1 | /* -*- C++ -*- |
---|
2 | * lemon/belmann_ford.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_BELMANN_FORD_H |
---|
18 | #define LEMON_BELMANN_FORD_H |
---|
19 | |
---|
20 | ///\ingroup flowalgs |
---|
21 | /// \file |
---|
22 | /// \brief BelmannFord algorithm. |
---|
23 | /// |
---|
24 | |
---|
25 | #include <lemon/list_graph.h> |
---|
26 | #include <lemon/invalid.h> |
---|
27 | #include <lemon/error.h> |
---|
28 | #include <lemon/maps.h> |
---|
29 | |
---|
30 | #include <limits> |
---|
31 | |
---|
32 | namespace lemon { |
---|
33 | |
---|
34 | /// \brief Default OperationTraits for the BelmannFord algorithm class. |
---|
35 | /// |
---|
36 | /// It defines all computational operations and constants which are |
---|
37 | /// used in the belmann ford algorithm. The default implementation |
---|
38 | /// is based on the numeric_limits class. If the numeric type does not |
---|
39 | /// have infinity value then the maximum value is used as extremal |
---|
40 | /// infinity value. |
---|
41 | template < |
---|
42 | typename Value, |
---|
43 | bool has_infinity = std::numeric_limits<Value>::has_infinity> |
---|
44 | struct BelmannFordDefaultOperationTraits { |
---|
45 | /// \brief Gives back the zero value of the type. |
---|
46 | static Value zero() { |
---|
47 | return static_cast<Value>(0); |
---|
48 | } |
---|
49 | /// \brief Gives back the positive infinity value of the type. |
---|
50 | static Value infinity() { |
---|
51 | return std::numeric_limits<Value>::infinity(); |
---|
52 | } |
---|
53 | /// \brief Gives back the sum of the given two elements. |
---|
54 | static Value plus(const Value& left, const Value& right) { |
---|
55 | return left + right; |
---|
56 | } |
---|
57 | /// \brief Gives back true only if the first value less than the second. |
---|
58 | static bool less(const Value& left, const Value& right) { |
---|
59 | return left < right; |
---|
60 | } |
---|
61 | }; |
---|
62 | |
---|
63 | template <typename Value> |
---|
64 | struct BelmannFordDefaultOperationTraits<Value, false> { |
---|
65 | static Value zero() { |
---|
66 | return static_cast<Value>(0); |
---|
67 | } |
---|
68 | static Value infinity() { |
---|
69 | return std::numeric_limits<Value>::max(); |
---|
70 | } |
---|
71 | static Value plus(const Value& left, const Value& right) { |
---|
72 | if (left == infinity() || right == infinity()) return infinity(); |
---|
73 | return left + right; |
---|
74 | } |
---|
75 | static bool less(const Value& left, const Value& right) { |
---|
76 | return left < right; |
---|
77 | } |
---|
78 | }; |
---|
79 | |
---|
80 | /// \brief Default traits class of BelmannFord class. |
---|
81 | /// |
---|
82 | /// Default traits class of BelmannFord class. |
---|
83 | /// \param _Graph Graph type. |
---|
84 | /// \param _LegthMap Type of length map. |
---|
85 | template<class _Graph, class _LengthMap> |
---|
86 | struct BelmannFordDefaultTraits { |
---|
87 | /// The graph type the algorithm runs on. |
---|
88 | typedef _Graph Graph; |
---|
89 | |
---|
90 | /// \brief The type of the map that stores the edge lengths. |
---|
91 | /// |
---|
92 | /// The type of the map that stores the edge lengths. |
---|
93 | /// It must meet the \ref concept::ReadMap "ReadMap" concept. |
---|
94 | typedef _LengthMap LengthMap; |
---|
95 | |
---|
96 | // The type of the length of the edges. |
---|
97 | typedef typename _LengthMap::Value Value; |
---|
98 | |
---|
99 | /// \brief Operation traits for belmann-ford algorithm. |
---|
100 | /// |
---|
101 | /// It defines the infinity type on the given Value type |
---|
102 | /// and the used operation. |
---|
103 | /// \see BelmannFordDefaultOperationTraits |
---|
104 | typedef BelmannFordDefaultOperationTraits<Value> OperationTraits; |
---|
105 | |
---|
106 | /// \brief The type of the map that stores the last edges of the |
---|
107 | /// shortest paths. |
---|
108 | /// |
---|
109 | /// The type of the map that stores the last |
---|
110 | /// edges of the shortest paths. |
---|
111 | /// It must meet the \ref concept::WriteMap "WriteMap" concept. |
---|
112 | /// |
---|
113 | typedef typename Graph::template NodeMap<typename _Graph::Edge> PredMap; |
---|
114 | |
---|
115 | /// \brief Instantiates a PredMap. |
---|
116 | /// |
---|
117 | /// This function instantiates a \ref PredMap. |
---|
118 | /// \param G is the graph, to which we would like to define the PredMap. |
---|
119 | /// \todo The graph alone may be insufficient for the initialization |
---|
120 | static PredMap *createPredMap(const _Graph& graph) { |
---|
121 | return new PredMap(graph); |
---|
122 | } |
---|
123 | |
---|
124 | /// \brief The type of the map that stores the dists of the nodes. |
---|
125 | /// |
---|
126 | /// The type of the map that stores the dists of the nodes. |
---|
127 | /// It must meet the \ref concept::WriteMap "WriteMap" concept. |
---|
128 | /// |
---|
129 | typedef typename Graph::template NodeMap<typename _LengthMap::Value> |
