lemon/bfs.h
author Alpar Juttner <alpar@cs.elte.hu>
Thu, 04 Aug 2011 22:00:57 +0200
changeset 924 3dcb45a871c3
parent 292 e7af73f1805e
child 329 d900fd1e760f
permissions -rw-r--r--
Update the AUTHORS file
     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) 2003-2008
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    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 
    33 namespace 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 meet the \ref concepts::WriteMap "WriteMap" concept.
    51     typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
    52     ///Instantiates a PredMap.
    53 
    54     ///This function instantiates a PredMap.
    55     ///\param g is the digraph, to which we would like to define the
    56     ///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 meet the \ref concepts::WriteMap "WriteMap" concept.
    66     typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
    67     ///Instantiates a ProcessedMap.
    68 
    69     ///This function instantiates a ProcessedMap.
    70     ///\param g is the digraph, to which
    71     ///we would like to define the ProcessedMap
    72 #ifdef DOXYGEN
    73     static ProcessedMap *createProcessedMap(const Digraph &g)
    74 #else
    75     static ProcessedMap *createProcessedMap(const Digraph &)
    76 #endif
    77     {
    78       return new ProcessedMap();
    79     }
    80 
    81     ///The type of the map that indicates which nodes are reached.
    82 
    83     ///The type of the map that indicates which nodes are reached.
    84     ///It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
    85     typedef typename Digraph::template NodeMap<bool> ReachedMap;
    86     ///Instantiates a ReachedMap.
    87 
    88     ///This function instantiates a ReachedMap.
    89     ///\param g is the digraph, to which
    90     ///we would like to define the ReachedMap.
    91     static ReachedMap *createReachedMap(const Digraph &g)
    92     {
    93       return new ReachedMap(g);
    94     }
    95 
    96     ///The type of the map that stores the distances of the nodes.
    97 
    98     ///The type of the map that stores the distances of the nodes.
    99     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   100     typedef typename Digraph::template NodeMap<int> DistMap;
   101     ///Instantiates a DistMap.
   102 
   103     ///This function instantiates a DistMap.
   104     ///\param g is the digraph, to which we would like to define the
   105     ///DistMap.
   106     static DistMap *createDistMap(const Digraph &g)
   107     {
   108       return new DistMap(g);
   109     }
   110   };
   111 
   112   ///%BFS algorithm class.
   113 
   114   ///\ingroup search
   115   ///This class provides an efficient implementation of the %BFS algorithm.
   116   ///
   117   ///There is also a \ref bfs() "function-type interface" for the BFS
   118   ///algorithm, which is convenient in the simplier cases and it can be
   119   ///used easier.
   120   ///
   121   ///\tparam GR The type of the digraph the algorithm runs on.
   122   ///The default value is \ref ListDigraph. The value of GR is not used
   123   ///directly by \ref Bfs, it is only passed to \ref BfsDefaultTraits.
   124   ///\tparam TR Traits class to set various data types used by the algorithm.
   125   ///The default traits class is
   126   ///\ref BfsDefaultTraits "BfsDefaultTraits<GR>".
   127   ///See \ref BfsDefaultTraits for the documentation of
   128   ///a Bfs traits class.
   129 #ifdef DOXYGEN
   130   template <typename GR,
   131             typename TR>
   132 #else
   133   template <typename GR=ListDigraph,
   134             typename TR=BfsDefaultTraits<GR> >
   135 #endif
   136   class Bfs {
   137   public:
   138 
   139     ///The type of the digraph the algorithm runs on.
   140     typedef typename TR::Digraph Digraph;
   141 
   142     ///\brief The type of the map that stores the predecessor arcs of the
   143     ///shortest paths.
   144     typedef typename TR::PredMap PredMap;
   145     ///The type of the map that stores the distances of the nodes.
   146     typedef typename TR::DistMap DistMap;
   147     ///The type of the map that indicates which nodes are reached.
   148     typedef typename TR::ReachedMap ReachedMap;
   149     ///The type of the map that indicates which nodes are processed.
   150     typedef typename TR::ProcessedMap ProcessedMap;
   151     ///The type of the paths.
   152     typedef PredMapPath<Digraph, PredMap> Path;
   153 
   154     ///The traits class.
   155     typedef TR Traits;
   156 
   157   private:
   158 
   159     typedef typename Digraph::Node Node;
   160     typedef typename Digraph::NodeIt NodeIt;
   161     typedef typename Digraph::Arc Arc;
   162     typedef typename Digraph::OutArcIt OutArcIt;
   163 
   164     //Pointer to the underlying digraph.
   165     const Digraph *G;
   166     //Pointer to the map of predecessor arcs.
   167     PredMap *_pred;
   168     //Indicates if _pred is locally allocated (true) or not.
   169     bool local_pred;
   170     //Pointer to the map of distances.
   171     DistMap *_dist;
   172     //Indicates if _dist is locally allocated (true) or not.
   173     bool local_dist;
   174     //Pointer to the map of reached status of the nodes.
   175     ReachedMap *_reached;
   176     //Indicates if _reached is locally allocated (true) or not.
   177     bool local_reached;
   178     //Pointer to the map of processed status of the nodes.
   179     ProcessedMap *_processed;
   180     //Indicates if _processed is locally allocated (true) or not.
   181     bool local_processed;
   182 
   183     std::vector<typename Digraph::Node> _queue;
   184     int _queue_head,_queue_tail,_queue_next_dist;
   185     int _curr_dist;
   186 
   187     //Creates the maps if necessary.
   188     void create_maps()
   189     {
   190       if(!_pred) {
   191         local_pred = true;
   192         _pred = Traits::createPredMap(*G);
   193       }
   194       if(!_dist) {
   195         local_dist = true;
   196         _dist = Traits::createDistMap(*G);
   197       }
   198       if(!_reached) {
   199         local_reached = true;
   200         _reached = Traits::createReachedMap(*G);
   201       }
   202       if(!_processed) {
   203         local_processed = true;
   204         _processed = Traits::createProcessedMap(*G);
   205       }
   206     }
   207 
   208   protected:
   209 
   210     Bfs() {}
   211 
   212   public:
   213 
   214     typedef Bfs Create;
   215 
   216     ///\name Named template parameters
   217 
   218     ///@{
   219 
   220     template <class T>
   221     struct SetPredMapTraits : public Traits {
   222       typedef T PredMap;
   223       static PredMap *createPredMap(const Digraph &)
   224       {
   225         LEMON_ASSERT(false, "PredMap is not initialized");
   226         return 0; // ignore warnings
   227       }
   228     };
   229     ///\brief \ref named-templ-param "Named parameter" for setting
   230     ///PredMap type.
