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alpar (Alpar Juttner)
alpar@cs.elte.hu
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/* -*- C++ -*-
2 2
 *
3 3
 * This file is a part of LEMON, a generic C++ optimization library
4 4
 *
5 5
 * Copyright (C) 2003-2008
6 6
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 7
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 8
 *
9 9
 * Permission to use, modify and distribute this software is granted
10 10
 * provided that this copyright notice appears in all copies. For
11 11
 * precise terms see the accompanying LICENSE file.
12 12
 *
13 13
 * This software is provided "AS IS" with no warranty of any kind,
14 14
 * express or implied, and with no claim as to its suitability for any
15 15
 * purpose.
16 16
 *
17 17
 */
18 18

	
19 19
#ifndef LEMON_BELLMAN_FORD_H
20 20
#define LEMON_BELLMAN_FORD_H
21 21

	
22 22
/// \ingroup shortest_path
23 23
/// \file
24 24
/// \brief Bellman-Ford algorithm.
25 25

	
26 26
#include <lemon/list_graph.h>
27 27
#include <lemon/bits/path_dump.h>
28 28
#include <lemon/core.h>
29 29
#include <lemon/error.h>
30 30
#include <lemon/maps.h>
31
#include <lemon/tolerance.h>
32 31
#include <lemon/path.h>
33 32

	
34 33
#include <limits>
35 34

	
36 35
namespace lemon {
37 36

	
38
  /// \brief Default operation traits for the BellmanFord algorithm class.
37
  /// \brief Default OperationTraits for the BellmanFord algorithm class.
39 38
  ///  
40 39
  /// This operation traits class defines all computational operations
41 40
  /// and constants that are used in the Bellman-Ford algorithm.
42 41
  /// The default implementation is based on the \c numeric_limits class.
43 42
  /// If the numeric type does not have infinity value, then the maximum
44 43
  /// value is used as extremal infinity value.
45
  ///
46
  /// \see BellmanFordToleranceOperationTraits
47 44
  template <
48 45
    typename V, 
49 46
    bool has_inf = std::numeric_limits<V>::has_infinity>
50 47
  struct BellmanFordDefaultOperationTraits {
51
    /// \brief Value type for the algorithm.
48
    /// \e
52 49
    typedef V Value;
53 50
    /// \brief Gives back the zero value of the type.
54 51
    static Value zero() {
55 52
      return static_cast<Value>(0);
56 53
    }
57 54
    /// \brief Gives back the positive infinity value of the type.
58 55
    static Value infinity() {
59 56
      return std::numeric_limits<Value>::infinity();
60 57
    }
61 58
    /// \brief Gives back the sum of the given two elements.
62 59
    static Value plus(const Value& left, const Value& right) {
63 60
      return left + right;
64 61
    }
65 62
    /// \brief Gives back \c true only if the first value is less than
66 63
    /// the second.
67 64
    static bool less(const Value& left, const Value& right) {
68 65
      return left < right;
69 66
    }
70 67
  };
71 68

	
72 69
  template <typename V>
73 70
  struct BellmanFordDefaultOperationTraits<V, false> {
74 71
    typedef V Value;
75 72
    static Value zero() {
76 73
      return static_cast<Value>(0);
77 74
    }
78 75
    static Value infinity() {
79 76
      return std::numeric_limits<Value>::max();
80 77
    }
81 78
    static Value plus(const Value& left, const Value& right) {
82 79
      if (left == infinity() || right == infinity()) return infinity();
83 80
      return left + right;
84 81
    }
85 82
    static bool less(const Value& left, const Value& right) {
86 83
      return left < right;
87 84
    }
88 85
  };
89 86
  
90
  /// \brief Operation traits for the BellmanFord algorithm class
91
  /// using tolerance.
92
  ///
93
  /// This operation traits class defines all computational operations
94
  /// and constants that are used in the Bellman-Ford algorithm.
95
  /// The only difference between this implementation and
96
  /// \ref BellmanFordDefaultOperationTraits is that this class uses
97
  /// the \ref Tolerance "tolerance technique" in its \ref less()
98
  /// function.
99
  ///
100
  /// \tparam V The value type.
101
  /// \tparam eps The epsilon value for the \ref less() function.
102
  /// By default, it is the epsilon value used by \ref Tolerance
103
  /// "Tolerance<V>".
104
  ///
105
  /// \see BellmanFordDefaultOperationTraits
106
#ifdef DOXYGEN
107
  template <typename V, V eps>
108
#else
109
  template <
110
    typename V,
111
    V eps = Tolerance<V>::def_epsilon>
112
#endif
113
  struct BellmanFordToleranceOperationTraits {
114
    /// \brief Value type for the algorithm.
115
    typedef V Value;
116
    /// \brief Gives back the zero value of the type.
117
    static Value zero() {
118
      return static_cast<Value>(0);
119
    }
120
    /// \brief Gives back the positive infinity value of the type.
121
    static Value infinity() {
122
      return std::numeric_limits<Value>::infinity();
123
    }
124
    /// \brief Gives back the sum of the given two elements.
125
    static Value plus(const Value& left, const Value& right) {
126
      return left + right;
127
    }
128
    /// \brief Gives back \c true only if the first value is less than
129
    /// the second.
130
    static bool less(const Value& left, const Value& right) {
131
      return left + eps < right;
132
    }
133
  };
134

	
135 87
  /// \brief Default traits class of BellmanFord class.
136 88
  ///
137 89
  /// Default traits class of BellmanFord class.
138 90
  /// \param GR The type of the digraph.
139 91
  /// \param LEN The type of the length map.
140 92
  template<typename GR, typename LEN>
141 93
  struct BellmanFordDefaultTraits {
142 94
    /// The type of the digraph the algorithm runs on. 
143 95
    typedef GR Digraph;
144 96

	
145 97
    /// \brief The type of the map that stores the arc lengths.
146 98
    ///
147 99
    /// The type of the map that stores the arc lengths.
148 100
    /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
149 101
    typedef LEN LengthMap;
150 102

	
151 103
    /// The type of the arc lengths.
152 104
    typedef typename LEN::Value Value;
153 105

	
154 106
    /// \brief Operation traits for Bellman-Ford algorithm.
155 107
    ///
156 108
    /// It defines the used operations and the infinity value for the
157 109
    /// given \c Value type.
158
    /// \see BellmanFordDefaultOperationTraits,
159
    /// BellmanFordToleranceOperationTraits
110
    /// \see BellmanFordDefaultOperationTraits
160 111
    typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
161 112
 
162 113
    /// \brief The type of the map that stores the last arcs of the 
163 114
    /// shortest paths.
164 115
    /// 
165 116
    /// The type of the map that stores the last
166 117
    /// arcs of the shortest paths.
167 118
    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
168 119
    typedef typename GR::template NodeMap<typename GR::Arc> PredMap;
169 120

	
170 121
    /// \brief Instantiates a \c PredMap.
171 122
    /// 
172 123
    /// This function instantiates a \ref PredMap. 
173 124
    /// \param g is the digraph to which we would like to define the
174 125
    /// \ref PredMap.
175 126
    static PredMap *createPredMap(const GR& g) {
176 127
      return new PredMap(g);
177 128
    }
178 129

	
179 130
    /// \brief The type of the map that stores the distances of the nodes.
180 131
    ///
181 132
    /// The type of the map that stores the distances of the nodes.
182 133
    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
183 134
    typedef typename GR::template NodeMap<typename LEN::Value> DistMap;
184 135

	
185 136
    /// \brief Instantiates a \c DistMap.
186 137
    ///
187 138
    /// This function instantiates a \ref DistMap. 
188 139
    /// \param g is the digraph to which we would like to define the 
189 140
    /// \ref DistMap.
190 141
    static DistMap *createDistMap(const GR& g) {
191 142
      return new DistMap(g);
192 143
    }
193 144

