COIN-OR::LEMON - Graph Library

source: lemon/lemon/bfs.h @ 764:684964884a2e

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1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2009
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 search
23///\file
24///\brief BFS algorithm.
25
26#include <lemon/list_graph.h>
27#include <lemon/bits/path_dump.h>
28#include <lemon/core.h>
29#include <lemon/error.h>
30#include <lemon/maps.h>
31#include <lemon/path.h>
32
33namespace lemon {
34
35  ///Default traits class of Bfs class.
36
37  ///Default traits class of Bfs class.
38  ///\tparam GR Digraph type.
39  template<class GR>
40  struct BfsDefaultTraits
41  {
42    ///The type of the digraph the algorithm runs on.
43    typedef GR Digraph;
44
45    ///\brief The type of the map that stores the predecessor
46    ///arcs of the shortest paths.
47    ///
48    ///The type of the map that stores the predecessor
49    ///arcs of the shortest paths.
50    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
51    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
52    ///Instantiates a \c PredMap.
53
54    ///This function instantiates a \ref PredMap.
55    ///\param g is the digraph, to which we would like to define the
56    ///\ref PredMap.
57    static PredMap *createPredMap(const Digraph &g)
58    {
59      return new PredMap(g);
60    }
61
62    ///The type of the map that indicates which nodes are processed.
63
64    ///The type of the map that indicates which nodes are processed.
65    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
66    ///By default it is a NullMap.
67    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
68    ///Instantiates a \c ProcessedMap.
69
70    ///This function instantiates a \ref ProcessedMap.
71    ///\param g is the digraph, to which
72    ///we would like to define the \ref ProcessedMap
73#ifdef DOXYGEN
74    static ProcessedMap *createProcessedMap(const Digraph &g)
75#else
76    static ProcessedMap *createProcessedMap(const Digraph &)
77#endif
78    {
79      return new ProcessedMap();
80    }
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 conform to the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
86    typedef typename Digraph::template NodeMap<bool> ReachedMap;
87    ///Instantiates a \c ReachedMap.
88
89    ///This function instantiates a \ref ReachedMap.
90    ///\param g is the digraph, to which
91    ///we would like to define the \ref ReachedMap.
92    static ReachedMap *createReachedMap(const Digraph &g)
93    {
94      return new ReachedMap(g);
95    }
96
97    ///The type of the map that stores the distances of the nodes.
98
99    ///The type of the map that stores the distances of the nodes.
100    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
101    typedef typename Digraph::template NodeMap<int> DistMap;
102    ///Instantiates a \c DistMap.
103
104    ///This function instantiates a \ref DistMap.
105    ///\param g is the digraph, to which we would like to define the
106    ///\ref DistMap.
107    static DistMap *createDistMap(const Digraph &g)
108    {
109      return new DistMap(g);
110    }
111  };
112
113  ///%BFS algorithm class.
114
115  ///\ingroup search
116  ///This class provides an efficient implementation of the %BFS algorithm.
117  ///
118  ///There is also a \ref bfs() "function-type interface" for the BFS
119  ///algorithm, which is convenient in the simplier cases and it can be
120  ///used easier.
121  ///
122  ///\tparam GR The type of the digraph the algorithm runs on.
123  ///The default type is \ref ListDigraph.
124#ifdef DOXYGEN
125  template <typename GR,
126            typename TR>
127#else
128  template <typename GR=ListDigraph,
129            typename TR=BfsDefaultTraits<GR> >
130#endif
131  class Bfs {
132  public:
133
134    ///The type of the digraph the algorithm runs on.
135    typedef typename TR::Digraph Digraph;
136
137    ///\brief The type of the map that stores the predecessor arcs of the
138    ///shortest paths.
139    typedef typename TR::PredMap PredMap;
140    ///The type of the map that stores the distances of the nodes.
141    typedef typename TR::DistMap DistMap;
142    ///The type of the map that indicates which nodes are reached.
143    typedef typename TR::ReachedMap ReachedMap;
144    ///The type of the map that indicates which nodes are processed.
145    typedef typename TR::ProcessedMap ProcessedMap;
146    ///The type of the paths.
147    typedef PredMapPath<Digraph, PredMap> Path;
148
149    ///The \ref BfsDefaultTraits "traits class" of the algorithm.
150    typedef TR Traits;
151
152  private:
153
154    typedef typename Digraph::Node Node;
155    typedef typename Digraph::NodeIt NodeIt;
156    typedef typename Digraph::Arc Arc;
157    typedef typename Digraph::OutArcIt OutArcIt;
158
159    //Pointer to the underlying digraph.
160    const Digraph *G;
161    //Pointer to the map of predecessor arcs.
162    PredMap *_pred;
163    //Indicates if _pred is locally allocated (true) or not.
164    bool local_pred;
165    //Pointer to the map of distances.
166    DistMap *_dist;
167    //Indicates if _dist is locally allocated (true) or not.
168    bool local_dist;
169    //Pointer to the map of reached status of the nodes.
170    ReachedMap *_reached;
171    //Indicates if _reached is locally allocated (true) or not.
172    bool local_reached;
173    //Pointer to the map of processed status of the nodes.
174    ProcessedMap *_processed;
175    //Indicates if _processed is locally allocated (true) or not.
176    bool local_processed;
177
178    std::vector<typename Digraph::Node> _queue;
179    int _queue_head,_queue_tail,_queue_next_dist;
180    int _curr_dist;
181
182    //Creates the maps if necessary.
183    void create_maps()
184    {
185      if(!_pred) {
186        local_pred = true;
187        _pred = Traits::createPredMap(*G);
188      }
189      if(!_dist) {
190        local_dist = true;
191        _dist = Traits::createDistMap(*G);
192      }
193      if(!_reached) {
194        local_reached = true;
195        _reached = Traits::createReachedMap(*G);
196      }
197      if(!_processed) {
198        local_processed = true;
199        _processed = Traits::createProcessedMap(*G);
200      }
201    }
202
203  protected:
204
205    Bfs() {}
206
207  public:
208
209    typedef Bfs Create;
210
211    ///\name Named Template Parameters
212
213    ///@{
214
215    template <class T>
216    struct SetPredMapTraits : public Traits {
217      typedef T PredMap;
218      static PredMap *createPredMap(const Digraph &)
219      {
220        LEMON_ASSERT(false, "PredMap is not initialized");
221        return 0; // ignore warnings
222      }
223    };
224    ///\brief \ref named-templ-param "Named parameter" for setting
225    ///\c PredMap type.
226    ///
227    ///\ref named-templ-param "Named parameter" for setting
228    ///\c PredMap type.
229    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
230    template <class T>
231    struct SetPredMap : public Bfs< Digraph, SetPredMapTraits<T> > {
232      typedef Bfs< Digraph, SetPredMapTraits<T> > Create;
233    };
234
235    template <class T>
236    struct SetDistMapTraits : public Traits {
237      typedef T DistMap;
238      static DistMap *createDistMap(const Digraph &)
239      {
240        LEMON_ASSERT(false, "DistMap is not initialized");
241        return 0; // ignore warnings
242      }
243    };
244    ///\brief \ref named-templ-param "Named parameter" for setting
245    ///\c DistMap type.
246    ///
247    ///\ref named-templ-param "Named parameter" for setting
248    ///\c DistMap type.
