[417] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
---|
| 2 | * |
---|
| 3 | * This file is a part of LEMON, a generic C++ optimization library. |
---|
| 4 | * |
---|
[440] | 5 | * Copyright (C) 2003-2009 |
---|
[417] | 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 | |
---|
[419] | 19 | #ifndef LEMON_CONNECTIVITY_H |
---|
| 20 | #define LEMON_CONNECTIVITY_H |
---|
[417] | 21 | |
---|
| 22 | #include <lemon/dfs.h> |
---|
| 23 | #include <lemon/bfs.h> |
---|
| 24 | #include <lemon/core.h> |
---|
| 25 | #include <lemon/maps.h> |
---|
| 26 | #include <lemon/adaptors.h> |
---|
| 27 | |
---|
| 28 | #include <lemon/concepts/digraph.h> |
---|
| 29 | #include <lemon/concepts/graph.h> |
---|
| 30 | #include <lemon/concept_check.h> |
---|
| 31 | |
---|
| 32 | #include <stack> |
---|
| 33 | #include <functional> |
---|
| 34 | |
---|
| 35 | /// \ingroup connectivity |
---|
| 36 | /// \file |
---|
| 37 | /// \brief Connectivity algorithms |
---|
| 38 | /// |
---|
| 39 | /// Connectivity algorithms |
---|
| 40 | |
---|
| 41 | namespace lemon { |
---|
| 42 | |
---|
| 43 | /// \ingroup connectivity |
---|
| 44 | /// |
---|
| 45 | /// \brief Check whether the given undirected graph is connected. |
---|
| 46 | /// |
---|
| 47 | /// Check whether the given undirected graph is connected. |
---|
| 48 | /// \param graph The undirected graph. |
---|
| 49 | /// \return %True when there is path between any two nodes in the graph. |
---|
| 50 | /// \note By definition, the empty graph is connected. |
---|
| 51 | template <typename Graph> |
---|
| 52 | bool connected(const Graph& graph) { |
---|
| 53 | checkConcept<concepts::Graph, Graph>(); |
---|
| 54 | typedef typename Graph::NodeIt NodeIt; |
---|
| 55 | if (NodeIt(graph) == INVALID) return true; |
---|
| 56 | Dfs<Graph> dfs(graph); |
---|
| 57 | dfs.run(NodeIt(graph)); |
---|
| 58 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 59 | if (!dfs.reached(it)) { |
---|
| 60 | return false; |
---|
| 61 | } |
---|
| 62 | } |
---|
| 63 | return true; |
---|
| 64 | } |
---|
| 65 | |
---|
| 66 | /// \ingroup connectivity |
---|
| 67 | /// |
---|
| 68 | /// \brief Count the number of connected components of an undirected graph |
---|
| 69 | /// |
---|
| 70 | /// Count the number of connected components of an undirected graph |
---|
| 71 | /// |
---|
| 72 | /// \param graph The graph. It must be undirected. |
---|
| 73 | /// \return The number of components |
---|
| 74 | /// \note By definition, the empty graph consists |
---|
| 75 | /// of zero connected components. |
---|
| 76 | template <typename Graph> |
---|
| 77 | int countConnectedComponents(const Graph &graph) { |
---|
| 78 | checkConcept<concepts::Graph, Graph>(); |
---|
| 79 | typedef typename Graph::Node Node; |
---|
| 80 | typedef typename Graph::Arc Arc; |
---|
| 81 | |
---|
| 82 | typedef NullMap<Node, Arc> PredMap; |
---|
| 83 | typedef NullMap<Node, int> DistMap; |
---|
| 84 | |
---|
| 85 | int compNum = 0; |
---|
| 86 | typename Bfs<Graph>:: |
---|
| 87 | template SetPredMap<PredMap>:: |
---|
| 88 | template SetDistMap<DistMap>:: |
---|
| 89 | Create bfs(graph); |
---|
| 90 | |
---|
| 91 | PredMap predMap; |
---|
| 92 | bfs.predMap(predMap); |
---|
| 93 | |
---|
| 94 | DistMap distMap; |
---|
| 95 | bfs.distMap(distMap); |
---|
| 96 | |
---|
| 97 | bfs.init(); |
---|
| 98 | for(typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
---|
| 99 | if (!bfs.reached(n)) { |
---|
| 100 | bfs.addSource(n); |
---|
| 101 | bfs.start(); |
---|
| 102 | ++compNum; |
---|
| 103 | } |
---|
| 104 | } |
---|
| 105 | return compNum; |
---|
| 106 | } |
---|
| 107 | |
---|
| 108 | /// \ingroup connectivity |
---|
| 109 | /// |
---|
| 110 | /// \brief Find the connected components of an undirected graph |
---|
| 111 | /// |
---|
| 112 | /// Find the connected components of an undirected graph. |
---|
| 113 | /// |
---|
| 114 | /// \param graph The graph. It must be undirected. |
---|
| 115 | /// \retval compMap A writable node map. The values will be set from 0 to |
---|
| 116 | /// the number of the connected components minus one. Each values of the map |
---|
| 117 | /// will be set exactly once, the values of a certain component will be |
---|
| 118 | /// set continuously. |
---|
| 119 | /// \return The number of components |
---|
| 120 | /// |
---|
| 121 | template <class Graph, class NodeMap> |
---|
| 122 | int connectedComponents(const Graph &graph, NodeMap &compMap) { |
---|
| 123 | checkConcept<concepts::Graph, Graph>(); |
---|
| 124 | typedef typename Graph::Node Node; |
---|
| 125 | typedef typename Graph::Arc Arc; |
---|
| 126 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
---|
| 127 | |
---|
| 128 | typedef NullMap<Node, Arc> PredMap; |
---|
| 129 | typedef NullMap<Node, int> DistMap; |
---|
| 130 | |
---|
| 131 | int compNum = 0; |
---|
| 132 | typename Bfs<Graph>:: |
---|
| 133 | template SetPredMap<PredMap>:: |
---|
| 134 | template SetDistMap<DistMap>:: |
---|
| 135 | Create bfs(graph); |
---|
| 136 | |
---|
| 137 | PredMap predMap; |
---|
| 138 | bfs.predMap(predMap); |
---|
| 139 | |
---|
| 140 | DistMap distMap; |
---|
| 141 | bfs.distMap(distMap); |
---|
| 142 | |
---|
| 143 | bfs.init(); |
---|
| 144 | for(typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
---|
| 145 | if(!bfs.reached(n)) { |
---|
| 146 | bfs.addSource(n); |
---|
| 147 | while (!bfs.emptyQueue()) { |
---|
| 148 | compMap.set(bfs.nextNode(), compNum); |
---|
| 149 | bfs.processNextNode(); |
---|
| 150 | } |
---|
| 151 | ++compNum; |
---|
| 152 | } |
---|
| 153 | } |
---|
| 154 | return compNum; |
---|
| 155 | } |
---|
| 156 | |
---|
[419] | 157 | namespace _connectivity_bits { |
---|
[417] | 158 | |
---|
| 159 | template <typename Digraph, typename Iterator > |
---|
| 160 | struct LeaveOrderVisitor : public DfsVisitor<Digraph> { |
---|
| 161 | public: |
---|
| 162 | typedef typename Digraph::Node Node; |
---|
| 163 | LeaveOrderVisitor(Iterator it) : _it(it) {} |
---|
| 164 | |
---|
| 165 | void leave(const Node& node) { |
---|
| 166 | *(_it++) = node; |
---|
| 167 | } |
---|
| 168 | |
---|
| 169 | private: |
---|
| 170 | Iterator _it; |
---|
| 171 | }; |
---|
| 172 | |
---|
| 173 | template <typename Digraph, typename Map> |
---|
| 174 | struct FillMapVisitor : public DfsVisitor<Digraph> { |
---|
| 175 | public: |
---|
| 176 | typedef typename Digraph::Node Node; |
---|
| 177 | typedef typename Map::Value Value; |
---|
| 178 | |
---|
| 179 | FillMapVisitor(Map& map, Value& value) |
---|
| 180 | : _map(map), _value(value) {} |
---|
| 181 | |
---|
| 182 | void reach(const Node& node) { |
---|
| 183 | _map.set(node, _value); |
---|
| 184 | } |
---|
| 185 | private: |
---|
| 186 | Map& _map; |
---|
| 187 | Value& _value; |
---|
| 188 | }; |
---|
| 189 | |
---|
| 190 | template <typename Digraph, typename ArcMap> |
---|
[419] | 191 | struct StronglyConnectedCutArcsVisitor : public DfsVisitor<Digraph> { |
---|
[417] | 192 | public: |
---|
| 193 | typedef typename Digraph::Node Node; |
---|
| 194 | typedef typename Digraph::Arc Arc; |
---|
| 195 | |
---|
[419] | 196 | StronglyConnectedCutArcsVisitor(const Digraph& digraph, |
---|
| 197 | ArcMap& cutMap, |
---|
| 198 | int& cutNum) |
---|
[417] | 199 | : _digraph(digraph), _cutMap(cutMap), _cutNum(cutNum), |
---|
[419] | 200 | _compMap(digraph, -1), _num(-1) { |
---|
[417] | 201 | } |
---|
| 202 | |
---|
[419] | 203 | void start(const Node&) { |
---|
[417] | 204 | ++_num; |
---|
| 205 | } |
---|
| 206 | |
---|
| 207 | void reach(const Node& node) { |
---|
| 208 | _compMap.set(node, _num); |
---|
| 209 | } |
---|
| 210 | |
---|
| 211 | void examine(const Arc& arc) { |
---|
| 212 | if (_compMap[_digraph.source(arc)] != |
---|
| 213 | _compMap[_digraph.target(arc)]) { |
---|
| 214 | _cutMap.set(arc, true); |
---|
| 215 | ++_cutNum; |
---|
| 216 | } |
---|
| 217 | } |
---|
| 218 | private: |
---|
| 219 | const Digraph& _digraph; |
---|
| 220 | ArcMap& _cutMap; |
---|
| 221 | int& _cutNum; |
---|
| 222 | |
---|
