/* -*- C++ -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2003-2007

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 #ifndef LEMON_BFS_H

 #define LEMON_BFS_H

 ///\ingroup search

 ///\file

 ///\brief Bfs algorithm.

 #include <lemon/list_graph.h>

 #include <lemon/graph_utils.h>

 #include <lemon/bits/path_dump.h>

 #include <lemon/bits/invalid.h>

 #include <lemon/error.h>

 #include <lemon/maps.h>

 namespace lemon {

   ///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 concepts::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);

     }

     ///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 concepts::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

 #ifdef DOXYGEN

     static ProcessedMap *createProcessedMap(const GR &g)

 #else

     static ProcessedMap *createProcessedMap(const GR &)

 #endif

     {

       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 concepts::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 concepts::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);

     }

   };

   ///%BFS algorithm class.

   ///\ingroup search

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

   ///

   ///\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 Alpar Juttner

 #ifdef DOXYGEN

   template <typename GR,

 	    typename TR>

 #else

   template <typename GR=ListGraph,

 	    typename TR=BfsDefaultTraits<GR> >

 #endif

   class Bfs {

   public:

     /**

      * \brief \ref Exception for uninitialized parameters.

      *

      * This error represents problems in the initialization

      * of the parameters of the algorithms.

      */

     class UninitializedParameter : public lemon::UninitializedParameter {

     public:

       virtual const char* what() const throw() {

 	return "lemon::Bfs::UninitializedParameter";

       }

     };

     typedef TR Traits;

     ///The type of the underlying graph.

     typedef typename TR::Graph Graph;

     ///\e

     typedef typename Graph::Node Node;

     ///\e

     typedef typename Graph::NodeIt NodeIt;

     ///\e

     typedef typename Graph::Edge Edge;

     ///\e

     typedef typename Graph::OutEdgeIt OutEdgeIt;

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

     ///edges of the shortest paths.

     typedef typename TR::PredMap PredMap;

     ///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;

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

     typedef typename TR::DistMap DistMap;

   private:

     /// Pointer to the underlying graph.

     const Graph *G;

     ///Pointer to the map of predecessors edges.

     PredMap *_pred;

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

     bool local_pred;

     ///Pointer to the map of distances.

     DistMap *_dist;

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

     bool local_dist;

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

     ReachedMap *_reached;

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

     bool local_reached;

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

     ProcessedMap *_processed;

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

     bool local_processed;

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

     int _queue_head,_queue_tail,_queue_next_dist;

     int _curr_dist;

     ///Creates the maps if necessary.

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

     void create_maps() 

     {

       if(!_pred) {

 	local_pred = true;

 	_pred = Traits::createPredMap(*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);

       }

     }

   protected:

     Bfs() {}

   public:

     typedef Bfs Create;

     ///\name Named template parameters

     ///@{

     template <class T>

     struct DefPredMapTraits : public Traits {

       typedef T PredMap;

       static PredMap *createPredMap(const Graph &) 

       {

 	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>

     struct DefPredMap : public Bfs< Graph, DefPredMapTraits<T> > { 

       typedef Bfs< Graph, DefPredMapTraits<T> > Create;

     };

     template <class T>

     struct DefDistMapTraits : public Traits {

       typedef T DistMap;

       static DistMap *createDistMap(const Graph &) 

       {

 	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>

     struct DefDistMap : public Bfs< Graph, DefDistMapTraits<T> > { 

       typedef Bfs< Graph, DefDistMapTraits<T> > Create;

     };

     template <class T>

     struct DefReachedMapTraits : public Traits {

       typedef T ReachedMap;

       static ReachedMap *createReachedMap(const Graph &) 

       {

 	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>

     struct DefReachedMap : public Bfs< Graph, DefReachedMapTraits<T> > { 

       typedef Bfs< Graph, DefReachedMapTraits<T> > Create;

     };

     template <class T>

     struct DefProcessedMapTraits : public Traits {

       typedef T ProcessedMap;

       static ProcessedMap *createProcessedMap(const Graph &) 

       {

 	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>

     struct DefProcessedMap : public Bfs< Graph, DefProcessedMapTraits<T> > {

       typedef Bfs< Graph, DefProcessedMapTraits<T> > Create;

     };

     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 explicitly, it will be automatically allocated.

     template <class T>

     struct DefProcessedMapToBeDefaultMap :

       public Bfs< Graph, DefGraphProcessedMapTraits> { 

       typedef Bfs< Graph, DefGraphProcessedMapTraits> Create;

     };

     ///@}

   public:      

     ///Constructor.

