graph.target(arc);
2.1526 + while (!pertinent(node, embed_arc, merge_roots)) {
2.1527 + arc = node_data[order_map[node]].first;
2.1528 + if (_graph.target(arc) == pred) {
2.1529 + arc = arc_lists[arc].next;
2.1530 + }
2.1531 + _kuratowski.set(arc, true);
2.1532 + pred = node;
2.1533 + node = _graph.target(arc);
2.1534 + }
2.1535 + }
2.1536 + _kuratowski.set(embed_arc[node], true);
2.1537 + }
2.1538 +
2.1539 + void markPredPath(Node node, Node snode, PredMap& pred_map) {
2.1540 + while (node != snode) {
2.1541 + _kuratowski.set(pred_map[node], true);
2.1542 + node = _graph.source(pred_map[node]);
2.1543 + }
2.1544 + }
2.1545 +
2.1546 + void markFacePath(Node ynode, Node xnode,
2.1547 + OrderMap& order_map, NodeData& node_data) {
2.1548 + Arc arc = node_data[order_map[ynode]].first;
2.1549 + Node node = _graph.target(arc);
2.1550 + _kuratowski.set(arc, true);
2.1551 +
2.1552 + while (node != xnode) {
2.1553 + arc = node_data[order_map[node]].first;
2.1554 + _kuratowski.set(arc, true);
2.1555 + node = _graph.target(arc);
2.1556 + }
2.1557 + }
2.1558 +
2.1559 + void markInternalPath(std::vector<Arc>& path) {
2.1560 + for (int i = 0; i < int(path.size()); ++i) {
2.1561 + _kuratowski.set(path[i], true);
2.1562 + }
2.1563 + }
2.1564 +
2.1565 + void markPilePath(std::vector<Arc>& path) {
2.1566 + for (int i = 0; i < int(path.size()); ++i) {
2.1567 + _kuratowski.set(path[i], true);
2.1568 + }
2.1569 + }
2.1570 +
2.1571 + void isolateKuratowski(Arc arc, NodeData& node_data,
2.1572 + ArcLists& arc_lists, FlipMap& flip_map,
2.1573 + OrderMap& order_map, OrderList& order_list,
2.1574 + PredMap& pred_map, ChildLists& child_lists,
2.1575 + AncestorMap& ancestor_map, LowMap& low_map,
2.1576 + EmbedArc& embed_arc, MergeRoots& merge_roots) {
2.1577 +
2.1578 + Node root = _graph.source(arc);
2.1579 + Node enode = _graph.target(arc);
2.1580 +
2.1581 + int rorder = order_map[root];
2.1582 +
2.1583 + TypeMap type_map(_graph, 0);
2.1584 +
2.1585 + int rn = findComponentRoot(root, enode, child_lists,
2.1586 + order_map, order_list);
2.1587 +
2.1588 + Node xnode = order_list[node_data[rn].next];
2.1589 + Node ynode = order_list[node_data[rn].prev];
2.1590 +
2.1591 + // Minor-A
2.1592 + {
2.1593 + while (!merge_roots[xnode].empty() || !merge_roots[ynode].empty()) {
2.1594 +
2.1595 + if (!merge_roots[xnode].empty()) {
2.1596 + root = xnode;
2.1597 + rn = merge_roots[xnode].front();
2.1598 + } else {
2.1599 + root = ynode;
2.1600 + rn = merge_roots[ynode].front();
2.1601 + }
2.1602 +
2.1603 + xnode = order_list[node_data[rn].next];
2.1604 + ynode = order_list[node_data[rn].prev];
2.1605 + }
2.1606 +
2.1607 + if (root != _graph.source(arc)) {
2.1608 + orientComponent(root, rn, order_map, pred_map,
2.1609 + node_data, arc_lists, flip_map, type_map);
2.1610 + markFacePath(root, root, order_map, node_data);
2.1611 + int xlp = markExternalPath(xnode, order_map, child_lists,
2.1612 + pred_map, ancestor_map, low_map);
2.1613 + int ylp = markExternalPath(ynode, order_map, child_lists,
2.1614 + pred_map, ancestor_map, low_map);
2.1615 + markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
2.1616 + Node lwnode = findPertinent(ynode, order_map, node_data,
2.1617 + embed_arc, merge_roots);
2.1618 +
2.1619 + markPertinentPath(lwnode, order_map, node_data, arc_lists,
2.1620 + embed_arc, merge_roots);
2.1621 +
2.1622 + return;
2.1623 + }
2.1624 + }
2.1625 +
2.1626 + orientComponent(root, rn, order_map, pred_map,
2.1627 + node_data, arc_lists, flip_map, type_map);
2.1628 +
2.1629 + Node wnode = findPertinent(ynode, order_map, node_data,
2.1630 + embed_arc, merge_roots);
2.1631 + setFaceFlags(root, wnode, ynode, xnode, order_map, node_data, type_map);
2.1632 +
2.1633 +
2.1634 + //Minor-B
2.1635 + if (!merge_roots[wnode].empty()) {
2.1636 + int cn = merge_roots[wnode].back();
2.1637 + Node rep = order_list[cn - order_list.size()];
2.1638 + if (low_map[rep] < rorder) {
2.1639 + markFacePath(root, root, order_map, node_data);
2.1640 + int xlp = markExternalPath(xnode, order_map, child_lists,
2.1641 + pred_map, ancestor_map, low_map);
2.1642 + int ylp = markExternalPath(ynode, order_map, child_lists,
2.1643 + pred_map, ancestor_map, low_map);
2.1644 +
2.1645 + Node lwnode, lznode;
2.1646 + markCommonPath(wnode, rorder, lwnode, lznode, order_list,
2.1647 + order_map, node_data, arc_lists, embed_arc,
2.1648 + merge_roots, child_lists, ancestor_map, low_map);
2.1649 +
2.1650 + markPertinentPath(lwnode, order_map, node_data, arc_lists,
2.1651 + embed_arc, merge_roots);
2.1652 + int zlp = markExternalPath(lznode, order_map, child_lists,
2.1653 + pred_map, ancestor_map, low_map);
2.1654 +
2.1655 + int minlp = xlp < ylp ? xlp : ylp;
2.1656 + if (zlp < minlp) minlp = zlp;
2.1657 +
2.1658 + int maxlp = xlp > ylp ? xlp : ylp;
2.1659 + if (zlp > maxlp) maxlp = zlp;
2.1660 +
2.1661 + markPredPath(order_list[maxlp], order_list[minlp], pred_map);
2.1662 +
2.1663 + return;
2.1664 + }
2.1665 + }
2.1666 +
2.1667 + Node pxnode, pynode;
2.1668 + std::vector<Arc> ipath;
2.1669 + findInternalPath(ipath, wnode, root, type_map, order_map,
2.1670 + node_data, arc_lists);
2.1671 + setInternalFlags(ipath, type_map);
2.1672 + pynode = _graph.source(ipath.front());
2.1673 + pxnode = _graph.target(ipath.back());
2.1674 +
2.1675 + wnode = findPertinent(pynode, order_map, node_data,
2.1676 + embed_arc, merge_roots);
2.1677 +
2.1678 + // Minor-C
2.1679 + {
2.1680 + if (type_map[_graph.source(ipath.front())] == HIGHY) {
2.1681 + if (type_map[_graph.target(ipath.back())] == HIGHX) {
2.1682 + markFacePath(xnode, pxnode, order_map, node_data);
2.1683 + }
2.1684 + markFacePath(root, xnode, order_map, node_data);
2.1685 + markPertinentPath(wnode, order_map, node_data, arc_lists,
2.1686 + embed_arc, merge_roots);
2.1687 + markInternalPath(ipath);
2.1688 + int xlp = markExternalPath(xnode, order_map, child_lists,
2.1689 + pred_map, ancestor_map, low_map);
2.1690 + int ylp = markExternalPath(ynode, order_map, child_lists,
2.1691 + pred_map, ancestor_map, low_map);
2.1692 + markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
2.1693 + return;
2.1694 + }
2.1695 +
2.1696 + if (type_map[_graph.target(ipath.back())] == HIGHX) {
2.1697 + markFacePath(ynode, root, order_map, node_data);
