1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2008 |
---|
6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
8 | * |
---|
9 | * Permission to use, modify and distribute this software is granted |
---|
10 | * provided that this copyright notice appears in all copies. For |
---|
11 | * precise terms see the accompanying LICENSE file. |
---|
12 | * |
---|
13 | * This software is provided "AS IS" with no warranty of any kind, |
---|
14 | * express or implied, and with no claim as to its suitability for any |
---|
15 | * purpose. |
---|
16 | * |
---|
17 | */ |
---|
18 | |
---|
19 | #ifndef LEMON_PLANARITY_H |
---|
20 | #define LEMON_PLANARITY_H |
---|
21 | |
---|
22 | /// \ingroup planar |
---|
23 | /// \file |
---|
24 | /// \brief Planarity checking, embedding, drawing and coloring |
---|
25 | |
---|
26 | #include <vector> |
---|
27 | #include <list> |
---|
28 | |
---|
29 | #include <lemon/dfs.h> |
---|
30 | #include <lemon/bfs.h> |
---|
31 | #include <lemon/radix_sort.h> |
---|
32 | #include <lemon/maps.h> |
---|
33 | #include <lemon/path.h> |
---|
34 | #include <lemon/iterable_maps.h> |
---|
35 | #include <lemon/edge_set.h> |
---|
36 | #include <lemon/bucket_heap.h> |
---|
37 | #include <lemon/ugraph_adaptor.h> |
---|
38 | #include <lemon/color.h> |
---|
39 | |
---|
40 | |
---|
41 | namespace lemon { |
---|
42 | |
---|
43 | namespace _planarity_bits { |
---|
44 | |
---|
45 | template <typename UGraph> |
---|
46 | struct PlanarityVisitor : DfsVisitor<UGraph> { |
---|
47 | |
---|
48 | typedef typename UGraph::Node Node; |
---|
49 | typedef typename UGraph::Edge Edge; |
---|
50 | |
---|
51 | typedef typename UGraph::template NodeMap<Edge> PredMap; |
---|
52 | |
---|
53 | typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
---|
54 | |
---|
55 | typedef typename UGraph::template NodeMap<int> OrderMap; |
---|
56 | typedef std::vector<Node> OrderList; |
---|
57 | |
---|
58 | typedef typename UGraph::template NodeMap<int> LowMap; |
---|
59 | typedef typename UGraph::template NodeMap<int> AncestorMap; |
---|
60 | |
---|
61 | PlanarityVisitor(const UGraph& ugraph, |
---|
62 | PredMap& pred_map, TreeMap& tree_map, |
---|
63 | OrderMap& order_map, OrderList& order_list, |
---|
64 | AncestorMap& ancestor_map, LowMap& low_map) |
---|
65 | : _ugraph(ugraph), _pred_map(pred_map), _tree_map(tree_map), |
---|
66 | _order_map(order_map), _order_list(order_list), |
---|
67 | _ancestor_map(ancestor_map), _low_map(low_map) {} |
---|
68 | |
---|
69 | void reach(const Node& node) { |
---|
70 | _order_map[node] = _order_list.size(); |
---|
71 | _low_map[node] = _order_list.size(); |
---|
72 | _ancestor_map[node] = _order_list.size(); |
---|
73 | _order_list.push_back(node); |
---|
74 | } |
---|
75 | |
---|
76 | void discover(const Edge& edge) { |
---|
77 | Node source = _ugraph.source(edge); |
---|
78 | Node target = _ugraph.target(edge); |
---|
79 | |
---|
80 | _tree_map[edge] = true; |
---|
81 | _pred_map[target] = edge; |
---|
82 | } |
---|
83 | |
---|
84 | void examine(const Edge& edge) { |
---|
85 | Node source = _ugraph.source(edge); |
---|
86 | Node target = _ugraph.target(edge); |
---|
87 | |
---|
88 | if (_order_map[target] < _order_map[source] && !_tree_map[edge]) { |
---|
89 | if (_low_map[source] > _order_map[target]) { |
---|
90 | _low_map[source] = _order_map[target]; |
---|
91 | } |
---|
92 | if (_ancestor_map[source] > _order_map[target]) { |
---|
93 | _ancestor_map[source] = _order_map[target]; |
---|
94 | } |
---|
95 | } |
---|
96 | } |
---|
97 | |
---|
98 | void backtrack(const Edge& edge) { |
---|
99 | Node source = _ugraph.source(edge); |
---|
100 | Node target = _ugraph.target(edge); |
---|
101 | |
---|
102 | if (_low_map[source] > _low_map[target]) { |
---|
103 | _low_map[source] = _low_map[target]; |
---|
104 | } |
---|
105 | } |
---|
106 | |
---|
107 | const UGraph& _ugraph; |
---|
108 | PredMap& _pred_map; |
---|
109 | TreeMap& _tree_map; |
---|
110 | OrderMap& _order_map; |
---|
111 | OrderList& _order_list; |
---|
112 | AncestorMap& _ancestor_map; |
---|
113 | LowMap& _low_map; |
---|
114 | }; |
---|
115 | |
---|
116 | template <typename UGraph, bool embedding = true> |
---|
117 | struct NodeDataNode { |
---|
118 | int prev, next; |
---|
119 | int visited; |
---|
120 | typename UGraph::Edge first; |
---|
121 | bool inverted; |
---|
122 | }; |
---|
123 | |
---|
124 | template <typename UGraph> |
---|
125 | struct NodeDataNode<UGraph, false> { |
---|
126 | int prev, next; |
---|
127 | int visited; |
---|
128 | }; |
---|
129 | |
---|
130 | template <typename UGraph> |
---|
131 | struct ChildListNode { |
---|
132 | typedef typename UGraph::Node Node; |
---|
133 | Node first; |
---|
134 | Node prev, next; |
---|
135 | }; |
---|
136 | |
---|
137 | template <typename UGraph> |
---|
138 | struct EdgeListNode { |
---|
139 | typename UGraph::Edge prev, next; |
---|
140 | }; |
---|
141 | |
---|
142 | } |
---|
143 | |
---|
144 | /// \ingroup planar |
---|
145 | /// |
---|
146 | /// \brief Planarity checking of an undirected simple graph |
---|
147 | /// |
---|
148 | /// This class implements the Boyer-Myrvold algorithm for planarity |
---|
149 | /// checking of an undirected graph. This class is a simplified |
---|
150 | /// version of the PlanarEmbedding algorithm class, and it does |
---|
151 | /// provide neither embedding nor kuratowski subdivisons. |
---|
152 | template <typename UGraph> |
---|
153 | class PlanarityChecking { |
---|
154 | private: |
---|
155 | |
---|
156 | UGRAPH_TYPEDEFS(typename UGraph); |
---|
157 | |
---|
158 | const UGraph& _ugraph; |
---|
159 | |
---|
160 | private: |
---|
161 | |
---|
162 | typedef typename UGraph::template NodeMap<Edge> PredMap; |
---|
163 | |
---|
164 | typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
---|
165 | |
---|
166 | typedef typename UGraph::template NodeMap<int> OrderMap; |
---|
167 | typedef std::vector<Node> OrderList; |
---|
168 | |
---|
169 | typedef typename UGraph::template NodeMap<int> LowMap; |
---|
170 | typedef typename UGraph::template NodeMap<int> AncestorMap; |
---|
171 | |
---|
172 | typedef _planarity_bits::NodeDataNode<UGraph> NodeDataNode; |
---|
173 | typedef std::vector<NodeDataNode> NodeData; |
---|
174 | |
---|
175 | typedef _planarity_bits::ChildListNode<UGraph> ChildListNode; |
---|
176 | typedef typename UGraph::template NodeMap<ChildListNode> ChildLists; |
---|
177 | |
---|
178 | typedef typename UGraph::template NodeMap<std::list<int> > MergeRoots; |
---|
179 | |
---|
180 | typedef typename UGraph::template NodeMap<bool> EmbedEdge; |
---|
181 | |
---|
182 | public: |
---|
183 | |
---|
184 | /// \brief Constructor |
---|
185 | /// |
---|
186 | /// \warining The graph should be simple, i.e. parallel and loop edge |
---|
187 | /// free. |
---|
188 | PlanarityChecking(const UGraph& ugraph) : _ugraph(ugraph) {} |
---|
189 | |
---|
190 | /// \brief Runs the algorithm. |
---|
191 | /// |
---|
192 | /// Runs the algorithm. |
---|
193 | /// \return %True when the graph is planar. |
---|
194 | bool run() { |
---|
195 | typedef _planarity_bits::PlanarityVisitor<UGraph> Visitor; |
---|
196 | |
---|
197 | PredMap pred_map(_ugraph, INVALID); |
---|
198 | TreeMap tree_map(_ugraph, false); |
---|
199 | |
---|
200 | OrderMap order_map(_ugraph, -1); |
---|
201 | OrderList order_list; |
---|
202 | |
---|
203 | AncestorMap ancestor_map(_ugraph, -1); |
---|
204 | LowMap low_map(_ugraph, -1); |
---|
205 | |
---|
206 | Visitor visitor(_ugraph, pred_map, tree_map, |
---|
207 | order_map, order_list, ancestor_map, low_map); |
---|
208 | DfsVisit<UGraph, Visitor> visit(_ugraph, visitor); |
---|
209 | visit.run(); |
---|
210 | |
---|
211 | ChildLists child_lists(_ugraph); |
---|
212 | createChildLists(tree_map, order_map, low_map, child_lists); |
---|
213 | |
---|
214 | NodeData node_data(2 * order_list.size()); |
---|
215 | |
---|
216 | EmbedEdge embed_edge(_ugraph, false); |
---|
217 | |
---|
218 | MergeRoots merge_roots(_ugraph); |
---|
219 | |
---|
220 | for (int i = order_list.size() - 1; i >= 0; --i) { |
---|
221 | |
---|
222 | Node node = order_list[i]; |
---|
223 | |
---|
224 | Node source = node; |
---|
225 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
226 | Node target = _ugraph.target(e); |
---|
227 | |
---|
228 | if (order_map[source] < order_map[target] && tree_map[e]) { |
---|
229 | initFace(target, node_data, order_map, order_list); |
---|
230 | } |
---|
231 | } |
---|
232 | |
---|
233 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
234 | Node target = _ugraph.target(e); |
---|
235 | |
---|
236 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
---|
237 | embed_edge[target] = true; |
---|
238 | walkUp(target, source, i, pred_map, low_map, |
---|
239 | order_map, order_list, node_data, merge_roots); |
---|
240 | } |
---|
241 | } |
---|
242 | |
---|
243 | for (typename MergeRoots::Value::iterator it = |
---|
244 | merge_roots[node].begin(); it != merge_roots[node].end(); ++it) { |
---|
245 | int rn = *it; |
---|
246 | walkDown(rn, i, node_data, order_list, child_lists, |
---|
247 | ancestor_map, low_map, embed_edge, merge_roots); |
---|
248 | } |
---|
249 | merge_roots[node].clear(); |
---|
250 | |
---|
251 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
252 | Node target = _ugraph.target(e); |
---|
253 | |
---|
254 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
---|
255 | if (embed_edge[target]) { |
---|
256 | return false; |
---|
257 | } |
---|
258 | } |
---|
259 | } |
---|
260 | } |
---|
261 | |
---|
262 | return true; |
---|
263 | } |
---|
264 | |
---|
265 | private: |
---|
266 | |
---|
267 | void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
---|
268 | const LowMap& low_map, ChildLists& child_lists) { |
---|
269 | |
---|
270 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
271 | Node source = n; |
---|
272 | |
---|
273 | std::vector<Node> targets; |
---|
274 | for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
275 | Node target = _ugraph.target(e); |
---|
276 | |
---|
277 | if (order_map[source] < order_map[target] && tree_map[e]) { |
---|
278 | targets.push_back(target); |
---|
279 | } |
---|
280 | } |
---|
281 | |
---|
282 | if (targets.size() == 0) { |
---|
283 | child_lists[source].first = INVALID; |
---|
284 | } else if (targets.size() == 1) { |
---|
285 | child_lists[source].first = targets[0]; |
---|
286 | child_lists[targets[0]].prev = INVALID; |
---|
287 | child_lists[targets[0]].next = INVALID; |
---|
288 | } else { |
---|
289 | radixSort(targets.begin(), targets.end(), mapFunctor(low_map)); |
---|
290 | for (int i = 1; i < int(targets.size()); ++i) { |
---|
291 | child_lists[targets[i]].prev = targets[i - 1]; |
---|
292 | child_lists[targets[i - 1]].next = targets[i]; |
---|
293 | } |
---|
294 | child_lists[targets.back()].next = INVALID; |
---|
295 | child_lists[targets.front()].prev = INVALID; |
---|
296 | child_lists[source].first = targets.front(); |
---|
297 | } |
---|
298 | } |
---|
299 | } |
---|
300 | |
---|
301 | void walkUp(const Node& node, Node root, int rorder, |
---|
302 | const PredMap& pred_map, const LowMap& low_map, |
---|
303 | const OrderMap& order_map, const OrderList& order_list, |
---|
304 | NodeData& node_data, MergeRoots& merge_roots) { |
---|
305 | |
---|
306 | int na, nb; |
---|
307 | bool da, db; |
---|
308 | |
---|
309 | na = nb = order_map[node]; |
---|
310 | da = true; db = false; |
---|
311 | |
---|
312 | while (true) { |
---|
313 | |
---|
314 | if (node_data[na].visited == rorder) break; |
---|
315 | if (node_data[nb].visited == rorder) break; |
---|
316 | |
---|
317 | node_data[na].visited = rorder; |
---|
318 | node_data[nb].visited = rorder; |
---|
319 | |
---|
320 | int rn = -1; |
---|
321 | |
---|
322 | if (na >= int(order_list.size())) { |
---|
323 | rn = na; |
---|
324 | } else if (nb >= int(order_list.size())) { |
---|
325 | rn = nb; |
---|
326 | } |
---|
327 | |
---|
328 | if (rn == -1) { |
---|
329 | int nn; |
---|
330 | |
---|
331 | nn = da ? node_data[na].prev : node_data[na].next; |
---|
332 | da = node_data[nn].prev != na; |
---|
333 | na = nn; |
---|
334 | |
---|
335 | nn = db ? node_data[nb].prev : node_data[nb].next; |
---|
336 | db = node_data[nn].prev != nb; |
---|
337 | nb = nn; |
---|
338 | |
---|
339 | } else { |
---|
340 | |
---|
341 | Node rep = order_list[rn - order_list.size()]; |
---|
342 | Node parent = _ugraph.source(pred_map[rep]); |
---|
343 | |
---|
344 | if (low_map[rep] < rorder) { |
---|
345 | merge_roots[parent].push_back(rn); |
---|
346 | } else { |
---|
347 | merge_roots[parent].push_front(rn); |
---|
348 | } |
---|
349 | |
---|
350 | if (parent != root) { |
---|
351 | na = nb = order_map[parent]; |
---|
352 | da = true; db = false; |
---|
353 | } else { |
---|
354 | break; |
---|
355 | } |
---|
356 | } |
---|
357 | } |
---|
