COIN-OR::LEMON - Graph Library

source: lemon/lemon/bellman_ford.h @ 1270:dceba191c00d

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1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2013
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19#ifndef LEMON_BELLMAN_FORD_H
20#define LEMON_BELLMAN_FORD_H
21
22/// \ingroup shortest_path
23/// \file
24/// \brief Bellman-Ford algorithm.
25
26#include <lemon/list_graph.h>
27#include <lemon/bits/path_dump.h>
28#include <lemon/core.h>
29#include <lemon/error.h>
30#include <lemon/maps.h>
31#include <lemon/path.h>
32
33#include <limits>
34
35namespace lemon {
36
37  /// \brief Default OperationTraits for the BellmanFord algorithm class.
38  ///
39  /// This operation traits class defines all computational operations
40  /// and constants that are used in the Bellman-Ford algorithm.
41  /// The default implementation is based on the \c numeric_limits class.
42  /// If the numeric type does not have infinity value, then the maximum
43  /// value is used as extremal infinity value.
44  template <
45    typename V,
46    bool has_inf = std::numeric_limits<V>::has_infinity>
47  struct BellmanFordDefaultOperationTraits {
48    /// \e
49    typedef V Value;
50    /// \brief Gives back the zero value of the type.
51    static Value zero() {
52      return static_cast<Value>(0);
53    }
54    /// \brief Gives back the positive infinity value of the type.
55    static Value infinity() {
56      return std::numeric_limits<Value>::infinity();
57    }
58    /// \brief Gives back the sum of the given two elements.
59    static Value plus(const Value& left, const Value& right) {
60      return left + right;
61    }
62    /// \brief Gives back \c true only if the first value is less than
63    /// the second.
64    static bool less(const Value& left, const Value& right) {
65      return left < right;
66    }
67  };
68
69  template <typename V>
70  struct BellmanFordDefaultOperationTraits<V, false> {
71    typedef V Value;
72    static Value zero() {
73      return static_cast<Value>(0);
74    }
75    static Value infinity() {
76      return std::numeric_limits<Value>::max();
77    }
78    static Value plus(const Value& left, const Value& right) {
79      if (left == infinity() || right == infinity()) return infinity();
80      return left + right;
81    }
82    static bool less(const Value& left, const Value& right) {
83      return left < right;
84    }
85  };
86
87  /// \brief Default traits class of BellmanFord class.
88  ///
89  /// Default traits class of BellmanFord class.
90  /// \param GR The type of the digraph.
91  /// \param LEN The type of the length map.
92  template<typename GR, typename LEN>
93  struct BellmanFordDefaultTraits {
94    /// The type of the digraph the algorithm runs on.
95    typedef GR Digraph;
96
97    /// \brief The type of the map that stores the arc lengths.
98    ///
99    /// The type of the map that stores the arc lengths.
100    /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
101    typedef LEN LengthMap;
102
103    /// The type of the arc lengths.
104    typedef typename LEN::Value Value;
105
106    /// \brief Operation traits for Bellman-Ford algorithm.
107    ///
108    /// It defines the used operations and the infinity value for the
109    /// given \c Value type.
110    /// \see BellmanFordDefaultOperationTraits
111    typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
112
113    /// \brief The type of the map that stores the last arcs of the
114    /// shortest paths.
115    ///
116    /// The type of the map that stores the last
117    /// arcs of the shortest paths.
118    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
119    typedef typename GR::template NodeMap<typename GR::Arc> PredMap;
120
121    /// \brief Instantiates a \c PredMap.
122    ///
123    /// This function instantiates a \ref PredMap.
124    /// \param g is the digraph to which we would like to define the
125    /// \ref PredMap.
126    static PredMap *createPredMap(const GR& g) {
127      return new PredMap(g);
128    }
129
130    /// \brief The type of the map that stores the distances of the nodes.
131    ///
132    /// The type of the map that stores the distances of the nodes.
133    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
134    typedef typename GR::template NodeMap<typename LEN::Value> DistMap;
135
136    /// \brief Instantiates a \c DistMap.
137    ///
138    /// This function instantiates a \ref DistMap.
139    /// \param g is the digraph to which we would like to define the
140    /// \ref DistMap.
141    static DistMap *createDistMap(const GR& g) {
142      return new DistMap(g);
143    }
144
145  };
146
147  /// \brief %BellmanFord algorithm class.
148  ///
149  /// \ingroup shortest_path
150  /// This class provides an efficient implementation of the Bellman-Ford
151  /// algorithm. The maximum time complexity of the algorithm is
152  /// <tt>O(nm)</tt>.
153  ///
154  /// The Bellman-Ford algorithm solves the single-source shortest path
155  /// problem when the arcs can have negative lengths, but the digraph
156  /// should not contain directed cycles with negative total length.
157  /// If all arc costs are non-negative, consider to use the Dijkstra
158  /// algorithm instead, since it is more efficient.
