lemon/bfs.h
author Alpar Juttner <alpar@cs.elte.hu>
Tue, 22 Apr 2008 17:52:01 +0100
changeset 145 95d905b6e33d
child 157 2ccc1afc2c52
permissions -rw-r--r--
Merge
     1 /* -*- C++ -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library
     4  *
     5  * Copyright (C) 2003-2008
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    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/graph_utils.h>
    28 #include <lemon/bits/path_dump.h>
    29 #include <lemon/bits/invalid.h>
    30 #include <lemon/error.h>
    31 #include <lemon/maps.h>
    32 
    33 namespace lemon {
    34 
    35 
    36   
    37   ///Default traits class of Bfs class.
    38 
    39   ///Default traits class of Bfs class.
    40   ///\param GR Digraph type.
    41   template<class GR>
    42   struct BfsDefaultTraits
    43   {
    44     ///The digraph type the algorithm runs on. 
    45     typedef GR Digraph;
    46     ///\brief The type of the map that stores the last
    47     ///arcs of the shortest paths.
    48     /// 
    49     ///The type of the map that stores the last
    50     ///arcs of the shortest paths.
    51     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
    52     ///
    53     typedef typename Digraph::template NodeMap<typename GR::Arc> PredMap;
    54     ///Instantiates a PredMap.
    55  
    56     ///This function instantiates a \ref PredMap. 
    57     ///\param G is the digraph, to which we would like to define the PredMap.
    58     ///\todo The digraph alone may be insufficient to initialize
    59     static PredMap *createPredMap(const GR &G) 
    60     {
    61       return new PredMap(G);
    62     }
    63     ///The type of the map that indicates which nodes are processed.
    64  
    65     ///The type of the map that indicates which nodes are processed.
    66     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
    67     ///\todo named parameter to set this type, function to read and write.
    68     typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
    69     ///Instantiates a ProcessedMap.
    70  
    71     ///This function instantiates a \ref ProcessedMap. 
    72     ///\param g is the digraph, to which
    73     ///we would like to define the \ref ProcessedMap
    74 #ifdef DOXYGEN
    75     static ProcessedMap *createProcessedMap(const GR &g)
    76 #else
    77     static ProcessedMap *createProcessedMap(const GR &)
    78 #endif
    79     {
    80       return new ProcessedMap();
    81     }
    82     ///The type of the map that indicates which nodes are reached.
    83  
    84     ///The type of the map that indicates which nodes are reached.
    85     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
    86     ///\todo named parameter to set this type, function to read and write.
    87     typedef typename Digraph::template NodeMap<bool> ReachedMap;
    88     ///Instantiates a ReachedMap.
    89  
    90     ///This function instantiates a \ref ReachedMap. 
    91     ///\param G is the digraph, to which
    92     ///we would like to define the \ref ReachedMap.
    93     static ReachedMap *createReachedMap(const GR &G)
    94     {
    95       return new ReachedMap(G);
    96     }
    97     ///The type of the map that stores the dists of the nodes.
    98  
    99     ///The type of the map that stores the dists of the nodes.
   100     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   101     ///
   102     typedef typename Digraph::template NodeMap<int> DistMap;
   103     ///Instantiates a DistMap.
   104  
   105     ///This function instantiates a \ref DistMap. 
   106     ///\param G is the digraph, to which we would like to define the \ref DistMap
   107     static DistMap *createDistMap(const GR &G)
   108     {
   109       return new DistMap(G);
   110     }
   111   };
   112   
   113   ///%BFS algorithm class.
   114   
   115   ///\ingroup search
   116   ///This class provides an efficient implementation of the %BFS algorithm.
   117   ///
   118   ///\param GR The digraph type the algorithm runs on. The default value is
   119   ///\ref ListDigraph. The value of GR is not used directly by Bfs, it
   120   ///is only passed to \ref BfsDefaultTraits.
   121   ///\param TR Traits class to set various data types used by the algorithm.
   122   ///The default traits class is
   123   ///\ref BfsDefaultTraits "BfsDefaultTraits<GR>".
   124   ///See \ref BfsDefaultTraits for the documentation of
   125   ///a Bfs traits class.
   126   ///
   127   ///\author Alpar Juttner
   128 
   129 #ifdef DOXYGEN
   130   template <typename GR,
   131 	    typename TR>
   132 #else
   133   template <typename GR=ListDigraph,
   134 	    typename TR=BfsDefaultTraits<GR> >
   135 #endif
   136   class Bfs {
   137   public:
   138     /**
   139      * \brief \ref Exception for uninitialized parameters.
   140      *
   141      * This error represents problems in the initialization
   142      * of the parameters of the algorithms.
   143      */
   144     class UninitializedParameter : public lemon::UninitializedParameter {
   145     public:
   146       virtual const char* what() const throw() {
   147 	return "lemon::Bfs::UninitializedParameter";
   148       }
   149     };
   150 
   151     typedef TR Traits;
   152     ///The type of the underlying digraph.
   153     typedef typename TR::Digraph Digraph;
   154     
   155     ///\brief The type of the map that stores the last
   156     ///arcs of the shortest paths.
   157     typedef typename TR::PredMap PredMap;
   158     ///The type of the map indicating which nodes are reached.
   159     typedef typename TR::ReachedMap ReachedMap;
   160     ///The type of the map indicating which nodes are processed.
   161     typedef typename TR::ProcessedMap ProcessedMap;
   162     ///The type of the map that stores the dists of the nodes.
   163     typedef typename TR::DistMap DistMap;
   164   private:
   165 
   166     typedef typename Digraph::Node Node;
   167     typedef typename Digraph::NodeIt NodeIt;
   168     typedef typename Digraph::Arc Arc;
   169     typedef typename Digraph::OutArcIt OutArcIt;
   170 
   171     /// Pointer to the underlying digraph.
   172     const Digraph *G;
   173     ///Pointer to the map of predecessors arcs.
   174     PredMap *_pred;
   175     ///Indicates if \ref _pred is locally allocated (\c true) or not.
   176     bool local_pred;
   177     ///Pointer to the map of distances.
   178     DistMap *_dist;
   179     ///Indicates if \ref _dist is locally allocated (\c true) or not.
   180     bool local_dist;
   181     ///Pointer to the map of reached status of the nodes.
   182     ReachedMap *_reached;
   183     ///Indicates if \ref _reached is locally allocated (\c true) or not.
   184     bool local_reached;
   185     ///Pointer to the map of processed status of the nodes.
   186     ProcessedMap *_processed;
   187     ///Indicates if \ref _processed is locally allocated (\c true) or not.
   188     bool local_processed;
   189 
   190     std::vector<typename Digraph::Node> _queue;
   191     int _queue_head,_queue_tail,_queue_next_dist;
   192     int _curr_dist;
   193 
   194     ///Creates the maps if necessary.
   195     
   196     ///\todo Better memory allocation (instead of new).