358 | } |
---|
359 | |
---|
360 | void walkDown(int rn, int rorder, NodeData& node_data, |
---|
361 | OrderList& order_list, ChildLists& child_lists, |
---|
362 | AncestorMap& ancestor_map, LowMap& low_map, |
---|
363 | EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
---|
364 | |
---|
365 | std::vector<std::pair<int, bool> > merge_stack; |
---|
366 | |
---|
367 | for (int di = 0; di < 2; ++di) { |
---|
368 | bool rd = di == 0; |
---|
369 | int pn = rn; |
---|
370 | int n = rd ? node_data[rn].next : node_data[rn].prev; |
---|
371 | |
---|
372 | while (n != rn) { |
---|
373 | |
---|
374 | Node node = order_list[n]; |
---|
375 | |
---|
376 | if (embed_edge[node]) { |
---|
377 | |
---|
378 | // Merging components on the critical path |
---|
379 | while (!merge_stack.empty()) { |
---|
380 | |
---|
381 | // Component root |
---|
382 | int cn = merge_stack.back().first; |
---|
383 | bool cd = merge_stack.back().second; |
---|
384 | merge_stack.pop_back(); |
---|
385 | |
---|
386 | // Parent of component |
---|
387 | int dn = merge_stack.back().first; |
---|
388 | bool dd = merge_stack.back().second; |
---|
389 | merge_stack.pop_back(); |
---|
390 | |
---|
391 | Node parent = order_list[dn]; |
---|
392 | |
---|
393 | // Erasing from merge_roots |
---|
394 | merge_roots[parent].pop_front(); |
---|
395 | |
---|
396 | Node child = order_list[cn - order_list.size()]; |
---|
397 | |
---|
398 | // Erasing from child_lists |
---|
399 | if (child_lists[child].prev != INVALID) { |
---|
400 | child_lists[child_lists[child].prev].next = |
---|
401 | child_lists[child].next; |
---|
402 | } else { |
---|
403 | child_lists[parent].first = child_lists[child].next; |
---|
404 | } |
---|
405 | |
---|
406 | if (child_lists[child].next != INVALID) { |
---|
407 | child_lists[child_lists[child].next].prev = |
---|
408 | child_lists[child].prev; |
---|
409 | } |
---|
410 | |
---|
411 | // Merging external faces |
---|
412 | { |
---|
413 | int en = cn; |
---|
414 | cn = cd ? node_data[cn].prev : node_data[cn].next; |
---|
415 | cd = node_data[cn].next == en; |
---|
416 | |
---|
417 | } |
---|
418 | |
---|
419 | if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
---|
420 | if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
---|
421 | |
---|
422 | } |
---|
423 | |
---|
424 | bool d = pn == node_data[n].prev; |
---|
425 | |
---|
426 | if (node_data[n].prev == node_data[n].next && |
---|
427 | node_data[n].inverted) { |
---|
428 | d = !d; |
---|
429 | } |
---|
430 | |
---|
431 | // Embedding edge into external face |
---|
432 | if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
---|
433 | if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
---|
434 | pn = rn; |
---|
435 | |
---|
436 | embed_edge[order_list[n]] = false; |
---|
437 | } |
---|
438 | |
---|
439 | if (!merge_roots[node].empty()) { |
---|
440 | |
---|
441 | bool d = pn == node_data[n].prev; |
---|
442 | |
---|
443 | merge_stack.push_back(std::make_pair(n, d)); |
---|
444 | |
---|
445 | int rn = merge_roots[node].front(); |
---|
446 | |
---|
447 | int xn = node_data[rn].next; |
---|
448 | Node xnode = order_list[xn]; |
---|
449 | |
---|
450 | int yn = node_data[rn].prev; |
---|
451 | Node ynode = order_list[yn]; |
---|
452 | |
---|
453 | bool rd; |
---|
454 | if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
455 | rd = true; |
---|
456 | } else if (!external(ynode, rorder, child_lists, |
---|
457 | ancestor_map, low_map)) { |
---|
458 | rd = false; |
---|
459 | } else if (pertinent(xnode, embed_edge, merge_roots)) { |
---|
460 | rd = true; |
---|
461 | } else { |
---|
462 | rd = false; |
---|
463 | } |
---|
464 | |
---|
465 | merge_stack.push_back(std::make_pair(rn, rd)); |
---|
466 | |
---|
467 | pn = rn; |
---|
468 | n = rd ? xn : yn; |
---|
469 | |
---|
470 | } else if (!external(node, rorder, child_lists, |
---|
471 | ancestor_map, low_map)) { |
---|
472 | int nn = (node_data[n].next != pn ? |
---|
473 | node_data[n].next : node_data[n].prev); |
---|
474 | |
---|
475 | bool nd = n == node_data[nn].prev; |
---|
476 | |
---|
477 | if (nd) node_data[nn].prev = pn; |
---|
478 | else node_data[nn].next = pn; |
---|
479 | |
---|
480 | if (n == node_data[pn].prev) node_data[pn].prev = nn; |
---|
481 | else node_data[pn].next = nn; |
---|
482 | |
---|
483 | node_data[nn].inverted = |
---|
484 | (node_data[nn].prev == node_data[nn].next && nd != rd); |
---|
485 | |
---|
486 | n = nn; |
---|
487 | } |
---|
488 | else break; |
---|
489 | |
---|
490 | } |
---|
491 | |
---|
492 | if (!merge_stack.empty() || n == rn) { |
---|
493 | break; |
---|
494 | } |
---|
495 | } |
---|
496 | } |
---|
497 | |
---|
498 | void initFace(const Node& node, NodeData& node_data, |
---|
499 | const OrderMap& order_map, const OrderList& order_list) { |
---|
500 | int n = order_map[node]; |
---|
501 | int rn = n + order_list.size(); |
---|
502 | |
---|
503 | node_data[n].next = node_data[n].prev = rn; |
---|
504 | node_data[rn].next = node_data[rn].prev = n; |
---|
505 | |
---|
506 | node_data[n].visited = order_list.size(); |
---|
507 | node_data[rn].visited = order_list.size(); |
---|
508 | |
---|
509 | } |
---|
510 | |
---|
511 | bool external(const Node& node, int rorder, |
---|
512 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
513 | LowMap& low_map) { |
---|
514 | Node child = child_lists[node].first; |
---|
515 | |
---|
516 | if (child != INVALID) { |
---|
517 | if (low_map[child] < rorder) return true; |
---|
518 | } |
---|
519 | |
---|
520 | if (ancestor_map[node] < rorder) return true; |
---|
521 | |
---|
522 | return false; |
---|
523 | } |
---|
524 | |
---|
525 | bool pertinent(const Node& node, const EmbedEdge& embed_edge, |
---|
526 | const MergeRoots& merge_roots) { |
---|
527 | return !merge_roots[node].empty() || embed_edge[node]; |
---|
528 | } |
---|
529 | |
---|
530 | }; |
---|
531 | |
---|
532 | /// \ingroup planar |
---|
533 | /// |
---|
534 | /// \brief Planar embedding of an undirected simple graph |
---|
535 | /// |
---|
536 | /// This class implements the Boyer-Myrvold algorithm for planar |
---|
537 | /// embedding of an undirected graph. The planar embeding is an |
---|
538 | /// ordering of the outgoing edges in each node, which is a possible |
---|
539 | /// configuration to draw the graph in the plane. If there is not |
---|
540 | /// such ordering then the graph contains a \f$ K_5 \f$ (full graph |
---|
541 | /// with 5 nodes) or an \f$ K_{3,3} \f$ (complete bipartite graph on |
---|
542 | /// 3 ANode and 3 BNode) subdivision. |
---|
543 | /// |
---|
544 | /// The current implementation calculates an embedding or an |
---|
545 | /// Kuratowski subdivision if the graph is not planar. The running |
---|
546 | /// time of the algorithm is \f$ O(n) \f$. |
---|
547 | template <typename UGraph> |
---|
548 | class PlanarEmbedding { |
---|
549 | private: |
---|
550 | |
---|
551 | UGRAPH_TYPEDEFS(typename UGraph); |
---|
552 | |
---|
553 | const UGraph& _ugraph; |
---|
554 | typename UGraph::template EdgeMap<Edge> _embedding; |
---|
555 | |
---|
556 | typename UGraph::template UEdgeMap<bool> _kuratowski; |
---|
557 | |
---|
558 | private: |
---|
559 | |
---|
560 | typedef typename UGraph::template NodeMap<Edge> PredMap; |
---|
561 | |
---|
562 | typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
---|
563 | |
---|
564 | typedef typename UGraph::template NodeMap<int> OrderMap; |
---|
565 | typedef std::vector<Node> OrderList; |
---|
566 | |
---|
567 | typedef typename UGraph::template NodeMap<int> LowMap; |
---|
568 | typedef typename UGraph::template NodeMap<int> AncestorMap; |
---|
569 | |
---|
570 | typedef _planarity_bits::NodeDataNode<UGraph> NodeDataNode; |
---|
571 | typedef std::vector<NodeDataNode> NodeData; |
---|
572 | |
---|
573 | typedef _planarity_bits::ChildListNode<UGraph> ChildListNode; |
---|
574 | typedef typename UGraph::template NodeMap<ChildListNode> ChildLists; |
---|
575 | |
---|
576 | typedef typename UGraph::template NodeMap<std::list<int> > MergeRoots; |
---|
577 | |
---|
578 | typedef typename UGraph::template NodeMap<Edge> EmbedEdge; |
---|
579 | |
---|
580 | typedef _planarity_bits::EdgeListNode<UGraph> EdgeListNode; |
---|
581 | typedef typename UGraph::template EdgeMap<EdgeListNode> EdgeLists; |
---|
582 | |
---|
583 | typedef typename UGraph::template NodeMap<bool> FlipMap; |
---|
584 | |
---|
585 | typedef typename UGraph::template NodeMap<int> TypeMap; |
---|
586 | |
---|
587 | enum IsolatorNodeType { |
---|
588 | HIGHX = 6, LOWX = 7, |
---|
589 | HIGHY = 8, LOWY = 9, |
---|
590 | ROOT = 10, PERTINENT = 11, |
---|
591 | INTERNAL = 12 |
---|
592 | }; |
---|
593 | |
---|
594 | public: |
---|
595 | |
---|
596 | /// \brief The map for store of embedding |
---|
597 | typedef typename UGraph::template EdgeMap<Edge> EmbeddingMap; |
---|
598 | |
---|
599 | /// \brief Constructor |
---|
600 | /// |
---|
601 | /// \warining The graph should be simple, i.e. parallel and loop edge |
---|
602 | /// free. |
---|
603 | PlanarEmbedding(const UGraph& ugraph) |
---|
604 | : _ugraph(ugraph), _embedding(_ugraph), _kuratowski(ugraph, false) {} |
---|
605 | |
---|
606 | /// \brief Runs the algorithm. |
---|
607 | /// |
---|
608 | /// Runs the algorithm. |
---|
609 | /// \param kuratowski If the parameter is false, then the |
---|
610 | /// algorithm does not calculate the isolate Kuratowski |
---|
611 | /// subdivisions. |
---|
612 | ///\return %True when the graph is planar. |
---|
613 | bool run(bool kuratowski = true) { |
---|
614 | typedef _planarity_bits::PlanarityVisitor<UGraph> Visitor; |
---|
615 | |
---|
616 | PredMap pred_map(_ugraph, INVALID); |
---|
617 | TreeMap tree_map(_ugraph, false); |
---|
618 | |
---|
619 | OrderMap order_map(_ugraph, -1); |
---|
620 | OrderList order_list; |
---|
621 | |
---|
622 | AncestorMap ancestor_map(_ugraph, -1); |
---|
623 | LowMap low_map(_ugraph, -1); |
---|
624 | |
---|
625 | Visitor visitor(_ugraph, pred_map, tree_map, |
---|
626 | order_map, order_list, ancestor_map, low_map); |
---|
627 | DfsVisit<UGraph, Visitor> visit(_ugraph, visitor); |
---|
628 | visit.run(); |
---|
629 | |
---|
630 | ChildLists child_lists(_ugraph); |
---|
631 | createChildLists(tree_map, order_map, low_map, child_lists); |
---|
632 | |
---|
633 | NodeData node_data(2 * order_list.size()); |
---|
634 | |
---|
635 | EmbedEdge embed_edge(_ugraph, INVALID); |
---|
636 | |
---|
637 | MergeRoots merge_roots(_ugraph); |
---|
638 | |
---|
639 | EdgeLists edge_lists(_ugraph); |
---|
640 | |
---|
641 | FlipMap flip_map(_ugraph, false); |
---|
642 | |
---|
643 | for (int i = order_list.size() - 1; i >= 0; --i) { |
---|
644 | |
---|
645 | Node node = order_list[i]; |
---|
646 | |
---|
647 | node_data[i].first = INVALID; |
---|
648 | |
---|
649 | Node source = node; |
---|
650 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
651 | Node target = _ugraph.target(e); |
---|
652 | |
---|
653 | if (order_map[source] < order_map[target] && tree_map[e]) { |
---|
654 | initFace(target, edge_lists, node_data, |
---|
655 | pred_map, order_map, order_list); |
---|
656 | } |
---|
657 | } |
---|
658 | |
---|
659 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
660 | Node target = _ugraph.target(e); |
---|
661 | |
---|
662 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
---|
663 | embed_edge[target] = e; |
---|
664 | walkUp(target, source, i, pred_map, low_map, |
---|
665 | order_map, order_list, node_data, merge_roots); |
---|
666 | } |
---|
667 | } |
---|
668 | |
---|
669 | for (typename MergeRoots::Value::iterator it = |
---|
670 | merge_roots[node].begin(); it != merge_roots[node].end(); ++it) { |
---|
671 | int rn = *it; |
---|
672 | walkDown(rn, i, node_data, edge_lists, flip_map, order_list, |
---|
673 | child_lists, ancestor_map, low_map, embed_edge, merge_roots); |
---|
674 | } |
---|
675 | merge_roots[node].clear(); |
---|
676 | |
---|
677 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
678 | Node target = _ugraph.target(e); |
---|
679 | |
---|
680 | if (order_map[source] < order_map[target] && !tree_map[e]) { |
---|
681 | if (embed_edge[target] != INVALID) { |
---|
682 | if (kuratowski) { |
---|
683 | isolateKuratowski(e, node_data, edge_lists, flip_map, |
---|
684 | order_map, order_list, pred_map, child_lists, |
---|
685 | ancestor_map, low_map, |
---|
686 | embed_edge, merge_roots); |
---|
687 | } |
---|
688 | return false; |
---|
689 | } |
---|
690 | } |
---|
691 | } |
---|
692 | } |
---|
693 | |
---|
694 | for (int i = 0; i < int(order_list.size()); ++i) { |
---|
695 | |
---|
696 | mergeRemainingFaces(order_list[i], node_data, order_list, order_map, |
---|
697 | child_lists, edge_lists); |
---|
698 | storeEmbedding(order_list[i], node_data, order_map, pred_map, |
---|
699 | edge_lists, flip_map); |
---|
700 | } |
---|
701 | |
---|