| 223 | typename Digraph::template NodeMap<int> _compMap; |
---|
| 224 | int _num; |
---|
| 225 | }; |
---|
| 226 | |
---|
| 227 | } |
---|
| 228 | |
---|
| 229 | |
---|
| 230 | /// \ingroup connectivity |
---|
| 231 | /// |
---|
| 232 | /// \brief Check whether the given directed graph is strongly connected. |
---|
| 233 | /// |
---|
| 234 | /// Check whether the given directed graph is strongly connected. The |
---|
| 235 | /// graph is strongly connected when any two nodes of the graph are |
---|
| 236 | /// connected with directed paths in both direction. |
---|
| 237 | /// \return %False when the graph is not strongly connected. |
---|
| 238 | /// \see connected |
---|
| 239 | /// |
---|
| 240 | /// \note By definition, the empty graph is strongly connected. |
---|
| 241 | template <typename Digraph> |
---|
| 242 | bool stronglyConnected(const Digraph& digraph) { |
---|
| 243 | checkConcept<concepts::Digraph, Digraph>(); |
---|
| 244 | |
---|
| 245 | typedef typename Digraph::Node Node; |
---|
| 246 | typedef typename Digraph::NodeIt NodeIt; |
---|
| 247 | |
---|
| 248 | typename Digraph::Node source = NodeIt(digraph); |
---|
| 249 | if (source == INVALID) return true; |
---|
| 250 | |
---|
[419] | 251 | using namespace _connectivity_bits; |
---|
[417] | 252 | |
---|
| 253 | typedef DfsVisitor<Digraph> Visitor; |
---|
| 254 | Visitor visitor; |
---|
| 255 | |
---|
| 256 | DfsVisit<Digraph, Visitor> dfs(digraph, visitor); |
---|
| 257 | dfs.init(); |
---|
| 258 | dfs.addSource(source); |
---|
| 259 | dfs.start(); |
---|
| 260 | |
---|
| 261 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
| 262 | if (!dfs.reached(it)) { |
---|
| 263 | return false; |
---|
| 264 | } |
---|
| 265 | } |
---|
| 266 | |
---|
| 267 | typedef ReverseDigraph<const Digraph> RDigraph; |
---|
[419] | 268 | typedef typename RDigraph::NodeIt RNodeIt; |
---|
[417] | 269 | RDigraph rdigraph(digraph); |
---|
| 270 | |
---|
| 271 | typedef DfsVisitor<Digraph> RVisitor; |
---|
| 272 | RVisitor rvisitor; |
---|
| 273 | |
---|
| 274 | DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor); |
---|
| 275 | rdfs.init(); |
---|
| 276 | rdfs.addSource(source); |
---|
| 277 | rdfs.start(); |
---|
| 278 | |
---|
[419] | 279 | for (RNodeIt it(rdigraph); it != INVALID; ++it) { |
---|
[417] | 280 | if (!rdfs.reached(it)) { |
---|
| 281 | return false; |
---|
| 282 | } |
---|
| 283 | } |
---|
| 284 | |
---|
| 285 | return true; |
---|
| 286 | } |
---|
| 287 | |
---|
| 288 | /// \ingroup connectivity |
---|
| 289 | /// |
---|
| 290 | /// \brief Count the strongly connected components of a directed graph |
---|
| 291 | /// |
---|
| 292 | /// Count the strongly connected components of a directed graph. |
---|
| 293 | /// The strongly connected components are the classes of an |
---|
| 294 | /// equivalence relation on the nodes of the graph. Two nodes are in |
---|
| 295 | /// the same class if they are connected with directed paths in both |
---|
| 296 | /// direction. |
---|
| 297 | /// |
---|
[425] | 298 | /// \param digraph The graph. |
---|
[417] | 299 | /// \return The number of components |
---|
| 300 | /// \note By definition, the empty graph has zero |
---|
| 301 | /// strongly connected components. |
---|
| 302 | template <typename Digraph> |
---|
| 303 | int countStronglyConnectedComponents(const Digraph& digraph) { |
---|
| 304 | checkConcept<concepts::Digraph, Digraph>(); |
---|
| 305 | |
---|
[419] | 306 | using namespace _connectivity_bits; |
---|
[417] | 307 | |
---|
| 308 | typedef typename Digraph::Node Node; |
---|
| 309 | typedef typename Digraph::Arc Arc; |
---|
| 310 | typedef typename Digraph::NodeIt NodeIt; |
---|
| 311 | typedef typename Digraph::ArcIt ArcIt; |
---|
| 312 | |
---|
| 313 | typedef std::vector<Node> Container; |
---|
| 314 | typedef typename Container::iterator Iterator; |
---|
| 315 | |
---|
| 316 | Container nodes(countNodes(digraph)); |
---|
| 317 | typedef LeaveOrderVisitor<Digraph, Iterator> Visitor; |
---|
| 318 | Visitor visitor(nodes.begin()); |
---|
| 319 | |
---|
| 320 | DfsVisit<Digraph, Visitor> dfs(digraph, visitor); |
---|
| 321 | dfs.init(); |
---|
| 322 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
| 323 | if (!dfs.reached(it)) { |
---|
| 324 | dfs.addSource(it); |
---|
| 325 | dfs.start(); |
---|
| 326 | } |
---|
| 327 | } |
---|
| 328 | |
---|
| 329 | typedef typename Container::reverse_iterator RIterator; |
---|
| 330 | typedef ReverseDigraph<const Digraph> RDigraph; |
---|
| 331 | |
---|
| 332 | RDigraph rdigraph(digraph); |
---|
| 333 | |
---|
| 334 | typedef DfsVisitor<Digraph> RVisitor; |
---|
| 335 | RVisitor rvisitor; |
---|
| 336 | |
---|
| 337 | DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor); |
---|
| 338 | |
---|
| 339 | int compNum = 0; |
---|
| 340 | |
---|
| 341 | rdfs.init(); |
---|
| 342 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
---|
| 343 | if (!rdfs.reached(*it)) { |
---|
| 344 | rdfs.addSource(*it); |
---|
| 345 | rdfs.start(); |
---|
| 346 | ++compNum; |
---|
| 347 | } |
---|
| 348 | } |
---|
| 349 | return compNum; |
---|
| 350 | } |
---|
| 351 | |
---|
| 352 | /// \ingroup connectivity |
---|
| 353 | /// |
---|
| 354 | /// \brief Find the strongly connected components of a directed graph |
---|
| 355 | /// |
---|
| 356 | /// Find the strongly connected components of a directed graph. The |
---|
| 357 | /// strongly connected components are the classes of an equivalence |
---|
| 358 | /// relation on the nodes of the graph. Two nodes are in |
---|
| 359 | /// relationship when there are directed paths between them in both |
---|
| 360 | /// direction. In addition, the numbering of components will satisfy |
---|
| 361 | /// that there is no arc going from a higher numbered component to |
---|
| 362 | /// a lower. |
---|
| 363 | /// |
---|
| 364 | /// \param digraph The digraph. |
---|
| 365 | /// \retval compMap A writable node map. The values will be set from 0 to |
---|
| 366 | /// the number of the strongly connected components minus one. Each value |
---|
| 367 | /// of the map will be set exactly once, the values of a certain component |
---|
| 368 | /// will be set continuously. |
---|
| 369 | /// \return The number of components |
---|
| 370 | /// |
---|
| 371 | template <typename Digraph, typename NodeMap> |
---|
| 372 | int stronglyConnectedComponents(const Digraph& digraph, NodeMap& compMap) { |
---|
| 373 | checkConcept<concepts::Digraph, Digraph>(); |
---|
| 374 | typedef typename Digraph::Node Node; |
---|
| 375 | typedef typename Digraph::NodeIt NodeIt; |
---|
| 376 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
---|
| 377 | |
---|
[419] | 378 | using namespace _connectivity_bits; |
---|
[417] | 379 | |
---|
| 380 | typedef std::vector<Node> Container; |
---|
| 381 | typedef typename Container::iterator Iterator; |
---|
| 382 | |
---|
| 383 | Container nodes(countNodes(digraph)); |
---|
| 384 | typedef LeaveOrderVisitor<Digraph, Iterator> Visitor; |
---|
| 385 | Visitor visitor(nodes.begin()); |
---|
| 386 | |
---|
| 387 | DfsVisit<Digraph, Visitor> dfs(digraph, visitor); |
---|
| 388 | dfs.init(); |
---|
| 389 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
| 390 | if (!dfs.reached(it)) { |
---|
| 391 | dfs.addSource(it); |
---|
| 392 | dfs.start(); |
---|
| 393 | } |
---|
| 394 | } |
---|
| 395 | |
---|
| 396 | typedef typename Container::reverse_iterator RIterator; |
---|
| 397 | typedef ReverseDigraph<const Digraph> RDigraph; |
---|
| 398 | |
---|
| 399 | RDigraph rdigraph(digraph); |
---|
| 400 | |
---|
| 401 | int compNum = 0; |
---|
| 402 | |
---|
| 403 | typedef FillMapVisitor<RDigraph, NodeMap> RVisitor; |
---|
| 404 | RVisitor rvisitor(compMap, compNum); |
---|
| 405 | |
---|
| 406 | DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor); |
---|
| 407 | |
---|
| 408 | rdfs.init(); |
---|
| 409 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
---|
| 410 | if (!rdfs.reached(*it)) { |
---|
| 411 | rdfs.addSource(*it); |
---|