159  ///
160  /// The arc lengths are passed to the algorithm using a
161  /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any
162  /// kind of length. The type of the length values is determined by the
163  /// \ref concepts::ReadMap::Value "Value" type of the length map.
164  ///
165  /// There is also a \ref bellmanFord() "function-type interface" for the
166  /// Bellman-Ford algorithm, which is convenient in the simplier cases and
167  /// it can be used easier.
168  ///
169  /// \tparam GR The type of the digraph the algorithm runs on.
170  /// The default type is \ref ListDigraph.
171  /// \tparam LEN A \ref concepts::ReadMap "readable" arc map that specifies
172  /// the lengths of the arcs. The default map type is
173  /// \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
174  /// \tparam TR The traits class that defines various types used by the
175  /// algorithm. By default, it is \ref BellmanFordDefaultTraits
176  /// "BellmanFordDefaultTraits<GR, LEN>".
177  /// In most cases, this parameter should not be set directly,
178  /// consider to use the named template parameters instead.
179#ifdef DOXYGEN
180  template <typename GR, typename LEN, typename TR>
181#else
182  template <typename GR=ListDigraph,
183            typename LEN=typename GR::template ArcMap<int>,
184            typename TR=BellmanFordDefaultTraits<GR,LEN> >
185#endif
186  class BellmanFord {
187  public:
188
189    ///The type of the underlying digraph.
190    typedef typename TR::Digraph Digraph;
191
192    /// \brief The type of the arc lengths.
193    typedef typename TR::LengthMap::Value Value;
194    /// \brief The type of the map that stores the arc lengths.
195    typedef typename TR::LengthMap LengthMap;
196    /// \brief The type of the map that stores the last
197    /// arcs of the shortest paths.
198    typedef typename TR::PredMap PredMap;
199    /// \brief The type of the map that stores the distances of the nodes.
200    typedef typename TR::DistMap DistMap;
201    /// The type of the paths.
202    typedef PredMapPath<Digraph, PredMap> Path;
203    ///\brief The \ref lemon::BellmanFordDefaultOperationTraits
204    /// "operation traits class" of the algorithm.
205    typedef typename TR::OperationTraits OperationTraits;
206
207    ///\brief The \ref lemon::BellmanFordDefaultTraits "traits class"
208    ///of the algorithm.
209    typedef TR Traits;
210
211  private:
212
213    typedef typename Digraph::Node Node;
214    typedef typename Digraph::NodeIt NodeIt;
215    typedef typename Digraph::Arc Arc;
216    typedef typename Digraph::OutArcIt OutArcIt;
217
218    // Pointer to the underlying digraph.
219    const Digraph *_gr;
220    // Pointer to the length map
221    const LengthMap *_length;
222    // Pointer to the map of predecessors arcs.
223    PredMap *_pred;
224    // Indicates if _pred is locally allocated (true) or not.
225    bool _local_pred;
226    // Pointer to the map of distances.
227    DistMap *_dist;
228    // Indicates if _dist is locally allocated (true) or not.
229    bool _local_dist;
230
231    typedef typename Digraph::template NodeMap<bool> MaskMap;
232    MaskMap *_mask;
233
234    std::vector<Node> _process;
235
236    // Creates the maps if necessary.
237    void create_maps() {
238      if(!_pred) {
239        _local_pred = true;
240        _pred = Traits::createPredMap(*_gr);
241      }
242      if(!_dist) {
243        _local_dist = true;
244        _dist = Traits::createDistMap(*_gr);
245      }
246      if(!_mask) {
247        _mask = new MaskMap(*_gr);
248      }
249    }
250
251  public :
252
253    typedef BellmanFord Create;
254
255    /// \name Named Template Parameters
256
257    ///@{
258
259    template <class T>
260    struct SetPredMapTraits : public Traits {
261      typedef T PredMap;
262      static PredMap *createPredMap(const Digraph&) {
263        LEMON_ASSERT(false, "PredMap is not initialized");
264        return 0; // ignore warnings
265      }
266    };
267
268    /// \brief \ref named-templ-param "Named parameter" for setting
269    /// \c PredMap type.
270    ///
271    /// \ref named-templ-param "Named parameter" for setting
272    /// \c PredMap type.
273    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
274    template <class T>
275    struct SetPredMap
276      : public BellmanFord< Digraph, LengthMap, SetPredMapTraits<T> > {
277      typedef BellmanFord< Digraph, LengthMap, SetPredMapTraits<T> > Create;
278    };
279
280    template <class T>
281    struct SetDistMapTraits : public Traits {
282      typedef T DistMap;
283      static DistMap *createDistMap(const Digraph&) {
284        LEMON_ASSERT(false, "DistMap is not initialized");
285        return 0; // ignore warnings
286      }
287    };
288
289    /// \brief \ref named-templ-param "Named parameter" for setting
290    /// \c DistMap type.
291    ///
292    /// \ref named-templ-param "Named parameter" for setting
293    /// \c DistMap type.