     ///\param _G the graph the algorithm will run on.

     ///

     Bfs(const Graph& _G) :

       G(&_G),

       _pred(NULL), local_pred(false),

       _dist(NULL), local_dist(false),

       _reached(NULL), local_reached(false),

       _processed(NULL), local_processed(false)

     { }

     ///Destructor.

     ~Bfs() 

     {

       if(local_pred) delete _pred;

       if(local_dist) delete _dist;

       if(local_reached) delete _reached;

       if(local_processed) delete _processed;

     }

     ///Sets the map storing the predecessor edges.

     ///Sets the map storing the predecessor edges.

     ///If you don't use this function before calling \ref run(),

     ///it will allocate one. The destructor deallocates this

     ///automatically allocated map, of course.

     ///\return <tt> (*this) </tt>

     Bfs &predMap(PredMap &m) 

     {

       if(local_pred) {

 	delete _pred;

 	local_pred=false;

       }

       _pred = &m;

       return *this;

     }

     ///Sets the map indicating the reached nodes.

     ///Sets the map indicating the reached nodes.

     ///If you don't use this function before calling \ref run(),

     ///it will allocate one. The destructor deallocates this

     ///automatically allocated map, of course.

     ///\return <tt> (*this) </tt>

     Bfs &reachedMap(ReachedMap &m) 

     {

       if(local_reached) {

 	delete _reached;

 	local_reached=false;

       }

       _reached = &m;

       return *this;

     }

     ///Sets the map indicating the processed nodes.

     ///Sets the map indicating the processed nodes.

     ///If you don't use this function before calling \ref run(),

     ///it will allocate one. The destructor deallocates this

     ///automatically allocated map, of course.

     ///\return <tt> (*this) </tt>

     Bfs &processedMap(ProcessedMap &m) 

     {

       if(local_processed) {

 	delete _processed;

 	local_processed=false;

       }

       _processed = &m;

       return *this;

     }

     ///Sets the map storing the distances calculated by the algorithm.

     ///Sets the map storing the distances calculated by the algorithm.

     ///If you don't use this function before calling \ref run(),

     ///it will allocate one. The destructor deallocates this

     ///automatically allocated map, of course.

     ///\return <tt> (*this) </tt>

     Bfs &distMap(DistMap &m) 

     {

       if(local_dist) {

 	delete _dist;

 	local_dist=false;

       }

       _dist = &m;

       return *this;

     }

   public:

     ///\name Execution control

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

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

     ///\n

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

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

     ///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);

 	_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.

     ///

     ///\return The processed node.

     ///

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

     Node 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);

 	  _dist->set(m,_curr_dist);

 	}

       return n;

     }

     ///Processes the next node.

     ///Processes the next node. And checks that the given target node

     ///is reached. If the target node is reachable from the processed

     ///node then the reached parameter will be set true. The reached

     ///parameter should be initially false.

     ///

     ///\param target The target node.

     ///\retval reach Indicates that the target node is reached.

     ///\return The processed node.

     ///

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

     Node processNextNode(Node target, bool& reach)

     {

       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);

 	  _dist->set(m,_curr_dist);

           reach = reach || (target == m);

 	}

       return n;

     }

     ///Processes the next node.

     ///Processes the next node. And checks that at least one of

     ///reached node has true value in the \c nm node map. If one node

     ///with true value is reachable from the processed node then the

     ///rnode parameter will be set to the first of such nodes.

     ///

     ///\param nm The node map of possible targets.

     ///\retval rnode The reached target node.

     ///\return The processed node.

     ///

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

     template<class NM>

     Node processNextNode(const NM& nm, Node& rnode)

     {

       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);

 	  _dist->set(m,_curr_dist);

 	  if (nm[m] && rnode == INVALID) rnode = m;

 	}

       return n;

     }

     ///Next node to be processed.

     ///Next node to be processed.

     ///

     ///\return The next node to be processed or INVALID if the queue is

     /// empty.

     Node nextNode()

     { 

       return _queue_tail<_queue_head?_queue[_queue_tail]:INVALID;

     }

     ///\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)

     {

       bool reach = false;

       while ( !emptyQueue() && !reach ) processNextNode(dest, reach);

     }

     ///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]</tt> true.

     ///

     ///\return The reached node \c v with <tt>nm[v]</tt> true or

     ///\c INVALID if no such node was found.

     template<class NM>

     Node start(const NM &nm)

     {

       Node rnode = INVALID;

       while ( !emptyQueue() && rnode == INVALID ) {

 	processNextNode(nm, rnode);

       }

       return rnode;

     }

     ///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 b.run(s) is just a shortcut of the following code.