   231     ///
   232     ///\ref named-templ-param "Named parameter" for setting
   233     ///PredMap type.
   234     template <class T>
   235     struct SetPredMap : public Bfs< Digraph, SetPredMapTraits<T> > {
   236       typedef Bfs< Digraph, SetPredMapTraits<T> > Create;
   237     };
   238 
   239     template <class T>
   240     struct SetDistMapTraits : public Traits {
   241       typedef T DistMap;
   242       static DistMap *createDistMap(const Digraph &)
   243       {
   244         LEMON_ASSERT(false, "DistMap is not initialized");
   245         return 0; // ignore warnings
   246       }
   247     };
   248     ///\brief \ref named-templ-param "Named parameter" for setting
   249     ///DistMap type.
   250     ///
   251     ///\ref named-templ-param "Named parameter" for setting
   252     ///DistMap type.
   253     template <class T>
   254     struct SetDistMap : public Bfs< Digraph, SetDistMapTraits<T> > {
   255       typedef Bfs< Digraph, SetDistMapTraits<T> > Create;
   256     };
   257 
   258     template <class T>
   259     struct SetReachedMapTraits : public Traits {
   260       typedef T ReachedMap;
   261       static ReachedMap *createReachedMap(const Digraph &)
   262       {
   263         LEMON_ASSERT(false, "ReachedMap is not initialized");
   264         return 0; // ignore warnings
   265       }
   266     };
   267     ///\brief \ref named-templ-param "Named parameter" for setting
   268     ///ReachedMap type.
   269     ///
   270     ///\ref named-templ-param "Named parameter" for setting
   271     ///ReachedMap type.
   272     template <class T>
   273     struct SetReachedMap : public Bfs< Digraph, SetReachedMapTraits<T> > {
   274       typedef Bfs< Digraph, SetReachedMapTraits<T> > Create;
   275     };
   276 
   277     template <class T>
   278     struct SetProcessedMapTraits : public Traits {
   279       typedef T ProcessedMap;
   280       static ProcessedMap *createProcessedMap(const Digraph &)
   281       {
   282         LEMON_ASSERT(false, "ProcessedMap is not initialized");
   283         return 0; // ignore warnings
   284       }
   285     };
   286     ///\brief \ref named-templ-param "Named parameter" for setting
   287     ///ProcessedMap type.
   288     ///
   289     ///\ref named-templ-param "Named parameter" for setting
   290     ///ProcessedMap type.
   291     template <class T>
   292     struct SetProcessedMap : public Bfs< Digraph, SetProcessedMapTraits<T> > {
   293       typedef Bfs< Digraph, SetProcessedMapTraits<T> > Create;
   294     };
   295 
   296     struct SetStandardProcessedMapTraits : public Traits {
   297       typedef typename Digraph::template NodeMap<bool> ProcessedMap;
   298       static ProcessedMap *createProcessedMap(const Digraph &g)
   299       {
   300         return new ProcessedMap(g);
   301         return 0; // ignore warnings
   302       }
   303     };
   304     ///\brief \ref named-templ-param "Named parameter" for setting
   305     ///ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
   306     ///
   307     ///\ref named-templ-param "Named parameter" for setting
   308     ///ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
   309     ///If you don't set it explicitly, it will be automatically allocated.
   310     struct SetStandardProcessedMap :
   311       public Bfs< Digraph, SetStandardProcessedMapTraits > {
   312       typedef Bfs< Digraph, SetStandardProcessedMapTraits > Create;
   313     };
   314 
   315     ///@}
   316 
   317   public:
   318 
   319     ///Constructor.
   320 
   321     ///Constructor.
   322     ///\param g The digraph the algorithm runs on.
   323     Bfs(const Digraph &g) :
   324       G(&g),
   325       _pred(NULL), local_pred(false),
   326       _dist(NULL), local_dist(false),
   327       _reached(NULL), local_reached(false),
   328       _processed(NULL), local_processed(false)
   329     { }
   330 
   331     ///Destructor.
   332     ~Bfs()
   333     {
   334       if(local_pred) delete _pred;
   335       if(local_dist) delete _dist;
   336       if(local_reached) delete _reached;
   337       if(local_processed) delete _processed;
   338     }
   339 
   340     ///Sets the map that stores the predecessor arcs.
   341 
   342     ///Sets the map that stores the predecessor arcs.
   343     ///If you don't use this function before calling \ref run(),
   344     ///it will allocate one. The destructor deallocates this
   345     ///automatically allocated map, 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(),
   361     ///it will allocate one. The destructor deallocates this
   362     ///automatically allocated map, of course.
   363     ///\return <tt> (*this) </tt>
   364     Bfs &reachedMap(ReachedMap &m)
   365     {
   366       if(local_reached) {
   367         delete _reached;
   368         local_reached=false;
   369       }
   370       _reached = &m;
   371       return *this;
   372     }
   373 
   374     ///Sets the map that indicates which nodes are processed.
   375 
   376     ///Sets the map that indicates which nodes are processed.
   377     ///If you don't use this function before calling \ref run(),
   378     ///it will allocate one. The destructor deallocates this
   379     ///automatically allocated map, of course.
   380     ///\return <tt> (*this) </tt>
   381     Bfs &processedMap(ProcessedMap &m)
   382     {
   383       if(local_processed) {
   384         delete _processed;
   385         local_processed=false;
   386       }
   387       _processed = &m;
   388       return *this;
   389     }
   390 
   391     ///Sets the map that stores the distances of the nodes.
   392 
   393     ///Sets the map that stores the distances of the nodes calculated by
   394     ///the algorithm.
   395     ///If you don't use this function before calling \ref run(),
   396     ///it will allocate one. The destructor deallocates this
   397     ///automatically allocated map, of course.
   398     ///\return <tt> (*this) </tt>
   399     Bfs &distMap(DistMap &m)
   400     {
   401       if(local_dist) {
   402         delete _dist;
   403         local_dist=false;
   404       }
   405       _dist = &m;
   406       return *this;
   407     }
   408 
   409   public:
   410 
   411     ///\name Execution control
   412     ///The simplest way to execute the algorithm is to use
   413     ///one of the member functions called \ref lemon::Bfs::run() "run()".
   414     ///\n
   415     ///If you need more control on the execution, first you must call
   416     ///\ref lemon::Bfs::init() "init()", then you can add several source
   417     ///nodes with \ref lemon::Bfs::addSource() "addSource()".
   418     ///Finally \ref lemon::Bfs::start() "start()" will perform the
   419     ///actual path computation.