294    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
295    template <class T>
296    struct SetDistMap
297      : public BellmanFord< Digraph, LengthMap, SetDistMapTraits<T> > {
298      typedef BellmanFord< Digraph, LengthMap, SetDistMapTraits<T> > Create;
299    };
300
301    template <class T>
302    struct SetOperationTraitsTraits : public Traits {
303      typedef T OperationTraits;
304    };
305
306    /// \brief \ref named-templ-param "Named parameter" for setting
307    /// \c OperationTraits type.
308    ///
309    /// \ref named-templ-param "Named parameter" for setting
310    /// \c OperationTraits type.
311    /// For more information, see \ref BellmanFordDefaultOperationTraits.
312    template <class T>
313    struct SetOperationTraits
314      : public BellmanFord< Digraph, LengthMap, SetOperationTraitsTraits<T> > {
315      typedef BellmanFord< Digraph, LengthMap, SetOperationTraitsTraits<T> >
316      Create;
317    };
318
319    ///@}
320
321  protected:
322
323    BellmanFord() {}
324
325  public:
326
327    /// \brief Constructor.
328    ///
329    /// Constructor.
330    /// \param g The digraph the algorithm runs on.
331    /// \param length The length map used by the algorithm.
332    BellmanFord(const Digraph& g, const LengthMap& length) :
333      _gr(&g), _length(&length),
334      _pred(0), _local_pred(false),
335      _dist(0), _local_dist(false), _mask(0) {}
336
337    ///Destructor.
338    ~BellmanFord() {
339      if(_local_pred) delete _pred;
340      if(_local_dist) delete _dist;
341      if(_mask) delete _mask;
342    }
343
344    /// \brief Sets the length map.
345    ///
346    /// Sets the length map.
347    /// \return <tt>(*this)</tt>
348    BellmanFord &lengthMap(const LengthMap &map) {
349      _length = &map;
350      return *this;
351    }
352
353    /// \brief Sets the map that stores the predecessor arcs.
354    ///
355    /// Sets the map that stores the predecessor arcs.
356    /// If you don't use this function before calling \ref run()
357    /// or \ref init(), an instance will be allocated automatically.
358    /// The destructor deallocates this automatically allocated map,
359    /// of course.
360    /// \return <tt>(*this)</tt>
361    BellmanFord &predMap(PredMap &map) {
362      if(_local_pred) {
363        delete _pred;
364        _local_pred=false;
365      }
366      _pred = &map;
367      return *this;
368    }
369
370    /// \brief Sets the map that stores the distances of the nodes.
371    ///
372    /// Sets the map that stores the distances of the nodes calculated
373    /// by the algorithm.
374    /// If you don't use this function before calling \ref run()
375    /// or \ref init(), an instance will be allocated automatically.
376    /// The destructor deallocates this automatically allocated map,
377    /// of course.
378    /// \return <tt>(*this)</tt>
379    BellmanFord &distMap(DistMap &map) {
380      if(_local_dist) {
381        delete _dist;
382        _local_dist=false;
383      }
384      _dist = &map;
385      return *this;
386    }
387
388    /// \name Execution Control
389    /// The simplest way to execute the Bellman-Ford algorithm is to use
390    /// one of the member functions called \ref run().\n
391    /// If you need better control on the execution, you have to call
392    /// \ref init() first, then you can add several source nodes
393    /// with \ref addSource(). Finally the actual path computation can be
394    /// performed with \ref start(), \ref checkedStart() or
395    /// \ref limitedStart().
396
397    ///@{
398
399    /// \brief Initializes the internal data structures.
400    ///
401    /// Initializes the internal data structures. The optional parameter
402    /// is the initial distance of each node.
403    void init(const Value value = OperationTraits::infinity()) {
404      create_maps();
405      for (NodeIt it(*_gr); it != INVALID; ++it) {
406        _pred->set(it, INVALID);
407        _dist->set(it, value);
408      }
409      _process.clear();
410      if (OperationTraits::less(value, OperationTraits::infinity())) {
411        for (NodeIt it(*_gr); it != INVALID; ++it) {
412          _process.push_back(it);
413          _mask->set(it, true);
414        }
415      } else {
416        for (NodeIt it(*_gr); it != INVALID; ++it) {
417          _mask->set(it, false);
418        }
419      }
420    }
421
422    /// \brief Adds a new source node.
423    ///
424    /// This function adds a new source node. The optional second parameter
425    /// is the initial distance of the node.
426    void addSource(Node source, Value dst = OperationTraits::zero()) {
427      _dist->set(source, dst);
428      if (!(*_mask)[source]) {
429        _process.push_back(source);
430        _mask->set(source, true);
431      }
432    }
433
434    /// \brief Executes one round from the Bellman-Ford algorithm.
435    ///
436    /// If the algoritm calculated the distances in the previous round
437    /// exactly for the paths of at most \c k arcs, then this function
438    /// will calculate the distances exactly for the paths of at most
439    /// <tt>k+1</tt> arcs. Performing \c k iterations using this function
440    /// calculates the shortest path distances exactly for the paths
441    /// consisting of at most \c k arcs.
