[522] | 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. |
---|
[606] | 38 | /// \param GR Digraph type. |
---|
[672] | 39 | /// \param CM Type of the cost map. |
---|
[606] | 40 | template <class GR, class CM> |
---|
[522] | 41 | struct MinCostArborescenceDefaultTraits{ |
---|
| 42 | |
---|
| 43 | /// \brief The digraph type the algorithm runs on. |
---|
[606] | 44 | typedef GR Digraph; |
---|
[522] | 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. |
---|
[672] | 49 | /// It must conform to the \ref concepts::ReadMap "ReadMap" concept. |
---|
[606] | 50 | typedef CM CostMap; |
---|
[522] | 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 |
---|
[672] | 61 | /// arborescence. It must conform to the \ref concepts::WriteMap |
---|
| 62 | /// "WriteMap" concept, and its value type must be \c bool |
---|
| 63 | /// (or convertible). Initially it will be set to \c false on each |
---|
| 64 | /// arc, then it will be set on each arborescence arc once. |
---|
[522] | 65 | typedef typename Digraph::template ArcMap<bool> ArborescenceMap; |
---|
| 66 | |
---|
[606] | 67 | /// \brief Instantiates a \c ArborescenceMap. |
---|
[522] | 68 | /// |
---|
[606] | 69 | /// This function instantiates a \c ArborescenceMap. |
---|
[672] | 70 | /// \param digraph The digraph to which we would like to calculate |
---|
| 71 | /// the \c ArborescenceMap. |
---|
[522] | 72 | static ArborescenceMap *createArborescenceMap(const Digraph &digraph){ |
---|
| 73 | return new ArborescenceMap(digraph); |
---|
| 74 | } |
---|
| 75 | |
---|
[606] | 76 | /// \brief The type of the \c PredMap |
---|
[522] | 77 | /// |
---|
[672] | 78 | /// The type of the \c PredMap. It must confrom to the |
---|
| 79 | /// \ref concepts::WriteMap "WriteMap" concept, and its value type |
---|
| 80 | /// must be the \c Arc type of the digraph. |
---|
[522] | 81 | typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap; |
---|
| 82 | |
---|
[606] | 83 | /// \brief Instantiates a \c PredMap. |
---|
[522] | 84 | /// |
---|
[606] | 85 | /// This function instantiates a \c PredMap. |
---|
| 86 | /// \param digraph The digraph to which we would like to define the |
---|
| 87 | /// \c PredMap. |
---|
[522] | 88 | static PredMap *createPredMap(const Digraph &digraph){ |
---|
| 89 | return new PredMap(digraph); |
---|
| 90 | } |
---|
| 91 | |
---|
| 92 | }; |
---|
| 93 | |
---|
| 94 | /// \ingroup spantree |
---|
| 95 | /// |
---|
[631] | 96 | /// \brief Minimum Cost Arborescence algorithm class. |
---|
[522] | 97 | /// |
---|
[672] | 98 | /// This class provides an efficient implementation of the |
---|
[631] | 99 | /// Minimum Cost Arborescence algorithm. The arborescence is a tree |
---|
[522] | 100 | /// which is directed from a given source node of the digraph. One or |
---|
[672] | 101 | /// more sources should be given to the algorithm and it will calculate |
---|
| 102 | /// the minimum cost subgraph that is the union of arborescences with the |
---|
[522] | 103 | /// given sources and spans all the nodes which are reachable from the |
---|
[606] | 104 | /// sources. The time complexity of the algorithm is O(n<sup>2</sup>+e). |
---|
[522] | 105 | /// |
---|
[672] | 106 | /// The algorithm also provides an optimal dual solution, therefore |
---|
[522] | 107 | /// the optimality of the solution can be checked. |
---|
| 108 | /// |
---|
[672] | 109 | /// \param GR The digraph type the algorithm runs on. |
---|
| 110 | /// \param CM A read-only arc map storing the costs of the |
---|
[522] | 111 | /// arcs. It is read once for each arc, so the map may involve in |
---|
[672] | 112 | /// relatively time consuming process to compute the arc costs if |
---|
[522] | 113 | /// it is necessary. The default map type is \ref |
---|
| 114 | /// concepts::Digraph::ArcMap "Digraph::ArcMap<int>". |
---|
[606] | 115 | /// \param TR Traits class to set various data types used |
---|
