COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/bfs.h @ 2339:c329fe995b40

Last change on this file since 2339:c329fe995b40 was 2335:27aa03cd3121, checked in by Balazs Dezso, 13 years ago

New path concept and path structures

TODO: BellmanFord::negativeCycle()

File size: 47.3 KB
Line 
1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2006
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_BFS_H
20#define LEMON_BFS_H
21
22///\ingroup flowalgs
23///\file
24///\brief Bfs algorithm.
25
26#include <lemon/list_graph.h>
27#include <lemon/graph_utils.h>
28#include <lemon/bits/path_dump.h>
29#include <lemon/bits/invalid.h>
30#include <lemon/error.h>
31#include <lemon/maps.h>
32
33namespace lemon {
34
35
36 
37  ///Default traits class of Bfs class.
38
39  ///Default traits class of Bfs class.
40  ///\param GR Graph type.
41  template<class GR>
42  struct BfsDefaultTraits
43  {
44    ///The graph type the algorithm runs on.
45    typedef GR Graph;
46    ///\brief The type of the map that stores the last
47    ///edges of the shortest paths.
48    ///
49    ///The type of the map that stores the last
50    ///edges of the shortest paths.
51    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
52    ///
53    typedef typename Graph::template NodeMap<typename GR::Edge> PredMap;
54    ///Instantiates a PredMap.
55 
56    ///This function instantiates a \ref PredMap.
57    ///\param G is the graph, to which we would like to define the PredMap.
58    ///\todo The graph alone may be insufficient to initialize
59    static PredMap *createPredMap(const GR &G)
60    {
61      return new PredMap(G);
62    }
63    ///The type of the map that indicates which nodes are processed.
64 
65    ///The type of the map that indicates which nodes are processed.
66    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
67    ///\todo named parameter to set this type, function to read and write.
68    typedef NullMap<typename Graph::Node,bool> ProcessedMap;
69    ///Instantiates a ProcessedMap.
70 
71    ///This function instantiates a \ref ProcessedMap.
72    ///\param g is the graph, to which
73    ///we would like to define the \ref ProcessedMap
74#ifdef DOXYGEN
75    static ProcessedMap *createProcessedMap(const GR &g)
76#else
77    static ProcessedMap *createProcessedMap(const GR &)
78#endif
79    {
80      return new ProcessedMap();
81    }
82    ///The type of the map that indicates which nodes are reached.
83 
84    ///The type of the map that indicates which nodes are reached.
85    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
86    ///\todo named parameter to set this type, function to read and write.
87    typedef typename Graph::template NodeMap<bool> ReachedMap;
88    ///Instantiates a ReachedMap.
89 
90    ///This function instantiates a \ref ReachedMap.
91    ///\param G is the graph, to which
92    ///we would like to define the \ref ReachedMap.
93    static ReachedMap *createReachedMap(const GR &G)
94    {
95      return new ReachedMap(G);
96    }
97    ///The type of the map that stores the dists of the nodes.
98 
99    ///The type of the map that stores the dists of the nodes.
100    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
101    ///
102    typedef typename Graph::template NodeMap<int> DistMap;
103    ///Instantiates a DistMap.
104 
105    ///This function instantiates a \ref DistMap.
106    ///\param G is the graph, to which we would like to define the \ref DistMap
107    static DistMap *createDistMap(const GR &G)
108    {
109      return new DistMap(G);
110    }
111  };
112 
113  ///%BFS algorithm class.
114 
115  ///\ingroup flowalgs
116  ///This class provides an efficient implementation of the %BFS algorithm.
117  ///
118  ///\param GR The graph type the algorithm runs on. The default value is
119  ///\ref ListGraph. The value of GR is not used directly by Bfs, it
120  ///is only passed to \ref BfsDefaultTraits.
121  ///\param TR Traits class to set various data types used by the algorithm.
122  ///The default traits class is
123  ///\ref BfsDefaultTraits "BfsDefaultTraits<GR>".
124  ///See \ref BfsDefaultTraits for the documentation of
125  ///a Bfs traits class.
126  ///
127  ///\author Alpar Juttner
128
129#ifdef DOXYGEN
130  template <typename GR,
131            typename TR>
132#else
133  template <typename GR=ListGraph,
134            typename TR=BfsDefaultTraits<GR> >
135#endif
136  class Bfs {
137  public:
138    /**
139     * \brief \ref Exception for uninitialized parameters.
140     *
141     * This error represents problems in the initialization
142     * of the parameters of the algorithms.
143     */
144    class UninitializedParameter : public lemon::UninitializedParameter {
145    public:
146      virtual const char* what() const throw() {
147        return "lemon::Bfs::UninitializedParameter";
148      }
149    };
150
151    typedef TR Traits;
152    ///The type of the underlying graph.
153    typedef typename TR::Graph Graph;
154    ///\e
155    typedef typename Graph::Node Node;
156    ///\e
157    typedef typename Graph::NodeIt NodeIt;
158    ///\e
159    typedef typename Graph::Edge Edge;
160    ///\e
161    typedef typename Graph::OutEdgeIt OutEdgeIt;
162   
163    ///\brief The type of the map that stores the last
164    ///edges of the shortest paths.
165    typedef typename TR::PredMap PredMap;
166    ///The type of the map indicating which nodes are reached.
167    typedef typename TR::ReachedMap ReachedMap;
168    ///The type of the map indicating which nodes are processed.
169    typedef typename TR::ProcessedMap ProcessedMap;
170    ///The type of the map that stores the dists of the nodes.
171    typedef typename TR::DistMap DistMap;
172  private:
173    /// Pointer to the underlying graph.
174    const Graph *G;
175    ///Pointer to the map of predecessors edges.
176    PredMap *_pred;
177    ///Indicates if \ref _pred is locally allocated (\c true) or not.
178    bool local_pred;
179    ///Pointer to the map of distances.
180    DistMap *_dist;
181    ///Indicates if \ref _dist is locally allocated (\c true) or not.
182    bool local_dist;
183    ///Pointer to the map of reached status of the nodes.
184    ReachedMap *_reached;
185    ///Indicates if \ref _reached is locally allocated (\c true) or not.
186    bool local_reached;
187    ///Pointer to the map of processed status of the nodes.
188    ProcessedMap *_processed;
189    ///Indicates if \ref _processed is locally allocated (\c true) or not.
190    bool local_processed;
191
192    std::vector<typename Graph::Node> _queue;
193    int _queue_head,_queue_tail,_queue_next_dist;
194    int _curr_dist;
195
196    ///Creates the maps if necessary.
197   
198    ///\todo Better memory allocation (instead of new).