	
194 145
  };
195 146
  
196 147
  /// \brief %BellmanFord algorithm class.
197 148
  ///
198 149
  /// \ingroup shortest_path
199 150
  /// This class provides an efficient implementation of the Bellman-Ford 
200 151
  /// algorithm. The maximum time complexity of the algorithm is
201 152
  /// <tt>O(ne)</tt>.
202 153
  ///
203 154
  /// The Bellman-Ford algorithm solves the single-source shortest path
204 155
  /// problem when the arcs can have negative lengths, but the digraph
205 156
  /// should not contain directed cycles with negative total length.
206 157
  /// If all arc costs are non-negative, consider to use the Dijkstra
207 158
  /// algorithm instead, since it is more efficient.
208 159
  ///
209 160
  /// The arc lengths are passed to the algorithm using a
210 161
  /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any 
211 162
  /// kind of length. The type of the length values is determined by the
212 163
  /// \ref concepts::ReadMap::Value "Value" type of the length map.
213 164
  ///
214 165
  /// There is also a \ref bellmanFord() "function-type interface" for the
215 166
  /// Bellman-Ford algorithm, which is convenient in the simplier cases and
216 167
  /// it can be used easier.
217 168
  ///
218 169
  /// \tparam GR The type of the digraph the algorithm runs on.
219 170
  /// The default type is \ref ListDigraph.
220 171
  /// \tparam LEN A \ref concepts::ReadMap "readable" arc map that specifies
221 172
  /// the lengths of the arcs. The default map type is
222 173
  /// \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
223 174
  /// \tparam TR The traits class that defines various types used by the
224 175
  /// algorithm. By default, it is \ref BellmanFordDefaultTraits
225 176
  /// "BellmanFordDefaultTraits<GR, LEN>".
226 177
  /// In most cases, this parameter should not be set directly,
227 178
  /// consider to use the named template parameters instead.
228 179
#ifdef DOXYGEN
229 180
  template <typename GR, typename LEN, typename TR>
230 181
#else
231 182
  template <typename GR=ListDigraph,
232 183
            typename LEN=typename GR::template ArcMap<int>,
233 184
            typename TR=BellmanFordDefaultTraits<GR,LEN> >
234 185
#endif
235 186
  class BellmanFord {
236 187
  public:
237 188

	
238 189
    ///The type of the underlying digraph.
239 190
    typedef typename TR::Digraph Digraph;
240 191
    
241 192
    /// \brief The type of the arc lengths.
242 193
    typedef typename TR::LengthMap::Value Value;
243 194
    /// \brief The type of the map that stores the arc lengths.
244 195
    typedef typename TR::LengthMap LengthMap;
245 196
    /// \brief The type of the map that stores the last
246 197
    /// arcs of the shortest paths.
247 198
    typedef typename TR::PredMap PredMap;
248 199
    /// \brief The type of the map that stores the distances of the nodes.
249 200
    typedef typename TR::DistMap DistMap;
250 201
    /// The type of the paths.
251 202
    typedef PredMapPath<Digraph, PredMap> Path;
252 203
    ///\brief The \ref BellmanFordDefaultOperationTraits
253 204
    /// "operation traits class" of the algorithm.
254 205
    typedef typename TR::OperationTraits OperationTraits;
255 206

	
256 207
    ///The \ref BellmanFordDefaultTraits "traits class" of the algorithm.
257 208
    typedef TR Traits;
258 209

	
259 210
  private:
260 211

	
261 212
    typedef typename Digraph::Node Node;
262 213
    typedef typename Digraph::NodeIt NodeIt;
263 214
    typedef typename Digraph::Arc Arc;
264 215
    typedef typename Digraph::OutArcIt OutArcIt;
265 216

	
266 217
    // Pointer to the underlying digraph.
267 218
    const Digraph *_gr;
268 219
    // Pointer to the length map
269 220
    const LengthMap *_length;
270 221
    // Pointer to the map of predecessors arcs.
271 222
    PredMap *_pred;
272 223
    // Indicates if _pred is locally allocated (true) or not.
273 224
    bool _local_pred;
274 225
    // Pointer to the map of distances.
275 226
    DistMap *_dist;
276 227
    // Indicates if _dist is locally allocated (true) or not.
277 228
    bool _local_dist;
278 229

	
279 230
    typedef typename Digraph::template NodeMap<bool> MaskMap;
280 231
    MaskMap *_mask;
281 232

	
282 233
    std::vector<Node> _process;
283 234

	
284 235
    // Creates the maps if necessary.
285 236
    void create_maps() {
286 237
      if(!_pred) {
287 238
	_local_pred = true;
288 239
	_pred = Traits::createPredMap(*_gr);
289 240
      }
290 241
      if(!_dist) {
291 242
	_local_dist = true;
292 243
	_dist = Traits::createDistMap(*_gr);
293 244
      }
294 245
      if(!_mask) {
295 246
        _mask = new MaskMap(*_gr);
296 247
      }
297 248
    }
298 249
    
299 250
  public :
300 251
 
301 252
    typedef BellmanFord Create;
302 253

	
303 254
    /// \name Named Template Parameters
304 255

	
305 256
    ///@{
306 257

	
307 258
    template <class T>
308 259
    struct SetPredMapTraits : public Traits {
309 260
      typedef T PredMap;
310 261
      static PredMap *createPredMap(const Digraph&) {
311 262
        LEMON_ASSERT(false, "PredMap is not initialized");
312 263
        return 0; // ignore warnings
313 264
      }
314 265
    };
315 266

	
316 267
    /// \brief \ref named-templ-param "Named parameter" for setting
317 268
    /// \c PredMap type.
318 269
    ///
319 270
    /// \ref named-templ-param "Named parameter" for setting
320 271
    /// \c PredMap type.
321 272
    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
322 273
    template <class T>
323 274
    struct SetPredMap 
324 275
      : public BellmanFord< Digraph, LengthMap, SetPredMapTraits<T> > {
325 276
      typedef BellmanFord< Digraph, LengthMap, SetPredMapTraits<T> > Create;
326 277
    };
327 278
    
328 279
    template <class T>
329 280
    struct SetDistMapTraits : public Traits {
330 281
      typedef T DistMap;
331 282
      static DistMap *createDistMap(const Digraph&) {
332 283
        LEMON_ASSERT(false, "DistMap is not initialized");
333 284
        return 0; // ignore warnings
334 285
      }
335 286
    };
336 287

	
337 288
    /// \brief \ref named-templ-param "Named parameter" for setting
338 289
    /// \c DistMap type.
339 290
    ///
340 291
    /// \ref named-templ-param "Named parameter" for setting
341 292
    /// \c DistMap type.
342 293
    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
343 294
    template <class T>
344 295
    struct SetDistMap 
345 296
      : public BellmanFord< Digraph, LengthMap, SetDistMapTraits<T> > {
346 297
      typedef BellmanFord< Digraph, LengthMap, SetDistMapTraits<T> > Create;
347 298
    };
348 299

	
349 300
    template <class T>
350 301
    struct SetOperationTraitsTraits : public Traits {
351 302
      typedef T OperationTraits;
352 303
    };
353 304
    
354 305
    /// \brief \ref named-templ-param "Named parameter" for setting 
355 306
    /// \c OperationTraits type.
356 307
    ///
357 308
    /// \ref named-templ-param "Named parameter" for setting
358 309
    /// \c OperationTraits type.
359 310
    /// For more information, see \ref BellmanFordDefaultOperationTraits.
360 311
    template <class T>
361 312
    struct SetOperationTraits
362 313
      : public BellmanFord< Digraph, LengthMap, SetOperationTraitsTraits<T> > {
363 314
      typedef BellmanFord< Digraph, LengthMap, SetOperationTraitsTraits<T> >
364 315
      Create;
365 316
    };
366 317
    
