| 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) 2003-2008 |
| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
| 8 | * |
| 9 | * Permission to use, modify and distribute this software is granted |
| 10 | * provided that this copyright notice appears in all copies. For |
| 11 | * precise terms see the accompanying LICENSE file. |
| 12 | * |
| 13 | * This software is provided "AS IS" with no warranty of any kind, |
| 14 | * express or implied, and with no claim as to its suitability for any |
| 15 | * purpose. |
| 16 | * |
| 17 | */ |
| 18 | |
| 19 | #ifndef LEMON_MIN_COST_ARBORESCENCE_H |
| 20 | #define LEMON_MIN_COST_ARBORESCENCE_H |
| 21 | |
| 22 | ///\ingroup spantree |
| 23 | ///\file |
| 24 | ///\brief Minimum Cost Arborescence algorithm. |
| 25 | |
| 26 | #include <vector> |
| 27 | |
| 28 | #include <lemon/list_graph.h> |
| 29 | #include <lemon/bin_heap.h> |
| 30 | #include <lemon/assert.h> |
| 31 | |
| 32 | namespace lemon { |
| 33 | |
| 34 | |
| 35 | /// \brief Default traits class for MinCostArborescence class. |
| 36 | /// |
| 37 | /// Default traits class for MinCostArborescence class. |
| 38 | /// \param _Digraph Digraph type. |
| 39 | /// \param _CostMap Type of cost map. |
| 40 | template <class _Digraph, class _CostMap> |
| 41 | struct MinCostArborescenceDefaultTraits{ |
| 42 | |
| 43 | /// \brief The digraph type the algorithm runs on. |
| 44 | typedef _Digraph Digraph; |
| 45 | |
| 46 | /// \brief The type of the map that stores the arc costs. |
| 47 | /// |
| 48 | /// The type of the map that stores the arc costs. |
| 49 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
| 50 | typedef _CostMap CostMap; |
| 51 | |
| 52 | /// \brief The value type of the costs. |
| 53 | /// |
| 54 | /// The value type of the costs. |
| 55 | typedef typename CostMap::Value Value; |
| 56 | |
| 57 | /// \brief The type of the map that stores which arcs are in the |
| 58 | /// arborescence. |
| 59 | /// |
| 60 | /// The type of the map that stores which arcs are in the |
| 61 | /// arborescence. It must meet the \ref concepts::WriteMap |
| 62 | /// "WriteMap" concept. Initially it will be set to false on each |
| 63 | /// arc. After it will set all arborescence arcs once. |
| 64 | typedef typename Digraph::template ArcMap<bool> ArborescenceMap; |
| 65 | |
| 66 | /// \brief Instantiates a ArborescenceMap. |
| 67 | /// |
| 68 | /// This function instantiates a \ref ArborescenceMap. |
| 69 | /// \param digraph is the graph, to which we would like to |
| 70 | /// calculate the ArborescenceMap. |
| 71 | static ArborescenceMap *createArborescenceMap(const Digraph &digraph){ |
| 72 | return new ArborescenceMap(digraph); |
| 73 | } |
| 74 | |
| 75 | /// \brief The type of the PredMap |
| 76 | /// |
| 77 | /// The type of the PredMap. It is a node map with an arc value type. |
| 78 | typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap; |
| 79 | |
| 80 | /// \brief Instantiates a PredMap. |
| 81 | /// |
| 82 | /// This function instantiates a \ref PredMap. |
| 83 | /// \param _digraph is the digraph, to which we would like to define the |
| 84 | /// PredMap. |
| 85 | static PredMap *createPredMap(const Digraph &digraph){ |
| 86 | return new PredMap(digraph); |
| 87 | } |
| 88 | |
| 89 | }; |
| 90 | |
| 91 | /// \ingroup spantree |
| 92 | /// |
| 93 | /// \brief %MinCostArborescence algorithm class. |
| 94 | /// |
| 95 | /// This class provides an efficient implementation of |