     ///\code

     ///  b.init();

     ///  b.addSource(s);

     ///  b.start();

     ///\endcode

     void run(Node s) {

       init();

       addSource(s);

       start();

     }

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

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

     ///

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

     ///0 otherwise.

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

     ///just a shortcut of the following code.

     ///\code

     ///  b.init();

     ///  b.addSource(s);

     ///  b.start(t);

     ///\endcode

     int run(Node s,Node t) {

       init();

       addSource(s);

       start(t);

       return reached(t) ? _curr_dist : 0;

     }

     ///@}

     ///\name Query Functions

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

     ///functions.\n

     ///Before the use of these functions,

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

     ///@{

     typedef PredMapPath<Graph, PredMap> Path;

     ///Gives back the shortest path.

     ///Gives back the shortest path.

     ///\pre The \c t should be reachable from the source.

     Path path(Node t) 

     {

       return Path(*G, *_pred, t);

     }

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

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

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

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

     ///of this function is undefined.

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

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

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

     ///of the shortest path tree,

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

     ///v. It is \ref INVALID

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

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

     ///\ref predNode().

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

     ///this function.

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

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

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

     ///of the shortest path tree,

     ///i.e. it returns the last but one node from a shortest path from the

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

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

     ///if \c v itself a root.

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

     ///tree used in \ref predEdge().

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

     ///using this function.

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

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

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

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

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

     ///be called before using this function.

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

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

     ///Returns a reference to the NodeMap of the edges of the

     ///shortest path tree.

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

     ///must be called before using this function.

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

     ///Checks if a node is reachable from the root.

     ///Returns \c true if \c v is reachable from the root.

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

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

     ///must be called before using this function.

     ///

     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 concepts::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

 #ifdef DOXYGEN

     static PredMap *createPredMap(const GR &g) 

 #else

     static PredMap *createPredMap(const GR &) 

 #endif

     {

       return new PredMap();

     }

     ///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 concepts::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

 #ifdef DOXYGEN

     static ProcessedMap *createProcessedMap(const GR &g)

 #else

     static ProcessedMap *createProcessedMap(const GR &)

 #endif

     {

       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 concepts::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 concepts::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

 #ifdef DOXYGEN

     static DistMap *createDistMap(const GR &g)

 #else

     static DistMap *createDistMap(const GR &)

 #endif

     {

       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 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),

 			   _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(reinterpret_cast<void*>(const_cast<GR*>(&g))), 

       _reached(0), _processed(0), _pred(0), _dist(0), _source(s) {}

   };

   /// A class to make the usage of Bfs algorithm easier

   /// This class is created to make it easier to use Bfs algorithm.

   /// It uses the functions and features of the plain \ref Bfs,

   /// but it is much simpler to use it.

   ///

   /// Simplicity means that the way to change the types defined

   /// in the traits class is based on functions that returns the new class

   /// and not on templatable built-in classes.

   /// When using the plain \ref Bfs

   /// the new class with the modified type comes from

   /// the original class by using the ::

   /// operator. In the case of \ref BfsWizard only

   /// a function have to be called and it will

   /// return the needed class.

   ///

   /// It does not have own \ref run method. When its \ref run method is called

   /// it initiates a plain \ref Bfs class, and calls the \ref Bfs::run

   /// method of it.

   template<class TR>

   class BfsWizard : public TR

   {

     typedef TR Base;

     ///The type of the underlying graph.

     typedef typename TR::Graph Graph;

     //\e

     typedef typename Graph::Node Node;

     //\e

     typedef typename Graph::NodeIt NodeIt;

     //\e

     typedef typename Graph::Edge Edge;

     //\e

     typedef typename Graph::OutEdgeIt OutEdgeIt;

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

     ///the reached nodes

     typedef typename TR::ReachedMap ReachedMap;

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

     ///the processed nodes

     typedef typename TR::ProcessedMap ProcessedMap;

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

     ///edges of the shortest paths.

     typedef typename TR::PredMap PredMap;

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

     typedef typename TR::DistMap DistMap;

   public:

     /// Constructor.

     BfsWizard() : TR() {}

     /// Constructor that requires parameters.

     /// Constructor that requires parameters.

     /// These parameters will be the default values for the traits class.

     BfsWizard(const Graph &g, Node s=INVALID) :

       TR(g,s) {}

     ///Copy constructor

     BfsWizard(const TR &b) : TR(b) {}

     ~BfsWizard() {}

     ///Runs Bfs algorithm from a given node.

     ///Runs Bfs algorithm from a given node.