   197     void create_maps() 
   198     {
   199       if(!_pred) {
   200 	local_pred = true;
   201 	_pred = Traits::createPredMap(*G);
   202       }
   203       if(!_dist) {
   204 	local_dist = true;
   205 	_dist = Traits::createDistMap(*G);
   206       }
   207       if(!_reached) {
   208 	local_reached = true;
   209 	_reached = Traits::createReachedMap(*G);
   210       }
   211       if(!_processed) {
   212 	local_processed = true;
   213 	_processed = Traits::createProcessedMap(*G);
   214       }
   215     }
   216 
   217   protected:
   218     
   219     Bfs() {}
   220     
   221   public:
   222  
   223     typedef Bfs Create;
   224 
   225     ///\name Named template parameters
   226 
   227     ///@{
   228 
   229     template <class T>
   230     struct DefPredMapTraits : public Traits {
   231       typedef T PredMap;
   232       static PredMap *createPredMap(const Digraph &) 
   233       {
   234 	throw UninitializedParameter();
   235       }
   236     };
   237     ///\brief \ref named-templ-param "Named parameter" for setting
   238     ///PredMap type
   239     ///
   240     ///\ref named-templ-param "Named parameter" for setting PredMap type
   241     ///
   242     template <class T>
   243     struct DefPredMap : public Bfs< Digraph, DefPredMapTraits<T> > { 
   244       typedef Bfs< Digraph, DefPredMapTraits<T> > Create;
   245     };
   246     
   247     template <class T>
   248     struct DefDistMapTraits : public Traits {
   249       typedef T DistMap;
   250       static DistMap *createDistMap(const Digraph &) 
   251       {
   252 	throw UninitializedParameter();
   253       }
   254     };
   255     ///\brief \ref named-templ-param "Named parameter" for setting
   256     ///DistMap type
   257     ///
   258     ///\ref named-templ-param "Named parameter" for setting DistMap type
   259     ///
   260     template <class T>
   261     struct DefDistMap : public Bfs< Digraph, DefDistMapTraits<T> > { 
   262       typedef Bfs< Digraph, DefDistMapTraits<T> > Create;
   263     };
   264     
   265     template <class T>
   266     struct DefReachedMapTraits : public Traits {
   267       typedef T ReachedMap;
   268       static ReachedMap *createReachedMap(const Digraph &) 
   269       {
   270 	throw UninitializedParameter();
   271       }
   272     };
   273     ///\brief \ref named-templ-param "Named parameter" for setting
   274     ///ReachedMap type
   275     ///
   276     ///\ref named-templ-param "Named parameter" for setting ReachedMap type
   277     ///
   278     template <class T>
   279     struct DefReachedMap : public Bfs< Digraph, DefReachedMapTraits<T> > { 
   280       typedef Bfs< Digraph, DefReachedMapTraits<T> > Create;
   281     };
   282     
   283     template <class T>
   284     struct DefProcessedMapTraits : public Traits {
   285       typedef T ProcessedMap;
   286       static ProcessedMap *createProcessedMap(const Digraph &) 
   287       {
   288 	throw UninitializedParameter();
   289       }
   290     };
   291     ///\brief \ref named-templ-param "Named parameter" for setting
   292     ///ProcessedMap type
   293     ///
   294     ///\ref named-templ-param "Named parameter" for setting ProcessedMap type
   295     ///
   296     template <class T>
   297     struct DefProcessedMap : public Bfs< Digraph, DefProcessedMapTraits<T> > {
   298       typedef Bfs< Digraph, DefProcessedMapTraits<T> > Create;
   299     };
   300     
   301     struct DefDigraphProcessedMapTraits : public Traits {
   302       typedef typename Digraph::template NodeMap<bool> ProcessedMap;
   303       static ProcessedMap *createProcessedMap(const Digraph &G) 
   304       {
   305 	return new ProcessedMap(G);
   306       }
   307     };
   308     ///\brief \ref named-templ-param "Named parameter"
   309     ///for setting the ProcessedMap type to be Digraph::NodeMap<bool>.
   310     ///
   311     ///\ref named-templ-param "Named parameter"
   312     ///for setting the ProcessedMap type to be Digraph::NodeMap<bool>.
   313     ///If you don't set it explicitly, it will be automatically allocated.
   314     template <class T>
   315     struct DefProcessedMapToBeDefaultMap :
   316       public Bfs< Digraph, DefDigraphProcessedMapTraits> { 
   317       typedef Bfs< Digraph, DefDigraphProcessedMapTraits> Create;
   318     };
   319     
   320     ///@}
   321 
   322   public:      
   323     
   324     ///Constructor.
   325     
   326     ///\param _G the digraph the algorithm will run on.
   327     ///
   328     Bfs(const Digraph& _G) :
   329       G(&_G),
   330       _pred(NULL), local_pred(false),
   331       _dist(NULL), local_dist(false),
   332       _reached(NULL), local_reached(false),
   333       _processed(NULL), local_processed(false)
   334     { }
   335     
   336     ///Destructor.
   337     ~Bfs() 
   338     {
   339       if(local_pred) delete _pred;
   340       if(local_dist) delete _dist;
   341       if(local_reached) delete _reached;
   342       if(local_processed) delete _processed;
   343     }
   344 
   345     ///Sets the map storing the predecessor arcs.
   346 
   347     ///Sets the map storing the predecessor arcs.
   348     ///If you don't use this function before calling \ref run(),
   349     ///it will allocate one. The destructor deallocates this
   350     ///automatically allocated map, of course.
   351     ///\return <tt> (*this) </tt>
   352     Bfs &predMap(PredMap &m) 
   353     {
   354       if(local_pred) {
   355 	delete _pred;
   356 	local_pred=false;
   357       }
   358       _pred = &m;
   359       return *this;
   360     }
   361 
   362     ///Sets the map indicating the reached nodes.
   363 
   364     ///Sets the map indicating the reached nodes.
   365     ///If you don't use this function before calling \ref run(),
   366     ///it will allocate one. The destructor deallocates this
   367     ///automatically allocated map, of course.
   368     ///\return <tt> (*this) </tt>
   369     Bfs &reachedMap(ReachedMap &m) 
   370     {
   371       if(local_reached) {
   372 	delete _reached;
   373 	local_reached=false;
   374       }
   375       _reached = &m;
   376       return *this;
   377     }
   378 
   379     ///Sets the map indicating the processed nodes.
   380 
   381     ///Sets the map indicating the processed nodes.
   382     ///If you don't use this function before calling \ref run(),
   383     ///it will allocate one. The destructor deallocates this
   384     ///automatically allocated map, of course.
   385     ///\return <tt> (*this) </tt>
   386     Bfs &processedMap(ProcessedMap &m) 
   387     {
   388       if(local_processed) {
   389 	delete _processed;
   390 	local_processed=false;
   391       }
   392       _processed = &m;
   393       return *this;
   394     }
   395 
   396     ///Sets the map storing the distances calculated by the algorithm.
   397 
   398     ///Sets the map storing the distances calculated by the algorithm.
   399     ///If you don't use this function before calling \ref run(),
   400     ///it will allocate one. The destructor deallocates this
   401     ///automatically allocated map, of course.
   402     ///\return <tt> (*this) </tt>
   403     Bfs &distMap(DistMap &m) 
   404     {
   405       if(local_dist) {
   406 	delete _dist;
   407 	local_dist=false;
   408       }
   409       _dist = &m;
   410       return *this;
   411     }
   412 
   413   public:
   414     ///\name Execution control
   415     ///The simplest way to execute the algorithm is to use
   416     ///one of the member functions called \c run(...).