199    void create_maps()
200    {
201      if(!_pred) {
202        local_pred = true;
203        _pred = Traits::createPredMap(*G);
204      }
205      if(!_dist) {
206        local_dist = true;
207        _dist = Traits::createDistMap(*G);
208      }
209      if(!_reached) {
210        local_reached = true;
211        _reached = Traits::createReachedMap(*G);
212      }
213      if(!_processed) {
214        local_processed = true;
215        _processed = Traits::createProcessedMap(*G);
216      }
217    }
218
219  protected:
220   
221    Bfs() {}
222   
223  public:
224 
225    typedef Bfs Create;
226
227    ///\name Named template parameters
228
229    ///@{
230
231    template <class T>
232    struct DefPredMapTraits : public Traits {
233      typedef T PredMap;
234      static PredMap *createPredMap(const Graph &)
235      {
236        throw UninitializedParameter();
237      }
238    };
239    ///\ref named-templ-param "Named parameter" for setting PredMap type
240
241    ///\ref named-templ-param "Named parameter" for setting PredMap type
242    ///
243    template <class T>
244    struct DefPredMap : public Bfs< Graph, DefPredMapTraits<T> > {
245      typedef Bfs< Graph, DefPredMapTraits<T> > Create;
246    };
247   
248    template <class T>
249    struct DefDistMapTraits : public Traits {
250      typedef T DistMap;
251      static DistMap *createDistMap(const Graph &)
252      {
253        throw UninitializedParameter();
254      }
255    };
256    ///\ref named-templ-param "Named parameter" for setting DistMap type
257
258    ///\ref named-templ-param "Named parameter" for setting DistMap type
259    ///
260    template <class T>
261    struct DefDistMap : public Bfs< Graph, DefDistMapTraits<T> > {
262      typedef Bfs< Graph, DefDistMapTraits<T> > Create;
263    };
264   
265    template <class T>
266    struct DefReachedMapTraits : public Traits {
267      typedef T ReachedMap;
268      static ReachedMap *createReachedMap(const Graph &)
269      {
270        throw UninitializedParameter();
271      }
272    };
273    ///\ref named-templ-param "Named parameter" for setting ReachedMap type
274
275    ///\ref named-templ-param "Named parameter" for setting ReachedMap type
276    ///
277    template <class T>
278    struct DefReachedMap : public Bfs< Graph, DefReachedMapTraits<T> > {
279      typedef Bfs< Graph, DefReachedMapTraits<T> > Create;
280    };
281   
282    template <class T>
283    struct DefProcessedMapTraits : public Traits {
284      typedef T ProcessedMap;
285      static ProcessedMap *createProcessedMap(const Graph &)
286      {
287        throw UninitializedParameter();
288      }
289    };
290    ///\ref named-templ-param "Named parameter" for setting ProcessedMap type
291
292    ///\ref named-templ-param "Named parameter" for setting ProcessedMap type
293    ///
294    template <class T>
295    struct DefProcessedMap : public Bfs< Graph, DefProcessedMapTraits<T> > {
296      typedef Bfs< Graph, DefProcessedMapTraits<T> > Create;
297    };
298   
299    struct DefGraphProcessedMapTraits : public Traits {
300      typedef typename Graph::template NodeMap<bool> ProcessedMap;
301      static ProcessedMap *createProcessedMap(const Graph &G)
302      {
303        return new ProcessedMap(G);
304      }
305    };
306    ///\brief \ref named-templ-param "Named parameter"
307    ///for setting the ProcessedMap type to be Graph::NodeMap<bool>.
308    ///
309    ///\ref named-templ-param "Named parameter"
310    ///for setting the ProcessedMap type to be Graph::NodeMap<bool>.
311    ///If you don't set it explicitly, it will be automatically allocated.
312    template <class T>
313    struct DefProcessedMapToBeDefaultMap :
314      public Bfs< Graph, DefGraphProcessedMapTraits> {
315      typedef Bfs< Graph, DefGraphProcessedMapTraits> Create;
316    };
317   
318    ///@}
319
320  public:     
321   
322    ///Constructor.
323   
324    ///\param _G the graph the algorithm will run on.
325    ///
326    Bfs(const Graph& _G) :
327      G(&_G),
328      _pred(NULL), local_pred(false),
329      _dist(NULL), local_dist(false),
330      _reached(NULL), local_reached(false),
331      _processed(NULL), local_processed(false)
332    { }
333   
334    ///Destructor.
335    ~Bfs()
336    {
337      if(local_pred) delete _pred;
338      if(local_dist) delete _dist;
339      if(local_reached) delete _reached;
340      if(local_processed) delete _processed;
341    }
342
343    ///Sets the map storing the predecessor edges.
344
345    ///Sets the map storing the predecessor edges.
346    ///If you don't use this function before calling \ref run(),
347    ///it will allocate one. The destructor deallocates this
348    ///automatically allocated map, of course.
349    ///\return <tt> (*this) </tt>
350    Bfs &predMap(PredMap &m)
351    {
352      if(local_pred) {
353        delete _pred;
354        local_pred=false;
355      }
356      _pred = &m;
357      return *this;
358    }
359
360    ///Sets the map indicating the reached nodes.
361
362    ///Sets the map indicating the reached nodes.
363    ///If you don't use this function before calling \ref run(),
364    ///it will allocate one. The destructor deallocates this
365    ///automatically allocated map, of course.
366    ///\return <tt> (*this) </tt>
367    Bfs &reachedMap(ReachedMap &m)
368    {
369      if(local_reached) {
370        delete _reached;
371        local_reached=false;
372      }
373      _reached = &m;
374      return *this;
375    }
376
377    ///Sets the map indicating the processed nodes.
378
379    ///Sets the map indicating the processed nodes.
380    ///If you don't use this function before calling \ref run(),
381    ///it will allocate one. The destructor deallocates this
382    ///automatically allocated map, of course.
383    ///\return <tt> (*this) </tt>
384    Bfs &processedMap(ProcessedMap &m)
385    {
386      if(local_processed) {
387        delete _processed;
388        local_processed=false;
389      }
390      _processed = &m;
391      return *this;
392    }
393
394    ///Sets the map storing the distances calculated by the algorithm.
395
396    ///Sets the map storing the distances calculated by the algorithm.
397    ///If you don't use this function before calling \ref run(),
398    ///it will allocate one. The destructor deallocates this
399    ///automatically allocated map, of course.
400    ///\return <tt> (*this) </tt>
401    Bfs &distMap(DistMap &m)
402    {
403      if(local_dist) {
404        delete _dist;
405        local_dist=false;
406      }
407      _dist = &m;
408      return *this;
409    }
410
411  public:
412    ///\name Execution control
413    ///The simplest way to execute the algorithm is to use
414    ///one of the member functions called \c run(...).