367 318
    ///@}
368 319

	
369 320
  protected:
370 321
    
371 322
    BellmanFord() {}
372 323

	
373 324
  public:      
374 325
    
375 326
    /// \brief Constructor.
376 327
    ///
377 328
    /// Constructor.
378 329
    /// \param g The digraph the algorithm runs on.
379 330
    /// \param length The length map used by the algorithm.
380 331
    BellmanFord(const Digraph& g, const LengthMap& length) :
381 332
      _gr(&g), _length(&length),
382 333
      _pred(0), _local_pred(false),
383 334
      _dist(0), _local_dist(false), _mask(0) {}
384 335
    
385 336
    ///Destructor.
386 337
    ~BellmanFord() {
387 338
      if(_local_pred) delete _pred;
388 339
      if(_local_dist) delete _dist;
389 340
      if(_mask) delete _mask;
390 341
    }
391 342

	
392 343
    /// \brief Sets the length map.
393 344
    ///
394 345
    /// Sets the length map.
395 346
    /// \return <tt>(*this)</tt>
396 347
    BellmanFord &lengthMap(const LengthMap &map) {
397 348
      _length = &map;
398 349
      return *this;
399 350
    }
400 351

	
401 352
    /// \brief Sets the map that stores the predecessor arcs.
402 353
    ///
403 354
    /// Sets the map that stores the predecessor arcs.
404 355
    /// If you don't use this function before calling \ref run()
405 356
    /// or \ref init(), an instance will be allocated automatically.
406 357
    /// The destructor deallocates this automatically allocated map,
407 358
    /// of course.
408 359
    /// \return <tt>(*this)</tt>
409 360
    BellmanFord &predMap(PredMap &map) {
410 361
      if(_local_pred) {
411 362
	delete _pred;
412 363
	_local_pred=false;
413 364
      }
414 365
      _pred = &map;
415 366
      return *this;
416 367
    }
417 368

	
418 369
    /// \brief Sets the map that stores the distances of the nodes.
419 370
    ///
420 371
    /// Sets the map that stores the distances of the nodes calculated
421 372
    /// by the algorithm.
422 373
    /// If you don't use this function before calling \ref run()
423 374
    /// or \ref init(), an instance will be allocated automatically.
424 375
    /// The destructor deallocates this automatically allocated map,
425 376
    /// of course.
426 377
    /// \return <tt>(*this)</tt>
427 378
    BellmanFord &distMap(DistMap &map) {
428 379
      if(_local_dist) {
429 380
	delete _dist;
430 381
	_local_dist=false;
431 382
      }
432 383
      _dist = &map;
433 384
      return *this;
434 385
    }
435 386

	
436 387
    /// \name Execution Control
437 388
    /// The simplest way to execute the Bellman-Ford algorithm is to use
438 389
    /// one of the member functions called \ref run().\n
439 390
    /// If you need better control on the execution, you have to call
440 391
    /// \ref init() first, then you can add several source nodes
441 392
    /// with \ref addSource(). Finally the actual path computation can be
442 393
    /// performed with \ref start(), \ref checkedStart() or
443 394
    /// \ref limitedStart().
444 395

	
445 396
    ///@{
446 397

	
447 398
    /// \brief Initializes the internal data structures.
448 399
    /// 
449 400
    /// Initializes the internal data structures. The optional parameter
450 401
    /// is the initial distance of each node.
451 402
    void init(const Value value = OperationTraits::infinity()) {
452 403
      create_maps();
453 404
      for (NodeIt it(*_gr); it != INVALID; ++it) {
454 405
	_pred->set(it, INVALID);
455 406
	_dist->set(it, value);
456 407
      }
457 408
      _process.clear();
458 409
      if (OperationTraits::less(value, OperationTraits::infinity())) {
459 410
	for (NodeIt it(*_gr); it != INVALID; ++it) {
460 411
	  _process.push_back(it);
461 412
	  _mask->set(it, true);
462 413
	}
463 414
      } else {
464 415
	for (NodeIt it(*_gr); it != INVALID; ++it) {
465 416
	  _mask->set(it, false);
466 417
	}
467 418
      }
468 419
    }
469 420
    
470 421
    /// \brief Adds a new source node.
471 422
    ///
472 423
    /// This function adds a new source node. The optional second parameter
473 424
    /// is the initial distance of the node.
474 425
    void addSource(Node source, Value dst = OperationTraits::zero()) {
475 426
      _dist->set(source, dst);
476 427
      if (!(*_mask)[source]) {
477 428
	_process.push_back(source);
478 429
	_mask->set(source, true);
479 430
      }
480 431
    }
481 432

	
482 433
    /// \brief Executes one round from the Bellman-Ford algorithm.
483 434
    ///
484 435
    /// If the algoritm calculated the distances in the previous round
485 436
    /// exactly for the paths of at most \c k arcs, then this function
486 437
    /// will calculate the distances exactly for the paths of at most
487 438
    /// <tt>k+1</tt> arcs. Performing \c k iterations using this function
488 439
    /// calculates the shortest path distances exactly for the paths
489 440
    /// consisting of at most \c k arcs.
490 441
    ///
491 442
    /// \warning The paths with limited arc number cannot be retrieved
492 443
    /// easily with \ref path() or \ref predArc() functions. If you also
493 444
    /// need the shortest paths and not only the distances, you should
494 445
    /// store the \ref predMap() "predecessor map" after each iteration
495 446
    /// and build the path manually.
496 447
    ///
497 448
    /// \return \c true when the algorithm have not found more shorter
498 449
    /// paths.
499 450
    ///
500 451
    /// \see ActiveIt
501 452
    bool processNextRound() {
502 453
      for (int i = 0; i < int(_process.size()); ++i) {
503 454
	_mask->set(_process[i], false);
504 455
      }
505 456
      std::vector<Node> nextProcess;
506 457
      std::vector<Value> values(_process.size());
507 458
      for (int i = 0; i < int(_process.size()); ++i) {
508 459
	values[i] = (*_dist)[_process[i]];
509 460
      }
510 461
      for (int i = 0; i < int(_process.size()); ++i) {
511 462
	for (OutArcIt it(*_gr, _process[i]); it != INVALID; ++it) {
512 463
	  Node target = _gr->target(it);
513 464
	  Value relaxed = OperationTraits::plus(values[i], (*_length)[it]);
514 465
	  if (OperationTraits::less(relaxed, (*_dist)[target])) {
515 466
	    _pred->set(target, it);
516 467
	    _dist->set(target, relaxed);
517 468
	    if (!(*_mask)[target]) {
518 469
	      _mask->set(target, true);
519 470
	      nextProcess.push_back(target);
520 471
	    }
521 472
	  }	  
522 473
	}
523 474
      }
524 475
      _process.swap(nextProcess);
525 476
      return _process.empty();
526 477
    }
527 478

	
528 479
    /// \brief Executes one weak round from the Bellman-Ford algorithm.
529 480
    ///
530 481
    /// If the algorithm calculated the distances in the previous round
531 482
    /// at least for the paths of at most \c k arcs, then this function
532 483
    /// will calculate the distances at least for the paths of at most
533 484
    /// <tt>k+1</tt> arcs.
534 485
    /// This function does not make it possible to calculate the shortest
535 486
    /// path distances exactly for paths consisting of at most \c k arcs,
536 487
    /// this is why it is called weak round.
537 488
    ///
538 489
    /// \return \c true when the algorithm have not found more shorter
539 490
    /// paths.
540 491
    ///
541 492
    /// \see ActiveIt
542 493
    bool processNextWeakRound() {
543 494
      for (int i = 0; i < int(_process.size()); ++i) {
544 495
	_mask->set(_process[i], false);
545 496
      }
546 497
      std::vector<Node> nextProcess;
547 498
      for (int i = 0; i < int(_process.size()); ++i) {
548 499
	for (OutArcIt it(*_gr, _process[i]); it != INVALID; ++it) {
549 500
	  Node target = _gr->target(it);
550 501
	  Value relaxed = 
551 502
	    OperationTraits::plus((*_dist)[_process[i]], (*_length)[it]);
552 503
	  if (OperationTraits::less(relaxed, (*_dist)[target])) {
553 504
	    _pred->set(target, it);
554 505
	    _dist->set(target, relaxed);
555 506
	    if (!(*_mask)[target]) {
556 507
	      _mask->set(target, true);
557 508
	      nextProcess.push_back(target);
558 509
	    }
559 510
	  }	  
560 511
	}
561 512
      }
562 513
      _process.swap(nextProcess);
563 514
      return _process.empty();
564 515
    }
565 516

