COIN-OR::LEMON - Graph Library

source: lemon/lemon/bellman_ford.h @ 746:75325dfccf38

Last change on this file since 746:75325dfccf38 was 746:75325dfccf38, checked in by Peter Kovacs <kpeter@…>, 11 years ago

Add negativeCycle() function to BellmanFord? (#51)

File size: 37.1 KB
RevLine 
[743]1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2008
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
[744]19#ifndef LEMON_BELLMAN_FORD_H
20#define LEMON_BELLMAN_FORD_H
[743]21
22/// \ingroup shortest_path
23/// \file
24/// \brief Bellman-Ford algorithm.
25
26#include <lemon/bits/path_dump.h>
27#include <lemon/core.h>
28#include <lemon/error.h>
29#include <lemon/maps.h>
[744]30#include <lemon/path.h>
[743]31
32#include <limits>
33
34namespace lemon {
35
36  /// \brief Default OperationTraits for the BellmanFord algorithm class.
37  /// 
[744]38  /// This operation traits class defines all computational operations
39  /// and constants that are used in the Bellman-Ford algorithm.
40  /// The default implementation is based on the \c numeric_limits class.
41  /// If the numeric type does not have infinity value, then the maximum
42  /// value is used as extremal infinity value.
[743]43  template <
[744]44    typename V,
45    bool has_inf = std::numeric_limits<V>::has_infinity>
[743]46  struct BellmanFordDefaultOperationTraits {
[744]47    /// \e
48    typedef V Value;
[743]49    /// \brief Gives back the zero value of the type.
50    static Value zero() {
51      return static_cast<Value>(0);
52    }
53    /// \brief Gives back the positive infinity value of the type.
54    static Value infinity() {
55      return std::numeric_limits<Value>::infinity();
56    }
57    /// \brief Gives back the sum of the given two elements.
58    static Value plus(const Value& left, const Value& right) {
59      return left + right;
60    }
[744]61    /// \brief Gives back \c true only if the first value is less than
62    /// the second.
[743]63    static bool less(const Value& left, const Value& right) {
64      return left < right;
65    }
66  };
67
[744]68  template <typename V>
69  struct BellmanFordDefaultOperationTraits<V, false> {
70    typedef V Value;
[743]71    static Value zero() {
72      return static_cast<Value>(0);
73    }
74    static Value infinity() {
75      return std::numeric_limits<Value>::max();
76    }
77    static Value plus(const Value& left, const Value& right) {
78      if (left == infinity() || right == infinity()) return infinity();
79      return left + right;
80    }
81    static bool less(const Value& left, const Value& right) {
82      return left < right;
83    }
84  };
85 
86  /// \brief Default traits class of BellmanFord class.
87  ///
88  /// Default traits class of BellmanFord class.
[744]89  /// \param GR The type of the digraph.
90  /// \param LEN The type of the length map.
91  template<typename GR, typename LEN>
[743]92  struct BellmanFordDefaultTraits {
[744]93    /// The type of the digraph the algorithm runs on.
94    typedef GR Digraph;
[743]95
96    /// \brief The type of the map that stores the arc lengths.
97    ///
98    /// The type of the map that stores the arc lengths.
[744]99    /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
100    typedef LEN LengthMap;
[743]101
[744]102    /// The type of the arc lengths.
103    typedef typename LEN::Value Value;
[743]104
105    /// \brief Operation traits for Bellman-Ford algorithm.
106    ///
[744]107    /// It defines the used operations and the infinity value for the
108    /// given \c Value type.
[743]109    /// \see BellmanFordDefaultOperationTraits
110    typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
111 
112    /// \brief The type of the map that stores the last arcs of the
113    /// shortest paths.
114    ///
115    /// The type of the map that stores the last
116    /// arcs of the shortest paths.
[744]117    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
118    typedef typename GR::template NodeMap<typename GR::Arc> PredMap;
[743]119
[744]120    /// \brief Instantiates a \c PredMap.
[743]121    ///
122    /// This function instantiates a \ref PredMap.
[744]123    /// \param g is the digraph to which we would like to define the
124    /// \ref PredMap.
125    static PredMap *createPredMap(const GR& g) {
126      return new PredMap(g);
[743]127    }
128
[744]129    /// \brief The type of the map that stores the distances of the nodes.
[743]130    ///
[744]131    /// The type of the map that stores the distances of the nodes.
132    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
133    typedef typename GR::template NodeMap<typename LEN::Value> DistMap;
[743]134
[744]135    /// \brief Instantiates a \c DistMap.
[743]136    ///
137    /// This function instantiates a \ref DistMap.
[744]138    /// \param g is the digraph to which we would like to define the
139    /// \ref DistMap.
140    static DistMap *createDistMap(const GR& g) {
141      return new DistMap(g);
[743]142    }
143
144  };
145 
146  /// \brief %BellmanFord algorithm class.
147  ///
148  /// \ingroup shortest_path
[744]149  /// This class provides an efficient implementation of the Bellman-Ford
150  /// algorithm. The maximum time complexity of the algorithm is
151  /// <tt>O(ne)</tt>.
152  ///
153  /// The Bellman-Ford algorithm solves the single-source shortest path
154  /// problem when the arcs can have negative lengths, but the digraph
155  /// should not contain directed cycles with negative total length.