| 96 | /// %MinCostArborescence algorithm. The arborescence is a tree |
| 97 | /// which is directed from a given source node of the digraph. One or |
| 98 | /// more sources should be given for the algorithm and it will calculate |
| 99 | /// the minimum cost subgraph which are union of arborescences with the |
| 100 | /// given sources and spans all the nodes which are reachable from the |
| 101 | /// sources. The time complexity of the algorithm is \f$ O(n^2+e) \f$. |
| 102 | /// |
| 103 | /// The algorithm provides also an optimal dual solution, therefore |
| 104 | /// the optimality of the solution can be checked. |
| 105 | /// |
| 106 | /// \param _Digraph The digraph type the algorithm runs on. The default value |
| 107 | /// is \ref ListDigraph. |
| 108 | /// \param _CostMap This read-only ArcMap determines the costs of the |
| 109 | /// arcs. It is read once for each arc, so the map may involve in |
| 110 | /// relatively time consuming process to compute the arc cost if |
| 111 | /// it is necessary. The default map type is \ref |
| 112 | /// concepts::Digraph::ArcMap "Digraph::ArcMap<int>". |
| 113 | /// \param _Traits Traits class to set various data types used |
| 114 | /// by the algorithm. The default traits class is |
| 115 | /// \ref MinCostArborescenceDefaultTraits |
| 116 | /// "MinCostArborescenceDefaultTraits<_Digraph, _CostMap>". See \ref |
| 117 | /// MinCostArborescenceDefaultTraits for the documentation of a |
| 118 | /// MinCostArborescence traits class. |
| 119 | /// |
| 120 | /// \author Balazs Dezso |
| 121 | #ifndef DOXYGEN |
| 122 | template <typename _Digraph = ListDigraph, |
| 123 | typename _CostMap = typename _Digraph::template ArcMap<int>, |
| 124 | typename _Traits = |
| 125 | MinCostArborescenceDefaultTraits<_Digraph, _CostMap> > |
| 126 | #else |
| 127 | template <typename _Digraph, typename _CostMap, typedef _Traits> |
| 128 | #endif |
| 129 | class MinCostArborescence { |
| 130 | public: |
| 131 | |
| 132 | /// The traits. |
| 133 | typedef _Traits Traits; |
| 134 | /// The type of the underlying digraph. |
| 135 | typedef typename Traits::Digraph Digraph; |
| 136 | /// The type of the map that stores the arc costs. |
| 137 | typedef typename Traits::CostMap CostMap; |
| 138 | ///The type of the costs of the arcs. |
| 139 | typedef typename Traits::Value Value; |
| 140 | ///The type of the predecessor map. |
| 141 | typedef typename Traits::PredMap PredMap; |
| 142 | ///The type of the map that stores which arcs are in the arborescence. |
| 143 | typedef typename Traits::ArborescenceMap ArborescenceMap; |
| 144 | |
| 145 | typedef MinCostArborescence Create; |
| 146 | |
| 147 | private: |
| 148 | |
| 149 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
| 150 | |
| 151 | struct CostArc { |
| 152 | |
| 153 | Arc arc; |
| 154 | Value value; |
| 155 | |
| 156 | CostArc() {} |
| 157 | CostArc(Arc _arc, Value _value) : arc(_arc), value(_value) {} |
| 158 | |
| 159 | }; |
| 160 | |
| 161 | const Digraph *_digraph; |
| 162 | const CostMap *_cost; |
| 163 | |
| 164 | PredMap *_pred; |
| 165 | bool local_pred; |
| 166 | |
| 167 | ArborescenceMap *_arborescence; |
| 168 | bool local_arborescence; |
| 169 | |
| 170 | typedef typename Digraph::template ArcMap<int> ArcOrder; |
| 171 | ArcOrder *_arc_order; |
| 172 | |
| 173 | typedef typename Digraph::template NodeMap<int> NodeOrder; |
| 174 | NodeOrder *_node_order; |
| 175 | |
| 176 | typedef typename Digraph::template NodeMap<CostArc> CostArcMap; |