   417     ///\n
   418     ///If you need more control on the execution,
   419     ///first you must call \ref init(), then you can add several source nodes
   420     ///with \ref addSource().
   421     ///Finally \ref start() will perform the actual path
   422     ///computation.
   423 
   424     ///@{
   425 
   426     ///\brief Initializes the internal data structures.
   427     ///
   428     ///Initializes the internal data structures.
   429     ///
   430     void init()
   431     {
   432       create_maps();
   433       _queue.resize(countNodes(*G));
   434       _queue_head=_queue_tail=0;
   435       _curr_dist=1;
   436       for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
   437 	_pred->set(u,INVALID);
   438 	_reached->set(u,false);
   439 	_processed->set(u,false);
   440       }
   441     }
   442     
   443     ///Adds a new source node.
   444 
   445     ///Adds a new source node to the set of nodes to be processed.
   446     ///
   447     void addSource(Node s)
   448     {
   449       if(!(*_reached)[s])
   450 	{
   451 	  _reached->set(s,true);
   452 	  _pred->set(s,INVALID);
   453 	  _dist->set(s,0);
   454 	  _queue[_queue_head++]=s;
   455 	  _queue_next_dist=_queue_head;
   456 	}
   457     }
   458     
   459     ///Processes the next node.
   460 
   461     ///Processes the next node.
   462     ///
   463     ///\return The processed node.
   464     ///
   465     ///\warning The queue must not be empty!
   466     Node processNextNode()
   467     {
   468       if(_queue_tail==_queue_next_dist) {
   469 	_curr_dist++;
   470 	_queue_next_dist=_queue_head;
   471       }
   472       Node n=_queue[_queue_tail++];
   473       _processed->set(n,true);
   474       Node m;
   475       for(OutArcIt e(*G,n);e!=INVALID;++e)
   476 	if(!(*_reached)[m=G->target(e)]) {
   477 	  _queue[_queue_head++]=m;
   478 	  _reached->set(m,true);
   479 	  _pred->set(m,e);
   480 	  _dist->set(m,_curr_dist);
   481 	}
   482       return n;
   483     }
   484 
   485     ///Processes the next node.
   486 
   487     ///Processes the next node. And checks that the given target node
   488     ///is reached. If the target node is reachable from the processed
   489     ///node then the reached parameter will be set true. The reached
   490     ///parameter should be initially false.
   491     ///
   492     ///\param target The target node.
   493     ///\retval reach Indicates that the target node is reached.
   494     ///\return The processed node.
   495     ///
   496     ///\warning The queue must not be empty!
   497     Node processNextNode(Node target, bool& reach)
   498     {
   499       if(_queue_tail==_queue_next_dist) {
   500 	_curr_dist++;
   501 	_queue_next_dist=_queue_head;
   502       }
   503       Node n=_queue[_queue_tail++];
   504       _processed->set(n,true);
   505       Node m;
   506       for(OutArcIt e(*G,n);e!=INVALID;++e)
   507 	if(!(*_reached)[m=G->target(e)]) {
   508 	  _queue[_queue_head++]=m;
   509 	  _reached->set(m,true);
   510 	  _pred->set(m,e);
   511 	  _dist->set(m,_curr_dist);
   512           reach = reach || (target == m);
   513 	}
   514       return n;
   515     }
   516 
   517     ///Processes the next node.
   518 
   519     ///Processes the next node. And checks that at least one of
   520     ///reached node has true value in the \c nm node map. If one node
   521     ///with true value is reachable from the processed node then the
   522     ///rnode parameter will be set to the first of such nodes.
   523     ///
   524     ///\param nm The node map of possible targets.
   525     ///\retval rnode The reached target node.
   526     ///\return The processed node.
   527     ///
   528     ///\warning The queue must not be empty!
   529     template<class NM>
   530     Node processNextNode(const NM& nm, Node& rnode)
   531     {
   532       if(_queue_tail==_queue_next_dist) {
   533 	_curr_dist++;
   534 	_queue_next_dist=_queue_head;
   535       }
   536       Node n=_queue[_queue_tail++];
   537       _processed->set(n,true);
   538       Node m;
   539       for(OutArcIt e(*G,n);e!=INVALID;++e)
   540 	if(!(*_reached)[m=G->target(e)]) {
   541 	  _queue[_queue_head++]=m;
   542 	  _reached->set(m,true);
   543 	  _pred->set(m,e);
   544 	  _dist->set(m,_curr_dist);
   545 	  if (nm[m] && rnode == INVALID) rnode = m;
   546 	}
   547       return n;
   548     }
   549       
   550     ///Next node to be processed.
   551 
   552     ///Next node to be processed.
   553     ///
   554     ///\return The next node to be processed or INVALID if the queue is
   555     /// empty.
   556     Node nextNode()
   557     { 
   558       return _queue_tail<_queue_head?_queue[_queue_tail]:INVALID;
   559     }
   560  
   561     ///\brief Returns \c false if there are nodes
   562     ///to be processed in the queue
   563     ///
   564     ///Returns \c false if there are nodes
   565     ///to be processed in the queue
   566     bool emptyQueue() { return _queue_tail==_queue_head; }
   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() { return _queue_head-_queue_tail; }
   571     
   572     ///Executes the algorithm.
   573 
   574     ///Executes the algorithm.
   575     ///
   576     ///\pre init() must be called and at least one node should be added
   577     ///with addSource() before using this function.
   578     ///
   579     ///This method runs the %BFS algorithm from the root node(s)
   580     ///in order to
   581     ///compute the
   582     ///shortest path to each node. The algorithm computes
   583     ///- The shortest path tree.
   584     ///- The distance of each node from the root(s).
   585     void start()
   586     {
   587       while ( !emptyQueue() ) processNextNode();
   588     }
   589     
   590     ///Executes the algorithm until \c dest is reached.
   591 
   592     ///Executes the algorithm until \c dest is reached.
   593     ///
   594     ///\pre init() must be called and at least one node should be added
   595     ///with addSource() before using this function.
   596     ///
   597     ///This method runs the %BFS algorithm from the root node(s)
   598     ///in order to compute the shortest path to \c dest.
   599     ///The algorithm computes
   600     ///- The shortest path to \c  dest.
   601     ///- The distance of \c dest from the root(s).
   602     void start(Node dest)
   603     {
   604       bool reach = false;
   605       while ( !emptyQueue() && !reach ) processNextNode(dest, reach);
   606     }
   607     
   608     ///Executes the algorithm until a condition is met.
   609 
   610     ///Executes the algorithm until a condition is met.
   611     ///
   612     ///\pre init() must be called and at least one node should be added
   613     ///with addSource() before using this function.
   614     ///
   615     ///\param nm must be a bool (or convertible) node map. The
   616     ///algorithm will stop when it reaches a node \c v with
   617     /// <tt>nm[v]</tt> true.
   618     ///
   619     ///\return The reached node \c v with <tt>nm[v]</tt> true or
   620     ///\c INVALID if no such node was found.
