1 | /* -*- C++ -*- |
---|
2 | * lemon/prim.h - Part of LEMON, a generic C++ optimization library |
---|
3 | * |
---|
4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
6 | * |
---|
7 | * Permission to use, modify and distribute this software is granted |
---|
8 | * provided that this copyright notice appears in all copies. For |
---|
9 | * precise terms see the accompanying LICENSE file. |
---|
10 | * |
---|
11 | * This software is provided "AS IS" with no warranty of any kind, |
---|
12 | * express or implied, and with no claim as to its suitability for any |
---|
13 | * purpose. |
---|
14 | * |
---|
15 | */ |
---|
16 | |
---|
17 | #ifndef LEMON_PRIM_H |
---|
18 | #define LEMON_PRIM_H |
---|
19 | |
---|
20 | ///\ingroup spantree |
---|
21 | ///\file |
---|
22 | ///\brief Prim algorithm to compute minimum spanning tree. |
---|
23 | |
---|
24 | #include <lemon/list_graph.h> |
---|
25 | #include <lemon/bin_heap.h> |
---|
26 | #include <lemon/invalid.h> |
---|
27 | #include <lemon/error.h> |
---|
28 | #include <lemon/maps.h> |
---|
29 | #include <lemon/traits.h> |
---|
30 | |
---|
31 | #include <lemon/concept/ugraph.h> |
---|
32 | |
---|
33 | namespace lemon { |
---|
34 | |
---|
35 | ///Default traits class of Prim class. |
---|
36 | |
---|
37 | ///Default traits class of Prim class. |
---|
38 | ///\param GR Graph type. |
---|
39 | ///\param LM Type of cost map. |
---|
40 | template<class GR, class LM> |
---|
41 | struct PrimDefaultTraits{ |
---|
42 | ///The graph type the algorithm runs on. |
---|
43 | typedef GR UGraph; |
---|
44 | ///The type of the map that stores the edge costs. |
---|
45 | |
---|
46 | ///The type of the map that stores the edge costs. |
---|
47 | ///It must meet the \ref concept::ReadMap "ReadMap" concept. |
---|
48 | typedef LM CostMap; |
---|
49 | //The type of the cost of the edges. |
---|
50 | typedef typename LM::Value Value; |
---|
51 | /// The cross reference type used by heap. |
---|
52 | |
---|
53 | /// The cross reference type used by heap. |
---|
54 | /// Usually it is \c UGraph::NodeMap<int>. |
---|
55 | typedef typename UGraph::template NodeMap<int> HeapCrossRef; |
---|
56 | ///Instantiates a HeapCrossRef. |
---|
57 | |
---|
58 | ///This function instantiates a \ref HeapCrossRef. |
---|
59 | /// \param _graph is the graph, to which we would like to define the |
---|
60 | /// HeapCrossRef. |
---|
61 | static HeapCrossRef *createHeapCrossRef(const GR &_graph){ |
---|
62 | return new HeapCrossRef(_graph); |
---|
63 | } |
---|
64 | |
---|
65 | ///The heap type used by Prim algorithm. |
---|
66 | |
---|
67 | ///The heap type used by Prim algorithm. |
---|
68 | /// |
---|
69 | ///\sa BinHeap |
---|
70 | ///\sa Prim |
---|
71 | typedef BinHeap<typename UGraph::Node, typename LM::Value, |
---|
72 | HeapCrossRef, std::less<Value> > Heap; |
---|
73 | |
---|
74 | static Heap *createHeap(HeapCrossRef& _ref){ |
---|
75 | return new Heap(_ref); |
---|
76 | } |
---|
77 | |
---|
78 | ///\brief The type of the map that stores the last |
---|
79 | ///edges of the minimum spanning tree. |
---|
80 | /// |
---|
81 | ///The type of the map that stores the last |
---|
82 | ///edges of the minimum spanning tree. |
---|
83 | ///It must meet the \ref concept::WriteMap "WriteMap" concept. |
---|
84 | /// |
---|
85 | typedef typename UGraph::template NodeMap<typename GR::UEdge> PredMap; |
---|
86 | ///Instantiates a PredMap. |
---|
87 | |
---|
88 | ///This function instantiates a \ref PredMap. |
---|
89 | ///\param _graph is the graph, to which we would like to define the PredMap. |
---|
90 | static PredMap *createPredMap(const GR &_graph){ |
---|
91 | return new PredMap(_graph); |
---|
92 | } |
---|
93 | |
---|
94 | ///The type of the map that stores whether an edge is in the |
---|
95 | ///spanning tree or not. |
---|
96 | |
---|
97 | ///The type of the map that stores whether an edge is in the |
---|
98 | ///spanning tree or not. |
---|
99 | ///By default it is a NullMap. |
---|
100 | typedef NullMap<typename UGraph::UEdge,bool> TreeMap; |
---|
101 | ///Instantiates a TreeMap. |
---|
102 | |
---|
103 | ///This function instantiates a \ref TreeMap. |
---|