415    ///\n
416    ///If you need more control on the execution,
417    ///first you must call \ref init(), then you can add several source nodes
418    ///with \ref addSource().
419    ///Finally \ref start() will perform the actual path
420    ///computation.
421
422    ///@{
423
424    ///Initializes the internal data structures.
425
426    ///Initializes the internal data structures.
427    ///
428    void init()
429    {
430      create_maps();
431      _queue.resize(countNodes(*G));
432      _queue_head=_queue_tail=0;
433      _curr_dist=1;
434      for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
435        _pred->set(u,INVALID);
436        _reached->set(u,false);
437        _processed->set(u,false);
438      }
439    }
440   
441    ///Adds a new source node.
442
443    ///Adds a new source node to the set of nodes to be processed.
444    ///
445    void addSource(Node s)
446    {
447      if(!(*_reached)[s])
448        {
449          _reached->set(s,true);
450          _pred->set(s,INVALID);
451          _dist->set(s,0);
452          _queue[_queue_head++]=s;
453          _queue_next_dist=_queue_head;
454        }
455    }
456   
457    ///Processes the next node.
458
459    ///Processes the next node.
460    ///
461    ///\return The processed node.
462    ///
463    ///\warning The queue must not be empty!
464    Node processNextNode()
465    {
466      if(_queue_tail==_queue_next_dist) {
467        _curr_dist++;
468        _queue_next_dist=_queue_head;
469      }
470      Node n=_queue[_queue_tail++];
471      _processed->set(n,true);
472      Node m;
473      for(OutEdgeIt e(*G,n);e!=INVALID;++e)
474        if(!(*_reached)[m=G->target(e)]) {
475          _queue[_queue_head++]=m;
476          _reached->set(m,true);
477          _pred->set(m,e);
478          _dist->set(m,_curr_dist);
479        }
480      return n;
481    }
482
483    ///Processes the next node.
484
485    ///Processes the next node. And checks that the given target node
486    ///is reached. If the target node is reachable from the processed
487    ///node then the reached parameter will be set true. The reached
488    ///parameter should be initially false.
489    ///
490    ///\param target The target node.
491    ///\retval reached Indicates that the target node is reached.
492    ///\return The processed node.
493    ///
494    ///\warning The queue must not be empty!
495    Node processNextNode(Node target, bool& reached)
496    {
497      if(_queue_tail==_queue_next_dist) {
498        _curr_dist++;
499        _queue_next_dist=_queue_head;
500      }
501      Node n=_queue[_queue_tail++];
502      _processed->set(n,true);
503      Node m;
504      for(OutEdgeIt e(*G,n);e!=INVALID;++e)
505        if(!(*_reached)[m=G->target(e)]) {
506          _queue[_queue_head++]=m;
507          _reached->set(m,true);
508          _pred->set(m,e);
509          _dist->set(m,_curr_dist);
510          reached = reached || (target == m);
511        }
512      return n;
513    }
514
515    ///Processes the next node.
516
517    ///Processes the next node. And checks that at least one of
518    ///reached node has true value in the \c nm nodemap. If one node
519    ///with true value is reachable from the processed node then the
520    ///reached parameter will be set true. The reached parameter
521    ///should be initially false.
522    ///
523    ///\param target The nodemaps of possible targets.
524    ///\retval reached Indicates that one of the target nodes is reached.
525    ///\return The processed node.
526    ///
527    ///\warning The queue must not be empty!
528    template<class NM>
529    Node processNextNode(const NM& nm, bool& reached)
530    {
531      if(_queue_tail==_queue_next_dist) {
532        _curr_dist++;
533        _queue_next_dist=_queue_head;
534      }
535      Node n=_queue[_queue_tail++];
536      _processed->set(n,true);
537      Node m;
538      for(OutEdgeIt e(*G,n);e!=INVALID;++e)
539        if(!(*_reached)[m=G->target(e)]) {
540          _queue[_queue_head++]=m;
541          _reached->set(m,true);
542          _pred->set(m,e);
543          _dist->set(m,_curr_dist);
544          reached = reached || nm[m];
545        }
546      return n;
547    }
548     
549    ///Next node to be processed.
550
551    ///Next node to be processed.
552    ///
553    ///\return The next node to be processed or INVALID if the queue is
554    /// empty.
555    Node nextNode()
556    {
557      return _queue_tail<_queue_head?_queue[_queue_tail]:INVALID;
558    }
559 
560    ///\brief Returns \c false if there are nodes
561    ///to be processed in the queue
562    ///
563    ///Returns \c false if there are nodes
564    ///to be processed in the queue
565    bool emptyQueue() { return _queue_tail==_queue_head; }
566    ///Returns the number of the nodes to be processed.
567   
568    ///Returns the number of the nodes to be processed in the queue.
569    ///
570    int queueSize() { return _queue_head-_queue_tail; }
571   
572    ///Executes the algorithm.
573
574    ///Executes the algorithm.
575    ///
576    ///\pre init() must be called and at least one node should be added
577    ///with addSource() before using this function.
578    ///
579    ///This method runs the %BFS algorithm from the root node(s)
580    ///in order to
581    ///compute the
582    ///shortest path to each node. The algorithm computes
583    ///- The shortest path tree.
584    ///- The distance of each node from the root(s).
585    ///
586    void start()
587    {
588      while ( !emptyQueue() ) processNextNode();
589    }
590   
591    ///Executes the algorithm until \c dest is reached.
592
593    ///Executes the algorithm until \c dest is reached.
594    ///
595    ///\pre init() must be called and at least one node should be added
596    ///with addSource() before using this function.
597    ///
598    ///This method runs the %BFS algorithm from the root node(s)
599    ///in order to
600    ///compute the
601    ///shortest path to \c dest. The algorithm computes
602    ///- The shortest path to \c  dest.
603    ///- The distance of \c dest from the root(s).
604    ///
605    void start(Node dest)
606    {
607      bool reached = false;
608      while ( !emptyQueue() && !reached) processNextNode(dest, reached);
609    }
610   
611    ///Executes the algorithm until a condition is met.
612
613    ///Executes the algorithm until a condition is met.
614    ///
615    ///\pre init() must be called and at least one node should be added
616    ///with addSource() before using this function.
617    ///
618    ///\param nm must be a bool (or convertible) node map. The
619    ///algorithm will stop when it reached a node \c v with
620    ///<tt>nm[v]</tt> true.
621    ///\todo query the reached target
622    template<class NM>
623    void start(const NM &nm)
624    {
625      bool reached = false;
626      while ( !emptyQueue() && !reached) processNextNode(nm, reached);
627    }
628   
629    ///Runs %BFS algorithm from node \c s.