702 | return true; |
---|
703 | } |
---|
704 | |
---|
705 | /// \brief Gives back the successor of an edge |
---|
706 | /// |
---|
707 | /// Gives back the successor of an edge. This function makes |
---|
708 | /// possible to query the cyclic order of the outgoing edges from |
---|
709 | /// a node. |
---|
710 | Edge next(const Edge& edge) const { |
---|
711 | return _embedding[edge]; |
---|
712 | } |
---|
713 | |
---|
714 | /// \brief Gives back the calculated embedding map |
---|
715 | /// |
---|
716 | /// The returned map contains the successor of each edge in the |
---|
717 | /// graph. |
---|
718 | const EmbeddingMap& embedding() const { |
---|
719 | return _embedding; |
---|
720 | } |
---|
721 | |
---|
722 | /// \brief Gives back true when the undirected edge is in the |
---|
723 | /// kuratowski subdivision |
---|
724 | /// |
---|
725 | /// Gives back true when the undirected edge is in the kuratowski |
---|
726 | /// subdivision |
---|
727 | bool kuratowski(const UEdge& uedge) { |
---|
728 | return _kuratowski[uedge]; |
---|
729 | } |
---|
730 | |
---|
731 | private: |
---|
732 | |
---|
733 | void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
---|
734 | const LowMap& low_map, ChildLists& child_lists) { |
---|
735 | |
---|
736 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
737 | Node source = n; |
---|
738 | |
---|
739 | std::vector<Node> targets; |
---|
740 | for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
741 | Node target = _ugraph.target(e); |
---|
742 | |
---|
743 | if (order_map[source] < order_map[target] && tree_map[e]) { |
---|
744 | targets.push_back(target); |
---|
745 | } |
---|
746 | } |
---|
747 | |
---|
748 | if (targets.size() == 0) { |
---|
749 | child_lists[source].first = INVALID; |
---|
750 | } else if (targets.size() == 1) { |
---|
751 | child_lists[source].first = targets[0]; |
---|
752 | child_lists[targets[0]].prev = INVALID; |
---|
753 | child_lists[targets[0]].next = INVALID; |
---|
754 | } else { |
---|
755 | radixSort(targets.begin(), targets.end(), mapFunctor(low_map)); |
---|
756 | for (int i = 1; i < int(targets.size()); ++i) { |
---|
757 | child_lists[targets[i]].prev = targets[i - 1]; |
---|
758 | child_lists[targets[i - 1]].next = targets[i]; |
---|
759 | } |
---|
760 | child_lists[targets.back()].next = INVALID; |
---|
761 | child_lists[targets.front()].prev = INVALID; |
---|
762 | child_lists[source].first = targets.front(); |
---|
763 | } |
---|
764 | } |
---|
765 | } |
---|
766 | |
---|
767 | void walkUp(const Node& node, Node root, int rorder, |
---|
768 | const PredMap& pred_map, const LowMap& low_map, |
---|
769 | const OrderMap& order_map, const OrderList& order_list, |
---|
770 | NodeData& node_data, MergeRoots& merge_roots) { |
---|
771 | |
---|
772 | int na, nb; |
---|
773 | bool da, db; |
---|
774 | |
---|
775 | na = nb = order_map[node]; |
---|
776 | da = true; db = false; |
---|
777 | |
---|
778 | while (true) { |
---|
779 | |
---|
780 | if (node_data[na].visited == rorder) break; |
---|
781 | if (node_data[nb].visited == rorder) break; |
---|
782 | |
---|
783 | node_data[na].visited = rorder; |
---|
784 | node_data[nb].visited = rorder; |
---|
785 | |
---|
786 | int rn = -1; |
---|
787 | |
---|
788 | if (na >= int(order_list.size())) { |
---|
789 | rn = na; |
---|
790 | } else if (nb >= int(order_list.size())) { |
---|
791 | rn = nb; |
---|
792 | } |
---|
793 | |
---|
794 | if (rn == -1) { |
---|
795 | int nn; |
---|
796 | |
---|
797 | nn = da ? node_data[na].prev : node_data[na].next; |
---|
798 | da = node_data[nn].prev != na; |
---|
799 | na = nn; |
---|
800 | |
---|
801 | nn = db ? node_data[nb].prev : node_data[nb].next; |
---|
802 | db = node_data[nn].prev != nb; |
---|
803 | nb = nn; |
---|
804 | |
---|
805 | } else { |
---|
806 | |
---|
807 | Node rep = order_list[rn - order_list.size()]; |
---|
808 | Node parent = _ugraph.source(pred_map[rep]); |
---|
809 | |
---|
810 | if (low_map[rep] < rorder) { |
---|
811 | merge_roots[parent].push_back(rn); |
---|
812 | } else { |
---|
813 | merge_roots[parent].push_front(rn); |
---|
814 | } |
---|
815 | |
---|
816 | if (parent != root) { |
---|
817 | na = nb = order_map[parent]; |
---|
818 | da = true; db = false; |
---|
819 | } else { |
---|
820 | break; |
---|
821 | } |
---|
822 | } |
---|
823 | } |
---|
824 | } |
---|
825 | |
---|
826 | void walkDown(int rn, int rorder, NodeData& node_data, |
---|
827 | EdgeLists& edge_lists, FlipMap& flip_map, |
---|
828 | OrderList& order_list, ChildLists& child_lists, |
---|
829 | AncestorMap& ancestor_map, LowMap& low_map, |
---|
830 | EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
---|
831 | |
---|
832 | std::vector<std::pair<int, bool> > merge_stack; |
---|
833 | |
---|
834 | for (int di = 0; di < 2; ++di) { |
---|
835 | bool rd = di == 0; |
---|
836 | int pn = rn; |
---|
837 | int n = rd ? node_data[rn].next : node_data[rn].prev; |
---|
838 | |
---|
839 | while (n != rn) { |
---|
840 | |
---|
841 | Node node = order_list[n]; |
---|
842 | |
---|
843 | if (embed_edge[node] != INVALID) { |
---|
844 | |
---|
845 | // Merging components on the critical path |
---|
846 | while (!merge_stack.empty()) { |
---|
847 | |
---|
848 | // Component root |
---|
849 | int cn = merge_stack.back().first; |
---|
850 | bool cd = merge_stack.back().second; |
---|
851 | merge_stack.pop_back(); |
---|
852 | |
---|
853 | // Parent of component |
---|
854 | int dn = merge_stack.back().first; |
---|
855 | bool dd = merge_stack.back().second; |
---|
856 | merge_stack.pop_back(); |
---|
857 | |
---|
858 | Node parent = order_list[dn]; |
---|
859 | |
---|
860 | // Erasing from merge_roots |
---|
861 | merge_roots[parent].pop_front(); |
---|
862 | |
---|
863 | Node child = order_list[cn - order_list.size()]; |
---|
864 | |
---|
865 | // Erasing from child_lists |
---|
866 | if (child_lists[child].prev != INVALID) { |
---|
867 | child_lists[child_lists[child].prev].next = |
---|
868 | child_lists[child].next; |
---|
869 | } else { |
---|
870 | child_lists[parent].first = child_lists[child].next; |
---|
871 | } |
---|
872 | |
---|
873 | if (child_lists[child].next != INVALID) { |
---|
874 | child_lists[child_lists[child].next].prev = |
---|
875 | child_lists[child].prev; |
---|
876 | } |
---|
877 | |
---|
878 | // Merging edges + flipping |
---|
879 | Edge de = node_data[dn].first; |
---|
880 | Edge ce = node_data[cn].first; |
---|
881 | |
---|
882 | flip_map[order_list[cn - order_list.size()]] = cd != dd; |
---|
883 | if (cd != dd) { |
---|
884 | std::swap(edge_lists[ce].prev, edge_lists[ce].next); |
---|
885 | ce = edge_lists[ce].prev; |
---|
886 | std::swap(edge_lists[ce].prev, edge_lists[ce].next); |
---|
887 | } |
---|
888 | |
---|
889 | { |
---|
890 | Edge dne = edge_lists[de].next; |
---|
891 | Edge cne = edge_lists[ce].next; |
---|
892 | |
---|
893 | edge_lists[de].next = cne; |
---|
894 | edge_lists[ce].next = dne; |
---|
895 | |
---|
896 | edge_lists[dne].prev = ce; |
---|
897 | edge_lists[cne].prev = de; |
---|
898 | } |
---|
899 | |
---|
900 | if (dd) { |
---|
901 | node_data[dn].first = ce; |
---|
902 | } |
---|
903 | |
---|
904 | // Merging external faces |
---|
905 | { |
---|
906 | int en = cn; |
---|
907 | cn = cd ? node_data[cn].prev : node_data[cn].next; |
---|
908 | cd = node_data[cn].next == en; |
---|
909 | |
---|
910 | if (node_data[cn].prev == node_data[cn].next && |
---|
911 | node_data[cn].inverted) { |
---|
912 | cd = !cd; |
---|
913 | } |
---|
914 | } |
---|
915 | |
---|
916 | if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
---|
917 | if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
---|
918 | |
---|
919 | } |
---|
920 | |
---|
921 | bool d = pn == node_data[n].prev; |
---|
922 | |
---|
923 | if (node_data[n].prev == node_data[n].next && |
---|
924 | node_data[n].inverted) { |
---|
925 | d = !d; |
---|
926 | } |
---|
927 | |
---|
928 | // Add new edge |
---|
929 | { |
---|
930 | Edge edge = embed_edge[node]; |
---|
931 | Edge re = node_data[rn].first; |
---|
932 | |
---|
933 | edge_lists[edge_lists[re].next].prev = edge; |
---|
934 | edge_lists[edge].next = edge_lists[re].next; |
---|
935 | edge_lists[edge].prev = re; |
---|
936 | edge_lists[re].next = edge; |
---|
937 | |
---|
938 | if (!rd) { |
---|
939 | node_data[rn].first = edge; |
---|
940 | } |
---|
941 | |
---|
942 | Edge rev = _ugraph.oppositeEdge(edge); |
---|
943 | Edge e = node_data[n].first; |
---|
944 | |
---|
945 | edge_lists[edge_lists[e].next].prev = rev; |
---|
946 | edge_lists[rev].next = edge_lists[e].next; |
---|
947 | edge_lists[rev].prev = e; |
---|
948 | edge_lists[e].next = rev; |
---|
949 | |
---|
950 | if (d) { |
---|
951 | node_data[n].first = rev; |
---|
952 | } |
---|
953 | |
---|
954 | } |
---|
955 | |
---|
956 | // Embedding edge into external face |
---|
957 | if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
---|
958 | if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
---|
959 | pn = rn; |
---|
960 | |
---|
961 | embed_edge[order_list[n]] = INVALID; |
---|
962 | } |
---|
963 | |
---|
964 | if (!merge_roots[node].empty()) { |
---|
965 | |
---|
966 | bool d = pn == node_data[n].prev; |
---|
967 | if (node_data[n].prev == node_data[n].next && |
---|
968 | node_data[n].inverted) { |
---|
969 | d = !d; |
---|
970 | } |
---|
971 | |
---|
972 | merge_stack.push_back(std::make_pair(n, d)); |
---|
973 | |
---|
974 | int rn = merge_roots[node].front(); |
---|
975 | |
---|
976 | int xn = node_data[rn].next; |
---|
977 | Node xnode = order_list[xn]; |
---|
978 | |
---|
979 | int yn = node_data[rn].prev; |
---|
980 | Node ynode = order_list[yn]; |
---|
981 | |
---|
982 | bool rd; |
---|
983 | if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
984 | rd = true; |
---|
985 | } else if (!external(ynode, rorder, child_lists, |
---|
986 | ancestor_map, low_map)) { |
---|
987 | rd = false; |
---|
988 | } else if (pertinent(xnode, embed_edge, merge_roots)) { |
---|
989 | rd = true; |
---|
990 | } else { |
---|
991 | rd = false; |
---|
992 | } |
---|
993 | |
---|
994 | merge_stack.push_back(std::make_pair(rn, rd)); |
---|
995 | |
---|
996 | pn = rn; |
---|
997 | n = rd ? xn : yn; |
---|
998 | |
---|
999 | } else if (!external(node, rorder, child_lists, |
---|
1000 | ancestor_map, low_map)) { |
---|
1001 | int nn = (node_data[n].next != pn ? |
---|
1002 | node_data[n].next : node_data[n].prev); |
---|
1003 | |
---|
1004 | bool nd = n == node_data[nn].prev; |
---|
1005 | |
---|
1006 | if (nd) node_data[nn].prev = pn; |
---|
1007 | else node_data[nn].next = pn; |
---|
1008 | |
---|
1009 | if (n == node_data[pn].prev) node_data[pn].prev = nn; |
---|
1010 | else node_data[pn].next = nn; |
---|
1011 | |
---|
1012 | node_data[nn].inverted = |
---|
1013 | (node_data[nn].prev == node_data[nn].next && nd != rd); |
---|
1014 | |
---|
1015 | n = nn; |
---|
1016 | } |
---|
1017 | else break; |
---|
1018 | |
---|
1019 | } |
---|
1020 | |
---|
1021 | if (!merge_stack.empty() || n == rn) { |
---|
1022 | break; |
---|
1023 | } |
---|
1024 | } |
---|
1025 | } |
---|
1026 | |
---|
1027 | void initFace(const Node& node, EdgeLists& edge_lists, |
---|
1028 | NodeData& node_data, const PredMap& pred_map, |
---|
1029 | const OrderMap& order_map, const OrderList& order_list) { |
---|
1030 | int n = order_map[node]; |
---|
1031 | int rn = n + order_list.size(); |
---|
1032 | |
---|
1033 | node_data[n].next = node_data[n].prev = rn; |
---|
1034 | node_data[rn].next = node_data[rn].prev = n; |
---|
1035 | |
---|
1036 | node_data[n].visited = order_list.size(); |
---|
1037 | node_data[rn].visited = order_list.size(); |
---|
1038 | |
---|
1039 | node_data[n].inverted = false; |
---|
1040 | node_data[rn].inverted = false; |
---|
1041 | |
---|
1042 | Edge edge = pred_map[node]; |
---|
1043 | Edge rev = _ugraph.oppositeEdge(edge); |
---|
1044 | |
---|
1045 | node_data[rn].first = edge; |
---|
1046 | node_data[n].first = rev; |
---|
1047 | |
---|
1048 | edge_lists[edge].prev = edge; |
---|
1049 | edge_lists[edge].next = edge; |
---|
1050 | |
---|
1051 | edge_lists[rev].prev = rev; |
---|
1052 | edge_lists[rev].next = rev; |
---|
1053 | |
---|
1054 | } |
---|
1055 | |
---|
1056 | void mergeRemainingFaces(const Node& node, NodeData& node_data, |
---|
1057 | OrderList& order_list, OrderMap& order_map, |
---|
1058 | ChildLists& child_lists, EdgeLists& edge_lists) { |
---|
1059 | while (child_lists[node].first != INVALID) { |
---|
1060 | int dd = order_map[node]; |
---|
1061 | Node child = child_lists[node].first; |
---|
1062 | int cd = order_map[child] + order_list.size(); |
---|
1063 | child_lists[node].first = child_lists[child].next; |
---|
1064 | |
---|
1065 | Edge de = node_data[dd].first; |
---|
1066 | Edge ce = node_data[cd].first; |
---|
1067 | |
---|
1068 | if (de != INVALID) { |
---|
1069 | Edge dne = edge_lists[de].next; |