[522] | 116 | /// by the algorithm. The default traits class is |
---|
| 117 | /// \ref MinCostArborescenceDefaultTraits |
---|
[672] | 118 | /// "MinCostArborescenceDefaultTraits<GR, CM>". |
---|
[522] | 119 | #ifndef DOXYGEN |
---|
[672] | 120 | template <typename GR, |
---|
[606] | 121 | typename CM = typename GR::template ArcMap<int>, |
---|
| 122 | typename TR = |
---|
| 123 | MinCostArborescenceDefaultTraits<GR, CM> > |
---|
[522] | 124 | #else |
---|
[606] | 125 | template <typename GR, typename CM, typedef TR> |
---|
[522] | 126 | #endif |
---|
| 127 | class MinCostArborescence { |
---|
| 128 | public: |
---|
| 129 | |
---|
[672] | 130 | /// \brief The \ref MinCostArborescenceDefaultTraits "traits class" |
---|
| 131 | /// of the algorithm. |
---|
[606] | 132 | typedef TR Traits; |
---|
[522] | 133 | /// The type of the underlying digraph. |
---|
| 134 | typedef typename Traits::Digraph Digraph; |
---|
| 135 | /// The type of the map that stores the arc costs. |
---|
| 136 | typedef typename Traits::CostMap CostMap; |
---|
| 137 | ///The type of the costs of the arcs. |
---|
| 138 | typedef typename Traits::Value Value; |
---|
| 139 | ///The type of the predecessor map. |
---|
| 140 | typedef typename Traits::PredMap PredMap; |
---|
| 141 | ///The type of the map that stores which arcs are in the arborescence. |
---|
| 142 | typedef typename Traits::ArborescenceMap ArborescenceMap; |
---|
| 143 | |
---|
| 144 | typedef MinCostArborescence Create; |
---|
| 145 | |
---|
| 146 | private: |
---|
| 147 | |
---|
| 148 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
---|
| 149 | |
---|
| 150 | struct CostArc { |
---|
| 151 | |
---|
| 152 | Arc arc; |
---|
| 153 | Value value; |
---|
| 154 | |
---|
| 155 | CostArc() {} |
---|
| 156 | CostArc(Arc _arc, Value _value) : arc(_arc), value(_value) {} |
---|
| 157 | |
---|
| 158 | }; |
---|
| 159 | |
---|
| 160 | const Digraph *_digraph; |
---|
| 161 | const CostMap *_cost; |
---|
| 162 | |
---|
| 163 | PredMap *_pred; |
---|
| 164 | bool local_pred; |
---|
| 165 | |
---|
| 166 | ArborescenceMap *_arborescence; |
---|
| 167 | bool local_arborescence; |
---|
| 168 | |
---|
| 169 | typedef typename Digraph::template ArcMap<int> ArcOrder; |
---|
| 170 | ArcOrder *_arc_order; |
---|
| 171 | |
---|
| 172 | typedef typename Digraph::template NodeMap<int> NodeOrder; |
---|
| 173 | NodeOrder *_node_order; |
---|
| 174 | |
---|
| 175 | typedef typename Digraph::template NodeMap<CostArc> CostArcMap; |
---|
| 176 | CostArcMap *_cost_arcs; |
---|
| 177 | |
---|
| 178 | struct StackLevel { |
---|
| 179 | |
---|
| 180 | std::vector<CostArc> arcs; |
---|
| 181 | int node_level; |
---|
| 182 | |
---|
| 183 | }; |
---|
| 184 | |
---|
| 185 | std::vector<StackLevel> level_stack; |
---|
| 186 | std::vector<Node> queue; |
---|
| 187 | |
---|
| 188 | typedef std::vector<typename Digraph::Node> DualNodeList; |
---|
| 189 | |
---|
| 190 | DualNodeList _dual_node_list; |
---|
| 191 | |
---|
| 192 | struct DualVariable { |
---|
| 193 | int begin, end; |
---|
| 194 | Value value; |
---|
| 195 | |
---|
| 196 | DualVariable(int _begin, int _end, Value _value) |
---|
| 197 | : begin(_begin), end(_end), value(_value) {} |
---|
| 198 | |
---|
| 199 | }; |
---|
| 200 | |
---|
| 201 | typedef std::vector<DualVariable> DualVariables; |
---|
| 202 | |
---|
| 203 | DualVariables _dual_variables; |
---|
| 204 | |
---|
| 205 | typedef typename Digraph::template NodeMap<int> HeapCrossRef; |
---|
| 206 | |
---|
| 207 | HeapCrossRef *_heap_cross_ref; |
---|
| 208 | |
---|
| 209 | typedef BinHeap<int, HeapCrossRef> Heap; |
---|
| 210 | |
---|
| 211 | Heap *_heap; |
---|
| 212 | |
---|
| 213 | protected: |
---|
| 214 | |
---|
| 215 | MinCostArborescence() {} |
---|
| 216 | |
---|
| 217 | private: |
---|
| 218 | |
---|
| 219 | void createStructures() { |
---|
| 220 | if (!_pred) { |
---|
| 221 | local_pred = true; |
---|
| 222 | _pred = Traits::createPredMap(*_digraph); |
---|
| 223 | } |