630   
631    ///This method runs the %BFS algorithm from a root node \c s
632    ///in order to
633    ///compute the
634    ///shortest path to each node. The algorithm computes
635    ///- The shortest path tree.
636    ///- The distance of each node from the root.
637    ///
638    ///\note b.run(s) is just a shortcut of the following code.
639    ///\code
640    ///  b.init();
641    ///  b.addSource(s);
642    ///  b.start();
643    ///\endcode
644    void run(Node s) {
645      init();
646      addSource(s);
647      start();
648    }
649   
650    ///Finds the shortest path between \c s and \c t.
651   
652    ///Finds the shortest path between \c s and \c t.
653    ///
654    ///\return The length of the shortest s---t path if there exists one,
655    ///0 otherwise.
656    ///\note Apart from the return value, b.run(s) is
657    ///just a shortcut of the following code.
658    ///\code
659    ///  b.init();
660    ///  b.addSource(s);
661    ///  b.start(t);
662    ///\endcode
663    int run(Node s,Node t) {
664      init();
665      addSource(s);
666      start(t);
667      return reached(t)? _curr_dist : 0;
668    }
669   
670    ///@}
671
672    ///\name Query Functions
673    ///The result of the %BFS algorithm can be obtained using these
674    ///functions.\n
675    ///Before the use of these functions,
676    ///either run() or start() must be calleb.
677   
678    ///@{
679
680    typedef PredMapPath<Graph, PredMap> Path;
681
682    ///Gives back the shortest path.
683   
684    ///Gives back the shortest path.
685    ///\pre The \c t should be reachable from the source.
686    Path path(Node t)
687    {
688      return Path(*G, *_pred, t);
689    }
690
691    ///The distance of a node from the root(s).
692
693    ///Returns the distance of a node from the root(s).
694    ///\pre \ref run() must be called before using this function.
695    ///\warning If node \c v in unreachable from the root(s) the return value
696    ///of this function is undefined.
697    int dist(Node v) const { return (*_dist)[v]; }
698
699    ///Returns the 'previous edge' of the shortest path tree.
700
701    ///For a node \c v it returns the 'previous edge'
702    ///of the shortest path tree,
703    ///i.e. it returns the last edge of a shortest path from the root(s) to \c
704    ///v. It is \ref INVALID
705    ///if \c v is unreachable from the root(s) or \c v is a root. The
706    ///shortest path tree used here is equal to the shortest path tree used in
707    ///\ref predNode().
708    ///\pre Either \ref run() or \ref start() must be called before using
709    ///this function.
710    Edge predEdge(Node v) const { return (*_pred)[v];}
711
712    ///Returns the 'previous node' of the shortest path tree.
713
714    ///For a node \c v it returns the 'previous node'
715    ///of the shortest path tree,
716    ///i.e. it returns the last but one node from a shortest path from the
717    ///root(a) to \c /v.
718    ///It is INVALID if \c v is unreachable from the root(s) or
719    ///if \c v itself a root.
720    ///The shortest path tree used here is equal to the shortest path
721    ///tree used in \ref predEdge().
722    ///\pre Either \ref run() or \ref start() must be called before
723    ///using this function.
724    Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
725                                  G->source((*_pred)[v]); }
726   
727    ///Returns a reference to the NodeMap of distances.
728
729    ///Returns a reference to the NodeMap of distances.
730    ///\pre Either \ref run() or \ref init() must
731    ///be called before using this function.
732    const DistMap &distMap() const { return *_dist;}
733 
734    ///Returns a reference to the shortest path tree map.
735
736    ///Returns a reference to the NodeMap of the edges of the
737    ///shortest path tree.
738    ///\pre Either \ref run() or \ref init()
739    ///must be called before using this function.
740    const PredMap &predMap() const { return *_pred;}
741 
742    ///Checks if a node is reachable from the root.
743
744    ///Returns \c true if \c v is reachable from the root.
745    ///\warning The source nodes are indicated as unreached.
746    ///\pre Either \ref run() or \ref start()
747    ///must be called before using this function.
748    ///
749    bool reached(Node v) { return (*_reached)[v]; }
750   
751    ///@}
752  };
753
754  ///Default traits class of Bfs function.
755
756  ///Default traits class of Bfs function.
757  ///\param GR Graph type.
758  template<class GR>
759  struct BfsWizardDefaultTraits
760  {
761    ///The graph type the algorithm runs on.
762    typedef GR Graph;
763    ///\brief The type of the map that stores the last
764    ///edges of the shortest paths.
765    ///
766    ///The type of the map that stores the last
767    ///edges of the shortest paths.
768    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
769    ///
770    typedef NullMap<typename Graph::Node,typename GR::Edge> PredMap;
771    ///Instantiates a PredMap.
772 
773    ///This function instantiates a \ref PredMap.
774    ///\param g is the graph, to which we would like to define the PredMap.
775    ///\todo The graph alone may be insufficient to initialize
776#ifdef DOXYGEN
777    static PredMap *createPredMap(const GR &g)
778#else
779    static PredMap *createPredMap(const GR &)
780#endif
781    {
782      return new PredMap();
783    }
784
785    ///The type of the map that indicates which nodes are processed.
786 
787    ///The type of the map that indicates which nodes are processed.
788    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
789    ///\todo named parameter to set this type, function to read and write.
790    typedef NullMap<typename Graph::Node,bool> ProcessedMap;
791    ///Instantiates a ProcessedMap.
792 
793    ///This function instantiates a \ref ProcessedMap.
794    ///\param g is the graph, to which
795    ///we would like to define the \ref ProcessedMap
796#ifdef DOXYGEN
797    static ProcessedMap *createProcessedMap(const GR &g)
798#else
799    static ProcessedMap *createProcessedMap(const GR &)
800#endif
801    {
802      return new ProcessedMap();
803    }
804    ///The type of the map that indicates which nodes are reached.
805 
806    ///The type of the map that indicates which nodes are reached.
807    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
808    ///\todo named parameter to set this type, function to read and write.
809    typedef typename Graph::template NodeMap<bool> ReachedMap;
810    ///Instantiates a ReachedMap.
811 
812    ///This function instantiates a \ref ReachedMap.
813    ///\param G is the graph, to which
814    ///we would like to define the \ref ReachedMap.
815    static ReachedMap *createReachedMap(const GR &G)
816    {
817      return new ReachedMap(G);
818    }
819    ///The type of the map that stores the dists of the nodes.
820 
821    ///The type of the map that stores the dists of the nodes.
822    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
823    ///
824    typedef NullMap<typename Graph::Node,int> DistMap;
825    ///Instantiates a DistMap.