| 177 | CostArcMap *_cost_arcs; |
| 178 | |
| 179 | struct StackLevel { |
| 180 | |
| 181 | std::vector<CostArc> arcs; |
| 182 | int node_level; |
| 183 | |
| 184 | }; |
| 185 | |
| 186 | std::vector<StackLevel> level_stack; |
| 187 | std::vector<Node> queue; |
| 188 | |
| 189 | typedef std::vector<typename Digraph::Node> DualNodeList; |
| 190 | |
| 191 | DualNodeList _dual_node_list; |
| 192 | |
| 193 | struct DualVariable { |
| 194 | int begin, end; |
| 195 | Value value; |
| 196 | |
| 197 | DualVariable(int _begin, int _end, Value _value) |
| 198 | : begin(_begin), end(_end), value(_value) {} |
| 199 | |
| 200 | }; |
| 201 | |
| 202 | typedef std::vector<DualVariable> DualVariables; |
| 203 | |
| 204 | DualVariables _dual_variables; |
| 205 | |
| 206 | typedef typename Digraph::template NodeMap<int> HeapCrossRef; |
| 207 | |
| 208 | HeapCrossRef *_heap_cross_ref; |
| 209 | |
| 210 | typedef BinHeap<int, HeapCrossRef> Heap; |
| 211 | |
| 212 | Heap *_heap; |
| 213 | |
| 214 | protected: |
| 215 | |
| 216 | MinCostArborescence() {} |
| 217 | |
| 218 | private: |
| 219 | |
| 220 | void createStructures() { |
| 221 | if (!_pred) { |
| 222 | local_pred = true; |
| 223 | _pred = Traits::createPredMap(*_digraph); |
| 224 | } |
| 225 | if (!_arborescence) { |
| 226 | local_arborescence = true; |
| 227 | _arborescence = Traits::createArborescenceMap(*_digraph); |
| 228 | } |
| 229 | if (!_arc_order) { |
| 230 | _arc_order = new ArcOrder(*_digraph); |
| 231 | } |
| 232 | if (!_node_order) { |
| 233 | _node_order = new NodeOrder(*_digraph); |
| 234 | } |
| 235 | if (!_cost_arcs) { |
| 236 | _cost_arcs = new CostArcMap(*_digraph); |
| 237 | } |
| 238 | if (!_heap_cross_ref) { |
| 239 | _heap_cross_ref = new HeapCrossRef(*_digraph, -1); |
| 240 | } |
| 241 | if (!_heap) { |
| 242 | _heap = new Heap(*_heap_cross_ref); |
| 243 | } |
| 244 | } |
| 245 | |
| 246 | void destroyStructures() { |
| 247 | if (local_arborescence) { |
| 248 | delete _arborescence; |
| 249 | } |
| 250 | if (local_pred) { |
| 251 | delete _pred; |
| 252 | } |
| 253 | if (_arc_order) { |
| 254 | delete _arc_order; |
| 255 | } |
| 256 | if (_node_order) { |
| 257 | delete _node_order; |
| 258 | } |
| 259 | if (_cost_arcs) { |
| 260 | delete _cost_arcs; |
| 261 | } |
| 262 | if (_heap) { |
| 263 | delete _heap; |
| 264 | } |
| 265 | if (_heap_cross_ref) { |
| 266 | delete _heap_cross_ref; |
| 267 | } |
| 268 | } |
| 269 | |
| 270 | Arc prepare(Node node) { |
| 271 | std::vector<Node> nodes; |
| 272 | (*_node_order)[node] = _dual_node_list.size(); |
| 273 | StackLevel level; |
| 274 | level.node_level = _dual_node_list.size(); |
| 275 | _dual_node_list.push_back(node); |
| 276 | for (InArcIt it(*_digraph, node); it != INVALID; ++it) { |
| 277 | Arc arc = it; |
| 278 | Node source = _digraph->source(arc); |
| 279 | Value value = (*_cost)[it]; |
| 280 | if (source == node || (*_node_order)[source] == -3) continue; |
| 281 | if ((*_cost_arcs)[source].arc == INVALID) { |
| 282 | (*_cost_arcs)[source].arc = arc; |
| 283 | (*_cost_arcs)[source].value = value; |
| 284 | nodes.push_back(source); |
| 285 | } else { |
| 286 | if ((*_cost_arcs)[source].value > value) { |
| 287 | (*_cost_arcs)[source].arc = arc; |
| 288 | (*_cost_arcs)[source].value = value; |
| 289 | } |
| 290 | } |
| 291 | } |
| 292 | CostArc minimum = (*_cost_arcs)[nodes[0]]; |
| 293 | for (int i = 1; i < int(nodes.size()); ++i) { |