     ///The node can be given by the \ref source function.

     void run()

     {

       if(Base::_source==INVALID) throw UninitializedParameter();

       Bfs<Graph,TR> alg(*reinterpret_cast<const Graph*>(Base::_g));

       if(Base::_reached)

 	alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));

       if(Base::_processed) 

         alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));

       if(Base::_pred) 

         alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));

       if(Base::_dist) 

         alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));

       alg.run(Base::_source);

     }

     ///Runs Bfs algorithm from the given node.

     ///Runs Bfs algorithm from the given node.

     ///\param s is the given source.

     void run(Node s)

     {

       Base::_source=s;

       run();

     }

     template<class T>

     struct DefPredMapBase : public Base {

       typedef T PredMap;

       static PredMap *createPredMap(const Graph &) { return 0; };

       DefPredMapBase(const TR &b) : TR(b) {}

     };

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

     ///function for setting PredMap

     ///

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

     ///function for setting PredMap

     ///

     template<class T>

     BfsWizard<DefPredMapBase<T> > predMap(const T &t) 

     {

       Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));

       return BfsWizard<DefPredMapBase<T> >(*this);

     }

     template<class T>

     struct DefReachedMapBase : public Base {

       typedef T ReachedMap;

       static ReachedMap *createReachedMap(const Graph &) { return 0; };

       DefReachedMapBase(const TR &b) : TR(b) {}

     };

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

     ///function for setting ReachedMap

     ///

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

     ///function for setting ReachedMap

     ///

     template<class T>

     BfsWizard<DefReachedMapBase<T> > reachedMap(const T &t) 

     {

       Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));

       return BfsWizard<DefReachedMapBase<T> >(*this);

     }

     template<class T>

     struct DefProcessedMapBase : public Base {

       typedef T ProcessedMap;

       static ProcessedMap *createProcessedMap(const Graph &) { return 0; };

       DefProcessedMapBase(const TR &b) : TR(b) {}

     };

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

     ///function for setting ProcessedMap

     ///

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

     ///function for setting ProcessedMap

     ///

     template<class T>

     BfsWizard<DefProcessedMapBase<T> > processedMap(const T &t) 

     {

       Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));

       return BfsWizard<DefProcessedMapBase<T> >(*this);

     }

     template<class T>

     struct DefDistMapBase : public Base {

       typedef T DistMap;

       static DistMap *createDistMap(const Graph &) { return 0; };

       DefDistMapBase(const TR &b) : TR(b) {}

     };

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

     ///function for setting DistMap type

     ///

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

     ///function for setting DistMap type

     ///

     template<class T>

     BfsWizard<DefDistMapBase<T> > distMap(const T &t) 

     {

       Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));

       return BfsWizard<DefDistMapBase<T> >(*this);

     }

     /// Sets the source node, from which the Bfs algorithm runs.

     /// Sets the source node, from which the Bfs algorithm runs.

     /// \param s is the source node.

     BfsWizard<TR> &source(Node s) 

     {

       Base::_source=s;

       return *this;

     }

   };

   ///Function type interface for Bfs algorithm.

   /// \ingroup search

   ///Function type interface for Bfs algorithm.

   ///

   ///This function also has several

   ///\ref named-templ-func-param "named parameters",

   ///they are declared as the members of class \ref BfsWizard.

   ///The following

   ///example shows how to use these parameters.

   ///\code

   ///  bfs(g,source).predMap(preds).run();

   ///\endcode

   ///\warning Don't forget to put the \ref BfsWizard::run() "run()"

   ///to the end of the parameter list.

   ///\sa BfsWizard

   ///\sa Bfs

   template<class GR>

   BfsWizard<BfsWizardBase<GR> >

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

   {

     return BfsWizard<BfsWizardBase<GR> >(g,s);

   }

 #ifdef DOXYGEN

   /// \brief Visitor class for bfs.

   ///  

   /// It gives a simple interface for a functional interface for bfs 

   /// traversal. The traversal on a linear data structure. 

   template <typename _Graph>

   struct BfsVisitor {

     typedef _Graph Graph;

     typedef typename Graph::Edge Edge;

     typedef typename Graph::Node Node;

     /// \brief Called when the edge reach a node.

     /// 

     /// It is called when the bfs find an edge which target is not

     /// reached yet.

     void discover(const Edge& edge) {}

     /// \brief Called when the node reached first time.

     /// 

     /// It is Called when the node reached first time.

     void reach(const Node& node) {}

     /// \brief Called when the edge examined but target of the edge 

     /// already discovered.