---|
| 224 | if (!_arborescence) { |
---|
| 225 | local_arborescence = true; |
---|
| 226 | _arborescence = Traits::createArborescenceMap(*_digraph); |
---|
| 227 | } |
---|
| 228 | if (!_arc_order) { |
---|
| 229 | _arc_order = new ArcOrder(*_digraph); |
---|
| 230 | } |
---|
| 231 | if (!_node_order) { |
---|
| 232 | _node_order = new NodeOrder(*_digraph); |
---|
| 233 | } |
---|
| 234 | if (!_cost_arcs) { |
---|
| 235 | _cost_arcs = new CostArcMap(*_digraph); |
---|
| 236 | } |
---|
| 237 | if (!_heap_cross_ref) { |
---|
| 238 | _heap_cross_ref = new HeapCrossRef(*_digraph, -1); |
---|
| 239 | } |
---|
| 240 | if (!_heap) { |
---|
| 241 | _heap = new Heap(*_heap_cross_ref); |
---|
| 242 | } |
---|
| 243 | } |
---|
| 244 | |
---|
| 245 | void destroyStructures() { |
---|
| 246 | if (local_arborescence) { |
---|
| 247 | delete _arborescence; |
---|
| 248 | } |
---|
| 249 | if (local_pred) { |
---|
| 250 | delete _pred; |
---|
| 251 | } |
---|
| 252 | if (_arc_order) { |
---|
| 253 | delete _arc_order; |
---|
| 254 | } |
---|
| 255 | if (_node_order) { |
---|
| 256 | delete _node_order; |
---|
| 257 | } |
---|
| 258 | if (_cost_arcs) { |
---|
| 259 | delete _cost_arcs; |
---|
| 260 | } |
---|
| 261 | if (_heap) { |
---|
| 262 | delete _heap; |
---|
| 263 | } |
---|
| 264 | if (_heap_cross_ref) { |
---|
| 265 | delete _heap_cross_ref; |
---|
| 266 | } |
---|
| 267 | } |
---|
| 268 | |
---|
| 269 | Arc prepare(Node node) { |
---|
| 270 | std::vector<Node> nodes; |
---|
| 271 | (*_node_order)[node] = _dual_node_list.size(); |
---|
| 272 | StackLevel level; |
---|
| 273 | level.node_level = _dual_node_list.size(); |
---|
| 274 | _dual_node_list.push_back(node); |
---|
| 275 | for (InArcIt it(*_digraph, node); it != INVALID; ++it) { |
---|
| 276 | Arc arc = it; |
---|
| 277 | Node source = _digraph->source(arc); |
---|
| 278 | Value value = (*_cost)[it]; |
---|
| 279 | if (source == node || (*_node_order)[source] == -3) continue; |
---|
| 280 | if ((*_cost_arcs)[source].arc == INVALID) { |
---|
| 281 | (*_cost_arcs)[source].arc = arc; |
---|
| 282 | (*_cost_arcs)[source].value = value; |
---|
| 283 | nodes.push_back(source); |
---|
| 284 | } else { |
---|
| 285 | if ((*_cost_arcs)[source].value > value) { |
---|
| 286 | (*_cost_arcs)[source].arc = arc; |
---|
| 287 | (*_cost_arcs)[source].value = value; |
---|
| 288 | } |
---|
| 289 | } |
---|
| 290 | } |
---|
| 291 | CostArc minimum = (*_cost_arcs)[nodes[0]]; |
---|
| 292 | for (int i = 1; i < int(nodes.size()); ++i) { |
---|
| 293 | if ((*_cost_arcs)[nodes[i]].value < minimum.value) { |
---|
| 294 | minimum = (*_cost_arcs)[nodes[i]]; |
---|
| 295 | } |
---|
| 296 | } |
---|
[628] | 297 | (*_arc_order)[minimum.arc] = _dual_variables.size(); |
---|
[522] | 298 | DualVariable var(_dual_node_list.size() - 1, |
---|
| 299 | _dual_node_list.size(), minimum.value); |
---|
| 300 | _dual_variables.push_back(var); |
---|
| 301 | for (int i = 0; i < int(nodes.size()); ++i) { |
---|
| 302 | (*_cost_arcs)[nodes[i]].value -= minimum.value; |
---|
| 303 | level.arcs.push_back((*_cost_arcs)[nodes[i]]); |
---|
| 304 | (*_cost_arcs)[nodes[i]].arc = INVALID; |
---|
| 305 | } |
---|
| 306 | level_stack.push_back(level); |
---|
| 307 | return minimum.arc; |
---|
| 308 | } |
---|
| 309 | |
---|
| 310 | Arc contract(Node node) { |
---|
| 311 | int node_bottom = bottom(node); |
---|
| 312 | std::vector<Node> nodes; |
---|
| 313 | while (!level_stack.empty() && |
---|
| 314 | level_stack.back().node_level >= node_bottom) { |
---|
| 315 | for (int i = 0; i < int(level_stack.back().arcs.size()); ++i) { |
---|
| 316 | Arc arc = level_stack.back().arcs[i].arc; |
---|
| 317 | Node source = _digraph->source(arc); |
---|
| 318 | Value value = level_stack.back().arcs[i].value; |
---|
| 319 | if ((*_node_order)[source] >= node_bottom) continue; |
---|
| 320 | if ((*_cost_arcs)[source].arc == INVALID) { |
---|
| 321 | (*_cost_arcs)[source].arc = arc; |