| 294 | if ((*_cost_arcs)[nodes[i]].value < minimum.value) { |
| 295 | minimum = (*_cost_arcs)[nodes[i]]; |
| 296 | } |
| 297 | } |
| 298 | _arc_order->set(minimum.arc, _dual_variables.size()); |
| 299 | DualVariable var(_dual_node_list.size() - 1, |
| 300 | _dual_node_list.size(), minimum.value); |
| 301 | _dual_variables.push_back(var); |
| 302 | for (int i = 0; i < int(nodes.size()); ++i) { |
| 303 | (*_cost_arcs)[nodes[i]].value -= minimum.value; |
| 304 | level.arcs.push_back((*_cost_arcs)[nodes[i]]); |
| 305 | (*_cost_arcs)[nodes[i]].arc = INVALID; |
| 306 | } |
| 307 | level_stack.push_back(level); |
| 308 | return minimum.arc; |
| 309 | } |
| 310 | |
| 311 | Arc contract(Node node) { |
| 312 | int node_bottom = bottom(node); |
| 313 | std::vector<Node> nodes; |
| 314 | while (!level_stack.empty() && |
| 315 | level_stack.back().node_level >= node_bottom) { |
| 316 | for (int i = 0; i < int(level_stack.back().arcs.size()); ++i) { |
| 317 | Arc arc = level_stack.back().arcs[i].arc; |
| 318 | Node source = _digraph->source(arc); |
| 319 | Value value = level_stack.back().arcs[i].value; |
| 320 | if ((*_node_order)[source] >= node_bottom) continue; |
| 321 | if ((*_cost_arcs)[source].arc == INVALID) { |
| 322 | (*_cost_arcs)[source].arc = arc; |
| 323 | (*_cost_arcs)[source].value = value; |
| 324 | nodes.push_back(source); |
| 325 | } else { |
| 326 | if ((*_cost_arcs)[source].value > value) { |
| 327 | (*_cost_arcs)[source].arc = arc; |
| 328 | (*_cost_arcs)[source].value = value; |
| 329 | } |
| 330 | } |
| 331 | } |
| 332 | level_stack.pop_back(); |
| 333 | } |
| 334 | CostArc minimum = (*_cost_arcs)[nodes[0]]; |
| 335 | for (int i = 1; i < int(nodes.size()); ++i) { |
| 336 | if ((*_cost_arcs)[nodes[i]].value < minimum.value) { |
| 337 | minimum = (*_cost_arcs)[nodes[i]]; |
| 338 | } |
| 339 | } |
| 340 | _arc_order->set(minimum.arc, _dual_variables.size()); |
| 341 | DualVariable var(node_bottom, _dual_node_list.size(), minimum.value); |
| 342 | _dual_variables.push_back(var); |
| 343 | StackLevel level; |
| 344 | level.node_level = node_bottom; |
| 345 | for (int i = 0; i < int(nodes.size()); ++i) { |
| 346 | (*_cost_arcs)[nodes[i]].value -= minimum.value; |
| 347 | level.arcs.push_back((*_cost_arcs)[nodes[i]]); |
| 348 | (*_cost_arcs)[nodes[i]].arc = INVALID; |
| 349 | } |
| 350 | level_stack.push_back(level); |
| 351 | return minimum.arc; |
| 352 | } |
| 353 | |
| 354 | int bottom(Node node) { |
| 355 | int k = level_stack.size() - 1; |
| 356 | while (level_stack[k].node_level > (*_node_order)[node]) { |
| 357 | --k; |
| 358 | } |
| 359 | return level_stack[k].node_level; |
| 360 | } |
| 361 | |
| 362 | void finalize(Arc arc) { |
| 363 | Node node = _digraph->target(arc); |
| 364 | _heap->push(node, (*_arc_order)[arc]); |
| 365 | _pred->set(node, arc); |
| 366 | while (!_heap->empty()) { |
| 367 | Node source = _heap->top(); |
| 368 | _heap->pop(); |
| 369 | _node_order->set(source, -1); |
| 370 | for (OutArcIt it(*_digraph, source); it != INVALID; ++it) { |
| 371 | if ((*_arc_order)[it] < 0) continue; |
| 372 | Node target = _digraph->target(it); |
| 373 | switch(_heap->state(target)) { |
| 374 | case Heap::PRE_HEAP: |
| 375 | _heap->push(target, (*_arc_order)[it]); |
| 376 | _pred->set(target, it); |
| 377 | break; |
| 378 | case Heap::IN_HEAP: |
| 379 | if ((*_arc_order)[it] < (*_heap)[target]) { |
| 380 | _heap->decrease(target, (*_arc_order)[it]); |
| 381 | _pred->set(target, it); |