| 412 | rdfs.start(); |
---|
| 413 | ++compNum; |
---|
| 414 | } |
---|
| 415 | } |
---|
| 416 | return compNum; |
---|
| 417 | } |
---|
| 418 | |
---|
| 419 | /// \ingroup connectivity |
---|
| 420 | /// |
---|
| 421 | /// \brief Find the cut arcs of the strongly connected components. |
---|
| 422 | /// |
---|
| 423 | /// Find the cut arcs of the strongly connected components. |
---|
| 424 | /// The strongly connected components are the classes of an equivalence |
---|
| 425 | /// relation on the nodes of the graph. Two nodes are in relationship |
---|
| 426 | /// when there are directed paths between them in both direction. |
---|
| 427 | /// The strongly connected components are separated by the cut arcs. |
---|
| 428 | /// |
---|
| 429 | /// \param graph The graph. |
---|
| 430 | /// \retval cutMap A writable node map. The values will be set true when the |
---|
| 431 | /// arc is a cut arc. |
---|
| 432 | /// |
---|
| 433 | /// \return The number of cut arcs |
---|
| 434 | template <typename Digraph, typename ArcMap> |
---|
| 435 | int stronglyConnectedCutArcs(const Digraph& graph, ArcMap& cutMap) { |
---|
| 436 | checkConcept<concepts::Digraph, Digraph>(); |
---|
| 437 | typedef typename Digraph::Node Node; |
---|
| 438 | typedef typename Digraph::Arc Arc; |
---|
| 439 | typedef typename Digraph::NodeIt NodeIt; |
---|
| 440 | checkConcept<concepts::WriteMap<Arc, bool>, ArcMap>(); |
---|
| 441 | |
---|
[419] | 442 | using namespace _connectivity_bits; |
---|
[417] | 443 | |
---|
| 444 | typedef std::vector<Node> Container; |
---|
| 445 | typedef typename Container::iterator Iterator; |
---|
| 446 | |
---|
| 447 | Container nodes(countNodes(graph)); |
---|
| 448 | typedef LeaveOrderVisitor<Digraph, Iterator> Visitor; |
---|
| 449 | Visitor visitor(nodes.begin()); |
---|
| 450 | |
---|
| 451 | DfsVisit<Digraph, Visitor> dfs(graph, visitor); |
---|
| 452 | dfs.init(); |
---|
| 453 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 454 | if (!dfs.reached(it)) { |
---|
| 455 | dfs.addSource(it); |
---|
| 456 | dfs.start(); |
---|
| 457 | } |
---|
| 458 | } |
---|
| 459 | |
---|
| 460 | typedef typename Container::reverse_iterator RIterator; |
---|
| 461 | typedef ReverseDigraph<const Digraph> RDigraph; |
---|
| 462 | |
---|
| 463 | RDigraph rgraph(graph); |
---|
| 464 | |
---|
| 465 | int cutNum = 0; |
---|
| 466 | |
---|
[419] | 467 | typedef StronglyConnectedCutArcsVisitor<RDigraph, ArcMap> RVisitor; |
---|
[417] | 468 | RVisitor rvisitor(rgraph, cutMap, cutNum); |
---|
| 469 | |
---|
| 470 | DfsVisit<RDigraph, RVisitor> rdfs(rgraph, rvisitor); |
---|
| 471 | |
---|
| 472 | rdfs.init(); |
---|
| 473 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
---|
| 474 | if (!rdfs.reached(*it)) { |
---|
| 475 | rdfs.addSource(*it); |
---|
| 476 | rdfs.start(); |
---|
| 477 | } |
---|
| 478 | } |
---|
| 479 | return cutNum; |
---|
| 480 | } |
---|
| 481 | |
---|
[419] | 482 | namespace _connectivity_bits { |
---|
[417] | 483 | |
---|
| 484 | template <typename Digraph> |
---|
| 485 | class CountBiNodeConnectedComponentsVisitor : public DfsVisitor<Digraph> { |
---|
| 486 | public: |
---|
| 487 | typedef typename Digraph::Node Node; |
---|
| 488 | typedef typename Digraph::Arc Arc; |
---|
| 489 | typedef typename Digraph::Edge Edge; |
---|
| 490 | |
---|
| 491 | CountBiNodeConnectedComponentsVisitor(const Digraph& graph, int &compNum) |
---|
| 492 | : _graph(graph), _compNum(compNum), |
---|
| 493 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 494 | |
---|
| 495 | void start(const Node& node) { |
---|
| 496 | _predMap.set(node, INVALID); |
---|
| 497 | } |
---|
| 498 | |
---|
| 499 | void reach(const Node& node) { |
---|
| 500 | _numMap.set(node, _num); |
---|
| 501 | _retMap.set(node, _num); |
---|
| 502 | ++_num; |
---|
| 503 | } |
---|
| 504 | |
---|
| 505 | void discover(const Arc& edge) { |
---|
| 506 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
---|
| 507 | } |
---|
| 508 | |
---|
| 509 | void examine(const Arc& edge) { |
---|
| 510 | if (_graph.source(edge) == _graph.target(edge) && |
---|
| 511 | _graph.direction(edge)) { |
---|
| 512 | ++_compNum; |
---|
| 513 | return; |
---|
| 514 | } |
---|
| 515 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) { |
---|
| 516 | return; |
---|
| 517 | } |
---|
| 518 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
---|
| 519 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
---|
| 520 | } |
---|
| 521 | } |
---|
| 522 | |
---|
| 523 | void backtrack(const Arc& edge) { |
---|
| 524 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 525 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 526 | } |
---|
| 527 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
---|
| 528 | ++_compNum; |
---|
| 529 | } |
---|
| 530 | } |
---|
| 531 | |
---|
| 532 | private: |
---|
| 533 | const Digraph& _graph; |
---|
| 534 | int& _compNum; |
---|
| 535 | |
---|
| 536 | typename Digraph::template NodeMap<int> _numMap; |
---|
| 537 | typename Digraph::template NodeMap<int> _retMap; |
---|
| 538 | typename Digraph::template NodeMap<Node> _predMap; |
---|
| 539 | int _num; |
---|
| 540 | }; |
---|
| 541 | |
---|
| 542 | template <typename Digraph, typename ArcMap> |
---|
| 543 | class BiNodeConnectedComponentsVisitor : public DfsVisitor<Digraph> { |
---|
| 544 | public: |
---|
| 545 | typedef typename Digraph::Node Node; |
---|
| 546 | typedef typename Digraph::Arc Arc; |
---|
| 547 | typedef typename Digraph::Edge Edge; |
---|
| 548 | |
---|
| 549 | BiNodeConnectedComponentsVisitor(const Digraph& graph, |
---|
| 550 | ArcMap& compMap, int &compNum) |
---|
| 551 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
| 552 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 553 | |
---|
| 554 | void start(const Node& node) { |
---|
| 555 | _predMap.set(node, INVALID); |
---|
| 556 | } |
---|
| 557 | |
---|
| 558 | void reach(const Node& node) { |
---|
| 559 | _numMap.set(node, _num); |
---|
| 560 | _retMap.set(node, _num); |
---|
| 561 | ++_num; |
---|
| 562 | } |
---|
| 563 | |
---|
| 564 | void discover(const Arc& edge) { |
---|
| 565 | Node target = _graph.target(edge); |
---|
| 566 | _predMap.set(target, edge); |
---|
| 567 | _edgeStack.push(edge); |
---|
| 568 | } |
---|
| 569 | |
---|
| 570 | void examine(const Arc& edge) { |
---|
| 571 | Node source = _graph.source(edge); |
---|
| 572 | Node target = _graph.target(edge); |
---|
| 573 | if (source == target && _graph.direction(edge)) { |
---|
| 574 | _compMap.set(edge, _compNum); |
---|
| 575 | ++_compNum; |
---|
| 576 | return; |
---|
| 577 | } |
---|
| 578 | if (_numMap[target] < _numMap[source]) { |
---|
| 579 | if (_predMap[source] != _graph.oppositeArc(edge)) { |
---|
| 580 | _edgeStack.push(edge); |
---|
| 581 | } |
---|
| 582 | } |
---|
| 583 | if (_predMap[source] != INVALID && |
---|
| 584 | target == _graph.source(_predMap[source])) { |
---|
| 585 | return; |
---|
| 586 | } |
---|
| 587 | if (_retMap[source] > _numMap[target]) { |
---|
| 588 | _retMap.set(source, _numMap[target]); |
---|
| 589 | } |
---|
| 590 | } |
---|
| 591 | |
---|
| 592 | void backtrack(const Arc& edge) { |
---|
| 593 | Node source = _graph.source(edge); |
---|
| 594 | Node target = _graph.target(edge); |
---|
| 595 | if (_retMap[source] > _retMap[target]) { |
---|
| 596 | _retMap.set(source, _retMap[target]); |
---|
| 597 | } |
---|
| 598 | if (_numMap[source] <= _retMap[target]) { |
---|
| 599 | while (_edgeStack.top() != edge) { |
---|
| 600 | _compMap.set(_edgeStack.top(), _compNum); |
---|
| 601 | _edgeStack.pop(); |
---|
| 602 | } |
---|
| 603 | _compMap.set(edge, _compNum); |
---|
| 604 | _edgeStack.pop(); |
---|
| 605 | ++_compNum; |
---|
| 606 | } |
---|
| 607 | } |
---|
| 608 | |
---|
| 609 | private: |
---|
| 610 | const Digraph& _graph; |
---|
| 611 | ArcMap& _compMap; |
---|
| 612 | int& _compNum; |
---|
| 613 | |
---|
| 614 | typename Digraph::template NodeMap<int> _numMap; |
---|
| 615 | typename Digraph::template NodeMap<int> _retMap; |