   621     template<class NM>
   622     Node start(const NM &nm)
   623     {
   624       Node rnode = INVALID;
   625       while ( !emptyQueue() && rnode == INVALID ) {
   626 	processNextNode(nm, rnode);
   627       }
   628       return rnode;
   629     }
   630     
   631     ///Runs %BFS algorithm from node \c s.
   632     
   633     ///This method runs the %BFS algorithm from a root node \c s
   634     ///in order to
   635     ///compute the
   636     ///shortest path to each node. The algorithm computes
   637     ///- The shortest path tree.
   638     ///- The distance of each node from the root.
   639     ///
   640     ///\note b.run(s) is just a shortcut of the following code.
   641     ///\code
   642     ///  b.init();
   643     ///  b.addSource(s);
   644     ///  b.start();
   645     ///\endcode
   646     void run(Node s) {
   647       init();
   648       addSource(s);
   649       start();
   650     }
   651     
   652     ///Finds the shortest path between \c s and \c t.
   653     
   654     ///Finds the shortest path between \c s and \c t.
   655     ///
   656     ///\return The length of the shortest s---t path if there exists one,
   657     ///0 otherwise.
   658     ///\note Apart from the return value, b.run(s) is
   659     ///just a shortcut of the following code.
   660     ///\code
   661     ///  b.init();
   662     ///  b.addSource(s);
   663     ///  b.start(t);
   664     ///\endcode
   665     int run(Node s,Node t) {
   666       init();
   667       addSource(s);
   668       start(t);
   669       return reached(t) ? _curr_dist : 0;
   670     }
   671     
   672     ///@}
   673 
   674     ///\name Query Functions
   675     ///The result of the %BFS algorithm can be obtained using these
   676     ///functions.\n
   677     ///Before the use of these functions,
   678     ///either run() or start() must be calleb.
   679     
   680     ///@{
   681 
   682     typedef PredMapPath<Digraph, PredMap> Path;
   683 
   684     ///Gives back the shortest path.
   685     
   686     ///Gives back the shortest path.
   687     ///\pre The \c t should be reachable from the source.
   688     Path path(Node t) 
   689     {
   690       return Path(*G, *_pred, t);
   691     }
   692 
   693     ///The distance of a node from the root(s).
   694 
   695     ///Returns the distance of a node from the root(s).
   696     ///\pre \ref run() must be called before using this function.
   697     ///\warning If node \c v in unreachable from the root(s) the return value
   698     ///of this function is undefined.
   699     int dist(Node v) const { return (*_dist)[v]; }
   700 
   701     ///Returns the 'previous arc' of the shortest path tree.
   702 
   703     ///For a node \c v it returns the 'previous arc'
   704     ///of the shortest path tree,
   705     ///i.e. it returns the last arc of a shortest path from the root(s) to \c
   706     ///v. It is \ref INVALID
   707     ///if \c v is unreachable from the root(s) or \c v is a root. The
   708     ///shortest path tree used here is equal to the shortest path tree used in
   709     ///\ref predNode().
   710     ///\pre Either \ref run() or \ref start() must be called before using
   711     ///this function.
   712     Arc predArc(Node v) const { return (*_pred)[v];}
   713 
   714     ///Returns the 'previous node' of the shortest path tree.
   715 
   716     ///For a node \c v it returns the 'previous node'
   717     ///of the shortest path tree,
   718     ///i.e. it returns the last but one node from a shortest path from the
   719     ///root(a) to \c /v.
   720     ///It is INVALID if \c v is unreachable from the root(s) or
   721     ///if \c v itself a root.
   722     ///The shortest path tree used here is equal to the shortest path
   723     ///tree used in \ref predArc().
   724     ///\pre Either \ref run() or \ref start() must be called before
   725     ///using this function.
   726     Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
   727 				  G->source((*_pred)[v]); }
   728     
   729     ///Returns a reference to the NodeMap of distances.
   730 
   731     ///Returns a reference to the NodeMap of distances.
   732     ///\pre Either \ref run() or \ref init() must
   733     ///be called before using this function.
   734     const DistMap &distMap() const { return *_dist;}
   735  
   736     ///Returns a reference to the shortest path tree map.
   737 
   738     ///Returns a reference to the NodeMap of the arcs of the
   739     ///shortest path tree.
   740     ///\pre Either \ref run() or \ref init()
   741     ///must be called before using this function.
   742     const PredMap &predMap() const { return *_pred;}
   743  
   744     ///Checks if a node is reachable from the root.
   745 
   746     ///Returns \c true if \c v is reachable from the root.
   747     ///\warning The source nodes are indicated as unreached.
   748     ///\pre Either \ref run() or \ref start()
   749     ///must be called before using this function.
   750     ///
   751     bool reached(Node v) { return (*_reached)[v]; }
   752     
   753     ///@}
   754   };
   755 
   756   ///Default traits class of Bfs function.
   757 
   758   ///Default traits class of Bfs function.
   759   ///\param GR Digraph type.
   760   template<class GR>
   761   struct BfsWizardDefaultTraits
   762   {
   763     ///The digraph type the algorithm runs on. 
   764     typedef GR Digraph;
   765     ///\brief The type of the map that stores the last
   766     ///arcs of the shortest paths.
   767     /// 
   768     ///The type of the map that stores the last
   769     ///arcs of the shortest paths.
   770     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   771     ///
   772     typedef NullMap<typename Digraph::Node,typename GR::Arc> PredMap;
   773     ///Instantiates a PredMap.
   774  
   775     ///This function instantiates a \ref PredMap. 
   776     ///\param g is the digraph, to which we would like to define the PredMap.
   777     ///\todo The digraph alone may be insufficient to initialize
   778 #ifdef DOXYGEN
   779     static PredMap *createPredMap(const GR &g) 
   780 #else
   781     static PredMap *createPredMap(const GR &) 
   782 #endif
   783     {
   784       return new PredMap();
   785     }
   786 
   787     ///The type of the map that indicates which nodes are processed.
   788  
   789     ///The type of the map that indicates which nodes are processed.
   790     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   791     ///\todo named parameter to set this type, function to read and write.
   792     typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
   793     ///Instantiates a ProcessedMap.
   794  
   795     ///This function instantiates a \ref ProcessedMap. 
   796     ///\param g is the digraph, to which
   797     ///we would like to define the \ref ProcessedMap
   798 #ifdef DOXYGEN
   799     static ProcessedMap *createProcessedMap(const GR &g)
   800 #else
   801     static ProcessedMap *createProcessedMap(const GR &)
   802 #endif
   803     {
   804       return new ProcessedMap();
   805     }
   806     ///The type of the map that indicates which nodes are reached.
   807  
   808     ///The type of the map that indicates which nodes are reached.
   809     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   810     ///\todo named parameter to set this type, function to read and write.
   811     typedef typename Digraph::template NodeMap<bool> ReachedMap;
   812     ///Instantiates a ReachedMap.
   813  
   814     ///This function instantiates a \ref ReachedMap. 
   815     ///\param G is the digraph, to which
   816     ///we would like to define the \ref ReachedMap.
   817     static ReachedMap *createReachedMap(const GR &G)
   818     {
   819       return new ReachedMap(G);
   820     }
   821     ///The type of the map that stores the dists of the nodes.
   822  
   823     ///The type of the map that stores the dists of the nodes.