2.1698 + markPertinentPath(wnode, order_map, node_data, arc_lists,
2.1699 + embed_arc, merge_roots);
2.1700 + markInternalPath(ipath);
2.1701 + int xlp = markExternalPath(xnode, order_map, child_lists,
2.1702 + pred_map, ancestor_map, low_map);
2.1703 + int ylp = markExternalPath(ynode, order_map, child_lists,
2.1704 + pred_map, ancestor_map, low_map);
2.1705 + markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
2.1706 + return;
2.1707 + }
2.1708 + }
2.1709 +
2.1710 + std::vector<Arc> ppath;
2.1711 + findPilePath(ppath, root, type_map, order_map, node_data, arc_lists);
2.1712 +
2.1713 + // Minor-D
2.1714 + if (!ppath.empty()) {
2.1715 + markFacePath(ynode, xnode, order_map, node_data);
2.1716 + markPertinentPath(wnode, order_map, node_data, arc_lists,
2.1717 + embed_arc, merge_roots);
2.1718 + markPilePath(ppath);
2.1719 + markInternalPath(ipath);
2.1720 + int xlp = markExternalPath(xnode, order_map, child_lists,
2.1721 + pred_map, ancestor_map, low_map);
2.1722 + int ylp = markExternalPath(ynode, order_map, child_lists,
2.1723 + pred_map, ancestor_map, low_map);
2.1724 + markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
2.1725 + return;
2.1726 + }
2.1727 +
2.1728 + // Minor-E*
2.1729 + {
2.1730 +
2.1731 + if (!external(wnode, rorder, child_lists, ancestor_map, low_map)) {
2.1732 + Node znode = findExternal(pynode, rorder, order_map,
2.1733 + child_lists, ancestor_map,
2.1734 + low_map, node_data);
2.1735 +
2.1736 + if (type_map[znode] == LOWY) {
2.1737 + markFacePath(root, xnode, order_map, node_data);
2.1738 + markPertinentPath(wnode, order_map, node_data, arc_lists,
2.1739 + embed_arc, merge_roots);
2.1740 + markInternalPath(ipath);
2.1741 + int xlp = markExternalPath(xnode, order_map, child_lists,
2.1742 + pred_map, ancestor_map, low_map);
2.1743 + int zlp = markExternalPath(znode, order_map, child_lists,
2.1744 + pred_map, ancestor_map, low_map);
2.1745 + markPredPath(root, order_list[xlp < zlp ? xlp : zlp], pred_map);
2.1746 + } else {
2.1747 + markFacePath(ynode, root, order_map, node_data);
2.1748 + markPertinentPath(wnode, order_map, node_data, arc_lists,
2.1749 + embed_arc, merge_roots);
2.1750 + markInternalPath(ipath);
2.1751 + int ylp = markExternalPath(ynode, order_map, child_lists,
2.1752 + pred_map, ancestor_map, low_map);
2.1753 + int zlp = markExternalPath(znode, order_map, child_lists,
2.1754 + pred_map, ancestor_map, low_map);
2.1755 + markPredPath(root, order_list[ylp < zlp ? ylp : zlp], pred_map);
2.1756 + }
2.1757 + return;
2.1758 + }
2.1759 +
2.1760 + int xlp = markExternalPath(xnode, order_map, child_lists,
2.1761 + pred_map, ancestor_map, low_map);
2.1762 + int ylp = markExternalPath(ynode, order_map, child_lists,
2.1763 + pred_map, ancestor_map, low_map);
2.1764 + int wlp = markExternalPath(wnode, order_map, child_lists,
2.1765 + pred_map, ancestor_map, low_map);
2.1766 +
2.1767 + if (wlp > xlp && wlp > ylp) {
2.1768 + markFacePath(root, root, order_map, node_data);
2.1769 + markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
2.1770 + return;
2.1771 + }
2.1772 +
2.1773 + markInternalPath(ipath);
2.1774 + markPertinentPath(wnode, order_map, node_data, arc_lists,
2.1775 + embed_arc, merge_roots);
2.1776 +
2.1777 + if (xlp > ylp && xlp > wlp) {
2.1778 + markFacePath(root, pynode, order_map, node_data);
2.1779 + markFacePath(wnode, xnode, order_map, node_data);
2.1780 + markPredPath(root, order_list[ylp < wlp ? ylp : wlp], pred_map);
2.1781 + return;
2.1782 + }
2.1783 +
2.1784 + if (ylp > xlp && ylp > wlp) {
2.1785 + markFacePath(pxnode, root, order_map, node_data);
2.1786 + markFacePath(ynode, wnode, order_map, node_data);
2.1787 + markPredPath(root, order_list[xlp < wlp ? xlp : wlp], pred_map);
2.1788 + return;
2.1789 + }
2.1790 +
2.1791 + if (pynode != ynode) {
2.1792 + markFacePath(pxnode, wnode, order_map, node_data);
2.1793 +
2.1794 + int minlp = xlp < ylp ? xlp : ylp;
2.1795 + if (wlp < minlp) minlp = wlp;
2.1796 +
2.1797 + int maxlp = xlp > ylp ? xlp : ylp;
2.1798 + if (wlp > maxlp) maxlp = wlp;
2.1799 +
2.1800 + markPredPath(order_list[maxlp], order_list[minlp], pred_map);
2.1801 + return;
2.1802 + }
2.1803 +
2.1804 + if (pxnode != xnode) {
2.1805 + markFacePath(wnode, pynode, order_map, node_data);
2.1806 +
2.1807 + int minlp = xlp < ylp ? xlp : ylp;
2.1808 + if (wlp < minlp) minlp = wlp;
2.1809 +
2.1810 + int maxlp = xlp > ylp ? xlp : ylp;
2.1811 + if (wlp > maxlp) maxlp = wlp;
2.1812 +
2.1813 + markPredPath(order_list[maxlp], order_list[minlp], pred_map);
2.1814 + return;
2.1815 + }
2.1816 +
2.1817 + markFacePath(root, root, order_map, node_data);
2.1818 + int minlp = xlp < ylp ? xlp : ylp;
2.1819 + if (wlp < minlp) minlp = wlp;
2.1820 + markPredPath(root, order_list[minlp], pred_map);
2.1821 + return;
2.1822 + }
2.1823 +
2.1824 + }
2.1825 +
2.1826 + };
2.1827 +
2.1828 + namespace _planarity_bits {
2.1829 +
2.1830 + template <typename Graph, typename EmbeddingMap>
2.1831 + void makeConnected(Graph& graph, EmbeddingMap& embedding) {
2.1832 + DfsVisitor<Graph> null_visitor;
2.1833 + DfsVisit<Graph, DfsVisitor<Graph> > dfs(graph, null_visitor);
2.1834 + dfs.init();
2.1835 +
2.1836 + typename Graph::Node u = INVALID;
2.1837 + for (typename Graph::NodeIt n(graph); n != INVALID; ++n) {
2.1838 + if (!dfs.reached(n)) {
2.1839 + dfs.addSource(n);
2.1840 + dfs.start();
2.1841 + if (u == INVALID) {
2.1842 + u = n;
2.1843 + } else {
2.1844 + typename Graph::Node v = n;
2.1845 +
2.1846 + typename Graph::Arc ue = typename Graph::OutArcIt(graph, u);
2.1847 + typename Graph::Arc ve = typename Graph::OutArcIt(graph, v);
2.1848 +
2.1849 + typename Graph::Arc e = graph.direct(graph.addEdge(u, v), true);
2.1850 +
2.1851 + if (ue != INVALID) {
2.1852 + embedding[e] = embedding[ue];
2.1853 + embedding[ue] = e;
2.1854 + } else {
2.1855 + embedding[e] = e;
2.1856 + }
2.1857 +
2.1858 + if (ve != INVALID) {
2.1859 + embedding[graph.oppositeArc(e)] = embedding[ve];
2.1860 + embedding[ve] = graph.oppositeArc(e);
2.1861 + } else {
2.1862 + embedding[graph.oppositeArc(e)] = graph.oppositeArc(e);
2.1863 + }
2.1864 + }
2.1865 + }
2.1866 + }
2.1867 + }
2.1868 +
2.1869 + template <typename Graph, typename EmbeddingMap>
2.1870 + void makeBiNodeConnected(Graph& graph, EmbeddingMap& embedding) {