---|
| 322 | (*_cost_arcs)[source].value = value; |
---|
| 323 | nodes.push_back(source); |
---|
| 324 | } else { |
---|
| 325 | if ((*_cost_arcs)[source].value > value) { |
---|
| 326 | (*_cost_arcs)[source].arc = arc; |
---|
| 327 | (*_cost_arcs)[source].value = value; |
---|
| 328 | } |
---|
| 329 | } |
---|
| 330 | } |
---|
| 331 | level_stack.pop_back(); |
---|
| 332 | } |
---|
| 333 | CostArc minimum = (*_cost_arcs)[nodes[0]]; |
---|
| 334 | for (int i = 1; i < int(nodes.size()); ++i) { |
---|
| 335 | if ((*_cost_arcs)[nodes[i]].value < minimum.value) { |
---|
| 336 | minimum = (*_cost_arcs)[nodes[i]]; |
---|
| 337 | } |
---|
| 338 | } |
---|
[628] | 339 | (*_arc_order)[minimum.arc] = _dual_variables.size(); |
---|
[522] | 340 | DualVariable var(node_bottom, _dual_node_list.size(), minimum.value); |
---|
| 341 | _dual_variables.push_back(var); |
---|
| 342 | StackLevel level; |
---|
| 343 | level.node_level = node_bottom; |
---|
| 344 | for (int i = 0; i < int(nodes.size()); ++i) { |
---|
| 345 | (*_cost_arcs)[nodes[i]].value -= minimum.value; |
---|
| 346 | level.arcs.push_back((*_cost_arcs)[nodes[i]]); |
---|
| 347 | (*_cost_arcs)[nodes[i]].arc = INVALID; |
---|
| 348 | } |
---|
| 349 | level_stack.push_back(level); |
---|
| 350 | return minimum.arc; |
---|
| 351 | } |
---|
| 352 | |
---|
| 353 | int bottom(Node node) { |
---|
| 354 | int k = level_stack.size() - 1; |
---|
| 355 | while (level_stack[k].node_level > (*_node_order)[node]) { |
---|
| 356 | --k; |
---|
| 357 | } |
---|
| 358 | return level_stack[k].node_level; |
---|
| 359 | } |
---|
| 360 | |
---|
| 361 | void finalize(Arc arc) { |
---|
| 362 | Node node = _digraph->target(arc); |
---|
| 363 | _heap->push(node, (*_arc_order)[arc]); |
---|
| 364 | _pred->set(node, arc); |
---|
| 365 | while (!_heap->empty()) { |
---|
| 366 | Node source = _heap->top(); |
---|
| 367 | _heap->pop(); |
---|
[628] | 368 | (*_node_order)[source] = -1; |
---|
[522] | 369 | for (OutArcIt it(*_digraph, source); it != INVALID; ++it) { |
---|
| 370 | if ((*_arc_order)[it] < 0) continue; |
---|
| 371 | Node target = _digraph->target(it); |
---|
| 372 | switch(_heap->state(target)) { |
---|
| 373 | case Heap::PRE_HEAP: |
---|
| 374 | _heap->push(target, (*_arc_order)[it]); |
---|
| 375 | _pred->set(target, it); |
---|
| 376 | break; |
---|
| 377 | case Heap::IN_HEAP: |
---|
| 378 | if ((*_arc_order)[it] < (*_heap)[target]) { |
---|
| 379 | _heap->decrease(target, (*_arc_order)[it]); |
---|
| 380 | _pred->set(target, it); |
---|
| 381 | } |
---|
| 382 | break; |
---|
| 383 | case Heap::POST_HEAP: |
---|
| 384 | break; |
---|
| 385 | } |
---|
| 386 | } |
---|
| 387 | _arborescence->set((*_pred)[source], true); |
---|
| 388 | } |
---|
| 389 | } |
---|
| 390 | |
---|
| 391 | |
---|
| 392 | public: |
---|
| 393 | |
---|
[631] | 394 | /// \name Named Template Parameters |
---|
[522] | 395 | |
---|
| 396 | /// @{ |
---|
| 397 | |
---|
| 398 | template <class T> |
---|
[672] | 399 | struct SetArborescenceMapTraits : public Traits { |
---|
[522] | 400 | typedef T ArborescenceMap; |
---|
| 401 | static ArborescenceMap *createArborescenceMap(const Digraph &) |
---|
| 402 | { |
---|
| 403 | LEMON_ASSERT(false, "ArborescenceMap is not initialized"); |
---|
| 404 | return 0; // ignore warnings |
---|
| 405 | } |
---|
| 406 | }; |
---|
| 407 | |
---|
| 408 | /// \brief \ref named-templ-param "Named parameter" for |
---|
[672] | 409 | /// setting \c ArborescenceMap type |
---|
[522] | 410 | /// |
---|
| 411 | /// \ref named-templ-param "Named parameter" for setting |
---|
[672] | 412 | /// \c ArborescenceMap type. |
---|
| 413 | /// It must conform to the \ref concepts::WriteMap "WriteMap" concept, |
---|
| 414 | /// and its value type must be \c bool (or convertible). |
---|
| 415 | /// Initially it will be set to \c false on each arc, |
---|
| 416 | /// then it will be set on each arborescence arc once. |
---|
[522] | 417 | template <class T> |