249    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
250    template <class T>
251    struct SetDistMap : public Bfs< Digraph, SetDistMapTraits<T> > {
252      typedef Bfs< Digraph, SetDistMapTraits<T> > Create;
253    };
254
255    template <class T>
256    struct SetReachedMapTraits : public Traits {
257      typedef T ReachedMap;
258      static ReachedMap *createReachedMap(const Digraph &)
259      {
260        LEMON_ASSERT(false, "ReachedMap is not initialized");
261        return 0; // ignore warnings
262      }
263    };
264    ///\brief \ref named-templ-param "Named parameter" for setting
265    ///\c ReachedMap type.
266    ///
267    ///\ref named-templ-param "Named parameter" for setting
268    ///\c ReachedMap type.
269    ///It must conform to the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
270    template <class T>
271    struct SetReachedMap : public Bfs< Digraph, SetReachedMapTraits<T> > {
272      typedef Bfs< Digraph, SetReachedMapTraits<T> > Create;
273    };
274
275    template <class T>
276    struct SetProcessedMapTraits : public Traits {
277      typedef T ProcessedMap;
278      static ProcessedMap *createProcessedMap(const Digraph &)
279      {
280        LEMON_ASSERT(false, "ProcessedMap is not initialized");
281        return 0; // ignore warnings
282      }
283    };
284    ///\brief \ref named-templ-param "Named parameter" for setting
285    ///\c ProcessedMap type.
286    ///
287    ///\ref named-templ-param "Named parameter" for setting
288    ///\c ProcessedMap type.
289    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
290    template <class T>
291    struct SetProcessedMap : public Bfs< Digraph, SetProcessedMapTraits<T> > {
292      typedef Bfs< Digraph, SetProcessedMapTraits<T> > Create;
293    };
294
295    struct SetStandardProcessedMapTraits : public Traits {
296      typedef typename Digraph::template NodeMap<bool> ProcessedMap;
297      static ProcessedMap *createProcessedMap(const Digraph &g)
298      {
299        return new ProcessedMap(g);
300        return 0; // ignore warnings
301      }
302    };
303    ///\brief \ref named-templ-param "Named parameter" for setting
304    ///\c ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
305    ///
306    ///\ref named-templ-param "Named parameter" for setting
307    ///\c ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
308    ///If you don't set it explicitly, it will be automatically allocated.
309    struct SetStandardProcessedMap :
310      public Bfs< Digraph, SetStandardProcessedMapTraits > {
311      typedef Bfs< Digraph, SetStandardProcessedMapTraits > Create;
312    };
313
314    ///@}
315
316  public:
317
318    ///Constructor.
319
320    ///Constructor.
321    ///\param g The digraph the algorithm runs on.
322    Bfs(const Digraph &g) :
323      G(&g),
324      _pred(NULL), local_pred(false),
325      _dist(NULL), local_dist(false),
326      _reached(NULL), local_reached(false),
327      _processed(NULL), local_processed(false)
328    { }
329
330    ///Destructor.
331    ~Bfs()
332    {
333      if(local_pred) delete _pred;
334      if(local_dist) delete _dist;
335      if(local_reached) delete _reached;
336      if(local_processed) delete _processed;
337    }
338
339    ///Sets the map that stores the predecessor arcs.
340
341    ///Sets the map that stores the predecessor arcs.
342    ///If you don't use this function before calling \ref run(Node) "run()"
343    ///or \ref init(), an instance will be allocated automatically.
344    ///The destructor deallocates this automatically allocated map,
345    ///of course.
346    ///\return <tt> (*this) </tt>
347    Bfs &predMap(PredMap &m)
348    {
349      if(local_pred) {
350        delete _pred;
351        local_pred=false;
352      }
353      _pred = &m;
354      return *this;
355    }
356
357    ///Sets the map that indicates which nodes are reached.
358
359    ///Sets the map that indicates which nodes are reached.
360    ///If you don't use this function before calling \ref run(Node) "run()"
361    ///or \ref init(), an instance will be allocated automatically.
362    ///The destructor deallocates this automatically allocated map,
363    ///of course.
364    ///\return <tt> (*this) </tt>
365    Bfs &reachedMap(ReachedMap &m)
366    {
367      if(local_reached) {
368        delete _reached;
369        local_reached=false;
370      }
371      _reached = &m;
372      return *this;
373    }
374
375    ///Sets the map that indicates which nodes are processed.
376
377    ///Sets the map that indicates which nodes are processed.
378    ///If you don't use this function before calling \ref run(Node) "run()"
379    ///or \ref init(), an instance will be allocated automatically.
380    ///The destructor deallocates this automatically allocated map,
381    ///of course.
382    ///\return <tt> (*this) </tt>
383    Bfs &processedMap(ProcessedMap &m)
384    {
385      if(local_processed) {
386        delete _processed;
387        local_processed=false;
388      }
389      _processed = &m;
390      return *this;
391    }
392
393    ///Sets the map that stores the distances of the nodes.
394
395    ///Sets the map that stores the distances of the nodes calculated by
396    ///the algorithm.
397    ///If you don't use this function before calling \ref run(Node) "run()"
398    ///or \ref init(), an instance will be allocated automatically.
399    ///The destructor deallocates this automatically allocated map,
400    ///of course.
401    ///\return <tt> (*this) </tt>
402    Bfs &distMap(DistMap &m)
403    {
404      if(local_dist) {
405        delete _dist;
406        local_dist=false;
407      }
408      _dist = &m;
409      return *this;
410    }
411
412  public:
413
414    ///\name Execution Control
415    ///The simplest way to execute the BFS algorithm is to use one of the
416    ///member functions called \ref run(Node) "run()".\n
417    ///If you need better control on the execution, you have to call
418    ///\ref init() first, then you can add several source nodes with
419    ///\ref addSource(). Finally the actual path computation can be
420    ///performed with one of the \ref start() functions.
421
422    ///@{
423
424    ///\brief Initializes the internal data structures.
425    ///
426    ///Initializes the internal data structures.
427    void init()
428    {
429      create_maps();
430      _queue.resize(countNodes(*G));
431      _queue_head=_queue_tail=0;
432      _curr_dist=1;
433      for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
434        _pred->set(u,INVALID);
435        _reached->set(u,false);
436        _processed->set(u,false);
437      }
438    }
439
440    ///Adds a new source node.
441
442    ///Adds a new source node to the set of nodes to be processed.
443    ///
444    void addSource(Node s)
445    {
446      if(!(*_reached)[s])
447        {
448          _reached->set(s,true);
449          _pred->set(s,INVALID);
450          _dist->set(s,0);
451          _queue[_queue_head++]=s;
452          _queue_next_dist=_queue_head;
453        }
454    }
455
456    ///Processes the next node.
457
458    ///Processes the next node.
459    ///
460    ///\return The processed node.
461    ///
462    ///\pre The queue must not be empty.
463    Node processNextNode()
464    {
465      if(_queue_tail==_queue_next_dist) {
466        _curr_dist++;
467        _queue_next_dist=_queue_head;
468      }
469      Node n=_queue[_queue_tail++];
470      _processed->set(n,true);
471      Node m;
472      for(OutArcIt e(*G,n);e!=INVALID;++e)
473        if(!(*_reached)[m=G->target(e)]) {
474          _queue[_queue_head++]=m;
475          _reached->set(m,true);
476          _pred->set(m,e);
477          _dist->set(m,_curr_dist);
478        }
479      return n;
480    }
481
482    ///Processes the next node.