---|
130 | DistMap; |
---|
131 | |
---|
132 | /// \brief Instantiates a DistMap. |
---|
133 | /// |
---|
134 | /// This function instantiates a \ref DistMap. |
---|
135 | /// \param G is the graph, to which we would like to define the |
---|
136 | /// \ref DistMap |
---|
137 | static DistMap *createDistMap(const _Graph& graph) { |
---|
138 | return new DistMap(graph); |
---|
139 | } |
---|
140 | |
---|
141 | }; |
---|
142 | |
---|
143 | /// \brief %BelmannFord algorithm class. |
---|
144 | /// |
---|
145 | /// \ingroup flowalgs |
---|
146 | /// This class provides an efficient implementation of \c Belmann-Ford |
---|
147 | /// algorithm. The edge lengths are passed to the algorithm using a |
---|
148 | /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any |
---|
149 | /// kind of length. |
---|
150 | /// |
---|
151 | /// The Belmann-Ford algorithm solves the shortest path from one node |
---|
152 | /// problem when the edges can have negative length but the graph should |
---|
153 | /// not contain cycles with negative sum of length. If we can assume |
---|
154 | /// that all edge is non-negative in the graph then the dijkstra algorithm |
---|
155 | /// should be used rather. |
---|
156 | /// |
---|
157 | /// The complexity of the algorithm is O(n * e). |
---|
158 | /// |
---|
159 | /// The type of the length is determined by the |
---|
160 | /// \ref concept::ReadMap::Value "Value" of the length map. |
---|
161 | /// |
---|
162 | /// \param _Graph The graph type the algorithm runs on. The default value |
---|
163 | /// is \ref ListGraph. The value of _Graph is not used directly by |
---|
164 | /// BelmannFord, it is only passed to \ref BelmannFordDefaultTraits. |
---|
165 | /// \param _LengthMap This read-only EdgeMap determines the lengths of the |
---|
166 | /// edges. The default map type is \ref concept::StaticGraph::EdgeMap |
---|
167 | /// "Graph::EdgeMap<int>". The value of _LengthMap is not used directly |
---|
168 | /// by BelmannFord, it is only passed to \ref BelmannFordDefaultTraits. |
---|
169 | /// \param _Traits Traits class to set various data types used by the |
---|
170 | /// algorithm. The default traits class is \ref BelmannFordDefaultTraits |
---|
171 | /// "BelmannFordDefaultTraits<_Graph,_LengthMap>". See \ref |
---|
172 | /// BelmannFordDefaultTraits for the documentation of a BelmannFord traits |
---|
173 | /// class. |
---|
174 | /// |
---|
175 | /// \author Balazs Dezso |
---|
176 | |
---|
177 | #ifdef DOXYGEN |
---|
178 | template <typename _Graph, typename _LengthMap, typename _Traits> |
---|
179 | #else |
---|
180 | template <typename _Graph=ListGraph, |
---|
181 | typename _LengthMap=typename _Graph::template EdgeMap<int>, |
---|
182 | typename _Traits=BelmannFordDefaultTraits<_Graph,_LengthMap> > |
---|
183 | #endif |
---|
184 | class BelmannFord { |
---|
185 | public: |
---|
186 | |
---|
187 | /// \brief \ref Exception for uninitialized parameters. |
---|
188 | /// |
---|
189 | /// This error represents problems in the initialization |
---|
190 | /// of the parameters of the algorithms. |
---|
191 | |
---|
192 | class UninitializedParameter : public lemon::UninitializedParameter { |
---|
193 | public: |
---|
194 | virtual const char* exceptionName() const { |
---|
195 | return "lemon::BelmannFord::UninitializedParameter"; |
---|
196 | } |
---|
197 | }; |
---|
198 | |
---|
199 | typedef _Traits Traits; |
---|
200 | ///The type of the underlying graph. |
---|
201 | typedef typename _Traits::Graph Graph; |
---|
202 | |
---|
203 | typedef typename Graph::Node Node; |
---|
204 | typedef typename Graph::NodeIt NodeIt; |
---|
205 | typedef typename Graph::Edge Edge; |
---|
206 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
207 | |
---|
208 | /// \brief The type of the length of the edges. |
---|
209 | typedef typename _Traits::LengthMap::Value Value; |
---|
210 | /// \brief The type of the map that stores the edge lengths. |
---|
211 | typedef typename _Traits::LengthMap LengthMap; |
---|
212 | /// \brief The type of the map that stores the last |
---|
213 | /// edges of the shortest paths. |
---|
214 | typedef typename _Traits::PredMap PredMap; |
---|
215 | /// \brief The type of the map that stores the dists of the nodes. |
---|
216 | typedef typename _Traits::DistMap DistMap; |
---|
217 | /// \brief The operation traits. |
---|
218 | typedef typename _Traits::OperationTraits OperationTraits; |
---|
219 | private: |
---|
220 | /// Pointer to the underlying graph. |
---|
221 | const Graph *graph; |
---|
222 | /// Pointer to the length map |
---|
223 | const LengthMap *length; |
---|
224 | ///Pointer to the map of predecessors edges. |
---|
225 | PredMap *_pred; |
---|
226 | ///Indicates if \ref _pred is locally allocated (\c true) or not. |
---|
227 | bool local_pred; |
---|
228 | ///Pointer to the map of distances. |
---|
229 | DistMap *_dist; |
---|
230 | ///Indicates if \ref _dist is locally allocated (\c true) or not. |