156  /// If all arc costs are non-negative, consider to use the Dijkstra
157  /// algorithm instead, since it is more efficient.
158  ///
159  /// The arc lengths are passed to the algorithm using a
[743]160  /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any
[744]161  /// kind of length. The type of the length values is determined by the
162  /// \ref concepts::ReadMap::Value "Value" type of the length map.
[743]163  ///
[744]164  /// There is also a \ref bellmanFord() "function-type interface" for the
165  /// Bellman-Ford algorithm, which is convenient in the simplier cases and
166  /// it can be used easier.
[743]167  ///
[744]168  /// \tparam GR The type of the digraph the algorithm runs on.
169  /// The default type is \ref ListDigraph.
170  /// \tparam LEN A \ref concepts::ReadMap "readable" arc map that specifies
171  /// the lengths of the arcs. The default map type is
172  /// \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
[743]173#ifdef DOXYGEN
[744]174  template <typename GR, typename LEN, typename TR>
[743]175#else
[744]176  template <typename GR=ListDigraph,
177            typename LEN=typename GR::template ArcMap<int>,
178            typename TR=BellmanFordDefaultTraits<GR,LEN> >
[743]179#endif
180  class BellmanFord {
181  public:
182
183    ///The type of the underlying digraph.
[744]184    typedef typename TR::Digraph Digraph;
185   
186    /// \brief The type of the arc lengths.
187    typedef typename TR::LengthMap::Value Value;
188    /// \brief The type of the map that stores the arc lengths.
189    typedef typename TR::LengthMap LengthMap;
190    /// \brief The type of the map that stores the last
191    /// arcs of the shortest paths.
192    typedef typename TR::PredMap PredMap;
193    /// \brief The type of the map that stores the distances of the nodes.
194    typedef typename TR::DistMap DistMap;
195    /// The type of the paths.
196    typedef PredMapPath<Digraph, PredMap> Path;
197    ///\brief The \ref BellmanFordDefaultOperationTraits
198    /// "operation traits class" of the algorithm.
199    typedef typename TR::OperationTraits OperationTraits;
200
201    ///The \ref BellmanFordDefaultTraits "traits class" of the algorithm.
202    typedef TR Traits;
203
204  private:
[743]205
206    typedef typename Digraph::Node Node;
207    typedef typename Digraph::NodeIt NodeIt;
208    typedef typename Digraph::Arc Arc;
209    typedef typename Digraph::OutArcIt OutArcIt;
[744]210
211    // Pointer to the underlying digraph.
212    const Digraph *_gr;
213    // Pointer to the length map
214    const LengthMap *_length;
215    // Pointer to the map of predecessors arcs.
[743]216    PredMap *_pred;
[744]217    // Indicates if _pred is locally allocated (true) or not.
218    bool _local_pred;
219    // Pointer to the map of distances.
[743]220    DistMap *_dist;
[744]221    // Indicates if _dist is locally allocated (true) or not.
222    bool _local_dist;
[743]223
224    typedef typename Digraph::template NodeMap<bool> MaskMap;
225    MaskMap *_mask;
226
227    std::vector<Node> _process;
228
[744]229    // Creates the maps if necessary.
[743]230    void create_maps() {
231      if(!_pred) {
[744]232        _local_pred = true;
233        _pred = Traits::createPredMap(*_gr);
[743]234      }
235      if(!_dist) {
[744]236        _local_dist = true;
237        _dist = Traits::createDistMap(*_gr);
[743]238      }
[744]239      _mask = new MaskMap(*_gr, false);
[743]240    }
241   
242  public :
243 
244    typedef BellmanFord Create;
245
[744]246    /// \name Named Template Parameters
[743]247
248    ///@{
249
250    template <class T>
[744]251    struct SetPredMapTraits : public Traits {
[743]252      typedef T PredMap;
253      static PredMap *createPredMap(const Digraph&) {
254        LEMON_ASSERT(false, "PredMap is not initialized");
255        return 0; // ignore warnings
256      }
257    };
258
[744]259    /// \brief \ref named-templ-param "Named parameter" for setting
260    /// \c PredMap type.
[743]261    ///
[744]262    /// \ref named-templ-param "Named parameter" for setting
263    /// \c PredMap type.
264    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
[743]265    template <class T>
266    struct SetPredMap
[744]267      : public BellmanFord< Digraph, LengthMap, SetPredMapTraits<T> > {
268      typedef BellmanFord< Digraph, LengthMap, SetPredMapTraits<T> > Create;
[743]269    };
270   
271    template <class T>
[744]272    struct SetDistMapTraits : public Traits {
[743]273      typedef T DistMap;
274      static DistMap *createDistMap(const Digraph&) {
275        LEMON_ASSERT(false, "DistMap is not initialized");
276        return 0; // ignore warnings
277      }
278    };
279
[744]280    /// \brief \ref named-templ-param "Named parameter" for setting
281    /// \c DistMap type.
[743]282    ///
[744]283    /// \ref named-templ-param "Named parameter" for setting
284    /// \c DistMap type.