---|
1070 | Edge cne = edge_lists[ce].next; |
---|
1071 | |
---|
1072 | edge_lists[de].next = cne; |
---|
1073 | edge_lists[ce].next = dne; |
---|
1074 | |
---|
1075 | edge_lists[dne].prev = ce; |
---|
1076 | edge_lists[cne].prev = de; |
---|
1077 | } |
---|
1078 | |
---|
1079 | node_data[dd].first = ce; |
---|
1080 | |
---|
1081 | } |
---|
1082 | } |
---|
1083 | |
---|
1084 | void storeEmbedding(const Node& node, NodeData& node_data, |
---|
1085 | OrderMap& order_map, PredMap& pred_map, |
---|
1086 | EdgeLists& edge_lists, FlipMap& flip_map) { |
---|
1087 | |
---|
1088 | if (node_data[order_map[node]].first == INVALID) return; |
---|
1089 | |
---|
1090 | if (pred_map[node] != INVALID) { |
---|
1091 | Node source = _ugraph.source(pred_map[node]); |
---|
1092 | flip_map[node] = flip_map[node] != flip_map[source]; |
---|
1093 | } |
---|
1094 | |
---|
1095 | Edge first = node_data[order_map[node]].first; |
---|
1096 | Edge prev = first; |
---|
1097 | |
---|
1098 | Edge edge = flip_map[node] ? |
---|
1099 | edge_lists[prev].prev : edge_lists[prev].next; |
---|
1100 | |
---|
1101 | _embedding[prev] = edge; |
---|
1102 | |
---|
1103 | while (edge != first) { |
---|
1104 | Edge next = edge_lists[edge].prev == prev ? |
---|
1105 | edge_lists[edge].next : edge_lists[edge].prev; |
---|
1106 | prev = edge; edge = next; |
---|
1107 | _embedding[prev] = edge; |
---|
1108 | } |
---|
1109 | } |
---|
1110 | |
---|
1111 | |
---|
1112 | bool external(const Node& node, int rorder, |
---|
1113 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
1114 | LowMap& low_map) { |
---|
1115 | Node child = child_lists[node].first; |
---|
1116 | |
---|
1117 | if (child != INVALID) { |
---|
1118 | if (low_map[child] < rorder) return true; |
---|
1119 | } |
---|
1120 | |
---|
1121 | if (ancestor_map[node] < rorder) return true; |
---|
1122 | |
---|
1123 | return false; |
---|
1124 | } |
---|
1125 | |
---|
1126 | bool pertinent(const Node& node, const EmbedEdge& embed_edge, |
---|
1127 | const MergeRoots& merge_roots) { |
---|
1128 | return !merge_roots[node].empty() || embed_edge[node] != INVALID; |
---|
1129 | } |
---|
1130 | |
---|
1131 | int lowPoint(const Node& node, OrderMap& order_map, ChildLists& child_lists, |
---|
1132 | AncestorMap& ancestor_map, LowMap& low_map) { |
---|
1133 | int low_point; |
---|
1134 | |
---|
1135 | Node child = child_lists[node].first; |
---|
1136 | |
---|
1137 | if (child != INVALID) { |
---|
1138 | low_point = low_map[child]; |
---|
1139 | } else { |
---|
1140 | low_point = order_map[node]; |
---|
1141 | } |
---|
1142 | |
---|
1143 | if (low_point > ancestor_map[node]) { |
---|
1144 | low_point = ancestor_map[node]; |
---|
1145 | } |
---|
1146 | |
---|
1147 | return low_point; |
---|
1148 | } |
---|
1149 | |
---|
1150 | int findComponentRoot(Node root, Node node, ChildLists& child_lists, |
---|
1151 | OrderMap& order_map, OrderList& order_list) { |
---|
1152 | |
---|
1153 | int order = order_map[root]; |
---|
1154 | int norder = order_map[node]; |
---|
1155 | |
---|
1156 | Node child = child_lists[root].first; |
---|
1157 | while (child != INVALID) { |
---|
1158 | int corder = order_map[child]; |
---|
1159 | if (corder > order && corder < norder) { |
---|
1160 | order = corder; |
---|
1161 | } |
---|
1162 | child = child_lists[child].next; |
---|
1163 | } |
---|
1164 | return order + order_list.size(); |
---|
1165 | } |
---|
1166 | |
---|
1167 | Node findPertinent(Node node, OrderMap& order_map, NodeData& node_data, |
---|
1168 | EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
---|
1169 | Node wnode =_ugraph.target(node_data[order_map[node]].first); |
---|
1170 | while (!pertinent(wnode, embed_edge, merge_roots)) { |
---|
1171 | wnode = _ugraph.target(node_data[order_map[wnode]].first); |
---|
1172 | } |
---|
1173 | return wnode; |
---|
1174 | } |
---|
1175 | |
---|
1176 | |
---|
1177 | Node findExternal(Node node, int rorder, OrderMap& order_map, |
---|
1178 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
1179 | LowMap& low_map, NodeData& node_data) { |
---|
1180 | Node wnode =_ugraph.target(node_data[order_map[node]].first); |
---|
1181 | while (!external(wnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
1182 | wnode = _ugraph.target(node_data[order_map[wnode]].first); |
---|
1183 | } |
---|
1184 | return wnode; |
---|
1185 | } |
---|
1186 | |
---|
1187 | void markCommonPath(Node node, int rorder, Node& wnode, Node& znode, |
---|
1188 | OrderList& order_list, OrderMap& order_map, |
---|
1189 | NodeData& node_data, EdgeLists& edge_lists, |
---|
1190 | EmbedEdge& embed_edge, MergeRoots& merge_roots, |
---|
1191 | ChildLists& child_lists, AncestorMap& ancestor_map, |
---|
1192 | LowMap& low_map) { |
---|
1193 | |
---|
1194 | Node cnode = node; |
---|
1195 | Node pred = INVALID; |
---|
1196 | |
---|
1197 | while (true) { |
---|
1198 | |
---|
1199 | bool pert = pertinent(cnode, embed_edge, merge_roots); |
---|
1200 | bool ext = external(cnode, rorder, child_lists, ancestor_map, low_map); |
---|
1201 | |
---|
1202 | if (pert && ext) { |
---|
1203 | if (!merge_roots[cnode].empty()) { |
---|
1204 | int cn = merge_roots[cnode].back(); |
---|
1205 | |
---|
1206 | if (low_map[order_list[cn - order_list.size()]] < rorder) { |
---|
1207 | Edge edge = node_data[cn].first; |
---|
1208 | _kuratowski.set(edge, true); |
---|
1209 | |
---|
1210 | pred = cnode; |
---|
1211 | cnode = _ugraph.target(edge); |
---|
1212 | |
---|
1213 | continue; |
---|
1214 | } |
---|
1215 | } |
---|
1216 | wnode = znode = cnode; |
---|
1217 | return; |
---|
1218 | |
---|
1219 | } else if (pert) { |
---|
1220 | wnode = cnode; |
---|
1221 | |
---|
1222 | while (!external(cnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
1223 | Edge edge = node_data[order_map[cnode]].first; |
---|
1224 | |
---|
1225 | if (_ugraph.target(edge) == pred) { |
---|
1226 | edge = edge_lists[edge].next; |
---|
1227 | } |
---|
1228 | _kuratowski.set(edge, true); |
---|
1229 | |
---|
1230 | Node next = _ugraph.target(edge); |
---|
1231 | pred = cnode; cnode = next; |
---|
1232 | } |
---|
1233 | |
---|
1234 | znode = cnode; |
---|
1235 | return; |
---|
1236 | |
---|
1237 | } else if (ext) { |
---|
1238 | znode = cnode; |
---|
1239 | |
---|
1240 | while (!pertinent(cnode, embed_edge, merge_roots)) { |
---|
1241 | Edge edge = node_data[order_map[cnode]].first; |
---|
1242 | |
---|
1243 | if (_ugraph.target(edge) == pred) { |
---|
1244 | edge = edge_lists[edge].next; |
---|
1245 | } |
---|
1246 | _kuratowski.set(edge, true); |
---|
1247 | |
---|
1248 | Node next = _ugraph.target(edge); |
---|
1249 | pred = cnode; cnode = next; |
---|
1250 | } |
---|
1251 | |
---|
1252 | wnode = cnode; |
---|
1253 | return; |
---|
1254 | |
---|
1255 | } else { |
---|
1256 | Edge edge = node_data[order_map[cnode]].first; |
---|
1257 | |
---|
1258 | if (_ugraph.target(edge) == pred) { |
---|
1259 | edge = edge_lists[edge].next; |
---|
1260 | } |
---|
1261 | _kuratowski.set(edge, true); |
---|
1262 | |
---|
1263 | Node next = _ugraph.target(edge); |
---|
1264 | pred = cnode; cnode = next; |
---|
1265 | } |
---|
1266 | |
---|
1267 | } |
---|
1268 | |
---|
1269 | } |
---|
1270 | |
---|
1271 | void orientComponent(Node root, int rn, OrderMap& order_map, |
---|
1272 | PredMap& pred_map, NodeData& node_data, |
---|
1273 | EdgeLists& edge_lists, FlipMap& flip_map, |
---|
1274 | TypeMap& type_map) { |
---|
1275 | node_data[order_map[root]].first = node_data[rn].first; |
---|
1276 | type_map[root] = 1; |
---|
1277 | |
---|
1278 | std::vector<Node> st, qu; |
---|
1279 | |
---|
1280 | st.push_back(root); |
---|
1281 | while (!st.empty()) { |
---|
1282 | Node node = st.back(); |
---|
1283 | st.pop_back(); |
---|
1284 | qu.push_back(node); |
---|
1285 | |
---|
1286 | Edge edge = node_data[order_map[node]].first; |
---|
1287 | |
---|
1288 | if (type_map[_ugraph.target(edge)] == 0) { |
---|
1289 | st.push_back(_ugraph.target(edge)); |
---|
1290 | type_map[_ugraph.target(edge)] = 1; |
---|
1291 | } |
---|
1292 | |
---|
1293 | Edge last = edge, pred = edge; |
---|
1294 | edge = edge_lists[edge].next; |
---|
1295 | while (edge != last) { |
---|
1296 | |
---|
1297 | if (type_map[_ugraph.target(edge)] == 0) { |
---|
1298 | st.push_back(_ugraph.target(edge)); |
---|
1299 | type_map[_ugraph.target(edge)] = 1; |
---|
1300 | } |
---|
1301 | |
---|
1302 | Edge next = edge_lists[edge].next != pred ? |
---|
1303 | edge_lists[edge].next : edge_lists[edge].prev; |
---|
1304 | pred = edge; edge = next; |
---|
1305 | } |
---|
1306 | |
---|
1307 | } |
---|
1308 | |
---|
1309 | type_map[root] = 2; |
---|
1310 | flip_map[root] = false; |
---|
1311 | |
---|
1312 | for (int i = 1; i < int(qu.size()); ++i) { |
---|
1313 | |
---|
1314 | Node node = qu[i]; |
---|
1315 | |
---|
1316 | while (type_map[node] != 2) { |
---|
1317 | st.push_back(node); |
---|
1318 | type_map[node] = 2; |
---|
1319 | node = _ugraph.source(pred_map[node]); |
---|
1320 | } |
---|
1321 | |
---|
1322 | bool flip = flip_map[node]; |
---|
1323 | |
---|
1324 | while (!st.empty()) { |
---|
1325 | node = st.back(); |
---|
1326 | st.pop_back(); |
---|
1327 | |
---|
1328 | flip_map[node] = flip != flip_map[node]; |
---|
1329 | flip = flip_map[node]; |
---|
1330 | |
---|
1331 | if (flip) { |
---|
1332 | Edge edge = node_data[order_map[node]].first; |
---|
1333 | std::swap(edge_lists[edge].prev, edge_lists[edge].next); |
---|
1334 | edge = edge_lists[edge].prev; |
---|
1335 | std::swap(edge_lists[edge].prev, edge_lists[edge].next); |
---|
1336 | node_data[order_map[node]].first = edge; |
---|
1337 | } |
---|
1338 | } |
---|
1339 | } |
---|
1340 | |
---|
1341 | for (int i = 0; i < int(qu.size()); ++i) { |
---|
1342 | |
---|
1343 | Edge edge = node_data[order_map[qu[i]]].first; |
---|
1344 | Edge last = edge, pred = edge; |
---|
1345 | |
---|
1346 | edge = edge_lists[edge].next; |
---|
1347 | while (edge != last) { |
---|
1348 | |
---|
1349 | if (edge_lists[edge].next == pred) { |
---|
1350 | std::swap(edge_lists[edge].next, edge_lists[edge].prev); |
---|
1351 | } |
---|
1352 | pred = edge; edge = edge_lists[edge].next; |
---|
1353 | } |
---|
1354 | |
---|
1355 | } |
---|
1356 | } |
---|
1357 | |
---|
1358 | void setFaceFlags(Node root, Node wnode, Node ynode, Node xnode, |
---|
1359 | OrderMap& order_map, NodeData& node_data, |
---|
1360 | TypeMap& type_map) { |
---|
1361 | Node node = _ugraph.target(node_data[order_map[root]].first); |
---|
1362 | |
---|
1363 | while (node != ynode) { |
---|
1364 | type_map[node] = HIGHY; |
---|
1365 | node = _ugraph.target(node_data[order_map[node]].first); |
---|
1366 | } |
---|
1367 | |
---|
1368 | while (node != wnode) { |
---|
1369 | type_map[node] = LOWY; |
---|
1370 | node = _ugraph.target(node_data[order_map[node]].first); |
---|
1371 | } |
---|
1372 | |
---|
1373 | node = _ugraph.target(node_data[order_map[wnode]].first); |
---|
1374 | |
---|
1375 | while (node != xnode) { |
---|
1376 | type_map[node] = LOWX; |
---|
1377 | node = _ugraph.target(node_data[order_map[node]].first); |
---|
1378 | } |
---|
1379 | type_map[node] = LOWX; |
---|
1380 | |
---|
1381 | node = _ugraph.target(node_data[order_map[xnode]].first); |
---|
1382 | while (node != root) { |
---|
1383 | type_map[node] = HIGHX; |
---|
1384 | node = _ugraph.target(node_data[order_map[node]].first); |
---|
1385 | } |
---|
1386 | |
---|
1387 | type_map[wnode] = PERTINENT; |
---|
1388 | type_map[root] = ROOT; |
---|
1389 | } |
---|
1390 | |
---|
1391 | void findInternalPath(std::vector<Edge>& ipath, |
---|
1392 | Node wnode, Node root, TypeMap& type_map, |
---|
1393 | OrderMap& order_map, NodeData& node_data, |
---|
1394 | EdgeLists& edge_lists) { |
---|
1395 | std::vector<Edge> st; |
---|
1396 | |
---|
1397 | Node node = wnode; |
---|
1398 | |
---|
1399 | while (node != root) { |
---|
1400 | Edge edge = edge_lists[node_data[order_map[node]].first].next; |
---|
1401 | st.push_back(edge); |
---|
1402 | node = _ugraph.target(edge); |
---|
1403 | } |
---|
1404 | |
---|
1405 | while (true) { |
---|
1406 | Edge edge = st.back(); |
---|
1407 | if (type_map[_ugraph.target(edge)] == LOWX || |
---|
1408 | type_map[_ugraph.target(edge)] == HIGHX) { |
---|
1409 | break; |
---|
1410 | } |
---|
1411 | if (type_map[_ugraph.target(edge)] == 2) { |
---|
1412 | type_map[_ugraph.target(edge)] = 3; |
---|
1413 | |
---|
1414 | edge = edge_lists[_ugraph.oppositeEdge(edge)].next; |
---|
1415 | st.push_back(edge); |
---|
1416 | } else { |
---|
1417 | st.pop_back(); |
---|
1418 | edge = edge_lists[edge].next; |
---|
1419 | |
---|
1420 | while (_ugraph.oppositeEdge(edge) == st.back()) { |
---|
1421 | edge = st.back(); |
---|
1422 | st.pop_back(); |
---|
1423 | edge = edge_lists[edge].next; |
---|
1424 | } |
---|
1425 | st.push_back(edge); |
---|
1426 | } |
---|
1427 | } |
---|
1428 | |