2.1871 + typename Graph::template ArcMap<bool> processed(graph);
2.1872 +
2.1873 + std::vector<typename Graph::Arc> arcs;
2.1874 + for (typename Graph::ArcIt e(graph); e != INVALID; ++e) {
2.1875 + arcs.push_back(e);
2.1876 + }
2.1877 +
2.1878 + IterableBoolMap<Graph, typename Graph::Node> visited(graph, false);
2.1879 +
2.1880 + for (int i = 0; i < int(arcs.size()); ++i) {
2.1881 + typename Graph::Arc pp = arcs[i];
2.1882 + if (processed[pp]) continue;
2.1883 +
2.1884 + typename Graph::Arc e = embedding[graph.oppositeArc(pp)];
2.1885 + processed[e] = true;
2.1886 + visited.set(graph.source(e), true);
2.1887 +
2.1888 + typename Graph::Arc p = e, l = e;
2.1889 + e = embedding[graph.oppositeArc(e)];
2.1890 +
2.1891 + while (e != l) {
2.1892 + processed[e] = true;
2.1893 +
2.1894 + if (visited[graph.source(e)]) {
2.1895 +
2.1896 + typename Graph::Arc n =
2.1897 + graph.direct(graph.addEdge(graph.source(p),
2.1898 + graph.target(e)), true);
2.1899 + embedding[n] = p;
2.1900 + embedding[graph.oppositeArc(pp)] = n;
2.1901 +
2.1902 + embedding[graph.oppositeArc(n)] =
2.1903 + embedding[graph.oppositeArc(e)];
2.1904 + embedding[graph.oppositeArc(e)] =
2.1905 + graph.oppositeArc(n);
2.1906 +
2.1907 + p = n;
2.1908 + e = embedding[graph.oppositeArc(n)];
2.1909 + } else {
2.1910 + visited.set(graph.source(e), true);
2.1911 + pp = p;
2.1912 + p = e;
2.1913 + e = embedding[graph.oppositeArc(e)];
2.1914 + }
2.1915 + }
2.1916 + visited.setAll(false);
2.1917 + }
2.1918 + }
2.1919 +
2.1920 +
2.1921 + template <typename Graph, typename EmbeddingMap>
2.1922 + void makeMaxPlanar(Graph& graph, EmbeddingMap& embedding) {
2.1923 +
2.1924 + typename Graph::template NodeMap<int> degree(graph);
2.1925 +
2.1926 + for (typename Graph::NodeIt n(graph); n != INVALID; ++n) {
2.1927 + degree[n] = countIncEdges(graph, n);
2.1928 + }
2.1929 +
2.1930 + typename Graph::template ArcMap<bool> processed(graph);
2.1931 + IterableBoolMap<Graph, typename Graph::Node> visited(graph, false);
2.1932 +
2.1933 + std::vector<typename Graph::Arc> arcs;
2.1934 + for (typename Graph::ArcIt e(graph); e != INVALID; ++e) {
2.1935 + arcs.push_back(e);
2.1936 + }
2.1937 +
2.1938 + for (int i = 0; i < int(arcs.size()); ++i) {
2.1939 + typename Graph::Arc e = arcs[i];
2.1940 +
2.1941 + if (processed[e]) continue;
2.1942 + processed[e] = true;
2.1943 +
2.1944 + typename Graph::Arc mine = e;
2.1945 + int mind = degree[graph.source(e)];
2.1946 +
2.1947 + int face_size = 1;
2.1948 +
2.1949 + typename Graph::Arc l = e;
2.1950 + e = embedding[graph.oppositeArc(e)];
2.1951 + while (l != e) {
2.1952 + processed[e] = true;
2.1953 +
2.1954 + ++face_size;
2.1955 +
2.1956 + if (degree[graph.source(e)] < mind) {
2.1957 + mine = e;
2.1958 + mind = degree[graph.source(e)];
2.1959 + }
2.1960 +
2.1961 + e = embedding[graph.oppositeArc(e)];
2.1962 + }
2.1963 +
2.1964 + if (face_size < 4) {
2.1965 + continue;
2.1966 + }
2.1967 +
2.1968 + typename Graph::Node s = graph.source(mine);
2.1969 + for (typename Graph::OutArcIt e(graph, s); e != INVALID; ++e) {
2.1970 + visited.set(graph.target(e), true);
2.1971 + }
2.1972 +
2.1973 + typename Graph::Arc oppe = INVALID;
2.1974 +
2.1975 + e = embedding[graph.oppositeArc(mine)];
2.1976 + e = embedding[graph.oppositeArc(e)];
2.1977 + while (graph.target(e) != s) {
2.1978 + if (visited[graph.source(e)]) {
2.1979 + oppe = e;
2.1980 + break;
2.1981 + }
2.1982 + e = embedding[graph.oppositeArc(e)];
2.1983 + }
2.1984 + visited.setAll(false);
2.1985 +
2.1986 + if (oppe == INVALID) {
2.1987 +
2.1988 + e = embedding[graph.oppositeArc(mine)];
2.1989 + typename Graph::Arc pn = mine, p = e;
2.1990 +
2.1991 + e = embedding[graph.oppositeArc(e)];
2.1992 + while (graph.target(e) != s) {
2.1993 + typename Graph::Arc n =
2.1994 + graph.direct(graph.addEdge(s, graph.source(e)), true);
2.1995 +
2.1996 + embedding[n] = pn;
2.1997 + embedding[graph.oppositeArc(n)] = e;
2.1998 + embedding[graph.oppositeArc(p)] = graph.oppositeArc(n);
2.1999 +
2.2000 + pn = n;
2.2001 +
2.2002 + p = e;
2.2003 + e = embedding[graph.oppositeArc(e)];
2.2004 + }
2.2005 +
2.2006 + embedding[graph.oppositeArc(e)] = pn;
2.2007 +
2.2008 + } else {
2.2009 +
2.2010 + mine = embedding[graph.oppositeArc(mine)];
2.2011 + s = graph.source(mine);
2.2012 + oppe = embedding[graph.oppositeArc(oppe)];
2.2013 + typename Graph::Node t = graph.source(oppe);
2.2014 +
2.2015 + typename Graph::Arc ce = graph.direct(graph.addEdge(s, t), true);
2.2016 + embedding[ce] = mine;
2.2017 + embedding[graph.oppositeArc(ce)] = oppe;
2.2018 +
2.2019 + typename Graph::Arc pn = ce, p = oppe;
2.2020 + e = embedding[graph.oppositeArc(oppe)];
2.2021 + while (graph.target(e) != s) {
2.2022 + typename Graph::Arc n =
2.2023 + graph.direct(graph.addEdge(s, graph.source(e)), true);
2.2024 +
2.2025 + embedding[n] = pn;
2.2026 + embedding[graph.oppositeArc(n)] = e;
2.2027 + embedding[graph.oppositeArc(p)] = graph.oppositeArc(n);
2.2028 +
2.2029 + pn = n;
2.2030 +
2.2031 + p = e;
2.2032 + e = embedding[graph.oppositeArc(e)];
2.2033 +
2.2034 + }
2.2035 + embedding[graph.oppositeArc(e)] = pn;
2.2036 +
2.2037 + pn = graph.oppositeArc(ce), p = mine;
2.2038 + e = embedding[graph.oppositeArc(mine)];
2.2039 + while (graph.target(e) != t) {
2.2040 + typename Graph::Arc n =
2.2041 + graph.direct(graph.addEdge(t, graph.source(e)), true);
2.2042 +
2.2043 + embedding[n] = pn;
2.2044 + embedding[graph.oppositeArc(n)] = e;
2.2045 + embedding[graph.oppositeArc(p)] = graph.oppositeArc(n);
2.2046 +
2.2047 + pn = n;
2.2048 +
2.2049 + p = e;
2.2050 + e = embedding[graph.oppositeArc(e)];
2.2051 +
2.2052 + }
2.2053 + embedding[graph.oppositeArc(e)] = pn;
2.2054 + }
2.2055 + }
2.2056 + }
2.2057 +
2.2058 + }
2.2059 +
2.2060 + /// \ingroup planar
2.2061 + ///
2.2062 + /// \brief Schnyder's planar drawing algorithm
2.2063 + ///
2.2064 + /// The planar drawing algorithm calculates positions for the nodes
2.2065 + /// in the plane which coordinates satisfy that if the arcs are
2.2066 + /// represented with straight lines then they will not intersect
2.2067 + /// each other.
2.2068 + ///
2.2069 + /// Scnyder's algorithm embeds the graph on \c (n-2,n-2) size grid,
2.2070 + /// i.e. each node will be located in the \c [0,n-2]x[0,n-2] square.
2.2071 + /// The time complexity of the algorithm is O(n).
