///

 ///\todo Revise Manual.

 #include <lemon/list_graph.h>

 #include <lemon/graph_utils.h>

 #include <lemon/bin_heap.h>

 #include <lemon/graph_utils.h>

 #include <lemon/error.h>

 #include <lemon/maps.h>

 /// \addtogroup flowalgs

 /// @{

   ///Default traits class of Bfs class.

   ///Default traits class of Bfs class.

   ///\param GR Graph type.

   template<class GR>

   struct BfsDefaultTraits

   {

     ///The graph type the algorithm runs on. 

     typedef GR Graph;

     ///\brief The type of the map that stores the last

     ///edges of the shortest paths.

     /// 

     ///The type of the map that stores the last

     ///edges of the shortest paths.

     ///It must meet the \ref concept::WriteMap "WriteMap" concept.

     ///

     typedef typename Graph::template NodeMap<typename GR::Edge> PredMap;

     ///Instantiates a PredMap.

     ///This function instantiates a \ref PredMap. 

     ///\param G is the graph, to which we would like to define the PredMap.

     ///\todo The graph alone may be insufficient to initialize

     static PredMap *createPredMap(const GR &G) 

     {

       return new PredMap(G);

     }

 //     ///\brief The type of the map that stores the last but one

 //     ///nodes of the shortest paths.

 //     ///

 //     ///The type of the map that stores the last but one

 //     ///nodes of the shortest paths.

 //     ///It must meet the \ref concept::WriteMap "WriteMap" concept.

 //     ///

 //     typedef NullMap<typename Graph::Node,typename Graph::Node> PredNodeMap;

 //     ///Instantiates a PredNodeMap.

 //     ///This function instantiates a \ref PredNodeMap. 

 //     ///\param G is the graph, to which

 //     ///we would like to define the \ref PredNodeMap

 //     static PredNodeMap *createPredNodeMap(const GR &G)

 //     {

 //       return new PredNodeMap();

 //     }

     ///The type of the map that indicates which nodes are processed.

     ///The type of the map that indicates which nodes are processed.

     ///It must meet the \ref concept::WriteMap "WriteMap" concept.

     ///\todo named parameter to set this type, function to read and write.

     typedef NullMap<typename Graph::Node,bool> ProcessedMap;

     ///Instantiates a ProcessedMap.

     ///This function instantiates a \ref ProcessedMap. 

     ///\param G is the graph, to which

     ///we would like to define the \ref ProcessedMap

     static ProcessedMap *createProcessedMap(const GR &G)

     {

       return new ProcessedMap();

     }

     ///The type of the map that indicates which nodes are reached.

     ///The type of the map that indicates which nodes are reached.

     ///It must meet the \ref concept::WriteMap "WriteMap" concept.

     ///\todo named parameter to set this type, function to read and write.

     typedef typename Graph::template NodeMap<bool> ReachedMap;

     ///Instantiates a ReachedMap.

     ///This function instantiates a \ref ReachedMap. 

     ///\param G is the graph, to which

     ///we would like to define the \ref ReachedMap.

     static ReachedMap *createReachedMap(const GR &G)

     {

       return new ReachedMap(G);

     }

     ///The type of the map that stores the dists of the nodes.

     ///The type of the map that stores the dists of the nodes.

     ///It must meet the \ref concept::WriteMap "WriteMap" concept.

     ///

     typedef typename Graph::template NodeMap<int> DistMap;

     ///Instantiates a DistMap.

     ///This function instantiates a \ref DistMap. 

     ///\param G is the graph, to which we would like to define the \ref DistMap

     static DistMap *createDistMap(const GR &G)

     {

       return new DistMap(G);

     }

   };

   ///This class provides an efficient implementation of %BFS algorithm.

   ///\ingroup flowalgs

   ///\param GR The graph type the algorithm runs on.

   ///This class provides an efficient implementation of the %BFS algorithm.

   ///This class does the same as Dijkstra does with constant 1 edge length,

   ///but it is faster.

   ///\author Alpar Juttner

   ///\param GR The graph type the algorithm runs on. The default value is

   ///\ref ListGraph. The value of GR is not used directly by Bfs, it

   ///is only passed to \ref BfsDefaultTraits.