---|
1429 | for (int i = 0; i < int(st.size()); ++i) { |
---|
1430 | if (type_map[_ugraph.target(st[i])] != LOWY && |
---|
1431 | type_map[_ugraph.target(st[i])] != HIGHY) { |
---|
1432 | for (; i < int(st.size()); ++i) { |
---|
1433 | ipath.push_back(st[i]); |
---|
1434 | } |
---|
1435 | } |
---|
1436 | } |
---|
1437 | } |
---|
1438 | |
---|
1439 | void setInternalFlags(std::vector<Edge>& ipath, TypeMap& type_map) { |
---|
1440 | for (int i = 1; i < int(ipath.size()); ++i) { |
---|
1441 | type_map[_ugraph.source(ipath[i])] = INTERNAL; |
---|
1442 | } |
---|
1443 | } |
---|
1444 | |
---|
1445 | void findPilePath(std::vector<Edge>& ppath, |
---|
1446 | Node root, TypeMap& type_map, OrderMap& order_map, |
---|
1447 | NodeData& node_data, EdgeLists& edge_lists) { |
---|
1448 | std::vector<Edge> st; |
---|
1449 | |
---|
1450 | st.push_back(_ugraph.oppositeEdge(node_data[order_map[root]].first)); |
---|
1451 | st.push_back(node_data[order_map[root]].first); |
---|
1452 | |
---|
1453 | while (st.size() > 1) { |
---|
1454 | Edge edge = st.back(); |
---|
1455 | if (type_map[_ugraph.target(edge)] == INTERNAL) { |
---|
1456 | break; |
---|
1457 | } |
---|
1458 | if (type_map[_ugraph.target(edge)] == 3) { |
---|
1459 | type_map[_ugraph.target(edge)] = 4; |
---|
1460 | |
---|
1461 | edge = edge_lists[_ugraph.oppositeEdge(edge)].next; |
---|
1462 | st.push_back(edge); |
---|
1463 | } else { |
---|
1464 | st.pop_back(); |
---|
1465 | edge = edge_lists[edge].next; |
---|
1466 | |
---|
1467 | while (!st.empty() && _ugraph.oppositeEdge(edge) == st.back()) { |
---|
1468 | edge = st.back(); |
---|
1469 | st.pop_back(); |
---|
1470 | edge = edge_lists[edge].next; |
---|
1471 | } |
---|
1472 | st.push_back(edge); |
---|
1473 | } |
---|
1474 | } |
---|
1475 | |
---|
1476 | for (int i = 1; i < int(st.size()); ++i) { |
---|
1477 | ppath.push_back(st[i]); |
---|
1478 | } |
---|
1479 | } |
---|
1480 | |
---|
1481 | |
---|
1482 | int markExternalPath(Node node, OrderMap& order_map, |
---|
1483 | ChildLists& child_lists, PredMap& pred_map, |
---|
1484 | AncestorMap& ancestor_map, LowMap& low_map) { |
---|
1485 | int lp = lowPoint(node, order_map, child_lists, |
---|
1486 | ancestor_map, low_map); |
---|
1487 | |
---|
1488 | if (ancestor_map[node] != lp) { |
---|
1489 | node = child_lists[node].first; |
---|
1490 | _kuratowski[pred_map[node]] = true; |
---|
1491 | |
---|
1492 | while (ancestor_map[node] != lp) { |
---|
1493 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
1494 | Node tnode = _ugraph.target(e); |
---|
1495 | if (order_map[tnode] > order_map[node] && low_map[tnode] == lp) { |
---|
1496 | node = tnode; |
---|
1497 | _kuratowski[e] = true; |
---|
1498 | break; |
---|
1499 | } |
---|
1500 | } |
---|
1501 | } |
---|
1502 | } |
---|
1503 | |
---|
1504 | for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) { |
---|
1505 | if (order_map[_ugraph.target(e)] == lp) { |
---|
1506 | _kuratowski[e] = true; |
---|
1507 | break; |
---|
1508 | } |
---|
1509 | } |
---|
1510 | |
---|
1511 | return lp; |
---|
1512 | } |
---|
1513 | |
---|
1514 | void markPertinentPath(Node node, OrderMap& order_map, |
---|
1515 | NodeData& node_data, EdgeLists& edge_lists, |
---|
1516 | EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
---|
1517 | while (embed_edge[node] == INVALID) { |
---|
1518 | int n = merge_roots[node].front(); |
---|
1519 | Edge edge = node_data[n].first; |
---|
1520 | |
---|
1521 | _kuratowski.set(edge, true); |
---|
1522 | |
---|
1523 | Node pred = node; |
---|
1524 | node = _ugraph.target(edge); |
---|
1525 | while (!pertinent(node, embed_edge, merge_roots)) { |
---|
1526 | edge = node_data[order_map[node]].first; |
---|
1527 | if (_ugraph.target(edge) == pred) { |
---|
1528 | edge = edge_lists[edge].next; |
---|
1529 | } |
---|
1530 | _kuratowski.set(edge, true); |
---|
1531 | pred = node; |
---|
1532 | node = _ugraph.target(edge); |
---|
1533 | } |
---|
1534 | } |
---|
1535 | _kuratowski.set(embed_edge[node], true); |
---|
1536 | } |
---|
1537 | |
---|
1538 | void markPredPath(Node node, Node snode, PredMap& pred_map) { |
---|
1539 | while (node != snode) { |
---|
1540 | _kuratowski.set(pred_map[node], true); |
---|
1541 | node = _ugraph.source(pred_map[node]); |
---|
1542 | } |
---|
1543 | } |
---|
1544 | |
---|
1545 | void markFacePath(Node ynode, Node xnode, |
---|
1546 | OrderMap& order_map, NodeData& node_data) { |
---|
1547 | Edge edge = node_data[order_map[ynode]].first; |
---|
1548 | Node node = _ugraph.target(edge); |
---|
1549 | _kuratowski.set(edge, true); |
---|
1550 | |
---|
1551 | while (node != xnode) { |
---|
1552 | edge = node_data[order_map[node]].first; |
---|
1553 | _kuratowski.set(edge, true); |
---|
1554 | node = _ugraph.target(edge); |
---|
1555 | } |
---|
1556 | } |
---|
1557 | |
---|
1558 | void markInternalPath(std::vector<Edge>& path) { |
---|
1559 | for (int i = 0; i < int(path.size()); ++i) { |
---|
1560 | _kuratowski.set(path[i], true); |
---|
1561 | } |
---|
1562 | } |
---|
1563 | |
---|
1564 | void markPilePath(std::vector<Edge>& path) { |
---|
1565 | for (int i = 0; i < int(path.size()); ++i) { |
---|
1566 | _kuratowski.set(path[i], true); |
---|
1567 | } |
---|
1568 | } |
---|
1569 | |
---|
1570 | void isolateKuratowski(Edge edge, NodeData& node_data, |
---|
1571 | EdgeLists& edge_lists, FlipMap& flip_map, |
---|
1572 | OrderMap& order_map, OrderList& order_list, |
---|
1573 | PredMap& pred_map, ChildLists& child_lists, |
---|
1574 | AncestorMap& ancestor_map, LowMap& low_map, |
---|
1575 | EmbedEdge& embed_edge, MergeRoots& merge_roots) { |
---|
1576 | |
---|
1577 | Node root = _ugraph.source(edge); |
---|
1578 | Node enode = _ugraph.target(edge); |
---|
1579 | |
---|
1580 | int rorder = order_map[root]; |
---|
1581 | |
---|
1582 | TypeMap type_map(_ugraph, 0); |
---|
1583 | |
---|
1584 | int rn = findComponentRoot(root, enode, child_lists, |
---|
1585 | order_map, order_list); |
---|
1586 | |
---|
1587 | Node xnode = order_list[node_data[rn].next]; |
---|
1588 | Node ynode = order_list[node_data[rn].prev]; |
---|
1589 | |
---|
1590 | // Minor-A |
---|
1591 | { |
---|
1592 | while (!merge_roots[xnode].empty() || !merge_roots[ynode].empty()) { |
---|
1593 | |
---|
1594 | if (!merge_roots[xnode].empty()) { |
---|
1595 | root = xnode; |
---|
1596 | rn = merge_roots[xnode].front(); |
---|
1597 | } else { |
---|
1598 | root = ynode; |
---|
1599 | rn = merge_roots[ynode].front(); |
---|
1600 | } |
---|
1601 | |
---|
1602 | xnode = order_list[node_data[rn].next]; |
---|
1603 | ynode = order_list[node_data[rn].prev]; |
---|
1604 | } |
---|
1605 | |
---|
1606 | if (root != _ugraph.source(edge)) { |
---|
1607 | orientComponent(root, rn, order_map, pred_map, |
---|
1608 | node_data, edge_lists, flip_map, type_map); |
---|
1609 | markFacePath(root, root, order_map, node_data); |
---|
1610 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1611 | pred_map, ancestor_map, low_map); |
---|
1612 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1613 | pred_map, ancestor_map, low_map); |
---|
1614 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
1615 | Node lwnode = findPertinent(ynode, order_map, node_data, |
---|
1616 | embed_edge, merge_roots); |
---|
1617 | |
---|
1618 | markPertinentPath(lwnode, order_map, node_data, edge_lists, |
---|
1619 | embed_edge, merge_roots); |
---|
1620 | |
---|
1621 | return; |
---|
1622 | } |
---|
1623 | } |
---|
1624 | |
---|
1625 | orientComponent(root, rn, order_map, pred_map, |
---|
1626 | node_data, edge_lists, flip_map, type_map); |
---|
1627 | |
---|
1628 | Node wnode = findPertinent(ynode, order_map, node_data, |
---|
1629 | embed_edge, merge_roots); |
---|
1630 | setFaceFlags(root, wnode, ynode, xnode, order_map, node_data, type_map); |
---|
1631 | |
---|
1632 | |
---|
1633 | //Minor-B |
---|
1634 | if (!merge_roots[wnode].empty()) { |
---|
1635 | int cn = merge_roots[wnode].back(); |
---|
1636 | Node rep = order_list[cn - order_list.size()]; |
---|
1637 | if (low_map[rep] < rorder) { |
---|
1638 | markFacePath(root, root, order_map, node_data); |
---|
1639 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1640 | pred_map, ancestor_map, low_map); |
---|
1641 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1642 | pred_map, ancestor_map, low_map); |
---|
1643 | |
---|
1644 | Node lwnode, lznode; |
---|
1645 | markCommonPath(wnode, rorder, lwnode, lznode, order_list, |
---|
1646 | order_map, node_data, edge_lists, embed_edge, |
---|
1647 | merge_roots, child_lists, ancestor_map, low_map); |
---|
1648 | |
---|
1649 | markPertinentPath(lwnode, order_map, node_data, edge_lists, |
---|
1650 | embed_edge, merge_roots); |
---|
1651 | int zlp = markExternalPath(lznode, order_map, child_lists, |
---|
1652 | pred_map, ancestor_map, low_map); |
---|
1653 | |
---|
1654 | int minlp = xlp < ylp ? xlp : ylp; |
---|
1655 | if (zlp < minlp) minlp = zlp; |
---|
1656 | |
---|
1657 | int maxlp = xlp > ylp ? xlp : ylp; |
---|
1658 | if (zlp > maxlp) maxlp = zlp; |
---|
1659 | |
---|
1660 | markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
---|
1661 | |
---|
1662 | return; |
---|
1663 | } |
---|
1664 | } |
---|
1665 | |
---|
1666 | Node pxnode, pynode; |
---|
1667 | std::vector<Edge> ipath; |
---|
1668 | findInternalPath(ipath, wnode, root, type_map, order_map, |
---|
1669 | node_data, edge_lists); |
---|
1670 | setInternalFlags(ipath, type_map); |
---|
1671 | pynode = _ugraph.source(ipath.front()); |
---|
1672 | pxnode = _ugraph.target(ipath.back()); |
---|
1673 | |
---|
1674 | wnode = findPertinent(pynode, order_map, node_data, |
---|
1675 | embed_edge, merge_roots); |
---|
1676 | |
---|
1677 | // Minor-C |
---|
1678 | { |
---|
1679 | if (type_map[_ugraph.source(ipath.front())] == HIGHY) { |
---|
1680 | if (type_map[_ugraph.target(ipath.back())] == HIGHX) { |
---|
1681 | markFacePath(xnode, pxnode, order_map, node_data); |
---|
1682 | } |
---|
1683 | markFacePath(root, xnode, order_map, node_data); |
---|
1684 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
1685 | embed_edge, merge_roots); |
---|
1686 | markInternalPath(ipath); |
---|
1687 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1688 | pred_map, ancestor_map, low_map); |
---|
1689 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1690 | pred_map, ancestor_map, low_map); |
---|
1691 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
1692 | return; |
---|
1693 | } |
---|
1694 | |
---|
1695 | if (type_map[_ugraph.target(ipath.back())] == HIGHX) { |
---|
1696 | markFacePath(ynode, root, order_map, node_data); |
---|
1697 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
1698 | embed_edge, merge_roots); |
---|
1699 | markInternalPath(ipath); |
---|
1700 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1701 | pred_map, ancestor_map, low_map); |
---|
1702 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1703 | pred_map, ancestor_map, low_map); |
---|
1704 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
1705 | return; |
---|
1706 | } |
---|
1707 | } |
---|
1708 | |
---|
1709 | std::vector<Edge> ppath; |
---|
1710 | findPilePath(ppath, root, type_map, order_map, node_data, edge_lists); |
---|
1711 | |
---|
1712 | // Minor-D |
---|
1713 | if (!ppath.empty()) { |
---|
1714 | markFacePath(ynode, xnode, order_map, node_data); |
---|
1715 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
1716 | embed_edge, merge_roots); |
---|
1717 | markPilePath(ppath); |
---|
1718 | markInternalPath(ipath); |
---|
1719 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1720 | pred_map, ancestor_map, low_map); |
---|
1721 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1722 | pred_map, ancestor_map, low_map); |
---|
1723 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
1724 | return; |
---|
1725 | } |
---|
1726 | |
---|
1727 | // Minor-E* |
---|
1728 | { |
---|
1729 | |
---|
1730 | if (!external(wnode, rorder, child_lists, ancestor_map, low_map)) { |
---|
1731 | Node znode = findExternal(pynode, rorder, order_map, |
---|
1732 | child_lists, ancestor_map, |
---|
1733 | low_map, node_data); |
---|
1734 | |
---|
1735 | if (type_map[znode] == LOWY) { |
---|
1736 | markFacePath(root, xnode, order_map, node_data); |
---|
1737 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
1738 | embed_edge, merge_roots); |
---|
1739 | markInternalPath(ipath); |
---|
1740 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1741 | pred_map, ancestor_map, low_map); |
---|
1742 | int zlp = markExternalPath(znode, order_map, child_lists, |
---|
1743 | pred_map, ancestor_map, low_map); |
---|
1744 | markPredPath(root, order_list[xlp < zlp ? xlp : zlp], pred_map); |
---|
1745 | } else { |
---|
1746 | markFacePath(ynode, root, order_map, node_data); |
---|
1747 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