2.2072 + template <typename Graph>
2.2073 + class PlanarDrawing {
2.2074 + public:
2.2075 +
2.2076 + TEMPLATE_GRAPH_TYPEDEFS(Graph);
2.2077 +
2.2078 + /// \brief The point type for store coordinates
2.2079 + typedef dim2::Point<int> Point;
2.2080 + /// \brief The map type for store coordinates
2.2081 + typedef typename Graph::template NodeMap<Point> PointMap;
2.2082 +
2.2083 +
2.2084 + /// \brief Constructor
2.2085 + ///
2.2086 + /// Constructor
2.2087 + /// \pre The graph should be simple, i.e. loop and parallel arc free.
2.2088 + PlanarDrawing(const Graph& graph)
2.2089 + : _graph(graph), _point_map(graph) {}
2.2090 +
2.2091 + private:
2.2092 +
2.2093 + template <typename AuxGraph, typename AuxEmbeddingMap>
2.2094 + void drawing(const AuxGraph& graph,
2.2095 + const AuxEmbeddingMap& next,
2.2096 + PointMap& point_map) {
2.2097 + TEMPLATE_GRAPH_TYPEDEFS(AuxGraph);
2.2098 +
2.2099 + typename AuxGraph::template ArcMap<Arc> prev(graph);
2.2100 +
2.2101 + for (NodeIt n(graph); n != INVALID; ++n) {
2.2102 + Arc e = OutArcIt(graph, n);
2.2103 +
2.2104 + Arc p = e, l = e;
2.2105 +
2.2106 + e = next[e];
2.2107 + while (e != l) {
2.2108 + prev[e] = p;
2.2109 + p = e;
2.2110 + e = next[e];
2.2111 + }
2.2112 + prev[e] = p;
2.2113 + }
2.2114 +
2.2115 + Node anode, bnode, cnode;
2.2116 +
2.2117 + {
2.2118 + Arc e = ArcIt(graph);
2.2119 + anode = graph.source(e);
2.2120 + bnode = graph.target(e);
2.2121 + cnode = graph.target(next[graph.oppositeArc(e)]);
2.2122 + }
2.2123 +
2.2124 + IterableBoolMap<AuxGraph, Node> proper(graph, false);
2.2125 + typename AuxGraph::template NodeMap<int> conn(graph, -1);
2.2126 +
2.2127 + conn[anode] = conn[bnode] = -2;
2.2128 + {
2.2129 + for (OutArcIt e(graph, anode); e != INVALID; ++e) {
2.2130 + Node m = graph.target(e);
2.2131 + if (conn[m] == -1) {
2.2132 + conn[m] = 1;
2.2133 + }
2.2134 + }
2.2135 + conn[cnode] = 2;
2.2136 +
2.2137 + for (OutArcIt e(graph, bnode); e != INVALID; ++e) {
2.2138 + Node m = graph.target(e);
2.2139 + if (conn[m] == -1) {
2.2140 + conn[m] = 1;
2.2141 + } else if (conn[m] != -2) {
2.2142 + conn[m] += 1;
2.2143 + Arc pe = graph.oppositeArc(e);
2.2144 + if (conn[graph.target(next[pe])] == -2) {
2.2145 + conn[m] -= 1;
2.2146 + }
2.2147 + if (conn[graph.target(prev[pe])] == -2) {
2.2148 + conn[m] -= 1;
2.2149 + }
2.2150 +
2.2151 + proper.set(m, conn[m] == 1);
2.2152 + }
2.2153 + }
2.2154 + }
2.2155 +
2.2156 +
2.2157 + typename AuxGraph::template ArcMap<int> angle(graph, -1);
2.2158 +
2.2159 + while (proper.trueNum() != 0) {
2.2160 + Node n = typename IterableBoolMap<AuxGraph, Node>::TrueIt(proper);
2.2161 + proper.set(n, false);
2.2162 + conn[n] = -2;
2.2163 +
2.2164 + for (OutArcIt e(graph, n); e != INVALID; ++e) {
2.2165 + Node m = graph.target(e);
2.2166 + if (conn[m] == -1) {
2.2167 + conn[m] = 1;
2.2168 + } else if (conn[m] != -2) {
2.2169 + conn[m] += 1;
2.2170 + Arc pe = graph.oppositeArc(e);
2.2171 + if (conn[graph.target(next[pe])] == -2) {
2.2172 + conn[m] -= 1;
2.2173 + }
2.2174 + if (conn[graph.target(prev[pe])] == -2) {
2.2175 + conn[m] -= 1;
2.2176 + }
2.2177 +
2.2178 + proper.set(m, conn[m] == 1);
2.2179 + }
2.2180 + }
2.2181 +
2.2182 + {
2.2183 + Arc e = OutArcIt(graph, n);
2.2184 + Arc p = e, l = e;
2.2185 +
2.2186 + e = next[e];
2.2187 + while (e != l) {
2.2188 +
2.2189 + if (conn[graph.target(e)] == -2 && conn[graph.target(p)] == -2) {
2.2190 + Arc f = e;
2.2191 + angle[f] = 0;
2.2192 + f = next[graph.oppositeArc(f)];
2.2193 + angle[f] = 1;
2.2194 + f = next[graph.oppositeArc(f)];
2.2195 + angle[f] = 2;
2.2196 + }
2.2197 +
2.2198 + p = e;
2.2199 + e = next[e];
2.2200 + }
2.2201 +
2.2202 + if (conn[graph.target(e)] == -2 && conn[graph.target(p)] == -2) {
2.2203 + Arc f = e;
2.2204 + angle[f] = 0;
2.2205 + f = next[graph.oppositeArc(f)];
2.2206 + angle[f] = 1;
2.2207 + f = next[graph.oppositeArc(f)];
2.2208 + angle[f] = 2;
2.2209 + }
2.2210 + }
2.2211 + }
2.2212 +
2.2213 + typename AuxGraph::template NodeMap<Node> apred(graph, INVALID);
2.2214 + typename AuxGraph::template NodeMap<Node> bpred(graph, INVALID);
2.2215 + typename AuxGraph::template NodeMap<Node> cpred(graph, INVALID);
2.2216 +
2.2217 + typename AuxGraph::template NodeMap<int> apredid(graph, -1);
2.2218 + typename AuxGraph::template NodeMap<int> bpredid(graph, -1);
2.2219 + typename AuxGraph::template NodeMap<int> cpredid(graph, -1);
2.2220 +
2.2221 + for (ArcIt e(graph); e != INVALID; ++e) {
2.2222 + if (angle[e] == angle[next[e]]) {
2.2223 + switch (angle[e]) {
2.2224 + case 2:
2.2225 + apred[graph.target(e)] = graph.source(e);
2.2226 + apredid[graph.target(e)] = graph.id(graph.source(e));
2.2227 + break;
2.2228 + case 1:
2.2229 + bpred[graph.target(e)] = graph.source(e);
2.2230 + bpredid[graph.target(e)] = graph.id(graph.source(e));
2.2231 + break;
2.2232 + case 0:
2.2233 + cpred[graph.target(e)] = graph.source(e);
2.2234 + cpredid[graph.target(e)] = graph.id(graph.source(e));
2.2235 + break;
2.2236 + }
2.2237 + }
2.2238 + }
2.2239 +
2.2240 + cpred[anode] = INVALID;
2.2241 + cpred[bnode] = INVALID;
2.2242 +
2.2243 + std::vector<Node> aorder, border, corder;
2.2244 +
2.2245 + {
2.2246 + typename AuxGraph::template NodeMap<bool> processed(graph, false);
2.2247 + std::vector<Node> st;
2.2248 + for (NodeIt n(graph); n != INVALID; ++n) {
2.2249 + if (!processed[n] && n != bnode && n != cnode) {
2.2250 + st.push_back(n);
2.2251 + processed[n] = true;
2.2252 + Node m = apred[n];
2.2253 + while (m != INVALID && !processed[m]) {
2.2254 + st.push_back(m);
2.2255 + processed[m] = true;
2.2256 + m = apred[m];
2.2257 + }
2.2258 + while (!st.empty()) {
2.2259 + aorder.push_back(st.back());
2.2260 + st.pop_back();
2.2261 + }
2.2262 + }
2.2263 + }
2.2264 + }
2.2265 +
2.2266 + {
2.2267 + typename AuxGraph::template NodeMap<bool> processed(graph, false);
2.2268 + std::vector<Node> st;
2.2269 + for (NodeIt n(graph); n != INVALID; ++n) {