826 
827    ///This function instantiates a \ref DistMap.
828    ///\param g is the graph, to which we would like to define the \ref DistMap
829#ifdef DOXYGEN
830    static DistMap *createDistMap(const GR &g)
831#else
832    static DistMap *createDistMap(const GR &)
833#endif
834    {
835      return new DistMap();
836    }
837  };
838 
839  /// Default traits used by \ref BfsWizard
840
841  /// To make it easier to use Bfs algorithm
842  ///we have created a wizard class.
843  /// This \ref BfsWizard class needs default traits,
844  ///as well as the \ref Bfs class.
845  /// The \ref BfsWizardBase is a class to be the default traits of the
846  /// \ref BfsWizard class.
847  template<class GR>
848  class BfsWizardBase : public BfsWizardDefaultTraits<GR>
849  {
850
851    typedef BfsWizardDefaultTraits<GR> Base;
852  protected:
853    /// Type of the nodes in the graph.
854    typedef typename Base::Graph::Node Node;
855
856    /// Pointer to the underlying graph.
857    void *_g;
858    ///Pointer to the map of reached nodes.
859    void *_reached;
860    ///Pointer to the map of processed nodes.
861    void *_processed;
862    ///Pointer to the map of predecessors edges.
863    void *_pred;
864    ///Pointer to the map of distances.
865    void *_dist;
866    ///Pointer to the source node.
867    Node _source;
868   
869    public:
870    /// Constructor.
871   
872    /// This constructor does not require parameters, therefore it initiates
873    /// all of the attributes to default values (0, INVALID).
874    BfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0),
875                           _dist(0), _source(INVALID) {}
876
877    /// Constructor.
878   
879    /// This constructor requires some parameters,
880    /// listed in the parameters list.
881    /// Others are initiated to 0.
882    /// \param g is the initial value of  \ref _g
883    /// \param s is the initial value of  \ref _source
884    BfsWizardBase(const GR &g, Node s=INVALID) :
885      _g((void *)&g), _reached(0), _processed(0), _pred(0),
886      _dist(0), _source(s) {}
887
888  };
889 
890  /// A class to make the usage of Bfs algorithm easier
891
892  /// This class is created to make it easier to use Bfs algorithm.
893  /// It uses the functions and features of the plain \ref Bfs,
894  /// but it is much simpler to use it.
895  ///
896  /// Simplicity means that the way to change the types defined
897  /// in the traits class is based on functions that returns the new class
898  /// and not on templatable built-in classes.
899  /// When using the plain \ref Bfs
900  /// the new class with the modified type comes from
901  /// the original class by using the ::
902  /// operator. In the case of \ref BfsWizard only
903  /// a function have to be called and it will
904  /// return the needed class.
905  ///
906  /// It does not have own \ref run method. When its \ref run method is called
907  /// it initiates a plain \ref Bfs class, and calls the \ref Bfs::run
908  /// method of it.
909  template<class TR>
910  class BfsWizard : public TR
911  {
912    typedef TR Base;
913
914    ///The type of the underlying graph.
915    typedef typename TR::Graph Graph;
916    //\e
917    typedef typename Graph::Node Node;
918    //\e
919    typedef typename Graph::NodeIt NodeIt;
920    //\e
921    typedef typename Graph::Edge Edge;
922    //\e
923    typedef typename Graph::OutEdgeIt OutEdgeIt;
924   
925    ///\brief The type of the map that stores
926    ///the reached nodes
927    typedef typename TR::ReachedMap ReachedMap;
928    ///\brief The type of the map that stores
929    ///the processed nodes
930    typedef typename TR::ProcessedMap ProcessedMap;
931    ///\brief The type of the map that stores the last
932    ///edges of the shortest paths.
933    typedef typename TR::PredMap PredMap;
934    ///The type of the map that stores the dists of the nodes.
935    typedef typename TR::DistMap DistMap;
936
937  public:
938    /// Constructor.
939    BfsWizard() : TR() {}
940
941    /// Constructor that requires parameters.
942
943    /// Constructor that requires parameters.
944    /// These parameters will be the default values for the traits class.
945    BfsWizard(const Graph &g, Node s=INVALID) :
946      TR(g,s) {}
947
948    ///Copy constructor
949    BfsWizard(const TR &b) : TR(b) {}
950
951    ~BfsWizard() {}
952
953    ///Runs Bfs algorithm from a given node.
954   
955    ///Runs Bfs algorithm from a given node.
956    ///The node can be given by the \ref source function.
957    void run()
958    {
959      if(Base::_source==INVALID) throw UninitializedParameter();
960      Bfs<Graph,TR> alg(*(Graph*)Base::_g);
961      if(Base::_reached)
962        alg.reachedMap(*(ReachedMap*)Base::_reached);
963      if(Base::_processed) alg.processedMap(*(ProcessedMap*)Base::_processed);
964      if(Base::_pred) alg.predMap(*(PredMap*)Base::_pred);
965      if(Base::_dist) alg.distMap(*(DistMap*)Base::_dist);
966      alg.run(Base::_source);
967    }
968
969    ///Runs Bfs algorithm from the given node.
970
971    ///Runs Bfs algorithm from the given node.
972    ///\param s is the given source.