   420 
   421     ///@{
   422 
   423     ///Initializes the internal data structures.
   424 
   425     ///Initializes the internal data structures.
   426     ///
   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     ///\brief Returns \c false if there are nodes
   561     ///to be processed.
   562     ///
   563     ///Returns \c false if there are nodes
   564     ///to be processed in the queue.
   565     bool emptyQueue() const { return _queue_tail==_queue_head; }
   566 
   567     ///Returns the number of the nodes to be processed.
   568 
   569     ///Returns the number of the nodes to be processed 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 result of the %BFS algorithm can be obtained using these
   735     ///functions.\n
   736     ///Either \ref lemon::Bfs::run() "run()" or \ref lemon::Bfs::start()
   737     ///"start()" must be called before using them.
   738 
   739     ///@{
   740 
   741     ///The shortest path to a node.
   742 
   743     ///Returns the shortest path to a node.
   744     ///
   745     ///\warning \c t should be reachable from the root(s).
   746     ///
   747     ///\pre Either \ref run() or \ref start() must be called before
   748     ///using this function.
   749     Path path(Node t) const { return Path(*G, *_pred, t); }
   750 
   751     ///The distance of a node from the root(s).
   752 
   753     ///Returns the distance of a node from the root(s).
   754     ///
   755     ///\warning If node \c v is not reachable from the root(s), then
   756     ///the return value of this function is undefined.
   757     ///
   758     ///\pre Either \ref run() or \ref start() must be called before
   759     ///using this function.
   760     int dist(Node v) const { return (*_dist)[v]; }
   761 
   762     ///Returns the 'previous arc' of the shortest path tree for a node.
   763 
   764     ///This function returns the 'previous arc' of the shortest path
   765     ///tree for the node \c v, i.e. it returns the last arc of a
   766     ///shortest path from the root(s) to \c v. It is \c INVALID if \c v
   767     ///is not reachable from the root(s) or if \c v is a root.
   768     ///
   769     ///The shortest path tree used here is equal to the shortest path
   770     ///tree used in \ref predNode().
   771     ///
   772     ///\pre Either \ref run() or \ref start() must be called before
   773     ///using this function.
   774     Arc predArc(Node v) const { return (*_pred)[v];}
   775 
   776     ///Returns the 'previous node' of the shortest path tree for a node.
   777 
   778     ///This function returns the 'previous node' of the shortest path
   779     ///tree for the node \c v, i.e. it returns the last but one node
   780     ///from a shortest path from the root(s) to \c v. It is \c INVALID
   781     ///if \c v is not reachable from the root(s) or if \c v is a root.
   782     ///
   783     ///The shortest path tree used here is equal to the shortest path
   784     ///tree used in \ref predArc().
   785     ///
   786     ///\pre Either \ref run() or \ref start() must be called before
   787     ///using this function.
   788     Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
   789                                   G->source((*_pred)[v]); }
   790 
   791     ///\brief Returns a const reference to the node map that stores the
   792     /// distances of the nodes.
   793     ///
   794     ///Returns a const reference to the node map that stores the distances
   795     ///of the nodes calculated by the algorithm.
   796     ///
   797     ///\pre Either \ref run() or \ref init()
   798     ///must be called before using this function.
   799     const DistMap &distMap() const { return *_dist;}
   800 
   801     ///\brief Returns a const reference to the node map that stores the
   802     ///predecessor arcs.
   803     ///
   804     ///Returns a const reference to the node map that stores the predecessor
   805     ///arcs, which form the shortest path tree.
   806     ///
   807     ///\pre Either \ref run() or \ref init()
   808     ///must be called before using this function.
   809     const PredMap &predMap() const { return *_pred;}
   810 
   811     ///Checks if a node is reachable from the root(s).
   812 
   813     ///Returns \c true if \c v is reachable from the root(s).
   814     ///\pre Either \ref run() or \ref start()
   815     ///must be called before using this function.
   816     bool reached(Node v) const { return (*_reached)[v]; }
   817 
   818     ///@}
   819   };
   820 
   821   ///Default traits class of bfs() function.
   822 
   823   ///Default traits class of bfs() function.
   824   ///\tparam GR Digraph type.
   825   template<class GR>
   826   struct BfsWizardDefaultTraits
   827   {
   828     ///The type of the digraph the algorithm runs on.
   829     typedef GR Digraph;
   830 
   831     ///\brief The type of the map that stores the predecessor
   832     ///arcs of the shortest paths.
   833     ///
   834     ///The type of the map that stores the predecessor
   835     ///arcs of the shortest paths.
   836     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   837     typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
   838     ///Instantiates a PredMap.
   839 
   840     ///This function instantiates a PredMap.
   841     ///\param g is the digraph, to which we would like to define the
   842     ///PredMap.
   843     static PredMap *createPredMap(const Digraph &g)
   844     {
   845       return new PredMap(g);
   846     }
   847 
   848     ///The type of the map that indicates which nodes are processed.
   849 
   850     ///The type of the map that indicates which nodes are processed.
   851     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   852     ///By default it is a NullMap.
   853     typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
   854     ///Instantiates a ProcessedMap.
   855 
   856     ///This function instantiates a ProcessedMap.
   857     ///\param g is the digraph, to which
   858     ///we would like to define the ProcessedMap.
   859 #ifdef DOXYGEN
   860     static ProcessedMap *createProcessedMap(const Digraph &g)
   861 #else
   862     static ProcessedMap *createProcessedMap(const Digraph &)
   863 #endif
   864     {
   865       return new ProcessedMap();
   866     }
   867 
   868     ///The type of the map that indicates which nodes are reached.
   869 
   870     ///The type of the map that indicates which nodes are reached.
   871     ///It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
   872     typedef typename Digraph::template NodeMap<bool> ReachedMap;
   873     ///Instantiates a ReachedMap.
   874 
   875     ///This function instantiates a ReachedMap.
   876     ///\param g is the digraph, to which
   877     ///we would like to define the ReachedMap.
   878     static ReachedMap *createReachedMap(const Digraph &g)
   879     {
   880       return new ReachedMap(g);
   881     }
   882 
   883     ///The type of the map that stores the distances of the nodes.
   884 
   885     ///The type of the map that stores the distances of the nodes.
   886     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   887     typedef typename Digraph::template NodeMap<int> DistMap;
   888     ///Instantiates a DistMap.
   889 
   890     ///This function instantiates a DistMap.
   891     ///\param g is the digraph, to which we would like to define
   892     ///the DistMap
   893     static DistMap *createDistMap(const Digraph &g)
   894     {
   895       return new DistMap(g);
   896     }
   897 
   898     ///The type of the shortest paths.