	
566 517
    /// \brief Executes the algorithm.
567 518
    ///
568 519
    /// Executes the algorithm.
569 520
    ///
570 521
    /// This method runs the Bellman-Ford algorithm from the root node(s)
571 522
    /// in order to compute the shortest path to each node.
572 523
    ///
573 524
    /// The algorithm computes
574 525
    /// - the shortest path tree (forest),
575 526
    /// - the distance of each node from the root(s).
576 527
    ///
577 528
    /// \pre init() must be called and at least one root node should be
578 529
    /// added with addSource() before using this function.
579 530
    void start() {
580 531
      int num = countNodes(*_gr) - 1;
581 532
      for (int i = 0; i < num; ++i) {
582 533
	if (processNextWeakRound()) break;
583 534
      }
584 535
    }
585 536

	
586 537
    /// \brief Executes the algorithm and checks the negative cycles.
587 538
    ///
588 539
    /// Executes the algorithm and checks the negative cycles.
589 540
    ///
590 541
    /// This method runs the Bellman-Ford algorithm from the root node(s)
591 542
    /// in order to compute the shortest path to each node and also checks
592 543
    /// if the digraph contains cycles with negative total length.
593 544
    ///
594 545
    /// The algorithm computes 
595 546
    /// - the shortest path tree (forest),
596 547
    /// - the distance of each node from the root(s).
597 548
    /// 
598 549
    /// \return \c false if there is a negative cycle in the digraph.
599 550
    ///
600 551
    /// \pre init() must be called and at least one root node should be
601 552
    /// added with addSource() before using this function. 
602 553
    bool checkedStart() {
603 554
      int num = countNodes(*_gr);
604 555
      for (int i = 0; i < num; ++i) {
605 556
	if (processNextWeakRound()) return true;
606 557
      }
607 558
      return _process.empty();
608 559
    }
609 560

	
610 561
    /// \brief Executes the algorithm with arc number limit.
611 562
    ///
612 563
    /// Executes the algorithm with arc number limit.
613 564
    ///
614 565
    /// This method runs the Bellman-Ford algorithm from the root node(s)
615 566
    /// in order to compute the shortest path distance for each node
616 567
    /// using only the paths consisting of at most \c num arcs.
617 568
    ///
618 569
    /// The algorithm computes
619 570
    /// - the limited distance of each node from the root(s),
620 571
    /// - the predecessor arc for each node.
621 572
    ///
622 573
    /// \warning The paths with limited arc number cannot be retrieved
623 574
    /// easily with \ref path() or \ref predArc() functions. If you also
624 575
    /// need the shortest paths and not only the distances, you should
625 576
    /// store the \ref predMap() "predecessor map" after each iteration
626 577
    /// and build the path manually.
627 578
    ///
628 579
    /// \pre init() must be called and at least one root node should be
629 580
    /// added with addSource() before using this function. 
630 581
    void limitedStart(int num) {
631 582
      for (int i = 0; i < num; ++i) {
632 583
	if (processNextRound()) break;
633 584
      }
634 585
    }
635 586
    
636 587
    /// \brief Runs the algorithm from the given root node.
637 588
    ///    
638 589
    /// This method runs the Bellman-Ford algorithm from the given root
639 590
    /// node \c s in order to compute the shortest path to each node.
640 591
    ///
641 592
    /// The algorithm computes
642 593
    /// - the shortest path tree (forest),
643 594
    /// - the distance of each node from the root(s).
644 595
    ///
645 596
    /// \note bf.run(s) is just a shortcut of the following code.
646 597
    /// \code
647 598
    ///   bf.init();
648 599
    ///   bf.addSource(s);
649 600
    ///   bf.start();
650 601
    /// \endcode
651 602
    void run(Node s) {
652 603
      init();
653 604
      addSource(s);
654 605
      start();
655 606
    }
656 607
    
657 608
    /// \brief Runs the algorithm from the given root node with arc
658 609
    /// number limit.
659 610
    ///    
660 611
    /// This method runs the Bellman-Ford algorithm from the given root
661 612
    /// node \c s in order to compute the shortest path distance for each
662 613
    /// node using only the paths consisting of at most \c num arcs.
663 614
    ///
664 615
    /// The algorithm computes
665 616
    /// - the limited distance of each node from the root(s),
666 617
    /// - the predecessor arc for each node.
667 618
    ///
668 619
    /// \warning The paths with limited arc number cannot be retrieved
669 620
    /// easily with \ref path() or \ref predArc() functions. If you also
670 621
    /// need the shortest paths and not only the distances, you should
671 622
    /// store the \ref predMap() "predecessor map" after each iteration
672 623
    /// and build the path manually.
673 624
    ///
674 625
    /// \note bf.run(s, num) is just a shortcut of the following code.
675 626
    /// \code
676 627
    ///   bf.init();
677 628
    ///   bf.addSource(s);
678 629
    ///   bf.limitedStart(num);
679 630
    /// \endcode
680 631
    void run(Node s, int num) {
681 632
      init();
682 633
      addSource(s);
683 634
      limitedStart(num);
684 635
    }
685 636
    
686 637
    ///@}
687 638

	
688 639
    /// \brief LEMON iterator for getting the active nodes.
689 640
    ///
690 641
    /// This class provides a common style LEMON iterator that traverses
691 642
    /// the active nodes of the Bellman-Ford algorithm after the last
692 643
    /// phase. These nodes should be checked in the next phase to
693 644
    /// find augmenting arcs outgoing from them.
694 645
    class ActiveIt {
695 646
    public:
696 647

	
697 648
      /// \brief Constructor.
698 649
      ///
699 650
      /// Constructor for getting the active nodes of the given BellmanFord
700 651
      /// instance. 
701 652
      ActiveIt(const BellmanFord& algorithm) : _algorithm(&algorithm)
702 653
      {
703 654
        _index = _algorithm->_process.size() - 1;
704 655
      }
705 656

	
706 657
      /// \brief Invalid constructor.
707 658
      ///
708 659
      /// Invalid constructor.
709 660
      ActiveIt(Invalid) : _algorithm(0), _index(-1) {}
710 661

	
711 662
      /// \brief Conversion to \c Node.
712 663
      ///
713 664
      /// Conversion to \c Node.
714 665
      operator Node() const { 
715 666
        return _index >= 0 ? _algorithm->_process[_index] : INVALID;
716 667
      }
717 668

	
718 669
      /// \brief Increment operator.
719 670
      ///
720 671
      /// Increment operator.
721 672
      ActiveIt& operator++() {
722 673
        --_index;
723 674
        return *this; 
724 675
      }
725 676

	
726 677
      bool operator==(const ActiveIt& it) const { 
727 678
        return static_cast<Node>(*this) == static_cast<Node>(it); 
728 679
      }
729 680
      bool operator!=(const ActiveIt& it) const { 
730 681
        return static_cast<Node>(*this) != static_cast<Node>(it); 
731 682
      }
732 683
      bool operator<(const ActiveIt& it) const { 
733 684
        return static_cast<Node>(*this) < static_cast<Node>(it); 
734 685
      }
735 686
      
736 687
    private:
737 688
      const BellmanFord* _algorithm;
738 689
      int _index;
739 690
    };
740 691
    
741 692
    /// \name Query Functions
742 693
    /// The result of the Bellman-Ford algorithm can be obtained using these
743 694
    /// functions.\n
744 695
    /// Either \ref run() or \ref init() should be called before using them.
745 696
    