---|
[672] | 418 | struct SetArborescenceMap |
---|
[522] | 419 | : public MinCostArborescence<Digraph, CostMap, |
---|
[672] | 420 | SetArborescenceMapTraits<T> > { |
---|
[522] | 421 | }; |
---|
| 422 | |
---|
| 423 | template <class T> |
---|
[672] | 424 | struct SetPredMapTraits : public Traits { |
---|
[522] | 425 | typedef T PredMap; |
---|
| 426 | static PredMap *createPredMap(const Digraph &) |
---|
| 427 | { |
---|
| 428 | LEMON_ASSERT(false, "PredMap is not initialized"); |
---|
[672] | 429 | return 0; // ignore warnings |
---|
[522] | 430 | } |
---|
| 431 | }; |
---|
| 432 | |
---|
| 433 | /// \brief \ref named-templ-param "Named parameter" for |
---|
[672] | 434 | /// setting \c PredMap type |
---|
[522] | 435 | /// |
---|
| 436 | /// \ref named-templ-param "Named parameter" for setting |
---|
[672] | 437 | /// \c PredMap type. |
---|
| 438 | /// It must meet the \ref concepts::WriteMap "WriteMap" concept, |
---|
| 439 | /// and its value type must be the \c Arc type of the digraph. |
---|
[522] | 440 | template <class T> |
---|
[672] | 441 | struct SetPredMap |
---|
| 442 | : public MinCostArborescence<Digraph, CostMap, SetPredMapTraits<T> > { |
---|
[522] | 443 | }; |
---|
| 444 | |
---|
| 445 | /// @} |
---|
| 446 | |
---|
| 447 | /// \brief Constructor. |
---|
| 448 | /// |
---|
[606] | 449 | /// \param digraph The digraph the algorithm will run on. |
---|
| 450 | /// \param cost The cost map used by the algorithm. |
---|
[522] | 451 | MinCostArborescence(const Digraph& digraph, const CostMap& cost) |
---|
| 452 | : _digraph(&digraph), _cost(&cost), _pred(0), local_pred(false), |
---|
| 453 | _arborescence(0), local_arborescence(false), |
---|
| 454 | _arc_order(0), _node_order(0), _cost_arcs(0), |
---|
| 455 | _heap_cross_ref(0), _heap(0) {} |
---|
| 456 | |
---|
| 457 | /// \brief Destructor. |
---|
| 458 | ~MinCostArborescence() { |
---|
| 459 | destroyStructures(); |
---|
| 460 | } |
---|
| 461 | |
---|
| 462 | /// \brief Sets the arborescence map. |
---|
| 463 | /// |
---|
| 464 | /// Sets the arborescence map. |
---|
[606] | 465 | /// \return <tt>(*this)</tt> |
---|
[522] | 466 | MinCostArborescence& arborescenceMap(ArborescenceMap& m) { |
---|
| 467 | if (local_arborescence) { |
---|
| 468 | delete _arborescence; |
---|
| 469 | } |
---|
| 470 | local_arborescence = false; |
---|
| 471 | _arborescence = &m; |
---|
| 472 | return *this; |
---|
| 473 | } |
---|
| 474 | |
---|
[672] | 475 | /// \brief Sets the predecessor map. |
---|
[522] | 476 | /// |
---|
[672] | 477 | /// Sets the predecessor map. |
---|
[606] | 478 | /// \return <tt>(*this)</tt> |
---|
[522] | 479 | MinCostArborescence& predMap(PredMap& m) { |
---|
| 480 | if (local_pred) { |
---|
| 481 | delete _pred; |
---|
| 482 | } |
---|
| 483 | local_pred = false; |
---|
| 484 | _pred = &m; |
---|
| 485 | return *this; |
---|
| 486 | } |
---|
| 487 | |
---|
[631] | 488 | /// \name Execution Control |
---|
[522] | 489 | /// The simplest way to execute the algorithm is to use |
---|
| 490 | /// one of the member functions called \c run(...). \n |
---|
| 491 | /// If you need more control on the execution, |
---|
| 492 | /// first you must call \ref init(), then you can add several |
---|
| 493 | /// source nodes with \ref addSource(). |
---|
| 494 | /// Finally \ref start() will perform the arborescence |
---|
| 495 | /// computation. |
---|
| 496 | |
---|
| 497 | ///@{ |
---|
| 498 | |
---|
| 499 | /// \brief Initializes the internal data structures. |
---|
| 500 | /// |
---|
| 501 | /// Initializes the internal data structures. |
---|
| 502 | /// |
---|
| 503 | void init() { |
---|
| 504 | createStructures(); |
---|
| 505 | _heap->clear(); |
---|
| 506 | for (NodeIt it(*_digraph); it != INVALID; ++it) { |
---|
| 507 | (*_cost_arcs)[it].arc = INVALID; |
---|
[628] | 508 | (*_node_order)[it] = -3; |
---|
| 509 | (*_heap_cross_ref)[it] = Heap::PRE_HEAP; |
---|