2.2270 + if (!processed[n] && n != cnode && n != anode) {
2.2271 + st.push_back(n);
2.2272 + processed[n] = true;
2.2273 + Node m = bpred[n];
2.2274 + while (m != INVALID && !processed[m]) {
2.2275 + st.push_back(m);
2.2276 + processed[m] = true;
2.2277 + m = bpred[m];
2.2278 + }
2.2279 + while (!st.empty()) {
2.2280 + border.push_back(st.back());
2.2281 + st.pop_back();
2.2282 + }
2.2283 + }
2.2284 + }
2.2285 + }
2.2286 +
2.2287 + {
2.2288 + typename AuxGraph::template NodeMap<bool> processed(graph, false);
2.2289 + std::vector<Node> st;
2.2290 + for (NodeIt n(graph); n != INVALID; ++n) {
2.2291 + if (!processed[n] && n != anode && n != bnode) {
2.2292 + st.push_back(n);
2.2293 + processed[n] = true;
2.2294 + Node m = cpred[n];
2.2295 + while (m != INVALID && !processed[m]) {
2.2296 + st.push_back(m);
2.2297 + processed[m] = true;
2.2298 + m = cpred[m];
2.2299 + }
2.2300 + while (!st.empty()) {
2.2301 + corder.push_back(st.back());
2.2302 + st.pop_back();
2.2303 + }
2.2304 + }
2.2305 + }
2.2306 + }
2.2307 +
2.2308 + typename AuxGraph::template NodeMap<int> atree(graph, 0);
2.2309 + for (int i = aorder.size() - 1; i >= 0; --i) {
2.2310 + Node n = aorder[i];
2.2311 + atree[n] = 1;
2.2312 + for (OutArcIt e(graph, n); e != INVALID; ++e) {
2.2313 + if (apred[graph.target(e)] == n) {
2.2314 + atree[n] += atree[graph.target(e)];
2.2315 + }
2.2316 + }
2.2317 + }
2.2318 +
2.2319 + typename AuxGraph::template NodeMap<int> btree(graph, 0);
2.2320 + for (int i = border.size() - 1; i >= 0; --i) {
2.2321 + Node n = border[i];
2.2322 + btree[n] = 1;
2.2323 + for (OutArcIt e(graph, n); e != INVALID; ++e) {
2.2324 + if (bpred[graph.target(e)] == n) {
2.2325 + btree[n] += btree[graph.target(e)];
2.2326 + }
2.2327 + }
2.2328 + }
2.2329 +
2.2330 + typename AuxGraph::template NodeMap<int> apath(graph, 0);
2.2331 + apath[bnode] = apath[cnode] = 1;
2.2332 + typename AuxGraph::template NodeMap<int> apath_btree(graph, 0);
2.2333 + apath_btree[bnode] = btree[bnode];
2.2334 + for (int i = 1; i < int(aorder.size()); ++i) {
2.2335 + Node n = aorder[i];
2.2336 + apath[n] = apath[apred[n]] + 1;
2.2337 + apath_btree[n] = btree[n] + apath_btree[apred[n]];
2.2338 + }
2.2339 +
2.2340 + typename AuxGraph::template NodeMap<int> bpath_atree(graph, 0);
2.2341 + bpath_atree[anode] = atree[anode];
2.2342 + for (int i = 1; i < int(border.size()); ++i) {
2.2343 + Node n = border[i];
2.2344 + bpath_atree[n] = atree[n] + bpath_atree[bpred[n]];
2.2345 + }
2.2346 +
2.2347 + typename AuxGraph::template NodeMap<int> cpath(graph, 0);
2.2348 + cpath[anode] = cpath[bnode] = 1;
2.2349 + typename AuxGraph::template NodeMap<int> cpath_atree(graph, 0);
2.2350 + cpath_atree[anode] = atree[anode];
2.2351 + typename AuxGraph::template NodeMap<int> cpath_btree(graph, 0);
2.2352 + cpath_btree[bnode] = btree[bnode];
2.2353 + for (int i = 1; i < int(corder.size()); ++i) {
2.2354 + Node n = corder[i];
2.2355 + cpath[n] = cpath[cpred[n]] + 1;
2.2356 + cpath_atree[n] = atree[n] + cpath_atree[cpred[n]];
2.2357 + cpath_btree[n] = btree[n] + cpath_btree[cpred[n]];
2.2358 + }
2.2359 +
2.2360 + typename AuxGraph::template NodeMap<int> third(graph);
2.2361 + for (NodeIt n(graph); n != INVALID; ++n) {
2.2362 + point_map[n].x =
2.2363 + bpath_atree[n] + cpath_atree[n] - atree[n] - cpath[n] + 1;
2.2364 + point_map[n].y =
2.2365 + cpath_btree[n] + apath_btree[n] - btree[n] - apath[n] + 1;
2.2366 + }
2.2367 +
2.2368 + }
2.2369 +
2.2370 + public:
2.2371 +
2.2372 + /// \brief Calculates the node positions
2.2373 + ///
2.2374 + /// This function calculates the node positions.
2.2375 + /// \return %True if the graph is planar.
2.2376 + bool run() {
2.2377 + PlanarEmbedding<Graph> pe(_graph);
2.2378 + if (!pe.run()) return false;
2.2379 +
2.2380 + run(pe);
2.2381 + return true;
2.2382 + }
2.2383 +
2.2384 + /// \brief Calculates the node positions according to a
2.2385 + /// combinatorical embedding
2.2386 + ///
2.2387 + /// This function calculates the node locations. The \c embedding
2.2388 + /// parameter should contain a valid combinatorical embedding, i.e.
2.2389 + /// a valid cyclic order of the arcs.
2.2390 + template <typename EmbeddingMap>
2.2391 + void run(const EmbeddingMap& embedding) {
2.2392 + typedef SmartEdgeSet<Graph> AuxGraph;
2.2393 +
2.2394 + if (3 * countNodes(_graph) - 6 == countEdges(_graph)) {
2.2395 + drawing(_graph, embedding, _point_map);
2.2396 + return;
2.2397 + }
2.2398 +
2.2399 + AuxGraph aux_graph(_graph);
2.2400 + typename AuxGraph::template ArcMap<typename AuxGraph::Arc>
2.2401 + aux_embedding(aux_graph);
2.2402 +
2.2403 + {
2.2404 +
2.2405 + typename Graph::template EdgeMap<typename AuxGraph::Edge>
2.2406 + ref(_graph);
2.2407 +
2.2408 + for (EdgeIt e(_graph); e != INVALID; ++e) {
2.2409 + ref[e] = aux_graph.addEdge(_graph.u(e), _graph.v(e));
2.2410 + }
2.2411 +
2.2412 + for (EdgeIt e(_graph); e != INVALID; ++e) {
2.2413 + Arc ee = embedding[_graph.direct(e, true)];
2.2414 + aux_embedding[aux_graph.direct(ref[e], true)] =
2.2415 + aux_graph.direct(ref[ee], _graph.direction(ee));
2.2416 + ee = embedding[_graph.direct(e, false)];
2.2417 + aux_embedding[aux_graph.direct(ref[e], false)] =
2.2418 + aux_graph.direct(ref[ee], _graph.direction(ee));
2.2419 + }
2.2420 + }
2.2421 + _planarity_bits::makeConnected(aux_graph, aux_embedding);
2.2422 + _planarity_bits::makeBiNodeConnected(aux_graph, aux_embedding);
2.2423 + _planarity_bits::makeMaxPlanar(aux_graph, aux_embedding);
2.2424 + drawing(aux_graph, aux_embedding, _point_map);
2.2425 + }
2.2426 +
2.2427 + /// \brief The coordinate of the given node
2.2428 + ///
2.2429 + /// The coordinate of the given node.
2.2430 + Point operator[](const Node& node) const {
2.2431 + return _point_map[node];
2.2432 + }
2.2433 +
2.2434 + /// \brief Returns the grid embedding in a \e NodeMap.
2.2435 + ///
2.2436 + /// Returns the grid embedding in a \e NodeMap of \c dim2::Point<int> .