483
484    ///Processes the next node and checks if the given target node
485    ///is reached. If the target node is reachable from the processed
486    ///node, then the \c reach parameter will be set to \c true.
487    ///
488    ///\param target The target node.
489    ///\retval reach Indicates if the target node is reached.
490    ///It should be initially \c false.
491    ///
492    ///\return The processed node.
493    ///
494    ///\pre The queue must not be empty.
495    Node processNextNode(Node target, bool& reach)
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(OutArcIt 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          reach = reach || (target == m);
511        }
512      return n;
513    }
514
515    ///Processes the next node.
516
517    ///Processes the next node and checks if at least one of reached
518    ///nodes has \c true value in the \c nm node map. If one node
519    ///with \c true value is reachable from the processed node, then the
520    ///\c rnode parameter will be set to the first of such nodes.
521    ///
522    ///\param nm A \c bool (or convertible) node map that indicates the
523    ///possible targets.
524    ///\retval rnode The reached target node.
525    ///It should be initially \c INVALID.
526    ///
527    ///\return The processed node.
528    ///
529    ///\pre The queue must not be empty.
530    template<class NM>
531    Node processNextNode(const NM& nm, Node& rnode)
532    {
533      if(_queue_tail==_queue_next_dist) {
534        _curr_dist++;
535        _queue_next_dist=_queue_head;
536      }
537      Node n=_queue[_queue_tail++];
538      _processed->set(n,true);
539      Node m;
540      for(OutArcIt e(*G,n);e!=INVALID;++e)
541        if(!(*_reached)[m=G->target(e)]) {
542          _queue[_queue_head++]=m;
543          _reached->set(m,true);
544          _pred->set(m,e);
545          _dist->set(m,_curr_dist);
546          if (nm[m] && rnode == INVALID) rnode = m;
547        }
548      return n;
549    }
550
551    ///The next node to be processed.
552
553    ///Returns the next node to be processed or \c INVALID if the queue
554    ///is empty.
555    Node nextNode() const
556    {
557      return _queue_tail<_queue_head?_queue[_queue_tail]:INVALID;
558    }
559
560    ///Returns \c false if there are nodes to be processed.
561
562    ///Returns \c false if there are nodes to be processed
563    ///in the queue.
564    bool emptyQueue() const { return _queue_tail==_queue_head; }
565
566    ///Returns the number of the nodes to be processed.
567
568    ///Returns the number of the nodes to be processed
569    ///in the queue.
570    int queueSize() const { return _queue_head-_queue_tail; }
571
572    ///Executes the algorithm.
573
574    ///Executes the algorithm.
575    ///
576    ///This method runs the %BFS algorithm from the root node(s)
577    ///in order to compute the shortest path to each node.
578    ///
579    ///The algorithm computes
580    ///- the shortest path tree (forest),
581    ///- the distance of each node from the root(s).
582    ///
583    ///\pre init() must be called and at least one root node should be
584    ///added with addSource() before using this function.
585    ///
586    ///\note <tt>b.start()</tt> is just a shortcut of the following code.
587    ///\code
588    ///  while ( !b.emptyQueue() ) {
589    ///    b.processNextNode();
590    ///  }
591    ///\endcode
592    void start()
593    {
594      while ( !emptyQueue() ) processNextNode();
595    }
596
597    ///Executes the algorithm until the given target node is reached.
598
599    ///Executes the algorithm until the given target node is reached.
600    ///
601    ///This method runs the %BFS algorithm from the root node(s)
602    ///in order to compute the shortest path to \c t.
603    ///
604    ///The algorithm computes
605    ///- the shortest path to \c t,
606    ///- the distance of \c t from the root(s).
607    ///
608    ///\pre init() must be called and at least one root node should be
609    ///added with addSource() before using this function.
610    ///
611    ///\note <tt>b.start(t)</tt> is just a shortcut of the following code.
612    ///\code
613    ///  bool reach = false;
614    ///  while ( !b.emptyQueue() && !reach ) {
615    ///    b.processNextNode(t, reach);
616    ///  }
617    ///\endcode
618    void start(Node t)
619    {
620      bool reach = false;
621      while ( !emptyQueue() && !reach ) processNextNode(t, reach);
622    }
623
624    ///Executes the algorithm until a condition is met.
625
626    ///Executes the algorithm until a condition is met.
627    ///
628    ///This method runs the %BFS algorithm from the root node(s) in
629    ///order to compute the shortest path to a node \c v with
630    /// <tt>nm[v]</tt> true, if such a node can be found.
631    ///
632    ///\param nm A \c bool (or convertible) node map. The algorithm
633    ///will stop when it reaches a node \c v with <tt>nm[v]</tt> true.
634    ///
635    ///\return The reached node \c v with <tt>nm[v]</tt> true or
636    ///\c INVALID if no such node was found.
637    ///
638    ///\pre init() must be called and at least one root node should be
639    ///added with addSource() before using this function.
640    ///
641    ///\note <tt>b.start(nm)</tt> is just a shortcut of the following code.
642    ///\code
643    ///  Node rnode = INVALID;
644    ///  while ( !b.emptyQueue() && rnode == INVALID ) {
645    ///    b.processNextNode(nm, rnode);
646    ///  }
647    ///  return rnode;
648    ///\endcode
649    template<class NodeBoolMap>
650    Node start(const NodeBoolMap &nm)
651    {
652      Node rnode = INVALID;
653      while ( !emptyQueue() && rnode == INVALID ) {
654        processNextNode(nm, rnode);
655      }
656      return rnode;
657    }
658
659    ///Runs the algorithm from the given source node.
660
661    ///This method runs the %BFS algorithm from node \c s
662    ///in order to compute the shortest path to each node.
663    ///
664    ///The algorithm computes
665    ///- the shortest path tree,
666    ///- the distance of each node from the root.
667    ///
668    ///\note <tt>b.run(s)</tt> is just a shortcut of the following code.
669    ///\code
670    ///  b.init();
671    ///  b.addSource(s);
672    ///  b.start();
673    ///\endcode
674    void run(Node s) {
675      init();
676      addSource(s);
677      start();
678    }
679
680    ///Finds the shortest path between \c s and \c t.
681
682    ///This method runs the %BFS algorithm from node \c s
683    ///in order to compute the shortest path to node \c t
684    ///(it stops searching when \c t is processed).
685    ///
686    ///\return \c true if \c t is reachable form \c s.
687    ///
688    ///\note Apart from the return value, <tt>b.run(s,t)</tt> is just a
689    ///shortcut of the following code.
690    ///\code
691    ///  b.init();
692    ///  b.addSource(s);
693    ///  b.start(t);
694    ///\endcode
695    bool run(Node s,Node t) {
696      init();
697      addSource(s);
698      start(t);
699      return reached(t);
700    }
701
702    ///Runs the algorithm to visit all nodes in the digraph.
703
704    ///This method runs the %BFS algorithm in order to
705    ///compute the shortest path to each node.