---|
231 | bool local_dist; |
---|
232 | |
---|
233 | typedef typename Graph::template NodeMap<bool> MaskMap; |
---|
234 | MaskMap *_mask; |
---|
235 | |
---|
236 | std::vector<Node> _process; |
---|
237 | |
---|
238 | /// Creates the maps if necessary. |
---|
239 | void create_maps() { |
---|
240 | if(!_pred) { |
---|
241 | local_pred = true; |
---|
242 | _pred = Traits::createPredMap(*graph); |
---|
243 | } |
---|
244 | if(!_dist) { |
---|
245 | local_dist = true; |
---|
246 | _dist = Traits::createDistMap(*graph); |
---|
247 | } |
---|
248 | _mask = new MaskMap(*graph, false); |
---|
249 | } |
---|
250 | |
---|
251 | public : |
---|
252 | |
---|
253 | typedef BelmannFord Create; |
---|
254 | |
---|
255 | /// \name Named template parameters |
---|
256 | |
---|
257 | ///@{ |
---|
258 | |
---|
259 | template <class T> |
---|
260 | struct DefPredMapTraits : public Traits { |
---|
261 | typedef T PredMap; |
---|
262 | static PredMap *createPredMap(const Graph&) { |
---|
263 | throw UninitializedParameter(); |
---|
264 | } |
---|
265 | }; |
---|
266 | |
---|
267 | /// \brief \ref named-templ-param "Named parameter" for setting PredMap |
---|
268 | /// type |
---|
269 | /// \ref named-templ-param "Named parameter" for setting PredMap type |
---|
270 | /// |
---|
271 | template <class T> |
---|
272 | struct DefPredMap { |
---|
273 | typedef BelmannFord< Graph, LengthMap, DefPredMapTraits<T> > Create; |
---|
274 | }; |
---|
275 | |
---|
276 | template <class T> |
---|
277 | struct DefDistMapTraits : public Traits { |
---|
278 | typedef T DistMap; |
---|
279 | static DistMap *createDistMap(const Graph& graph) { |
---|
280 | throw UninitializedParameter(); |
---|
281 | } |
---|
282 | }; |
---|
283 | |
---|
284 | /// \brief \ref named-templ-param "Named parameter" for setting DistMap |
---|
285 | /// type |
---|
286 | /// |
---|
287 | /// \ref named-templ-param "Named parameter" for setting DistMap type |
---|
288 | /// |
---|
289 | template <class T> |
---|
290 | struct DefDistMap |
---|
291 | : public BelmannFord< Graph, LengthMap, DefDistMapTraits<T> > { |
---|
292 | typedef BelmannFord< Graph, LengthMap, DefDistMapTraits<T> > Create; |
---|
293 | }; |
---|
294 | |
---|
295 | template <class T> |
---|
296 | struct DefOperationTraitsTraits : public Traits { |
---|
297 | typedef T OperationTraits; |
---|
298 | }; |
---|
299 | |
---|
300 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
301 | /// OperationTraits type |
---|
302 | /// |
---|
303 | /// \ref named-templ-param "Named parameter" for setting OperationTraits |
---|
304 | /// type |
---|
305 | template <class T> |
---|
306 | struct DefOperationTraits |
---|
307 | : public BelmannFord< Graph, LengthMap, DefOperationTraitsTraits<T> > { |
---|
308 | typedef BelmannFord< Graph, LengthMap, DefOperationTraitsTraits<T> > |
---|
309 | Create; |
---|
310 | }; |
---|
311 | |
---|
312 | ///@} |
---|
313 | |
---|
314 | protected: |
---|
315 | |
---|
316 | BelmannFord() {} |
---|
317 | |
---|
318 | public: |
---|
319 | |
---|
320 | /// \brief Constructor. |
---|
321 | /// |
---|
322 | /// \param _graph the graph the algorithm will run on. |
---|
323 | /// \param _length the length map used by the algorithm. |
---|
324 | BelmannFord(const Graph& _graph, const LengthMap& _length) : |
---|
325 | graph(&_graph), length(&_length), |
---|
326 | _pred(0), local_pred(false), |
---|
327 | _dist(0), local_dist(false) {} |
---|
328 | |
---|
329 | ///Destructor. |
---|
330 | ~BelmannFord() { |
---|
331 | if(local_pred) delete _pred; |
---|
332 | if(local_dist) delete _dist; |
---|
333 | delete _mask; |
---|
334 | } |
---|
335 | |
---|
336 | /// \brief Sets the length map. |
---|
337 | /// |
---|
338 | /// Sets the length map. |
---|
339 | /// \return \c (*this) |
---|
340 | BelmannFord &lengthMap(const LengthMap &m) { |
---|
341 | length = &m; |
---|
342 | return *this; |
---|
343 | } |
---|
344 | |
---|
345 | /// \brief Sets the map storing the predecessor edges. |
---|
346 | /// |
---|
347 | /// Sets the map storing the predecessor edges. |
---|
348 | /// If you don't use this function before calling \ref run(), |
---|
349 | /// it will allocate one. The destuctor deallocates this |
---|
350 | /// automatically allocated map, of course. |
---|
351 | /// \return \c (*this) |
---|
352 | BelmannFord &predMap(PredMap &m) { |
---|
353 | if(local_pred) { |
---|
354 | delete _pred; |
---|
355 | local_pred=false; |
---|
356 | } |
---|
357 | _pred = &m; |
---|
358 | return *this; |
---|
359 | } |
---|
360 | |
---|
361 | /// \brief Sets the map storing the distances calculated by the algorithm. |
---|
362 | /// |
---|
363 | /// Sets the map storing the distances calculated by the algorithm. |
---|
364 | /// If you don't use this function before calling \ref run(), |
---|
365 | /// it will allocate one. The destuctor deallocates this |
---|
366 | /// automatically allocated map, of course. |
---|
367 | /// \return \c (*this) |
---|