   ///\param TR Traits class to set various data types used by the algorithm.

   ///The default traits class is

   ///\ref BfsDefaultTraits "BfsDefaultTraits<GR>".

   ///See \ref BfsDefaultTraits for the documentation of

   ///a Bfs traits class.

   ///

   ///\author Jacint Szabo and Alpar Juttner

   ///\todo A compare object would be nice.

   template <typename GR>

   template <typename GR,

 	    typename TR>

   template <typename GR>

   template <typename GR=ListGraph,

 	    typename TR=BfsDefaultTraits<GR> >

   class Bfs{

   class Bfs {

     typedef GR Graph;

     typedef typename TR::Graph Graph;

     typedef typename Graph::template NodeMap<Edge> PredMap;

     typedef typename TR::PredMap PredMap;

     ///\brief The type of the map that stores the last but one

 //     ///\brief The type of the map that stores the last but one

     ///nodes of the shortest paths.

 //     ///nodes of the shortest paths.

     typedef typename Graph::template NodeMap<Node> PredNodeMap;

 //     typedef typename TR::PredNodeMap PredNodeMap;

     ///The type of the map indicating which nodes are reached.

     typedef typename TR::ReachedMap ReachedMap;

     ///The type of the map indicating which nodes are processed.

     typedef typename TR::ProcessedMap ProcessedMap;

     typedef typename Graph::template NodeMap<int> DistMap;

     typedef typename TR::DistMap DistMap;

     PredMap *predecessor;

     PredMap *_pred;

     ///Indicates if \ref predecessor is locally allocated (\c true) or not.

     ///Indicates if \ref _pred is locally allocated (\c true) or not.

     bool local_predecessor;

     bool local_pred;

     ///Pointer to the map of predecessors nodes.

 //     ///Pointer to the map of predecessors nodes.

     PredNodeMap *pred_node;

 //     PredNodeMap *_predNode;

     ///Indicates if \ref pred_node is locally allocated (\c true) or not.

 //     ///Indicates if \ref _predNode is locally allocated (\c true) or not.

     bool local_pred_node;

 //     bool local_predNode;

     DistMap *distance;

     DistMap *_dist;

     ///Indicates if \ref distance is locally allocated (\c true) or not.

     ///Indicates if \ref _dist is locally allocated (\c true) or not.

     bool local_distance;

     bool local_dist;

     ///Pointer to the map of reached status of the nodes.

     ///The source node of the last execution.

     ReachedMap *_reached;

     Node source;

     ///Indicates if \ref _reached is locally allocated (\c true) or not.

     bool local_reached;

     ///Pointer to the map of processed status of the nodes.

     ///Initializes the maps.

     ProcessedMap *_processed;

     void init_maps() 

     ///Indicates if \ref _processed is locally allocated (\c true) or not.

     {

     bool local_processed;

       if(!predecessor) {

 	local_predecessor = true;

     std::vector<typename Graph::Node> _queue;

 	predecessor = new PredMap(*G);

     int _queue_head,_queue_tail,_queue_next_dist;

       }

     int _curr_dist;

       if(!pred_node) {

 //     ///The source node of the last execution.

 	local_pred_node = true;

 //     Node source;

 	pred_node = new PredNodeMap(*G);

       }

     ///Creates the maps if necessary.

       if(!distance) {

 	local_distance = true;

     ///\todo Error if \c G are \c NULL.

 	distance = new DistMap(*G);

     ///\todo Better memory allocation (instead of new).

       }

     void create_maps() 

     }

     {

       if(!_pred) {

   public :    

 	local_pred = true;

 	_pred = Traits::createPredMap(*G);

       }

 //       if(!_predNode) {

 // 	local_predNode = true;

 // 	_predNode = Traits::createPredNodeMap(*G);

 //       }

       if(!_dist) {

 	local_dist = true;

 	_dist = Traits::createDistMap(*G);

       }

       if(!_reached) {

 	local_reached = true;

 	_reached = Traits::createReachedMap(*G);

       }

       if(!_processed) {

 	local_processed = true;

 	_processed = Traits::createProcessedMap(*G);

       }

     }

   public :