---|
| 616 | typename Digraph::template NodeMap<Arc> _predMap; |
---|
| 617 | std::stack<Edge> _edgeStack; |
---|
| 618 | int _num; |
---|
| 619 | }; |
---|
| 620 | |
---|
| 621 | |
---|
| 622 | template <typename Digraph, typename NodeMap> |
---|
| 623 | class BiNodeConnectedCutNodesVisitor : public DfsVisitor<Digraph> { |
---|
| 624 | public: |
---|
| 625 | typedef typename Digraph::Node Node; |
---|
| 626 | typedef typename Digraph::Arc Arc; |
---|
| 627 | typedef typename Digraph::Edge Edge; |
---|
| 628 | |
---|
| 629 | BiNodeConnectedCutNodesVisitor(const Digraph& graph, NodeMap& cutMap, |
---|
| 630 | int& cutNum) |
---|
| 631 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
| 632 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 633 | |
---|
| 634 | void start(const Node& node) { |
---|
| 635 | _predMap.set(node, INVALID); |
---|
| 636 | rootCut = false; |
---|
| 637 | } |
---|
| 638 | |
---|
| 639 | void reach(const Node& node) { |
---|
| 640 | _numMap.set(node, _num); |
---|
| 641 | _retMap.set(node, _num); |
---|
| 642 | ++_num; |
---|
| 643 | } |
---|
| 644 | |
---|
| 645 | void discover(const Arc& edge) { |
---|
| 646 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
---|
| 647 | } |
---|
| 648 | |
---|
| 649 | void examine(const Arc& edge) { |
---|
| 650 | if (_graph.source(edge) == _graph.target(edge) && |
---|
| 651 | _graph.direction(edge)) { |
---|
| 652 | if (!_cutMap[_graph.source(edge)]) { |
---|
| 653 | _cutMap.set(_graph.source(edge), true); |
---|
| 654 | ++_cutNum; |
---|
| 655 | } |
---|
| 656 | return; |
---|
| 657 | } |
---|
| 658 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) return; |
---|
| 659 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
---|
| 660 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
---|
| 661 | } |
---|
| 662 | } |
---|
| 663 | |
---|
| 664 | void backtrack(const Arc& edge) { |
---|
| 665 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 666 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 667 | } |
---|
| 668 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
---|
| 669 | if (_predMap[_graph.source(edge)] != INVALID) { |
---|
| 670 | if (!_cutMap[_graph.source(edge)]) { |
---|
| 671 | _cutMap.set(_graph.source(edge), true); |
---|
| 672 | ++_cutNum; |
---|
| 673 | } |
---|
| 674 | } else if (rootCut) { |
---|
| 675 | if (!_cutMap[_graph.source(edge)]) { |
---|
| 676 | _cutMap.set(_graph.source(edge), true); |
---|
| 677 | ++_cutNum; |
---|
| 678 | } |
---|
| 679 | } else { |
---|
| 680 | rootCut = true; |
---|
| 681 | } |
---|
| 682 | } |
---|
| 683 | } |
---|
| 684 | |
---|
| 685 | private: |
---|
| 686 | const Digraph& _graph; |
---|
| 687 | NodeMap& _cutMap; |
---|
| 688 | int& _cutNum; |
---|
| 689 | |
---|
| 690 | typename Digraph::template NodeMap<int> _numMap; |
---|
| 691 | typename Digraph::template NodeMap<int> _retMap; |
---|
| 692 | typename Digraph::template NodeMap<Node> _predMap; |
---|
| 693 | std::stack<Edge> _edgeStack; |
---|
| 694 | int _num; |
---|
| 695 | bool rootCut; |
---|
| 696 | }; |
---|
| 697 | |
---|
| 698 | } |
---|
| 699 | |
---|
| 700 | template <typename Graph> |
---|
| 701 | int countBiNodeConnectedComponents(const Graph& graph); |
---|
| 702 | |
---|
| 703 | /// \ingroup connectivity |
---|
| 704 | /// |
---|
| 705 | /// \brief Checks the graph is bi-node-connected. |
---|
| 706 | /// |
---|
| 707 | /// This function checks that the undirected graph is bi-node-connected |
---|
| 708 | /// graph. The graph is bi-node-connected if any two undirected edge is |
---|
| 709 | /// on same circle. |
---|
| 710 | /// |
---|
| 711 | /// \param graph The graph. |
---|
| 712 | /// \return %True when the graph bi-node-connected. |
---|
| 713 | template <typename Graph> |
---|
| 714 | bool biNodeConnected(const Graph& graph) { |
---|
| 715 | return countBiNodeConnectedComponents(graph) <= 1; |
---|
| 716 | } |
---|
| 717 | |
---|
| 718 | /// \ingroup connectivity |
---|
| 719 | /// |
---|
| 720 | /// \brief Count the biconnected components. |
---|
| 721 | /// |
---|
| 722 | /// This function finds the bi-node-connected components in an undirected |
---|
| 723 | /// graph. The biconnected components are the classes of an equivalence |
---|
| 724 | /// relation on the undirected edges. Two undirected edge is in relationship |
---|
| 725 | /// when they are on same circle. |
---|
| 726 | /// |
---|
| 727 | /// \param graph The graph. |
---|
| 728 | /// \return The number of components. |
---|
| 729 | template <typename Graph> |
---|
| 730 | int countBiNodeConnectedComponents(const Graph& graph) { |
---|
| 731 | checkConcept<concepts::Graph, Graph>(); |
---|
| 732 | typedef typename Graph::NodeIt NodeIt; |
---|
| 733 | |
---|
[419] | 734 | using namespace _connectivity_bits; |
---|
[417] | 735 | |
---|
| 736 | typedef CountBiNodeConnectedComponentsVisitor<Graph> Visitor; |
---|
| 737 | |
---|
| 738 | int compNum = 0; |
---|
| 739 | Visitor visitor(graph, compNum); |
---|
| 740 | |
---|
| 741 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
| 742 | dfs.init(); |
---|
| 743 | |
---|
| 744 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 745 | if (!dfs.reached(it)) { |
---|
| 746 | dfs.addSource(it); |
---|
| 747 | dfs.start(); |
---|
| 748 | } |
---|
| 749 | } |
---|
| 750 | return compNum; |
---|
| 751 | } |
---|
| 752 | |
---|
| 753 | /// \ingroup connectivity |
---|
| 754 | /// |
---|
| 755 | /// \brief Find the bi-node-connected components. |
---|
| 756 | /// |
---|
| 757 | /// This function finds the bi-node-connected components in an undirected |
---|
| 758 | /// graph. The bi-node-connected components are the classes of an equivalence |
---|
| 759 | /// relation on the undirected edges. Two undirected edge are in relationship |
---|
| 760 | /// when they are on same circle. |
---|
| 761 | /// |
---|
| 762 | /// \param graph The graph. |
---|
| 763 | /// \retval compMap A writable uedge map. The values will be set from 0 |
---|
| 764 | /// to the number of the biconnected components minus one. Each values |
---|
| 765 | /// of the map will be set exactly once, the values of a certain component |
---|
| 766 | /// will be set continuously. |
---|
| 767 | /// \return The number of components. |
---|
| 768 | /// |
---|
| 769 | template <typename Graph, typename EdgeMap> |
---|
| 770 | int biNodeConnectedComponents(const Graph& graph, |
---|
| 771 | EdgeMap& compMap) { |
---|
| 772 | checkConcept<concepts::Graph, Graph>(); |
---|
| 773 | typedef typename Graph::NodeIt NodeIt; |
---|
| 774 | typedef typename Graph::Edge Edge; |
---|
| 775 | checkConcept<concepts::WriteMap<Edge, int>, EdgeMap>(); |
---|
| 776 | |
---|
[419] | 777 | using namespace _connectivity_bits; |
---|
[417] | 778 | |
---|
| 779 | typedef BiNodeConnectedComponentsVisitor<Graph, EdgeMap> Visitor; |
---|
| 780 | |
---|
| 781 | int compNum = 0; |
---|
| 782 | Visitor visitor(graph, compMap, compNum); |
---|
| 783 | |
---|
| 784 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
| 785 | dfs.init(); |
---|
| 786 | |
---|
| 787 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 788 | if (!dfs.reached(it)) { |
---|
| 789 | dfs.addSource(it); |
---|
| 790 | dfs.start(); |
---|
| 791 | } |
---|
| 792 | } |
---|
| 793 | return compNum; |
---|
| 794 | } |
---|
| 795 | |
---|
| 796 | /// \ingroup connectivity |
---|
| 797 | /// |
---|
| 798 | /// \brief Find the bi-node-connected cut nodes. |
---|
| 799 | /// |
---|
| 800 | /// This function finds the bi-node-connected cut nodes in an undirected |
---|
| 801 | /// graph. The bi-node-connected components are the classes of an equivalence |
---|
| 802 | /// relation on the undirected edges. Two undirected edges are in |
---|
| 803 | /// relationship when they are on same circle. The biconnected components |
---|
| 804 | /// are separted by nodes which are the cut nodes of the components. |
---|
| 805 | /// |
---|
| 806 | /// \param graph The graph. |
---|