285    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
[743]286    template <class T>
287    struct SetDistMap
[744]288      : public BellmanFord< Digraph, LengthMap, SetDistMapTraits<T> > {
289      typedef BellmanFord< Digraph, LengthMap, SetDistMapTraits<T> > Create;
[743]290    };
[744]291
[743]292    template <class T>
[744]293    struct SetOperationTraitsTraits : public Traits {
[743]294      typedef T OperationTraits;
295    };
296   
297    /// \brief \ref named-templ-param "Named parameter" for setting
[744]298    /// \c OperationTraits type.
[743]299    ///
[744]300    /// \ref named-templ-param "Named parameter" for setting
301    /// \c OperationTraits type.
302    /// For more information see \ref BellmanFordDefaultOperationTraits.
[743]303    template <class T>
304    struct SetOperationTraits
[744]305      : public BellmanFord< Digraph, LengthMap, SetOperationTraitsTraits<T> > {
306      typedef BellmanFord< Digraph, LengthMap, SetOperationTraitsTraits<T> >
[743]307      Create;
308    };
309   
310    ///@}
311
312  protected:
313   
314    BellmanFord() {}
315
316  public:     
317   
318    /// \brief Constructor.
319    ///
[744]320    /// Constructor.
321    /// \param g The digraph the algorithm runs on.
322    /// \param length The length map used by the algorithm.
323    BellmanFord(const Digraph& g, const LengthMap& length) :
324      _gr(&g), _length(&length),
325      _pred(0), _local_pred(false),
326      _dist(0), _local_dist(false), _mask(0) {}
[743]327   
328    ///Destructor.
329    ~BellmanFord() {
[744]330      if(_local_pred) delete _pred;
331      if(_local_dist) delete _dist;
[743]332      if(_mask) delete _mask;
333    }
334
335    /// \brief Sets the length map.
336    ///
337    /// Sets the length map.
[744]338    /// \return <tt>(*this)</tt>
339    BellmanFord &lengthMap(const LengthMap &map) {
340      _length = &map;
[743]341      return *this;
342    }
343
[744]344    /// \brief Sets the map that stores the predecessor arcs.
[743]345    ///
[744]346    /// Sets the map that stores the predecessor arcs.
347    /// If you don't use this function before calling \ref run()
348    /// or \ref init(), an instance will be allocated automatically.
349    /// The destructor deallocates this automatically allocated map,
350    /// of course.
351    /// \return <tt>(*this)</tt>
352    BellmanFord &predMap(PredMap &map) {
353      if(_local_pred) {
[743]354        delete _pred;
[744]355        _local_pred=false;
[743]356      }
[744]357      _pred = &map;
[743]358      return *this;
359    }
360
[744]361    /// \brief Sets the map that stores the distances of the nodes.
[743]362    ///
[744]363    /// Sets the map that stores the distances of the nodes calculated
364    /// by the algorithm.
365    /// If you don't use this function before calling \ref run()
366    /// or \ref init(), an instance will be allocated automatically.
367    /// The destructor deallocates this automatically allocated map,
368    /// of course.
369    /// \return <tt>(*this)</tt>
370    BellmanFord &distMap(DistMap &map) {
371      if(_local_dist) {
[743]372        delete _dist;
[744]373        _local_dist=false;
[743]374      }
[744]375      _dist = &map;
[743]376      return *this;
377    }
378
[744]379    /// \name Execution Control
380    /// The simplest way to execute the Bellman-Ford algorithm is to use
381    /// one of the member functions called \ref run().\n
382    /// If you need better control on the execution, you have to call
383    /// \ref init() first, then you can add several source nodes
384    /// with \ref addSource(). Finally the actual path computation can be
385    /// performed with \ref start(), \ref checkedStart() or
386    /// \ref limitedStart().
[743]387
388    ///@{
389
390    /// \brief Initializes the internal data structures.
391    ///
[744]392    /// Initializes the internal data structures. The optional parameter
393    /// is the initial distance of each node.
[743]394    void init(const Value value = OperationTraits::infinity()) {
395      create_maps();
[744]396      for (NodeIt it(*_gr); it != INVALID; ++it) {
[743]397        _pred->set(it, INVALID);
398        _dist->set(it, value);
399      }
400      _process.clear();
401      if (OperationTraits::less(value, OperationTraits::infinity())) {
[744]402        for (NodeIt it(*_gr); it != INVALID; ++it) {
[743]403          _process.push_back(it);
404          _mask->set(it, true);
405        }
406      }
407    }
408   
409    /// \brief Adds a new source node.
410    ///
[744]411    /// This function adds a new source node. The optional second parameter
412    /// is the initial distance of the node.
[743]413    void addSource(Node source, Value dst = OperationTraits::zero()) {
414      _dist->set(source, dst);
415      if (!(*_mask)[source]) {
416        _process.push_back(source);
417        _mask->set(source, true);
418      }
419    }
420
421    /// \brief Executes one round from the Bellman-Ford algorithm.
422    ///
423    /// If the algoritm calculated the distances in the previous round
[744]424    /// exactly for the paths of at most \c k arcs, then this function
425    /// will calculate the distances exactly for the paths of at most
426    /// <tt>k+1</tt> arcs. Performing \c k iterations using this function
427    /// calculates the shortest path distances exactly for the paths
428    /// consisting of at most \c k arcs.