2.2437 + const PointMap& coords() const {
2.2438 + return _point_map;
2.2439 + }
2.2440 +
2.2441 + private:
2.2442 +
2.2443 + const Graph& _graph;
2.2444 + PointMap _point_map;
2.2445 +
2.2446 + };
2.2447 +
2.2448 + namespace _planarity_bits {
2.2449 +
2.2450 + template <typename ColorMap>
2.2451 + class KempeFilter {
2.2452 + public:
2.2453 + typedef typename ColorMap::Key Key;
2.2454 + typedef bool Value;
2.2455 +
2.2456 + KempeFilter(const ColorMap& color_map,
2.2457 + const typename ColorMap::Value& first,
2.2458 + const typename ColorMap::Value& second)
2.2459 + : _color_map(color_map), _first(first), _second(second) {}
2.2460 +
2.2461 + Value operator[](const Key& key) const {
2.2462 + return _color_map[key] == _first || _color_map[key] == _second;
2.2463 + }
2.2464 +
2.2465 + private:
2.2466 + const ColorMap& _color_map;
2.2467 + typename ColorMap::Value _first, _second;
2.2468 + };
2.2469 + }
2.2470 +
2.2471 + /// \ingroup planar
2.2472 + ///
2.2473 + /// \brief Coloring planar graphs
2.2474 + ///
2.2475 + /// The graph coloring problem is the coloring of the graph nodes
2.2476 + /// that there are not adjacent nodes with the same color. The
2.2477 + /// planar graphs can be always colored with four colors, it is
2.2478 + /// proved by Appel and Haken and their proofs provide a quadratic
2.2479 + /// time algorithm for four coloring, but it could not be used to
2.2480 + /// implement efficient algorithm. The five and six coloring can be
2.2481 + /// made in linear time, but in this class the five coloring has
2.2482 + /// quadratic worst case time complexity. The two coloring (if
2.2483 + /// possible) is solvable with a graph search algorithm and it is
2.2484 + /// implemented in \ref bipartitePartitions() function in LEMON. To
2.2485 + /// decide whether the planar graph is three colorable is
2.2486 + /// NP-complete.
2.2487 + ///
2.2488 + /// This class contains member functions for calculate colorings
2.2489 + /// with five and six colors. The six coloring algorithm is a simple
2.2490 + /// greedy coloring on the backward minimum outgoing order of nodes.
2.2491 + /// This order can be computed as in each phase the node with least
2.2492 + /// outgoing arcs to unprocessed nodes is chosen. This order
2.2493 + /// guarantees that when a node is chosen for coloring it has at
2.2494 + /// most five already colored adjacents. The five coloring algorithm
2.2495 + /// use the same method, but if the greedy approach fails to color
2.2496 + /// with five colors, i.e. the node has five already different
2.2497 + /// colored neighbours, it swaps the colors in one of the connected
2.2498 + /// two colored sets with the Kempe recoloring method.
2.2499 + template <typename Graph>
2.2500 + class PlanarColoring {
2.2501 + public:
2.2502 +
2.2503 + TEMPLATE_GRAPH_TYPEDEFS(Graph);
2.2504 +
2.2505 + /// \brief The map type for store color indexes
2.2506 + typedef typename Graph::template NodeMap<int> IndexMap;
2.2507 + /// \brief The map type for store colors
2.2508 + typedef ComposeMap<Palette, IndexMap> ColorMap;
2.2509 +
2.2510 + /// \brief Constructor
2.2511 + ///
2.2512 + /// Constructor
2.2513 + /// \pre The graph should be simple, i.e. loop and parallel arc free.
2.2514 + PlanarColoring(const Graph& graph)
2.2515 + : _graph(graph), _color_map(graph), _palette(0) {
2.2516 + _palette.add(Color(1,0,0));
2.2517 + _palette.add(Color(0,1,0));
2.2518 + _palette.add(Color(0,0,1));
2.2519 + _palette.add(Color(1,1,0));
2.2520 + _palette.add(Color(1,0,1));
2.2521 + _palette.add(Color(0,1,1));
2.2522 + }
2.2523 +
2.2524 + /// \brief Returns the \e NodeMap of color indexes
2.2525 + ///
2.2526 + /// Returns the \e NodeMap of color indexes. The values are in the
2.2527 + /// range \c [0..4] or \c [0..5] according to the coloring method.
2.2528 + IndexMap colorIndexMap() const {
2.2529 + return _color_map;
2.2530 + }
2.2531 +
2.2532 + /// \brief Returns the \e NodeMap of colors
2.2533 + ///
2.2534 + /// Returns the \e NodeMap of colors. The values are five or six
2.2535 + /// distinct \ref lemon::Color "colors".
2.2536 + ColorMap colorMap() const {
2.2537 + return composeMap(_palette, _color_map);
2.2538 + }
2.2539 +
2.2540 + /// \brief Returns the color index of the node
2.2541 + ///
2.2542 + /// Returns the color index of the node. The values are in the
2.2543 + /// range \c [0..4] or \c [0..5] according to the coloring method.
2.2544 + int colorIndex(const Node& node) const {
2.2545 + return _color_map[node];
2.2546 + }
2.2547 +
2.2548 + /// \brief Returns the color of the node
2.2549 + ///
2.2550 + /// Returns the color of the node. The values are five or six
2.2551 + /// distinct \ref lemon::Color "colors".
2.2552 + Color color(const Node& node) const {
2.2553 + return _palette[_color_map[node]];
2.2554 + }
2.2555 +
2.2556 +
2.2557 + /// \brief Calculates a coloring with at most six colors
2.2558 + ///
2.2559 + /// This function calculates a coloring with at most six colors. The time
2.2560 + /// complexity of this variant is linear in the size of the graph.
2.2561 + /// \return %True when the algorithm could color the graph with six color.
2.2562 + /// If the algorithm fails, then the graph could not be planar.
2.2563 + /// \note This function can return true if the graph is not
2.2564 + /// planar but it can be colored with 6 colors.
2.2565 + bool runSixColoring() {
2.2566 +
2.2567 + typename Graph::template NodeMap<int> heap_index(_graph, -1);
2.2568 + BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index);
2.2569 +
2.2570 + for (NodeIt n(_graph); n != INVALID; ++n) {
2.2571 + _color_map[n] = -2;
2.2572 + heap.push(n, countOutArcs(_graph, n));
2.2573 + }
2.2574 +
2.2575 + std::vector<Node> order;
2.2576 +
2.2577 + while (!heap.empty()) {
2.2578 + Node n = heap.top();
2.2579 + heap.pop();
2.2580 + _color_map[n] = -1;
2.2581 + order.push_back(n);
2.2582 + for (OutArcIt e(_graph, n); e != INVALID; ++e) {
2.2583 + Node t = _graph.runningNode(e);
2.2584 + if (_color_map[t] == -2) {
2.2585 + heap.decrease(t, heap[t] - 1);
2.2586 + }
2.2587 + }
2.2588 + }
2.2589 +
2.2590 + for (int i = order.size() - 1; i >= 0; --i) {
2.2591 + std::vector<bool> forbidden(6, false);
2.2592 + for (OutArcIt e(_graph, order[i]); e != INVALID; ++e) {
2.2593 + Node t = _graph.runningNode(e);
2.2594 + if (_color_map[t] != -1) {
2.2595 + forbidden[_color_map[t]] = true;
2.2596 + }
2.2597 + }
2.2598 + for (int k = 0; k < 6; ++k) {
2.2599 + if (!forbidden[k]) {
2.2600 + _color_map[order[i]] = k;
2.2601 + break;
2.2602 + }
2.2603 + }
2.2604 + if (_color_map[order[i]] == -1) {
2.2605 + return false;
2.2606 + }
2.2607 + }
2.2608 + return true;
2.2609 + }
2.2610 +
2.2611 + private:
2.2612 +
2.2613 + bool recolor(const Node& u, const Node& v) {
2.2614 + int ucolor = _color_map[u];
2.2615 + int vcolor = _color_map[v];
2.2616 + typedef _planarity_bits::KempeFilter<IndexMap> KempeFilter;
2.2617 + KempeFilter filter(_color_map, ucolor, vcolor);
2.2618 +
2.2619 + typedef FilterNodes<const Graph, const KempeFilter> KempeGraph;
2.2620 + KempeGraph kempe_graph(_graph, filter);
2.2621 +
2.2622 + std::vector<Node> comp;
2.2623 + Bfs<KempeGraph> bfs(kempe_graph);
2.2624 + bfs.init();
2.2625 + bfs.addSource(u);
2.2626 + while (!bfs.emptyQueue()) {
2.2627 + Node n = bfs.nextNode();
2.2628 + if (n == v) return false;
2.2629 + comp.push_back(n);
2.2630 + bfs.processNextNode();
2.2631 + }
2.2632 +
2.2633 + int scolor = ucolor + vcolor;
2.2634 + for (int i = 0; i < static_cast<int>(comp.size()); ++i) {
2.2635 + _color_map[comp[i]] = scolor - _color_map[comp[i]];
2.2636 + }
2.2637 +
2.2638 + return true;
2.2639 + }
2.2640 +
2.2641 + template <typename EmbeddingMap>
2.2642 + void kempeRecoloring(const Node& node, const EmbeddingMap& embedding) {
2.2643 + std::vector<Node> nodes;
2.2644 + nodes.reserve(4);
2.2645 +
2.2646 + for (Arc e = OutArcIt(_graph, node); e != INVALID; e = embedding[e]) {
2.2647 + Node t = _graph.target(e);
2.2648 + if (_color_map[t] != -1) {
2.2649 + nodes.push_back(t);
2.2650 + if (nodes.size() == 4) break;
2.2651 + }
2.2652 + }
2.2653 +
2.2654 + int color = _color_map[nodes[0]];
2.2655 + if (recolor(nodes[0], nodes[2])) {
2.2656 + _color_map[node] = color;
2.2657 + } else {
2.2658 + color = _color_map[nodes[1]];
2.2659 + recolor(nodes[1], nodes[3]);
2.2660 + _color_map[node] = color;
2.2661 + }
2.2662 + }
2.2663 +
2.2664 + public:
2.2665 +
2.2666 + /// \brief Calculates a coloring with at most five colors
2.2667 + ///
2.2668 + /// This function calculates a coloring with at most five
2.2669 + /// colors. The worst case time complexity of this variant is
2.2670 + /// quadratic in the size of the graph.