368 | BelmannFord &distMap(DistMap &m) { |
---|
369 | if(local_dist) { |
---|
370 | delete _dist; |
---|
371 | local_dist=false; |
---|
372 | } |
---|
373 | _dist = &m; |
---|
374 | return *this; |
---|
375 | } |
---|
376 | |
---|
377 | /// \name Execution control |
---|
378 | /// The simplest way to execute the algorithm is to use |
---|
379 | /// one of the member functions called \c run(...). |
---|
380 | /// \n |
---|
381 | /// If you need more control on the execution, |
---|
382 | /// first you must call \ref init(), then you can add several source nodes |
---|
383 | /// with \ref addSource(). |
---|
384 | /// Finally \ref start() will perform the actual path |
---|
385 | /// computation. |
---|
386 | |
---|
387 | ///@{ |
---|
388 | |
---|
389 | /// \brief Initializes the internal data structures. |
---|
390 | /// |
---|
391 | /// Initializes the internal data structures. |
---|
392 | void init(const Value value = OperationTraits::infinity()) { |
---|
393 | create_maps(); |
---|
394 | for (NodeIt it(*graph); it != INVALID; ++it) { |
---|
395 | _pred->set(it, INVALID); |
---|
396 | _dist->set(it, value); |
---|
397 | } |
---|
398 | _process.clear(); |
---|
399 | if (OperationTraits::less(value, OperationTraits::infinity())) { |
---|
400 | for (NodeIt it(*graph); it != INVALID; ++it) { |
---|
401 | _process.push_back(it); |
---|
402 | } |
---|
403 | } |
---|
404 | } |
---|
405 | |
---|
406 | /// \brief Adds a new source node. |
---|
407 | /// |
---|
408 | /// The optional second parameter is the initial distance of the node. |
---|
409 | /// It just sets the distance of the node to the given value. |
---|
410 | void addSource(Node source, Value dst = OperationTraits::zero()) { |
---|
411 | _dist->set(source, dst); |
---|
412 | if (!(*_mask)[source]) { |
---|
413 | _process.push_back(source); |
---|
414 | _mask->set(source, true); |
---|
415 | } |
---|
416 | } |
---|
417 | |
---|
418 | /// \brief Executes one round from the belmann ford algorithm. |
---|
419 | /// |
---|
420 | /// If the algoritm calculated the distances in the previous round |
---|
421 | /// strictly for all at most k length pathes then it will calculate the |
---|
422 | /// distances strictly for all at most k + 1 length pathes. With k |
---|
423 | /// iteration this function calculates the at most k length pathes. |
---|
424 | bool processNextRound() { |
---|
425 | for (int i = 0; i < (int)_process.size(); ++i) { |
---|
426 | _mask->set(_process[i], false); |
---|
427 | } |
---|
428 | std::vector<Node> nextProcess; |
---|
429 | std::vector<Value> values(_process.size()); |
---|
430 | for (int i = 0; i < (int)_process.size(); ++i) { |
---|
431 | values[i] = _dist[_process[i]]; |
---|
432 | } |
---|
433 | for (int i = 0; i < (int)_process.size(); ++i) { |
---|
434 | for (OutEdgeIt it(*graph, _process[i]); it != INVALID; ++it) { |
---|
435 | Node target = graph->target(it); |
---|
436 | Value relaxed = OperationTraits::plus(values[i], (*length)[it]); |
---|
437 | if (OperationTraits::less(relaxed, (*_dist)[target])) { |
---|
438 | _pred->set(target, it); |
---|
439 | _dist->set(target, relaxed); |
---|
440 | if (!(*_mask)[target]) { |
---|
441 | _mask->set(target, true); |
---|
442 | nextProcess.push_back(target); |
---|
443 | } |
---|
444 | } |
---|
445 | } |
---|
446 | } |
---|
447 | _process.swap(nextProcess); |
---|
448 | return _process.empty(); |
---|
449 | } |
---|
450 | |
---|
451 | /// \brief Executes one weak round from the belmann ford algorithm. |
---|
452 | /// |
---|
453 | /// If the algorithm calculated the distances in the |
---|
454 | /// previous round at least for all at most k length pathes then it will |
---|
455 | /// calculate the distances at least for all at most k + 1 length pathes. |
---|
456 | /// This function does not make possible to calculate strictly the |
---|
457 | /// at most k length minimal pathes, this way it called just weak round. |
---|
458 | bool processNextWeakRound() { |
---|
459 | for (int i = 0; i < (int)_process.size(); ++i) { |
---|
460 | _mask->set(_process[i], false); |
---|
461 | } |
---|
462 | std::vector<Node> nextProcess; |
---|
463 | for (int i = 0; i < (int)_process.size(); ++i) { |
---|
464 | for (OutEdgeIt it(*graph, _process[i]); it != INVALID; ++it) { |
---|
465 | Node target = graph->target(it); |
---|
466 | Value relaxed = |
---|
467 | OperationTraits::plus((*_dist)[_process[i]], (*length)[it]); |
---|
468 | if (OperationTraits::less(relaxed, (*_dist)[target])) { |
---|
469 | _pred->set(target, it); |
---|
470 | _dist->set(target, relaxed); |
---|
471 | if (!(*_mask)[target]) { |
---|
472 | _mask->set(target, true); |
---|
473 | nextProcess.push_back(target); |
---|
474 | } |
---|
475 | } |
---|
476 | } |
---|
477 | } |
---|
478 | for (int i = 0; i < (int)nextProcess.size(); ++i) { |
---|
479 | _mask->set(nextProcess[i], false); |
---|
480 | } |
---|
481 | _process.swap(nextProcess); |
---|
482 | return _process.empty(); |
---|