706    ///
707    ///The algorithm computes
708    ///- the shortest path tree (forest),
709    ///- the distance of each node from the root(s).
710    ///
711    ///\note <tt>b.run(s)</tt> is just a shortcut of the following code.
712    ///\code
713    ///  b.init();
714    ///  for (NodeIt n(gr); n != INVALID; ++n) {
715    ///    if (!b.reached(n)) {
716    ///      b.addSource(n);
717    ///      b.start();
718    ///    }
719    ///  }
720    ///\endcode
721    void run() {
722      init();
723      for (NodeIt n(*G); n != INVALID; ++n) {
724        if (!reached(n)) {
725          addSource(n);
726          start();
727        }
728      }
729    }
730
731    ///@}
732
733    ///\name Query Functions
734    ///The results of the BFS algorithm can be obtained using these
735    ///functions.\n
736    ///Either \ref run(Node) "run()" or \ref start() should be called
737    ///before using them.
738
739    ///@{
740
741    ///The shortest path to the given node.
742
743    ///Returns the shortest path to the given node from the root(s).
744    ///
745    ///\warning \c t should be reached from the root(s).
746    ///
747    ///\pre Either \ref run(Node) "run()" or \ref init()
748    ///must be called before using this function.
749    Path path(Node t) const { return Path(*G, *_pred, t); }
750
751    ///The distance of the given node from the root(s).
752
753    ///Returns the distance of the given node from the root(s).
754    ///
755    ///\warning If node \c v is not reached from the root(s), then
756    ///the return value of this function is undefined.
757    ///
758    ///\pre Either \ref run(Node) "run()" or \ref init()
759    ///must be called before using this function.
760    int dist(Node v) const { return (*_dist)[v]; }
761
762    ///\brief Returns the 'previous arc' of the shortest path tree for
763    ///the given node.
764    ///
765    ///This function returns the 'previous arc' of the shortest path
766    ///tree for the node \c v, i.e. it returns the last arc of a
767    ///shortest path from a root to \c v. It is \c INVALID if \c v
768    ///is not reached from the root(s) or if \c v is a root.
769    ///
770    ///The shortest path tree used here is equal to the shortest path
771    ///tree used in \ref predNode() and \ref predMap().
772    ///
773    ///\pre Either \ref run(Node) "run()" or \ref init()
774    ///must be called before using this function.
775    Arc predArc(Node v) const { return (*_pred)[v];}
776
777    ///\brief Returns the 'previous node' of the shortest path tree for
778    ///the given node.
779    ///
780    ///This function returns the 'previous node' of the shortest path
781    ///tree for the node \c v, i.e. it returns the last but one node
782    ///of a shortest path from a root to \c v. It is \c INVALID
783    ///if \c v is not reached from the root(s) or if \c v is a root.
784    ///
785    ///The shortest path tree used here is equal to the shortest path
786    ///tree used in \ref predArc() and \ref predMap().
787    ///
788    ///\pre Either \ref run(Node) "run()" or \ref init()
789    ///must be called before using this function.
790    Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
791                                  G->source((*_pred)[v]); }
792
793    ///\brief Returns a const reference to the node map that stores the
794    /// distances of the nodes.
795    ///
796    ///Returns a const reference to the node map that stores the distances
797    ///of the nodes calculated by the algorithm.
798    ///
799    ///\pre Either \ref run(Node) "run()" or \ref init()
800    ///must be called before using this function.
801    const DistMap &distMap() const { return *_dist;}
802
803    ///\brief Returns a const reference to the node map that stores the
804    ///predecessor arcs.
805    ///
806    ///Returns a const reference to the node map that stores the predecessor
807    ///arcs, which form the shortest path tree (forest).
808    ///
809    ///\pre Either \ref run(Node) "run()" or \ref init()
810    ///must be called before using this function.
811    const PredMap &predMap() const { return *_pred;}
812
813    ///Checks if the given node is reached from the root(s).
814
815    ///Returns \c true if \c v is reached from the root(s).
816    ///
817    ///\pre Either \ref run(Node) "run()" or \ref init()
818    ///must be called before using this function.
819    bool reached(Node v) const { return (*_reached)[v]; }
820
821    ///@}
822  };
823
824  ///Default traits class of bfs() function.
825
826  ///Default traits class of bfs() function.
827  ///\tparam GR Digraph type.
828  template<class GR>
829  struct BfsWizardDefaultTraits
830  {
831    ///The type of the digraph the algorithm runs on.
832    typedef GR Digraph;
833
834    ///\brief The type of the map that stores the predecessor
835    ///arcs of the shortest paths.
836    ///
837    ///The type of the map that stores the predecessor
838    ///arcs of the shortest paths.
839    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
840    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
841    ///Instantiates a PredMap.
842
843    ///This function instantiates a PredMap.
844    ///\param g is the digraph, to which we would like to define the
845    ///PredMap.
846    static PredMap *createPredMap(const Digraph &g)
847    {
848      return new PredMap(g);
849    }
850
851    ///The type of the map that indicates which nodes are processed.
852
853    ///The type of the map that indicates which nodes are processed.
854    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
855    ///By default it is a NullMap.
856    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
857    ///Instantiates a ProcessedMap.
858
859    ///This function instantiates a ProcessedMap.
860    ///\param g is the digraph, to which
861    ///we would like to define the ProcessedMap.
862#ifdef DOXYGEN
863    static ProcessedMap *createProcessedMap(const Digraph &g)
864#else
865    static ProcessedMap *createProcessedMap(const Digraph &)
866#endif
867    {
868      return new ProcessedMap();
869    }
870
871    ///The type of the map that indicates which nodes are reached.
872
873    ///The type of the map that indicates which nodes are reached.
874    ///It must conform to the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
875    typedef typename Digraph::template NodeMap<bool> ReachedMap;
876    ///Instantiates a ReachedMap.
877
878    ///This function instantiates a ReachedMap.
879    ///\param g is the digraph, to which
880    ///we would like to define the ReachedMap.
881    static ReachedMap *createReachedMap(const Digraph &g)
882    {
883      return new ReachedMap(g);
884    }
885
886    ///The type of the map that stores the distances of the nodes.
887
888    ///The type of the map that stores the distances of the nodes.
889    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
890    typedef typename Digraph::template NodeMap<int> DistMap;
891    ///Instantiates a DistMap.
892
893    ///This function instantiates a DistMap.
894    ///\param g is the digraph, to which we would like to define
895    ///the DistMap
896    static DistMap *createDistMap(const Digraph &g)
897    {
898      return new DistMap(g);
899    }
900
901    ///The type of the shortest paths.
902
903    ///The type of the shortest paths.
904    ///It must conform to the \ref concepts::Path "Path" concept.
905    typedef lemon::Path<Digraph> Path;
906  };
907
908  /// Default traits class used by BfsWizard
909
910  /// Default traits class used by BfsWizard.
911  /// \tparam GR The type of the digraph.
912  template<class GR>
913  class BfsWizardBase : public BfsWizardDefaultTraits<GR>
914  {
915
916    typedef BfsWizardDefaultTraits<GR> Base;
917  protected:
918    //The type of the nodes in the digraph.
919    typedef typename Base::Digraph::Node Node;
920
921    //Pointer to the digraph the algorithm runs on.
922    void *_g;
923    //Pointer to the map of reached nodes.