442    ///
443    /// \warning The paths with limited arc number cannot be retrieved
444    /// easily with \ref path() or \ref predArc() functions. If you also
445    /// need the shortest paths and not only the distances, you should
446    /// store the \ref predMap() "predecessor map" after each iteration
447    /// and build the path manually.
448    ///
449    /// \return \c true when the algorithm have not found more shorter
450    /// paths.
451    ///
452    /// \see ActiveIt
453    bool processNextRound() {
454      for (int i = 0; i < int(_process.size()); ++i) {
455        _mask->set(_process[i], false);
456      }
457      std::vector<Node> nextProcess;
458      std::vector<Value> values(_process.size());
459      for (int i = 0; i < int(_process.size()); ++i) {
460        values[i] = (*_dist)[_process[i]];
461      }
462      for (int i = 0; i < int(_process.size()); ++i) {
463        for (OutArcIt it(*_gr, _process[i]); it != INVALID; ++it) {
464          Node target = _gr->target(it);
465          Value relaxed = OperationTraits::plus(values[i], (*_length)[it]);
466          if (OperationTraits::less(relaxed, (*_dist)[target])) {
467            _pred->set(target, it);
468            _dist->set(target, relaxed);
469            if (!(*_mask)[target]) {
470              _mask->set(target, true);
471              nextProcess.push_back(target);
472            }
473          }
474        }
475      }
476      _process.swap(nextProcess);
477      return _process.empty();
478    }
479
480    /// \brief Executes one weak round from the Bellman-Ford algorithm.
481    ///
482    /// If the algorithm calculated the distances in the previous round
483    /// at least for the paths of at most \c k arcs, then this function
484    /// will calculate the distances at least for the paths of at most
485    /// <tt>k+1</tt> arcs.
486    /// This function does not make it possible to calculate the shortest
487    /// path distances exactly for paths consisting of at most \c k arcs,
488    /// this is why it is called weak round.
489    ///
490    /// \return \c true when the algorithm have not found more shorter
491    /// paths.
492    ///
493    /// \see ActiveIt
494    bool processNextWeakRound() {
495      for (int i = 0; i < int(_process.size()); ++i) {
496        _mask->set(_process[i], false);
497      }
498      std::vector<Node> nextProcess;
499      for (int i = 0; i < int(_process.size()); ++i) {
500        for (OutArcIt it(*_gr, _process[i]); it != INVALID; ++it) {
501          Node target = _gr->target(it);
502          Value relaxed =
503            OperationTraits::plus((*_dist)[_process[i]], (*_length)[it]);
504          if (OperationTraits::less(relaxed, (*_dist)[target])) {
505            _pred->set(target, it);
506            _dist->set(target, relaxed);
507            if (!(*_mask)[target]) {
508              _mask->set(target, true);
509              nextProcess.push_back(target);
510            }
511          }
512        }
513      }
514      _process.swap(nextProcess);
515      return _process.empty();
516    }
517
518    /// \brief Executes the algorithm.
519    ///
520    /// Executes the algorithm.
521    ///
522    /// This method runs the Bellman-Ford algorithm from the root node(s)
523    /// in order to compute the shortest path to each node.
524    ///
525    /// The algorithm computes
526    /// - the shortest path tree (forest),
527    /// - the distance of each node from the root(s).
528    ///
529    /// \pre init() must be called and at least one root node should be
530    /// added with addSource() before using this function.
531    void start() {
532      int num = countNodes(*_gr) - 1;
533      for (int i = 0; i < num; ++i) {
534        if (processNextWeakRound()) break;
535      }
536    }
537
538    /// \brief Executes the algorithm and checks the negative cycles.
539    ///
540    /// Executes the algorithm and checks the negative cycles.
541    ///
542    /// This method runs the Bellman-Ford algorithm from the root node(s)
543    /// in order to compute the shortest path to each node and also checks
544    /// if the digraph contains cycles with negative total length.
545    ///
546    /// The algorithm computes
547    /// - the shortest path tree (forest),
548    /// - the distance of each node from the root(s).
549    ///
550    /// \return \c false if there is a negative cycle in the digraph.
551    ///
552    /// \pre init() must be called and at least one root node should be
553    /// added with addSource() before using this function.
554    bool checkedStart() {
555      int num = countNodes(*_gr);
556      for (int i = 0; i < num; ++i) {
557        if (processNextWeakRound()) return true;
558      }
559      return _process.empty();
560    }
561
562    /// \brief Executes the algorithm with arc number limit.
563    ///
564    /// Executes the algorithm with arc number limit.
565    ///
566    /// This method runs the Bellman-Ford algorithm from the root node(s)
567    /// in order to compute the shortest path distance for each node
568    /// using only the paths consisting of at most \c num arcs.
569    ///
570    /// The algorithm computes
571    /// - the limited distance of each node from the root(s),
572    /// - the predecessor arc for each node.