[743]429    ///
430    /// \warning The paths with limited arc number cannot be retrieved
[744]431    /// easily with \ref path() or \ref predArc() functions. If you also
432    /// need the shortest paths and not only the distances, you should
433    /// store the \ref predMap() "predecessor map" after each iteration
434    /// and build the path manually.
[743]435    ///
436    /// \return \c true when the algorithm have not found more shorter
437    /// paths.
[744]438    ///
439    /// \see ActiveIt
[743]440    bool processNextRound() {
441      for (int i = 0; i < int(_process.size()); ++i) {
442        _mask->set(_process[i], false);
443      }
444      std::vector<Node> nextProcess;
445      std::vector<Value> values(_process.size());
446      for (int i = 0; i < int(_process.size()); ++i) {
447        values[i] = (*_dist)[_process[i]];
448      }
449      for (int i = 0; i < int(_process.size()); ++i) {
[744]450        for (OutArcIt it(*_gr, _process[i]); it != INVALID; ++it) {
451          Node target = _gr->target(it);
452          Value relaxed = OperationTraits::plus(values[i], (*_length)[it]);
[743]453          if (OperationTraits::less(relaxed, (*_dist)[target])) {
454            _pred->set(target, it);
455            _dist->set(target, relaxed);
456            if (!(*_mask)[target]) {
457              _mask->set(target, true);
458              nextProcess.push_back(target);
459            }
460          }       
461        }
462      }
463      _process.swap(nextProcess);
464      return _process.empty();
465    }
466
467    /// \brief Executes one weak round from the Bellman-Ford algorithm.
468    ///
[744]469    /// If the algorithm calculated the distances in the previous round
470    /// at least for the paths of at most \c k arcs, then this function
471    /// will calculate the distances at least for the paths of at most
472    /// <tt>k+1</tt> arcs.
473    /// This function does not make it possible to calculate the shortest
474    /// path distances exactly for paths consisting of at most \c k arcs,
475    /// this is why it is called weak round.
476    ///
477    /// \return \c true when the algorithm have not found more shorter
478    /// paths.
479    ///
480    /// \see ActiveIt
[743]481    bool processNextWeakRound() {
482      for (int i = 0; i < int(_process.size()); ++i) {
483        _mask->set(_process[i], false);
484      }
485      std::vector<Node> nextProcess;
486      for (int i = 0; i < int(_process.size()); ++i) {
[744]487        for (OutArcIt it(*_gr, _process[i]); it != INVALID; ++it) {
488          Node target = _gr->target(it);
[743]489          Value relaxed =
[744]490            OperationTraits::plus((*_dist)[_process[i]], (*_length)[it]);
[743]491          if (OperationTraits::less(relaxed, (*_dist)[target])) {
492            _pred->set(target, it);
493            _dist->set(target, relaxed);
494            if (!(*_mask)[target]) {
495              _mask->set(target, true);
496              nextProcess.push_back(target);
497            }
498          }       
499        }
500      }
501      _process.swap(nextProcess);
502      return _process.empty();
503    }
504
505    /// \brief Executes the algorithm.
506    ///
[744]507    /// Executes the algorithm.
[743]508    ///
[744]509    /// This method runs the Bellman-Ford algorithm from the root node(s)
510    /// in order to compute the shortest path to each node.
511    ///
512    /// The algorithm computes
513    /// - the shortest path tree (forest),
514    /// - the distance of each node from the root(s).
515    ///
516    /// \pre init() must be called and at least one root node should be
517    /// added with addSource() before using this function.
[743]518    void start() {
[744]519      int num = countNodes(*_gr) - 1;
[743]520      for (int i = 0; i < num; ++i) {
521        if (processNextWeakRound()) break;
522      }
523    }
524
525    /// \brief Executes the algorithm and checks the negative cycles.
526    ///
[744]527    /// Executes the algorithm and checks the negative cycles.
[743]528    ///
[744]529    /// This method runs the Bellman-Ford algorithm from the root node(s)
530    /// in order to compute the shortest path to each node and also checks
531    /// if the digraph contains cycles with negative total length.
532    ///
533    /// The algorithm computes
534    /// - the shortest path tree (forest),
535    /// - the distance of each node from the root(s).
[743]536    ///
537    /// \return \c false if there is a negative cycle in the digraph.
[744]538    ///
539    /// \pre init() must be called and at least one root node should be
540    /// added with addSource() before using this function.
[743]541    bool checkedStart() {
[744]542      int num = countNodes(*_gr);
[743]543      for (int i = 0; i < num; ++i) {
544        if (processNextWeakRound()) return true;
545      }
546      return _process.empty();
547    }
548
[744]549    /// \brief Executes the algorithm with arc number limit.
[743]550    ///
[744]551    /// Executes the algorithm with arc number limit.
[743]552    ///
[744]553    /// This method runs the Bellman-Ford algorithm from the root node(s)
554    /// in order to compute the shortest path distance for each node
555    /// using only the paths consisting of at most \c num arcs.
556    ///
557    /// The algorithm computes
558    /// - the limited distance of each node from the root(s),
559    /// - the predecessor arc for each node.