[522] | 510 | _pred->set(it, INVALID); |
---|
| 511 | } |
---|
| 512 | for (ArcIt it(*_digraph); it != INVALID; ++it) { |
---|
| 513 | _arborescence->set(it, false); |
---|
[628] | 514 | (*_arc_order)[it] = -1; |
---|
[522] | 515 | } |
---|
| 516 | _dual_node_list.clear(); |
---|
| 517 | _dual_variables.clear(); |
---|
| 518 | } |
---|
| 519 | |
---|
| 520 | /// \brief Adds a new source node. |
---|
| 521 | /// |
---|
| 522 | /// Adds a new source node to the algorithm. |
---|
| 523 | void addSource(Node source) { |
---|
| 524 | std::vector<Node> nodes; |
---|
| 525 | nodes.push_back(source); |
---|
| 526 | while (!nodes.empty()) { |
---|
| 527 | Node node = nodes.back(); |
---|
| 528 | nodes.pop_back(); |
---|
| 529 | for (OutArcIt it(*_digraph, node); it != INVALID; ++it) { |
---|
| 530 | Node target = _digraph->target(it); |
---|
| 531 | if ((*_node_order)[target] == -3) { |
---|
| 532 | (*_node_order)[target] = -2; |
---|
| 533 | nodes.push_back(target); |
---|
| 534 | queue.push_back(target); |
---|
| 535 | } |
---|
| 536 | } |
---|
| 537 | } |
---|
| 538 | (*_node_order)[source] = -1; |
---|
| 539 | } |
---|
| 540 | |
---|
| 541 | /// \brief Processes the next node in the priority queue. |
---|
| 542 | /// |
---|
| 543 | /// Processes the next node in the priority queue. |
---|
| 544 | /// |
---|
| 545 | /// \return The processed node. |
---|
| 546 | /// |
---|
[672] | 547 | /// \warning The queue must not be empty. |
---|
[522] | 548 | Node processNextNode() { |
---|
| 549 | Node node = queue.back(); |
---|
| 550 | queue.pop_back(); |
---|
| 551 | if ((*_node_order)[node] == -2) { |
---|
| 552 | Arc arc = prepare(node); |
---|
| 553 | Node source = _digraph->source(arc); |
---|
| 554 | while ((*_node_order)[source] != -1) { |
---|
| 555 | if ((*_node_order)[source] >= 0) { |
---|
| 556 | arc = contract(source); |
---|
| 557 | } else { |
---|
| 558 | arc = prepare(source); |
---|
| 559 | } |
---|
| 560 | source = _digraph->source(arc); |
---|
| 561 | } |
---|
| 562 | finalize(arc); |
---|
| 563 | level_stack.clear(); |
---|
| 564 | } |
---|
| 565 | return node; |
---|
| 566 | } |
---|
| 567 | |
---|
| 568 | /// \brief Returns the number of the nodes to be processed. |
---|
| 569 | /// |
---|
[672] | 570 | /// Returns the number of the nodes to be processed in the priority |
---|
| 571 | /// queue. |
---|
[522] | 572 | int queueSize() const { |
---|
| 573 | return queue.size(); |
---|
| 574 | } |
---|
| 575 | |
---|
| 576 | /// \brief Returns \c false if there are nodes to be processed. |
---|
| 577 | /// |
---|
| 578 | /// Returns \c false if there are nodes to be processed. |
---|
| 579 | bool emptyQueue() const { |
---|
| 580 | return queue.empty(); |
---|
| 581 | } |
---|
| 582 | |
---|
| 583 | /// \brief Executes the algorithm. |
---|
| 584 | /// |
---|
| 585 | /// Executes the algorithm. |
---|
| 586 | /// |
---|
| 587 | /// \pre init() must be called and at least one node should be added |
---|
| 588 | /// with addSource() before using this function. |
---|
| 589 | /// |
---|
| 590 | ///\note mca.start() is just a shortcut of the following code. |
---|
| 591 | ///\code |
---|
| 592 | ///while (!mca.emptyQueue()) { |
---|
| 593 | /// mca.processNextNode(); |
---|
| 594 | ///} |
---|
| 595 | ///\endcode |
---|
| 596 | void start() { |
---|
| 597 | while (!emptyQueue()) { |
---|
| 598 | processNextNode(); |
---|
| 599 | } |
---|
| 600 | } |
---|
| 601 | |
---|
| 602 | /// \brief Runs %MinCostArborescence algorithm from node \c s. |
---|
| 603 | /// |
---|
| 604 | /// This method runs the %MinCostArborescence algorithm from |
---|
| 605 | /// a root node \c s. |
---|
| 606 | /// |
---|
| 607 | /// \note mca.run(s) is just a shortcut of the following code. |
---|
| 608 | /// \code |
---|
| 609 | /// mca.init(); |
---|
| 610 | /// mca.addSource(s); |
---|
| 611 | /// mca.start(); |
---|
| 612 | /// \endcode |
---|
[672] | 613 | void run(Node s) { |
---|