   899 
   900     ///The type of the shortest paths.
   901     ///It must meet the \ref concepts::Path "Path" concept.
   902     typedef lemon::Path<Digraph> Path;
   903   };
   904 
   905   /// Default traits class used by BfsWizard
   906 
   907   /// To make it easier to use Bfs algorithm
   908   /// we have created a wizard class.
   909   /// This \ref BfsWizard class needs default traits,
   910   /// as well as the \ref Bfs class.
   911   /// The \ref BfsWizardBase is a class to be the default traits of the
   912   /// \ref BfsWizard class.
   913   template<class GR>
   914   class BfsWizardBase : public BfsWizardDefaultTraits<GR>
   915   {
   916 
   917     typedef BfsWizardDefaultTraits<GR> Base;
   918   protected:
   919     //The type of the nodes in the digraph.
   920     typedef typename Base::Digraph::Node Node;
   921 
   922     //Pointer to the digraph the algorithm runs on.
   923     void *_g;
   924     //Pointer to the map of reached nodes.
   925     void *_reached;
   926     //Pointer to the map of processed nodes.
   927     void *_processed;
   928     //Pointer to the map of predecessors arcs.
   929     void *_pred;
   930     //Pointer to the map of distances.
   931     void *_dist;
   932     //Pointer to the shortest path to the target node.
   933     void *_path;
   934     //Pointer to the distance of the target node.
   935     int *_di;
   936 
   937     public:
   938     /// Constructor.
   939 
   940     /// This constructor does not require parameters, therefore it initiates
   941     /// all of the attributes to \c 0.
   942     BfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0),
   943                       _dist(0), _path(0), _di(0) {}
   944 
   945     /// Constructor.
   946 
   947     /// This constructor requires one parameter,
   948     /// others are initiated to \c 0.
   949     /// \param g The digraph the algorithm runs on.
   950     BfsWizardBase(const GR &g) :
   951       _g(reinterpret_cast<void*>(const_cast<GR*>(&g))),
   952       _reached(0), _processed(0), _pred(0), _dist(0),  _path(0), _di(0) {}
   953 
   954   };
   955 
   956   /// Auxiliary class for the function-type interface of BFS algorithm.
   957 
   958   /// This auxiliary class is created to implement the
   959   /// \ref bfs() "function-type interface" of \ref Bfs algorithm.
   960   /// It does not have own \ref run() method, it uses the functions
   961   /// and features of the plain \ref Bfs.
   962   ///
   963   /// This class should only be used through the \ref bfs() function,
   964   /// which makes it easier to use the algorithm.
   965   template<class TR>
   966   class BfsWizard : public TR
   967   {
   968     typedef TR Base;
   969 
   970     ///The type of the digraph the algorithm runs on.
   971     typedef typename TR::Digraph Digraph;
   972 
   973     typedef typename Digraph::Node Node;
   974     typedef typename Digraph::NodeIt NodeIt;
   975     typedef typename Digraph::Arc Arc;
   976     typedef typename Digraph::OutArcIt OutArcIt;
   977 
   978     ///\brief The type of the map that stores the predecessor
   979     ///arcs of the shortest paths.
   980     typedef typename TR::PredMap PredMap;
   981     ///\brief The type of the map that stores the distances of the nodes.
   982     typedef typename TR::DistMap DistMap;
   983     ///\brief The type of the map that indicates which nodes are reached.
   984     typedef typename TR::ReachedMap ReachedMap;
   985     ///\brief The type of the map that indicates which nodes are processed.
   986     typedef typename TR::ProcessedMap ProcessedMap;
   987     ///The type of the shortest paths
   988     typedef typename TR::Path Path;
   989 
   990   public:
   991 
   992     /// Constructor.
   993     BfsWizard() : TR() {}
   994 
   995     /// Constructor that requires parameters.
   996 
   997     /// Constructor that requires parameters.
   998     /// These parameters will be the default values for the traits class.
   999     /// \param g The digraph the algorithm runs on.
  1000     BfsWizard(const Digraph &g) :
  1001       TR(g) {}
  1002 
  1003     ///Copy constructor
  1004     BfsWizard(const TR &b) : TR(b) {}
  1005 
  1006     ~BfsWizard() {}
  1007 
  1008     ///Runs BFS algorithm from the given source node.
  1009 
  1010     ///This method runs BFS algorithm from node \c s
  1011     ///in order to compute the shortest path to each node.
  1012     void run(Node s)
  1013     {
  1014       Bfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
  1015       if (Base::_pred)
  1016         alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
  1017       if (Base::_dist)
  1018         alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
  1019       if (Base::_reached)
  1020         alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
  1021       if (Base::_processed)
  1022         alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
  1023       if (s!=INVALID)
  1024         alg.run(s);
  1025       else
  1026         alg.run();
  1027     }
  1028 
  1029     ///Finds the shortest path between \c s and \c t.
  1030 
  1031     ///This method runs BFS algorithm from node \c s
  1032     ///in order to compute the shortest path to node \c t
  1033     ///(it stops searching when \c t is processed).
  1034     ///
  1035     ///\return \c true if \c t is reachable form \c s.
  1036     bool run(Node s, Node t)
  1037     {
  1038       Bfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
  1039       if (Base::_pred)
  1040         alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
  1041       if (Base::_dist)
  1042         alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
  1043       if (Base::_reached)
  1044         alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
  1045       if (Base::_processed)
  1046         alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
  1047       alg.run(s,t);
  1048       if (Base::_path)
  1049         *reinterpret_cast<Path*>(Base::_path) = alg.path(t);
  1050       if (Base::_di)
  1051         *Base::_di = alg.dist(t);
  1052       return alg.reached(t);
  1053     }
  1054 
  1055     ///Runs BFS algorithm to visit all nodes in the digraph.
  1056 
  1057     ///This method runs BFS algorithm in order to compute
  1058     ///the shortest path to each node.
  1059     void run()
  1060     {
  1061       run(INVALID);
  1062     }
  1063 
  1064     template<class T>
  1065     struct SetPredMapBase : public Base {
  1066       typedef T PredMap;
  1067       static PredMap *createPredMap(const Digraph &) { return 0; };
  1068       SetPredMapBase(const TR &b) : TR(b) {}
  1069     };
  1070     ///\brief \ref named-func-param "Named parameter"
  1071     ///for setting PredMap object.
  1072     ///
  1073     ///\ref named-func-param "Named parameter"
  1074     ///for setting PredMap object.