     ///\name Named template parameters

     ///@{

     template <class T>

     struct DefPredMapTraits : public Traits {

       typedef T PredMap;

       static PredMap *createPredMap(const Graph &G) 

       {

 	throw UninitializedParameter();

       }

     };

     ///\ref named-templ-param "Named parameter" for setting PredMap type

     ///\ref named-templ-param "Named parameter" for setting PredMap type

     ///

     template <class T>

     class DefPredMap : public Bfs< Graph,

 					DefPredMapTraits<T> > { };

 //     template <class T>

 //     struct DefPredNodeMapTraits : public Traits {

 //       typedef T PredNodeMap;

 //       static PredNodeMap *createPredNodeMap(const Graph &G) 

 //       {

 // 	throw UninitializedParameter();

 //       }

 //     };

 //     ///\ref named-templ-param "Named parameter" for setting PredNodeMap type

 //     ///\ref named-templ-param "Named parameter" for setting PredNodeMap type

 //     ///

 //     template <class T>

 //     class DefPredNodeMap : public Bfs< Graph,

 // 					    LengthMap,

 // 					    DefPredNodeMapTraits<T> > { };

     template <class T>

     struct DefDistMapTraits : public Traits {

       typedef T DistMap;

       static DistMap *createDistMap(const Graph &G) 

       {

 	throw UninitializedParameter();

       }

     };

     ///\ref named-templ-param "Named parameter" for setting DistMap type

     ///\ref named-templ-param "Named parameter" for setting DistMap type

     ///

     template <class T>

     class DefDistMap : public Bfs< Graph,

 				   DefDistMapTraits<T> > { };

     template <class T>

     struct DefReachedMapTraits : public Traits {

       typedef T ReachedMap;

       static ReachedMap *createReachedMap(const Graph &G) 

       {

 	throw UninitializedParameter();

       }

     };

     ///\ref named-templ-param "Named parameter" for setting ReachedMap type

     ///\ref named-templ-param "Named parameter" for setting ReachedMap type

     ///

     template <class T>

     class DefReachedMap : public Bfs< Graph,

 				      DefReachedMapTraits<T> > { };

     struct DefGraphReachedMapTraits : public Traits {

       typedef typename Graph::template NodeMap<bool> ReachedMap;

       static ReachedMap *createReachedMap(const Graph &G) 

       {

 	return new ReachedMap(G);

       }

     };

     template <class T>

     struct DefProcessedMapTraits : public Traits {

       typedef T ProcessedMap;

       static ProcessedMap *createProcessedMap(const Graph &G) 

       {

 	throw UninitializedParameter();

       }

     };

     ///\ref named-templ-param "Named parameter" for setting ProcessedMap type

     ///\ref named-templ-param "Named parameter" for setting ProcessedMap type

     ///

     template <class T>

     class DefProcessedMap : public Bfs< Graph,

 					DefProcessedMapTraits<T> > { };

     struct DefGraphProcessedMapTraits : public Traits {

       typedef typename Graph::template NodeMap<bool> ProcessedMap;

       static ProcessedMap *createProcessedMap(const Graph &G) 

       {

 	return new ProcessedMap(G);

       }

     };

     ///\brief \ref named-templ-param "Named parameter"

     ///for setting the ProcessedMap type to be Graph::NodeMap<bool>.

     ///

     ///\ref named-templ-param "Named parameter"

     ///for setting the ProcessedMap type to be Graph::NodeMap<bool>.

     ///If you don't set it explicitely, it will be automatically allocated.

     template <class T>

     class DefProcessedMapToBeDefaultMap :

       public Bfs< Graph,

 		  DefGraphProcessedMapTraits> { };

     ///@}

   public:      

       predecessor(NULL), local_predecessor(false),

       _pred(NULL), local_pred(false),

       pred_node(NULL), local_pred_node(false),

 //       _predNode(NULL), local_predNode(false),

       distance(NULL), local_distance(false)

       _dist(NULL), local_dist(false),

       _reached(NULL), local_reached(false),

       _processed(NULL), local_processed(false)

       if(local_predecessor) delete predecessor;

       if(local_pred) delete _pred;

       if(local_pred_node) delete pred_node;

 //       if(local_predNode) delete _predNode;

       if(local_distance) delete distance;

       if(local_dist) delete _dist;

       if(local_reached) delete _reached;

       if(local_processed) delete _processed;

     Bfs &setPredMap(PredMap &m) 

     Bfs &predMap(PredMap &m) 

     {

     {

       if(local_predecessor) {

       if(local_pred) {

 	delete predecessor;

 	delete _pred;

 	local_predecessor=false;

 	local_pred=false;

       }

       }

       predecessor = &m;

       _pred = &m;

     ///Sets the map storing the predecessor nodes.