   824     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   825     ///
   826     typedef NullMap<typename Digraph::Node,int> DistMap;
   827     ///Instantiates a DistMap.
   828  
   829     ///This function instantiates a \ref DistMap. 
   830     ///\param g is the digraph, to which we would like to define the \ref DistMap
   831 #ifdef DOXYGEN
   832     static DistMap *createDistMap(const GR &g)
   833 #else
   834     static DistMap *createDistMap(const GR &)
   835 #endif
   836     {
   837       return new DistMap();
   838     }
   839   };
   840   
   841   /// Default traits used by \ref BfsWizard
   842 
   843   /// To make it easier to use Bfs algorithm
   844   ///we have created a wizard class.
   845   /// This \ref BfsWizard class needs default traits,
   846   ///as well as the \ref Bfs class.
   847   /// The \ref BfsWizardBase is a class to be the default traits of the
   848   /// \ref BfsWizard class.
   849   template<class GR>
   850   class BfsWizardBase : public BfsWizardDefaultTraits<GR>
   851   {
   852 
   853     typedef BfsWizardDefaultTraits<GR> Base;
   854   protected:
   855     /// Type of the nodes in the digraph.
   856     typedef typename Base::Digraph::Node Node;
   857 
   858     /// Pointer to the underlying digraph.
   859     void *_g;
   860     ///Pointer to the map of reached nodes.
   861     void *_reached;
   862     ///Pointer to the map of processed nodes.
   863     void *_processed;
   864     ///Pointer to the map of predecessors arcs.
   865     void *_pred;
   866     ///Pointer to the map of distances.
   867     void *_dist;
   868     ///Pointer to the source node.
   869     Node _source;
   870     
   871     public:
   872     /// Constructor.
   873     
   874     /// This constructor does not require parameters, therefore it initiates
   875     /// all of the attributes to default values (0, INVALID).
   876     BfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0),
   877 			   _dist(0), _source(INVALID) {}
   878 
   879     /// Constructor.
   880     
   881     /// This constructor requires some parameters,
   882     /// listed in the parameters list.
   883     /// Others are initiated to 0.
   884     /// \param g is the initial value of  \ref _g
   885     /// \param s is the initial value of  \ref _source
   886     BfsWizardBase(const GR &g, Node s=INVALID) :
   887       _g(reinterpret_cast<void*>(const_cast<GR*>(&g))), 
   888       _reached(0), _processed(0), _pred(0), _dist(0), _source(s) {}
   889 
   890   };
   891   
   892   /// A class to make the usage of Bfs algorithm easier
   893 
   894   /// This class is created to make it easier to use Bfs algorithm.
   895   /// It uses the functions and features of the plain \ref Bfs,
   896   /// but it is much simpler to use it.
   897   ///
   898   /// Simplicity means that the way to change the types defined
   899   /// in the traits class is based on functions that returns the new class
   900   /// and not on templatable built-in classes.
   901   /// When using the plain \ref Bfs
   902   /// the new class with the modified type comes from
   903   /// the original class by using the ::
   904   /// operator. In the case of \ref BfsWizard only
   905   /// a function have to be called and it will
   906   /// return the needed class.
   907   ///
   908   /// It does not have own \ref run method. When its \ref run method is called
   909   /// it initiates a plain \ref Bfs class, and calls the \ref Bfs::run
   910   /// method of it.
   911   template<class TR>
   912   class BfsWizard : public TR
   913   {
   914     typedef TR Base;
   915 
   916     ///The type of the underlying digraph.
   917     typedef typename TR::Digraph Digraph;
   918     //\e
   919     typedef typename Digraph::Node Node;
   920     //\e
   921     typedef typename Digraph::NodeIt NodeIt;
   922     //\e
   923     typedef typename Digraph::Arc Arc;
   924     //\e
   925     typedef typename Digraph::OutArcIt OutArcIt;
   926     
   927     ///\brief The type of the map that stores
   928     ///the reached nodes
   929     typedef typename TR::ReachedMap ReachedMap;
   930     ///\brief The type of the map that stores
   931     ///the processed nodes
   932     typedef typename TR::ProcessedMap ProcessedMap;
   933     ///\brief The type of the map that stores the last
   934     ///arcs of the shortest paths.
   935     typedef typename TR::PredMap PredMap;
   936     ///The type of the map that stores the dists of the nodes.
   937     typedef typename TR::DistMap DistMap;
   938 
   939   public:
   940     /// Constructor.
   941     BfsWizard() : TR() {}
   942 
   943     /// Constructor that requires parameters.
   944 
   945     /// Constructor that requires parameters.
   946     /// These parameters will be the default values for the traits class.
   947     BfsWizard(const Digraph &g, Node s=INVALID) :
   948       TR(g,s) {}
   949 
   950     ///Copy constructor
   951     BfsWizard(const TR &b) : TR(b) {}
   952 
   953     ~BfsWizard() {}
   954 
   955     ///Runs Bfs algorithm from a given node.
   956     
   957     ///Runs Bfs algorithm from a given node.
   958     ///The node can be given by the \ref source function.
   959     void run()
   960     {
   961       if(Base::_source==INVALID) throw UninitializedParameter();
   962       Bfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
   963       if(Base::_reached)
   964 	alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
   965       if(Base::_processed) 
   966         alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
   967       if(Base::_pred) 
   968         alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
   969       if(Base::_dist) 
   970         alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
   971       alg.run(Base::_source);
   972     }
   973 
   974     ///Runs Bfs algorithm from the given node.
   975 
   976     ///Runs Bfs algorithm from the given node.
   977     ///\param s is the given source.