2.2671 + template <typename EmbeddingMap>
2.2672 + void runFiveColoring(const EmbeddingMap& embedding) {
2.2673 +
2.2674 + typename Graph::template NodeMap<int> heap_index(_graph, -1);
2.2675 + BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index);
2.2676 +
2.2677 + for (NodeIt n(_graph); n != INVALID; ++n) {
2.2678 + _color_map[n] = -2;
2.2679 + heap.push(n, countOutArcs(_graph, n));
2.2680 + }
2.2681 +
2.2682 + std::vector<Node> order;
2.2683 +
2.2684 + while (!heap.empty()) {
2.2685 + Node n = heap.top();
2.2686 + heap.pop();
2.2687 + _color_map[n] = -1;
2.2688 + order.push_back(n);
2.2689 + for (OutArcIt e(_graph, n); e != INVALID; ++e) {
2.2690 + Node t = _graph.runningNode(e);
2.2691 + if (_color_map[t] == -2) {
2.2692 + heap.decrease(t, heap[t] - 1);
2.2693 + }
2.2694 + }
2.2695 + }
2.2696 +
2.2697 + for (int i = order.size() - 1; i >= 0; --i) {
2.2698 + std::vector<bool> forbidden(5, false);
2.2699 + for (OutArcIt e(_graph, order[i]); e != INVALID; ++e) {
2.2700 + Node t = _graph.runningNode(e);
2.2701 + if (_color_map[t] != -1) {
2.2702 + forbidden[_color_map[t]] = true;
2.2703 + }
2.2704 + }
2.2705 + for (int k = 0; k < 5; ++k) {
2.2706 + if (!forbidden[k]) {
2.2707 + _color_map[order[i]] = k;
2.2708 + break;
2.2709 + }
2.2710 + }
2.2711 + if (_color_map[order[i]] == -1) {
2.2712 + kempeRecoloring(order[i], embedding);
2.2713 + }
2.2714 + }
2.2715 + }
2.2716 +
2.2717 + /// \brief Calculates a coloring with at most five colors
2.2718 + ///
2.2719 + /// This function calculates a coloring with at most five
2.2720 + /// colors. The worst case time complexity of this variant is
2.2721 + /// quadratic in the size of the graph.
2.2722 + /// \return %True when the graph is planar.
2.2723 + bool runFiveColoring() {
2.2724 + PlanarEmbedding<Graph> pe(_graph);
2.2725 + if (!pe.run()) return false;
2.2726 +
2.2727 + runFiveColoring(pe.embeddingMap());
2.2728 + return true;
2.2729 + }
2.2730 +
2.2731 + private:
2.2732 +
2.2733 + const Graph& _graph;
2.2734 + IndexMap _color_map;
2.2735 + Palette _palette;
2.2736 + };
2.2737 +
2.2738 +}
2.2739 +
2.2740 +#endif
3.1 --- a/test/CMakeLists.txt Mon Aug 31 20:27:38 2009 +0200
3.2 +++ b/test/CMakeLists.txt Wed Sep 09 15:32:03 2009 +0200
3.3 @@ -33,6 +33,7 @@
3.4 min_cost_arborescence_test
3.5 min_cost_flow_test
3.6 path_test
3.7 + planarity_test
3.8 preflow_test
3.9 radix_sort_test
3.10 random_test
4.1 --- a/test/Makefile.am Mon Aug 31 20:27:38 2009 +0200
4.2 +++ b/test/Makefile.am Wed Sep 09 15:32:03 2009 +0200
4.3 @@ -31,6 +31,7 @@
4.4 test/min_cost_arborescence_test \
4.5 test/min_cost_flow_test \
4.6 test/path_test \
4.7 + test/planarity_test \
4.8 test/preflow_test \
4.9 test/radix_sort_test \
4.10 test/random_test \
4.11 @@ -79,6 +80,7 @@
4.12 test_min_cost_arborescence_test_SOURCES = test/min_cost_arborescence_test.cc
4.13 test_min_cost_flow_test_SOURCES = test/min_cost_flow_test.cc
4.14 test_path_test_SOURCES = test/path_test.cc
4.15 +test_planarity_test_SOURCES = test/planarity_test.cc
4.16 test_preflow_test_SOURCES = test/preflow_test.cc
4.17 test_radix_sort_test_SOURCES = test/radix_sort_test.cc
4.18 test_suurballe_test_SOURCES = test/suurballe_test.cc
5.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
5.2 +++ b/test/planarity_test.cc Wed Sep 09 15:32:03 2009 +0200
5.3 @@ -0,0 +1,259 @@
5.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
5.5 + *
5.6 + * This file is a part of LEMON, a generic C++ optimization library.
5.7 + *
5.8 + * Copyright (C) 2003-2009
5.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
5.11 + *
5.12 + * Permission to use, modify and distribute this software is granted
5.13 + * provided that this copyright notice appears in all copies. For
5.14 + * precise terms see the accompanying LICENSE file.
5.15 + *
5.16 + * This software is provided "AS IS" with no warranty of any kind,
5.17 + * express or implied, and with no claim as to its suitability for any
5.18 + * purpose.