483 | } |
---|
484 | |
---|
485 | /// \brief Executes the algorithm. |
---|
486 | /// |
---|
487 | /// \pre init() must be called and at least one node should be added |
---|
488 | /// with addSource() before using this function. |
---|
489 | /// |
---|
490 | /// This method runs the %BelmannFord algorithm from the root node(s) |
---|
491 | /// in order to compute the shortest path to each node. The algorithm |
---|
492 | /// computes |
---|
493 | /// - The shortest path tree. |
---|
494 | /// - The distance of each node from the root(s). |
---|
495 | void start() { |
---|
496 | int num = countNodes(*graph) - 1; |
---|
497 | for (int i = 0; i < num; ++i) { |
---|
498 | if (processNextWeakRound()) break; |
---|
499 | } |
---|
500 | } |
---|
501 | |
---|
502 | /// \brief Executes the algorithm and checks the negative cycles. |
---|
503 | /// |
---|
504 | /// \pre init() must be called and at least one node should be added |
---|
505 | /// with addSource() before using this function. If there is |
---|
506 | /// a negative cycles in the graph it gives back false. |
---|
507 | /// |
---|
508 | /// This method runs the %BelmannFord algorithm from the root node(s) |
---|
509 | /// in order to compute the shortest path to each node. The algorithm |
---|
510 | /// computes |
---|
511 | /// - The shortest path tree. |
---|
512 | /// - The distance of each node from the root(s). |
---|
513 | bool checkedStart() { |
---|
514 | int num = countNodes(*graph); |
---|
515 | for (int i = 0; i < num; ++i) { |
---|
516 | if (processNextWeakRound()) return true; |
---|
517 | } |
---|
518 | return false; |
---|
519 | } |
---|
520 | |
---|
521 | /// \brief Executes the algorithm with path length limit. |
---|
522 | /// |
---|
523 | /// \pre init() must be called and at least one node should be added |
---|
524 | /// with addSource() before using this function. |
---|
525 | /// |
---|
526 | /// This method runs the %BelmannFord algorithm from the root node(s) |
---|
527 | /// in order to compute the shortest path with at most \c length edge |
---|
528 | /// long pathes to each node. The algorithm computes |
---|
529 | /// - The shortest path tree. |
---|
530 | /// - The limited distance of each node from the root(s). |
---|
531 | void limitedStart(int length) { |
---|
532 | for (int i = 0; i < length; ++i) { |
---|
533 | if (processNextRound()) break; |
---|
534 | } |
---|
535 | } |
---|
536 | |
---|
537 | /// \brief Runs %BelmannFord algorithm from node \c s. |
---|
538 | /// |
---|
539 | /// This method runs the %BelmannFord algorithm from a root node \c s |
---|
540 | /// in order to compute the shortest path to each node. The algorithm |
---|
541 | /// computes |
---|
542 | /// - The shortest path tree. |
---|
543 | /// - The distance of each node from the root. |
---|
544 | /// |
---|
545 | /// \note d.run(s) is just a shortcut of the following code. |
---|
546 | /// \code |
---|
547 | /// d.init(); |
---|
548 | /// d.addSource(s); |
---|
549 | /// d.start(); |
---|
550 | /// \endcode |
---|
551 | void run(Node s) { |
---|
552 | init(); |
---|
553 | addSource(s); |
---|
554 | start(); |
---|
555 | } |
---|
556 | |
---|
557 | ///@} |
---|
558 | |
---|
559 | /// \name Query Functions |
---|
560 | /// The result of the %BelmannFord algorithm can be obtained using these |
---|
561 | /// functions.\n |
---|
562 | /// Before the use of these functions, |
---|
563 | /// either run() or start() must be called. |
---|
564 | |
---|
565 | ///@{ |
---|
566 | |
---|
567 | /// \brief Copies the shortest path to \c t into \c p |
---|
568 | /// |
---|
569 | /// This function copies the shortest path to \c t into \c p. |
---|
570 | /// If it \c t is a source itself or unreachable, then it does not |
---|
571 | /// alter \c p. |
---|
572 | /// |
---|
573 | /// \return Returns \c true if a path to \c t was actually copied to \c p, |
---|
574 | /// \c false otherwise. |
---|
575 | /// \sa DirPath |
---|
576 | template <typename Path> |
---|
577 | bool getPath(Path &p, Node t) { |
---|
578 | if(reached(t)) { |
---|
579 | p.clear(); |
---|
580 | typename Path::Builder b(p); |
---|
581 | for(b.setStartNode(t);predEdge(t)!=INVALID;t=predNode(t)) |
---|
582 | b.pushFront(predEdge(t)); |
---|
583 | b.commit(); |
---|
584 | return true; |
---|
585 | } |
---|
586 | return false; |
---|
587 | } |
---|
588 | |
---|
589 | /// \brief The distance of a node from the root. |
---|
590 | /// |
---|
591 | /// Returns the distance of a node from the root. |
---|
592 | /// \pre \ref run() must be called before using this function. |
---|
593 | /// \warning If node \c v in unreachable from the root the return value |
---|
594 | /// of this funcion is undefined. |
---|
595 | Value dist(Node v) const { return (*_dist)[v]; } |
---|
596 | |
---|
597 | /// \brief Returns the 'previous edge' of the shortest path tree. |
---|
598 | /// |
---|
599 | /// For a node \c v it returns the 'previous edge' of the shortest path |
---|