     ///Sets the map indicating the reached nodes.

     ///Sets the map storing the predecessor nodes.

     ///Sets the map indicating the reached nodes.

     Bfs &setPredNodeMap(PredNodeMap &m) 

     Bfs &reachedMap(ReachedMap &m) 

     {

     {

       if(local_pred_node) {

       if(local_reached) {

 	delete pred_node;

 	delete _reached;

 	local_pred_node=false;

 	local_reached=false;

       }

       }

       pred_node = &m;

       _reached = &m;

     Bfs &setDistMap(DistMap &m) 

     Bfs &distMap(DistMap &m) 

     {

     {

       if(local_distance) {

       if(local_dist) {

 	delete distance;

 	delete _dist;

 	local_distance=false;

 	local_dist=false;

       }

       }

       distance = &m;

       _dist = &m;

   ///Runs %BFS algorithm from node \c s.

   public:

     ///\name Execution control

   ///This method runs the %BFS algorithm from a root node \c s

     ///The simplest way to execute the algorithm is to use

   ///in order to

     ///one of the member functions called \c run(...).

   ///compute a

     ///\n

   ///shortest path to each node. The algorithm computes

     ///If you need more control on the execution,

   ///- The %BFS tree.

     ///first you must call \ref init(), then you can add several source nodes

   ///- The distance of each node from the root.

     ///with \ref addSource().

     ///Finally \ref start() will perform the actual path

     ///computation.

     ///@{

     ///Initializes the internal data structures.

     ///Initializes the internal data structures.

     ///

     void init()

     {

       create_maps();

       _queue.resize(countNodes(*G));

       _queue_head=_queue_tail=0;

       _curr_dist=1;

       for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {

 	_pred->set(u,INVALID);

 // 	_predNode->set(u,INVALID);

 	_reached->set(u,false);

 	_processed->set(u,false);

       }

     }

     ///Adds a new source node.

     ///Adds a new source node to the set of nodes to be processed.

     ///

     void addSource(Node s)

     {

       if(!(*_reached)[s])

 	{

 	  _reached->set(s,true);

 	  _pred->set(s,INVALID);

 	  _dist->set(s,0);

 	  _queue[_queue_head++]=s;

 	  _queue_next_dist=_queue_head;

 	}

     }

     ///Processes the next node.

     ///Processes the next node.

     ///

     ///\warning The queue must not be empty!

     void processNextNode()

     {

       if(_queue_tail==_queue_next_dist) {

 	_curr_dist++;

 	_queue_next_dist=_queue_head;

       }

       Node n=_queue[_queue_tail++];

       _processed->set(n,true);

       Node m;

       for(OutEdgeIt e(*G,n);e!=INVALID;++e)

 	if(!(*_reached)[m=G->target(e)]) {

 	  _queue[_queue_head++]=m;

 	  _reached->set(m,true);

 	  _pred->set(m,e);

 // 	  _pred_node->set(m,n);

 	  _dist->set(m,_curr_dist);

 	}

     }

     ///\brief Returns \c false if there are nodes

     ///to be processed in the queue

     ///

     ///Returns \c false if there are nodes

     ///to be processed in the queue

     bool emptyQueue() { return _queue_tail==_queue_head; }

     ///Returns the number of the nodes to be processed.

     ///Returns the number of the nodes to be processed in the queue.

     ///

     int queueSize() { return _queue_head-_queue_tail; }

     ///Executes the algorithm.

     ///Executes the algorithm.

     ///

     ///\pre init() must be called and at least one node should be added

     ///with addSource() before using this function.

     ///

     ///This method runs the %BFS algorithm from the root node(s)

     ///in order to

     ///compute the

     ///shortest path to each node. The algorithm computes

     ///- The shortest path tree.