573    ///
574    /// \warning The paths with limited arc number cannot be retrieved
575    /// easily with \ref path() or \ref predArc() functions. If you also
576    /// need the shortest paths and not only the distances, you should
577    /// store the \ref predMap() "predecessor map" after each iteration
578    /// and build the path manually.
579    ///
580    /// \pre init() must be called and at least one root node should be
581    /// added with addSource() before using this function.
582    void limitedStart(int num) {
583      for (int i = 0; i < num; ++i) {
584        if (processNextRound()) break;
585      }
586    }
587
588    /// \brief Runs the algorithm from the given root node.
589    ///
590    /// This method runs the Bellman-Ford algorithm from the given root
591    /// node \c s in order to compute the shortest path to each node.
592    ///
593    /// The algorithm computes
594    /// - the shortest path tree (forest),
595    /// - the distance of each node from the root(s).
596    ///
597    /// \note bf.run(s) is just a shortcut of the following code.
598    /// \code
599    ///   bf.init();
600    ///   bf.addSource(s);
601    ///   bf.start();
602    /// \endcode
603    void run(Node s) {
604      init();
605      addSource(s);
606      start();
607    }
608
609    /// \brief Runs the algorithm from the given root node with arc
610    /// number limit.
611    ///
612    /// This method runs the Bellman-Ford algorithm from the given root
613    /// node \c s in order to compute the shortest path distance for each
614    /// node using only the paths consisting of at most \c num arcs.
615    ///
616    /// The algorithm computes
617    /// - the limited distance of each node from the root(s),
618    /// - the predecessor arc for each node.
619    ///
620    /// \warning The paths with limited arc number cannot be retrieved
621    /// easily with \ref path() or \ref predArc() functions. If you also
622    /// need the shortest paths and not only the distances, you should
623    /// store the \ref predMap() "predecessor map" after each iteration
624    /// and build the path manually.
625    ///
626    /// \note bf.run(s, num) is just a shortcut of the following code.
627    /// \code
628    ///   bf.init();
629    ///   bf.addSource(s);
630    ///   bf.limitedStart(num);
631    /// \endcode
632    void run(Node s, int num) {
633      init();
634      addSource(s);
635      limitedStart(num);
636    }
637
638    ///@}
639
640    /// \brief LEMON iterator for getting the active nodes.
641    ///
642    /// This class provides a common style LEMON iterator that traverses
643    /// the active nodes of the Bellman-Ford algorithm after the last
644    /// phase. These nodes should be checked in the next phase to
645    /// find augmenting arcs outgoing from them.
646    class ActiveIt {
647    public:
648
649      /// \brief Constructor.
650      ///
651      /// Constructor for getting the active nodes of the given BellmanFord
652      /// instance.
653      ActiveIt(const BellmanFord& algorithm) : _algorithm(&algorithm)
654      {
655        _index = _algorithm->_process.size() - 1;
656      }
657
658      /// \brief Invalid constructor.
659      ///
660      /// Invalid constructor.
661      ActiveIt(Invalid) : _algorithm(0), _index(-1) {}
662
663      /// \brief Conversion to \c Node.
664      ///
665      /// Conversion to \c Node.
666      operator Node() const {
667        return _index >= 0 ? _algorithm->_process[_index] : INVALID;
668      }
669
670      /// \brief Increment operator.
671      ///
672      /// Increment operator.
673      ActiveIt& operator++() {
674        --_index;
675        return *this;
676      }
677
678      bool operator==(const ActiveIt& it) const {
679        return static_cast<Node>(*this) == static_cast<Node>(it);
680      }
681      bool operator!=(const ActiveIt& it) const {
682        return static_cast<Node>(*this) != static_cast<Node>(it);
683      }
684      bool operator<(const ActiveIt& it) const {
685        return static_cast<Node>(*this) < static_cast<Node>(it);
686      }
687
688    private:
689      const BellmanFord* _algorithm;
690      int _index;
691    };
692
693    /// \name Query Functions
694    /// The result of the Bellman-Ford algorithm can be obtained using these
695    /// functions.\n
696    /// Either \ref run() or \ref init() should be called before using them.
697
698    ///@{
699
700    /// \brief The shortest path to the given node.
701    ///
702    /// Gives back the shortest path to the given node from the root(s).
703    ///
704    /// \warning \c t should be reached from the root(s).
705    ///
706    /// \pre Either \ref run() or \ref init() must be called before
707    /// using this function.
708    Path path(Node t) const
709    {
710      return Path(*_gr, *_pred, t);
711    }
712
713    /// \brief The distance of the given node from the root(s).
714    ///
715    /// Returns the distance of the given node from the root(s).
716    ///
717    /// \warning If node \c v is not reached from the root(s), then
718    /// the return value of this function is undefined.
719    ///
720    /// \pre Either \ref run() or \ref init() must be called before
721    /// using this function.
722    Value dist(Node v) const { return (*_dist)[v]; }
723
724    /// \brief Returns the 'previous arc' of the shortest path tree for
725    /// the given node.