5.19 + *
5.20 + */
5.21 +
5.22 +#include <iostream>
5.23 +
5.24 +#include <lemon/planarity.h>
5.25 +
5.26 +#include <lemon/smart_graph.h>
5.27 +#include <lemon/lgf_reader.h>
5.28 +#include <lemon/connectivity.h>
5.29 +#include <lemon/dim2.h>
5.30 +
5.31 +#include "test_tools.h"
5.32 +
5.33 +using namespace lemon;
5.34 +using namespace lemon::dim2;
5.35 +
5.36 +const int lgfn = 4;
5.37 +const std::string lgf[lgfn] = {
5.38 + "@nodes\n"
5.39 + "label\n"
5.40 + "0\n"
5.41 + "1\n"
5.42 + "2\n"
5.43 + "3\n"
5.44 + "4\n"
5.45 + "@edges\n"
5.46 + " label\n"
5.47 + "0 1 0\n"
5.48 + "0 2 0\n"
5.49 + "0 3 0\n"
5.50 + "0 4 0\n"
5.51 + "1 2 0\n"
5.52 + "1 3 0\n"
5.53 + "1 4 0\n"
5.54 + "2 3 0\n"
5.55 + "2 4 0\n"
5.56 + "3 4 0\n",
5.57 +
5.58 + "@nodes\n"
5.59 + "label\n"
5.60 + "0\n"
5.61 + "1\n"
5.62 + "2\n"
5.63 + "3\n"
5.64 + "4\n"
5.65 + "@edges\n"
5.66 + " label\n"
5.67 + "0 1 0\n"
5.68 + "0 2 0\n"
5.69 + "0 3 0\n"
5.70 + "0 4 0\n"
5.71 + "1 2 0\n"
5.72 + "1 3 0\n"
5.73 + "2 3 0\n"
5.74 + "2 4 0\n"
5.75 + "3 4 0\n",
5.76 +
5.77 + "@nodes\n"
5.78 + "label\n"
5.79 + "0\n"
5.80 + "1\n"
5.81 + "2\n"
5.82 + "3\n"
5.83 + "4\n"
5.84 + "5\n"
5.85 + "@edges\n"
5.86 + " label\n"
5.87 + "0 3 0\n"
5.88 + "0 4 0\n"
5.89 + "0 5 0\n"
5.90 + "1 3 0\n"
5.91 + "1 4 0\n"
5.92 + "1 5 0\n"
5.93 + "2 3 0\n"
5.94 + "2 4 0\n"
5.95 + "2 5 0\n",
5.96 +
5.97 + "@nodes\n"
5.98 + "label\n"
5.99 + "0\n"
5.100 + "1\n"
5.101 + "2\n"
5.102 + "3\n"
5.103 + "4\n"
5.104 + "5\n"
5.105 + "@edges\n"
5.106 + " label\n"
5.107 + "0 3 0\n"
5.108 + "0 4 0\n"
5.109 + "0 5 0\n"
5.110 + "1 3 0\n"
5.111 + "1 4 0\n"
5.112 + "1 5 0\n"
5.113 + "2 3 0\n"
5.114 + "2 5 0\n"
5.115 +};
5.116 +
5.117 +
5.118 +
5.119 +typedef SmartGraph Graph;
5.120 +GRAPH_TYPEDEFS(Graph);
5.121 +
5.122 +typedef PlanarEmbedding<SmartGraph> PE;
5.123 +typedef PlanarDrawing<SmartGraph> PD;
5.124 +typedef PlanarColoring<SmartGraph> PC;
5.125 +
5.126 +void checkEmbedding(const Graph& graph, PE& pe) {
5.127 + int face_num = 0;
5.128 +
5.129 + Graph::ArcMap<int> face(graph, -1);
5.130 +
5.131 + for (ArcIt a(graph); a != INVALID; ++a) {
5.132 + if (face[a] == -1) {
5.133 + Arc b = a;
5.134 + while (face[b] == -1) {
5.135 + face[b] = face_num;
5.136 + b = pe.next(graph.oppositeArc(b));
5.137 + }
5.138 + check(face[b] == face_num, "Wrong face");
5.139 + ++face_num;
5.140 + }
5.141 + }
5.142 + check(face_num + countNodes(graph) - countConnectedComponents(graph) ==
5.143 + countEdges(graph) + 1, "Euler test does not passed");
5.144 +}
5.145 +
5.146 +void checkKuratowski(const Graph& graph, PE& pe) {
5.147 + std::map<int, int> degs;
5.148 + for (NodeIt n(graph); n != INVALID; ++n) {
5.149 + int deg = 0;
5.150 + for (IncEdgeIt e(graph, n); e != INVALID; ++e) {
5.151 + if (pe.kuratowski(e)) {
5.152 + ++deg;
5.153 + }
5.154 + }
5.155 + ++degs[deg];
5.156 + }
5.157 + for (std::map<int, int>::iterator it = degs.begin(); it != degs.end(); ++it) {
5.158 + check(it->first == 0 || it->first == 2 ||
5.159 + (it->first == 3 && it->second == 6) ||
5.160 + (it->first == 4 && it->second == 5),
5.161 + "Wrong degree in Kuratowski graph");
5.162 + }
5.163 +
5.164 + // Not full test
5.165 + check((degs[3] == 0) != (degs[4] == 0), "Wrong Kuratowski graph");
5.166 +}
5.167 +
5.168 +bool intersect(Point<int> e1, Point<int> e2, Point<int> f1, Point<int> f2) {
5.169 + int l, r;
5.170 + if (std::min(e1.x, e2.x) > std::max(f1.x, f2.x)) return false;
5.171 + if (std::max(e1.x, e2.x) < std::min(f1.x, f2.x)) return false;
5.172 + if (std::min(e1.y, e2.y) > std::max(f1.y, f2.y)) return false;
5.173 + if (std::max(e1.y, e2.y) < std::min(f1.y, f2.y)) return false;
5.174 +
5.175 + l = (e2.x - e1.x) * (f1.y - e1.y) - (e2.y - e1.y) * (f1.x - e1.x);
5.176 + r = (e2.x - e1.x) * (f2.y - e1.y) - (e2.y - e1.y) * (f2.x - e1.x);
5.177 + if (!((l >= 0 && r <= 0) || (l <= 0 && r >= 0))) return false;
5.178 + l = (f2.x - f1.x) * (e1.y - f1.y) - (f2.y - f1.y) * (e1.x - f1.x);
5.179 + r = (f2.x - f1.x) * (e2.y - f1.y) - (f2.y - f1.y) * (e2.x - f1.x);
5.180 + if (!((l >= 0 && r <= 0) || (l <= 0 && r >= 0))) return false;
5.181 + return true;
5.182 +}
5.183 +
5.184 +bool collinear(Point<int> p, Point<int> q, Point<int> r) {
5.185 + int v;
5.186 + v = (q.x - p.x) * (r.y - p.y) - (q.y - p.y) * (r.x - p.x);
5.187 + if (v != 0) return false;
5.188 + v = (q.x - p.x) * (r.x - p.x) + (q.y - p.y) * (r.y - p.y);
5.189 + if (v < 0) return false;
5.190 + return true;
5.191 +}
5.192 +
5.193 +void checkDrawing(const Graph& graph, PD& pd) {
5.194 + for (Graph::NodeIt n(graph); n != INVALID; ++n) {
5.195 + Graph::NodeIt m(n);
5.196 + for (++m; m != INVALID; ++m) {
5.197 + check(pd[m] != pd[n], "Two nodes with identical coordinates");
5.198 + }
5.199 + }
5.200 +
5.201 + for (Graph::EdgeIt e(graph); e != INVALID; ++e) {
5.202 + for (Graph::EdgeIt f(e); f != e; ++f) {
5.203 + Point<int> e1 = pd[graph.u(e)];
5.204 + Point<int> e2 = pd[graph.v(e)];
5.205 + Point<int> f1 = pd[graph.u(f)];
5.206 + Point<int> f2 = pd[graph.v(f)];
5.207 +
5.208 + if (graph.u(e) == graph.u(f)) {
5.209 + check(!collinear(e1, e2, f2), "Wrong drawing");
5.210 + } else if (graph.u(e) == graph.v(f)) {
5.211 + check(!collinear(e1, e2, f1), "Wrong drawing");
5.212 + } else if (graph.v(e) == graph.u(f)) {
5.213 + check(!collinear(e2, e1, f2), "Wrong drawing");
5.214 + } else if (graph.v(e) == graph.v(f)) {
5.215 + check(!collinear(e2, e1, f1), "Wrong drawing");
5.216 + } else {
5.217 + check(!intersect(e1, e2, f1, f2), "Wrong drawing");
5.218 + }
5.219 + }
5.220 + }
5.221 +}
5.222 +
5.223 +void checkColoring(const Graph& graph, PC& pc, int num) {
5.224 + for (NodeIt n(graph); n != INVALID; ++n) {
5.225 + check(pc.colorIndex(n) >= 0 && pc.colorIndex(n) < num,
5.226 + "Wrong coloring");
5.227 + }
5.228 + for (EdgeIt e(graph); e != INVALID; ++e) {
5.229 + check(pc.colorIndex(graph.u(e)) != pc.colorIndex(graph.v(e)),
5.230 + "Wrong coloring");
5.231 + }
5.232 +}
5.233 +
5.234 +int main() {
5.235 +
5.236 + for (int i = 0; i < lgfn; ++i) {
5.237 + std::istringstream lgfs(lgf[i]);
5.238 +
5.239 + SmartGraph graph;
5.240 + graphReader(graph, lgfs).run();
5.241 +
5.242 + check(simpleGraph(graph), "Test graphs must be simple");
5.243 +
5.244 + PE pe(graph);
5.245 + if (pe.run()) {
5.246 + checkEmbedding(graph, pe);
5.247 +
5.248 + PlanarDrawing<Graph> pd(graph);
5.249 + pd.run(pe.embedding());
5.250 + checkDrawing(graph, pd);
5.251 +
5.252 + PlanarColoring<Graph> pc(graph);
5.253 + pc.runFiveColoring(pe.embedding());
5.254 + checkColoring(graph, pc, 5);
5.255 +
5.256 + } else {
5.257 + checkKuratowski(graph, pe);
5.258 + }
5.259 + }
5.260 +
5.261 + return 0;
5.262 +}