[743]560    ///
561    /// \warning The paths with limited arc number cannot be retrieved
[744]562    /// easily with \ref path() or \ref predArc() functions. If you also
563    /// need the shortest paths and not only the distances, you should
564    /// store the \ref predMap() "predecessor map" after each iteration
565    /// and build the path manually.
[743]566    ///
[744]567    /// \pre init() must be called and at least one root node should be
568    /// added with addSource() before using this function.
[743]569    void limitedStart(int num) {
570      for (int i = 0; i < num; ++i) {
571        if (processNextRound()) break;
572      }
573    }
574   
[744]575    /// \brief Runs the algorithm from the given root node.
[743]576    ///   
[744]577    /// This method runs the Bellman-Ford algorithm from the given root
578    /// node \c s in order to compute the shortest path to each node.
[743]579    ///
[744]580    /// The algorithm computes
581    /// - the shortest path tree (forest),
582    /// - the distance of each node from the root(s).
583    ///
584    /// \note bf.run(s) is just a shortcut of the following code.
585    /// \code
586    ///   bf.init();
587    ///   bf.addSource(s);
588    ///   bf.start();
589    /// \endcode
[743]590    void run(Node s) {
591      init();
592      addSource(s);
593      start();
594    }
595   
[744]596    /// \brief Runs the algorithm from the given root node with arc
597    /// number limit.
[743]598    ///   
[744]599    /// This method runs the Bellman-Ford algorithm from the given root
600    /// node \c s in order to compute the shortest path distance for each
601    /// node using only the paths consisting of at most \c num arcs.
[743]602    ///
[744]603    /// The algorithm computes
604    /// - the limited distance of each node from the root(s),
605    /// - the predecessor arc for each node.
606    ///
607    /// \warning The paths with limited arc number cannot be retrieved
608    /// easily with \ref path() or \ref predArc() functions. If you also
609    /// need the shortest paths and not only the distances, you should
610    /// store the \ref predMap() "predecessor map" after each iteration
611    /// and build the path manually.
612    ///
613    /// \note bf.run(s, num) is just a shortcut of the following code.
614    /// \code
615    ///   bf.init();
616    ///   bf.addSource(s);
617    ///   bf.limitedStart(num);
618    /// \endcode
[743]619    void run(Node s, int num) {
620      init();
621      addSource(s);
622      limitedStart(num);
623    }
624   
625    ///@}
626
[744]627    /// \brief LEMON iterator for getting the active nodes.
[743]628    ///
[744]629    /// This class provides a common style LEMON iterator that traverses
630    /// the active nodes of the Bellman-Ford algorithm after the last
631    /// phase. These nodes should be checked in the next phase to
632    /// find augmenting arcs outgoing from them.
[743]633    class ActiveIt {
634    public:
635
636      /// \brief Constructor.
637      ///
[744]638      /// Constructor for getting the active nodes of the given BellmanFord
639      /// instance.
[743]640      ActiveIt(const BellmanFord& algorithm) : _algorithm(&algorithm)
641      {
642        _index = _algorithm->_process.size() - 1;
643      }
644
645      /// \brief Invalid constructor.
646      ///
647      /// Invalid constructor.
648      ActiveIt(Invalid) : _algorithm(0), _index(-1) {}
649
[744]650      /// \brief Conversion to \c Node.
[743]651      ///
[744]652      /// Conversion to \c Node.
[743]653      operator Node() const {
654        return _index >= 0 ? _algorithm->_process[_index] : INVALID;
655      }
656
657      /// \brief Increment operator.
658      ///
659      /// Increment operator.
660      ActiveIt& operator++() {
661        --_index;
662        return *this;
663      }
664
665      bool operator==(const ActiveIt& it) const {
666        return static_cast<Node>(*this) == static_cast<Node>(it);
667      }
668      bool operator!=(const ActiveIt& it) const {
669        return static_cast<Node>(*this) != static_cast<Node>(it);
670      }
671      bool operator<(const ActiveIt& it) const {
672        return static_cast<Node>(*this) < static_cast<Node>(it);
673      }
674     
675    private:
676      const BellmanFord* _algorithm;
677      int _index;
678    };
[744]679   
680    /// \name Query Functions
681    /// The result of the Bellman-Ford algorithm can be obtained using these
682    /// functions.\n
683    /// Either \ref run() or \ref init() should be called before using them.
684   
685    ///@{
[743]686
[744]687    /// \brief The shortest path to the given node.
688    ///   
689    /// Gives back the shortest path to the given node from the root(s).
690    ///
691    /// \warning \c t should be reached from the root(s).
692    ///
693    /// \pre Either \ref run() or \ref init() must be called before
694    /// using this function.
695    Path path(Node t) const
696    {
697      return Path(*_gr, *_pred, t);
698    }
699         
700    /// \brief The distance of the given node from the root(s).
701    ///
702    /// Returns the distance of the given node from the root(s).
703    ///
704    /// \warning If node \c v is not reached from the root(s), then
705    /// the return value of this function is undefined.
706    ///
707    /// \pre Either \ref run() or \ref init() must be called before
708    /// using this function.
709    Value dist(Node v) const { return (*_dist)[v]; }
[743]710
[744]711    /// \brief Returns the 'previous arc' of the shortest path tree for
712    /// the given node.