[522] | 614 | init(); |
---|
[672] | 615 | addSource(s); |
---|
[522] | 616 | start(); |
---|
| 617 | } |
---|
| 618 | |
---|
| 619 | ///@} |
---|
| 620 | |
---|
[672] | 621 | /// \name Query Functions |
---|
| 622 | /// The result of the %MinCostArborescence algorithm can be obtained |
---|
| 623 | /// using these functions.\n |
---|
| 624 | /// Either run() or start() must be called before using them. |
---|
| 625 | |
---|
| 626 | /// @{ |
---|
| 627 | |
---|
| 628 | /// \brief Returns the cost of the arborescence. |
---|
| 629 | /// |
---|
| 630 | /// Returns the cost of the arborescence. |
---|
| 631 | Value arborescenceCost() const { |
---|
| 632 | Value sum = 0; |
---|
| 633 | for (ArcIt it(*_digraph); it != INVALID; ++it) { |
---|
| 634 | if (arborescence(it)) { |
---|
| 635 | sum += (*_cost)[it]; |
---|
| 636 | } |
---|
| 637 | } |
---|
| 638 | return sum; |
---|
| 639 | } |
---|
| 640 | |
---|
| 641 | /// \brief Returns \c true if the arc is in the arborescence. |
---|
| 642 | /// |
---|
| 643 | /// Returns \c true if the given arc is in the arborescence. |
---|
| 644 | /// \param arc An arc of the digraph. |
---|
| 645 | /// \pre \ref run() must be called before using this function. |
---|
| 646 | bool arborescence(Arc arc) const { |
---|
| 647 | return (*_pred)[_digraph->target(arc)] == arc; |
---|
| 648 | } |
---|
| 649 | |
---|
| 650 | /// \brief Returns a const reference to the arborescence map. |
---|
| 651 | /// |
---|
| 652 | /// Returns a const reference to the arborescence map. |
---|
| 653 | /// \pre \ref run() must be called before using this function. |
---|
| 654 | const ArborescenceMap& arborescenceMap() const { |
---|
| 655 | return *_arborescence; |
---|
| 656 | } |
---|
| 657 | |
---|
| 658 | /// \brief Returns the predecessor arc of the given node. |
---|
| 659 | /// |
---|
| 660 | /// Returns the predecessor arc of the given node. |
---|
| 661 | /// \pre \ref run() must be called before using this function. |
---|
| 662 | Arc pred(Node node) const { |
---|
| 663 | return (*_pred)[node]; |
---|
| 664 | } |
---|
| 665 | |
---|
| 666 | /// \brief Returns a const reference to the pred map. |
---|
| 667 | /// |
---|
| 668 | /// Returns a const reference to the pred map. |
---|
| 669 | /// \pre \ref run() must be called before using this function. |
---|
| 670 | const PredMap& predMap() const { |
---|
| 671 | return *_pred; |
---|
| 672 | } |
---|
| 673 | |
---|
| 674 | /// \brief Indicates that a node is reachable from the sources. |
---|
| 675 | /// |
---|
| 676 | /// Indicates that a node is reachable from the sources. |
---|
| 677 | bool reached(Node node) const { |
---|
| 678 | return (*_node_order)[node] != -3; |
---|
| 679 | } |
---|
| 680 | |
---|
| 681 | /// \brief Indicates that a node is processed. |
---|
| 682 | /// |
---|
| 683 | /// Indicates that a node is processed. The arborescence path exists |
---|
| 684 | /// from the source to the given node. |
---|
| 685 | bool processed(Node node) const { |
---|
| 686 | return (*_node_order)[node] == -1; |
---|
| 687 | } |
---|
| 688 | |
---|
| 689 | /// \brief Returns the number of the dual variables in basis. |
---|
| 690 | /// |
---|
| 691 | /// Returns the number of the dual variables in basis. |
---|
| 692 | int dualNum() const { |
---|
| 693 | return _dual_variables.size(); |
---|
| 694 | } |
---|
| 695 | |
---|
| 696 | /// \brief Returns the value of the dual solution. |
---|
| 697 | /// |
---|
| 698 | /// Returns the value of the dual solution. It should be |
---|
| 699 | /// equal to the arborescence value. |
---|
| 700 | Value dualValue() const { |
---|
| 701 | Value sum = 0; |
---|
| 702 | for (int i = 0; i < int(_dual_variables.size()); ++i) { |
---|
| 703 | sum += _dual_variables[i].value; |
---|
| 704 | } |
---|
| 705 | return sum; |
---|
| 706 | } |
---|
| 707 | |
---|
| 708 | /// \brief Returns the number of the nodes in the dual variable. |
---|
| 709 | /// |
---|