924    void *_reached;
925    //Pointer to the map of processed nodes.
926    void *_processed;
927    //Pointer to the map of predecessors arcs.
928    void *_pred;
929    //Pointer to the map of distances.
930    void *_dist;
931    //Pointer to the shortest path to the target node.
932    void *_path;
933    //Pointer to the distance of the target node.
934    int *_di;
935
936    public:
937    /// Constructor.
938
939    /// This constructor does not require parameters, it initiates
940    /// all of the attributes to \c 0.
941    BfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0),
942                      _dist(0), _path(0), _di(0) {}
943
944    /// Constructor.
945
946    /// This constructor requires one parameter,
947    /// others are initiated to \c 0.
948    /// \param g The digraph the algorithm runs on.
949    BfsWizardBase(const GR &g) :
950      _g(reinterpret_cast<void*>(const_cast<GR*>(&g))),
951      _reached(0), _processed(0), _pred(0), _dist(0),  _path(0), _di(0) {}
952
953  };
954
955  /// Auxiliary class for the function-type interface of BFS algorithm.
956
957  /// This auxiliary class is created to implement the
958  /// \ref bfs() "function-type interface" of \ref Bfs algorithm.
959  /// It does not have own \ref run(Node) "run()" method, it uses the
960  /// functions and features of the plain \ref Bfs.
961  ///
962  /// This class should only be used through the \ref bfs() function,
963  /// which makes it easier to use the algorithm.
964  template<class TR>
965  class BfsWizard : public TR
966  {
967    typedef TR Base;
968
969    typedef typename TR::Digraph Digraph;
970
971    typedef typename Digraph::Node Node;
972    typedef typename Digraph::NodeIt NodeIt;
973    typedef typename Digraph::Arc Arc;
974    typedef typename Digraph::OutArcIt OutArcIt;
975
976    typedef typename TR::PredMap PredMap;
977    typedef typename TR::DistMap DistMap;
978    typedef typename TR::ReachedMap ReachedMap;
979    typedef typename TR::ProcessedMap ProcessedMap;
980    typedef typename TR::Path Path;
981
982  public:
983
984    /// Constructor.
985    BfsWizard() : TR() {}
986
987    /// Constructor that requires parameters.
988
989    /// Constructor that requires parameters.
990    /// These parameters will be the default values for the traits class.
991    /// \param g The digraph the algorithm runs on.
992    BfsWizard(const Digraph &g) :
993      TR(g) {}
994
995    ///Copy constructor
996    BfsWizard(const TR &b) : TR(b) {}
997
998    ~BfsWizard() {}
999
1000    ///Runs BFS algorithm from the given source node.
1001
1002    ///This method runs BFS algorithm from node \c s
1003    ///in order to compute the shortest path to each node.
1004    void run(Node s)
1005    {
1006      Bfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
1007      if (Base::_pred)
1008        alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
1009      if (Base::_dist)
1010        alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
1011      if (Base::_reached)
1012        alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
1013      if (Base::_processed)
1014        alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
1015      if (s!=INVALID)
1016        alg.run(s);
1017      else
1018        alg.run();
1019    }
1020
1021    ///Finds the shortest path between \c s and \c t.
1022
1023    ///This method runs BFS algorithm from node \c s
1024    ///in order to compute the shortest path to node \c t
1025    ///(it stops searching when \c t is processed).
1026    ///
1027    ///\return \c true if \c t is reachable form \c s.
1028    bool run(Node s, Node t)
1029    {
1030      Bfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
1031      if (Base::_pred)
1032        alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
1033      if (Base::_dist)
1034        alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
1035      if (Base::_reached)
1036        alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
1037      if (Base::_processed)
1038        alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
1039      alg.run(s,t);
1040      if (Base::_path)
1041        *reinterpret_cast<Path*>(Base::_path) = alg.path(t);
1042      if (Base::_di)
1043        *Base::_di = alg.dist(t);
1044      return alg.reached(t);
1045    }
1046
1047    ///Runs BFS algorithm to visit all nodes in the digraph.
1048
1049    ///This method runs BFS algorithm in order to compute
1050    ///the shortest path to each node.
1051    void run()
1052    {
1053      run(INVALID);
1054    }
1055
1056    template<class T>
1057    struct SetPredMapBase : public Base {
1058      typedef T PredMap;
1059      static PredMap *createPredMap(const Digraph &) { return 0; };
1060      SetPredMapBase(const TR &b) : TR(b) {}
1061    };
1062
1063    ///\brief \ref named-templ-param "Named parameter" for setting
1064    ///the predecessor map.
1065    ///
1066    ///\ref named-templ-param "Named parameter" function for setting
1067    ///the map that stores the predecessor arcs of the nodes.
1068    template<class T>
1069    BfsWizard<SetPredMapBase<T> > predMap(const T &t)
1070    {
1071      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
1072      return BfsWizard<SetPredMapBase<T> >(*this);
1073    }
1074
1075    template<class T>
1076    struct SetReachedMapBase : public Base {
1077      typedef T ReachedMap;
1078      static ReachedMap *createReachedMap(const Digraph &) { return 0; };
1079      SetReachedMapBase(const TR &b) : TR(b) {}
1080    };
1081
1082    ///\brief \ref named-templ-param "Named parameter" for setting
1083    ///the reached map.
1084    ///
1085    ///\ref named-templ-param "Named parameter" function for setting
1086    ///the map that indicates which nodes are reached.
1087    template<class T>
1088    BfsWizard<SetReachedMapBase<T> > reachedMap(const T &t)
1089    {
1090      Base::_reached=reinterpret_cast<void*>(const_cast<T*>(&t));
1091      return BfsWizard<SetReachedMapBase<T> >(*this);
1092    }
1093
1094    template<class T>
1095    struct SetDistMapBase : public Base {
1096      typedef T DistMap;
1097      static DistMap *createDistMap(const Digraph &) { return 0; };
1098      SetDistMapBase(const TR &b) : TR(b) {}
1099    };
1100
1101    ///\brief \ref named-templ-param "Named parameter" for setting
1102    ///the distance map.
1103    ///
1104    ///\ref named-templ-param "Named parameter" function for setting
1105    ///the map that stores the distances of the nodes calculated
1106    ///by the algorithm.
1107    template<class T>
1108    BfsWizard<SetDistMapBase<T> > distMap(const T &t)
1109    {
1110      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
1111      return BfsWizard<SetDistMapBase<T> >(*this);
1112    }
1113
1114    template<class T>
1115    struct SetProcessedMapBase : public Base {
1116      typedef T ProcessedMap;
1117      static ProcessedMap *createProcessedMap(const Digraph &) { return 0; };
1118      SetProcessedMapBase(const TR &b) : TR(b) {}
1119    };
1120
1121    ///\brief \ref named-func-param "Named parameter" for setting
1122    ///the processed map.
1123    ///
1124    ///\ref named-templ-param "Named parameter" function for setting
1125    ///the map that indicates which nodes are processed.
1126    template<class T>
1127    BfsWizard<SetProcessedMapBase<T> > processedMap(const T &t)
1128    {
1129      Base::_processed=reinterpret_cast<void*>(const_cast<T*>(&t));
1130      return BfsWizard<SetProcessedMapBase<T> >(*this);
1131    }
1132
1133    template<class T>
1134    struct SetPathBase : public Base {
1135      typedef T Path;
1136      SetPathBase(const TR &b) : TR(b) {}
1137    };
1138    ///\brief \ref named-func-param "Named parameter"
1139    ///for getting the shortest path to the target node.