746 697
    ///@{
747 698

	
748 699
    /// \brief The shortest path to the given node.
749 700
    ///    
750 701
    /// Gives back the shortest path to the given node from the root(s).
751 702
    ///
752 703
    /// \warning \c t should be reached from the root(s).
753 704
    ///
754 705
    /// \pre Either \ref run() or \ref init() must be called before
755 706
    /// using this function.
756 707
    Path path(Node t) const
757 708
    {
758 709
      return Path(*_gr, *_pred, t);
759 710
    }
760 711
	  
761 712
    /// \brief The distance of the given node from the root(s).
762 713
    ///
763 714
    /// Returns the distance of the given node from the root(s).
764 715
    ///
765 716
    /// \warning If node \c v is not reached from the root(s), then
766 717
    /// the return value of this function is undefined.
767 718
    ///
768 719
    /// \pre Either \ref run() or \ref init() must be called before
769 720
    /// using this function.
770 721
    Value dist(Node v) const { return (*_dist)[v]; }
771 722

	
772 723
    /// \brief Returns the 'previous arc' of the shortest path tree for
773 724
    /// the given node.
774 725
    ///
775 726
    /// This function returns the 'previous arc' of the shortest path
776 727
    /// tree for node \c v, i.e. it returns the last arc of a
777 728
    /// shortest path from a root to \c v. It is \c INVALID if \c v
778 729
    /// is not reached from the root(s) or if \c v is a root.
779 730
    ///
780 731
    /// The shortest path tree used here is equal to the shortest path
781 732
    /// tree used in \ref predNode() and \ref predMap().
782 733
    ///
783 734
    /// \pre Either \ref run() or \ref init() must be called before
784 735
    /// using this function.
785 736
    Arc predArc(Node v) const { return (*_pred)[v]; }
786 737

	
787 738
    /// \brief Returns the 'previous node' of the shortest path tree for
788 739
    /// the given node.
789 740
    ///
790 741
    /// This function returns the 'previous node' of the shortest path
791 742
    /// tree for node \c v, i.e. it returns the last but one node of
792 743
    /// a shortest path from a root to \c v. It is \c INVALID if \c v
793 744
    /// is not reached from the root(s) or if \c v is a root.
794 745
    ///
795 746
    /// The shortest path tree used here is equal to the shortest path
796 747
    /// tree used in \ref predArc() and \ref predMap().
797 748
    ///
798 749
    /// \pre Either \ref run() or \ref init() must be called before
799 750
    /// using this function.
800 751
    Node predNode(Node v) const { 
801 752
      return (*_pred)[v] == INVALID ? INVALID : _gr->source((*_pred)[v]); 
802 753
    }
803 754
    
804 755
    /// \brief Returns a const reference to the node map that stores the
805 756
    /// distances of the nodes.
806 757
    ///
807 758
    /// Returns a const reference to the node map that stores the distances
808 759
    /// of the nodes calculated by the algorithm.
809 760
    ///
810 761
    /// \pre Either \ref run() or \ref init() must be called before
811 762
    /// using this function.
812 763
    const DistMap &distMap() const { return *_dist;}
813 764
 
814 765
    /// \brief Returns a const reference to the node map that stores the
815 766
    /// predecessor arcs.
816 767
    ///
817 768
    /// Returns a const reference to the node map that stores the predecessor
818 769
    /// arcs, which form the shortest path tree (forest).
819 770
    ///
820 771
    /// \pre Either \ref run() or \ref init() must be called before
821 772
    /// using this function.
822 773
    const PredMap &predMap() const { return *_pred; }
823 774
 
824 775
    /// \brief Checks if a node is reached from the root(s).
825 776
    ///
826 777
    /// Returns \c true if \c v is reached from the root(s).
827 778
    ///
828 779
    /// \pre Either \ref run() or \ref init() must be called before
829 780
    /// using this function.
830 781
    bool reached(Node v) const {
831 782
      return (*_dist)[v] != OperationTraits::infinity();
832 783
    }
833 784

	
834 785
    /// \brief Gives back a negative cycle.
835 786
    ///    
836 787
    /// This function gives back a directed cycle with negative total
837 788
    /// length if the algorithm has already found one.
838 789
    /// Otherwise it gives back an empty path.
839 790
    lemon::Path<Digraph> negativeCycle() const {
840 791
      typename Digraph::template NodeMap<int> state(*_gr, -1);
841 792
      lemon::Path<Digraph> cycle;
842 793
      for (int i = 0; i < int(_process.size()); ++i) {
843 794
        if (state[_process[i]] != -1) continue;
844 795
        for (Node v = _process[i]; (*_pred)[v] != INVALID;
845 796
             v = _gr->source((*_pred)[v])) {
846 797
          if (state[v] == i) {
847 798
            cycle.addFront((*_pred)[v]);
848 799
            for (Node u = _gr->source((*_pred)[v]); u != v;
849 800
                 u = _gr->source((*_pred)[u])) {
850 801
              cycle.addFront((*_pred)[u]);
851 802
            }
852 803
            return cycle;
853 804
          }
854 805
          else if (state[v] >= 0) {
855 806
            break;
856 807
          }
857 808
          state[v] = i;
858 809
        }
859 810
      }
860 811
      return cycle;
861 812
    }
862 813
    
863 814
    ///@}
864 815
  };
865 816
 
866 817
  /// \brief Default traits class of bellmanFord() function.
867 818
  ///
868 819
  /// Default traits class of bellmanFord() function.
869 820
  /// \tparam GR The type of the digraph.
870 821
  /// \tparam LEN The type of the length map.
871 822
  template <typename GR, typename LEN>
872 823
  struct BellmanFordWizardDefaultTraits {
873 824
    /// The type of the digraph the algorithm runs on. 
874 825
    typedef GR Digraph;
875 826

	
876 827
    /// \brief The type of the map that stores the arc lengths.
877 828
    ///
878 829
    /// The type of the map that stores the arc lengths.
879 830
    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
880 831
    typedef LEN LengthMap;
881 832

	
882 833
    /// The type of the arc lengths.
883 834
    typedef typename LEN::Value Value;
884 835

	
885 836
    /// \brief Operation traits for Bellman-Ford algorithm.
886 837
    ///
887 838
    /// It defines the used operations and the infinity value for the
888 839
    /// given \c Value type.
889
    /// \see BellmanFordDefaultOperationTraits,
890
    /// BellmanFordToleranceOperationTraits
840
    /// \see BellmanFordDefaultOperationTraits
891 841
    typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
892 842

	
893 843
    /// \brief The type of the map that stores the last
894 844
    /// arcs of the shortest paths.
895 845
    /// 
896 846
    /// The type of the map that stores the last arcs of the shortest paths.
897 847
    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
898 848
    typedef typename GR::template NodeMap<typename GR::Arc> PredMap;
899 849

	
900 850
    /// \brief Instantiates a \c PredMap.
901 851
    /// 
902 852
    /// This function instantiates a \ref PredMap.
903 853
    /// \param g is the digraph to which we would like to define the
904 854
    /// \ref PredMap.
905 855
    static PredMap *createPredMap(const GR &g) {
906 856
      return new PredMap(g);
907 857
    }
908 858

	
909 859
    /// \brief The type of the map that stores the distances of the nodes.
910 860
    ///
911 861
    /// The type of the map that stores the distances of the nodes.
912 862
    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
913 863
    typedef typename GR::template NodeMap<Value> DistMap;
914 864

	
915 865
    /// \brief Instantiates a \c DistMap.
916 866
    ///
917 867
    /// This function instantiates a \ref DistMap. 
918 868
    /// \param g is the digraph to which we would like to define the
919 869
    /// \ref DistMap.
920 870
    static DistMap *createDistMap(const GR &g) {
921 871
      return new DistMap(g);
922 872
    }
923 873

	
924 874
    ///The type of the shortest paths.
925 875

	
926 876
    ///The type of the shortest paths.
927 877
    ///It must meet the \ref concepts::Path "Path" concept.
928 878
    typedef lemon::Path<Digraph> Path;
929 879
  };
930 880
  