726    ///
727    /// This function returns the 'previous arc' of the shortest path
728    /// tree for node \c v, i.e. it returns the last arc of a
729    /// shortest path from a root to \c v. It is \c INVALID if \c v
730    /// is not reached from the root(s) or if \c v is a root.
731    ///
732    /// The shortest path tree used here is equal to the shortest path
733    /// tree used in \ref predNode() and \ref predMap().
734    ///
735    /// \pre Either \ref run() or \ref init() must be called before
736    /// using this function.
737    Arc predArc(Node v) const { return (*_pred)[v]; }
738
739    /// \brief Returns the 'previous node' of the shortest path tree for
740    /// the given node.
741    ///
742    /// This function returns the 'previous node' of the shortest path
743    /// tree for node \c v, i.e. it returns the last but one node of
744    /// a shortest path from a root to \c v. It is \c INVALID if \c v
745    /// is not reached from the root(s) or if \c v is a root.
746    ///
747    /// The shortest path tree used here is equal to the shortest path
748    /// tree used in \ref predArc() and \ref predMap().
749    ///
750    /// \pre Either \ref run() or \ref init() must be called before
751    /// using this function.
752    Node predNode(Node v) const {
753      return (*_pred)[v] == INVALID ? INVALID : _gr->source((*_pred)[v]);
754    }
755
756    /// \brief Returns a const reference to the node map that stores the
757    /// distances of the nodes.
758    ///
759    /// Returns a const reference to the node map that stores the distances
760    /// of the nodes calculated by the algorithm.
761    ///
762    /// \pre Either \ref run() or \ref init() must be called before
763    /// using this function.
764    const DistMap &distMap() const { return *_dist;}
765
766    /// \brief Returns a const reference to the node map that stores the
767    /// predecessor arcs.
768    ///
769    /// Returns a const reference to the node map that stores the predecessor
770    /// arcs, which form the shortest path tree (forest).
771    ///
772    /// \pre Either \ref run() or \ref init() must be called before
773    /// using this function.
774    const PredMap &predMap() const { return *_pred; }
775
776    /// \brief Checks if a node is reached from the root(s).
777    ///
778    /// Returns \c true if \c v is reached from the root(s).
779    ///
780    /// \pre Either \ref run() or \ref init() must be called before
781    /// using this function.
782    bool reached(Node v) const {
783      return (*_dist)[v] != OperationTraits::infinity();
784    }
785
786    /// \brief Gives back a negative cycle.
787    ///
788    /// This function gives back a directed cycle with negative total
789    /// length if the algorithm has already found one.
790    /// Otherwise it gives back an empty path.
791    lemon::Path<Digraph> negativeCycle() const {
792      typename Digraph::template NodeMap<int> state(*_gr, -1);
793      lemon::Path<Digraph> cycle;
794      for (int i = 0; i < int(_process.size()); ++i) {
795        if (state[_process[i]] != -1) continue;
796        for (Node v = _process[i]; (*_pred)[v] != INVALID;
797             v = _gr->source((*_pred)[v])) {
798          if (state[v] == i) {
799            cycle.addFront((*_pred)[v]);
800            for (Node u = _gr->source((*_pred)[v]); u != v;
801                 u = _gr->source((*_pred)[u])) {
802              cycle.addFront((*_pred)[u]);
803            }
804            return cycle;
805          }
806          else if (state[v] >= 0) {
807            break;
808          }
809          state[v] = i;
810        }
811      }
812      return cycle;
813    }
814
815    ///@}
816  };
817
818  /// \brief Default traits class of bellmanFord() function.
819  ///
820  /// Default traits class of bellmanFord() function.
821  /// \tparam GR The type of the digraph.
822  /// \tparam LEN The type of the length map.
823  template <typename GR, typename LEN>
824  struct BellmanFordWizardDefaultTraits {
825    /// The type of the digraph the algorithm runs on.
826    typedef GR Digraph;
827
828    /// \brief The type of the map that stores the arc lengths.
829    ///
830    /// The type of the map that stores the arc lengths.
831    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
832    typedef LEN LengthMap;
833
834    /// The type of the arc lengths.
835    typedef typename LEN::Value Value;
836
837    /// \brief Operation traits for Bellman-Ford algorithm.
838    ///
839    /// It defines the used operations and the infinity value for the
840    /// given \c Value type.
841    /// \see BellmanFordDefaultOperationTraits
842    typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
843
844    /// \brief The type of the map that stores the last
845    /// arcs of the shortest paths.
846    ///
847    /// The type of the map that stores the last arcs of the shortest paths.
848    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
849    typedef typename GR::template NodeMap<typename GR::Arc> PredMap;
850
851    /// \brief Instantiates a \c PredMap.
852    ///
853    /// This function instantiates a \ref PredMap.
854    /// \param g is the digraph to which we would like to define the
855    /// \ref PredMap.
856    static PredMap *createPredMap(const GR &g) {
857      return new PredMap(g);
858    }
859
860    /// \brief The type of the map that stores the distances of the nodes.