1748 | embed_edge, merge_roots); |
---|
1749 | markInternalPath(ipath); |
---|
1750 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1751 | pred_map, ancestor_map, low_map); |
---|
1752 | int zlp = markExternalPath(znode, order_map, child_lists, |
---|
1753 | pred_map, ancestor_map, low_map); |
---|
1754 | markPredPath(root, order_list[ylp < zlp ? ylp : zlp], pred_map); |
---|
1755 | } |
---|
1756 | return; |
---|
1757 | } |
---|
1758 | |
---|
1759 | int xlp = markExternalPath(xnode, order_map, child_lists, |
---|
1760 | pred_map, ancestor_map, low_map); |
---|
1761 | int ylp = markExternalPath(ynode, order_map, child_lists, |
---|
1762 | pred_map, ancestor_map, low_map); |
---|
1763 | int wlp = markExternalPath(wnode, order_map, child_lists, |
---|
1764 | pred_map, ancestor_map, low_map); |
---|
1765 | |
---|
1766 | if (wlp > xlp && wlp > ylp) { |
---|
1767 | markFacePath(root, root, order_map, node_data); |
---|
1768 | markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map); |
---|
1769 | return; |
---|
1770 | } |
---|
1771 | |
---|
1772 | markInternalPath(ipath); |
---|
1773 | markPertinentPath(wnode, order_map, node_data, edge_lists, |
---|
1774 | embed_edge, merge_roots); |
---|
1775 | |
---|
1776 | if (xlp > ylp && xlp > wlp) { |
---|
1777 | markFacePath(root, pynode, order_map, node_data); |
---|
1778 | markFacePath(wnode, xnode, order_map, node_data); |
---|
1779 | markPredPath(root, order_list[ylp < wlp ? ylp : wlp], pred_map); |
---|
1780 | return; |
---|
1781 | } |
---|
1782 | |
---|
1783 | if (ylp > xlp && ylp > wlp) { |
---|
1784 | markFacePath(pxnode, root, order_map, node_data); |
---|
1785 | markFacePath(ynode, wnode, order_map, node_data); |
---|
1786 | markPredPath(root, order_list[xlp < wlp ? xlp : wlp], pred_map); |
---|
1787 | return; |
---|
1788 | } |
---|
1789 | |
---|
1790 | if (pynode != ynode) { |
---|
1791 | markFacePath(pxnode, wnode, order_map, node_data); |
---|
1792 | |
---|
1793 | int minlp = xlp < ylp ? xlp : ylp; |
---|
1794 | if (wlp < minlp) minlp = wlp; |
---|
1795 | |
---|
1796 | int maxlp = xlp > ylp ? xlp : ylp; |
---|
1797 | if (wlp > maxlp) maxlp = wlp; |
---|
1798 | |
---|
1799 | markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
---|
1800 | return; |
---|
1801 | } |
---|
1802 | |
---|
1803 | if (pxnode != xnode) { |
---|
1804 | markFacePath(wnode, pynode, order_map, node_data); |
---|
1805 | |
---|
1806 | int minlp = xlp < ylp ? xlp : ylp; |
---|
1807 | if (wlp < minlp) minlp = wlp; |
---|
1808 | |
---|
1809 | int maxlp = xlp > ylp ? xlp : ylp; |
---|
1810 | if (wlp > maxlp) maxlp = wlp; |
---|
1811 | |
---|
1812 | markPredPath(order_list[maxlp], order_list[minlp], pred_map); |
---|
1813 | return; |
---|
1814 | } |
---|
1815 | |
---|
1816 | markFacePath(root, root, order_map, node_data); |
---|
1817 | int minlp = xlp < ylp ? xlp : ylp; |
---|
1818 | if (wlp < minlp) minlp = wlp; |
---|
1819 | markPredPath(root, order_list[minlp], pred_map); |
---|
1820 | return; |
---|
1821 | } |
---|
1822 | |
---|
1823 | } |
---|
1824 | |
---|
1825 | }; |
---|
1826 | |
---|
1827 | namespace _planarity_bits { |
---|
1828 | |
---|
1829 | template <typename UGraph, typename EmbeddingMap> |
---|
1830 | void makeConnected(UGraph& ugraph, EmbeddingMap& embedding) { |
---|
1831 | DfsVisitor<UGraph> null_visitor; |
---|
1832 | DfsVisit<UGraph, DfsVisitor<UGraph> > dfs(ugraph, null_visitor); |
---|
1833 | dfs.init(); |
---|
1834 | |
---|
1835 | typename UGraph::Node u = INVALID; |
---|
1836 | for (typename UGraph::NodeIt n(ugraph); n != INVALID; ++n) { |
---|
1837 | if (!dfs.reached(n)) { |
---|
1838 | dfs.addSource(n); |
---|
1839 | dfs.start(); |
---|
1840 | if (u == INVALID) { |
---|
1841 | u = n; |
---|
1842 | } else { |
---|
1843 | typename UGraph::Node v = n; |
---|
1844 | |
---|
1845 | typename UGraph::Edge ue = typename UGraph::OutEdgeIt(ugraph, u); |
---|
1846 | typename UGraph::Edge ve = typename UGraph::OutEdgeIt(ugraph, v); |
---|
1847 | |
---|
1848 | typename UGraph::Edge e = ugraph.direct(ugraph.addEdge(u, v), true); |
---|
1849 | |
---|
1850 | if (ue != INVALID) { |
---|
1851 | embedding[e] = embedding[ue]; |
---|
1852 | embedding[ue] = e; |
---|
1853 | } else { |
---|
1854 | embedding[e] = e; |
---|
1855 | } |
---|
1856 | |
---|
1857 | if (ve != INVALID) { |
---|
1858 | embedding[ugraph.oppositeEdge(e)] = embedding[ve]; |
---|
1859 | embedding[ve] = ugraph.oppositeEdge(e); |
---|
1860 | } else { |
---|
1861 | embedding[ugraph.oppositeEdge(e)] = ugraph.oppositeEdge(e); |
---|
1862 | } |
---|
1863 | } |
---|
1864 | } |
---|
1865 | } |
---|
1866 | } |
---|
1867 | |
---|
1868 | template <typename UGraph, typename EmbeddingMap> |
---|
1869 | void makeBiNodeConnected(UGraph& ugraph, EmbeddingMap& embedding) { |
---|
1870 | typename UGraph::template EdgeMap<bool> processed(ugraph); |
---|
1871 | |
---|
1872 | std::vector<typename UGraph::Edge> edges; |
---|
1873 | for (typename UGraph::EdgeIt e(ugraph); e != INVALID; ++e) { |
---|
1874 | edges.push_back(e); |
---|
1875 | } |
---|
1876 | |
---|
1877 | IterableBoolMap<UGraph, typename UGraph::Node> visited(ugraph, false); |
---|
1878 | |
---|
1879 | for (int i = 0; i < int(edges.size()); ++i) { |
---|
1880 | typename UGraph::Edge pp = edges[i]; |
---|
1881 | if (processed[pp]) continue; |
---|
1882 | |
---|
1883 | typename UGraph::Edge e = embedding[ugraph.oppositeEdge(pp)]; |
---|
1884 | processed[e] = true; |
---|
1885 | visited.set(ugraph.source(e), true); |
---|
1886 | |
---|
1887 | typename UGraph::Edge p = e, l = e; |
---|
1888 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
1889 | |
---|
1890 | while (e != l) { |
---|
1891 | processed[e] = true; |
---|
1892 | |
---|
1893 | if (visited[ugraph.source(e)]) { |
---|
1894 | |
---|
1895 | typename UGraph::Edge n = |
---|
1896 | ugraph.direct(ugraph.addEdge(ugraph.source(p), |
---|
1897 | ugraph.target(e)), true); |
---|
1898 | embedding[n] = p; |
---|
1899 | embedding[ugraph.oppositeEdge(pp)] = n; |
---|
1900 | |
---|
1901 | embedding[ugraph.oppositeEdge(n)] = |
---|
1902 | embedding[ugraph.oppositeEdge(e)]; |
---|
1903 | embedding[ugraph.oppositeEdge(e)] = |
---|
1904 | ugraph.oppositeEdge(n); |
---|
1905 | |
---|
1906 | p = n; |
---|
1907 | e = embedding[ugraph.oppositeEdge(n)]; |
---|
1908 | } else { |
---|
1909 | visited.set(ugraph.source(e), true); |
---|
1910 | pp = p; |
---|
1911 | p = e; |
---|
1912 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
1913 | } |
---|
1914 | } |
---|
1915 | visited.setAll(false); |
---|
1916 | } |
---|
1917 | } |
---|
1918 | |
---|
1919 | |
---|
1920 | template <typename UGraph, typename EmbeddingMap> |
---|
1921 | void makeMaxPlanar(UGraph& ugraph, EmbeddingMap& embedding) { |
---|
1922 | |
---|
1923 | typename UGraph::template NodeMap<int> degree(ugraph); |
---|
1924 | |
---|
1925 | for (typename UGraph::NodeIt n(ugraph); n != INVALID; ++n) { |
---|
1926 | degree[n] = countIncEdges(ugraph, n); |
---|
1927 | } |
---|
1928 | |
---|
1929 | typename UGraph::template EdgeMap<bool> processed(ugraph); |
---|
1930 | IterableBoolMap<UGraph, typename UGraph::Node> visited(ugraph, false); |
---|
1931 | |
---|
1932 | std::vector<typename UGraph::Edge> edges; |
---|
1933 | for (typename UGraph::EdgeIt e(ugraph); e != INVALID; ++e) { |
---|
1934 | edges.push_back(e); |
---|
1935 | } |
---|
1936 | |
---|
1937 | for (int i = 0; i < int(edges.size()); ++i) { |
---|
1938 | typename UGraph::Edge e = edges[i]; |
---|
1939 | |
---|
1940 | if (processed[e]) continue; |
---|
1941 | processed[e] = true; |
---|
1942 | |
---|
1943 | typename UGraph::Edge mine = e; |
---|
1944 | int mind = degree[ugraph.source(e)]; |
---|
1945 | |
---|
1946 | int face_size = 1; |
---|
1947 | |
---|
1948 | typename UGraph::Edge l = e; |
---|
1949 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
1950 | while (l != e) { |
---|
1951 | processed[e] = true; |
---|
1952 | |
---|
1953 | ++face_size; |
---|
1954 | |
---|
1955 | if (degree[ugraph.source(e)] < mind) { |
---|
1956 | mine = e; |
---|
1957 | mind = degree[ugraph.source(e)]; |
---|
1958 | } |
---|
1959 | |
---|
1960 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
1961 | } |
---|
1962 | |
---|
1963 | if (face_size < 4) { |
---|
1964 | continue; |
---|
1965 | } |
---|
1966 | |
---|
1967 | typename UGraph::Node s = ugraph.source(mine); |
---|
1968 | for (typename UGraph::OutEdgeIt e(ugraph, s); e != INVALID; ++e) { |
---|
1969 | visited.set(ugraph.target(e), true); |
---|
1970 | } |
---|
1971 | |
---|
1972 | typename UGraph::Edge oppe = INVALID; |
---|
1973 | |
---|
1974 | e = embedding[ugraph.oppositeEdge(mine)]; |
---|
1975 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
1976 | while (ugraph.target(e) != s) { |
---|
1977 | if (visited[ugraph.source(e)]) { |
---|
1978 | oppe = e; |
---|
1979 | break; |
---|
1980 | } |
---|
1981 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
1982 | } |
---|
1983 | visited.setAll(false); |
---|
1984 | |
---|
1985 | if (oppe == INVALID) { |
---|
1986 | |
---|
1987 | e = embedding[ugraph.oppositeEdge(mine)]; |
---|
1988 | typename UGraph::Edge pn = mine, p = e; |
---|
1989 | |
---|
1990 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
1991 | while (ugraph.target(e) != s) { |
---|
1992 | typename UGraph::Edge n = |
---|
1993 | ugraph.direct(ugraph.addEdge(s, ugraph.source(e)), true); |
---|
1994 | |
---|
1995 | embedding[n] = pn; |
---|
1996 | embedding[ugraph.oppositeEdge(n)] = e; |
---|
1997 | embedding[ugraph.oppositeEdge(p)] = ugraph.oppositeEdge(n); |
---|
1998 | |
---|
1999 | pn = n; |
---|
2000 | |
---|
2001 | p = e; |
---|
2002 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
2003 | } |
---|
2004 | |
---|
2005 | embedding[ugraph.oppositeEdge(e)] = pn; |
---|
2006 | |
---|
2007 | } else { |
---|
2008 | |
---|
2009 | mine = embedding[ugraph.oppositeEdge(mine)]; |
---|
2010 | s = ugraph.source(mine); |
---|
2011 | oppe = embedding[ugraph.oppositeEdge(oppe)]; |
---|
2012 | typename UGraph::Node t = ugraph.source(oppe); |
---|
2013 | |
---|
2014 | typename UGraph::Edge ce = ugraph.direct(ugraph.addEdge(s, t), true); |
---|
2015 | embedding[ce] = mine; |
---|
2016 | embedding[ugraph.oppositeEdge(ce)] = oppe; |
---|
2017 | |
---|
2018 | typename UGraph::Edge pn = ce, p = oppe; |
---|
2019 | e = embedding[ugraph.oppositeEdge(oppe)]; |
---|
2020 | while (ugraph.target(e) != s) { |
---|
2021 | typename UGraph::Edge n = |
---|
2022 | ugraph.direct(ugraph.addEdge(s, ugraph.source(e)), true); |
---|
2023 | |
---|
2024 | embedding[n] = pn; |
---|
2025 | embedding[ugraph.oppositeEdge(n)] = e; |
---|
2026 | embedding[ugraph.oppositeEdge(p)] = ugraph.oppositeEdge(n); |
---|
2027 | |
---|
2028 | pn = n; |
---|
2029 | |
---|
2030 | p = e; |
---|
2031 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
2032 | |
---|
2033 | } |
---|
2034 | embedding[ugraph.oppositeEdge(e)] = pn; |
---|
2035 | |
---|
2036 | pn = ugraph.oppositeEdge(ce), p = mine; |
---|
2037 | e = embedding[ugraph.oppositeEdge(mine)]; |
---|
2038 | while (ugraph.target(e) != t) { |
---|
2039 | typename UGraph::Edge n = |
---|
2040 | ugraph.direct(ugraph.addEdge(t, ugraph.source(e)), true); |
---|
2041 | |
---|
2042 | embedding[n] = pn; |
---|
2043 | embedding[ugraph.oppositeEdge(n)] = e; |
---|
2044 | embedding[ugraph.oppositeEdge(p)] = ugraph.oppositeEdge(n); |
---|
2045 | |
---|
2046 | pn = n; |
---|
2047 | |
---|
2048 | p = e; |
---|
2049 | e = embedding[ugraph.oppositeEdge(e)]; |
---|
2050 | |
---|
2051 | } |
---|
2052 | embedding[ugraph.oppositeEdge(e)] = pn; |
---|
2053 | } |
---|
2054 | } |
---|
2055 | } |
---|
2056 | |
---|
2057 | } |
---|
2058 | |
---|
2059 | /// \ingroup planar |
---|
2060 | /// |
---|
2061 | /// \brief Schnyder's planar drawing algorithms |
---|
2062 | /// |
---|
2063 | /// The planar drawing algorithm calculates location for each node |
---|
2064 | /// in the plane, which coordinates satisfies that if each edge is |
---|
2065 | /// represented with a straight line then the edges will not |
---|
2066 | /// intersect each other. |
---|
2067 | /// |
---|
2068 | /// Scnyder's algorithm embeds the graph on \c (n-2,n-2) size grid, |
---|
2069 | /// ie. each node will be located in the \c [0,n-2]x[0,n-2] square. |
---|
2070 | /// The time complexity of the algorithm is O(n). |
---|
2071 | template <typename UGraph> |
---|
2072 | class PlanarDrawing { |
---|
2073 | public: |
---|
2074 | |
---|
2075 | UGRAPH_TYPEDEFS(typename UGraph); |
---|
2076 | |
---|
2077 | /// \brief The point type for store coordinates |
---|
2078 | typedef dim2::Point<int> Point; |
---|
2079 | /// \brief The map type for store coordinates |
---|
2080 | typedef typename UGraph::template NodeMap<Point> PointMap; |
---|
2081 | |
---|
2082 | |
---|
2083 | /// \brief Constructor |
---|
2084 | /// |
---|
2085 | /// Constructor |
---|
