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