861    ///
862    /// The type of the map that stores the distances of the nodes.
863    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
864    typedef typename GR::template NodeMap<Value> DistMap;
865
866    /// \brief Instantiates a \c DistMap.
867    ///
868    /// This function instantiates a \ref DistMap.
869    /// \param g is the digraph to which we would like to define the
870    /// \ref DistMap.
871    static DistMap *createDistMap(const GR &g) {
872      return new DistMap(g);
873    }
874
875    ///The type of the shortest paths.
876
877    ///The type of the shortest paths.
878    ///It must meet the \ref concepts::Path "Path" concept.
879    typedef lemon::Path<Digraph> Path;
880  };
881
882  /// \brief Default traits class used by BellmanFordWizard.
883  ///
884  /// Default traits class used by BellmanFordWizard.
885  /// \tparam GR The type of the digraph.
886  /// \tparam LEN The type of the length map.
887  template <typename GR, typename LEN>
888  class BellmanFordWizardBase
889    : public BellmanFordWizardDefaultTraits<GR, LEN> {
890
891    typedef BellmanFordWizardDefaultTraits<GR, LEN> Base;
892  protected:
893    // Type of the nodes in the digraph.
894    typedef typename Base::Digraph::Node Node;
895
896    // Pointer to the underlying digraph.
897    void *_graph;
898    // Pointer to the length map
899    void *_length;
900    // Pointer to the map of predecessors arcs.
901    void *_pred;
902    // Pointer to the map of distances.
903    void *_dist;
904    //Pointer to the shortest path to the target node.
905    void *_path;
906    //Pointer to the distance of the target node.
907    void *_di;
908
909    public:
910    /// Constructor.
911
912    /// This constructor does not require parameters, it initiates
913    /// all of the attributes to default values \c 0.
914    BellmanFordWizardBase() :
915      _graph(0), _length(0), _pred(0), _dist(0), _path(0), _di(0) {}
916
917    /// Constructor.
918
919    /// This constructor requires two parameters,
920    /// others are initiated to \c 0.
921    /// \param gr The digraph the algorithm runs on.
922    /// \param len The length map.
923    BellmanFordWizardBase(const GR& gr,
924                          const LEN& len) :
925      _graph(reinterpret_cast<void*>(const_cast<GR*>(&gr))),
926      _length(reinterpret_cast<void*>(const_cast<LEN*>(&len))),
927      _pred(0), _dist(0), _path(0), _di(0) {}
928
929  };
930
931  /// \brief Auxiliary class for the function-type interface of the
932  /// \ref BellmanFord "Bellman-Ford" algorithm.
933  ///
934  /// This auxiliary class is created to implement the
935  /// \ref bellmanFord() "function-type interface" of the
936  /// \ref BellmanFord "Bellman-Ford" algorithm.
937  /// It does not have own \ref run() method, it uses the
938  /// functions and features of the plain \ref BellmanFord.
939  ///
940  /// This class should only be used through the \ref bellmanFord()
941  /// function, which makes it easier to use the algorithm.
942  ///
943  /// \tparam TR The traits class that defines various types used by the
944  /// algorithm.
945  template<class TR>
946  class BellmanFordWizard : public TR {
947    typedef TR Base;
948
949    typedef typename TR::Digraph Digraph;
950
951    typedef typename Digraph::Node Node;
952    typedef typename Digraph::NodeIt NodeIt;
953    typedef typename Digraph::Arc Arc;
954    typedef typename Digraph::OutArcIt ArcIt;
955
956    typedef typename TR::LengthMap LengthMap;
957    typedef typename LengthMap::Value Value;
958    typedef typename TR::PredMap PredMap;
959    typedef typename TR::DistMap DistMap;
960    typedef typename TR::Path Path;
961
962  public:
963    /// Constructor.
964    BellmanFordWizard() : TR() {}
965
966    /// \brief Constructor that requires parameters.
967    ///
968    /// Constructor that requires parameters.
969    /// These parameters will be the default values for the traits class.
970    /// \param gr The digraph the algorithm runs on.
971    /// \param len The length map.
972    BellmanFordWizard(const Digraph& gr, const LengthMap& len)
973      : TR(gr, len) {}
974
975    /// \brief Copy constructor
976    BellmanFordWizard(const TR &b) : TR(b) {}
977
978    ~BellmanFordWizard() {}
979
980    /// \brief Runs the Bellman-Ford algorithm from the given source node.
981    ///
982    /// This method runs the Bellman-Ford algorithm from the given source
983    /// node in order to compute the shortest path to each node.
984    void run(Node s) {
985      BellmanFord<Digraph,LengthMap,TR>
986        bf(*reinterpret_cast<const Digraph*>(Base::_graph),
987           *reinterpret_cast<const LengthMap*>(Base::_length));
988      if (Base::_pred) bf.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
989      if (Base::_dist) bf.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
990      bf.run(s);
991    }
992
993    /// \brief Runs the Bellman-Ford algorithm to find the shortest path
994    /// between \c s and \c t.