713    ///
714    /// This function returns the 'previous arc' of the shortest path
715    /// tree for node \c v, i.e. it returns the last arc of a
716    /// shortest path from a root to \c v. It is \c INVALID if \c v
717    /// is not reached from the root(s) or if \c v is a root.
718    ///
719    /// The shortest path tree used here is equal to the shortest path
720    /// tree used in \ref predNode() and \predMap().
721    ///
722    /// \pre Either \ref run() or \ref init() must be called before
723    /// using this function.
724    Arc predArc(Node v) const { return (*_pred)[v]; }
725
726    /// \brief Returns the 'previous node' of the shortest path tree for
727    /// the given node.
728    ///
729    /// This function returns the 'previous node' of the shortest path
730    /// tree for node \c v, i.e. it returns the last but one node of
731    /// a shortest path from a root to \c v. It is \c INVALID if \c v
732    /// is not reached from the root(s) or if \c v is a root.
733    ///
734    /// The shortest path tree used here is equal to the shortest path
735    /// tree used in \ref predArc() and \predMap().
736    ///
737    /// \pre Either \ref run() or \ref init() must be called before
738    /// using this function.
739    Node predNode(Node v) const {
740      return (*_pred)[v] == INVALID ? INVALID : _gr->source((*_pred)[v]);
741    }
742   
743    /// \brief Returns a const reference to the node map that stores the
744    /// distances of the nodes.
745    ///
746    /// Returns a const reference to the node map that stores the distances
747    /// of the nodes calculated by the algorithm.
748    ///
749    /// \pre Either \ref run() or \ref init() must be called before
750    /// using this function.
751    const DistMap &distMap() const { return *_dist;}
752 
753    /// \brief Returns a const reference to the node map that stores the
754    /// predecessor arcs.
755    ///
756    /// Returns a const reference to the node map that stores the predecessor
757    /// arcs, which form the shortest path tree (forest).
758    ///
759    /// \pre Either \ref run() or \ref init() must be called before
760    /// using this function.
761    const PredMap &predMap() const { return *_pred; }
762 
763    /// \brief Checks if a node is reached from the root(s).
764    ///
765    /// Returns \c true if \c v is reached from the root(s).
766    ///
767    /// \pre Either \ref run() or \ref init() must be called before
768    /// using this function.
769    bool reached(Node v) const {
770      return (*_dist)[v] != OperationTraits::infinity();
[743]771    }
772
[746]773    /// \brief Gives back a negative cycle.
774    ///   
775    /// This function gives back a directed cycle with negative total
776    /// length if the algorithm has already found one.
777    /// Otherwise it gives back an empty path.
778    lemon::Path<Digraph> negativeCycle() {
779      typename Digraph::template NodeMap<int> state(*_gr, -1);
780      lemon::Path<Digraph> cycle;
781      for (int i = 0; i < int(_process.size()); ++i) {
782        if (state[_process[i]] != -1) continue;
783        for (Node v = _process[i]; (*_pred)[v] != INVALID;
784             v = _gr->source((*_pred)[v])) {
785          if (state[v] == i) {
786            cycle.addFront((*_pred)[v]);
787            for (Node u = _gr->source((*_pred)[v]); u != v;
788                 u = _gr->source((*_pred)[u])) {
789              cycle.addFront((*_pred)[u]);
790            }
791            return cycle;
792          }
793          else if (state[v] >= 0) {
794            break;
795          }
796          state[v] = i;
797        }
798      }
799      return cycle;
800    }
[743]801   
802    ///@}
803  };
804 
[744]805  /// \brief Default traits class of bellmanFord() function.
[743]806  ///
[744]807  /// Default traits class of bellmanFord() function.
808  /// \tparam GR The type of the digraph.
809  /// \tparam LEN The type of the length map.
810  template <typename GR, typename LEN>
[743]811  struct BellmanFordWizardDefaultTraits {
[744]812    /// The type of the digraph the algorithm runs on.
813    typedef GR Digraph;
[743]814
815    /// \brief The type of the map that stores the arc lengths.
816    ///
817    /// The type of the map that stores the arc lengths.
818    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
[744]819    typedef LEN LengthMap;
[743]820
[744]821    /// The type of the arc lengths.
822    typedef typename LEN::Value Value;
[743]823
824    /// \brief Operation traits for Bellman-Ford algorithm.
825    ///
[744]826    /// It defines the used operations and the infinity value for the
827    /// given \c Value type.
[743]828    /// \see BellmanFordDefaultOperationTraits
829    typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
830
831    /// \brief The type of the map that stores the last
832    /// arcs of the shortest paths.
833    ///
[744]834    /// The type of the map that stores the last arcs of the shortest paths.
835    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
836    typedef typename GR::template NodeMap<typename GR::Arc> PredMap;
[743]837
[744]838    /// \brief Instantiates a \c PredMap.
[743]839    ///
[744]840    /// This function instantiates a \ref PredMap.
841    /// \param g is the digraph to which we would like to define the
842    /// \ref PredMap.
843    static PredMap *createPredMap(const GR &g) {
844      return new PredMap(g);
[743]845    }
[744]846
847    /// \brief The type of the map that stores the distances of the nodes.
[743]848    ///
[744]849    /// The type of the map that stores the distances of the nodes.