| 382 | } |
| 383 | break; |
| 384 | case Heap::POST_HEAP: |
| 385 | break; |
| 386 | } |
| 387 | } |
| 388 | _arborescence->set((*_pred)[source], true); |
| 389 | } |
| 390 | } |
| 391 | |
| 392 | |
| 393 | public: |
| 394 | |
| 395 | /// \name Named template parameters |
| 396 | |
| 397 | /// @{ |
| 398 | |
| 399 | template <class T> |
| 400 | struct DefArborescenceMapTraits : public Traits { |
| 401 | typedef T ArborescenceMap; |
| 402 | static ArborescenceMap *createArborescenceMap(const Digraph &) |
| 403 | { |
| 404 | LEMON_ASSERT(false, "ArborescenceMap is not initialized"); |
| 405 | return 0; // ignore warnings |
| 406 | } |
| 407 | }; |
| 408 | |
| 409 | /// \brief \ref named-templ-param "Named parameter" for |
| 410 | /// setting ArborescenceMap type |
| 411 | /// |
| 412 | /// \ref named-templ-param "Named parameter" for setting |
| 413 | /// ArborescenceMap type |
| 414 | template <class T> |
| 415 | struct DefArborescenceMap |
| 416 | : public MinCostArborescence<Digraph, CostMap, |
| 417 | DefArborescenceMapTraits<T> > { |
| 418 | }; |
| 419 | |
| 420 | template <class T> |
| 421 | struct DefPredMapTraits : public Traits { |
| 422 | typedef T PredMap; |
| 423 | static PredMap *createPredMap(const Digraph &) |
| 424 | { |
| 425 | LEMON_ASSERT(false, "PredMap is not initialized"); |
| 426 | } |
| 427 | }; |
| 428 | |
| 429 | /// \brief \ref named-templ-param "Named parameter" for |
| 430 | /// setting PredMap type |
| 431 | /// |
| 432 | /// \ref named-templ-param "Named parameter" for setting |
| 433 | /// PredMap type |
| 434 | template <class T> |
| 435 | struct DefPredMap |
| 436 | : public MinCostArborescence<Digraph, CostMap, DefPredMapTraits<T> > { |
| 437 | }; |
| 438 | |
| 439 | /// @} |
| 440 | |
| 441 | /// \brief Constructor. |
| 442 | /// |
| 443 | /// \param _digraph The digraph the algorithm will run on. |
| 444 | /// \param _cost The cost map used by the algorithm. |
| 445 | MinCostArborescence(const Digraph& digraph, const CostMap& cost) |
| 446 | : _digraph(&digraph), _cost(&cost), _pred(0), local_pred(false), |
| 447 | _arborescence(0), local_arborescence(false), |
| 448 | _arc_order(0), _node_order(0), _cost_arcs(0), |
| 449 | _heap_cross_ref(0), _heap(0) {} |
| 450 | |
| 451 | /// \brief Destructor. |
| 452 | ~MinCostArborescence() { |
| 453 | destroyStructures(); |
| 454 | } |
| 455 | |
| 456 | /// \brief Sets the arborescence map. |
| 457 | /// |
| 458 | /// Sets the arborescence map. |
| 459 | /// \return \c (*this) |
| 460 | MinCostArborescence& arborescenceMap(ArborescenceMap& m) { |
| 461 | if (local_arborescence) { |
| 462 | delete _arborescence; |
| 463 | } |
| 464 | local_arborescence = false; |
| 465 | _arborescence = &m; |
| 466 | return *this; |
| 467 | } |
| 468 | |
| 469 | /// \brief Sets the arborescence map. |
| 470 | /// |
| 471 | /// Sets the arborescence map. |
| 472 | /// \return \c (*this) |
| 473 | MinCostArborescence& predMap(PredMap& m) { |
| 474 | if (local_pred) { |
| 475 | delete _pred; |
| 476 | } |
| 477 | local_pred = false; |
| 478 | _pred = &m; |
| 479 | return *this; |
| 480 | } |
| 481 | |
| 482 | /// \name Query Functions |
| 483 | /// The result of the %MinCostArborescence algorithm can be obtained |
| 484 | /// using these functions.\n |
| 485 | /// Before the use of these functions, |
| 486 | /// either run() or start() must be called. |
| 487 | |
| 488 | /// @{ |
| 489 | |
| 490 | /// \brief Returns a reference to the arborescence map. |