| 807 | /// \retval cutMap A writable edge map. The values will be set true when |
---|
| 808 | /// the node separate two or more components. |
---|
| 809 | /// \return The number of the cut nodes. |
---|
| 810 | template <typename Graph, typename NodeMap> |
---|
| 811 | int biNodeConnectedCutNodes(const Graph& graph, NodeMap& cutMap) { |
---|
| 812 | checkConcept<concepts::Graph, Graph>(); |
---|
| 813 | typedef typename Graph::Node Node; |
---|
| 814 | typedef typename Graph::NodeIt NodeIt; |
---|
| 815 | checkConcept<concepts::WriteMap<Node, bool>, NodeMap>(); |
---|
| 816 | |
---|
[419] | 817 | using namespace _connectivity_bits; |
---|
[417] | 818 | |
---|
| 819 | typedef BiNodeConnectedCutNodesVisitor<Graph, NodeMap> Visitor; |
---|
| 820 | |
---|
| 821 | int cutNum = 0; |
---|
| 822 | Visitor visitor(graph, cutMap, cutNum); |
---|
| 823 | |
---|
| 824 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
| 825 | dfs.init(); |
---|
| 826 | |
---|
| 827 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 828 | if (!dfs.reached(it)) { |
---|
| 829 | dfs.addSource(it); |
---|
| 830 | dfs.start(); |
---|
| 831 | } |
---|
| 832 | } |
---|
| 833 | return cutNum; |
---|
| 834 | } |
---|
| 835 | |
---|
[419] | 836 | namespace _connectivity_bits { |
---|
[417] | 837 | |
---|
| 838 | template <typename Digraph> |
---|
| 839 | class CountBiEdgeConnectedComponentsVisitor : public DfsVisitor<Digraph> { |
---|
| 840 | public: |
---|
| 841 | typedef typename Digraph::Node Node; |
---|
| 842 | typedef typename Digraph::Arc Arc; |
---|
| 843 | typedef typename Digraph::Edge Edge; |
---|
| 844 | |
---|
| 845 | CountBiEdgeConnectedComponentsVisitor(const Digraph& graph, int &compNum) |
---|
| 846 | : _graph(graph), _compNum(compNum), |
---|
| 847 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 848 | |
---|
| 849 | void start(const Node& node) { |
---|
| 850 | _predMap.set(node, INVALID); |
---|
| 851 | } |
---|
| 852 | |
---|
| 853 | void reach(const Node& node) { |
---|
| 854 | _numMap.set(node, _num); |
---|
| 855 | _retMap.set(node, _num); |
---|
| 856 | ++_num; |
---|
| 857 | } |
---|
| 858 | |
---|
| 859 | void leave(const Node& node) { |
---|
| 860 | if (_numMap[node] <= _retMap[node]) { |
---|
| 861 | ++_compNum; |
---|
| 862 | } |
---|
| 863 | } |
---|
| 864 | |
---|
| 865 | void discover(const Arc& edge) { |
---|
| 866 | _predMap.set(_graph.target(edge), edge); |
---|
| 867 | } |
---|
| 868 | |
---|
| 869 | void examine(const Arc& edge) { |
---|
| 870 | if (_predMap[_graph.source(edge)] == _graph.oppositeArc(edge)) { |
---|
| 871 | return; |
---|
| 872 | } |
---|
| 873 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 874 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 875 | } |
---|
| 876 | } |
---|
| 877 | |
---|
| 878 | void backtrack(const Arc& edge) { |
---|
| 879 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 880 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 881 | } |
---|
| 882 | } |
---|
| 883 | |
---|
| 884 | private: |
---|
| 885 | const Digraph& _graph; |
---|
| 886 | int& _compNum; |
---|
| 887 | |
---|
| 888 | typename Digraph::template NodeMap<int> _numMap; |
---|
| 889 | typename Digraph::template NodeMap<int> _retMap; |
---|
| 890 | typename Digraph::template NodeMap<Arc> _predMap; |
---|
| 891 | int _num; |
---|
| 892 | }; |
---|
| 893 | |
---|
| 894 | template <typename Digraph, typename NodeMap> |
---|
| 895 | class BiEdgeConnectedComponentsVisitor : public DfsVisitor<Digraph> { |
---|
| 896 | public: |
---|
| 897 | typedef typename Digraph::Node Node; |
---|
| 898 | typedef typename Digraph::Arc Arc; |
---|
| 899 | typedef typename Digraph::Edge Edge; |
---|
| 900 | |
---|
| 901 | BiEdgeConnectedComponentsVisitor(const Digraph& graph, |
---|
| 902 | NodeMap& compMap, int &compNum) |
---|
| 903 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
| 904 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 905 | |
---|
| 906 | void start(const Node& node) { |
---|
| 907 | _predMap.set(node, INVALID); |
---|
| 908 | } |
---|
| 909 | |
---|
| 910 | void reach(const Node& node) { |
---|
| 911 | _numMap.set(node, _num); |
---|
| 912 | _retMap.set(node, _num); |
---|
| 913 | _nodeStack.push(node); |
---|
| 914 | ++_num; |
---|
| 915 | } |
---|
| 916 | |
---|
| 917 | void leave(const Node& node) { |
---|
| 918 | if (_numMap[node] <= _retMap[node]) { |
---|
| 919 | while (_nodeStack.top() != node) { |
---|
| 920 | _compMap.set(_nodeStack.top(), _compNum); |
---|
| 921 | _nodeStack.pop(); |
---|
| 922 | } |
---|
| 923 | _compMap.set(node, _compNum); |
---|
| 924 | _nodeStack.pop(); |
---|
| 925 | ++_compNum; |
---|
| 926 | } |
---|
| 927 | } |
---|
| 928 | |
---|
| 929 | void discover(const Arc& edge) { |
---|
| 930 | _predMap.set(_graph.target(edge), edge); |
---|
| 931 | } |
---|
| 932 | |
---|
| 933 | void examine(const Arc& edge) { |
---|
| 934 | if (_predMap[_graph.source(edge)] == _graph.oppositeArc(edge)) { |
---|
| 935 | return; |
---|
| 936 | } |
---|
| 937 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 938 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 939 | } |
---|
| 940 | } |
---|
| 941 | |
---|
| 942 | void backtrack(const Arc& edge) { |
---|
| 943 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 944 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 945 | } |
---|
| 946 | } |
---|
| 947 | |
---|
| 948 | private: |
---|
| 949 | const Digraph& _graph; |
---|
| 950 | NodeMap& _compMap; |
---|
| 951 | int& _compNum; |
---|
| 952 | |
---|
| 953 | typename Digraph::template NodeMap<int> _numMap; |
---|
| 954 | typename Digraph::template NodeMap<int> _retMap; |
---|
| 955 | typename Digraph::template NodeMap<Arc> _predMap; |
---|
| 956 | std::stack<Node> _nodeStack; |
---|
| 957 | int _num; |
---|
| 958 | }; |
---|
| 959 | |
---|
| 960 | |
---|
| 961 | template <typename Digraph, typename ArcMap> |
---|
| 962 | class BiEdgeConnectedCutEdgesVisitor : public DfsVisitor<Digraph> { |
---|
| 963 | public: |
---|
| 964 | typedef typename Digraph::Node Node; |
---|
| 965 | typedef typename Digraph::Arc Arc; |
---|
| 966 | typedef typename Digraph::Edge Edge; |
---|
| 967 | |
---|
| 968 | BiEdgeConnectedCutEdgesVisitor(const Digraph& graph, |
---|
| 969 | ArcMap& cutMap, int &cutNum) |
---|
| 970 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
| 971 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 972 | |
---|
| 973 | void start(const Node& node) { |
---|
| 974 | _predMap[node] = INVALID; |
---|
| 975 | } |
---|
| 976 | |
---|
| 977 | void reach(const Node& node) { |
---|
| 978 | _numMap.set(node, _num); |
---|
| 979 | _retMap.set(node, _num); |
---|
| 980 | ++_num; |
---|
| 981 | } |
---|
| 982 | |
---|
| 983 | void leave(const Node& node) { |
---|
| 984 | if (_numMap[node] <= _retMap[node]) { |
---|
| 985 | if (_predMap[node] != INVALID) { |
---|
| 986 | _cutMap.set(_predMap[node], true); |
---|
| 987 | ++_cutNum; |
---|
| 988 | } |
---|
| 989 | } |
---|
| 990 | } |
---|
| 991 | |
---|
| 992 | void discover(const Arc& edge) { |
---|
| 993 | _predMap.set(_graph.target(edge), edge); |
---|
| 994 | } |
---|
| 995 | |
---|
| 996 | void examine(const Arc& edge) { |
---|
| 997 | if (_predMap[_graph.source(edge)] == _graph.oppositeArc(edge)) { |
---|
| 998 | return; |
---|
| 999 | } |
---|
| 1000 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 1001 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 1002 | } |
---|
| 1003 | } |
---|
| 1004 | |
---|
| 1005 | void backtrack(const Arc& edge) { |
---|
| 1006 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 1007 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 1008 | } |
---|
| 1009 | } |
---|
| 1010 | |
---|
| 1011 | private: |
---|
| 1012 | const Digraph& _graph; |
---|
| 1013 | ArcMap& _cutMap; |
---|
| 1014 | int& _cutNum; |
---|
| 1015 | |
---|
| 1016 | typename Digraph::template NodeMap<int> _numMap; |
---|
| 1017 | typename Digraph::template NodeMap<int> _retMap; |
---|
| 1018 | typename Digraph::template NodeMap<Arc> _predMap; |
---|