104 | /// |
---|
105 | ///The first parameter is the graph, to which |
---|
106 | ///we would like to define the \ref TreeMap |
---|
107 | static TreeMap *createTreeMap(const GR &){ |
---|
108 | return new TreeMap(); |
---|
109 | } |
---|
110 | |
---|
111 | ///The type of the map that stores whether a nodes is processed. |
---|
112 | |
---|
113 | ///The type of the map that stores whether a nodes is processed. |
---|
114 | ///It must meet the \ref concept::WriteMap "WriteMap" concept. |
---|
115 | ///By default it is a NodeMap<bool>. |
---|
116 | typedef NullMap<typename UGraph::Node,bool> ProcessedMap; |
---|
117 | ///Instantiates a ProcessedMap. |
---|
118 | |
---|
119 | ///This function instantiates a \ref ProcessedMap. |
---|
120 | ///\param _graph is the graph, to which |
---|
121 | ///we would like to define the \ref ProcessedMap |
---|
122 | #ifdef DOXYGEN |
---|
123 | static ProcessedMap *createProcessedMap(const GR &_graph) |
---|
124 | #else |
---|
125 | static ProcessedMap *createProcessedMap(const GR &) |
---|
126 | #endif |
---|
127 | { |
---|
128 | return new ProcessedMap(); |
---|
129 | } |
---|
130 | }; |
---|
131 | |
---|
132 | ///%Prim algorithm class to find a minimum spanning tree. |
---|
133 | |
---|
134 | /// \ingroup spantree |
---|
135 | ///This class provides an efficient implementation of %Prim algorithm. |
---|
136 | /// |
---|
137 | ///The running time is O(e*log n) where e is the number of edges and |
---|
138 | ///n is the number of nodes in the graph. |
---|
139 | /// |
---|
140 | ///The edge costs are passed to the algorithm using a |
---|
141 | ///\ref concept::ReadMap "ReadMap", |
---|
142 | ///so it is easy to change it to any kind of cost. |
---|
143 | /// |
---|
144 | ///The type of the cost is determined by the |
---|
145 | ///\ref concept::ReadMap::Value "Value" of the cost map. |
---|
146 | /// |
---|
147 | ///It is also possible to change the underlying priority heap. |
---|
148 | /// |
---|
149 | ///\param GR The graph type the algorithm runs on. The default value |
---|
150 | ///is \ref ListUGraph. The value of GR is not used directly by |
---|
151 | ///Prim, it is only passed to \ref PrimDefaultTraits. |
---|
152 | /// |
---|
153 | ///\param LM This read-only UEdgeMap determines the costs of the |
---|
154 | ///edges. It is read once for each edge, so the map may involve in |
---|
155 | ///relatively time consuming process to compute the edge cost if |
---|
156 | ///it is necessary. The default map type is \ref |
---|
157 | ///concept::UGraph::UEdgeMap "UGraph::UEdgeMap<int>". The value |
---|
158 | ///of LM is not used directly by Prim, it is only passed to \ref |
---|
159 | ///PrimDefaultTraits. |
---|
160 | /// |
---|
161 | ///\param TR Traits class to set |
---|
162 | ///various data types used by the algorithm. The default traits |
---|
163 | ///class is \ref PrimDefaultTraits |
---|
164 | ///"PrimDefaultTraits<GR,LM>". See \ref |
---|
165 | ///PrimDefaultTraits for the documentation of a Prim traits |
---|
166 | ///class. |
---|
167 | /// |
---|
168 | ///\author Balazs Attila Mihaly |
---|
169 | |
---|
170 | #ifdef DOXYGEN |
---|
171 | template <typename GR, |
---|
172 | typename LM, |
---|
173 | typename TR> |
---|
174 | #else |
---|
175 | template <typename GR=ListUGraph, |
---|
176 | typename LM=typename GR::template UEdgeMap<int>, |
---|
177 | typename TR=PrimDefaultTraits<GR,LM> > |
---|
178 | #endif |
---|
179 | class Prim { |
---|
180 | public: |
---|
181 | /** |
---|
182 | * \brief \ref Exception for uninitialized parameters. |
---|
183 | * |
---|
184 | * This error represents problems in the initialization |
---|
185 | * of the parameters of the algorithms. |
---|
186 | */ |
---|
187 | class UninitializedParameter : public lemon::UninitializedParameter { |
---|
188 | public: |
---|
189 | virtual const char* exceptionName() const { |
---|
190 | return "lemon::Prim::UninitializedParameter"; |
---|
191 | } |
---|
192 | }; |
---|
193 | |
---|
194 | typedef TR Traits; |
---|
195 | ///The type of the underlying graph. |
---|
196 | typedef typename TR::UGraph UGraph; |
---|
197 | ///\e |
---|
198 | typedef typename UGraph::Node Node; |