931 881
  /// \brief Default traits class used by BellmanFordWizard.
932 882
  ///
933 883
  /// Default traits class used by BellmanFordWizard.
934 884
  /// \tparam GR The type of the digraph.
935 885
  /// \tparam LEN The type of the length map.
936 886
  template <typename GR, typename LEN>
937 887
  class BellmanFordWizardBase 
938 888
    : public BellmanFordWizardDefaultTraits<GR, LEN> {
939 889

	
940 890
    typedef BellmanFordWizardDefaultTraits<GR, LEN> Base;
941 891
  protected:
942 892
    // Type of the nodes in the digraph.
943 893
    typedef typename Base::Digraph::Node Node;
944 894

	
945 895
    // Pointer to the underlying digraph.
946 896
    void *_graph;
947 897
    // Pointer to the length map
948 898
    void *_length;
949 899
    // Pointer to the map of predecessors arcs.
950 900
    void *_pred;
951 901
    // Pointer to the map of distances.
952 902
    void *_dist;
953 903
    //Pointer to the shortest path to the target node.
954 904
    void *_path;
955 905
    //Pointer to the distance of the target node.
956 906
    void *_di;
957 907

	
958 908
    public:
959 909
    /// Constructor.
960 910
    
961 911
    /// This constructor does not require parameters, it initiates
962 912
    /// all of the attributes to default values \c 0.
963 913
    BellmanFordWizardBase() :
964 914
      _graph(0), _length(0), _pred(0), _dist(0), _path(0), _di(0) {}
965 915

	
966 916
    /// Constructor.
967 917
    
968 918
    /// This constructor requires two parameters,
969 919
    /// others are initiated to \c 0.
970 920
    /// \param gr The digraph the algorithm runs on.
971 921
    /// \param len The length map.
972 922
    BellmanFordWizardBase(const GR& gr, 
973 923
			  const LEN& len) :
974 924
      _graph(reinterpret_cast<void*>(const_cast<GR*>(&gr))), 
975 925
      _length(reinterpret_cast<void*>(const_cast<LEN*>(&len))), 
976 926
      _pred(0), _dist(0), _path(0), _di(0) {}
977 927

	
978 928
  };
979 929
  
980 930
  /// \brief Auxiliary class for the function-type interface of the
981 931
  /// \ref BellmanFord "Bellman-Ford" algorithm.
982 932
  ///
983 933
  /// This auxiliary class is created to implement the
984 934
  /// \ref bellmanFord() "function-type interface" of the
985 935
  /// \ref BellmanFord "Bellman-Ford" algorithm.
986 936
  /// It does not have own \ref run() method, it uses the
987 937
  /// functions and features of the plain \ref BellmanFord.
988 938
  ///
989 939
  /// This class should only be used through the \ref bellmanFord()
990 940
  /// function, which makes it easier to use the algorithm.
991 941
  ///
992 942
  /// \tparam TR The traits class that defines various types used by the
993 943
  /// algorithm.
994 944
  template<class TR>
995 945
  class BellmanFordWizard : public TR {
996 946
    typedef TR Base;
997 947

	
998 948
    typedef typename TR::Digraph Digraph;
999 949

	
1000 950
    typedef typename Digraph::Node Node;
1001 951
    typedef typename Digraph::NodeIt NodeIt;
1002 952
    typedef typename Digraph::Arc Arc;
1003 953
    typedef typename Digraph::OutArcIt ArcIt;
1004 954
    
1005 955
    typedef typename TR::LengthMap LengthMap;
1006 956
    typedef typename LengthMap::Value Value;
1007 957
    typedef typename TR::PredMap PredMap;
1008 958
    typedef typename TR::DistMap DistMap;
1009 959
    typedef typename TR::Path Path;
1010 960

	
1011 961
  public:
1012 962
    /// Constructor.
1013 963
    BellmanFordWizard() : TR() {}
1014 964

	
1015 965
    /// \brief Constructor that requires parameters.
1016 966
    ///
1017 967
    /// Constructor that requires parameters.
1018 968
    /// These parameters will be the default values for the traits class.
1019 969
    /// \param gr The digraph the algorithm runs on.
1020 970
    /// \param len The length map.
1021 971
    BellmanFordWizard(const Digraph& gr, const LengthMap& len) 
1022 972
      : TR(gr, len) {}
1023 973

	
1024 974
    /// \brief Copy constructor
1025 975
    BellmanFordWizard(const TR &b) : TR(b) {}
1026 976

	
1027 977
    ~BellmanFordWizard() {}
1028 978

	
1029 979
    /// \brief Runs the Bellman-Ford algorithm from the given source node.
1030 980
    ///    
1031 981
    /// This method runs the Bellman-Ford algorithm from the given source
1032 982
    /// node in order to compute the shortest path to each node.
1033 983
    void run(Node s) {
1034 984
      BellmanFord<Digraph,LengthMap,TR> 
1035 985
	bf(*reinterpret_cast<const Digraph*>(Base::_graph), 
1036 986
           *reinterpret_cast<const LengthMap*>(Base::_length));
1037 987
      if (Base::_pred) bf.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
1038 988
      if (Base::_dist) bf.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
1039 989
      bf.run(s);
1040 990
    }
1041 991

	
1042 992
    /// \brief Runs the Bellman-Ford algorithm to find the shortest path
1043 993
    /// between \c s and \c t.
1044 994
    ///
1045 995
    /// This method runs the Bellman-Ford algorithm from node \c s
1046 996
    /// in order to compute the shortest path to node \c t.
1047 997
    /// Actually, it computes the shortest path to each node, but using
1048 998
    /// this function you can retrieve the distance and the shortest path
1049 999
    /// for a single target node easier.
1050 1000
    ///
1051 1001
    /// \return \c true if \c t is reachable form \c s.
1052 1002
    bool run(Node s, Node t) {
1053 1003
      BellmanFord<Digraph,LengthMap,TR>
1054 1004
        bf(*reinterpret_cast<const Digraph*>(Base::_graph),
1055 1005
           *reinterpret_cast<const LengthMap*>(Base::_length));
1056 1006
      if (Base::_pred) bf.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
1057 1007
      if (Base::_dist) bf.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
1058 1008
      bf.run(s);
1059 1009
      if (Base::_path) *reinterpret_cast<Path*>(Base::_path) = bf.path(t);
1060 1010
      if (Base::_di) *reinterpret_cast<Value*>(Base::_di) = bf.dist(t);
1061 1011
      return bf.reached(t);
1062 1012
    }
1063 1013

	
1064 1014
    template<class T>
1065 1015
    struct SetPredMapBase : public Base {
1066 1016
      typedef T PredMap;
1067 1017
      static PredMap *createPredMap(const Digraph &) { return 0; };
1068 1018
      SetPredMapBase(const TR &b) : TR(b) {}
1069 1019
    };
1070 1020
    
1071 1021
    /// \brief \ref named-templ-param "Named parameter" for setting
1072 1022
    /// the predecessor map.
1073 1023
    ///
1074 1024
    /// \ref named-templ-param "Named parameter" for setting
1075 1025
    /// the map that stores the predecessor arcs of the nodes.
1076 1026
    template<class T>
1077 1027
    BellmanFordWizard<SetPredMapBase<T> > predMap(const T &t) {
1078 1028
      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
1079 1029
      return BellmanFordWizard<SetPredMapBase<T> >(*this);
1080 1030
    }
1081 1031
    
1082 1032
    template<class T>
1083 1033
    struct SetDistMapBase : public Base {
1084 1034
      typedef T DistMap;
1085 1035
      static DistMap *createDistMap(const Digraph &) { return 0; };
1086 1036
      SetDistMapBase(const TR &b) : TR(b) {}
1087 1037
    };
1088 1038
    