| 1019 | int _num; |
---|
| 1020 | }; |
---|
| 1021 | } |
---|
| 1022 | |
---|
| 1023 | template <typename Graph> |
---|
| 1024 | int countBiEdgeConnectedComponents(const Graph& graph); |
---|
| 1025 | |
---|
| 1026 | /// \ingroup connectivity |
---|
| 1027 | /// |
---|
| 1028 | /// \brief Checks that the graph is bi-edge-connected. |
---|
| 1029 | /// |
---|
| 1030 | /// This function checks that the graph is bi-edge-connected. The undirected |
---|
| 1031 | /// graph is bi-edge-connected when any two nodes are connected with two |
---|
| 1032 | /// edge-disjoint paths. |
---|
| 1033 | /// |
---|
| 1034 | /// \param graph The undirected graph. |
---|
| 1035 | /// \return The number of components. |
---|
| 1036 | template <typename Graph> |
---|
| 1037 | bool biEdgeConnected(const Graph& graph) { |
---|
| 1038 | return countBiEdgeConnectedComponents(graph) <= 1; |
---|
| 1039 | } |
---|
| 1040 | |
---|
| 1041 | /// \ingroup connectivity |
---|
| 1042 | /// |
---|
| 1043 | /// \brief Count the bi-edge-connected components. |
---|
| 1044 | /// |
---|
| 1045 | /// This function count the bi-edge-connected components in an undirected |
---|
| 1046 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
| 1047 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
| 1048 | /// connected with at least two edge-disjoint paths. |
---|
| 1049 | /// |
---|
| 1050 | /// \param graph The undirected graph. |
---|
| 1051 | /// \return The number of components. |
---|
| 1052 | template <typename Graph> |
---|
| 1053 | int countBiEdgeConnectedComponents(const Graph& graph) { |
---|
| 1054 | checkConcept<concepts::Graph, Graph>(); |
---|
| 1055 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1056 | |
---|
[419] | 1057 | using namespace _connectivity_bits; |
---|
[417] | 1058 | |
---|
| 1059 | typedef CountBiEdgeConnectedComponentsVisitor<Graph> Visitor; |
---|
| 1060 | |
---|
| 1061 | int compNum = 0; |
---|
| 1062 | Visitor visitor(graph, compNum); |
---|
| 1063 | |
---|
| 1064 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
| 1065 | dfs.init(); |
---|
| 1066 | |
---|
| 1067 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1068 | if (!dfs.reached(it)) { |
---|
| 1069 | dfs.addSource(it); |
---|
| 1070 | dfs.start(); |
---|
| 1071 | } |
---|
| 1072 | } |
---|
| 1073 | return compNum; |
---|
| 1074 | } |
---|
| 1075 | |
---|
| 1076 | /// \ingroup connectivity |
---|
| 1077 | /// |
---|
| 1078 | /// \brief Find the bi-edge-connected components. |
---|
| 1079 | /// |
---|
| 1080 | /// This function finds the bi-edge-connected components in an undirected |
---|
| 1081 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
| 1082 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
| 1083 | /// connected at least two edge-disjoint paths. |
---|
| 1084 | /// |
---|
| 1085 | /// \param graph The graph. |
---|
| 1086 | /// \retval compMap A writable node map. The values will be set from 0 to |
---|
| 1087 | /// the number of the biconnected components minus one. Each values |
---|
| 1088 | /// of the map will be set exactly once, the values of a certain component |
---|
| 1089 | /// will be set continuously. |
---|
| 1090 | /// \return The number of components. |
---|
| 1091 | /// |
---|
| 1092 | template <typename Graph, typename NodeMap> |
---|
| 1093 | int biEdgeConnectedComponents(const Graph& graph, NodeMap& compMap) { |
---|
| 1094 | checkConcept<concepts::Graph, Graph>(); |
---|
| 1095 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1096 | typedef typename Graph::Node Node; |
---|
| 1097 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
---|
| 1098 | |
---|
[419] | 1099 | using namespace _connectivity_bits; |
---|
[417] | 1100 | |
---|
| 1101 | typedef BiEdgeConnectedComponentsVisitor<Graph, NodeMap> Visitor; |
---|
| 1102 | |
---|
| 1103 | int compNum = 0; |
---|
| 1104 | Visitor visitor(graph, compMap, compNum); |
---|
| 1105 | |
---|
| 1106 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
| 1107 | dfs.init(); |
---|
| 1108 | |
---|
| 1109 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1110 | if (!dfs.reached(it)) { |
---|
| 1111 | dfs.addSource(it); |
---|
| 1112 | dfs.start(); |
---|
| 1113 | } |
---|
| 1114 | } |
---|
| 1115 | return compNum; |
---|
| 1116 | } |
---|
| 1117 | |
---|
| 1118 | /// \ingroup connectivity |
---|
| 1119 | /// |
---|
| 1120 | /// \brief Find the bi-edge-connected cut edges. |
---|
| 1121 | /// |
---|
| 1122 | /// This function finds the bi-edge-connected components in an undirected |
---|
| 1123 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
| 1124 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
| 1125 | /// connected with at least two edge-disjoint paths. The bi-edge-connected |
---|
| 1126 | /// components are separted by edges which are the cut edges of the |
---|
| 1127 | /// components. |
---|
| 1128 | /// |
---|
| 1129 | /// \param graph The graph. |
---|
| 1130 | /// \retval cutMap A writable node map. The values will be set true when the |
---|
| 1131 | /// edge is a cut edge. |
---|
| 1132 | /// \return The number of cut edges. |
---|
| 1133 | template <typename Graph, typename EdgeMap> |
---|
| 1134 | int biEdgeConnectedCutEdges(const Graph& graph, EdgeMap& cutMap) { |
---|
| 1135 | checkConcept<concepts::Graph, Graph>(); |
---|
| 1136 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1137 | typedef typename Graph::Edge Edge; |
---|
| 1138 | checkConcept<concepts::WriteMap<Edge, bool>, EdgeMap>(); |
---|
| 1139 | |
---|
[419] | 1140 | using namespace _connectivity_bits; |
---|
[417] | 1141 | |
---|
| 1142 | typedef BiEdgeConnectedCutEdgesVisitor<Graph, EdgeMap> Visitor; |
---|
| 1143 | |
---|
| 1144 | int cutNum = 0; |
---|
| 1145 | Visitor visitor(graph, cutMap, cutNum); |
---|
| 1146 | |
---|
| 1147 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
| 1148 | dfs.init(); |
---|
| 1149 | |
---|
| 1150 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1151 | if (!dfs.reached(it)) { |
---|
| 1152 | dfs.addSource(it); |
---|
| 1153 | dfs.start(); |
---|
| 1154 | } |
---|
| 1155 | } |
---|
| 1156 | return cutNum; |
---|
| 1157 | } |
---|
| 1158 | |
---|
| 1159 | |
---|
[419] | 1160 | namespace _connectivity_bits { |
---|
[417] | 1161 | |
---|
| 1162 | template <typename Digraph, typename IntNodeMap> |
---|
| 1163 | class TopologicalSortVisitor : public DfsVisitor<Digraph> { |
---|
| 1164 | public: |
---|
| 1165 | typedef typename Digraph::Node Node; |
---|
| 1166 | typedef typename Digraph::Arc edge; |
---|
| 1167 | |
---|
| 1168 | TopologicalSortVisitor(IntNodeMap& order, int num) |
---|
| 1169 | : _order(order), _num(num) {} |
---|
| 1170 | |
---|
| 1171 | void leave(const Node& node) { |
---|
| 1172 | _order.set(node, --_num); |
---|
| 1173 | } |
---|
| 1174 | |
---|
| 1175 | private: |
---|
| 1176 | IntNodeMap& _order; |
---|
| 1177 | int _num; |
---|
| 1178 | }; |
---|
| 1179 | |
---|
| 1180 | } |
---|
| 1181 | |
---|
| 1182 | /// \ingroup connectivity |
---|
| 1183 | /// |
---|
| 1184 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
| 1185 | /// |
---|
| 1186 | /// Sort the nodes of a DAG into topolgical order. |
---|
| 1187 | /// |
---|
| 1188 | /// \param graph The graph. It must be directed and acyclic. |
---|
| 1189 | /// \retval order A writable node map. The values will be set from 0 to |
---|
| 1190 | /// the number of the nodes in the graph minus one. Each values of the map |
---|
| 1191 | /// will be set exactly once, the values will be set descending order. |
---|
| 1192 | /// |
---|
| 1193 | /// \see checkedTopologicalSort |
---|
| 1194 | /// \see dag |
---|
| 1195 | template <typename Digraph, typename NodeMap> |
---|
| 1196 | void topologicalSort(const Digraph& graph, NodeMap& order) { |
---|
[419] | 1197 | using namespace _connectivity_bits; |
---|
[417] | 1198 | |
---|
| 1199 | checkConcept<concepts::Digraph, Digraph>(); |
---|
| 1200 | checkConcept<concepts::WriteMap<typename Digraph::Node, int>, NodeMap>(); |
---|
| 1201 | |
---|