     ///- The distance of each node from the root(s).

     ///

     void start()

     {

       while ( !emptyQueue() ) processNextNode();

     }

     ///Executes the algorithm until \c dest is reached.

     ///Executes the algorithm until \c dest is reached.

     ///

     ///\pre init() must be called and at least one node should be added

     ///with addSource() before using this function.

     ///

     ///This method runs the %BFS algorithm from the root node(s)

     ///in order to

     ///compute the

     ///shortest path to \c dest. The algorithm computes

     ///- The shortest path to \c  dest.

     ///- The distance of \c dest from the root(s).

     ///

     void start(Node dest)

     {

       while ( !emptyQueue() && _queue[_queue_tail]!=dest ) processNextNode();

     }

     ///Executes the algorithm until a condition is met.

     ///Executes the algorithm until a condition is met.

     ///

     ///\pre init() must be called and at least one node should be added

     ///with addSource() before using this function.

     ///

     ///\param nm must be a bool (or convertible) node map. The algorithm

     ///will stop when it reaches a node \c v with <tt>nm[v]==true</tt>.

     template<class NM>

       void start(const NM &nm)

       {

 	while ( !emptyQueue() && !nm[_queue[_queue_tail]] ) processNextNode();

       }

     ///Runs %BFS algorithm from node \c s.

     ///This method runs the %BFS algorithm from a root node \c s

     ///in order to

     ///compute the

     ///shortest path to each node. The algorithm computes

     ///- The shortest path tree.

     ///- The distance of each node from the root.

     ///

     ///\note d.run(s) is just a shortcut of the following code.

     ///\code

     ///  d.init();

     ///  d.addSource(s);

     ///  d.start();

     ///\endcode

       init();

       init_maps();

       addSource(s);

       start();

       source = s;

     }

       for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {

     ///Finds the shortest path between \c s and \c t.

 	predecessor->set(u,INVALID);

 	pred_node->set(u,INVALID);

     ///Finds the shortest path between \c s and \c t.

       }

     ///

     ///\return The length of the shortest s---t path if there exists one,

       int N = countNodes(*G);

     ///0 otherwise.

       std::vector<typename Graph::Node> Q(N);

     ///\note Apart from the return value, d.run(s) is

       int Qh=0;

     ///just a shortcut of the following code.

       int Qt=0;

     ///\code

     ///  d.init();

       Q[Qh++]=source;

     ///  d.addSource(s);

       distance->set(s, 0);

     ///  d.start(t);

       do {

     ///\endcode

 	Node m;

     int run(Node s,Node t) {

 	Node n=Q[Qt++];

       init();

 	int d= (*distance)[n]+1;

       addSource(s);

       start(t);

 	for(OutEdgeIt e(*G,n);e!=INVALID;++e)

       return reached(t)?_curr_dist-1+(_queue_tail==_queue_next_dist):0;

 	  if((m=G->target(e))!=s && (*predecessor)[m]==INVALID) {

     }

 	    Q[Qh++]=m;

 	    predecessor->set(m,e);

     ///@}

 	    pred_node->set(m,n);

 	    distance->set(m,d);

     ///\name Query Functions

 	  }

     ///The result of the %BFS algorithm can be obtained using these

       } while(Qt!=Qh);

     ///functions.\n

     }

     ///Before the use of these functions,

     ///either run() or start() must be called.

     ///The distance of a node from the root.

     ///@{

     ///Returns the distance of a node from the root.

     ///The distance of a node from the root(s).

     ///Returns the distance of a node from the root(s).

     ///\warning If node \c v in unreachable from the root the return value

     ///\warning If node \c v in unreachable from the root(s) the return value

     int dist(Node v) const { return (*distance)[v]; }

     int dist(Node v) const { return (*_dist)[v]; }

     ///Returns the 'previous edge' of the %BFS path tree.

     ///Returns the 'previous edge' of the shortest path tree.