---|
199 | ///\e |
---|
200 | typedef typename UGraph::NodeIt NodeIt; |
---|
201 | ///\e |
---|
202 | typedef typename UGraph::UEdge UEdge; |
---|
203 | ///\e |
---|
204 | typedef typename UGraph::IncEdgeIt IncEdgeIt; |
---|
205 | |
---|
206 | ///The type of the cost of the edges. |
---|
207 | typedef typename TR::CostMap::Value Value; |
---|
208 | ///The type of the map that stores the edge costs. |
---|
209 | typedef typename TR::CostMap CostMap; |
---|
210 | ///\brief The type of the map that stores the last |
---|
211 | ///predecessor edges of the spanning tree. |
---|
212 | typedef typename TR::PredMap PredMap; |
---|
213 | ///Edges of the spanning tree. |
---|
214 | typedef typename TR::TreeMap TreeMap; |
---|
215 | ///The type of the map indicating if a node is processed. |
---|
216 | typedef typename TR::ProcessedMap ProcessedMap; |
---|
217 | ///The cross reference type used for the current heap. |
---|
218 | typedef typename TR::HeapCrossRef HeapCrossRef; |
---|
219 | ///The heap type used by the prim algorithm. |
---|
220 | typedef typename TR::Heap Heap; |
---|
221 | private: |
---|
222 | /// Pointer to the underlying graph. |
---|
223 | const UGraph *graph; |
---|
224 | /// Pointer to the cost map |
---|
225 | const CostMap *cost; |
---|
226 | ///Pointer to the map of predecessors edges. |
---|
227 | PredMap *_pred; |
---|
228 | ///Indicates if \ref _pred is locally allocated (\c true) or not. |
---|
229 | bool local_pred; |
---|
230 | ///Pointer to the map of tree edges. |
---|
231 | TreeMap *_tree; |
---|
232 | ///Indicates if \ref _tree is locally allocated (\c true) or not. |
---|
233 | bool local_tree; |
---|
234 | ///Pointer to the map of processed status of the nodes. |
---|
235 | ProcessedMap *_processed; |
---|
236 | ///Indicates if \ref _processed is locally allocated (\c true) or not. |
---|
237 | bool local_processed; |
---|
238 | ///Pointer to the heap cross references. |
---|
239 | HeapCrossRef *_heap_cross_ref; |
---|
240 | ///Indicates if \ref _heap_cross_ref is locally allocated (\c true) or not. |
---|
241 | bool local_heap_cross_ref; |
---|
242 | ///Pointer to the heap. |
---|
243 | Heap *_heap; |
---|
244 | ///Indicates if \ref _heap is locally allocated (\c true) or not. |
---|
245 | bool local_heap; |
---|
246 | |
---|
247 | ///Creates the maps if necessary. |
---|
248 | void create_maps(){ |
---|
249 | if(!_pred) { |
---|
250 | local_pred = true; |
---|
251 | _pred = Traits::createPredMap(*graph); |
---|
252 | } |
---|
253 | if(!_tree) { |
---|
254 | local_tree = true; |
---|
255 | _tree = Traits::createTreeMap(*graph); |
---|
256 | } |
---|
257 | if(!_processed) { |
---|
258 | local_processed = true; |
---|
259 | _processed = Traits::createProcessedMap(*graph); |
---|
260 | } |
---|
261 | if (!_heap_cross_ref) { |
---|
262 | local_heap_cross_ref = true; |
---|
263 | _heap_cross_ref = Traits::createHeapCrossRef(*graph); |
---|
264 | } |
---|
265 | if (!_heap) { |
---|
266 | local_heap = true; |
---|
267 | _heap = Traits::createHeap(*_heap_cross_ref); |
---|
268 | } |
---|
269 | } |
---|
270 | |
---|
271 | public : |
---|
272 | |
---|
273 | typedef Prim Create; |
---|
274 | |
---|
275 | ///\name Named template parameters |
---|
276 | |
---|
277 | ///@{ |
---|
278 | |
---|
279 | template <class T> |
---|
280 | struct DefPredMapTraits : public Traits { |
---|
281 | typedef T PredMap; |
---|
282 | static PredMap *createPredMap(const UGraph &_graph){ |
---|
283 | throw UninitializedParameter(); |
---|
284 | } |
---|
285 | }; |
---|
286 | ///\ref named-templ-param "Named parameter" for setting PredMap type |
---|
287 | |
---|
288 | ///\ref named-templ-param "Named parameter" for setting PredMap type |
---|
289 | /// |
---|
290 | template <class T> |
---|
291 | struct DefPredMap |
---|
292 | : public Prim< UGraph, CostMap, DefPredMapTraits<T> > { |
---|
293 | typedef Prim< UGraph, CostMap, DefPredMapTraits<T> > Create; |
---|
294 | }; |
---|
295 | |
---|
296 | template <class T> |
---|
297 | struct DefProcessedMapTraits : public Traits { |
---|
298 | typedef T ProcessedMap; |
---|
299 | static ProcessedMap *createProcessedMap(const UGraph &_graph){ |