| 710 | /// Returns the number of the nodes in the dual variable. |
---|
| 711 | int dualSize(int k) const { |
---|
| 712 | return _dual_variables[k].end - _dual_variables[k].begin; |
---|
| 713 | } |
---|
| 714 | |
---|
| 715 | /// \brief Returns the value of the dual variable. |
---|
| 716 | /// |
---|
| 717 | /// Returns the the value of the dual variable. |
---|
| 718 | Value dualValue(int k) const { |
---|
| 719 | return _dual_variables[k].value; |
---|
| 720 | } |
---|
| 721 | |
---|
| 722 | /// \brief LEMON iterator for getting a dual variable. |
---|
| 723 | /// |
---|
| 724 | /// This class provides a common style LEMON iterator for getting a |
---|
| 725 | /// dual variable of \ref MinCostArborescence algorithm. |
---|
| 726 | /// It iterates over a subset of the nodes. |
---|
| 727 | class DualIt { |
---|
| 728 | public: |
---|
| 729 | |
---|
| 730 | /// \brief Constructor. |
---|
| 731 | /// |
---|
| 732 | /// Constructor for getting the nodeset of the dual variable |
---|
| 733 | /// of \ref MinCostArborescence algorithm. |
---|
| 734 | DualIt(const MinCostArborescence& algorithm, int variable) |
---|
| 735 | : _algorithm(&algorithm) |
---|
| 736 | { |
---|
| 737 | _index = _algorithm->_dual_variables[variable].begin; |
---|
| 738 | _last = _algorithm->_dual_variables[variable].end; |
---|
| 739 | } |
---|
| 740 | |
---|
| 741 | /// \brief Conversion to \c Node. |
---|
| 742 | /// |
---|
| 743 | /// Conversion to \c Node. |
---|
| 744 | operator Node() const { |
---|
| 745 | return _algorithm->_dual_node_list[_index]; |
---|
| 746 | } |
---|
| 747 | |
---|
| 748 | /// \brief Increment operator. |
---|
| 749 | /// |
---|
| 750 | /// Increment operator. |
---|
| 751 | DualIt& operator++() { |
---|
| 752 | ++_index; |
---|
| 753 | return *this; |
---|
| 754 | } |
---|
| 755 | |
---|
| 756 | /// \brief Validity checking |
---|
| 757 | /// |
---|
| 758 | /// Checks whether the iterator is invalid. |
---|
| 759 | bool operator==(Invalid) const { |
---|
| 760 | return _index == _last; |
---|
| 761 | } |
---|
| 762 | |
---|
| 763 | /// \brief Validity checking |
---|
| 764 | /// |
---|
| 765 | /// Checks whether the iterator is valid. |
---|
| 766 | bool operator!=(Invalid) const { |
---|
| 767 | return _index != _last; |
---|
| 768 | } |
---|
| 769 | |
---|
| 770 | private: |
---|
| 771 | const MinCostArborescence* _algorithm; |
---|
| 772 | int _index, _last; |
---|
| 773 | }; |
---|
| 774 | |
---|
| 775 | /// @} |
---|
| 776 | |
---|
[522] | 777 | }; |
---|
| 778 | |
---|
| 779 | /// \ingroup spantree |
---|
| 780 | /// |
---|
| 781 | /// \brief Function type interface for MinCostArborescence algorithm. |
---|
| 782 | /// |
---|
| 783 | /// Function type interface for MinCostArborescence algorithm. |
---|
[672] | 784 | /// \param digraph The digraph the algorithm runs on. |
---|
| 785 | /// \param cost An arc map storing the costs. |
---|
| 786 | /// \param source The source node of the arborescence. |
---|
| 787 | /// \retval arborescence An arc map with \c bool (or convertible) value |
---|
| 788 | /// type that stores the arborescence. |
---|
| 789 | /// \return The total cost of the arborescence. |
---|
[522] | 790 | /// |
---|
| 791 | /// \sa MinCostArborescence |
---|
| 792 | template <typename Digraph, typename CostMap, typename ArborescenceMap> |
---|
| 793 | typename CostMap::Value minCostArborescence(const Digraph& digraph, |
---|
| 794 | const CostMap& cost, |
---|
| 795 | typename Digraph::Node source, |
---|
| 796 | ArborescenceMap& arborescence) { |
---|
| 797 | typename MinCostArborescence<Digraph, CostMap> |
---|
[672] | 798 | ::template SetArborescenceMap<ArborescenceMap> |
---|
[522] | 799 | ::Create mca(digraph, cost); |
---|
| 800 | mca.arborescenceMap(arborescence); |
---|
| 801 | mca.run(source); |
---|
[672] | 802 | return mca.arborescenceCost(); |
---|
[522] | 803 | } |
---|
| 804 | |
---|
| 805 | } |
---|
| 806 | |
---|
| 807 | #endif |
---|