| 491 | /// |
| 492 | /// Returns a reference to the arborescence map. |
| 493 | const ArborescenceMap& arborescenceMap() const { |
| 494 | return *_arborescence; |
| 495 | } |
| 496 | |
| 497 | /// \brief Returns true if the arc is in the arborescence. |
| 498 | /// |
| 499 | /// Returns true if the arc is in the arborescence. |
| 500 | /// \param arc The arc of the digraph. |
| 501 | /// \pre \ref run() must be called before using this function. |
| 502 | bool arborescence(Arc arc) const { |
| 503 | return (*_pred)[_digraph->target(arc)] == arc; |
| 504 | } |
| 505 | |
| 506 | /// \brief Returns a reference to the pred map. |
| 507 | /// |
| 508 | /// Returns a reference to the pred map. |
| 509 | const PredMap& predMap() const { |
| 510 | return *_pred; |
| 511 | } |
| 512 | |
| 513 | /// \brief Returns the predecessor arc of the given node. |
| 514 | /// |
| 515 | /// Returns the predecessor arc of the given node. |
| 516 | Arc pred(Node node) const { |
| 517 | return (*_pred)[node]; |
| 518 | } |
| 519 | |
| 520 | /// \brief Returns the cost of the arborescence. |
| 521 | /// |
| 522 | /// Returns the cost of the arborescence. |
| 523 | Value arborescenceValue() const { |
| 524 | Value sum = 0; |
| 525 | for (ArcIt it(*_digraph); it != INVALID; ++it) { |
| 526 | if (arborescence(it)) { |
| 527 | sum += (*_cost)[it]; |
| 528 | } |
| 529 | } |
| 530 | return sum; |
| 531 | } |
| 532 | |
| 533 | /// \brief Indicates that a node is reachable from the sources. |
| 534 | /// |
| 535 | /// Indicates that a node is reachable from the sources. |
| 536 | bool reached(Node node) const { |
| 537 | return (*_node_order)[node] != -3; |
| 538 | } |
| 539 | |
| 540 | /// \brief Indicates that a node is processed. |
| 541 | /// |
| 542 | /// Indicates that a node is processed. The arborescence path exists |
| 543 | /// from the source to the given node. |
| 544 | bool processed(Node node) const { |
| 545 | return (*_node_order)[node] == -1; |
| 546 | } |
| 547 | |
| 548 | /// \brief Returns the number of the dual variables in basis. |
| 549 | /// |
| 550 | /// Returns the number of the dual variables in basis. |
| 551 | int dualNum() const { |
| 552 | return _dual_variables.size(); |
| 553 | } |
| 554 | |
| 555 | /// \brief Returns the value of the dual solution. |
| 556 | /// |
| 557 | /// Returns the value of the dual solution. It should be |
| 558 | /// equal to the arborescence value. |
| 559 | Value dualValue() const { |
| 560 | Value sum = 0; |
| 561 | for (int i = 0; i < int(_dual_variables.size()); ++i) { |
| 562 | sum += _dual_variables[i].value; |
| 563 | } |
| 564 | return sum; |
| 565 | } |
| 566 | |
| 567 | /// \brief Returns the number of the nodes in the dual variable. |
| 568 | /// |
| 569 | /// Returns the number of the nodes in the dual variable. |
| 570 | int dualSize(int k) const { |
| 571 | return _dual_variables[k].end - _dual_variables[k].begin; |
| 572 | } |
| 573 | |
| 574 | /// \brief Returns the value of the dual variable. |
| 575 | /// |
| 576 | /// Returns the the value of the dual variable. |
| 577 | const Value& dualValue(int k) const { |
| 578 | return _dual_variables[k].value; |
| 579 | } |
| 580 | |
| 581 | /// \brief Lemon iterator for get a dual variable. |
| 582 | /// |
| 583 | /// Lemon iterator for get a dual variable. This class provides |
| 584 | /// a common style lemon iterator which gives back a subset of |
| 585 | /// the nodes. |