1089 1039
    /// \brief \ref named-templ-param "Named parameter" for setting
1090 1040
    /// the distance map.
1091 1041
    ///
1092 1042
    /// \ref named-templ-param "Named parameter" for setting
1093 1043
    /// the map that stores the distances of the nodes calculated
1094 1044
    /// by the algorithm.
1095 1045
    template<class T>
1096 1046
    BellmanFordWizard<SetDistMapBase<T> > distMap(const T &t) {
1097 1047
      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
1098 1048
      return BellmanFordWizard<SetDistMapBase<T> >(*this);
1099 1049
    }
1100 1050

	
1101 1051
    template<class T>
1102 1052
    struct SetPathBase : public Base {
1103 1053
      typedef T Path;
1104 1054
      SetPathBase(const TR &b) : TR(b) {}
1105 1055
    };
1106 1056

	
1107 1057
    /// \brief \ref named-func-param "Named parameter" for getting
1108 1058
    /// the shortest path to the target node.
1109 1059
    ///
1110 1060
    /// \ref named-func-param "Named parameter" for getting
1111 1061
    /// the shortest path to the target node.
1112 1062
    template<class T>
1113 1063
    BellmanFordWizard<SetPathBase<T> > path(const T &t)
1114 1064
    {
1115 1065
      Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t));
1116 1066
      return BellmanFordWizard<SetPathBase<T> >(*this);
1117 1067
    }
1118 1068

	
1119 1069
    /// \brief \ref named-func-param "Named parameter" for getting
1120 1070
    /// the distance of the target node.
1121 1071
    ///
1122 1072
    /// \ref named-func-param "Named parameter" for getting
1123 1073
    /// the distance of the target node.
1124 1074
    BellmanFordWizard dist(const Value &d)
1125 1075
    {
1126 1076
      Base::_di=reinterpret_cast<void*>(const_cast<Value*>(&d));
1127 1077
      return *this;
1128 1078
    }
1129 1079
    
1130 1080
  };
1131 1081
  
1132 1082
  /// \brief Function type interface for the \ref BellmanFord "Bellman-Ford"
1133 1083
  /// algorithm.
1134 1084
  ///
1135 1085
  /// \ingroup shortest_path
1136 1086
  /// Function type interface for the \ref BellmanFord "Bellman-Ford"
1137 1087
  /// algorithm.
1138 1088
  ///
1139 1089
  /// This function also has several \ref named-templ-func-param 
1140 1090
  /// "named parameters", they are declared as the members of class 
1141 1091
  /// \ref BellmanFordWizard.
1142 1092
  /// The following examples show how to use these parameters.
1143 1093
  /// \code
1144 1094
  ///   // Compute shortest path from node s to each node
1145 1095
  ///   bellmanFord(g,length).predMap(preds).distMap(dists).run(s);
1146 1096
  ///
1147 1097
  ///   // Compute shortest path from s to t
1148 1098
  ///   bool reached = bellmanFord(g,length).path(p).dist(d).run(s,t);
1149 1099
  /// \endcode
1150 1100
  /// \warning Don't forget to put the \ref BellmanFordWizard::run() "run()"
1151 1101
  /// to the end of the parameter list.
1152 1102
  /// \sa BellmanFordWizard
1153 1103
  /// \sa BellmanFord
1154 1104
  template<typename GR, typename LEN>
1155 1105
  BellmanFordWizard<BellmanFordWizardBase<GR,LEN> >
1156 1106
  bellmanFord(const GR& digraph,
1157 1107
	      const LEN& length)
1158 1108
  {
1159 1109
    return BellmanFordWizard<BellmanFordWizardBase<GR,LEN> >(digraph, length);
1160 1110
  }
1161 1111

	
1162 1112
} //END OF NAMESPACE LEMON
1163 1113

	
1164 1114
#endif
1165 1115

	
Ignore white space 6 line context
1 1
/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 2
 *
3 3
 * This file is a part of LEMON, a generic C++ optimization library.
4 4
 *
5 5
 * Copyright (C) 2003-2009
6 6
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 7
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 8
 *
9 9
 * Permission to use, modify and distribute this software is granted
10 10
 * provided that this copyright notice appears in all copies. For
11 11
 * precise terms see the accompanying LICENSE file.
12 12
 *
13 13
 * This software is provided "AS IS" with no warranty of any kind,
14 14
 * express or implied, and with no claim as to its suitability for any
15 15
 * purpose.
16 16
 *
17 17
 */
18 18

	
19 19
#include <lemon/concepts/digraph.h>
20 20
#include <lemon/smart_graph.h>
21 21
#include <lemon/list_graph.h>
22 22
#include <lemon/lgf_reader.h>
23 23
#include <lemon/bellman_ford.h>
24 24
#include <lemon/path.h>
25 25

	
26 26
#include "graph_test.h"
27 27
#include "test_tools.h"
28 28

	
29 29
using namespace lemon;
30 30

	
31 31
char test_lgf[] =
32 32
  "@nodes\n"
33 33
  "label\n"
34 34
  "0\n"
35 35
  "1\n"
36 36
  "2\n"
37 37
  "3\n"
38 38
  "4\n"
39 39
  "@arcs\n"
40 40
  "    length\n"
41 41
  "0 1 3\n"
42 42
  "1 2 -3\n"
43 43
  "1 2 -5\n"
44 44
  "1 3 -2\n"
45 45
  "0 2 -1\n"
46 46
  "1 2 -4\n"
47 47
  "0 3 2\n"
48 48
  "4 2 -5\n"
49 49
  "2 3 1\n"
50 50
  "@attributes\n"
51 51
  "source 0\n"
52 52
  "target 3\n";
53 53

	
54 54

	
55 55
void checkBellmanFordCompile()
56 56
{
57 57
  typedef int Value;
58 58
  typedef concepts::Digraph Digraph;
59 59
  typedef concepts::ReadMap<Digraph::Arc,Value> LengthMap;
60 60
  typedef BellmanFord<Digraph, LengthMap> BF;
61 61
  typedef Digraph::Node Node;
62 62
  typedef Digraph::Arc Arc;
63 63

	
64 64
  Digraph gr;
65 65
  Node s, t, n;
66 66
  Arc e;
67 67
  Value l;
68 68
  int k=3;
69 69
  bool b;
70 70
  BF::DistMap d(gr);
71 71
  BF::PredMap p(gr);
72 72
  LengthMap length;
73 73
  concepts::Path<Digraph> pp;
74 74

	
75 75
  {
76 76
    BF bf_test(gr,length);
77 77
    const BF& const_bf_test = bf_test;
78 78

	
79 79
    bf_test.run(s);
80 80
    bf_test.run(s,k);
81 81

	
82 82
    bf_test.init();
83 83
    bf_test.addSource(s);
84 84
    bf_test.addSource(s, 1);
85 85
    b = bf_test.processNextRound();
86 86
    b = bf_test.processNextWeakRound();
87 87

	
88 88
    bf_test.start();
89 89
    bf_test.checkedStart();
90 90
    bf_test.limitedStart(k);
91 91

	
92 92
    l  = const_bf_test.dist(t);
93 93
    e  = const_bf_test.predArc(t);
94 94
    s  = const_bf_test.predNode(t);
95 95
    b  = const_bf_test.reached(t);
96 96
    d  = const_bf_test.distMap();
97 97
    p  = const_bf_test.predMap();
98 98
    pp = const_bf_test.path(t);
99 99
    pp = const_bf_test.negativeCycle();
100 100
    
101 101
    for (BF::ActiveIt it(const_bf_test); it != INVALID; ++it) {}
102 102
  }
103 103
  {
104 104
    BF::SetPredMap<concepts::ReadWriteMap<Node,Arc> >
105 105
      ::SetDistMap<concepts::ReadWriteMap<Node,Value> >
106 106
      ::SetOperationTraits<BellmanFordDefaultOperationTraits<Value> >
107
      ::SetOperationTraits<BellmanFordToleranceOperationTraits<Value, 0> >
108 107
      ::Create bf_test(gr,length);
109 108