---|
300 | throw UninitializedParameter(); |
---|
301 | } |
---|
302 | }; |
---|
303 | ///\ref named-templ-param "Named parameter" for setting ProcessedMap type |
---|
304 | |
---|
305 | ///\ref named-templ-param "Named parameter" for setting ProcessedMap type |
---|
306 | /// |
---|
307 | template <class T> |
---|
308 | struct DefProcessedMap |
---|
309 | : public Prim< UGraph, CostMap, DefProcessedMapTraits<T> > { |
---|
310 | typedef Prim< UGraph, CostMap, DefProcessedMapTraits<T> > Create; |
---|
311 | }; |
---|
312 | |
---|
313 | struct DefGraphProcessedMapTraits : public Traits { |
---|
314 | typedef typename UGraph::template NodeMap<bool> ProcessedMap; |
---|
315 | static ProcessedMap *createProcessedMap(const UGraph &_graph){ |
---|
316 | return new ProcessedMap(_graph); |
---|
317 | } |
---|
318 | }; |
---|
319 | |
---|
320 | |
---|
321 | template <class H, class CR> |
---|
322 | struct DefHeapTraits : public Traits { |
---|
323 | typedef CR HeapCrossRef; |
---|
324 | typedef H Heap; |
---|
325 | static HeapCrossRef *createHeapCrossRef(const UGraph &) { |
---|
326 | throw UninitializedParameter(); |
---|
327 | } |
---|
328 | static Heap *createHeap(HeapCrossRef &){ |
---|
329 | return UninitializedParameter(); |
---|
330 | } |
---|
331 | }; |
---|
332 | ///\ref named-templ-param "Named parameter" for setting heap and cross |
---|
333 | ///reference type |
---|
334 | |
---|
335 | ///\ref named-templ-param "Named parameter" for setting heap and cross |
---|
336 | ///reference type |
---|
337 | /// |
---|
338 | template <class H, class CR = typename UGraph::template NodeMap<int> > |
---|
339 | struct DefHeap |
---|
340 | : public Prim< UGraph, CostMap, DefHeapTraits<H, CR> > { |
---|
341 | typedef Prim< UGraph, CostMap, DefHeapTraits<H, CR> > Create; |
---|
342 | }; |
---|
343 | |
---|
344 | template <class H, class CR> |
---|
345 | struct DefStandardHeapTraits : public Traits { |
---|
346 | typedef CR HeapCrossRef; |
---|
347 | typedef H Heap; |
---|
348 | static HeapCrossRef *createHeapCrossRef(const UGraph &_graph) { |
---|
349 | return new HeapCrossRef(_graph); |
---|
350 | } |
---|
351 | static Heap *createHeap(HeapCrossRef &ref){ |
---|
352 | return new Heap(ref); |
---|
353 | } |
---|
354 | }; |
---|
355 | ///\ref named-templ-param "Named parameter" for setting heap and cross |
---|
356 | ///reference type with automatic allocation |
---|
357 | |
---|
358 | ///\ref named-templ-param "Named parameter" for setting heap and cross |
---|
359 | ///reference type. It can allocate the heap and the cross reference |
---|
360 | ///object if the cross reference's constructor waits for the graph as |
---|
361 | ///parameter and the heap's constructor waits for the cross reference. |
---|
362 | template <class H, class CR = typename UGraph::template NodeMap<int> > |
---|
363 | struct DefStandardHeap |
---|
364 | : public Prim< UGraph, CostMap, DefStandardHeapTraits<H, CR> > { |
---|
365 | typedef Prim< UGraph, CostMap, DefStandardHeapTraits<H, CR> > |
---|
366 | Create; |
---|
367 | }; |
---|
368 | |
---|
369 | template <class TM> |
---|
370 | struct DefTreeMapTraits : public Traits { |
---|
371 | typedef TM TreeMap; |
---|
372 | static TreeMap *createTreeMap(const UGraph &) { |
---|
373 | throw UninitializedParameter(); |
---|
374 | } |
---|
375 | }; |
---|
376 | ///\ref named-templ-param "Named parameter" for setting TreeMap |
---|
377 | |
---|
378 | ///\ref named-templ-param "Named parameter" for setting TreeMap |
---|
379 | /// |
---|
380 | template <class TM> |
---|
381 | struct DefTreeMap |
---|
382 | : public Prim< UGraph, CostMap, DefTreeMapTraits<TM> > { |
---|
383 | typedef Prim< UGraph, CostMap, DefTreeMapTraits<TM> > Create; |
---|
384 | }; |
---|
385 | |
---|
386 | struct DefGraphTreeMapTraits : public Traits { |
---|
387 | typedef typename UGraph::template NodeMap<bool> TreeMap; |
---|
388 | static TreeMap *createTreeMap(const UGraph &_graph){ |
---|
389 | return new TreeMap(_graph); |
---|
390 | } |
---|
391 | }; |
---|
392 | |
---|
393 | ///@} |
---|
394 | |
---|
395 | |
---|
396 | protected: |
---|
397 | |
---|
398 | Prim() {} |