1140    ///
1141    ///\ref named-func-param "Named parameter"
1142    ///for getting the shortest path to the target node.
1143    template<class T>
1144    BfsWizard<SetPathBase<T> > path(const T &t)
1145    {
1146      Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t));
1147      return BfsWizard<SetPathBase<T> >(*this);
1148    }
1149
1150    ///\brief \ref named-func-param "Named parameter"
1151    ///for getting the distance of the target node.
1152    ///
1153    ///\ref named-func-param "Named parameter"
1154    ///for getting the distance of the target node.
1155    BfsWizard dist(const int &d)
1156    {
1157      Base::_di=const_cast<int*>(&d);
1158      return *this;
1159    }
1160
1161  };
1162
1163  ///Function-type interface for BFS algorithm.
1164
1165  /// \ingroup search
1166  ///Function-type interface for BFS algorithm.
1167  ///
1168  ///This function also has several \ref named-func-param "named parameters",
1169  ///they are declared as the members of class \ref BfsWizard.
1170  ///The following examples show how to use these parameters.
1171  ///\code
1172  ///  // Compute shortest path from node s to each node
1173  ///  bfs(g).predMap(preds).distMap(dists).run(s);
1174  ///
1175  ///  // Compute shortest path from s to t
1176  ///  bool reached = bfs(g).path(p).dist(d).run(s,t);
1177  ///\endcode
1178  ///\warning Don't forget to put the \ref BfsWizard::run(Node) "run()"
1179  ///to the end of the parameter list.
1180  ///\sa BfsWizard
1181  ///\sa Bfs
1182  template<class GR>
1183  BfsWizard<BfsWizardBase<GR> >
1184  bfs(const GR &digraph)
1185  {
1186    return BfsWizard<BfsWizardBase<GR> >(digraph);
1187  }
1188
1189#ifdef DOXYGEN
1190  /// \brief Visitor class for BFS.
1191  ///
1192  /// This class defines the interface of the BfsVisit events, and
1193  /// it could be the base of a real visitor class.
1194  template <typename GR>
1195  struct BfsVisitor {
1196    typedef GR Digraph;
1197    typedef typename Digraph::Arc Arc;
1198    typedef typename Digraph::Node Node;
1199    /// \brief Called for the source node(s) of the BFS.
1200    ///
1201    /// This function is called for the source node(s) of the BFS.
1202    void start(const Node& node) {}
1203    /// \brief Called when a node is reached first time.
1204    ///
1205    /// This function is called when a node is reached first time.
1206    void reach(const Node& node) {}
1207    /// \brief Called when a node is processed.
1208    ///
1209    /// This function is called when a node is processed.
1210    void process(const Node& node) {}
1211    /// \brief Called when an arc reaches a new node.
1212    ///
1213    /// This function is called when the BFS finds an arc whose target node
1214    /// is not reached yet.
1215    void discover(const Arc& arc) {}
1216    /// \brief Called when an arc is examined but its target node is
1217    /// already discovered.
1218    ///
1219    /// This function is called when an arc is examined but its target node is
1220    /// already discovered.
1221    void examine(const Arc& arc) {}
1222  };
1223#else
1224  template <typename GR>
1225  struct BfsVisitor {
1226    typedef GR Digraph;
1227    typedef typename Digraph::Arc Arc;
1228    typedef typename Digraph::Node Node;
1229    void start(const Node&) {}
1230    void reach(const Node&) {}
1231    void process(const Node&) {}
1232    void discover(const Arc&) {}
1233    void examine(const Arc&) {}
1234
1235    template <typename _Visitor>
1236    struct Constraints {
1237      void constraints() {
1238        Arc arc;
1239        Node node;
1240        visitor.start(node);
1241        visitor.reach(node);
1242        visitor.process(node);
1243        visitor.discover(arc);
1244        visitor.examine(arc);
1245      }
1246      _Visitor& visitor;
1247    };
1248  };
1249#endif
1250
1251  /// \brief Default traits class of BfsVisit class.
1252  ///
1253  /// Default traits class of BfsVisit class.
1254  /// \tparam GR The type of the digraph the algorithm runs on.
1255  template<class GR>
1256  struct BfsVisitDefaultTraits {
1257
1258    /// \brief The type of the digraph the algorithm runs on.
1259    typedef GR Digraph;
1260
1261    /// \brief The type of the map that indicates which nodes are reached.
1262    ///
1263    /// The type of the map that indicates which nodes are reached.
1264    /// It must conform to the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
1265    typedef typename Digraph::template NodeMap<bool> ReachedMap;
1266
1267    /// \brief Instantiates a ReachedMap.
1268    ///
1269    /// This function instantiates a ReachedMap.
1270    /// \param digraph is the digraph, to which
1271    /// we would like to define the ReachedMap.
1272    static ReachedMap *createReachedMap(const Digraph &digraph) {
1273      return new ReachedMap(digraph);
1274    }
1275
1276  };
1277
1278  /// \ingroup search
1279  ///
1280  /// \brief BFS algorithm class with visitor interface.
1281  ///
1282  /// This class provides an efficient implementation of the BFS algorithm
1283  /// with visitor interface.
1284  ///
1285  /// The BfsVisit class provides an alternative interface to the Bfs
1286  /// class. It works with callback mechanism, the BfsVisit object calls
1287  /// the member functions of the \c Visitor class on every BFS event.
1288  ///
1289  /// This interface of the BFS algorithm should be used in special cases
1290  /// when extra actions have to be performed in connection with certain
1291  /// events of the BFS algorithm. Otherwise consider to use Bfs or bfs()
1292  /// instead.
1293  ///
1294  /// \tparam GR The type of the digraph the algorithm runs on.
1295  /// The default type is \ref ListDigraph.
1296  /// The value of GR is not used directly by \ref BfsVisit,
1297  /// it is only passed to \ref BfsVisitDefaultTraits.
1298  /// \tparam VS The Visitor type that is used by the algorithm.
1299  /// \ref BfsVisitor "BfsVisitor<GR>" is an empty visitor, which
1300  /// does not observe the BFS events. If you want to observe the BFS
1301  /// events, you should implement your own visitor class.
1302  /// \tparam TR Traits class to set various data types used by the
1303  /// algorithm. The default traits class is
1304  /// \ref BfsVisitDefaultTraits "BfsVisitDefaultTraits<GR>".
1305  /// See \ref BfsVisitDefaultTraits for the documentation of
1306  /// a BFS visit traits class.
1307#ifdef DOXYGEN
1308  template <typename GR, typename VS, typename TR>
1309#else
1310  template <typename GR = ListDigraph,
1311            typename VS = BfsVisitor<GR>,
1312            typename TR = BfsVisitDefaultTraits<GR> >
1313#endif
1314  class BfsVisit {
1315  public:
1316
1317    ///The traits class.
1318    typedef TR Traits;
1319
1320    ///The type of the digraph the algorithm runs on.
1321    typedef typename Traits::Digraph Digraph;
1322
1323    ///The visitor type used by the algorithm.