973    void run(Node s)
974    {
975      Base::_source=s;
976      run();
977    }
978
979    template<class T>
980    struct DefPredMapBase : public Base {
981      typedef T PredMap;
982      static PredMap *createPredMap(const Graph &) { return 0; };
983      DefPredMapBase(const TR &b) : TR(b) {}
984    };
985   
986    ///\brief \ref named-templ-param "Named parameter"
987    ///function for setting PredMap
988    ///
989    /// \ref named-templ-param "Named parameter"
990    ///function for setting PredMap
991    ///
992    template<class T>
993    BfsWizard<DefPredMapBase<T> > predMap(const T &t)
994    {
995      Base::_pred=(void *)&t;
996      return BfsWizard<DefPredMapBase<T> >(*this);
997    }
998   
999 
1000    template<class T>
1001    struct DefReachedMapBase : public Base {
1002      typedef T ReachedMap;
1003      static ReachedMap *createReachedMap(const Graph &) { return 0; };
1004      DefReachedMapBase(const TR &b) : TR(b) {}
1005    };
1006   
1007    ///\brief \ref named-templ-param "Named parameter"
1008    ///function for setting ReachedMap
1009    ///
1010    /// \ref named-templ-param "Named parameter"
1011    ///function for setting ReachedMap
1012    ///
1013    template<class T>
1014    BfsWizard<DefReachedMapBase<T> > reachedMap(const T &t)
1015    {
1016      Base::_pred=(void *)&t;
1017      return BfsWizard<DefReachedMapBase<T> >(*this);
1018    }
1019   
1020
1021    template<class T>
1022    struct DefProcessedMapBase : public Base {
1023      typedef T ProcessedMap;
1024      static ProcessedMap *createProcessedMap(const Graph &) { return 0; };
1025      DefProcessedMapBase(const TR &b) : TR(b) {}
1026    };
1027   
1028    ///\brief \ref named-templ-param "Named parameter"
1029    ///function for setting ProcessedMap
1030    ///
1031    /// \ref named-templ-param "Named parameter"
1032    ///function for setting ProcessedMap
1033    ///
1034    template<class T>
1035    BfsWizard<DefProcessedMapBase<T> > processedMap(const T &t)
1036    {
1037      Base::_pred=(void *)&t;
1038      return BfsWizard<DefProcessedMapBase<T> >(*this);
1039    }
1040   
1041   
1042    template<class T>
1043    struct DefDistMapBase : public Base {
1044      typedef T DistMap;
1045      static DistMap *createDistMap(const Graph &) { return 0; };
1046      DefDistMapBase(const TR &b) : TR(b) {}
1047    };
1048   
1049    ///\brief \ref named-templ-param "Named parameter"
1050    ///function for setting DistMap type
1051    ///
1052    /// \ref named-templ-param "Named parameter"
1053    ///function for setting DistMap type
1054    ///
1055    template<class T>
1056    BfsWizard<DefDistMapBase<T> > distMap(const T &t)
1057    {
1058      Base::_dist=(void *)&t;
1059      return BfsWizard<DefDistMapBase<T> >(*this);
1060    }
1061   
1062    /// Sets the source node, from which the Bfs algorithm runs.
1063
1064    /// Sets the source node, from which the Bfs algorithm runs.
1065    /// \param s is the source node.
1066    BfsWizard<TR> &source(Node s)
1067    {
1068      Base::_source=s;
1069      return *this;
1070    }
1071   
1072  };
1073 
1074  ///Function type interface for Bfs algorithm.
1075
1076  /// \ingroup flowalgs
1077  ///Function type interface for Bfs algorithm.
1078  ///
1079  ///This function also has several
1080  ///\ref named-templ-func-param "named parameters",
1081  ///they are declared as the members of class \ref BfsWizard.
1082  ///The following
1083  ///example shows how to use these parameters.
1084  ///\code
1085  ///  bfs(g,source).predMap(preds).run();
1086  ///\endcode
1087  ///\warning Don't forget to put the \ref BfsWizard::run() "run()"
1088  ///to the end of the parameter list.
1089  ///\sa BfsWizard
1090  ///\sa Bfs
1091  template<class GR>
1092  BfsWizard<BfsWizardBase<GR> >
1093  bfs(const GR &g,typename GR::Node s=INVALID)
1094  {
1095    return BfsWizard<BfsWizardBase<GR> >(g,s);
1096  }
1097
1098#ifdef DOXYGEN
1099  /// \brief Visitor class for bfs.
1100  /// 
1101  /// It gives a simple interface for a functional interface for bfs
1102  /// traversal. The traversal on a linear data structure.
1103  template <typename _Graph>
1104  struct BfsVisitor {
1105    typedef _Graph Graph;
1106    typedef typename Graph::Edge Edge;
1107    typedef typename Graph::Node Node;
1108    /// \brief Called when the edge reach a node.
1109    ///
1110    /// It is called when the bfs find an edge which target is not
1111    /// reached yet.
1112    void discover(const Edge& edge) {}
1113    /// \brief Called when the node reached first time.
1114    ///
1115    /// It is Called when the node reached first time.
1116    void reach(const Node& node) {}
1117    /// \brief Called when the edge examined but target of the edge
1118    /// already discovered.
1119    ///
1120    /// It called when the edge examined but the target of the edge
1121    /// already discovered.
1122    void examine(const Edge& edge) {}
1123    /// \brief Called for the source node of the bfs.
1124    ///
1125    /// It is called for the source node of the bfs.
1126    void start(const Node& node) {}
1127    /// \brief Called when the node processed.
1128    ///
1129    /// It is Called when the node processed.
1130    void process(const Node& node) {}
1131  };
1132#else
1133  template <typename _Graph>
1134  struct BfsVisitor {
1135    typedef _Graph Graph;
1136    typedef typename Graph::Edge Edge;
1137    typedef typename Graph::Node Node;
1138    void discover(const Edge&) {}
1139    void reach(const Node&) {}
1140    void examine(const Edge&) {}
1141    void start(const Node&) {}
1142    void process(const Node&) {}
1143
1144    template <typename _Visitor>
1145    struct Constraints {
1146      void constraints() {
1147        Edge edge;
1148        Node node;
1149        visitor.discover(edge);
1150        visitor.reach(node);
1151        visitor.examine(edge);
1152        visitor.start(node);
1153        visitor.process(node);
1154      }
1155      _Visitor& visitor;
1156    };
1157  };
1158#endif
1159
1160  /// \brief Default traits class of BfsVisit class.
1161  ///
1162  /// Default traits class of BfsVisit class.
1163  /// \param _Graph Graph type.
1164  template<class _Graph>
1165  struct BfsVisitDefaultTraits {
1166
1167    /// \brief The graph type the algorithm runs on.
1168    typedef _Graph Graph;
1169
1170    /// \brief The type of the map that indicates which nodes are reached.
1171    ///
1172    /// The type of the map that indicates which nodes are reached.
1173    /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
1174    /// \todo named parameter to set this type, function to read and write.
1175    typedef typename Graph::template NodeMap<bool> ReachedMap;
1176
1177    /// \brief Instantiates a ReachedMap.
1178    ///
1179    /// This function instantiates a \ref ReachedMap.
1180    /// \param graph is the graph, to which
1181    /// we would like to define the \ref ReachedMap.
1182    static ReachedMap *createReachedMap(const Graph &graph) {
1183      return new ReachedMap(graph);
1184    }
1185
1186  };
1187 
1188  /// %BFS Visit algorithm class.
1189 
1190  /// \ingroup flowalgs
1191  /// This class provides an efficient implementation of the %BFS algorithm
1192  /// with visitor interface.
1193  ///
1194  /// The %BfsVisit class provides an alternative interface to the Bfs
1195  /// class. It works with callback mechanism, the BfsVisit object calls
1196  /// on every bfs event the \c Visitor class member functions.
1197  ///
1198  /// \param _Graph The graph type the algorithm runs on. The default value is
1199  /// \ref ListGraph. The value of _Graph is not used directly by Bfs, it
1200  /// is only passed to \ref BfsDefaultTraits.