     ///For a node \c v it returns the 'previous edge' of the %BFS tree,

     ///For a node \c v it returns the 'previous edge'

     ///i.e. it returns the last edge of a shortest path from the root to \c

     ///of the shortest path tree,

     ///i.e. it returns the last edge of a shortest path from the root(s) to \c

     ///if \c v is unreachable from the root or if \c v=s. The

     ///if \c v is unreachable from the root(s) or \c v is a root. The

     ///%BFS tree used here is equal to the %BFS tree used in

     ///shortest path tree used here is equal to the shortest path tree used in

     ///\ref predNode(Node v).  \pre \ref run() must be called before using

     ///\ref predNode(Node v).

     ///\pre Either \ref run() or \ref start() must be called before using

     Edge pred(Node v) const { return (*predecessor)[v]; }

     ///\todo predEdge could be a better name.

     Edge pred(Node v) const { return (*_pred)[v];}

     ///Returns the 'previous node' of the %BFS tree.

     ///Returns the 'previous node' of the shortest path tree.

     ///For a node \c v it returns the 'previous node' on the %BFS tree,

     ///For a node \c v it returns the 'previous node'

     ///of the shortest path tree,

     ///root to \c /v. It is INVALID if \c v is unreachable from the root or if

     ///root(a) to \c /v.

     ///\c v=s. The shortest path tree used here is equal to the %BFS

     ///It is INVALID if \c v is unreachable from the root(s) or

     ///tree used in \ref pred(Node v).  \pre \ref run() must be called before

     ///if \c v itself a root.

     ///The shortest path tree used here is equal to the shortest path

     ///tree used in \ref pred(Node v).

     ///\pre Either \ref run() or \ref start() must be called before

     Node predNode(Node v) const { return (*pred_node)[v]; }

     Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:

 				  G->source((*_pred)[v]); }

     ///Returns a reference to the NodeMap of distances. \pre \ref run() must

     ///Returns a reference to the NodeMap of distances.

     ///\pre Either \ref run() or \ref init() must

     const DistMap &distMap() const { return *distance;}

     const DistMap &distMap() const { return *_dist;}

     ///Returns a reference to the %BFS tree map.

     ///Returns a reference to the shortest path tree map.

     ///%BFS tree.

     ///shortest path tree.

     ///\pre \ref run() must be called before using this function.

     ///\pre Either \ref run() or \ref init()

     const PredMap &predMap() const { return *predecessor;}

     ///must be called before using this function.

     const PredMap &predMap() const { return *_pred;}

     ///Returns a reference to the map of last but one nodes of shortest paths.

 //     ///Returns a reference to the map of nodes of shortest paths.

     ///Returns a reference to the NodeMap of the last but one nodes on the

     ///%BFS tree.

 //     ///Returns a reference to the NodeMap of the last but one nodes of the

     ///\pre \ref run() must be called before using this function.

 //     ///shortest path tree.

     const PredNodeMap &predNodeMap() const { return *pred_node;}

 //     ///\pre \ref run() must be called before using this function.

 //     const PredNodeMap &predNodeMap() const { return *_predNode;}

     ///\note The root node is reported to be reached!

     ///\warning The source nodes are inditated as unreached.

     ///

     ///\pre Either \ref run() or \ref start()

     ///\pre \ref run() must be called before using this function.

     ///must be called before using this function.

     ///

     ///

     bool reached(Node v) { return v==source || (*predecessor)[v]!=INVALID; }

     bool reached(Node v) { return (*_reached)[v]; }

     ///@}

   };

   ///Default traits class of Bfs function.

   ///Default traits class of Bfs function.

   ///\param GR Graph type.

   template<class GR>

   struct BfsWizardDefaultTraits

   {

     ///The graph type the algorithm runs on. 

     typedef GR Graph;

     ///\brief The type of the map that stores the last

     ///edges of the shortest paths.

     /// 

     ///The type of the map that stores the last

     ///edges of the shortest paths.

     ///It must meet the \ref concept::WriteMap "WriteMap" concept.

     ///

     typedef NullMap<typename Graph::Node,typename GR::Edge> PredMap;

     ///Instantiates a PredMap.

     ///This function instantiates a \ref PredMap. 

     ///\param G is the graph, to which we would like to define the PredMap.

     ///\todo The graph alone may be insufficient to initialize

     static PredMap *createPredMap(const GR &G) 

     {

       return new PredMap();

     }

 //     ///\brief The type of the map that stores the last but one

 //     ///nodes of the shortest paths.