2086 | /// \pre The ugraph should be simple, ie. loop and parallel edge free. |
---|
2087 | PlanarDrawing(const UGraph& ugraph) |
---|
2088 | : _ugraph(ugraph), _point_map(ugraph) {} |
---|
2089 | |
---|
2090 | private: |
---|
2091 | |
---|
2092 | template <typename AuxUGraph, typename AuxEmbeddingMap> |
---|
2093 | void drawing(const AuxUGraph& ugraph, |
---|
2094 | const AuxEmbeddingMap& next, |
---|
2095 | PointMap& point_map) { |
---|
2096 | UGRAPH_TYPEDEFS(typename AuxUGraph); |
---|
2097 | |
---|
2098 | typename AuxUGraph::template EdgeMap<Edge> prev(ugraph); |
---|
2099 | |
---|
2100 | for (NodeIt n(ugraph); n != INVALID; ++n) { |
---|
2101 | Edge e = OutEdgeIt(ugraph, n); |
---|
2102 | |
---|
2103 | Edge p = e, l = e; |
---|
2104 | |
---|
2105 | e = next[e]; |
---|
2106 | while (e != l) { |
---|
2107 | prev[e] = p; |
---|
2108 | p = e; |
---|
2109 | e = next[e]; |
---|
2110 | } |
---|
2111 | prev[e] = p; |
---|
2112 | } |
---|
2113 | |
---|
2114 | Node anode, bnode, cnode; |
---|
2115 | |
---|
2116 | { |
---|
2117 | Edge e = EdgeIt(ugraph); |
---|
2118 | anode = ugraph.source(e); |
---|
2119 | bnode = ugraph.target(e); |
---|
2120 | cnode = ugraph.target(next[ugraph.oppositeEdge(e)]); |
---|
2121 | } |
---|
2122 | |
---|
2123 | IterableBoolMap<AuxUGraph, Node> proper(ugraph, false); |
---|
2124 | typename AuxUGraph::template NodeMap<int> conn(ugraph, -1); |
---|
2125 | |
---|
2126 | conn[anode] = conn[bnode] = -2; |
---|
2127 | { |
---|
2128 | for (OutEdgeIt e(ugraph, anode); e != INVALID; ++e) { |
---|
2129 | Node m = ugraph.target(e); |
---|
2130 | if (conn[m] == -1) { |
---|
2131 | conn[m] = 1; |
---|
2132 | } |
---|
2133 | } |
---|
2134 | conn[cnode] = 2; |
---|
2135 | |
---|
2136 | for (OutEdgeIt e(ugraph, bnode); e != INVALID; ++e) { |
---|
2137 | Node m = ugraph.target(e); |
---|
2138 | if (conn[m] == -1) { |
---|
2139 | conn[m] = 1; |
---|
2140 | } else if (conn[m] != -2) { |
---|
2141 | conn[m] += 1; |
---|
2142 | Edge pe = ugraph.oppositeEdge(e); |
---|
2143 | if (conn[ugraph.target(next[pe])] == -2) { |
---|
2144 | conn[m] -= 1; |
---|
2145 | } |
---|
2146 | if (conn[ugraph.target(prev[pe])] == -2) { |
---|
2147 | conn[m] -= 1; |
---|
2148 | } |
---|
2149 | |
---|
2150 | proper.set(m, conn[m] == 1); |
---|
2151 | } |
---|
2152 | } |
---|
2153 | } |
---|
2154 | |
---|
2155 | |
---|
2156 | typename AuxUGraph::template EdgeMap<int> angle(ugraph, -1); |
---|
2157 | |
---|
2158 | while (proper.trueNum() != 0) { |
---|
2159 | Node n = typename IterableBoolMap<AuxUGraph, Node>::TrueIt(proper); |
---|
2160 | proper.set(n, false); |
---|
2161 | conn[n] = -2; |
---|
2162 | |
---|
2163 | for (OutEdgeIt e(ugraph, n); e != INVALID; ++e) { |
---|
2164 | Node m = ugraph.target(e); |
---|
2165 | if (conn[m] == -1) { |
---|
2166 | conn[m] = 1; |
---|
2167 | } else if (conn[m] != -2) { |
---|
2168 | conn[m] += 1; |
---|
2169 | Edge pe = ugraph.oppositeEdge(e); |
---|
2170 | if (conn[ugraph.target(next[pe])] == -2) { |
---|
2171 | conn[m] -= 1; |
---|
2172 | } |
---|
2173 | if (conn[ugraph.target(prev[pe])] == -2) { |
---|
2174 | conn[m] -= 1; |
---|
2175 | } |
---|
2176 | |
---|
2177 | proper.set(m, conn[m] == 1); |
---|
2178 | } |
---|
2179 | } |
---|
2180 | |
---|
2181 | { |
---|
2182 | Edge e = OutEdgeIt(ugraph, n); |
---|
2183 | Edge p = e, l = e; |
---|
2184 | |
---|
2185 | e = next[e]; |
---|
2186 | while (e != l) { |
---|
2187 | |
---|
2188 | if (conn[ugraph.target(e)] == -2 && conn[ugraph.target(p)] == -2) { |
---|
2189 | Edge f = e; |
---|
2190 | angle[f] = 0; |
---|
2191 | f = next[ugraph.oppositeEdge(f)]; |
---|
2192 | angle[f] = 1; |
---|
2193 | f = next[ugraph.oppositeEdge(f)]; |
---|
2194 | angle[f] = 2; |
---|
2195 | } |
---|
2196 | |
---|
2197 | p = e; |
---|
2198 | e = next[e]; |
---|
2199 | } |
---|
2200 | |
---|
2201 | if (conn[ugraph.target(e)] == -2 && conn[ugraph.target(p)] == -2) { |
---|
2202 | Edge f = e; |
---|
2203 | angle[f] = 0; |
---|
2204 | f = next[ugraph.oppositeEdge(f)]; |
---|
2205 | angle[f] = 1; |
---|
2206 | f = next[ugraph.oppositeEdge(f)]; |
---|
2207 | angle[f] = 2; |
---|
2208 | } |
---|
2209 | } |
---|
2210 | } |
---|
2211 | |
---|
2212 | typename AuxUGraph::template NodeMap<Node> apred(ugraph, INVALID); |
---|
2213 | typename AuxUGraph::template NodeMap<Node> bpred(ugraph, INVALID); |
---|
2214 | typename AuxUGraph::template NodeMap<Node> cpred(ugraph, INVALID); |
---|
2215 | |
---|
2216 | typename AuxUGraph::template NodeMap<int> apredid(ugraph, -1); |
---|
2217 | typename AuxUGraph::template NodeMap<int> bpredid(ugraph, -1); |
---|
2218 | typename AuxUGraph::template NodeMap<int> cpredid(ugraph, -1); |
---|
2219 | |
---|
2220 | for (EdgeIt e(ugraph); e != INVALID; ++e) { |
---|
2221 | if (angle[e] == angle[next[e]]) { |
---|
2222 | switch (angle[e]) { |
---|
2223 | case 2: |
---|
2224 | apred[ugraph.target(e)] = ugraph.source(e); |
---|
2225 | apredid[ugraph.target(e)] = ugraph.id(ugraph.source(e)); |
---|
2226 | break; |
---|
2227 | case 1: |
---|
2228 | bpred[ugraph.target(e)] = ugraph.source(e); |
---|
2229 | bpredid[ugraph.target(e)] = ugraph.id(ugraph.source(e)); |
---|
2230 | break; |
---|
2231 | case 0: |
---|
2232 | cpred[ugraph.target(e)] = ugraph.source(e); |
---|
2233 | cpredid[ugraph.target(e)] = ugraph.id(ugraph.source(e)); |
---|
2234 | break; |
---|
2235 | } |
---|
2236 | } |
---|
2237 | } |
---|
2238 | |
---|
2239 | cpred[anode] = INVALID; |
---|
2240 | cpred[bnode] = INVALID; |
---|
2241 | |
---|
2242 | std::vector<Node> aorder, border, corder; |
---|
2243 | |
---|
2244 | { |
---|
2245 | typename AuxUGraph::template NodeMap<bool> processed(ugraph, false); |
---|
2246 | std::vector<Node> st; |
---|
2247 | for (NodeIt n(ugraph); n != INVALID; ++n) { |
---|
2248 | if (!processed[n] && n != bnode && n != cnode) { |
---|
2249 | st.push_back(n); |
---|
2250 | processed[n] = true; |
---|
2251 | Node m = apred[n]; |
---|
2252 | while (m != INVALID && !processed[m]) { |
---|
2253 | st.push_back(m); |
---|
2254 | processed[m] = true; |
---|
2255 | m = apred[m]; |
---|
2256 | } |
---|
2257 | while (!st.empty()) { |
---|
2258 | aorder.push_back(st.back()); |
---|
2259 | st.pop_back(); |
---|
2260 | } |
---|
2261 | } |
---|
2262 | } |
---|
2263 | } |
---|
2264 | |
---|
2265 | { |
---|
2266 | typename AuxUGraph::template NodeMap<bool> processed(ugraph, false); |
---|
2267 | std::vector<Node> st; |
---|
2268 | for (NodeIt n(ugraph); n != INVALID; ++n) { |
---|
2269 | if (!processed[n] && n != cnode && n != anode) { |
---|
2270 | st.push_back(n); |
---|
2271 | processed[n] = true; |
---|
2272 | Node m = bpred[n]; |
---|
2273 | while (m != INVALID && !processed[m]) { |
---|
2274 | st.push_back(m); |
---|
2275 | processed[m] = true; |
---|
2276 | m = bpred[m]; |
---|
2277 | } |
---|
2278 | while (!st.empty()) { |
---|
2279 | border.push_back(st.back()); |
---|
2280 | st.pop_back(); |
---|
2281 | } |
---|
2282 | } |
---|
2283 | } |
---|
2284 | } |
---|
2285 | |
---|
2286 | { |
---|
2287 | typename AuxUGraph::template NodeMap<bool> processed(ugraph, false); |
---|
2288 | std::vector<Node> st; |
---|
2289 | for (NodeIt n(ugraph); n != INVALID; ++n) { |
---|
2290 | if (!processed[n] && n != anode && n != bnode) { |
---|
2291 | st.push_back(n); |
---|
2292 | processed[n] = true; |
---|
2293 | Node m = cpred[n]; |
---|
2294 | while (m != INVALID && !processed[m]) { |
---|
2295 | st.push_back(m); |
---|
2296 | processed[m] = true; |
---|
2297 | m = cpred[m]; |
---|
2298 | } |
---|
2299 | while (!st.empty()) { |
---|
2300 | corder.push_back(st.back()); |
---|
2301 | st.pop_back(); |
---|
2302 | } |
---|
2303 | } |
---|
2304 | } |
---|
2305 | } |
---|
2306 | |
---|
2307 | typename AuxUGraph::template NodeMap<int> atree(ugraph, 0); |
---|
2308 | for (int i = aorder.size() - 1; i >= 0; --i) { |
---|
2309 | Node n = aorder[i]; |
---|
2310 | atree[n] = 1; |
---|
2311 | for (OutEdgeIt e(ugraph, n); e != INVALID; ++e) { |
---|
2312 | if (apred[ugraph.target(e)] == n) { |
---|
2313 | atree[n] += atree[ugraph.target(e)]; |
---|
2314 | } |
---|
2315 | } |
---|
2316 | } |
---|
2317 | |
---|
2318 | typename AuxUGraph::template NodeMap<int> btree(ugraph, 0); |
---|
2319 | for (int i = border.size() - 1; i >= 0; --i) { |
---|
2320 | Node n = border[i]; |
---|
2321 | btree[n] = 1; |
---|
2322 | for (OutEdgeIt e(ugraph, n); e != INVALID; ++e) { |
---|
2323 | if (bpred[ugraph.target(e)] == n) { |
---|
2324 | btree[n] += btree[ugraph.target(e)]; |
---|
2325 | } |
---|
2326 | } |
---|
2327 | } |
---|
2328 | |
---|
2329 | typename AuxUGraph::template NodeMap<int> apath(ugraph, 0); |
---|
2330 | apath[bnode] = apath[cnode] = 1; |
---|
2331 | typename AuxUGraph::template NodeMap<int> apath_btree(ugraph, 0); |
---|
2332 | apath_btree[bnode] = btree[bnode]; |
---|
2333 | for (int i = 1; i < int(aorder.size()); ++i) { |
---|
2334 | Node n = aorder[i]; |
---|
2335 | apath[n] = apath[apred[n]] + 1; |
---|
2336 | apath_btree[n] = btree[n] + apath_btree[apred[n]]; |
---|
2337 | } |
---|
2338 | |
---|
2339 | typename AuxUGraph::template NodeMap<int> bpath_atree(ugraph, 0); |
---|
2340 | bpath_atree[anode] = atree[anode]; |
---|
2341 | for (int i = 1; i < int(border.size()); ++i) { |
---|
2342 | Node n = border[i]; |
---|
2343 | bpath_atree[n] = atree[n] + bpath_atree[bpred[n]]; |
---|
2344 | } |
---|
2345 | |
---|
2346 | typename AuxUGraph::template NodeMap<int> cpath(ugraph, 0); |
---|
2347 | cpath[anode] = cpath[bnode] = 1; |
---|
2348 | typename AuxUGraph::template NodeMap<int> cpath_atree(ugraph, 0); |
---|
2349 | cpath_atree[anode] = atree[anode]; |
---|
2350 | typename AuxUGraph::template NodeMap<int> cpath_btree(ugraph, 0); |
---|
2351 | cpath_btree[bnode] = btree[bnode]; |
---|
2352 | for (int i = 1; i < int(corder.size()); ++i) { |
---|
2353 | Node n = corder[i]; |
---|
2354 | cpath[n] = cpath[cpred[n]] + 1; |
---|
2355 | cpath_atree[n] = atree[n] + cpath_atree[cpred[n]]; |
---|
2356 | cpath_btree[n] = btree[n] + cpath_btree[cpred[n]]; |
---|
2357 | } |
---|
2358 | |
---|
2359 | typename AuxUGraph::template NodeMap<int> third(ugraph); |
---|
2360 | for (NodeIt n(ugraph); n != INVALID; ++n) { |
---|
2361 | point_map[n].x = |
---|
2362 | bpath_atree[n] + cpath_atree[n] - atree[n] - cpath[n] + 1; |
---|
2363 | point_map[n].y = |
---|
2364 | cpath_btree[n] + apath_btree[n] - btree[n] - apath[n] + 1; |
---|
2365 | } |
---|
2366 | |
---|
2367 | } |
---|
2368 | |
---|
2369 | public: |
---|
2370 | |
---|
2371 | /// \brief Calculates the node locations |
---|
2372 | /// |
---|
2373 | /// This function calculates the node locations. |
---|
2374 | bool run() { |
---|
2375 | PlanarEmbedding<UGraph> pe(_ugraph); |
---|
2376 | if (!pe.run()) return false; |
---|
2377 | |
---|
2378 | run(pe); |
---|
2379 | return true; |
---|
2380 | } |
---|
2381 | |
---|
2382 | /// \brief Calculates the node locations according to a |
---|
2383 | /// combinatorical embedding |
---|
2384 | /// |
---|
2385 | /// This function calculates the node locations. The \c embedding |
---|
2386 | /// parameter should contain a valid combinatorical embedding, ie. |
---|
2387 | /// a valid cyclic order of the edges. |
---|
2388 | template <typename EmbeddingMap> |
---|
2389 | void run(const EmbeddingMap& embedding) { |
---|
2390 | typedef SmartUEdgeSet<UGraph> AuxUGraph; |
---|
2391 | |
---|
2392 | if (3 * countNodes(_ugraph) - 6 == countUEdges(_ugraph)) { |
---|
2393 | drawing(_ugraph, embedding, _point_map); |
---|
2394 | return; |
---|
2395 | } |
---|
2396 | |
---|
2397 | AuxUGraph aux_ugraph(_ugraph); |
---|
2398 | typename AuxUGraph::template EdgeMap<typename AuxUGraph::Edge> |
---|
2399 | aux_embedding(aux_ugraph); |
---|
2400 | |
---|
2401 | { |
---|
2402 | |
---|
2403 | typename UGraph::template UEdgeMap<typename AuxUGraph::UEdge> |
---|
2404 | ref(_ugraph); |
---|
2405 | |
---|
2406 | for (UEdgeIt e(_ugraph); e != INVALID; ++e) { |
---|
2407 | ref[e] = aux_ugraph.addEdge(_ugraph.source(e), _ugraph.target(e)); |
---|
2408 | } |
---|
2409 | |
---|
2410 | for (UEdgeIt e(_ugraph); e != INVALID; ++e) { |
---|
2411 | Edge ee = embedding[_ugraph.direct(e, true)]; |
---|
2412 | aux_embedding[aux_ugraph.direct(ref[e], true)] = |
---|
2413 | aux_ugraph.direct(ref[ee], _ugraph.direction(ee)); |
---|
2414 | ee = embedding[_ugraph.direct(e, false)]; |
---|
2415 | aux_embedding[aux_ugraph.direct(ref[e], false)] = |
---|
2416 | aux_ugraph.direct(ref[ee], _ugraph.direction(ee)); |
---|
2417 | } |
---|
2418 | } |
---|
2419 | _planarity_bits::makeConnected(aux_ugraph, aux_embedding); |
---|
2420 | _planarity_bits::makeBiNodeConnected(aux_ugraph, aux_embedding); |
---|
2421 | _planarity_bits::makeMaxPlanar(aux_ugraph, aux_embedding); |
---|
2422 | drawing(aux_ugraph, aux_embedding, _point_map); |
---|
2423 | } |
---|
2424 | |
---|
2425 | /// \brief The coordinate of the given node |
---|
2426 | /// |