  1075     template<class T>
  1076     BfsWizard<SetPredMapBase<T> > predMap(const T &t)
  1077     {
  1078       Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
  1079       return BfsWizard<SetPredMapBase<T> >(*this);
  1080     }
  1081 
  1082     template<class T>
  1083     struct SetReachedMapBase : public Base {
  1084       typedef T ReachedMap;
  1085       static ReachedMap *createReachedMap(const Digraph &) { return 0; };
  1086       SetReachedMapBase(const TR &b) : TR(b) {}
  1087     };
  1088     ///\brief \ref named-func-param "Named parameter"
  1089     ///for setting ReachedMap object.
  1090     ///
  1091     /// \ref named-func-param "Named parameter"
  1092     ///for setting ReachedMap object.
  1093     template<class T>
  1094     BfsWizard<SetReachedMapBase<T> > reachedMap(const T &t)
  1095     {
  1096       Base::_reached=reinterpret_cast<void*>(const_cast<T*>(&t));
  1097       return BfsWizard<SetReachedMapBase<T> >(*this);
  1098     }
  1099 
  1100     template<class T>
  1101     struct SetDistMapBase : public Base {
  1102       typedef T DistMap;
  1103       static DistMap *createDistMap(const Digraph &) { return 0; };
  1104       SetDistMapBase(const TR &b) : TR(b) {}
  1105     };
  1106     ///\brief \ref named-func-param "Named parameter"
  1107     ///for setting DistMap object.
  1108     ///
  1109     /// \ref named-func-param "Named parameter"
  1110     ///for setting DistMap object.
  1111     template<class T>
  1112     BfsWizard<SetDistMapBase<T> > distMap(const T &t)
  1113     {
  1114       Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
  1115       return BfsWizard<SetDistMapBase<T> >(*this);
  1116     }
  1117 
  1118     template<class T>
  1119     struct SetProcessedMapBase : public Base {
  1120       typedef T ProcessedMap;
  1121       static ProcessedMap *createProcessedMap(const Digraph &) { return 0; };
  1122       SetProcessedMapBase(const TR &b) : TR(b) {}
  1123     };
  1124     ///\brief \ref named-func-param "Named parameter"
  1125     ///for setting ProcessedMap object.
  1126     ///
  1127     /// \ref named-func-param "Named parameter"
  1128     ///for setting ProcessedMap object.
  1129     template<class T>
  1130     BfsWizard<SetProcessedMapBase<T> > processedMap(const T &t)
  1131     {
  1132       Base::_processed=reinterpret_cast<void*>(const_cast<T*>(&t));
  1133       return BfsWizard<SetProcessedMapBase<T> >(*this);
  1134     }
  1135 
  1136     template<class T>
  1137     struct SetPathBase : public Base {
  1138       typedef T Path;
  1139       SetPathBase(const TR &b) : TR(b) {}
  1140     };
  1141     ///\brief \ref named-func-param "Named parameter"
  1142     ///for getting the shortest path to the target node.
  1143     ///
  1144     ///\ref named-func-param "Named parameter"
  1145     ///for getting the shortest path to the target node.
  1146     template<class T>
  1147     BfsWizard<SetPathBase<T> > path(const T &t)
  1148     {
  1149       Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t));
  1150       return BfsWizard<SetPathBase<T> >(*this);
  1151     }
  1152 
  1153     ///\brief \ref named-func-param "Named parameter"
  1154     ///for getting the distance of the target node.
  1155     ///
  1156     ///\ref named-func-param "Named parameter"
  1157     ///for getting the distance of the target node.
  1158     BfsWizard dist(const int &d)
  1159     {
  1160       Base::_di=const_cast<int*>(&d);
  1161       return *this;
  1162     }
  1163 
  1164   };
  1165 
  1166   ///Function-type interface for BFS algorithm.
  1167 
  1168   /// \ingroup search
  1169   ///Function-type interface for BFS algorithm.
  1170   ///
  1171   ///This function also has several \ref named-func-param "named parameters",
  1172   ///they are declared as the members of class \ref BfsWizard.
  1173   ///The following examples show how to use these parameters.
  1174   ///\code
  1175   ///  // Compute shortest path from node s to each node
  1176   ///  bfs(g).predMap(preds).distMap(dists).run(s);
  1177   ///
  1178   ///  // Compute shortest path from s to t
  1179   ///  bool reached = bfs(g).path(p).dist(d).run(s,t);
  1180   ///\endcode
  1181   ///\warning Don't forget to put the \ref BfsWizard::run() "run()"
  1182   ///to the end of the parameter list.
  1183   ///\sa BfsWizard
  1184   ///\sa Bfs
  1185   template<class GR>
  1186   BfsWizard<BfsWizardBase<GR> >
  1187   bfs(const GR &digraph)
  1188   {
  1189     return BfsWizard<BfsWizardBase<GR> >(digraph);
  1190   }
  1191 
  1192 #ifdef DOXYGEN
  1193   /// \brief Visitor class for BFS.
  1194   ///
  1195   /// This class defines the interface of the BfsVisit events, and
  1196   /// it could be the base of a real visitor class.
  1197   template <typename _Digraph>
  1198   struct BfsVisitor {
  1199     typedef _Digraph Digraph;
  1200     typedef typename Digraph::Arc Arc;
  1201     typedef typename Digraph::Node Node;
  1202     /// \brief Called for the source node(s) of the BFS.
  1203     ///
  1204     /// This function is called for the source node(s) of the BFS.
  1205     void start(const Node& node) {}
  1206     /// \brief Called when a node is reached first time.
  1207     ///
  1208     /// This function is called when a node is reached first time.
  1209     void reach(const Node& node) {}
  1210     /// \brief Called when a node is processed.
  1211     ///
  1212     /// This function is called when a node is processed.
  1213     void process(const Node& node) {}
  1214     /// \brief Called when an arc reaches a new node.
  1215     ///
  1216     /// This function is called when the BFS finds an arc whose target node
  1217     /// is not reached yet.
  1218     void discover(const Arc& arc) {}
  1219     /// \brief Called when an arc is examined but its target node is
  1220     /// already discovered.
  1221     ///
  1222     /// This function is called when an arc is examined but its target node is
  1223     /// already discovered.