---|
399 | |
---|
400 | public: |
---|
401 | |
---|
402 | ///Constructor. |
---|
403 | |
---|
404 | ///\param _graph the graph the algorithm will run on. |
---|
405 | ///\param _cost the cost map used by the algorithm. |
---|
406 | Prim(const UGraph& _graph, const CostMap& _cost) : |
---|
407 | graph(&_graph), cost(&_cost), |
---|
408 | _pred(NULL), local_pred(false), |
---|
409 | _tree(NULL), local_tree(false), |
---|
410 | _processed(NULL), local_processed(false), |
---|
411 | _heap_cross_ref(NULL), local_heap_cross_ref(false), |
---|
412 | _heap(NULL), local_heap(false) |
---|
413 | { |
---|
414 | checkConcept<concept::UGraph, UGraph>(); |
---|
415 | } |
---|
416 | |
---|
417 | ///Destructor. |
---|
418 | ~Prim(){ |
---|
419 | if(local_pred) delete _pred; |
---|
420 | if(local_tree) delete _tree; |
---|
421 | if(local_processed) delete _processed; |
---|
422 | if(local_heap_cross_ref) delete _heap_cross_ref; |
---|
423 | if(local_heap) delete _heap; |
---|
424 | } |
---|
425 | |
---|
426 | ///\brief Sets the cost map. |
---|
427 | |
---|
428 | ///Sets the cost map. |
---|
429 | ///\return <tt> (*this) </tt> |
---|
430 | Prim &costMap(const CostMap &m){ |
---|
431 | cost = &m; |
---|
432 | return *this; |
---|
433 | } |
---|
434 | |
---|
435 | ///\brief Sets the map storing the predecessor edges. |
---|
436 | |
---|
437 | ///Sets the map storing the predecessor edges. |
---|
438 | ///If you don't use this function before calling \ref run(), |
---|
439 | ///it will allocate one. The destuctor deallocates this |
---|
440 | ///automatically allocated map, of course. |
---|
441 | ///\return <tt> (*this) </tt> |
---|
442 | Prim &predMap(PredMap &m){ |
---|
443 | if(local_pred) { |
---|
444 | delete _pred; |
---|
445 | local_pred=false; |
---|
446 | } |
---|
447 | _pred = &m; |
---|
448 | return *this; |
---|
449 | } |
---|
450 | |
---|
451 | ///\brief Sets the map storing the tree edges. |
---|
452 | |
---|
453 | ///Sets the map storing the tree edges. |
---|
454 | ///If you don't use this function before calling \ref run(), |
---|
455 | ///it will allocate one. The destuctor deallocates this |
---|
456 | ///automatically allocated map, of course. |
---|
457 | ///By default this is a NullMap. |
---|
458 | ///\return <tt> (*this) </tt> |
---|
459 | Prim &treeMap(TreeMap &m){ |
---|
460 | if(local_tree) { |
---|
461 | delete _tree; |
---|
462 | local_tree=false; |
---|
463 | } |
---|
464 | _tree = &m; |
---|
465 | return *this; |
---|
466 | } |
---|
467 | |
---|
468 | ///\brief Sets the heap and the cross reference used by algorithm. |
---|
469 | |
---|
470 | ///Sets the heap and the cross reference used by algorithm. |
---|
471 | ///If you don't use this function before calling \ref run(), |
---|
472 | ///it will allocate one. The destuctor deallocates this |
---|
473 | ///automatically allocated map, of course. |
---|
474 | ///\return <tt> (*this) </tt> |
---|
475 | Prim &heap(Heap& heap, HeapCrossRef &crossRef){ |
---|
476 | if(local_heap_cross_ref) { |
---|
477 | delete _heap_cross_ref; |
---|
478 | local_heap_cross_ref=false; |
---|
479 | } |
---|
480 | _heap_cross_ref = &crossRef; |
---|
481 | if(local_heap) { |
---|
482 | delete _heap; |
---|
483 | local_heap=false; |
---|
484 | } |
---|
485 | _heap = &heap; |
---|
486 | return *this; |
---|
487 | } |
---|
488 | |
---|
489 | public: |
---|
490 | ///\name Execution control |
---|
491 | ///The simplest way to execute the algorithm is to use |
---|
492 | ///one of the member functions called \c run(...). |
---|
493 | ///\n |
---|
494 | ///If you need more control on the execution, |
---|
495 | ///first you must call \ref init(), then you can add several source nodes |
---|
496 | ///with \ref addSource(). |
---|
497 | ///Finally \ref start() will perform the actual path |
---|
498 | ///computation. |
---|
499 | |
---|
500 | ///@{ |
---|
501 | |
---|
502 | ///\brief Initializes the internal data structures. |
---|
503 | |
---|
504 | ///Initializes the internal data structures. |
---|
505 | /// |
---|
506 | void init(){ |
---|
507 | create_maps(); |
---|
508 | _heap->clear(); |
---|
509 | for ( NodeIt u(*graph) ; u!=INVALID ; ++u ) { |