| 1202 | typedef typename Digraph::Node Node; |
---|
| 1203 | typedef typename Digraph::NodeIt NodeIt; |
---|
| 1204 | typedef typename Digraph::Arc Arc; |
---|
| 1205 | |
---|
| 1206 | TopologicalSortVisitor<Digraph, NodeMap> |
---|
| 1207 | visitor(order, countNodes(graph)); |
---|
| 1208 | |
---|
| 1209 | DfsVisit<Digraph, TopologicalSortVisitor<Digraph, NodeMap> > |
---|
| 1210 | dfs(graph, visitor); |
---|
| 1211 | |
---|
| 1212 | dfs.init(); |
---|
| 1213 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1214 | if (!dfs.reached(it)) { |
---|
| 1215 | dfs.addSource(it); |
---|
| 1216 | dfs.start(); |
---|
| 1217 | } |
---|
| 1218 | } |
---|
| 1219 | } |
---|
| 1220 | |
---|
| 1221 | /// \ingroup connectivity |
---|
| 1222 | /// |
---|
| 1223 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
| 1224 | /// |
---|
| 1225 | /// Sort the nodes of a DAG into topolgical order. It also checks |
---|
| 1226 | /// that the given graph is DAG. |
---|
| 1227 | /// |
---|
[425] | 1228 | /// \param digraph The graph. It must be directed and acyclic. |
---|
[417] | 1229 | /// \retval order A readable - writable node map. The values will be set |
---|
| 1230 | /// from 0 to the number of the nodes in the graph minus one. Each values |
---|
| 1231 | /// of the map will be set exactly once, the values will be set descending |
---|
| 1232 | /// order. |
---|
| 1233 | /// \return %False when the graph is not DAG. |
---|
| 1234 | /// |
---|
| 1235 | /// \see topologicalSort |
---|
| 1236 | /// \see dag |
---|
| 1237 | template <typename Digraph, typename NodeMap> |
---|
[419] | 1238 | bool checkedTopologicalSort(const Digraph& digraph, NodeMap& order) { |
---|
| 1239 | using namespace _connectivity_bits; |
---|
[417] | 1240 | |
---|
| 1241 | checkConcept<concepts::Digraph, Digraph>(); |
---|
| 1242 | checkConcept<concepts::ReadWriteMap<typename Digraph::Node, int>, |
---|
| 1243 | NodeMap>(); |
---|
| 1244 | |
---|
| 1245 | typedef typename Digraph::Node Node; |
---|
| 1246 | typedef typename Digraph::NodeIt NodeIt; |
---|
| 1247 | typedef typename Digraph::Arc Arc; |
---|
| 1248 | |
---|
[419] | 1249 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
| 1250 | order.set(it, -1); |
---|
| 1251 | } |
---|
[417] | 1252 | |
---|
| 1253 | TopologicalSortVisitor<Digraph, NodeMap> |
---|
[419] | 1254 | visitor(order, countNodes(digraph)); |
---|
[417] | 1255 | |
---|
| 1256 | DfsVisit<Digraph, TopologicalSortVisitor<Digraph, NodeMap> > |
---|
[419] | 1257 | dfs(digraph, visitor); |
---|
[417] | 1258 | |
---|
| 1259 | dfs.init(); |
---|
[419] | 1260 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
[417] | 1261 | if (!dfs.reached(it)) { |
---|
| 1262 | dfs.addSource(it); |
---|
| 1263 | while (!dfs.emptyQueue()) { |
---|
[419] | 1264 | Arc arc = dfs.nextArc(); |
---|
| 1265 | Node target = digraph.target(arc); |
---|
[417] | 1266 | if (dfs.reached(target) && order[target] == -1) { |
---|
| 1267 | return false; |
---|
| 1268 | } |
---|
| 1269 | dfs.processNextArc(); |
---|
| 1270 | } |
---|
| 1271 | } |
---|
| 1272 | } |
---|
| 1273 | return true; |
---|
| 1274 | } |
---|
| 1275 | |
---|
| 1276 | /// \ingroup connectivity |
---|
| 1277 | /// |
---|
| 1278 | /// \brief Check that the given directed graph is a DAG. |
---|
| 1279 | /// |
---|
| 1280 | /// Check that the given directed graph is a DAG. The DAG is |
---|
| 1281 | /// an Directed Acyclic Digraph. |
---|
| 1282 | /// \return %False when the graph is not DAG. |
---|
| 1283 | /// \see acyclic |
---|
| 1284 | template <typename Digraph> |
---|
[419] | 1285 | bool dag(const Digraph& digraph) { |
---|
[417] | 1286 | |
---|
| 1287 | checkConcept<concepts::Digraph, Digraph>(); |
---|
| 1288 | |
---|
| 1289 | typedef typename Digraph::Node Node; |
---|
| 1290 | typedef typename Digraph::NodeIt NodeIt; |
---|
| 1291 | typedef typename Digraph::Arc Arc; |
---|
| 1292 | |
---|
| 1293 | typedef typename Digraph::template NodeMap<bool> ProcessedMap; |
---|
| 1294 | |
---|
| 1295 | typename Dfs<Digraph>::template SetProcessedMap<ProcessedMap>:: |
---|
[419] | 1296 | Create dfs(digraph); |
---|
[417] | 1297 | |
---|
[419] | 1298 | ProcessedMap processed(digraph); |
---|
[417] | 1299 | dfs.processedMap(processed); |
---|
| 1300 | |
---|
| 1301 | dfs.init(); |
---|
[419] | 1302 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
[417] | 1303 | if (!dfs.reached(it)) { |
---|
| 1304 | dfs.addSource(it); |
---|
| 1305 | while (!dfs.emptyQueue()) { |
---|
| 1306 | Arc edge = dfs.nextArc(); |
---|
[419] | 1307 | Node target = digraph.target(edge); |
---|
[417] | 1308 | if (dfs.reached(target) && !processed[target]) { |
---|
| 1309 | return false; |
---|
| 1310 | } |
---|
| 1311 | dfs.processNextArc(); |
---|
| 1312 | } |
---|
| 1313 | } |
---|
| 1314 | } |
---|
| 1315 | return true; |
---|
| 1316 | } |
---|
| 1317 | |
---|
| 1318 | /// \ingroup connectivity |
---|
| 1319 | /// |
---|
| 1320 | /// \brief Check that the given undirected graph is acyclic. |
---|
| 1321 | /// |
---|
| 1322 | /// Check that the given undirected graph acyclic. |
---|
| 1323 | /// \param graph The undirected graph. |
---|
| 1324 | /// \return %True when there is no circle in the graph. |
---|
| 1325 | /// \see dag |
---|
| 1326 | template <typename Graph> |
---|
| 1327 | bool acyclic(const Graph& graph) { |
---|
| 1328 | checkConcept<concepts::Graph, Graph>(); |
---|
| 1329 | typedef typename Graph::Node Node; |
---|
| 1330 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1331 | typedef typename Graph::Arc Arc; |
---|
| 1332 | Dfs<Graph> dfs(graph); |
---|
| 1333 | dfs.init(); |
---|
| 1334 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1335 | if (!dfs.reached(it)) { |
---|
| 1336 | dfs.addSource(it); |
---|
| 1337 | while (!dfs.emptyQueue()) { |
---|
| 1338 | Arc edge = dfs.nextArc(); |
---|
| 1339 | Node source = graph.source(edge); |
---|
| 1340 | Node target = graph.target(edge); |
---|
| 1341 | if (dfs.reached(target) && |
---|
| 1342 | dfs.predArc(source) != graph.oppositeArc(edge)) { |
---|
| 1343 | return false; |
---|
| 1344 | } |
---|
| 1345 | dfs.processNextArc(); |
---|
| 1346 | } |
---|
| 1347 | } |
---|
| 1348 | } |
---|
| 1349 | return true; |
---|
| 1350 | } |
---|
| 1351 | |
---|
| 1352 | /// \ingroup connectivity |
---|
| 1353 | /// |
---|
| 1354 | /// \brief Check that the given undirected graph is tree. |
---|
| 1355 | /// |
---|
| 1356 | /// Check that the given undirected graph is tree. |
---|
| 1357 | /// \param graph The undirected graph. |
---|
| 1358 | /// \return %True when the graph is acyclic and connected. |
---|
| 1359 | template <typename Graph> |
---|
| 1360 | bool tree(const Graph& graph) { |
---|
| 1361 | checkConcept<concepts::Graph, Graph>(); |
---|
| 1362 | typedef typename Graph::Node Node; |
---|
| 1363 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1364 | typedef typename Graph::Arc Arc; |
---|
| 1365 | Dfs<Graph> dfs(graph); |
---|
| 1366 | dfs.init(); |
---|
| 1367 | dfs.addSource(NodeIt(graph)); |
---|
| 1368 | while (!dfs.emptyQueue()) { |
---|
| 1369 | Arc edge = dfs.nextArc(); |
---|
| 1370 | Node source = graph.source(edge); |
---|
| 1371 | Node target = graph.target(edge); |
---|
| 1372 | if (dfs.reached(target) && |
---|
| 1373 | dfs.predArc(source) != graph.oppositeArc(edge)) { |
---|
| 1374 | return false; |
---|
| 1375 | } |
---|
| 1376 | dfs.processNextArc(); |
---|
| 1377 | } |
---|
| 1378 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1379 | if (!dfs.reached(it)) { |
---|
| 1380 | return false; |
---|
| 1381 | } |
---|
| 1382 | } |
---|
| 1383 | return true; |
---|
| 1384 | } |
---|
| 1385 | |
---|
[419] | 1386 | namespace _connectivity_bits { |
---|
[417] | 1387 | |
---|
| 1388 | template <typename Digraph> |
---|
| 1389 | class BipartiteVisitor : public BfsVisitor<Digraph> { |
---|
| 1390 | public: |
---|
| 1391 | typedef typename Digraph::Arc Arc; |
---|
| 1392 | typedef typename Digraph::Node Node; |
---|
| 1393 | |
---|