---|
2427 | /// The coordinate of the given node. |
---|
2428 | Point operator[](const Node& node) { |
---|
2429 | return _point_map[node]; |
---|
2430 | } |
---|
2431 | |
---|
2432 | /// \brief Returns the grid embedding in a \e NodeMap. |
---|
2433 | /// |
---|
2434 | /// Returns the grid embedding in a \e NodeMap of \c dim2::Point<int> . |
---|
2435 | const PointMap& coords() const { |
---|
2436 | return _point_map; |
---|
2437 | } |
---|
2438 | |
---|
2439 | private: |
---|
2440 | |
---|
2441 | const UGraph& _ugraph; |
---|
2442 | PointMap _point_map; |
---|
2443 | |
---|
2444 | }; |
---|
2445 | |
---|
2446 | namespace _planarity_bits { |
---|
2447 | |
---|
2448 | template <typename ColorMap> |
---|
2449 | class KempeFilter { |
---|
2450 | public: |
---|
2451 | typedef typename ColorMap::Key Key; |
---|
2452 | typedef bool Value; |
---|
2453 | |
---|
2454 | KempeFilter(const ColorMap& color_map, |
---|
2455 | const typename ColorMap::Value& first, |
---|
2456 | const typename ColorMap::Value& second) |
---|
2457 | : _color_map(color_map), _first(first), _second(second) {} |
---|
2458 | |
---|
2459 | Value operator[](const Key& key) const { |
---|
2460 | return _color_map[key] == _first || _color_map[key] == _second; |
---|
2461 | } |
---|
2462 | |
---|
2463 | private: |
---|
2464 | const ColorMap& _color_map; |
---|
2465 | typename ColorMap::Value _first, _second; |
---|
2466 | }; |
---|
2467 | } |
---|
2468 | |
---|
2469 | /// \ingroup planar |
---|
2470 | /// |
---|
2471 | /// \brief Coloring planar graphs |
---|
2472 | /// |
---|
2473 | /// The graph coloring problem is the coloring of the graph nodes |
---|
2474 | /// such way that there are not adjacent nodes with the same |
---|
2475 | /// color. The planar graphs can be always colored with four colors, |
---|
2476 | /// it is proved by Appel and Haken and their proofs provide a |
---|
2477 | /// quadratic time algorithm for four coloring, but it could not be |
---|
2478 | /// used to implement efficient algorithm. The five and six coloring |
---|
2479 | /// can be made in linear time, but in this class the five coloring |
---|
2480 | /// has quadratic worst case time complexity. The two coloring (if |
---|
2481 | /// possible) is solvable with a graph search algorithm and it is |
---|
2482 | /// implemented in \ref bipartitePartitions() function in Lemon. To |
---|
2483 | /// decide whether the planar graph is three colorable is |
---|
2484 | /// NP-complete. |
---|
2485 | /// |
---|
2486 | /// This class contains member functions for calculate colorings |
---|
2487 | /// with five and six colors. The six coloring algorithm is a simple |
---|
2488 | /// greedy coloring on the backward minimum outgoing order of nodes. |
---|
2489 | /// This order can be computed such way, that in each phase the node |
---|
2490 | /// with least outgoing edges to unprocessed nodes is choosen. This |
---|
2491 | /// order guarantees that at the time of coloring of a node it has |
---|
2492 | /// at most five already colored adjacents. The five coloring |
---|
2493 | /// algorithm works in the same way, but if the greedy approach |
---|
2494 | /// fails to color with five color, ie. the node has five already |
---|
2495 | /// different colored neighbours, it swaps the colors in one |
---|
2496 | /// connected two colored set with the Kempe recoloring method. |
---|
2497 | template <typename UGraph> |
---|
2498 | class PlanarColoring { |
---|
2499 | public: |
---|
2500 | |
---|
2501 | UGRAPH_TYPEDEFS(typename UGraph); |
---|
2502 | |
---|
2503 | /// \brief The map type for store color indexes |
---|
2504 | typedef typename UGraph::template NodeMap<int> IndexMap; |
---|
2505 | /// \brief The map type for store colors |
---|
2506 | typedef ComposeMap<Palette, IndexMap> ColorMap; |
---|
2507 | |
---|
2508 | /// \brief Constructor |
---|
2509 | /// |
---|
2510 | /// Constructor |
---|
2511 | /// \pre The ugraph should be simple, ie. loop and parallel edge free. |
---|
2512 | PlanarColoring(const UGraph& ugraph) |
---|
2513 | : _ugraph(ugraph), _color_map(ugraph), _palette(0) { |
---|
2514 | _palette.add(Color(1,0,0)); |
---|
2515 | _palette.add(Color(0,1,0)); |
---|
2516 | _palette.add(Color(0,0,1)); |
---|
2517 | _palette.add(Color(1,1,0)); |
---|
2518 | _palette.add(Color(1,0,1)); |
---|
2519 | _palette.add(Color(0,1,1)); |
---|
2520 | } |
---|
2521 | |
---|
2522 | /// \brief Returns the \e NodeMap of color indexes |
---|
2523 | /// |
---|
2524 | /// Returns the \e NodeMap of color indexes. The values are in the |
---|
2525 | /// range \c [0..4] or \c [0..5] according to the five coloring or |
---|
2526 | /// six coloring. |
---|
2527 | IndexMap colorIndexMap() const { |
---|
2528 | return _color_map; |
---|
2529 | } |
---|
2530 | |
---|
2531 | /// \brief Returns the \e NodeMap of colors |
---|
2532 | /// |
---|
2533 | /// Returns the \e NodeMap of colors. The values are five or six |
---|
2534 | /// distinct \ref lemon::Color "colors". |
---|
2535 | ColorMap colorMap() const { |
---|
2536 | return composeMap(_palette, _color_map); |
---|
2537 | } |
---|
2538 | |
---|
2539 | /// \brief Returns the color index of the node |
---|
2540 | /// |
---|
2541 | /// Returns the color index of the node. The values are in the |
---|
2542 | /// range \c [0..4] or \c [0..5] according to the five coloring or |
---|
2543 | /// six coloring. |
---|
2544 | int colorIndex(const Node& node) const { |
---|
2545 | return _color_map[node]; |
---|
2546 | } |
---|
2547 | |
---|
2548 | /// \brief Returns the color of the node |
---|
2549 | /// |
---|
2550 | /// Returns the color of the node. The values are five or six |
---|
2551 | /// distinct \ref lemon::Color "colors". |
---|
2552 | int color(const Node& node) const { |
---|
2553 | return _palette[_color_map[node]]; |
---|
2554 | } |
---|
2555 | |
---|
2556 | |
---|
2557 | /// \brief Calculates a coloring with at most six colors |
---|
2558 | /// |
---|
2559 | /// This function calculates a coloring with at most six colors. The time |
---|
2560 | /// complexity of this variant is linear in the size of the graph. |
---|
2561 | /// \return %True when the algorithm could color the graph with six color. |
---|
2562 | /// If the algorithm fails, then the graph could not be planar. |
---|
2563 | bool runSixColoring() { |
---|
2564 | |
---|
2565 | typename UGraph::template NodeMap<int> heap_index(_ugraph, -1); |
---|
2566 | BucketHeap<typename UGraph::template NodeMap<int> > heap(heap_index); |
---|
2567 | |
---|
2568 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
2569 | _color_map[n] = -2; |
---|
2570 | heap.push(n, countOutEdges(_ugraph, n)); |
---|
2571 | } |
---|
2572 | |
---|
2573 | std::vector<Node> order; |
---|
2574 | |
---|
2575 | while (!heap.empty()) { |
---|
2576 | Node n = heap.top(); |
---|
2577 | heap.pop(); |
---|
2578 | _color_map[n] = -1; |
---|
2579 | order.push_back(n); |
---|
2580 | for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
2581 | Node t = _ugraph.runningNode(e); |
---|
2582 | if (_color_map[t] == -2) { |
---|
2583 | heap.decrease(t, heap[t] - 1); |
---|
2584 | } |
---|
2585 | } |
---|
2586 | } |
---|
2587 | |
---|
2588 | for (int i = order.size() - 1; i >= 0; --i) { |
---|
2589 | std::vector<bool> forbidden(6, false); |
---|
2590 | for (OutEdgeIt e(_ugraph, order[i]); e != INVALID; ++e) { |
---|
2591 | Node t = _ugraph.runningNode(e); |
---|
2592 | if (_color_map[t] != -1) { |
---|
2593 | forbidden[_color_map[t]] = true; |
---|
2594 | } |
---|
2595 | } |
---|
2596 | for (int k = 0; k < 6; ++k) { |
---|
2597 | if (!forbidden[k]) { |
---|
2598 | _color_map[order[i]] = k; |
---|
2599 | break; |
---|
2600 | } |
---|
2601 | } |
---|
2602 | if (_color_map[order[i]] == -1) { |
---|
2603 | return false; |
---|
2604 | } |
---|
2605 | } |
---|
2606 | return true; |
---|
2607 | } |
---|
2608 | |
---|
2609 | private: |
---|
2610 | |
---|
2611 | bool recolor(const Node& u, const Node& v) { |
---|
2612 | int ucolor = _color_map[u]; |
---|
2613 | int vcolor = _color_map[v]; |
---|
2614 | typedef _planarity_bits::KempeFilter<IndexMap> KempeFilter; |
---|
2615 | KempeFilter filter(_color_map, ucolor, vcolor); |
---|
2616 | |
---|
2617 | typedef NodeSubUGraphAdaptor<const UGraph, const KempeFilter> KempeUGraph; |
---|
2618 | KempeUGraph kempe_ugraph(_ugraph, filter); |
---|
2619 | |
---|
2620 | std::vector<Node> comp; |
---|
2621 | Bfs<KempeUGraph> bfs(kempe_ugraph); |
---|
2622 | bfs.init(); |
---|
2623 | bfs.addSource(u); |
---|
2624 | while (!bfs.emptyQueue()) { |
---|
2625 | Node n = bfs.nextNode(); |
---|
2626 | if (n == v) return false; |
---|
2627 | comp.push_back(n); |
---|
2628 | bfs.processNextNode(); |
---|
2629 | } |
---|
2630 | |
---|
2631 | int scolor = ucolor + vcolor; |
---|
2632 | for (int i = 0; i < static_cast<int>(comp.size()); ++i) { |
---|
2633 | _color_map[comp[i]] = scolor - _color_map[comp[i]]; |
---|
2634 | } |
---|
2635 | |
---|
2636 | return true; |
---|
2637 | } |
---|
2638 | |
---|
2639 | template <typename EmbeddingMap> |
---|
2640 | void kempeRecoloring(const Node& node, const EmbeddingMap& embedding) { |
---|
2641 | std::vector<Node> nodes; |
---|
2642 | nodes.reserve(4); |
---|
2643 | |
---|
2644 | for (Edge e = OutEdgeIt(_ugraph, node); e != INVALID; e = embedding[e]) { |
---|
2645 | Node t = _ugraph.target(e); |
---|
2646 | if (_color_map[t] != -1) { |
---|
2647 | nodes.push_back(t); |
---|
2648 | if (nodes.size() == 4) break; |
---|
2649 | } |
---|
2650 | } |
---|
2651 | |
---|
2652 | int color = _color_map[nodes[0]]; |
---|
2653 | if (recolor(nodes[0], nodes[2])) { |
---|
2654 | _color_map[node] = color; |
---|
2655 | } else { |
---|
2656 | color = _color_map[nodes[1]]; |
---|
2657 | recolor(nodes[1], nodes[3]); |
---|
2658 | _color_map[node] = color; |
---|
2659 | } |
---|
2660 | } |
---|
2661 | |
---|
2662 | public: |
---|
2663 | |
---|
2664 | /// \brief Calculates a coloring with at most five colors |
---|
2665 | /// |
---|
2666 | /// This function calculates a coloring with at most five |
---|
2667 | /// colors. The wirst case time complexity of this variant is |
---|
2668 | /// quadratic in the size of the graph. |
---|
2669 | template <typename EmbeddingMap> |
---|
2670 | void runFiveColoring(const EmbeddingMap& embedding) { |
---|
2671 | |
---|
2672 | typename UGraph::template NodeMap<int> heap_index(_ugraph, -1); |
---|
2673 | BucketHeap<typename UGraph::template NodeMap<int> > heap(heap_index); |
---|
2674 | |
---|
2675 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
2676 | _color_map[n] = -2; |
---|
2677 | heap.push(n, countOutEdges(_ugraph, n)); |
---|
2678 | } |
---|
2679 | |
---|
2680 | std::vector<Node> order; |
---|
2681 | |
---|
2682 | while (!heap.empty()) { |
---|
2683 | Node n = heap.top(); |
---|
2684 | heap.pop(); |
---|
2685 | _color_map[n] = -1; |
---|
2686 | order.push_back(n); |
---|
2687 | for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
2688 | Node t = _ugraph.runningNode(e); |
---|
2689 | if (_color_map[t] == -2) { |
---|
2690 | heap.decrease(t, heap[t] - 1); |
---|
2691 | } |
---|
2692 | } |
---|
2693 | } |
---|
2694 | |
---|
2695 | for (int i = order.size() - 1; i >= 0; --i) { |
---|
2696 | std::vector<bool> forbidden(5, false); |
---|
2697 | for (OutEdgeIt e(_ugraph, order[i]); e != INVALID; ++e) { |
---|
2698 | Node t = _ugraph.runningNode(e); |
---|
2699 | if (_color_map[t] != -1) { |
---|
2700 | forbidden[_color_map[t]] = true; |
---|
2701 | } |
---|
2702 | } |
---|
2703 | for (int k = 0; k < 5; ++k) { |
---|
2704 | if (!forbidden[k]) { |
---|
2705 | _color_map[order[i]] = k; |
---|
2706 | break; |
---|
2707 | } |
---|
2708 | } |
---|
2709 | if (_color_map[order[i]] == -1) { |
---|
2710 | kempeRecoloring(order[i], embedding); |
---|
2711 | } |
---|
2712 | } |
---|
2713 | } |
---|
2714 | |
---|
2715 | /// \brief Calculates a coloring with at most five colors |
---|
2716 | /// |
---|
2717 | /// This function calculates a coloring with at most five |
---|
2718 | /// colors. The worst case time complexity of this variant is |
---|
2719 | /// quadratic in the size of the graph, but it most cases it does |
---|
2720 | /// not have to use Kempe recoloring method, in this case it is |
---|
2721 | /// equivalent with the runSixColoring() algorithm. |
---|
2722 | /// \return %True when the graph is planar. |
---|
2723 | bool runFiveColoring() { |
---|
2724 | PlanarEmbedding<UGraph> pe(_ugraph); |
---|
2725 | if (!pe.run()) return false; |
---|
2726 | |
---|
2727 | runFiveColoring(pe.embeddingMap()); |
---|
2728 | return true; |
---|
2729 | } |
---|
2730 | |
---|
2731 | private: |
---|
2732 | |
---|
2733 | const UGraph& _ugraph; |
---|
2734 | IndexMap _color_map; |
---|
2735 | Palette _palette; |
---|
2736 | }; |
---|
2737 | |
---|
2738 | } |
---|
2739 | |
---|
2740 | #endif |
---|