---|
510 | _pred->set(u,INVALID); |
---|
511 | _processed->set(u,false); |
---|
512 | _heap_cross_ref->set(u,Heap::PRE_HEAP); |
---|
513 | } |
---|
514 | } |
---|
515 | |
---|
516 | ///\brief Adds a new source node. |
---|
517 | |
---|
518 | ///Adds a new source node to the priority heap. |
---|
519 | /// |
---|
520 | ///It checks if the node has already been added to the heap and |
---|
521 | ///it is pushed to the heap only if it was not in the heap. |
---|
522 | void addSource(Node s){ |
---|
523 | if(_heap->state(s) != Heap::IN_HEAP) { |
---|
524 | _heap->push(s,Value()); |
---|
525 | } |
---|
526 | } |
---|
527 | ///\brief Processes the next node in the priority heap |
---|
528 | |
---|
529 | ///Processes the next node in the priority heap. |
---|
530 | /// |
---|
531 | ///\return The processed node. |
---|
532 | /// |
---|
533 | ///\warning The priority heap must not be empty! |
---|
534 | Node processNextNode(){ |
---|
535 | Node v=_heap->top(); |
---|
536 | _heap->pop(); |
---|
537 | _processed->set(v,true); |
---|
538 | |
---|
539 | for(IncEdgeIt e(*graph,v); e!=INVALID; ++e) { |
---|
540 | Node w=graph->oppositeNode(v,e); |
---|
541 | switch(_heap->state(w)) { |
---|
542 | case Heap::PRE_HEAP: |
---|
543 | _heap->push(w,(*cost)[e]); |
---|
544 | _pred->set(w,e); |
---|
545 | break; |
---|
546 | case Heap::IN_HEAP: |
---|
547 | if ( (*cost)[e] < (*_heap)[w] ) { |
---|
548 | _heap->decrease(w,(*cost)[e]); |
---|
549 | _pred->set(w,e); |
---|
550 | } |
---|
551 | break; |
---|
552 | case Heap::POST_HEAP: |
---|
553 | break; |
---|
554 | } |
---|
555 | } |
---|
556 | if ((*_pred)[v]!=INVALID)_tree->set((*_pred)[v],true); |
---|
557 | return v; |
---|
558 | } |
---|
559 | |
---|
560 | ///\brief Next node to be processed. |
---|
561 | |
---|
562 | ///Next node to be processed. |
---|
563 | /// |
---|
564 | ///\return The next node to be processed or INVALID if the priority heap |
---|
565 | /// is empty. |
---|
566 | Node nextNode(){ |
---|
567 | return _heap->empty()?_heap->top():INVALID; |
---|
568 | } |
---|
569 | |
---|
570 | ///\brief Returns \c false if there are nodes to be processed in the priority heap |
---|
571 | /// |
---|
572 | ///Returns \c false if there are nodes |
---|
573 | ///to be processed in the priority heap |
---|
574 | bool emptyQueue() { return _heap->empty(); } |
---|
575 | ///\brief Returns the number of the nodes to be processed in the priority heap |
---|
576 | |
---|
577 | ///Returns the number of the nodes to be processed in the priority heap |
---|
578 | /// |
---|
579 | int queueSize() { return _heap->size(); } |
---|
580 | |
---|
581 | ///\brief Executes the algorithm. |
---|
582 | |
---|
583 | ///Executes the algorithm. |
---|
584 | /// |
---|
585 | ///\pre init() must be called and at least one node should be added |
---|
586 | ///with addSource() before using this function. |
---|
587 | /// |
---|
588 | ///This method runs the %Prim algorithm from the node(s) |
---|
589 | ///in order to compute the |
---|
590 | ///minimum spanning tree. |
---|
591 | /// |
---|
592 | void start(){ |
---|
593 | while ( !_heap->empty() ) processNextNode(); |
---|
594 | } |
---|
595 | |
---|
596 | ///\brief Executes the algorithm until a condition is met. |
---|
597 | |
---|
598 | ///Executes the algorithm until a condition is met. |
---|
599 | /// |
---|
600 | ///\pre init() must be called and at least one node should be added |
---|
601 | ///with addSource() before using this function. |
---|
602 | /// |
---|
603 | ///\param nm must be a bool (or convertible) node map. The algorithm |
---|
604 | ///will stop when it reaches a node \c v with <tt>nm[v]==true</tt>. |
---|
605 | template<class NodeBoolMap> |
---|
606 | void start(const NodeBoolMap &nm){ |
---|
607 | while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode(); |
---|
608 | if ( !_heap->empty() ) _processed->set(_heap->top(),true); |
---|
609 | } |
---|
610 | |
---|
611 | ///\brief Runs %Prim algorithm. |
---|
612 | |
---|
613 | ///This method runs the %Prim algorithm |
---|
614 | ///in order to compute the |
---|
615 | ///minimum spanning tree (or minimum spanning forest). |