600 | /// tree, i.e. it returns the last edge of a shortest path from the root |
---|
601 | /// to \c v. It is \ref INVALID if \c v is unreachable from the root or |
---|
602 | /// if \c v=s. The shortest path tree used here is equal to the shortest |
---|
603 | /// path tree used in \ref predNode(). |
---|
604 | /// \pre \ref run() must be called before using |
---|
605 | /// this function. |
---|
606 | Edge predEdge(Node v) const { return (*_pred)[v]; } |
---|
607 | |
---|
608 | /// \brief Returns the 'previous node' of the shortest path tree. |
---|
609 | /// |
---|
610 | /// For a node \c v it returns the 'previous node' of the shortest path |
---|
611 | /// tree, i.e. it returns the last but one node from a shortest path from |
---|
612 | /// the root to \c /v. It is INVALID if \c v is unreachable from the root |
---|
613 | /// or if \c v=s. The shortest path tree used here is equal to the |
---|
614 | /// shortest path tree used in \ref predEdge(). \pre \ref run() must be |
---|
615 | /// called before using this function. |
---|
616 | Node predNode(Node v) const { |
---|
617 | return (*_pred)[v] == INVALID ? INVALID : graph->source((*_pred)[v]); |
---|
618 | } |
---|
619 | |
---|
620 | /// \brief Returns a reference to the NodeMap of distances. |
---|
621 | /// |
---|
622 | /// Returns a reference to the NodeMap of distances. \pre \ref run() must |
---|
623 | /// be called before using this function. |
---|
624 | const DistMap &distMap() const { return *_dist;} |
---|
625 | |
---|
626 | /// \brief Returns a reference to the shortest path tree map. |
---|
627 | /// |
---|
628 | /// Returns a reference to the NodeMap of the edges of the |
---|
629 | /// shortest path tree. |
---|
630 | /// \pre \ref run() must be called before using this function. |
---|
631 | const PredMap &predMap() const { return *_pred; } |
---|
632 | |
---|
633 | /// \brief Checks if a node is reachable from the root. |
---|
634 | /// |
---|
635 | /// Returns \c true if \c v is reachable from the root. |
---|
636 | /// \pre \ref run() must be called before using this function. |
---|
637 | /// |
---|
638 | bool reached(Node v) { return (*_dist)[v] != OperationTraits::infinity(); } |
---|
639 | |
---|
640 | ///@} |
---|
641 | }; |
---|
642 | |
---|
643 | /// \brief Default traits class of BelmannFord function. |
---|
644 | /// |
---|
645 | /// Default traits class of BelmannFord function. |
---|
646 | /// \param _Graph Graph type. |
---|
647 | /// \param _LengthMap Type of length map. |
---|
648 | template <typename _Graph, typename _LengthMap> |
---|
649 | struct BelmannFordWizardDefaultTraits { |
---|
650 | /// \brief The graph type the algorithm runs on. |
---|
651 | typedef _Graph Graph; |
---|
652 | |
---|
653 | /// \brief The type of the map that stores the edge lengths. |
---|
654 | /// |
---|
655 | /// The type of the map that stores the edge lengths. |
---|
656 | /// It must meet the \ref concept::ReadMap "ReadMap" concept. |
---|
657 | typedef _LengthMap LengthMap; |
---|
658 | |
---|
659 | /// \brief The value type of the length map. |
---|
660 | typedef typename _LengthMap::Value Value; |
---|
661 | |
---|
662 | /// \brief Operation traits for belmann-ford algorithm. |
---|
663 | /// |
---|
664 | /// It defines the infinity type on the given Value type |
---|
665 | /// and the used operation. |
---|
666 | /// \see BelmannFordDefaultOperationTraits |
---|
667 | typedef BelmannFordDefaultOperationTraits<Value> OperationTraits; |
---|
668 | |
---|
669 | /// \brief The type of the map that stores the last |
---|
670 | /// edges of the shortest paths. |
---|
671 | /// |
---|
672 | /// The type of the map that stores the last |
---|
673 | /// edges of the shortest paths. |
---|
674 | /// It must meet the \ref concept::WriteMap "WriteMap" concept. |
---|
675 | typedef NullMap <typename _Graph::Node,typename _Graph::Edge> PredMap; |
---|
676 | |
---|
677 | /// \brief Instantiates a PredMap. |
---|
678 | /// |
---|
679 | /// This function instantiates a \ref PredMap. |
---|
680 | static PredMap *createPredMap(const _Graph &) { |
---|
681 | return new PredMap(); |
---|
682 | } |
---|
683 | /// \brief The type of the map that stores the dists of the nodes. |
---|
684 | /// |
---|
685 | /// The type of the map that stores the dists of the nodes. |
---|
686 | /// It must meet the \ref concept::WriteMap "WriteMap" concept. |
---|
687 | typedef NullMap<typename Graph::Node, Value> DistMap; |
---|
688 | /// \brief Instantiates a DistMap. |
---|
689 | /// |
---|
690 | /// This function instantiates a \ref DistMap. |
---|
691 | static DistMap *createDistMap(const _Graph &) { |
---|
692 | return new DistMap(); |
---|
693 | } |
---|
694 | }; |
---|
695 | |
---|
696 | /// \brief Default traits used by \ref BelmannFordWizard |
---|
697 | /// |
---|
698 | /// To make it easier to use BelmannFord algorithm |
---|
699 | /// we have created a wizard class. |
---|
700 | /// This \ref BelmannFordWizard class needs default traits, |