   978     void run(Node s)
   979     {
   980       Base::_source=s;
   981       run();
   982     }
   983 
   984     template<class T>
   985     struct DefPredMapBase : public Base {
   986       typedef T PredMap;
   987       static PredMap *createPredMap(const Digraph &) { return 0; };
   988       DefPredMapBase(const TR &b) : TR(b) {}
   989     };
   990     
   991     ///\brief \ref named-templ-param "Named parameter"
   992     ///function for setting PredMap
   993     ///
   994     /// \ref named-templ-param "Named parameter"
   995     ///function for setting PredMap
   996     ///
   997     template<class T>
   998     BfsWizard<DefPredMapBase<T> > predMap(const T &t) 
   999     {
  1000       Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
  1001       return BfsWizard<DefPredMapBase<T> >(*this);
  1002     }
  1003     
  1004  
  1005     template<class T>
  1006     struct DefReachedMapBase : public Base {
  1007       typedef T ReachedMap;
  1008       static ReachedMap *createReachedMap(const Digraph &) { return 0; };
  1009       DefReachedMapBase(const TR &b) : TR(b) {}
  1010     };
  1011     
  1012     ///\brief \ref named-templ-param "Named parameter"
  1013     ///function for setting ReachedMap
  1014     ///
  1015     /// \ref named-templ-param "Named parameter"
  1016     ///function for setting ReachedMap
  1017     ///
  1018     template<class T>
  1019     BfsWizard<DefReachedMapBase<T> > reachedMap(const T &t) 
  1020     {
  1021       Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
  1022       return BfsWizard<DefReachedMapBase<T> >(*this);
  1023     }
  1024     
  1025 
  1026     template<class T>
  1027     struct DefProcessedMapBase : public Base {
  1028       typedef T ProcessedMap;
  1029       static ProcessedMap *createProcessedMap(const Digraph &) { return 0; };
  1030       DefProcessedMapBase(const TR &b) : TR(b) {}
  1031     };
  1032     
  1033     ///\brief \ref named-templ-param "Named parameter"
  1034     ///function for setting ProcessedMap
  1035     ///
  1036     /// \ref named-templ-param "Named parameter"
  1037     ///function for setting ProcessedMap
  1038     ///
  1039     template<class T>
  1040     BfsWizard<DefProcessedMapBase<T> > processedMap(const T &t) 
  1041     {
  1042       Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
  1043       return BfsWizard<DefProcessedMapBase<T> >(*this);
  1044     }
  1045     
  1046    
  1047     template<class T>
  1048     struct DefDistMapBase : public Base {
  1049       typedef T DistMap;
  1050       static DistMap *createDistMap(const Digraph &) { return 0; };
  1051       DefDistMapBase(const TR &b) : TR(b) {}
  1052     };
  1053     
  1054     ///\brief \ref named-templ-param "Named parameter"
  1055     ///function for setting DistMap type
  1056     ///
  1057     /// \ref named-templ-param "Named parameter"
  1058     ///function for setting DistMap type
  1059     ///
  1060     template<class T>
  1061     BfsWizard<DefDistMapBase<T> > distMap(const T &t) 
  1062     {
  1063       Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
  1064       return BfsWizard<DefDistMapBase<T> >(*this);
  1065     }
  1066     
  1067     /// Sets the source node, from which the Bfs algorithm runs.
  1068 
  1069     /// Sets the source node, from which the Bfs algorithm runs.
  1070     /// \param s is the source node.
  1071     BfsWizard<TR> &source(Node s) 
  1072     {
  1073       Base::_source=s;
  1074       return *this;
  1075     }
  1076     
  1077   };
  1078   
  1079   ///Function type interface for Bfs algorithm.
  1080 
  1081   /// \ingroup search
  1082   ///Function type interface for Bfs algorithm.
  1083   ///
  1084   ///This function also has several
  1085   ///\ref named-templ-func-param "named parameters",
  1086   ///they are declared as the members of class \ref BfsWizard.
  1087   ///The following
  1088   ///example shows how to use these parameters.
  1089   ///\code
  1090   ///  bfs(g,source).predMap(preds).run();
  1091   ///\endcode
  1092   ///\warning Don't forget to put the \ref BfsWizard::run() "run()"
  1093   ///to the end of the parameter list.
  1094   ///\sa BfsWizard
  1095   ///\sa Bfs
  1096   template<class GR>
  1097   BfsWizard<BfsWizardBase<GR> >
  1098   bfs(const GR &g,typename GR::Node s=INVALID)
  1099   {
  1100     return BfsWizard<BfsWizardBase<GR> >(g,s);
  1101   }
  1102 
  1103 #ifdef DOXYGEN
  1104   /// \brief Visitor class for bfs.
  1105   ///  
  1106   /// This class defines the interface of the BfsVisit events, and
  1107   /// it could be the base of a real Visitor class.
  1108   template <typename _Digraph>
  1109   struct BfsVisitor {
  1110     typedef _Digraph Digraph;
  1111     typedef typename Digraph::Arc Arc;
  1112     typedef typename Digraph::Node Node;
  1113     /// \brief Called when the arc reach a node.
  1114     /// 
  1115     /// It is called when the bfs find an arc which target is not
  1116     /// reached yet.
  1117     void discover(const Arc& arc) {}
  1118     /// \brief Called when the node reached first time.
  1119     /// 
  1120     /// It is Called when the node reached first time.
  1121     void reach(const Node& node) {}
  1122     /// \brief Called when the arc examined but target of the arc 
  1123     /// already discovered.
  1124     /// 
  1125     /// It called when the arc examined but the target of the arc 
  1126     /// already discovered.
  1127     void examine(const Arc& arc) {}
  1128     /// \brief Called for the source node of the bfs.
  1129     /// 
  1130     /// It is called for the source node of the bfs.
  1131     void start(const Node& node) {}
  1132     /// \brief Called when the node processed.
  1133     /// 
  1134     /// It is Called when the node processed.
  1135     void process(const Node& node) {}
  1136   };
  1137 #else
  1138   template <typename _Digraph>
  1139   struct BfsVisitor {
  1140     typedef _Digraph Digraph;
  1141     typedef typename Digraph::Arc Arc;
  1142     typedef typename Digraph::Node Node;
  1143     void discover(const Arc&) {}
  1144     void reach(const Node&) {}
  1145     void examine(const Arc&) {}
  1146     void start(const Node&) {}
  1147     void process(const Node&) {}
  1148 
  1149     template <typename _Visitor>
  1150     struct Constraints {
  1151       void constraints() {
  1152 	Arc arc;
  1153 	Node node;
  1154 	visitor.discover(arc);
  1155 	visitor.reach(node);
  1156 	visitor.examine(arc);
  1157 	visitor.start(node);
  1158         visitor.process(node);
  1159       }
  1160       _Visitor& visitor;
  1161     };
  1162   };
  1163 #endif
  1164 
  1165   /// \brief Default traits class of BfsVisit class.
  1166   ///
  1167   /// Default traits class of BfsVisit class.
  1168   /// \param _Digraph Digraph type.
  1169   template<class _Digraph>
  1170   struct BfsVisitDefaultTraits {
  1171 
  1172     /// \brief The digraph type the algorithm runs on. 
  1173     typedef _Digraph Digraph;
  1174 
  1175     /// \brief The type of the map that indicates which nodes are reached.
  1176     /// 
  1177     /// The type of the map that indicates which nodes are reached.
  1178     /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
  1179     /// \todo named parameter to set this type, function to read and write.
  1180     typedef typename Digraph::template NodeMap<bool> ReachedMap;
  1181 
  1182     /// \brief Instantiates a ReachedMap.
  1183     ///
  1184     /// This function instantiates a \ref ReachedMap. 
  1185     /// \param digraph is the digraph, to which
  1186     /// we would like to define the \ref ReachedMap.
  1187     static ReachedMap *createReachedMap(const Digraph &digraph) {
  1188       return new ReachedMap(digraph);
  1189     }
  1190 
  1191   };
  1192 
  1193   /// \ingroup search
  1194   ///  
  1195   /// \brief %BFS Visit algorithm class.
  1196   ///  
  1197   /// This class provides an efficient implementation of the %BFS algorithm
  1198   /// with visitor interface.
  1199   ///
  1200   /// The %BfsVisit class provides an alternative interface to the Bfs
  1201   /// class. It works with callback mechanism, the BfsVisit object calls
  1202   /// on every bfs event the \c Visitor class member functions. 
  1203   ///
  1204   /// \param _Digraph The digraph type the algorithm runs on. The default value is
  1205   /// \ref ListDigraph. The value of _Digraph is not used directly by Bfs, it
  1206   /// is only passed to \ref BfsDefaultTraits.
