COIN-OR::LEMON - Graph Library

source: lemon/lemon/bellman_ford.h @ 835:c92296660262

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