995    ///
996    /// This method runs the Bellman-Ford algorithm from node \c s
997    /// in order to compute the shortest path to node \c t.
998    /// Actually, it computes the shortest path to each node, but using
999    /// this function you can retrieve the distance and the shortest path
1000    /// for a single target node easier.
1001    ///
1002    /// \return \c true if \c t is reachable form \c s.
1003    bool run(Node s, Node t) {
1004      BellmanFord<Digraph,LengthMap,TR>
1005        bf(*reinterpret_cast<const Digraph*>(Base::_graph),
1006           *reinterpret_cast<const LengthMap*>(Base::_length));
1007      if (Base::_pred) bf.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
1008      if (Base::_dist) bf.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
1009      bf.run(s);
1010      if (Base::_path) *reinterpret_cast<Path*>(Base::_path) = bf.path(t);
1011      if (Base::_di) *reinterpret_cast<Value*>(Base::_di) = bf.dist(t);
1012      return bf.reached(t);
1013    }
1014
1015    template<class T>
1016    struct SetPredMapBase : public Base {
1017      typedef T PredMap;
1018      static PredMap *createPredMap(const Digraph &) { return 0; };
1019      SetPredMapBase(const TR &b) : TR(b) {}
1020    };
1021
1022    /// \brief \ref named-templ-param "Named parameter" for setting
1023    /// the predecessor map.
1024    ///
1025    /// \ref named-templ-param "Named parameter" for setting
1026    /// the map that stores the predecessor arcs of the nodes.
1027    template<class T>
1028    BellmanFordWizard<SetPredMapBase<T> > predMap(const T &t) {
1029      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
1030      return BellmanFordWizard<SetPredMapBase<T> >(*this);
1031    }
1032
1033    template<class T>
1034    struct SetDistMapBase : public Base {
1035      typedef T DistMap;
1036      static DistMap *createDistMap(const Digraph &) { return 0; };
1037      SetDistMapBase(const TR &b) : TR(b) {}
1038    };
1039
1040    /// \brief \ref named-templ-param "Named parameter" for setting
1041    /// the distance map.
1042    ///
1043    /// \ref named-templ-param "Named parameter" for setting
1044    /// the map that stores the distances of the nodes calculated
1045    /// by the algorithm.
1046    template<class T>
1047    BellmanFordWizard<SetDistMapBase<T> > distMap(const T &t) {
1048      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
1049      return BellmanFordWizard<SetDistMapBase<T> >(*this);
1050    }
1051
1052    template<class T>
1053    struct SetPathBase : public Base {
1054      typedef T Path;
1055      SetPathBase(const TR &b) : TR(b) {}
1056    };
1057
1058    /// \brief \ref named-func-param "Named parameter" for getting
1059    /// the shortest path to the target node.
1060    ///
1061    /// \ref named-func-param "Named parameter" for getting
1062    /// the shortest path to the target node.
1063    template<class T>
1064    BellmanFordWizard<SetPathBase<T> > path(const T &t)
1065    {
1066      Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t));
1067      return BellmanFordWizard<SetPathBase<T> >(*this);
1068    }
1069
1070    /// \brief \ref named-func-param "Named parameter" for getting
1071    /// the distance of the target node.
1072    ///
1073    /// \ref named-func-param "Named parameter" for getting
1074    /// the distance of the target node.
1075    BellmanFordWizard dist(const Value &d)
1076    {
1077      Base::_di=reinterpret_cast<void*>(const_cast<Value*>(&d));
1078      return *this;
1079    }
1080
1081  };
1082
1083  /// \brief Function type interface for the \ref BellmanFord "Bellman-Ford"
1084  /// algorithm.
1085  ///
1086  /// \ingroup shortest_path
1087  /// Function type interface for the \ref BellmanFord "Bellman-Ford"
1088  /// algorithm.
1089  ///
1090  /// This function also has several \ref named-templ-func-param
1091  /// "named parameters", they are declared as the members of class
1092  /// \ref BellmanFordWizard.
1093  /// The following examples show how to use these parameters.
1094  /// \code
1095  ///   // Compute shortest path from node s to each node
1096  ///   bellmanFord(g,length).predMap(preds).distMap(dists).run(s);
1097  ///
1098  ///   // Compute shortest path from s to t
1099  ///   bool reached = bellmanFord(g,length).path(p).dist(d).run(s,t);
1100  /// \endcode
1101  /// \warning Don't forget to put the \ref BellmanFordWizard::run() "run()"
1102  /// to the end of the parameter list.
1103  /// \sa BellmanFordWizard
1104  /// \sa BellmanFord
1105  template<typename GR, typename LEN>
1106  BellmanFordWizard<BellmanFordWizardBase<GR,LEN> >
1107  bellmanFord(const GR& digraph,
1108              const LEN& length)
1109  {
1110    return BellmanFordWizard<BellmanFordWizardBase<GR,LEN> >(digraph, length);
1111  }
1112
1113} //END OF NAMESPACE LEMON
1114
1115#endif
1116
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