  1207   /// \param _Visitor The Visitor object for the algorithm. The 
  1208   /// \ref BfsVisitor "BfsVisitor<_Digraph>" is an empty Visitor which
  1209   /// does not observe the Bfs events. If you want to observe the bfs
  1210   /// events you should implement your own Visitor class.
  1211   /// \param _Traits Traits class to set various data types used by the 
  1212   /// algorithm. The default traits class is
  1213   /// \ref BfsVisitDefaultTraits "BfsVisitDefaultTraits<_Digraph>".
  1214   /// See \ref BfsVisitDefaultTraits for the documentation of
  1215   /// a Bfs visit traits class.
  1216   ///
  1217   /// \author Jacint Szabo, Alpar Juttner and Balazs Dezso
  1218 #ifdef DOXYGEN
  1219   template <typename _Digraph, typename _Visitor, typename _Traits>
  1220 #else
  1221   template <typename _Digraph = ListDigraph,
  1222 	    typename _Visitor = BfsVisitor<_Digraph>,
  1223 	    typename _Traits = BfsDefaultTraits<_Digraph> >
  1224 #endif
  1225   class BfsVisit {
  1226   public:
  1227     
  1228     /// \brief \ref Exception for uninitialized parameters.
  1229     ///
  1230     /// This error represents problems in the initialization
  1231     /// of the parameters of the algorithms.
  1232     class UninitializedParameter : public lemon::UninitializedParameter {
  1233     public:
  1234       virtual const char* what() const throw() 
  1235       {
  1236 	return "lemon::BfsVisit::UninitializedParameter";
  1237       }
  1238     };
  1239 
  1240     typedef _Traits Traits;
  1241 
  1242     typedef typename Traits::Digraph Digraph;
  1243 
  1244     typedef _Visitor Visitor;
  1245 
  1246     ///The type of the map indicating which nodes are reached.
  1247     typedef typename Traits::ReachedMap ReachedMap;
  1248 
  1249   private:
  1250 
  1251     typedef typename Digraph::Node Node;
  1252     typedef typename Digraph::NodeIt NodeIt;
  1253     typedef typename Digraph::Arc Arc;
  1254     typedef typename Digraph::OutArcIt OutArcIt;
  1255 
  1256     /// Pointer to the underlying digraph.
  1257     const Digraph *_digraph;
  1258     /// Pointer to the visitor object.
  1259     Visitor *_visitor;
  1260     ///Pointer to the map of reached status of the nodes.
  1261     ReachedMap *_reached;
  1262     ///Indicates if \ref _reached is locally allocated (\c true) or not.
  1263     bool local_reached;
  1264 
  1265     std::vector<typename Digraph::Node> _list;
  1266     int _list_front, _list_back;
  1267 
  1268     /// \brief Creates the maps if necessary.
  1269     ///
  1270     /// Creates the maps if necessary.
  1271     void create_maps() {
  1272       if(!_reached) {
  1273 	local_reached = true;
  1274 	_reached = Traits::createReachedMap(*_digraph);
  1275       }
  1276     }
  1277 
  1278   protected:
  1279 
  1280     BfsVisit() {}
  1281     
  1282   public:
  1283 
  1284     typedef BfsVisit Create;
  1285 
  1286     /// \name Named template parameters
  1287 
  1288     ///@{
  1289     template <class T>
  1290     struct DefReachedMapTraits : public Traits {
  1291       typedef T ReachedMap;
  1292       static ReachedMap *createReachedMap(const Digraph &digraph) {
  1293 	throw UninitializedParameter();
  1294       }
  1295     };
  1296     /// \brief \ref named-templ-param "Named parameter" for setting 
  1297     /// ReachedMap type
  1298     ///
  1299     /// \ref named-templ-param "Named parameter" for setting ReachedMap type
  1300     template <class T>
  1301     struct DefReachedMap : public BfsVisit< Digraph, Visitor,
  1302 					    DefReachedMapTraits<T> > {
  1303       typedef BfsVisit< Digraph, Visitor, DefReachedMapTraits<T> > Create;
  1304     };
  1305     ///@}
  1306 
  1307   public:      
  1308     
  1309     /// \brief Constructor.
  1310     ///
  1311     /// Constructor.
  1312     ///
  1313     /// \param digraph the digraph the algorithm will run on.
  1314     /// \param visitor The visitor of the algorithm.
  1315     ///
  1316     BfsVisit(const Digraph& digraph, Visitor& visitor) 
  1317       : _digraph(&digraph), _visitor(&visitor),
  1318 	_reached(0), local_reached(false) {}
  1319     
  1320     /// \brief Destructor.
  1321     ///
  1322     /// Destructor.
  1323     ~BfsVisit() {
  1324       if(local_reached) delete _reached;
  1325     }
  1326 
  1327     /// \brief Sets the map indicating if a node is reached.
  1328     ///
  1329     /// Sets the map indicating if a node is reached.
  1330     /// If you don't use this function before calling \ref run(),
  1331     /// it will allocate one. The destuctor deallocates this
  1332     /// automatically allocated map, of course.
  1333     /// \return <tt> (*this) </tt>
  1334     BfsVisit &reachedMap(ReachedMap &m) {
  1335       if(local_reached) {
  1336 	delete _reached;
  1337 	local_reached = false;
  1338       }
  1339       _reached = &m;
  1340       return *this;
  1341     }
  1342 
  1343   public:
  1344     /// \name Execution control
  1345     /// The simplest way to execute the algorithm is to use
  1346     /// one of the member functions called \c run(...).
  1347     /// \n
  1348     /// If you need more control on the execution,
  1349     /// first you must call \ref init(), then you can adda source node
  1350     /// with \ref addSource().
  1351     /// Finally \ref start() will perform the actual path
  1352     /// computation.
  1353 
  1354     /// @{
  1355     /// \brief Initializes the internal data structures.
  1356     ///
  1357     /// Initializes the internal data structures.
  1358     ///
  1359     void init() {
  1360       create_maps();
  1361       _list.resize(countNodes(*_digraph));
  1362       _list_front = _list_back = -1;
  1363       for (NodeIt u(*_digraph) ; u != INVALID ; ++u) {
  1364 	_reached->set(u, false);
  1365       }
  1366     }
  1367     
  1368     /// \brief Adds a new source node.
  1369     ///
  1370     /// Adds a new source node to the set of nodes to be processed.
  1371     void addSource(Node s) {
  1372       if(!(*_reached)[s]) {
  1373 	  _reached->set(s,true);
  1374 	  _visitor->start(s);
  1375 	  _visitor->reach(s);
  1376           _list[++_list_back] = s;
  1377 	}
  1378     }
  1379     
  1380     /// \brief Processes the next node.
  1381     ///
  1382     /// Processes the next node.
  1383     ///
  1384     /// \return The processed node.
  1385     ///
  1386     /// \pre The queue must not be empty!
  1387     Node processNextNode() { 
  1388       Node n = _list[++_list_front];
  1389       _visitor->process(n);
  1390       Arc e;
  1391       for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
  1392         Node m = _digraph->target(e);
  1393         if (!(*_reached)[m]) {
  1394           _visitor->discover(e);
  1395           _visitor->reach(m);
  1396           _reached->set(m, true);
  1397           _list[++_list_back] = m;
  1398         } else {
  1399           _visitor->examine(e);
  1400         }
  1401       }
  1402       return n;
  1403     }
  1404 
  1405     /// \brief Processes the next node.