| 586 | class DualIt { |
| 587 | public: |
| 588 | |
| 589 | /// \brief Constructor. |
| 590 | /// |
| 591 | /// Constructor for get the nodeset of the variable. |
| 592 | DualIt(const MinCostArborescence& algorithm, int variable) |
| 593 | : _algorithm(&algorithm) |
| 594 | { |
| 595 | _index = _algorithm->_dual_variables[variable].begin; |
| 596 | _last = _algorithm->_dual_variables[variable].end; |
| 597 | } |
| 598 | |
| 599 | /// \brief Conversion to node. |
| 600 | /// |
| 601 | /// Conversion to node. |
| 602 | operator Node() const { |
| 603 | return _algorithm->_dual_node_list[_index]; |
| 604 | } |
| 605 | |
| 606 | /// \brief Increment operator. |
| 607 | /// |
| 608 | /// Increment operator. |
| 609 | DualIt& operator++() { |
| 610 | ++_index; |
| 611 | return *this; |
| 612 | } |
| 613 | |
| 614 | /// \brief Validity checking |
| 615 | /// |
| 616 | /// Checks whether the iterator is invalid. |
| 617 | bool operator==(Invalid) const { |
| 618 | return _index == _last; |
| 619 | } |
| 620 | |
| 621 | /// \brief Validity checking |
| 622 | /// |
| 623 | /// Checks whether the iterator is valid. |
| 624 | bool operator!=(Invalid) const { |
| 625 | return _index != _last; |
| 626 | } |
| 627 | |
| 628 | private: |
| 629 | const MinCostArborescence* _algorithm; |
| 630 | int _index, _last; |
| 631 | }; |
| 632 | |
| 633 | /// @} |
| 634 | |
| 635 | /// \name Execution control |
| 636 | /// The simplest way to execute the algorithm is to use |
| 637 | /// one of the member functions called \c run(...). \n |
| 638 | /// If you need more control on the execution, |
| 639 | /// first you must call \ref init(), then you can add several |
| 640 | /// source nodes with \ref addSource(). |
| 641 | /// Finally \ref start() will perform the arborescence |
| 642 | /// computation. |
| 643 | |
| 644 | ///@{ |
| 645 | |
| 646 | /// \brief Initializes the internal data structures. |
| 647 | /// |
| 648 | /// Initializes the internal data structures. |
| 649 | /// |
| 650 | void init() { |
| 651 | createStructures(); |
| 652 | _heap->clear(); |
| 653 | for (NodeIt it(*_digraph); it != INVALID; ++it) { |
| 654 | (*_cost_arcs)[it].arc = INVALID; |
| 655 | _node_order->set(it, -3); |
| 656 | _heap_cross_ref->set(it, Heap::PRE_HEAP); |
| 657 | _pred->set(it, INVALID); |
| 658 | } |
| 659 | for (ArcIt it(*_digraph); it != INVALID; ++it) { |
| 660 | _arborescence->set(it, false); |
| 661 | _arc_order->set(it, -1); |
| 662 | } |
| 663 | _dual_node_list.clear(); |
| 664 | _dual_variables.clear(); |
| 665 | } |
| 666 | |
| 667 | /// \brief Adds a new source node. |
| 668 | /// |
| 669 | /// Adds a new source node to the algorithm. |
| 670 | void addSource(Node source) { |
| 671 | std::vector<Node> nodes; |
| 672 | nodes.push_back(source); |
| 673 | while (!nodes.empty()) { |
| 674 | Node node = nodes.back(); |
| 675 | nodes.pop_back(); |
| 676 | for (OutArcIt it(*_digraph, node); it != INVALID; ++it) { |
| 677 | Node target = _digraph->target(it); |
| 678 | if ((*_node_order)[target] == -3) { |
| 679 | (*_node_order)[target] = -2; |
| 680 | nodes.push_back(target); |
| 681 | queue.push_back(target); |
| 682 | } |
| 683 | } |
| 684 | } |
| 685 | (*_node_order)[source] = -1; |
| 686 | } |
| 687 | |
| 688 | /// \brief Processes the next node in the priority queue. |
| 689 | /// |
| 690 | /// Processes the next node in the priority queue. |
| 691 | /// |
| 692 | /// \return The processed node. |
| 693 | /// |