---|
701 | /// as well as the \ref BelmannFord class. |
---|
702 | /// The \ref BelmannFordWizardBase is a class to be the default traits of the |
---|
703 | /// \ref BelmannFordWizard class. |
---|
704 | /// \todo More named parameters are required... |
---|
705 | template<class _Graph,class _LengthMap> |
---|
706 | class BelmannFordWizardBase |
---|
707 | : public BelmannFordWizardDefaultTraits<_Graph,_LengthMap> { |
---|
708 | |
---|
709 | typedef BelmannFordWizardDefaultTraits<_Graph,_LengthMap> Base; |
---|
710 | protected: |
---|
711 | /// Type of the nodes in the graph. |
---|
712 | typedef typename Base::Graph::Node Node; |
---|
713 | |
---|
714 | /// Pointer to the underlying graph. |
---|
715 | void *_graph; |
---|
716 | /// Pointer to the length map |
---|
717 | void *_length; |
---|
718 | ///Pointer to the map of predecessors edges. |
---|
719 | void *_pred; |
---|
720 | ///Pointer to the map of distances. |
---|
721 | void *_dist; |
---|
722 | ///Pointer to the source node. |
---|
723 | Node _source; |
---|
724 | |
---|
725 | public: |
---|
726 | /// Constructor. |
---|
727 | |
---|
728 | /// This constructor does not require parameters, therefore it initiates |
---|
729 | /// all of the attributes to default values (0, INVALID). |
---|
730 | BelmannFordWizardBase() : _graph(0), _length(0), _pred(0), |
---|
731 | _dist(0), _source(INVALID) {} |
---|
732 | |
---|
733 | /// Constructor. |
---|
734 | |
---|
735 | /// This constructor requires some parameters, |
---|
736 | /// listed in the parameters list. |
---|
737 | /// Others are initiated to 0. |
---|
738 | /// \param graph is the initial value of \ref _graph |
---|
739 | /// \param length is the initial value of \ref _length |
---|
740 | /// \param source is the initial value of \ref _source |
---|
741 | BelmannFordWizardBase(const _Graph& graph, |
---|
742 | const _LengthMap& length, |
---|
743 | Node source = INVALID) : |
---|
744 | _graph((void *)&graph), _length((void *)&length), _pred(0), |
---|
745 | _dist(0), _source(source) {} |
---|
746 | |
---|
747 | }; |
---|
748 | |
---|
749 | /// A class to make the usage of BelmannFord algorithm easier |
---|
750 | |
---|
751 | /// This class is created to make it easier to use BelmannFord algorithm. |
---|
752 | /// It uses the functions and features of the plain \ref BelmannFord, |
---|
753 | /// but it is much simpler to use it. |
---|
754 | /// |
---|
755 | /// Simplicity means that the way to change the types defined |
---|
756 | /// in the traits class is based on functions that returns the new class |
---|
757 | /// and not on templatable built-in classes. |
---|
758 | /// When using the plain \ref BelmannFord |
---|
759 | /// the new class with the modified type comes from |
---|
760 | /// the original class by using the :: |
---|
761 | /// operator. In the case of \ref BelmannFordWizard only |
---|
762 | /// a function have to be called and it will |
---|
763 | /// return the needed class. |
---|
764 | /// |
---|
765 | /// It does not have own \ref run method. When its \ref run method is called |
---|
766 | /// it initiates a plain \ref BelmannFord class, and calls the \ref |
---|
767 | /// BelmannFord::run method of it. |
---|
768 | template<class _Traits> |
---|
769 | class BelmannFordWizard : public _Traits { |
---|
770 | typedef _Traits Base; |
---|
771 | |
---|
772 | ///The type of the underlying graph. |
---|
773 | typedef typename _Traits::Graph Graph; |
---|
774 | |
---|
775 | typedef typename Graph::Node Node; |
---|
776 | typedef typename Graph::NodeIt NodeIt; |
---|
777 | typedef typename Graph::Edge Edge; |
---|
778 | typedef typename Graph::OutEdgeIt EdgeIt; |
---|
779 | |
---|
780 | ///The type of the map that stores the edge lengths. |
---|
781 | typedef typename _Traits::LengthMap LengthMap; |
---|
782 | |
---|
783 | ///The type of the length of the edges. |
---|
784 | typedef typename LengthMap::Value Value; |
---|
785 | |
---|
786 | ///\brief The type of the map that stores the last |
---|
787 | ///edges of the shortest paths. |
---|
788 | typedef typename _Traits::PredMap PredMap; |
---|
789 | |
---|
790 | ///The type of the map that stores the dists of the nodes. |
---|
791 | typedef typename _Traits::DistMap DistMap; |
---|
792 | |
---|
793 | public: |
---|
794 | /// Constructor. |
---|
795 | BelmannFordWizard() : _Traits() {} |
---|
796 | |
---|
797 | /// \brief Constructor that requires parameters. |
---|
798 | /// |
---|
799 | /// Constructor that requires parameters. |
---|
800 | /// These parameters will be the default values for the traits class. |
---|
801 | BelmannFordWizard(const Graph& graph, const LengthMap& length, |
---|
802 | Node source = INVALID) |
---|
803 | : _Traits(graph, length, source) {} |
---|
804 | |
---|
805 | /// \brief Copy constructor |
---|
806 | BelmannFordWizard(const _Traits &b) : _Traits(b) {} |
---|
807 | |
---|
808 | ~BelmannFordWizard() {} |
---|
809 | |