1201  /// \param _Visitor The Visitor object for the algorithm. The
1202  /// \ref BfsVisitor "BfsVisitor<_Graph>" is an empty Visitor which
1203  /// does not observe the Bfs events. If you want to observe the bfs
1204  /// events you should implement your own Visitor class.
1205  /// \param _Traits Traits class to set various data types used by the
1206  /// algorithm. The default traits class is
1207  /// \ref BfsVisitDefaultTraits "BfsVisitDefaultTraits<_Graph>".
1208  /// See \ref BfsVisitDefaultTraits for the documentation of
1209  /// a Bfs visit traits class.
1210  ///
1211  /// \author Jacint Szabo, Alpar Juttner and Balazs Dezso
1212#ifdef DOXYGEN
1213  template <typename _Graph, typename _Visitor, typename _Traits>
1214#else
1215  template <typename _Graph = ListGraph,
1216            typename _Visitor = BfsVisitor<_Graph>,
1217            typename _Traits = BfsDefaultTraits<_Graph> >
1218#endif
1219  class BfsVisit {
1220  public:
1221   
1222    /// \brief \ref Exception for uninitialized parameters.
1223    ///
1224    /// This error represents problems in the initialization
1225    /// of the parameters of the algorithms.
1226    class UninitializedParameter : public lemon::UninitializedParameter {
1227    public:
1228      virtual const char* what() const throw()
1229      {
1230        return "lemon::BfsVisit::UninitializedParameter";
1231      }
1232    };
1233
1234    typedef _Traits Traits;
1235
1236    typedef typename Traits::Graph Graph;
1237
1238    typedef _Visitor Visitor;
1239
1240    ///The type of the map indicating which nodes are reached.
1241    typedef typename Traits::ReachedMap ReachedMap;
1242
1243  private:
1244
1245    typedef typename Graph::Node Node;
1246    typedef typename Graph::NodeIt NodeIt;
1247    typedef typename Graph::Edge Edge;
1248    typedef typename Graph::OutEdgeIt OutEdgeIt;
1249
1250    /// Pointer to the underlying graph.
1251    const Graph *_graph;
1252    /// Pointer to the visitor object.
1253    Visitor *_visitor;
1254    ///Pointer to the map of reached status of the nodes.
1255    ReachedMap *_reached;
1256    ///Indicates if \ref _reached is locally allocated (\c true) or not.
1257    bool local_reached;
1258
1259    std::vector<typename Graph::Node> _list;
1260    int _list_front, _list_back;
1261
1262    /// \brief Creates the maps if necessary.
1263    ///
1264    /// Creates the maps if necessary.
1265    void create_maps() {
1266      if(!_reached) {
1267        local_reached = true;
1268        _reached = Traits::createReachedMap(*_graph);
1269      }
1270    }
1271
1272  protected:
1273
1274    BfsVisit() {}
1275   
1276  public:
1277
1278    typedef BfsVisit Create;
1279
1280    /// \name Named template parameters
1281
1282    ///@{
1283    template <class T>
1284    struct DefReachedMapTraits : public Traits {
1285      typedef T ReachedMap;
1286      static ReachedMap *createReachedMap(const Graph &graph) {
1287        throw UninitializedParameter();
1288      }
1289    };
1290    /// \brief \ref named-templ-param "Named parameter" for setting
1291    /// ReachedMap type
1292    ///
1293    /// \ref named-templ-param "Named parameter" for setting ReachedMap type
1294    template <class T>
1295    struct DefReachedMap : public BfsVisit< Graph, Visitor,
1296                                            DefReachedMapTraits<T> > {
1297      typedef BfsVisit< Graph, Visitor, DefReachedMapTraits<T> > Create;
1298    };
1299    ///@}
1300
1301  public:     
1302   
1303    /// \brief Constructor.
1304    ///
1305    /// Constructor.
1306    ///
1307    /// \param graph the graph the algorithm will run on.
1308    /// \param visitor The visitor of the algorithm.
1309    ///
1310    BfsVisit(const Graph& graph, Visitor& visitor)
1311      : _graph(&graph), _visitor(&visitor),
1312        _reached(0), local_reached(false) {}
1313   
1314    /// \brief Destructor.
1315    ///
1316    /// Destructor.
1317    ~BfsVisit() {
1318      if(local_reached) delete _reached;
1319    }
1320
1321    /// \brief Sets the map indicating if a node is reached.
1322    ///
1323    /// Sets the map indicating if a node is reached.
1324    /// If you don't use this function before calling \ref run(),
1325    /// it will allocate one. The destuctor deallocates this
1326    /// automatically allocated map, of course.
1327    /// \return <tt> (*this) </tt>
1328    BfsVisit &reachedMap(ReachedMap &m) {
1329      if(local_reached) {
1330        delete _reached;
1331        local_reached = false;
1332      }
1333      _reached = &m;
1334      return *this;
1335    }
1336
1337  public:
1338    /// \name Execution control
1339    /// The simplest way to execute the algorithm is to use
1340    /// one of the member functions called \c run(...).
1341    /// \n
1342    /// If you need more control on the execution,
1343    /// first you must call \ref init(), then you can adda source node
1344    /// with \ref addSource().
1345    /// Finally \ref start() will perform the actual path
1346    /// computation.
1347
1348    /// @{
1349    /// \brief Initializes the internal data structures.
1350    ///
1351    /// Initializes the internal data structures.
1352    ///
1353    void init() {
1354      create_maps();
1355      _list.resize(countNodes(*_graph));
1356      _list_front = _list_back = -1;
1357      for (NodeIt u(*_graph) ; u != INVALID ; ++u) {
1358        _reached->set(u, false);
1359      }
1360    }
1361   
1362    /// \brief Adds a new source node.
1363    ///
1364    /// Adds a new source node to the set of nodes to be processed.
1365    void addSource(Node s) {
1366      if(!(*_reached)[s]) {
1367          _reached->set(s,true);
1368          _visitor->start(s);
1369          _visitor->reach(s);
1370          _list[++_list_back] = s;
1371        }
1372    }
1373   
1374    /// \brief Processes the next node.
1375    ///
1376    /// Processes the next node.
1377    ///
1378    /// \return The processed node.
1379    ///
1380    /// \pre The queue must not be empty!
1381    Node processNextNode() {
1382      Node n = _list[++_list_front];
1383      _visitor->process(n);
1384      Edge e;
1385      for (_graph->firstOut(e, n); e != INVALID; _graph->nextOut(e)) {
1386        Node m = _graph->target(e);
1387        if (!(*_reached)[m]) {
1388          _visitor->discover(e);
1389          _visitor->reach(m);
1390          _reached->set(m, true);
1391          _list[++_list_back] = m;
1392        } else {
1393          _visitor->examine(e);
1394        }
1395      }
1396      return n;
1397    }
1398
1399    /// \brief Processes the next node.