  1224     void examine(const Arc& arc) {}
  1225   };
  1226 #else
  1227   template <typename _Digraph>
  1228   struct BfsVisitor {
  1229     typedef _Digraph Digraph;
  1230     typedef typename Digraph::Arc Arc;
  1231     typedef typename Digraph::Node Node;
  1232     void start(const Node&) {}
  1233     void reach(const Node&) {}
  1234     void process(const Node&) {}
  1235     void discover(const Arc&) {}
  1236     void examine(const Arc&) {}
  1237 
  1238     template <typename _Visitor>
  1239     struct Constraints {
  1240       void constraints() {
  1241         Arc arc;
  1242         Node node;
  1243         visitor.start(node);
  1244         visitor.reach(node);
  1245         visitor.process(node);
  1246         visitor.discover(arc);
  1247         visitor.examine(arc);
  1248       }
  1249       _Visitor& visitor;
  1250     };
  1251   };
  1252 #endif
  1253 
  1254   /// \brief Default traits class of BfsVisit class.
  1255   ///
  1256   /// Default traits class of BfsVisit class.
  1257   /// \tparam _Digraph The type of the digraph the algorithm runs on.
  1258   template<class _Digraph>
  1259   struct BfsVisitDefaultTraits {
  1260 
  1261     /// \brief The type of the digraph the algorithm runs on.
  1262     typedef _Digraph Digraph;
  1263 
  1264     /// \brief The type of the map that indicates which nodes are reached.
  1265     ///
  1266     /// The type of the map that indicates which nodes are reached.
  1267     /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
  1268     typedef typename Digraph::template NodeMap<bool> ReachedMap;
  1269 
  1270     /// \brief Instantiates a ReachedMap.
  1271     ///
  1272     /// This function instantiates a ReachedMap.
  1273     /// \param digraph is the digraph, to which
  1274     /// we would like to define the ReachedMap.
  1275     static ReachedMap *createReachedMap(const Digraph &digraph) {
  1276       return new ReachedMap(digraph);
  1277     }
  1278 
  1279   };
  1280 
  1281   /// \ingroup search
  1282   ///
  1283   /// \brief %BFS algorithm class with visitor interface.
  1284   ///
  1285   /// This class provides an efficient implementation of the %BFS algorithm
  1286   /// with visitor interface.
  1287   ///
  1288   /// The %BfsVisit class provides an alternative interface to the Bfs
  1289   /// class. It works with callback mechanism, the BfsVisit object calls
  1290   /// the member functions of the \c Visitor class on every BFS event.
  1291   ///
  1292   /// This interface of the BFS algorithm should be used in special cases
  1293   /// when extra actions have to be performed in connection with certain
  1294   /// events of the BFS algorithm. Otherwise consider to use Bfs or bfs()
  1295   /// instead.
  1296   ///
  1297   /// \tparam _Digraph The type of the digraph the algorithm runs on.
  1298   /// The default value is
  1299   /// \ref ListDigraph. The value of _Digraph is not used directly by
  1300   /// \ref BfsVisit, it is only passed to \ref BfsVisitDefaultTraits.
  1301   /// \tparam _Visitor The Visitor type that is used by the algorithm.
  1302   /// \ref BfsVisitor "BfsVisitor<_Digraph>" is an empty visitor, which
  1303   /// does not observe the BFS events. If you want to observe the BFS
  1304   /// events, you should implement your own visitor class.
  1305   /// \tparam _Traits Traits class to set various data types used by the
  1306   /// algorithm. The default traits class is
  1307   /// \ref BfsVisitDefaultTraits "BfsVisitDefaultTraits<_Digraph>".
  1308   /// See \ref BfsVisitDefaultTraits for the documentation of
  1309   /// a BFS visit traits class.
  1310 #ifdef DOXYGEN
  1311   template <typename _Digraph, typename _Visitor, typename _Traits>
  1312 #else
  1313   template <typename _Digraph = ListDigraph,
  1314             typename _Visitor = BfsVisitor<_Digraph>,
  1315             typename _Traits = BfsVisitDefaultTraits<_Digraph> >
  1316 #endif
  1317   class BfsVisit {
  1318   public:
  1319 
  1320     ///The traits class.
  1321     typedef _Traits Traits;
  1322 
  1323     ///The type of the digraph the algorithm runs on.
  1324     typedef typename Traits::Digraph Digraph;
  1325 
  1326     ///The visitor type used by the algorithm.
  1327     typedef _Visitor Visitor;
  1328 
  1329     ///The type of the map that indicates which nodes are reached.
  1330     typedef typename Traits::ReachedMap ReachedMap;
  1331 
  1332   private:
  1333 
  1334     typedef typename Digraph::Node Node;
  1335     typedef typename Digraph::NodeIt NodeIt;
  1336     typedef typename Digraph::Arc Arc;
  1337     typedef typename Digraph::OutArcIt OutArcIt;
  1338 
  1339     //Pointer to the underlying digraph.
  1340     const Digraph *_digraph;
  1341     //Pointer to the visitor object.
  1342     Visitor *_visitor;
  1343     //Pointer to the map of reached status of the nodes.
  1344     ReachedMap *_reached;
  1345     //Indicates if _reached is locally allocated (true) or not.
  1346     bool local_reached;
  1347 
  1348     std::vector<typename Digraph::Node> _list;
  1349     int _list_front, _list_back;
  1350 
  1351     //Creates the maps if necessary.
  1352     void create_maps() {
  1353       if(!_reached) {
  1354         local_reached = true;
  1355         _reached = Traits::createReachedMap(*_digraph);
  1356       }
  1357     }
  1358 
  1359   protected:
  1360 
  1361     BfsVisit() {}
  1362 
  1363   public:
  1364 
  1365     typedef BfsVisit Create;
  1366 
  1367     /// \name Named template parameters
  1368 
  1369     ///@{
  1370     template <class T>
  1371     struct SetReachedMapTraits : public Traits {
  1372       typedef T ReachedMap;
  1373       static ReachedMap *createReachedMap(const Digraph &digraph) {
  1374         LEMON_ASSERT(false, "ReachedMap is not initialized");
  1375         return 0; // ignore warnings
  1376       }
  1377     };
  1378     /// \brief \ref named-templ-param "Named parameter" for setting
  1379     /// ReachedMap type.
  1380     ///
  1381     /// \ref named-templ-param "Named parameter" for setting ReachedMap type.
  1382     template <class T>
  1383     struct SetReachedMap : public BfsVisit< Digraph, Visitor,
  1384                                             SetReachedMapTraits<T> > {
  1385       typedef BfsVisit< Digraph, Visitor, SetReachedMapTraits<T> > Create;
  1386     };
  1387     ///@}
  1388 
  1389   public:
  1390 
  1391     /// \brief Constructor.
  1392     ///
  1393     /// Constructor.
  1394     ///
  1395     /// \param digraph The digraph the algorithm runs on.
  1396     /// \param visitor The visitor object of the algorithm.