1324    typedef VS Visitor;
1325
1326    ///The type of the map that indicates which nodes are reached.
1327    typedef typename Traits::ReachedMap ReachedMap;
1328
1329  private:
1330
1331    typedef typename Digraph::Node Node;
1332    typedef typename Digraph::NodeIt NodeIt;
1333    typedef typename Digraph::Arc Arc;
1334    typedef typename Digraph::OutArcIt OutArcIt;
1335
1336    //Pointer to the underlying digraph.
1337    const Digraph *_digraph;
1338    //Pointer to the visitor object.
1339    Visitor *_visitor;
1340    //Pointer to the map of reached status of the nodes.
1341    ReachedMap *_reached;
1342    //Indicates if _reached is locally allocated (true) or not.
1343    bool local_reached;
1344
1345    std::vector<typename Digraph::Node> _list;
1346    int _list_front, _list_back;
1347
1348    //Creates the maps if necessary.
1349    void create_maps() {
1350      if(!_reached) {
1351        local_reached = true;
1352        _reached = Traits::createReachedMap(*_digraph);
1353      }
1354    }
1355
1356  protected:
1357
1358    BfsVisit() {}
1359
1360  public:
1361
1362    typedef BfsVisit Create;
1363
1364    /// \name Named Template Parameters
1365
1366    ///@{
1367    template <class T>
1368    struct SetReachedMapTraits : public Traits {
1369      typedef T ReachedMap;
1370      static ReachedMap *createReachedMap(const Digraph &digraph) {
1371        LEMON_ASSERT(false, "ReachedMap is not initialized");
1372        return 0; // ignore warnings
1373      }
1374    };
1375    /// \brief \ref named-templ-param "Named parameter" for setting
1376    /// ReachedMap type.
1377    ///
1378    /// \ref named-templ-param "Named parameter" for setting ReachedMap type.
1379    template <class T>
1380    struct SetReachedMap : public BfsVisit< Digraph, Visitor,
1381                                            SetReachedMapTraits<T> > {
1382      typedef BfsVisit< Digraph, Visitor, SetReachedMapTraits<T> > Create;
1383    };
1384    ///@}
1385
1386  public:
1387
1388    /// \brief Constructor.
1389    ///
1390    /// Constructor.
1391    ///
1392    /// \param digraph The digraph the algorithm runs on.
1393    /// \param visitor The visitor object of the algorithm.
1394    BfsVisit(const Digraph& digraph, Visitor& visitor)
1395      : _digraph(&digraph), _visitor(&visitor),
1396        _reached(0), local_reached(false) {}
1397
1398    /// \brief Destructor.
1399    ~BfsVisit() {
1400      if(local_reached) delete _reached;
1401    }
1402
1403    /// \brief Sets the map that indicates which nodes are reached.
1404    ///
1405    /// Sets the map that indicates which nodes are reached.
1406    /// If you don't use this function before calling \ref run(Node) "run()"
1407    /// or \ref init(), an instance will be allocated automatically.
1408    /// The destructor deallocates this automatically allocated map,
1409    /// of course.
1410    /// \return <tt> (*this) </tt>
1411    BfsVisit &reachedMap(ReachedMap &m) {
1412      if(local_reached) {
1413        delete _reached;
1414        local_reached = false;
1415      }
1416      _reached = &m;
1417      return *this;
1418    }
1419
1420  public:
1421
1422    /// \name Execution Control
1423    /// The simplest way to execute the BFS algorithm is to use one of the
1424    /// member functions called \ref run(Node) "run()".\n
1425    /// If you need better control on the execution, you have to call
1426    /// \ref init() first, then you can add several source nodes with
1427    /// \ref addSource(). Finally the actual path computation can be
1428    /// performed with one of the \ref start() functions.
1429
1430    /// @{
1431
1432    /// \brief Initializes the internal data structures.
1433    ///
1434    /// Initializes the internal data structures.
1435    void init() {
1436      create_maps();
1437      _list.resize(countNodes(*_digraph));
1438      _list_front = _list_back = -1;
1439      for (NodeIt u(*_digraph) ; u != INVALID ; ++u) {
1440        _reached->set(u, false);
1441      }
1442    }
1443
1444    /// \brief Adds a new source node.
1445    ///
1446    /// Adds a new source node to the set of nodes to be processed.
1447    void addSource(Node s) {
1448      if(!(*_reached)[s]) {
1449          _reached->set(s,true);
1450          _visitor->start(s);
1451          _visitor->reach(s);
1452          _list[++_list_back] = s;
1453        }
1454    }
1455
1456    /// \brief Processes the next node.
1457    ///
1458    /// Processes the next node.
1459    ///
1460    /// \return The processed node.
1461    ///
1462    /// \pre The queue must not be empty.
1463    Node processNextNode() {
1464      Node n = _list[++_list_front];
1465      _visitor->process(n);
1466      Arc e;
1467      for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
1468        Node m = _digraph->target(e);
1469        if (!(*_reached)[m]) {
1470          _visitor->discover(e);
1471          _visitor->reach(m);
1472          _reached->set(m, true);
1473          _list[++_list_back] = m;
1474        } else {
1475          _visitor->examine(e);
1476        }
1477      }
1478      return n;
1479    }
1480
1481    /// \brief Processes the next node.
1482    ///
1483    /// Processes the next node and checks if the given target node
1484    /// is reached. If the target node is reachable from the processed
1485    /// node, then the \c reach parameter will be set to \c true.
1486    ///
1487    /// \param target The target node.
1488    /// \retval reach Indicates if the target node is reached.
1489    /// It should be initially \c false.
1490    ///
1491    /// \return The processed node.
1492    ///
1493    /// \pre The queue must not be empty.
1494    Node processNextNode(Node target, bool& reach) {
1495      Node n = _list[++_list_front];
1496      _visitor->process(n);
1497      Arc e;
1498      for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
1499        Node m = _digraph->target(e);
1500        if (!(*_reached)[m]) {
1501          _visitor->discover(e);
1502          _visitor->reach(m);
1503          _reached->set(m, true);
1504          _list[++_list_back] = m;
1505          reach = reach || (target == m);
1506        } else {
1507          _visitor->examine(e);
1508        }
1509      }
1510      return n;
1511    }
1512
1513    /// \brief Processes the next node.
1514    ///
1515    /// Processes the next node and checks if at least one of reached
1516    /// nodes has \c true value in the \c nm node map. If one node
1517    /// with \c true value is reachable from the processed node, then the
1518    /// \c rnode parameter will be set to the first of such nodes.
1519    ///
1520    /// \param nm A \c bool (or convertible) node map that indicates the
1521    /// possible targets.
1522    /// \retval rnode The reached target node.
1523    /// It should be initially \c INVALID.
1524    ///
1525    /// \return The processed node.
1526    ///
1527    /// \pre The queue must not be empty.
1528    template <typename NM>
1529    Node processNextNode(const NM& nm, Node& rnode) {
1530      Node n = _list[++_list_front];
1531      _visitor->process(n);
1532      Arc e;
1533      for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
1534        Node m = _digraph->target(e);
1535        if (!(*_reached)[m]) {
1536          _visitor->discover(e);
1537          _visitor->reach(m);
1538          _reached->set(m, true);
1539          _list[++_list_back] = m;
1540          if (nm[m] && rnode == INVALID) rnode = m;
1541        } else {
1542          _visitor->examine(e);
1543        }
1544      }
1545      return n;
1546    }
1547
1548    /// \brief The next node to be processed.