  1406     ///
  1407     /// Processes the next node. And checks that the given target node
  1408     /// is reached. If the target node is reachable from the processed
  1409     /// node then the reached parameter will be set true. The reached
  1410     /// parameter should be initially false.
  1411     ///
  1412     /// \param target The target node.
  1413     /// \retval reach Indicates that the target node is reached.
  1414     /// \return The processed node.
  1415     ///
  1416     /// \warning The queue must not be empty!
  1417     Node processNextNode(Node target, bool& reach) {
  1418       Node n = _list[++_list_front];
  1419       _visitor->process(n);
  1420       Arc e;
  1421       for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
  1422         Node m = _digraph->target(e);
  1423         if (!(*_reached)[m]) {
  1424           _visitor->discover(e);
  1425           _visitor->reach(m);
  1426           _reached->set(m, true);
  1427           _list[++_list_back] = m;
  1428           reach = reach || (target == m);
  1429         } else {
  1430           _visitor->examine(e);
  1431         }
  1432       }
  1433       return n;
  1434     }
  1435 
  1436     /// \brief Processes the next node.
  1437     ///
  1438     /// Processes the next node. And checks that at least one of
  1439     /// reached node has true value in the \c nm node map. If one node
  1440     /// with true value is reachable from the processed node then the
  1441     /// rnode parameter will be set to the first of such nodes.
  1442     ///
  1443     /// \param nm The node map of possible targets.
  1444     /// \retval rnode The reached target node.
  1445     /// \return The processed node.
  1446     ///
  1447     /// \warning The queue must not be empty!
  1448     template <typename NM>
  1449     Node processNextNode(const NM& nm, Node& rnode) {
  1450       Node n = _list[++_list_front];
  1451       _visitor->process(n);
  1452       Arc e;
  1453       for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
  1454         Node m = _digraph->target(e);
  1455         if (!(*_reached)[m]) {
  1456           _visitor->discover(e);
  1457           _visitor->reach(m);
  1458           _reached->set(m, true);
  1459           _list[++_list_back] = m;
  1460           if (nm[m] && rnode == INVALID) rnode = m;
  1461         } else {
  1462           _visitor->examine(e);
  1463         }
  1464       }
  1465       return n;
  1466     }
  1467 
  1468     /// \brief Next node to be processed.
  1469     ///
  1470     /// Next node to be processed.
  1471     ///
  1472     /// \return The next node to be processed or INVALID if the stack is
  1473     /// empty.
  1474     Node nextNode() { 
  1475       return _list_front != _list_back ? _list[_list_front + 1] : INVALID;
  1476     }
  1477 
  1478     /// \brief Returns \c false if there are nodes
  1479     /// to be processed in the queue
  1480     ///
  1481     /// Returns \c false if there are nodes
  1482     /// to be processed in the queue
  1483     bool emptyQueue() { return _list_front == _list_back; }
  1484 
  1485     /// \brief Returns the number of the nodes to be processed.
  1486     ///
  1487     /// Returns the number of the nodes to be processed in the queue.
  1488     int queueSize() { return _list_back - _list_front; }
  1489     
  1490     /// \brief Executes the algorithm.
  1491     ///
  1492     /// Executes the algorithm.
  1493     ///
  1494     /// \pre init() must be called and at least one node should be added
  1495     /// with addSource() before using this function.
  1496     void start() {
  1497       while ( !emptyQueue() ) processNextNode();
  1498     }
  1499     
  1500     /// \brief Executes the algorithm until \c dest is reached.
  1501     ///
  1502     /// Executes the algorithm until \c dest is reached.
  1503     ///
  1504     /// \pre init() must be called and at least one node should be added
  1505     /// with addSource() before using this function.
  1506     void start(Node dest) {
  1507       bool reach = false;
  1508       while ( !emptyQueue() && !reach ) processNextNode(dest, reach);
  1509     }
  1510     
  1511     /// \brief Executes the algorithm until a condition is met.
  1512     ///
  1513     /// Executes the algorithm until a condition is met.
  1514     ///
  1515     /// \pre init() must be called and at least one node should be added
  1516     /// with addSource() before using this function.
  1517     ///
  1518     ///\param nm must be a bool (or convertible) node map. The
  1519     ///algorithm will stop when it reaches a node \c v with
  1520     /// <tt>nm[v]</tt> true.
  1521     ///
  1522     ///\return The reached node \c v with <tt>nm[v]</tt> true or
  1523     ///\c INVALID if no such node was found.
  1524     template <typename NM>
  1525     Node start(const NM &nm) {
  1526       Node rnode = INVALID;
  1527       while ( !emptyQueue() && rnode == INVALID ) {
  1528 	processNextNode(nm, rnode);
  1529       }
  1530       return rnode;
  1531     }
  1532 
  1533     /// \brief Runs %BFSVisit algorithm from node \c s.
  1534     ///
  1535     /// This method runs the %BFS algorithm from a root node \c s.
  1536     /// \note b.run(s) is just a shortcut of the following code.
  1537     ///\code
  1538     ///   b.init();
  1539     ///   b.addSource(s);
  1540     ///   b.start();
  1541     ///\endcode
  1542     void run(Node s) {
  1543       init();
  1544       addSource(s);
  1545       start();
  1546     }
  1547 
  1548     /// \brief Runs %BFSVisit algorithm to visit all nodes in the digraph.
  1549     ///    
  1550     /// This method runs the %BFS algorithm in order to
  1551     /// compute the %BFS path to each node. The algorithm computes
  1552     /// - The %BFS tree.
  1553     /// - The distance of each node from the root in the %BFS tree.
  1554     ///
  1555     ///\note b.run() is just a shortcut of the following code.
  1556     ///\code
  1557     ///  b.init();
  1558     ///  for (NodeIt it(digraph); it != INVALID; ++it) {
  1559     ///    if (!b.reached(it)) {
  1560     ///      b.addSource(it);
  1561     ///      b.start();
  1562     ///    }
  1563     ///  }
  1564     ///\endcode
  1565     void run() {
  1566       init();
  1567       for (NodeIt it(*_digraph); it != INVALID; ++it) {
  1568         if (!reached(it)) {
  1569           addSource(it);
  1570           start();
  1571         }
  1572       }
  1573     }
  1574     ///@}
  1575 
  1576     /// \name Query Functions
  1577     /// The result of the %BFS algorithm can be obtained using these
  1578     /// functions.\n
  1579     /// Before the use of these functions,
  1580     /// either run() or start() must be called.
  1581     ///@{
  1582 
  1583     /// \brief Checks if a node is reachable from the root.
  1584     ///
  1585     /// Returns \c true if \c v is reachable from the root(s).
  1586     /// \warning The source nodes are inditated as unreachable.
  1587     /// \pre Either \ref run() or \ref start()
  1588     /// must be called before using this function.
  1589     ///
  1590     bool reached(Node v) { return (*_reached)[v]; }
  1591     ///@}
  1592   };
  1593 
  1594 } //END OF NAMESPACE LEMON
  1595 
  1596 #endif
  1597