---|
616 | ///The method also works on graphs that has more than one components. |
---|
617 | ///In this case it computes the minimum spanning forest. |
---|
618 | void run() { |
---|
619 | init(); |
---|
620 | for(NodeIt it(*graph);it!=INVALID;++it){ |
---|
621 | if(!processed(it)){ |
---|
622 | addSource(it); |
---|
623 | start(); |
---|
624 | } |
---|
625 | } |
---|
626 | } |
---|
627 | |
---|
628 | ///\brief Runs %Prim algorithm from node \c s. |
---|
629 | |
---|
630 | ///This method runs the %Prim algorithm from node \c s |
---|
631 | ///in order to |
---|
632 | ///compute the |
---|
633 | ///minimun spanning tree |
---|
634 | /// |
---|
635 | ///\note d.run(s) is just a shortcut of the following code. |
---|
636 | ///\code |
---|
637 | /// d.init(); |
---|
638 | /// d.addSource(s); |
---|
639 | /// d.start(); |
---|
640 | ///\endcode |
---|
641 | ///\note If the graph has more than one components, the method |
---|
642 | ///will compute the minimun spanning tree for only one component. |
---|
643 | /// |
---|
644 | ///See \ref run() if you want to compute the minimal spanning forest. |
---|
645 | void run(Node s){ |
---|
646 | init(); |
---|
647 | addSource(s); |
---|
648 | start(); |
---|
649 | } |
---|
650 | |
---|
651 | ///@} |
---|
652 | |
---|
653 | ///\name Query Functions |
---|
654 | ///The result of the %Prim algorithm can be obtained using these |
---|
655 | ///functions.\n |
---|
656 | ///Before the use of these functions, |
---|
657 | ///either run() or start() must be called. |
---|
658 | |
---|
659 | ///@{ |
---|
660 | |
---|
661 | ///\brief Returns the 'previous edge' of the minimum spanning tree. |
---|
662 | |
---|
663 | ///For a node \c v it returns the 'previous edge' of the minimum spanning tree, |
---|
664 | ///i.e. it returns the edge from where \c v was reached. For a source node |
---|
665 | ///or an unreachable node it is \ref INVALID. |
---|
666 | ///The minimum spanning tree used here is equal to the minimum spanning tree used |
---|
667 | ///in \ref predNode(). \pre \ref run() or \ref start() must be called before |
---|
668 | ///using this function. |
---|
669 | UEdge predEdge(Node v) const { return (*_pred)[v]; } |
---|
670 | |
---|
671 | ///\brief Returns the 'previous node' of the minimum spanning tree. |
---|
672 | |
---|
673 | ///For a node \c v it returns the 'previous node' of the minimum spanning tree, |
---|
674 | ///i.e. it returns the node from where \c v was reached. For a source node |
---|
675 | ///or an unreachable node it is \ref INVALID. |
---|
676 | //The minimum spanning tree used here is equal to the minimum spanning |
---|
677 | ///tree used in \ref predEdge(). \pre \ref run() or \ref start() must be called |
---|
678 | ///before using this function. |
---|
679 | Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID: |
---|
680 | graph->source((*_pred)[v]); } |
---|
681 | |
---|
682 | ///\brief Returns a reference to the NodeMap of the edges of the minimum spanning tree. |
---|
683 | |
---|
684 | ///Returns a reference to the NodeMap of the edges of the |
---|
685 | ///minimum spanning tree. |
---|
686 | ///\pre \ref run() or \ref start() must be called before using this function. |
---|
687 | const PredMap &predMap() const { return *_pred;} |
---|
688 | |
---|
689 | ///\brief Returns a reference to the tree edges map. |
---|
690 | |
---|
691 | ///Returns a reference to the TreeEdgeMap of the edges of the |
---|
692 | ///minimum spanning tree. The value of the map is \c true only if the edge is in |
---|
693 | ///the minimum spanning tree. |
---|
694 | ///\warning By default, the TreeEdgeMap is a NullMap. |
---|
695 | /// |
---|
696 | ///If it is not set before the execution of the algorithm, use the \ref |
---|
697 | ///treeMap(TreeMap&) function (after the execution) to set an UEdgeMap with the |
---|
698 | ///edges of the minimum spanning tree in O(n) time where n is the number of |
---|
699 | ///nodes in the graph. |
---|
700 | ///\pre \ref run() or \ref start() must be called before using this function. |
---|
701 | const TreeMap &treeMap() const { return *_tree;} |
---|
702 | |
---|