| 1394 | BipartiteVisitor(const Digraph& graph, bool& bipartite) |
---|
| 1395 | : _graph(graph), _part(graph), _bipartite(bipartite) {} |
---|
| 1396 | |
---|
| 1397 | void start(const Node& node) { |
---|
| 1398 | _part[node] = true; |
---|
| 1399 | } |
---|
| 1400 | void discover(const Arc& edge) { |
---|
| 1401 | _part.set(_graph.target(edge), !_part[_graph.source(edge)]); |
---|
| 1402 | } |
---|
| 1403 | void examine(const Arc& edge) { |
---|
| 1404 | _bipartite = _bipartite && |
---|
| 1405 | _part[_graph.target(edge)] != _part[_graph.source(edge)]; |
---|
| 1406 | } |
---|
| 1407 | |
---|
| 1408 | private: |
---|
| 1409 | |
---|
| 1410 | const Digraph& _graph; |
---|
| 1411 | typename Digraph::template NodeMap<bool> _part; |
---|
| 1412 | bool& _bipartite; |
---|
| 1413 | }; |
---|
| 1414 | |
---|
| 1415 | template <typename Digraph, typename PartMap> |
---|
| 1416 | class BipartitePartitionsVisitor : public BfsVisitor<Digraph> { |
---|
| 1417 | public: |
---|
| 1418 | typedef typename Digraph::Arc Arc; |
---|
| 1419 | typedef typename Digraph::Node Node; |
---|
| 1420 | |
---|
| 1421 | BipartitePartitionsVisitor(const Digraph& graph, |
---|
| 1422 | PartMap& part, bool& bipartite) |
---|
| 1423 | : _graph(graph), _part(part), _bipartite(bipartite) {} |
---|
| 1424 | |
---|
| 1425 | void start(const Node& node) { |
---|
| 1426 | _part.set(node, true); |
---|
| 1427 | } |
---|
| 1428 | void discover(const Arc& edge) { |
---|
| 1429 | _part.set(_graph.target(edge), !_part[_graph.source(edge)]); |
---|
| 1430 | } |
---|
| 1431 | void examine(const Arc& edge) { |
---|
| 1432 | _bipartite = _bipartite && |
---|
| 1433 | _part[_graph.target(edge)] != _part[_graph.source(edge)]; |
---|
| 1434 | } |
---|
| 1435 | |
---|
| 1436 | private: |
---|
| 1437 | |
---|
| 1438 | const Digraph& _graph; |
---|
| 1439 | PartMap& _part; |
---|
| 1440 | bool& _bipartite; |
---|
| 1441 | }; |
---|
| 1442 | } |
---|
| 1443 | |
---|
| 1444 | /// \ingroup connectivity |
---|
| 1445 | /// |
---|
| 1446 | /// \brief Check if the given undirected graph is bipartite or not |
---|
| 1447 | /// |
---|
| 1448 | /// The function checks if the given undirected \c graph graph is bipartite |
---|
| 1449 | /// or not. The \ref Bfs algorithm is used to calculate the result. |
---|
| 1450 | /// \param graph The undirected graph. |
---|
| 1451 | /// \return %True if \c graph is bipartite, %false otherwise. |
---|
| 1452 | /// \sa bipartitePartitions |
---|
| 1453 | template<typename Graph> |
---|
| 1454 | inline bool bipartite(const Graph &graph){ |
---|
[419] | 1455 | using namespace _connectivity_bits; |
---|
[417] | 1456 | |
---|
| 1457 | checkConcept<concepts::Graph, Graph>(); |
---|
| 1458 | |
---|
| 1459 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1460 | typedef typename Graph::ArcIt ArcIt; |
---|
| 1461 | |
---|
| 1462 | bool bipartite = true; |
---|
| 1463 | |
---|
| 1464 | BipartiteVisitor<Graph> |
---|
| 1465 | visitor(graph, bipartite); |
---|
| 1466 | BfsVisit<Graph, BipartiteVisitor<Graph> > |
---|
| 1467 | bfs(graph, visitor); |
---|
| 1468 | bfs.init(); |
---|
| 1469 | for(NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1470 | if(!bfs.reached(it)){ |
---|
| 1471 | bfs.addSource(it); |
---|
| 1472 | while (!bfs.emptyQueue()) { |
---|
| 1473 | bfs.processNextNode(); |
---|
| 1474 | if (!bipartite) return false; |
---|
| 1475 | } |
---|
| 1476 | } |
---|
| 1477 | } |
---|
| 1478 | return true; |
---|
| 1479 | } |
---|
| 1480 | |
---|
| 1481 | /// \ingroup connectivity |
---|
| 1482 | /// |
---|
| 1483 | /// \brief Check if the given undirected graph is bipartite or not |
---|
| 1484 | /// |
---|
| 1485 | /// The function checks if the given undirected graph is bipartite |
---|
| 1486 | /// or not. The \ref Bfs algorithm is used to calculate the result. |
---|
| 1487 | /// During the execution, the \c partMap will be set as the two |
---|
| 1488 | /// partitions of the graph. |
---|
| 1489 | /// \param graph The undirected graph. |
---|
| 1490 | /// \retval partMap A writable bool map of nodes. It will be set as the |
---|
| 1491 | /// two partitions of the graph. |
---|
| 1492 | /// \return %True if \c graph is bipartite, %false otherwise. |
---|
| 1493 | template<typename Graph, typename NodeMap> |
---|
| 1494 | inline bool bipartitePartitions(const Graph &graph, NodeMap &partMap){ |
---|
[419] | 1495 | using namespace _connectivity_bits; |
---|
[417] | 1496 | |
---|
| 1497 | checkConcept<concepts::Graph, Graph>(); |
---|
| 1498 | |
---|
| 1499 | typedef typename Graph::Node Node; |
---|
| 1500 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1501 | typedef typename Graph::ArcIt ArcIt; |
---|
| 1502 | |
---|
| 1503 | bool bipartite = true; |
---|
| 1504 | |
---|
| 1505 | BipartitePartitionsVisitor<Graph, NodeMap> |
---|
| 1506 | visitor(graph, partMap, bipartite); |
---|
| 1507 | BfsVisit<Graph, BipartitePartitionsVisitor<Graph, NodeMap> > |
---|
| 1508 | bfs(graph, visitor); |
---|
| 1509 | bfs.init(); |
---|
| 1510 | for(NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1511 | if(!bfs.reached(it)){ |
---|
| 1512 | bfs.addSource(it); |
---|
| 1513 | while (!bfs.emptyQueue()) { |
---|
| 1514 | bfs.processNextNode(); |
---|
| 1515 | if (!bipartite) return false; |
---|
| 1516 | } |
---|
| 1517 | } |
---|
| 1518 | } |
---|
| 1519 | return true; |
---|
| 1520 | } |
---|
| 1521 | |
---|
| 1522 | /// \brief Returns true when there are not loop edges in the graph. |
---|
| 1523 | /// |
---|
| 1524 | /// Returns true when there are not loop edges in the graph. |
---|
| 1525 | template <typename Digraph> |
---|
[419] | 1526 | bool loopFree(const Digraph& digraph) { |
---|
| 1527 | for (typename Digraph::ArcIt it(digraph); it != INVALID; ++it) { |
---|
| 1528 | if (digraph.source(it) == digraph.target(it)) return false; |
---|
[417] | 1529 | } |
---|
| 1530 | return true; |
---|
| 1531 | } |
---|
| 1532 | |
---|
| 1533 | /// \brief Returns true when there are not parallel edges in the graph. |
---|
| 1534 | /// |
---|
| 1535 | /// Returns true when there are not parallel edges in the graph. |
---|
| 1536 | template <typename Digraph> |
---|
[419] | 1537 | bool parallelFree(const Digraph& digraph) { |
---|
| 1538 | typename Digraph::template NodeMap<bool> reached(digraph, false); |
---|
| 1539 | for (typename Digraph::NodeIt n(digraph); n != INVALID; ++n) { |
---|
| 1540 | for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) { |
---|
| 1541 | if (reached[digraph.target(a)]) return false; |
---|
| 1542 | reached.set(digraph.target(a), true); |
---|
[417] | 1543 | } |
---|
[419] | 1544 | for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) { |
---|
| 1545 | reached.set(digraph.target(a), false); |
---|
[417] | 1546 | } |
---|
| 1547 | } |
---|
| 1548 | return true; |
---|
| 1549 | } |
---|
| 1550 | |
---|
| 1551 | /// \brief Returns true when there are not loop edges and parallel |
---|
| 1552 | /// edges in the graph. |
---|
| 1553 | /// |
---|
| 1554 | /// Returns true when there are not loop edges and parallel edges in |
---|
| 1555 | /// the graph. |
---|
| 1556 | template <typename Digraph> |
---|
[419] | 1557 | bool simpleDigraph(const Digraph& digraph) { |
---|
| 1558 | typename Digraph::template NodeMap<bool> reached(digraph, false); |
---|
| 1559 | for (typename Digraph::NodeIt n(digraph); n != INVALID; ++n) { |
---|
[417] | 1560 | reached.set(n, true); |
---|
[419] | 1561 | for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) { |
---|
| 1562 | if (reached[digraph.target(a)]) return false; |
---|
| 1563 | reached.set(digraph.target(a), true); |
---|
[417] | 1564 | } |
---|
[419] | 1565 | for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) { |
---|
| 1566 | reached.set(digraph.target(a), false); |
---|
[417] | 1567 | } |
---|
| 1568 | reached.set(n, false); |
---|
| 1569 | } |
---|
| 1570 | return true; |
---|
| 1571 | } |
---|
| 1572 | |
---|
| 1573 | } //namespace lemon |
---|
| 1574 | |
---|
[419] | 1575 | #endif //LEMON_CONNECTIVITY_H |
---|