850    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
851    typedef typename GR::template NodeMap<Value> DistMap;
852
853    /// \brief Instantiates a \c DistMap.
[743]854    ///
855    /// This function instantiates a \ref DistMap.
[744]856    /// \param g is the digraph to which we would like to define the
857    /// \ref DistMap.
858    static DistMap *createDistMap(const GR &g) {
859      return new DistMap(g);
[743]860    }
[744]861
862    ///The type of the shortest paths.
863
864    ///The type of the shortest paths.
865    ///It must meet the \ref concepts::Path "Path" concept.
866    typedef lemon::Path<Digraph> Path;
[743]867  };
868 
[744]869  /// \brief Default traits class used by BellmanFordWizard.
[743]870  ///
[744]871  /// Default traits class used by BellmanFordWizard.
872  /// \tparam GR The type of the digraph.
873  /// \tparam LEN The type of the length map.
874  template <typename GR, typename LEN>
[743]875  class BellmanFordWizardBase
[744]876    : public BellmanFordWizardDefaultTraits<GR, LEN> {
[743]877
[744]878    typedef BellmanFordWizardDefaultTraits<GR, LEN> Base;
[743]879  protected:
[744]880    // Type of the nodes in the digraph.
[743]881    typedef typename Base::Digraph::Node Node;
882
[744]883    // Pointer to the underlying digraph.
[743]884    void *_graph;
[744]885    // Pointer to the length map
[743]886    void *_length;
[744]887    // Pointer to the map of predecessors arcs.
[743]888    void *_pred;
[744]889    // Pointer to the map of distances.
[743]890    void *_dist;
[744]891    //Pointer to the shortest path to the target node.
892    void *_path;
893    //Pointer to the distance of the target node.
894    void *_di;
[743]895
896    public:
897    /// Constructor.
898   
[744]899    /// This constructor does not require parameters, it initiates
900    /// all of the attributes to default values \c 0.
901    BellmanFordWizardBase() :
902      _graph(0), _length(0), _pred(0), _dist(0), _path(0), _di(0) {}
[743]903
904    /// Constructor.
905   
[744]906    /// This constructor requires two parameters,
907    /// others are initiated to \c 0.
908    /// \param gr The digraph the algorithm runs on.
909    /// \param len The length map.
910    BellmanFordWizardBase(const GR& gr,
911                          const LEN& len) :
912      _graph(reinterpret_cast<void*>(const_cast<GR*>(&gr))),
913      _length(reinterpret_cast<void*>(const_cast<LEN*>(&len))),
914      _pred(0), _dist(0), _path(0), _di(0) {}
[743]915
916  };
917 
[744]918  /// \brief Auxiliary class for the function-type interface of the
919  /// \ref BellmanFord "Bellman-Ford" algorithm.
920  ///
921  /// This auxiliary class is created to implement the
922  /// \ref bellmanFord() "function-type interface" of the
923  /// \ref BellmanFord "Bellman-Ford" algorithm.
924  /// It does not have own \ref run() method, it uses the
925  /// functions and features of the plain \ref BellmanFord.
926  ///
927  /// This class should only be used through the \ref bellmanFord()
928  /// function, which makes it easier to use the algorithm.
929  template<class TR>
930  class BellmanFordWizard : public TR {
931    typedef TR Base;
[743]932
[744]933    typedef typename TR::Digraph Digraph;
[743]934
935    typedef typename Digraph::Node Node;
936    typedef typename Digraph::NodeIt NodeIt;
937    typedef typename Digraph::Arc Arc;
938    typedef typename Digraph::OutArcIt ArcIt;
939   
[744]940    typedef typename TR::LengthMap LengthMap;
[743]941    typedef typename LengthMap::Value Value;
[744]942    typedef typename TR::PredMap PredMap;
943    typedef typename TR::DistMap DistMap;
944    typedef typename TR::Path Path;
[743]945
946  public:
947    /// Constructor.
[744]948    BellmanFordWizard() : TR() {}
[743]949
950    /// \brief Constructor that requires parameters.
951    ///
952    /// Constructor that requires parameters.
953    /// These parameters will be the default values for the traits class.
[744]954    /// \param gr The digraph the algorithm runs on.
955    /// \param len The length map.
956    BellmanFordWizard(const Digraph& gr, const LengthMap& len)
957      : TR(gr, len) {}
[743]958
959    /// \brief Copy constructor
[744]960    BellmanFordWizard(const TR &b) : TR(b) {}
[743]961
962    ~BellmanFordWizard() {}
963
[744]964    /// \brief Runs the Bellman-Ford algorithm from the given source node.
[743]965    ///   
[744]966    /// This method runs the Bellman-Ford algorithm from the given source
967    /// node in order to compute the shortest path to each node.
968    void run(Node s) {
969      BellmanFord<Digraph,LengthMap,TR>
[743]970        bf(*reinterpret_cast<const Digraph*>(Base::_graph),
971           *reinterpret_cast<const LengthMap*>(Base::_length));
972      if (Base::_pred) bf.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
973      if (Base::_dist) bf.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
[744]974      bf.run(s);
[743]975    }
976
[744]977    /// \brief Runs the Bellman-Ford algorithm to find the shortest path
978    /// between \c s and \c t.