1549    ///
1550    /// Returns the next node to be processed or \c INVALID if the queue
1551    /// is empty.
1552    Node nextNode() const {
1553      return _list_front != _list_back ? _list[_list_front + 1] : INVALID;
1554    }
1555
1556    /// \brief Returns \c false if there are nodes
1557    /// to be processed.
1558    ///
1559    /// Returns \c false if there are nodes
1560    /// to be processed in the queue.
1561    bool emptyQueue() const { return _list_front == _list_back; }
1562
1563    /// \brief Returns the number of the nodes to be processed.
1564    ///
1565    /// Returns the number of the nodes to be processed in the queue.
1566    int queueSize() const { return _list_back - _list_front; }
1567
1568    /// \brief Executes the algorithm.
1569    ///
1570    /// Executes the algorithm.
1571    ///
1572    /// This method runs the %BFS algorithm from the root node(s)
1573    /// in order to compute the shortest path to each node.
1574    ///
1575    /// The algorithm computes
1576    /// - the shortest path tree (forest),
1577    /// - the distance of each node from the root(s).
1578    ///
1579    /// \pre init() must be called and at least one root node should be added
1580    /// with addSource() before using this function.
1581    ///
1582    /// \note <tt>b.start()</tt> is just a shortcut of the following code.
1583    /// \code
1584    ///   while ( !b.emptyQueue() ) {
1585    ///     b.processNextNode();
1586    ///   }
1587    /// \endcode
1588    void start() {
1589      while ( !emptyQueue() ) processNextNode();
1590    }
1591
1592    /// \brief Executes the algorithm until the given target node is reached.
1593    ///
1594    /// Executes the algorithm until the given target node is reached.
1595    ///
1596    /// This method runs the %BFS algorithm from the root node(s)
1597    /// in order to compute the shortest path to \c t.
1598    ///
1599    /// The algorithm computes
1600    /// - the shortest path to \c t,
1601    /// - the distance of \c t from the root(s).
1602    ///
1603    /// \pre init() must be called and at least one root node should be
1604    /// added with addSource() before using this function.
1605    ///
1606    /// \note <tt>b.start(t)</tt> is just a shortcut of the following code.
1607    /// \code
1608    ///   bool reach = false;
1609    ///   while ( !b.emptyQueue() && !reach ) {
1610    ///     b.processNextNode(t, reach);
1611    ///   }
1612    /// \endcode
1613    void start(Node t) {
1614      bool reach = false;
1615      while ( !emptyQueue() && !reach ) processNextNode(t, reach);
1616    }
1617
1618    /// \brief Executes the algorithm until a condition is met.
1619    ///
1620    /// Executes the algorithm until a condition is met.
1621    ///
1622    /// This method runs the %BFS algorithm from the root node(s) in
1623    /// order to compute the shortest path to a node \c v with
1624    /// <tt>nm[v]</tt> true, if such a node can be found.
1625    ///
1626    /// \param nm must be a bool (or convertible) node map. The
1627    /// algorithm will stop when it reaches a node \c v with
1628    /// <tt>nm[v]</tt> true.
1629    ///
1630    /// \return The reached node \c v with <tt>nm[v]</tt> true or
1631    /// \c INVALID if no such node was found.
1632    ///
1633    /// \pre init() must be called and at least one root node should be
1634    /// added with addSource() before using this function.
1635    ///
1636    /// \note <tt>b.start(nm)</tt> is just a shortcut of the following code.
1637    /// \code
1638    ///   Node rnode = INVALID;
1639    ///   while ( !b.emptyQueue() && rnode == INVALID ) {
1640    ///     b.processNextNode(nm, rnode);
1641    ///   }
1642    ///   return rnode;
1643    /// \endcode
1644    template <typename NM>
1645    Node start(const NM &nm) {
1646      Node rnode = INVALID;
1647      while ( !emptyQueue() && rnode == INVALID ) {
1648        processNextNode(nm, rnode);
1649      }
1650      return rnode;
1651    }
1652
1653    /// \brief Runs the algorithm from the given source node.
1654    ///
1655    /// This method runs the %BFS algorithm from node \c s
1656    /// in order to compute the shortest path to each node.
1657    ///
1658    /// The algorithm computes
1659    /// - the shortest path tree,
1660    /// - the distance of each node from the root.
1661    ///
1662    /// \note <tt>b.run(s)</tt> is just a shortcut of the following code.
1663    ///\code
1664    ///   b.init();
1665    ///   b.addSource(s);
1666    ///   b.start();
1667    ///\endcode
1668    void run(Node s) {
1669      init();
1670      addSource(s);
1671      start();
1672    }
1673
1674    /// \brief Finds the shortest path between \c s and \c t.
1675    ///
1676    /// This method runs the %BFS algorithm from node \c s
1677    /// in order to compute the shortest path to node \c t
1678    /// (it stops searching when \c t is processed).
1679    ///
1680    /// \return \c true if \c t is reachable form \c s.
1681    ///
1682    /// \note Apart from the return value, <tt>b.run(s,t)</tt> is just a
1683    /// shortcut of the following code.
1684    ///\code
1685    ///   b.init();
1686    ///   b.addSource(s);
1687    ///   b.start(t);
1688    ///\endcode
1689    bool run(Node s,Node t) {
1690      init();
1691      addSource(s);
1692      start(t);
1693      return reached(t);
1694    }
1695
1696    /// \brief Runs the algorithm to visit all nodes in the digraph.
1697    ///
1698    /// This method runs the %BFS algorithm in order to
1699    /// compute the shortest path to each node.
1700    ///
1701    /// The algorithm computes
1702    /// - the shortest path tree (forest),
1703    /// - the distance of each node from the root(s).
1704    ///
1705    /// \note <tt>b.run(s)</tt> is just a shortcut of the following code.
1706    ///\code
1707    ///  b.init();
1708    ///  for (NodeIt n(gr); n != INVALID; ++n) {
1709    ///    if (!b.reached(n)) {
1710    ///      b.addSource(n);
1711    ///      b.start();
1712    ///    }
1713    ///  }
1714    ///\endcode
1715    void run() {
1716      init();
1717      for (NodeIt it(*_digraph); it != INVALID; ++it) {
1718        if (!reached(it)) {
1719          addSource(it);
1720          start();
1721        }
1722      }
1723    }
1724
1725    ///@}
1726
1727    /// \name Query Functions
1728    /// The results of the BFS algorithm can be obtained using these
1729    /// functions.\n
1730    /// Either \ref run(Node) "run()" or \ref start() should be called
1731    /// before using them.
1732
1733    ///@{
1734
1735    /// \brief Checks if the given node is reached from the root(s).
1736    ///
1737    /// Returns \c true if \c v is reached from the root(s).
1738    ///
1739    /// \pre Either \ref run(Node) "run()" or \ref init()
1740    /// must be called before using this function.
1741    bool reached(Node v) const { return (*_reached)[v]; }
1742
1743    ///@}
1744
1745  };
1746
1747} //END OF NAMESPACE LEMON
1748
1749#endif
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