  1397     BfsVisit(const Digraph& digraph, Visitor& visitor)
  1398       : _digraph(&digraph), _visitor(&visitor),
  1399         _reached(0), local_reached(false) {}
  1400 
  1401     /// \brief Destructor.
  1402     ~BfsVisit() {
  1403       if(local_reached) delete _reached;
  1404     }
  1405 
  1406     /// \brief Sets the map that indicates which nodes are reached.
  1407     ///
  1408     /// Sets the map that indicates which nodes are reached.
  1409     /// If you don't use this function before calling \ref run(),
  1410     /// it will allocate one. The destructor deallocates this
  1411     /// automatically allocated map, of course.
  1412     /// \return <tt> (*this) </tt>
  1413     BfsVisit &reachedMap(ReachedMap &m) {
  1414       if(local_reached) {
  1415         delete _reached;
  1416         local_reached = false;
  1417       }
  1418       _reached = &m;
  1419       return *this;
  1420     }
  1421 
  1422   public:
  1423 
  1424     /// \name Execution control
  1425     /// The simplest way to execute the algorithm is to use
  1426     /// one of the member functions called \ref lemon::BfsVisit::run()
  1427     /// "run()".
  1428     /// \n
  1429     /// If you need more control on the execution, first you must call
  1430     /// \ref lemon::BfsVisit::init() "init()", then you can add several
  1431     /// source nodes with \ref lemon::BfsVisit::addSource() "addSource()".
  1432     /// Finally \ref lemon::BfsVisit::start() "start()" will perform the
  1433     /// actual path computation.
  1434 
  1435     /// @{
  1436 
  1437     /// \brief Initializes the internal data structures.
  1438     ///
  1439     /// Initializes the internal data structures.
  1440     void init() {
  1441       create_maps();
  1442       _list.resize(countNodes(*_digraph));
  1443       _list_front = _list_back = -1;
  1444       for (NodeIt u(*_digraph) ; u != INVALID ; ++u) {
  1445         _reached->set(u, false);
  1446       }
  1447     }
  1448 
  1449     /// \brief Adds a new source node.
  1450     ///
  1451     /// Adds a new source node to the set of nodes to be processed.
  1452     void addSource(Node s) {
  1453       if(!(*_reached)[s]) {
  1454           _reached->set(s,true);
  1455           _visitor->start(s);
  1456           _visitor->reach(s);
  1457           _list[++_list_back] = s;
  1458         }
  1459     }
  1460 
  1461     /// \brief Processes the next node.
  1462     ///
  1463     /// Processes the next node.
  1464     ///
  1465     /// \return The processed node.
  1466     ///
  1467     /// \pre The queue must not be empty.
  1468     Node processNextNode() {
  1469       Node n = _list[++_list_front];
  1470       _visitor->process(n);
  1471       Arc e;
  1472       for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
  1473         Node m = _digraph->target(e);
  1474         if (!(*_reached)[m]) {
  1475           _visitor->discover(e);
  1476           _visitor->reach(m);
  1477           _reached->set(m, true);
  1478           _list[++_list_back] = m;
  1479         } else {
  1480           _visitor->examine(e);
  1481         }
  1482       }
  1483       return n;
  1484     }
  1485 
  1486     /// \brief Processes the next node.
  1487     ///
  1488     /// Processes the next node and checks if the given target node
  1489     /// is reached. If the target node is reachable from the processed
  1490     /// node, then the \c reach parameter will be set to \c true.
  1491     ///
  1492     /// \param target The target node.
  1493     /// \retval reach Indicates if the target node is reached.
  1494     /// It should be initially \c false.
  1495     ///
  1496     /// \return The processed node.
  1497     ///
  1498     /// \pre The queue must not be empty.
  1499     Node processNextNode(Node target, bool& reach) {
  1500       Node n = _list[++_list_front];
  1501       _visitor->process(n);
  1502       Arc e;
  1503       for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
  1504         Node m = _digraph->target(e);
  1505         if (!(*_reached)[m]) {
  1506           _visitor->discover(e);
  1507           _visitor->reach(m);
  1508           _reached->set(m, true);
  1509           _list[++_list_back] = m;
  1510           reach = reach || (target == m);
  1511         } else {
  1512           _visitor->examine(e);
  1513         }
  1514       }
  1515       return n;
  1516     }
  1517 
  1518     /// \brief Processes the next node.
  1519     ///
  1520     /// Processes the next node and checks if at least one of reached
  1521     /// nodes has \c true value in the \c nm node map. If one node
  1522     /// with \c true value is reachable from the processed node, then the
  1523     /// \c rnode parameter will be set to the first of such nodes.
  1524     ///
  1525     /// \param nm A \c bool (or convertible) node map that indicates the
  1526     /// possible targets.
  1527     /// \retval rnode The reached target node.
  1528     /// It should be initially \c INVALID.
  1529     ///
  1530     /// \return The processed node.
  1531     ///
  1532     /// \pre The queue must not be empty.
  1533     template <typename NM>
  1534     Node processNextNode(const NM& nm, Node& rnode) {
  1535       Node n = _list[++_list_front];
  1536       _visitor->process(n);
  1537       Arc e;
  1538       for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
  1539         Node m = _digraph->target(e);
  1540         if (!(*_reached)[m]) {
  1541           _visitor->discover(e);
  1542           _visitor->reach(m);
  1543           _reached->set(m, true);
  1544           _list[++_list_back] = m;
  1545           if (nm[m] && rnode == INVALID) rnode = m;
  1546         } else {
  1547           _visitor->examine(e);
  1548         }
  1549       }
  1550       return n;
  1551     }
  1552 
  1553     /// \brief The next node to be processed.
  1554     ///
  1555     /// Returns the next node to be processed or \c INVALID if the queue
  1556     /// is empty.
  1557     Node nextNode() const {
  1558       return _list_front != _list_back ? _list[_list_front + 1] : INVALID;
  1559     }
  1560 
  1561     /// \brief Returns \c false if there are nodes
  1562     /// to be processed.
  1563     ///
  1564     /// Returns \c false if there are nodes
  1565     /// to be processed in the queue.
  1566     bool emptyQueue() const { return _list_front == _list_back; }
  1567 
  1568     /// \brief Returns the number of the nodes to be processed.
  1569     ///
  1570     /// Returns the number of the nodes to be processed in the queue.
  1571     int queueSize() const { return _list_back - _list_front; }
  1572 
  1573     /// \brief Executes the algorithm.
  1574     ///
  1575     /// Executes the algorithm.
  1576     ///
  1577     /// This method runs the %BFS algorithm from the root node(s)
  1578     /// in order to compute the shortest path to each node.