---|
810 | /// \brief Runs BelmannFord algorithm from a given node. |
---|
811 | /// |
---|
812 | /// Runs BelmannFord algorithm from a given node. |
---|
813 | /// The node can be given by the \ref source function. |
---|
814 | void run() { |
---|
815 | if(Base::_source == INVALID) throw UninitializedParameter(); |
---|
816 | BelmannFord<Graph,LengthMap,_Traits> |
---|
817 | bf(*(Graph*)Base::_graph, *(LengthMap*)Base::_length); |
---|
818 | if (Base::_pred) bf.predMap(*(PredMap*)Base::_pred); |
---|
819 | if (Base::_dist) bf.distMap(*(DistMap*)Base::_dist); |
---|
820 | bf.run(Base::_source); |
---|
821 | } |
---|
822 | |
---|
823 | /// \brief Runs BelmannFord algorithm from the given node. |
---|
824 | /// |
---|
825 | /// Runs BelmannFord algorithm from the given node. |
---|
826 | /// \param s is the given source. |
---|
827 | void run(Node source) { |
---|
828 | Base::_source = source; |
---|
829 | run(); |
---|
830 | } |
---|
831 | |
---|
832 | template<class T> |
---|
833 | struct DefPredMapBase : public Base { |
---|
834 | typedef T PredMap; |
---|
835 | static PredMap *createPredMap(const Graph &) { return 0; }; |
---|
836 | DefPredMapBase(const _Traits &b) : _Traits(b) {} |
---|
837 | }; |
---|
838 | |
---|
839 | ///\brief \ref named-templ-param "Named parameter" |
---|
840 | ///function for setting PredMap type |
---|
841 | /// |
---|
842 | /// \ref named-templ-param "Named parameter" |
---|
843 | ///function for setting PredMap type |
---|
844 | /// |
---|
845 | template<class T> |
---|
846 | BelmannFordWizard<DefPredMapBase<T> > predMap(const T &t) |
---|
847 | { |
---|
848 | Base::_pred=(void *)&t; |
---|
849 | return BelmannFordWizard<DefPredMapBase<T> >(*this); |
---|
850 | } |
---|
851 | |
---|
852 | template<class T> |
---|
853 | struct DefDistMapBase : public Base { |
---|
854 | typedef T DistMap; |
---|
855 | static DistMap *createDistMap(const Graph &) { return 0; }; |
---|
856 | DefDistMapBase(const _Traits &b) : _Traits(b) {} |
---|
857 | }; |
---|
858 | |
---|
859 | ///\brief \ref named-templ-param "Named parameter" |
---|
860 | ///function for setting DistMap type |
---|
861 | /// |
---|
862 | /// \ref named-templ-param "Named parameter" |
---|
863 | ///function for setting DistMap type |
---|
864 | /// |
---|
865 | template<class T> |
---|
866 | BelmannFordWizard<DefDistMapBase<T> > distMap(const T &t) { |
---|
867 | Base::_dist=(void *)&t; |
---|
868 | return BelmannFordWizard<DefDistMapBase<T> >(*this); |
---|
869 | } |
---|
870 | |
---|
871 | template<class T> |
---|
872 | struct DefOperationTraitsBase : public Base { |
---|
873 | typedef T OperationTraits; |
---|
874 | DefOperationTraitsBase(const _Traits &b) : _Traits(b) {} |
---|
875 | }; |
---|
876 | |
---|
877 | ///\brief \ref named-templ-param "Named parameter" |
---|
878 | ///function for setting OperationTraits type |
---|
879 | /// |
---|
880 | /// \ref named-templ-param "Named parameter" |
---|
881 | ///function for setting OperationTraits type |
---|
882 | /// |
---|
883 | template<class T> |
---|
884 | BelmannFordWizard<DefOperationTraitsBase<T> > distMap() { |
---|
885 | return BelmannFordWizard<DefDistMapBase<T> >(*this); |
---|
886 | } |
---|
887 | |
---|
888 | /// \brief Sets the source node, from which the BelmannFord algorithm runs. |
---|
889 | /// |
---|
890 | /// Sets the source node, from which the BelmannFord algorithm runs. |
---|
891 | /// \param s is the source node. |
---|
892 | BelmannFordWizard<_Traits>& source(Node source) { |
---|
893 | Base::_source = source; |
---|
894 | return *this; |
---|
895 | } |
---|
896 | |
---|
897 | }; |
---|
898 | |
---|
899 | /// \brief Function type interface for BelmannFord algorithm. |
---|
900 | /// |
---|
901 | /// \ingroup flowalgs |
---|
902 | /// Function type interface for BelmannFord algorithm. |
---|
903 | /// |
---|
904 | /// This function also has several \ref named-templ-func-param |
---|
905 | /// "named parameters", they are declared as the members of class |
---|
906 | /// \ref BelmannFordWizard. |
---|
907 | /// The following |
---|
908 | /// example shows how to use these parameters. |
---|
909 | /// \code |
---|
910 | /// belmannford(g,length,source).predMap(preds).run(); |
---|
911 | /// \endcode |
---|
912 | /// \warning Don't forget to put the \ref BelmannFordWizard::run() "run()" |
---|
913 | /// to the end of the parameter list. |
---|
914 | /// \sa BelmannFordWizard |
---|
915 | /// \sa BelmannFord |
---|
916 | template<class _Graph, class _LengthMap> |
---|
917 | BelmannFordWizard<BelmannFordWizardBase<_Graph,_LengthMap> > |
---|
918 | belmannFord(const _Graph& graph, |
---|
919 | const _LengthMap& length, |
---|
920 | typename _Graph::Node source = INVALID) { |
---|
921 | return BelmannFordWizard<BelmannFordWizardBase<_Graph,_LengthMap> > |
---|
922 | (graph, length, source); |
---|
923 | } |
---|
924 | |
---|
925 | } //END OF NAMESPACE LEMON |
---|
926 | |
---|
927 | #endif |
---|
928 | |
---|