[743]979    ///
[744]980    /// This method runs the Bellman-Ford algorithm from node \c s
981    /// in order to compute the shortest path to node \c t.
982    /// Actually, it computes the shortest path to each node, but using
983    /// this function you can retrieve the distance and the shortest path
984    /// for a single target node easier.
985    ///
986    /// \return \c true if \c t is reachable form \c s.
987    bool run(Node s, Node t) {
988      BellmanFord<Digraph,LengthMap,TR>
989        bf(*reinterpret_cast<const Digraph*>(Base::_graph),
990           *reinterpret_cast<const LengthMap*>(Base::_length));
991      if (Base::_pred) bf.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
992      if (Base::_dist) bf.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
993      bf.run(s);
994      if (Base::_path) *reinterpret_cast<Path*>(Base::_path) = bf.path(t);
995      if (Base::_di) *reinterpret_cast<Value*>(Base::_di) = bf.dist(t);
996      return bf.reached(t);
[743]997    }
998
999    template<class T>
[744]1000    struct SetPredMapBase : public Base {
[743]1001      typedef T PredMap;
1002      static PredMap *createPredMap(const Digraph &) { return 0; };
[744]1003      SetPredMapBase(const TR &b) : TR(b) {}
[743]1004    };
1005   
[744]1006    /// \brief \ref named-templ-param "Named parameter" for setting
1007    /// the predecessor map.
[743]1008    ///
[744]1009    /// \ref named-templ-param "Named parameter" for setting
1010    /// the map that stores the predecessor arcs of the nodes.
[743]1011    template<class T>
[744]1012    BellmanFordWizard<SetPredMapBase<T> > predMap(const T &t) {
[743]1013      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
[744]1014      return BellmanFordWizard<SetPredMapBase<T> >(*this);
[743]1015    }
1016   
1017    template<class T>
[744]1018    struct SetDistMapBase : public Base {
[743]1019      typedef T DistMap;
1020      static DistMap *createDistMap(const Digraph &) { return 0; };
[744]1021      SetDistMapBase(const TR &b) : TR(b) {}
[743]1022    };
1023   
[744]1024    /// \brief \ref named-templ-param "Named parameter" for setting
1025    /// the distance map.
[743]1026    ///
[744]1027    /// \ref named-templ-param "Named parameter" for setting
1028    /// the map that stores the distances of the nodes calculated
1029    /// by the algorithm.
[743]1030    template<class T>
[744]1031    BellmanFordWizard<SetDistMapBase<T> > distMap(const T &t) {
[743]1032      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
[744]1033      return BellmanFordWizard<SetDistMapBase<T> >(*this);
[743]1034    }
1035
1036    template<class T>
[744]1037    struct SetPathBase : public Base {
1038      typedef T Path;
1039      SetPathBase(const TR &b) : TR(b) {}
[743]1040    };
[744]1041
1042    /// \brief \ref named-func-param "Named parameter" for getting
1043    /// the shortest path to the target node.
[743]1044    ///
[744]1045    /// \ref named-func-param "Named parameter" for getting
1046    /// the shortest path to the target node.
1047    template<class T>
1048    BellmanFordWizard<SetPathBase<T> > path(const T &t)
1049    {
1050      Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t));
1051      return BellmanFordWizard<SetPathBase<T> >(*this);
1052    }
1053
1054    /// \brief \ref named-func-param "Named parameter" for getting
1055    /// the distance of the target node.
[743]1056    ///
[744]1057    /// \ref named-func-param "Named parameter" for getting
1058    /// the distance of the target node.
1059    BellmanFordWizard dist(const Value &d)
1060    {
1061      Base::_di=reinterpret_cast<void*>(const_cast<Value*>(&d));
[743]1062      return *this;
1063    }
1064   
1065  };
1066 
[744]1067  /// \brief Function type interface for the \ref BellmanFord "Bellman-Ford"
1068  /// algorithm.
[743]1069  ///
1070  /// \ingroup shortest_path
[744]1071  /// Function type interface for the \ref BellmanFord "Bellman-Ford"
1072  /// algorithm.
[743]1073  ///
1074  /// This function also has several \ref named-templ-func-param
1075  /// "named parameters", they are declared as the members of class
1076  /// \ref BellmanFordWizard.
[744]1077  /// The following examples show how to use these parameters.
1078  /// \code
1079  ///   // Compute shortest path from node s to each node
1080  ///   bellmanFord(g,length).predMap(preds).distMap(dists).run(s);
1081  ///
1082  ///   // Compute shortest path from s to t
1083  ///   bool reached = bellmanFord(g,length).path(p).dist(d).run(s,t);
1084  /// \endcode
[743]1085  /// \warning Don't forget to put the \ref BellmanFordWizard::run() "run()"
1086  /// to the end of the parameter list.
1087  /// \sa BellmanFordWizard
1088  /// \sa BellmanFord
[744]1089  template<typename GR, typename LEN>
1090  BellmanFordWizard<BellmanFordWizardBase<GR,LEN> >
1091  bellmanFord(const GR& digraph,
1092              const LEN& length)
1093  {
1094    return BellmanFordWizard<BellmanFordWizardBase<GR,LEN> >(digraph, length);
[743]1095  }
1096
1097} //END OF NAMESPACE LEMON
1098
1099#endif
1100
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