703 | ///\brief Sets the tree edges map. |
---|
704 | |
---|
705 | ///Sets the TreeMap of the edges of the minimum spanning tree. |
---|
706 | ///The map values belonging to the edges of the minimum |
---|
707 | ///spanning tree are set to \c tree_edge_value or \c true by default, |
---|
708 | ///the other map values remain untouched. |
---|
709 | /// |
---|
710 | ///\pre \ref run() or \ref start() must be called before using this function. |
---|
711 | |
---|
712 | template<class TreeMap> |
---|
713 | void quickTreeEdges( |
---|
714 | TreeMap& tree, |
---|
715 | const typename TreeMap::Value& tree_edge_value=true) const { |
---|
716 | for(NodeIt i(*graph);i!=INVALID;++i){ |
---|
717 | if((*_pred)[i]!=INVALID) tree.set((*_pred)[i],tree_edge_value); |
---|
718 | } |
---|
719 | } |
---|
720 | |
---|
721 | ///\brief Sets the tree edges map. |
---|
722 | |
---|
723 | ///Sets the TreeMap of the edges of the minimum spanning tree. |
---|
724 | ///The map values belonging to the edges of the minimum |
---|
725 | ///spanning tree are set to \c tree_edge_value or \c true by default while |
---|
726 | ///the edge values not belonging to the minimum spanning tree are set to |
---|
727 | ///\c tree_default_value or \c false by default. |
---|
728 | /// |
---|
729 | ///\pre \ref run() or \ref start() must be called before using this function. |
---|
730 | |
---|
731 | template<class TreeMap> |
---|
732 | void treeEdges( |
---|
733 | TreeMap& tree, |
---|
734 | const typename TreeMap::Value& tree_edge_value=true, |
---|
735 | const typename TreeMap::Value& tree_default_value=false) const { |
---|
736 | for(typename ItemSetTraits<UGraph,UEdge>::ItemIt i(*graph);i!=INVALID;++i) |
---|
737 | tree.set(i,tree_default_value); |
---|
738 | for(NodeIt i(*graph);i!=INVALID;++i){ |
---|
739 | if((*_pred)[i]!=INVALID) tree.set((*_pred)[i],tree_edge_value); |
---|
740 | } |
---|
741 | } |
---|
742 | |
---|
743 | ///\brief Checks if a node is reachable from the starting node. |
---|
744 | |
---|
745 | ///Returns \c true if \c v is reachable from the starting node. |
---|
746 | ///\warning The source nodes are inditated as unreached. |
---|
747 | ///\pre \ref run() or \ref start() must be called before using this function. |
---|
748 | /// |
---|
749 | bool reached(Node v) { return (*_heap_cross_ref)[v] != Heap::PRE_HEAP; } |
---|
750 | |
---|
751 | ///\brief Checks if a node is processed. |
---|
752 | |
---|
753 | ///Returns \c true if \c v is processed, i.e. \c v is already connencted to the |
---|
754 | ///minimum spanning tree. |
---|
755 | ///\pre \ref run() or \ref start() must be called before using this function. |
---|
756 | /// |
---|
757 | bool processed(Node v) { return (*_heap_cross_ref)[v] == Heap::POST_HEAP; } |
---|
758 | |
---|
759 | |
---|
760 | ///\brief Checks if an edge is in the spanning tree or not. |
---|
761 | |
---|
762 | ///Checks if an edge is in the spanning tree or not. |
---|
763 | ///\param e is the edge that will be checked |
---|
764 | ///\return \c true if e is in the spanning tree, \c false otherwise |
---|
765 | bool tree(UEdge e){ |
---|
766 | return (*_pred)[*graph.source(e)]==e || (*_pred)[*graph.target(e)]==e; |
---|
767 | } |
---|
768 | ///@} |
---|
769 | }; |
---|
770 | |
---|
771 | |
---|
772 | /// \ingroup spantree |
---|
773 | /// |
---|
774 | /// \brief Function type interface for Prim algorithm. |
---|
775 | /// |
---|
776 | /// Function type interface for Prim algorithm. |
---|
777 | /// \param graph the UGraph that the algorithm runs on |
---|
778 | /// \param cost the CostMap of the edges |
---|
779 | /// \retval tree the EdgeMap that contains whether an edge is in |
---|
780 | /// the spanning tree or not |
---|
781 | /// |
---|
782 | ///\sa Prim |
---|
783 | template<class Graph,class CostMap,class TreeMap> |
---|
784 | void prim(const Graph& graph, const CostMap& cost,TreeMap& tree){ |
---|
785 | typename Prim<Graph,CostMap>::template DefTreeMap<TreeMap>:: |
---|
786 | Create prm(graph,cost); |
---|
787 | prm.treeMap(tree); |
---|
788 | prm.run(); |
---|
789 | }; |
---|
790 | |
---|
791 | } //END OF NAMESPACE LEMON |
---|
792 | |
---|
793 | #endif |
---|