1400    ///
1401    /// Processes the next node. And checks that the given target node
1402    /// is reached. If the target node is reachable from the processed
1403    /// node then the reached parameter will be set true. The reached
1404    /// parameter should be initially false.
1405    ///
1406    /// \param target The target node.
1407    /// \retval reached Indicates that the target node is reached.
1408    /// \return The processed node.
1409    ///
1410    /// \warning The queue must not be empty!
1411    Node processNextNode(Node target, bool& reached) {
1412      Node n = _list[++_list_front];
1413      _visitor->process(n);
1414      Edge e;
1415      for (_graph->firstOut(e, n); e != INVALID; _graph->nextOut(e)) {
1416        Node m = _graph->target(e);
1417        if (!(*_reached)[m]) {
1418          _visitor->discover(e);
1419          _visitor->reach(m);
1420          _reached->set(m, true);
1421          _list[++_list_back] = m;
1422          reached = reached || (target == m);
1423        } else {
1424          _visitor->examine(e);
1425        }
1426      }
1427      return n;
1428    }
1429
1430    /// \brief Processes the next node.
1431    ///
1432    /// Processes the next node. And checks that at least one of
1433    /// reached node has true value in the \c nm nodemap. If one node
1434    /// with true value is reachable from the processed node then the
1435    /// reached parameter will be set true. The reached parameter
1436    /// should be initially false.
1437    ///
1438    /// \param target The nodemaps of possible targets.
1439    /// \retval reached Indicates that one of the target nodes is reached.
1440    /// \return The processed node.
1441    ///
1442    /// \warning The queue must not be empty!
1443    template <typename NM>
1444    Node processNextNode(const NM& nm, bool& reached) {
1445      Node n = _list[++_list_front];
1446      _visitor->process(n);
1447      Edge e;
1448      for (_graph->firstOut(e, n); e != INVALID; _graph->nextOut(e)) {
1449        Node m = _graph->target(e);
1450        if (!(*_reached)[m]) {
1451          _visitor->discover(e);
1452          _visitor->reach(m);
1453          _reached->set(m, true);
1454          _list[++_list_back] = m;
1455          reached = reached || nm[m];
1456        } else {
1457          _visitor->examine(e);
1458        }
1459      }
1460      return n;
1461    }
1462
1463    /// \brief Next node to be processed.
1464    ///
1465    /// Next node to be processed.
1466    ///
1467    /// \return The next node to be processed or INVALID if the stack is
1468    /// empty.
1469    Node nextNode() {
1470      return _list_front != _list_back ? _list[_list_front + 1] : INVALID;
1471    }
1472
1473    /// \brief Returns \c false if there are nodes
1474    /// to be processed in the queue
1475    ///
1476    /// Returns \c false if there are nodes
1477    /// to be processed in the queue
1478    bool emptyQueue() { return _list_front == _list_back; }
1479
1480    /// \brief Returns the number of the nodes to be processed.
1481    ///
1482    /// Returns the number of the nodes to be processed in the queue.
1483    int queueSize() { return _list_back - _list_front; }
1484   
1485    /// \brief Executes the algorithm.
1486    ///
1487    /// Executes the algorithm.
1488    ///
1489    /// \pre init() must be called and at least one node should be added
1490    /// with addSource() before using this function.
1491    void start() {
1492      while ( !emptyQueue() ) processNextNode();
1493    }
1494   
1495    /// \brief Executes the algorithm until \c dest is reached.
1496    ///
1497    /// Executes the algorithm until \c dest is reached.
1498    ///
1499    /// \pre init() must be called and at least one node should be added
1500    /// with addSource() before using this function.
1501    void start(Node dest) {
1502      bool reached = false;
1503      while (!emptyQueue() && !reached) {
1504        processNextNode(dest, reached);
1505      }
1506    }
1507   
1508    /// \brief Executes the algorithm until a condition is met.
1509    ///
1510    /// Executes the algorithm until a condition is met.
1511    ///
1512    /// \pre init() must be called and at least one node should be added
1513    /// with addSource() before using this function.
1514    ///
1515    ///\param nm must be a bool (or convertible) node map. The
1516    ///algorithm will stop when it reached a node \c v with
1517    ///<tt>nm[v]</tt> true.
1518    template <typename NM>
1519    void start(const NM &nm) {
1520      bool reached = false;
1521      while (!emptyQueue() && !reached) {
1522        processNextNode(nm, reached);
1523      }
1524    }
1525
1526    /// \brief Runs %BFSVisit algorithm from node \c s.
1527    ///
1528    /// This method runs the %BFS algorithm from a root node \c s.
1529    /// \note b.run(s) is just a shortcut of the following code.
1530    ///\code
1531    ///   b.init();
1532    ///   b.addSource(s);
1533    ///   b.start();
1534    ///\endcode
1535    void run(Node s) {
1536      init();
1537      addSource(s);
1538      start();
1539    }
1540
1541    /// \brief Runs %BFSVisit algorithm to visit all nodes in the graph.
1542    ///   
1543    /// This method runs the %BFS algorithm in order to
1544    /// compute the %BFS path to each node. The algorithm computes
1545    /// - The %BFS tree.
1546    /// - The distance of each node from the root in the %BFS tree.
1547    ///
1548    ///\note b.run() is just a shortcut of the following code.
1549    ///\code
1550    ///  b.init();
1551    ///  for (NodeIt it(graph); it != INVALID; ++it) {
1552    ///    if (!b.reached(it)) {
1553    ///      b.addSource(it);
1554    ///      b.start();
1555    ///    }
1556    ///  }
1557    ///\endcode
1558    void run() {
1559      init();
1560      for (NodeIt it(*_graph); it != INVALID; ++it) {
1561        if (!reached(it)) {
1562          addSource(it);
1563          start();
1564        }
1565      }
1566    }
1567    ///@}
1568
1569    /// \name Query Functions
1570    /// The result of the %BFS algorithm can be obtained using these
1571    /// functions.\n
1572    /// Before the use of these functions,
1573    /// either run() or start() must be called.
1574    ///@{
1575
1576    /// \brief Checks if a node is reachable from the root.
1577    ///
1578    /// Returns \c true if \c v is reachable from the root(s).
1579    /// \warning The source nodes are inditated as unreachable.
1580    /// \pre Either \ref run() or \ref start()
1581    /// must be called before using this function.
1582    ///
1583    bool reached(Node v) { return (*_reached)[v]; }
1584    ///@}
1585  };
1586
1587} //END OF NAMESPACE LEMON
1588
1589#endif
1590
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