| 694 | /// \warning The queue must not be empty! |
| 695 | Node processNextNode() { |
| 696 | Node node = queue.back(); |
| 697 | queue.pop_back(); |
| 698 | if ((*_node_order)[node] == -2) { |
| 699 | Arc arc = prepare(node); |
| 700 | Node source = _digraph->source(arc); |
| 701 | while ((*_node_order)[source] != -1) { |
| 702 | if ((*_node_order)[source] >= 0) { |
| 703 | arc = contract(source); |
| 704 | } else { |
| 705 | arc = prepare(source); |
| 706 | } |
| 707 | source = _digraph->source(arc); |
| 708 | } |
| 709 | finalize(arc); |
| 710 | level_stack.clear(); |
| 711 | } |
| 712 | return node; |
| 713 | } |
| 714 | |
| 715 | /// \brief Returns the number of the nodes to be processed. |
| 716 | /// |
| 717 | /// Returns the number of the nodes to be processed. |
| 718 | int queueSize() const { |
| 719 | return queue.size(); |
| 720 | } |
| 721 | |
| 722 | /// \brief Returns \c false if there are nodes to be processed. |
| 723 | /// |
| 724 | /// Returns \c false if there are nodes to be processed. |
| 725 | bool emptyQueue() const { |
| 726 | return queue.empty(); |
| 727 | } |
| 728 | |
| 729 | /// \brief Executes the algorithm. |
| 730 | /// |
| 731 | /// Executes the algorithm. |
| 732 | /// |
| 733 | /// \pre init() must be called and at least one node should be added |
| 734 | /// with addSource() before using this function. |
| 735 | /// |
| 736 | ///\note mca.start() is just a shortcut of the following code. |
| 737 | ///\code |
| 738 | ///while (!mca.emptyQueue()) { |
| 739 | /// mca.processNextNode(); |
| 740 | ///} |
| 741 | ///\endcode |
| 742 | void start() { |
| 743 | while (!emptyQueue()) { |
| 744 | processNextNode(); |
| 745 | } |
| 746 | } |
| 747 | |
| 748 | /// \brief Runs %MinCostArborescence algorithm from node \c s. |
| 749 | /// |
| 750 | /// This method runs the %MinCostArborescence algorithm from |
| 751 | /// a root node \c s. |
| 752 | /// |
| 753 | /// \note mca.run(s) is just a shortcut of the following code. |
| 754 | /// \code |
| 755 | /// mca.init(); |
| 756 | /// mca.addSource(s); |
| 757 | /// mca.start(); |
| 758 | /// \endcode |
| 759 | void run(Node node) { |
| 760 | init(); |
| 761 | addSource(node); |
| 762 | start(); |
| 763 | } |
| 764 | |
| 765 | ///@} |
| 766 | |
| 767 | }; |
| 768 | |
| 769 | /// \ingroup spantree |
| 770 | /// |
| 771 | /// \brief Function type interface for MinCostArborescence algorithm. |
| 772 | /// |
| 773 | /// Function type interface for MinCostArborescence algorithm. |
| 774 | /// \param digraph The Digraph that the algorithm runs on. |
| 775 | /// \param cost The CostMap of the arcs. |
| 776 | /// \param source The source of the arborescence. |
| 777 | /// \retval arborescence The bool ArcMap which stores the arborescence. |
| 778 | /// \return The cost of the arborescence. |
| 779 | /// |
| 780 | /// \sa MinCostArborescence |
| 781 | template <typename Digraph, typename CostMap, typename ArborescenceMap> |
| 782 | typename CostMap::Value minCostArborescence(const Digraph& digraph, |
| 783 | const CostMap& cost, |
| 784 | typename Digraph::Node source, |
| 785 | ArborescenceMap& arborescence) { |
| 786 | typename MinCostArborescence<Digraph, CostMap> |
| 787 | ::template DefArborescenceMap<ArborescenceMap> |
| 788 | ::Create mca(digraph, cost); |
| 789 | mca.arborescenceMap(arborescence); |
| 790 | mca.run(source); |
| 791 | return mca.arborescenceValue(); |
| 792 | } |
| 793 | |
| 794 | } |
| 795 | |
| 796 | #endif |