	
110 109
    LengthMap length_map;
111 110
    concepts::ReadWriteMap<Node,Arc> pred_map;
112 111
    concepts::ReadWriteMap<Node,Value> dist_map;
113 112
    
114 113
    bf_test
115 114
      .lengthMap(length_map)
116 115
      .predMap(pred_map)
117 116
      .distMap(dist_map);
118 117

	
119 118
    bf_test.run(s);
120 119
    bf_test.run(s,k);
121 120

	
122 121
    bf_test.init();
123 122
    bf_test.addSource(s);
124 123
    bf_test.addSource(s, 1);
125 124
    b = bf_test.processNextRound();
126 125
    b = bf_test.processNextWeakRound();
127 126

	
128 127
    bf_test.start();
129 128
    bf_test.checkedStart();
130 129
    bf_test.limitedStart(k);
131 130

	
132 131
    l  = bf_test.dist(t);
133 132
    e  = bf_test.predArc(t);
134 133
    s  = bf_test.predNode(t);
135 134
    b  = bf_test.reached(t);
136 135
    pp = bf_test.path(t);
137 136
    pp = bf_test.negativeCycle();
138 137
  }
139 138
}
140 139

	
141 140
void checkBellmanFordFunctionCompile()
142 141
{
143 142
  typedef int Value;
144 143
  typedef concepts::Digraph Digraph;
145 144
  typedef Digraph::Arc Arc;
146 145
  typedef Digraph::Node Node;
147 146
  typedef concepts::ReadMap<Digraph::Arc,Value> LengthMap;
148 147

	
149 148
  Digraph g;
150 149
  bool b;
151 150
  bellmanFord(g,LengthMap()).run(Node());
152 151
  b = bellmanFord(g,LengthMap()).run(Node(),Node());
153 152
  bellmanFord(g,LengthMap())
154 153
    .predMap(concepts::ReadWriteMap<Node,Arc>())
155 154
    .distMap(concepts::ReadWriteMap<Node,Value>())
156 155
    .run(Node());
157 156
  b=bellmanFord(g,LengthMap())
158 157
    .predMap(concepts::ReadWriteMap<Node,Arc>())
159 158
    .distMap(concepts::ReadWriteMap<Node,Value>())
160 159
    .path(concepts::Path<Digraph>())
161 160
    .dist(Value())
162 161
    .run(Node(),Node());
163 162
}
164 163

	
165 164

	
166 165
template <typename Digraph, typename Value>
167 166
void checkBellmanFord() {
168 167
  TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
169 168
  typedef typename Digraph::template ArcMap<Value> LengthMap;
170 169

	
171 170
  Digraph gr;
172 171
  Node s, t;
173 172
  LengthMap length(gr);
174 173

	
175 174
  std::istringstream input(test_lgf);
176 175
  digraphReader(gr, input).
177 176
    arcMap("length", length).
178 177
    node("source", s).
179 178
    node("target", t).
180 179
    run();
181 180

	
182 181
  BellmanFord<Digraph, LengthMap>
183 182
    bf(gr, length);
184 183
  bf.run(s);
185 184
  Path<Digraph> p = bf.path(t);
186 185

	
187 186
  check(bf.reached(t) && bf.dist(t) == -1, "Bellman-Ford found a wrong path.");
188 187
  check(p.length() == 3, "path() found a wrong path.");
189 188
  check(checkPath(gr, p), "path() found a wrong path.");
190 189
  check(pathSource(gr, p) == s, "path() found a wrong path.");
191 190
  check(pathTarget(gr, p) == t, "path() found a wrong path.");
192 191
  
193 192
  ListPath<Digraph> path;
194 193
  Value dist;
195 194
  bool reached = bellmanFord(gr,length).path(path).dist(dist).run(s,t);
196 195

	
197 196
  check(reached && dist == -1, "Bellman-Ford found a wrong path.");
198 197
  check(path.length() == 3, "path() found a wrong path.");
199 198
  check(checkPath(gr, path), "path() found a wrong path.");
200 199
  check(pathSource(gr, path) == s, "path() found a wrong path.");
201 200
  check(pathTarget(gr, path) == t, "path() found a wrong path.");
202 201

	
203 202
  for(ArcIt e(gr); e!=INVALID; ++e) {
204 203
    Node u=gr.source(e);
205 204
    Node v=gr.target(e);
206 205
    check(!bf.reached(u) || (bf.dist(v) - bf.dist(u) <= length[e]),
207 206
          "Wrong output. dist(target)-dist(source)-arc_length=" <<
208 207
          bf.dist(v) - bf.dist(u) - length[e]);
209 208
  }
210 209

	
211 210
  for(NodeIt v(gr); v!=INVALID; ++v) {
212 211
    if (bf.reached(v)) {
213 212
      check(v==s || bf.predArc(v)!=INVALID, "Wrong tree.");
214 213
      if (bf.predArc(v)!=INVALID ) {
215 214
        Arc e=bf.predArc(v);
216 215
        Node u=gr.source(e);
217 216
        check(u==bf.predNode(v),"Wrong tree.");
218 217
        check(bf.dist(v) - bf.dist(u) == length[e],
219 218
              "Wrong distance! Difference: " <<
220 219
              bf.dist(v) - bf.dist(u) - length[e]);
221 220
      }
222 221
    }
223 222
  }
224 223
}
225 224

	
226 225
void checkBellmanFordNegativeCycle() {
227 226
  DIGRAPH_TYPEDEFS(SmartDigraph);
228 227

	
229 228
  SmartDigraph gr;
230 229
  IntArcMap length(gr);
231 230
  
232 231
  Node n1 = gr.addNode();
233 232
  Node n2 = gr.addNode();
234 233
  Node n3 = gr.addNode();
235 234
  Node n4 = gr.addNode();
236 235
  
237 236
  Arc a1 = gr.addArc(n1, n2);
238 237
  Arc a2 = gr.addArc(n2, n2);
239 238
  
240 239
  length[a1] = 2;
241 240
  length[a2] = -1;
242 241
  
243 242
  {
244 243
    BellmanFord<SmartDigraph, IntArcMap> bf(gr, length);
245 244
    bf.run(n1);
246 245
    StaticPath<SmartDigraph> p = bf.negativeCycle();
247 246
    check(p.length() == 1 && p.front() == p.back() && p.front() == a2,
248 247
          "Wrong negative cycle.");
249 248
  }
250 249
 
251 250
  length[a2] = 0;
252 251
  
253 252
  {
254 253
    BellmanFord<SmartDigraph, IntArcMap> bf(gr, length);
255 254
    bf.run(n1);
256 255
    check(bf.negativeCycle().empty(),
257 256
          "Negative cycle should not be found.");
258 257
  }
259 258
  
260 259
  length[gr.addArc(n1, n3)] = 5;
261 260
  length[gr.addArc(n4, n3)] = 1;
262 261
  length[gr.addArc(n2, n4)] = 2;
263 262
  length[gr.addArc(n3, n2)] = -4;
264 263
  
265 264
  {
266 265
    BellmanFord<SmartDigraph, IntArcMap> bf(gr, length);
267 266
    bf.init();
268 267
    bf.addSource(n1);
269 268
    for (int i = 0; i < 4; ++i) {
270 269
      check(bf.negativeCycle().empty(),
271 270
            "Negative cycle should not be found.");
272 271
      bf.processNextRound();
273 272
    }
274 273
    StaticPath<SmartDigraph> p = bf.negativeCycle();
275 274
    check(p.length() == 3, "Wrong negative cycle.");
276 275
    check(length[p.nth(0)] + length[p.nth(1)] + length[p.nth(2)] == -1,
277 276
          "Wrong negative cycle.");
278 277
  }
279 278
}
280 279

	
281 280
int main() {
282 281
  checkBellmanFord<ListDigraph, int>();
283 282
  checkBellmanFord<SmartDigraph, double>();
284 283
  checkBellmanFordNegativeCycle();
285 284
  return 0;
286 285
}
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