  1579     ///
  1580     /// The algorithm computes
  1581     /// - the shortest path tree (forest),
  1582     /// - the distance of each node from the root(s).
  1583     ///
  1584     /// \pre init() must be called and at least one root node should be added
  1585     /// with addSource() before using this function.
  1586     ///
  1587     /// \note <tt>b.start()</tt> is just a shortcut of the following code.
  1588     /// \code
  1589     ///   while ( !b.emptyQueue() ) {
  1590     ///     b.processNextNode();
  1591     ///   }
  1592     /// \endcode
  1593     void start() {
  1594       while ( !emptyQueue() ) processNextNode();
  1595     }
  1596 
  1597     /// \brief Executes the algorithm until the given target node is reached.
  1598     ///
  1599     /// Executes the algorithm until the given target node is reached.
  1600     ///
  1601     /// This method runs the %BFS algorithm from the root node(s)
  1602     /// in order to compute the shortest path to \c t.
  1603     ///
  1604     /// The algorithm computes
  1605     /// - the shortest path to \c t,
  1606     /// - the distance of \c t from the root(s).
  1607     ///
  1608     /// \pre init() must be called and at least one root node should be
  1609     /// added with addSource() before using this function.
  1610     ///
  1611     /// \note <tt>b.start(t)</tt> is just a shortcut of the following code.
  1612     /// \code
  1613     ///   bool reach = false;
  1614     ///   while ( !b.emptyQueue() && !reach ) {
  1615     ///     b.processNextNode(t, reach);
  1616     ///   }
  1617     /// \endcode
  1618     void start(Node t) {
  1619       bool reach = false;
  1620       while ( !emptyQueue() && !reach ) processNextNode(t, reach);
  1621     }
  1622 
  1623     /// \brief Executes the algorithm until a condition is met.
  1624     ///
  1625     /// Executes the algorithm until a condition is met.
  1626     ///
  1627     /// This method runs the %BFS algorithm from the root node(s) in
  1628     /// order to compute the shortest path to a node \c v with
  1629     /// <tt>nm[v]</tt> true, if such a node can be found.
  1630     ///
  1631     /// \param nm must be a bool (or convertible) node map. The
  1632     /// algorithm will stop when it reaches a node \c v with
  1633     /// <tt>nm[v]</tt> true.
  1634     ///
  1635     /// \return The reached node \c v with <tt>nm[v]</tt> true or
  1636     /// \c INVALID if no such node was found.
  1637     ///
  1638     /// \pre init() must be called and at least one root node should be
  1639     /// added with addSource() before using this function.
  1640     ///
  1641     /// \note <tt>b.start(nm)</tt> is just a shortcut of the following code.
  1642     /// \code
  1643     ///   Node rnode = INVALID;
  1644     ///   while ( !b.emptyQueue() && rnode == INVALID ) {
  1645     ///     b.processNextNode(nm, rnode);
  1646     ///   }
  1647     ///   return rnode;
  1648     /// \endcode
  1649     template <typename NM>
  1650     Node start(const NM &nm) {
  1651       Node rnode = INVALID;
  1652       while ( !emptyQueue() && rnode == INVALID ) {
  1653         processNextNode(nm, rnode);
  1654       }
  1655       return rnode;
  1656     }
  1657 
  1658     /// \brief Runs the algorithm from the given source node.
  1659     ///
  1660     /// This method runs the %BFS algorithm from node \c s
  1661     /// in order to compute the shortest path to each node.
  1662     ///
  1663     /// The algorithm computes
  1664     /// - the shortest path tree,
  1665     /// - the distance of each node from the root.
  1666     ///
  1667     /// \note <tt>b.run(s)</tt> is just a shortcut of the following code.
  1668     ///\code
  1669     ///   b.init();
  1670     ///   b.addSource(s);
  1671     ///   b.start();
  1672     ///\endcode
  1673     void run(Node s) {
  1674       init();
  1675       addSource(s);
  1676       start();
  1677     }
  1678 
  1679     /// \brief Finds the shortest path between \c s and \c t.
  1680     ///
  1681     /// This method runs the %BFS algorithm from node \c s
  1682     /// in order to compute the shortest path to node \c t
  1683     /// (it stops searching when \c t is processed).
  1684     ///
  1685     /// \return \c true if \c t is reachable form \c s.
  1686     ///
  1687     /// \note Apart from the return value, <tt>b.run(s,t)</tt> is just a
  1688     /// shortcut of the following code.
  1689     ///\code
  1690     ///   b.init();
  1691     ///   b.addSource(s);
  1692     ///   b.start(t);
  1693     ///\endcode
  1694     bool run(Node s,Node t) {
  1695       init();
  1696       addSource(s);
  1697       start(t);
  1698       return reached(t);
  1699     }
  1700 
  1701     /// \brief Runs the algorithm to visit all nodes in the digraph.
  1702     ///
  1703     /// This method runs the %BFS algorithm in order to
  1704     /// compute the shortest path to each node.
  1705     ///
  1706     /// The algorithm computes
  1707     /// - the shortest path tree (forest),
  1708     /// - the distance of each node from the root(s).
  1709     ///
  1710     /// \note <tt>b.run(s)</tt> is just a shortcut of the following code.
  1711     ///\code
  1712     ///  b.init();
  1713     ///  for (NodeIt n(gr); n != INVALID; ++n) {
  1714     ///    if (!b.reached(n)) {
  1715     ///      b.addSource(n);
  1716     ///      b.start();
  1717     ///    }
  1718     ///  }
  1719     ///\endcode
  1720     void run() {
  1721       init();
  1722       for (NodeIt it(*_digraph); it != INVALID; ++it) {
  1723         if (!reached(it)) {
  1724           addSource(it);
  1725           start();
  1726         }
  1727       }
  1728     }
  1729 
  1730     ///@}
  1731 
  1732     /// \name Query Functions
  1733     /// The result of the %BFS algorithm can be obtained using these
  1734     /// functions.\n
  1735     /// Either \ref lemon::BfsVisit::run() "run()" or
  1736     /// \ref lemon::BfsVisit::start() "start()" must be called before
  1737     /// using them.
  1738     ///@{
  1739 
  1740     /// \brief Checks if a node is reachable from the root(s).
  1741     ///
  1742     /// Returns \c true if \c v is reachable from the root(s).
  1743     /// \pre Either \ref run() or \ref start()
  1744     /// must be called before using this function.
  1745     bool reached(Node v) { return (*_reached)[v]; }
  1746 
  1747     ///@}
  1748 
  1749   };
  1750 
  1751 } //END OF NAMESPACE LEMON
  1752 
  1753 #endif