 //     ///

 //     ///The type of the map that stores the last but one

 //     ///nodes of the shortest paths.

 //     ///It must meet the \ref concept::WriteMap "WriteMap" concept.

 //     ///

 //     typedef NullMap<typename Graph::Node,typename Graph::Node> PredNodeMap;

 //     ///Instantiates a PredNodeMap.

 //     ///This function instantiates a \ref PredNodeMap. 

 //     ///\param G is the graph, to which

 //     ///we would like to define the \ref PredNodeMap

 //     static PredNodeMap *createPredNodeMap(const GR &G)

 //     {

 //       return new PredNodeMap();

 //     }

     ///The type of the map that indicates which nodes are processed.

     ///The type of the map that indicates which nodes are processed.

     ///It must meet the \ref concept::WriteMap "WriteMap" concept.

     ///\todo named parameter to set this type, function to read and write.

     typedef NullMap<typename Graph::Node,bool> ProcessedMap;

     ///Instantiates a ProcessedMap.

     ///This function instantiates a \ref ProcessedMap. 

     ///\param G is the graph, to which

     ///we would like to define the \ref ProcessedMap

     static ProcessedMap *createProcessedMap(const GR &G)

     {

       return new ProcessedMap();

     }

     ///The type of the map that indicates which nodes are reached.

     ///The type of the map that indicates which nodes are reached.

     ///It must meet the \ref concept::WriteMap "WriteMap" concept.

     ///\todo named parameter to set this type, function to read and write.

     typedef typename Graph::template NodeMap<bool> ReachedMap;

     ///Instantiates a ReachedMap.

     ///This function instantiates a \ref ReachedMap. 

     ///\param G is the graph, to which

     ///we would like to define the \ref ReachedMap.

     static ReachedMap *createReachedMap(const GR &G)

     {

       return new ReachedMap(G);

     }

     ///The type of the map that stores the dists of the nodes.

     ///The type of the map that stores the dists of the nodes.

     ///It must meet the \ref concept::WriteMap "WriteMap" concept.

     ///

     typedef NullMap<typename Graph::Node,int> DistMap;

     ///Instantiates a DistMap.

     ///This function instantiates a \ref DistMap. 

     ///\param G is the graph, to which we would like to define the \ref DistMap

     static DistMap *createDistMap(const GR &G)

     {

       return new DistMap();

     }

 /// @}

   /// Default traits used by \ref BfsWizard

   /// To make it easier to use Bfs algorithm

   ///we have created a wizard class.

   /// This \ref BfsWizard class needs default traits,

   ///as well as the \ref Bfs class.

   /// The \ref BfsWizardBase is a class to be the default traits of the

   /// \ref BfsWizard class.

   template<class GR>

   class BfsWizardBase : public BfsWizardDefaultTraits<GR>

   {

     typedef BfsWizardDefaultTraits<GR> Base;

   protected:

     /// Type of the nodes in the graph.

     typedef typename Base::Graph::Node Node;

     /// Pointer to the underlying graph.

     void *_g;

     ///Pointer to the map of reached nodes.

     void *_reached;

     ///Pointer to the map of processed nodes.

     void *_processed;

     ///Pointer to the map of predecessors edges.

     void *_pred;

 //     ///Pointer to the map of predecessors nodes.

 //     void *_predNode;

     ///Pointer to the map of distances.

     void *_dist;

     ///Pointer to the source node.

     Node _source;

     public:

     /// Constructor.

     /// This constructor does not require parameters, therefore it initiates

     /// all of the attributes to default values (0, INVALID).

     BfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0),

 // 			   _predNode(0),

 			   _dist(0), _source(INVALID) {}

     /// Constructor.

     /// This constructor requires some parameters,

     /// listed in the parameters list.

     /// Others are initiated to 0.

     /// \param g is the initial value of  \ref _g

     /// \param s is the initial value of  \ref _source

     BfsWizardBase(const GR &g, Node s=INVALID) :

       _g((void *)&g), _reached(0), _processed(0), _pred(0),

 //       _predNode(0),

       _dist(0), _source(s) {}

   };