     /// 

     /// It called when the edge examined but the target of the edge 

     /// already discovered.

     void examine(const Edge& edge) {}

     /// \brief Called for the source node of the bfs.

     /// 

     /// It is called for the source node of the bfs.

     void start(const Node& node) {}

     /// \brief Called when the node processed.

     /// 

     /// It is Called when the node processed.

     void process(const Node& node) {}

   };

 #else

   template <typename _Graph>

   struct BfsVisitor {

     typedef _Graph Graph;

     typedef typename Graph::Edge Edge;

     typedef typename Graph::Node Node;

     void discover(const Edge&) {}

     void reach(const Node&) {}

     void examine(const Edge&) {}

     void start(const Node&) {}

     void process(const Node&) {}

     template <typename _Visitor>

     struct Constraints {

       void constraints() {

 	Edge edge;

 	Node node;

 	visitor.discover(edge);

 	visitor.reach(node);

 	visitor.examine(edge);

 	visitor.start(node);

         visitor.process(node);

       }

       _Visitor& visitor;

     };

   };

 #endif

   /// \brief Default traits class of BfsVisit class.

   ///

   /// Default traits class of BfsVisit class.

   /// \param _Graph Graph type.

   template<class _Graph>

   struct BfsVisitDefaultTraits {

     /// \brief The graph type the algorithm runs on. 

     typedef _Graph Graph;

     /// \brief 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 concepts::WriteMap "WriteMap" concept.

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

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

     /// \brief Instantiates a ReachedMap.

     ///

     /// This function instantiates a \ref ReachedMap. 

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

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

     static ReachedMap *createReachedMap(const Graph &graph) {

       return new ReachedMap(graph);

     }

   };

   /// %BFS Visit algorithm class.

   /// \ingroup search

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

   /// with visitor interface.

   ///

   /// The %BfsVisit class provides an alternative interface to the Bfs

   /// class. It works with callback mechanism, the BfsVisit object calls

   /// on every bfs event the \c Visitor class member functions. 

   ///

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

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

   /// is only passed to \ref BfsDefaultTraits.

   /// \param _Visitor The Visitor object for the algorithm. The 

   /// \ref BfsVisitor "BfsVisitor<_Graph>" is an empty Visitor which

   /// does not observe the Bfs events. If you want to observe the bfs

   /// events you should implement your own Visitor class.

   /// \param _Traits Traits class to set various data types used by the 

   /// algorithm. The default traits class is

   /// \ref BfsVisitDefaultTraits "BfsVisitDefaultTraits<_Graph>".

   /// See \ref BfsVisitDefaultTraits for the documentation of

   /// a Bfs visit traits class.

   ///

   /// \author Jacint Szabo, Alpar Juttner and Balazs Dezso

 #ifdef DOXYGEN

   template <typename _Graph, typename _Visitor, typename _Traits>

 #else

   template <typename _Graph = ListGraph,

 	    typename _Visitor = BfsVisitor<_Graph>,

 	    typename _Traits = BfsDefaultTraits<_Graph> >

 #endif

   class BfsVisit {

   public:

     /// \brief \ref Exception for uninitialized parameters.

     ///

     /// This error represents problems in the initialization

     /// of the parameters of the algorithms.

     class UninitializedParameter : public lemon::UninitializedParameter {

     public:

       virtual const char* what() const throw() 

       {

 	return "lemon::BfsVisit::UninitializedParameter";

       }

     };

     typedef _Traits Traits;

     typedef typename Traits::Graph Graph;

     typedef _Visitor Visitor;

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

     typedef typename Traits::ReachedMap ReachedMap;

   private:

     typedef typename Graph::Node Node;

     typedef typename Graph::NodeIt NodeIt;

     typedef typename Graph::Edge Edge;

     typedef typename Graph::OutEdgeIt OutEdgeIt;

     /// Pointer to the underlying graph.

     const Graph *_graph;

     /// Pointer to the visitor object.

     Visitor *_visitor;

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

     ReachedMap *_reached;

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

     bool local_reached;

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

     int _list_front, _list_back;

     /// \brief Creates the maps if necessary.

     ///

     /// Creates the maps if necessary.

     void create_maps() {

       if(!_reached) {

 	local_reached = true;

 	_reached = Traits::createReachedMap(*_graph);

       }

     }

   protected:

     BfsVisit() {}

   public:

     typedef BfsVisit Create;

     /// \name Named template parameters

     ///@{

     template <class T>

     struct DefReachedMapTraits : public Traits {

       typedef T ReachedMap;

       static ReachedMap *createReachedMap(const Graph &graph) {

 	throw UninitializedParameter();

       }

     };

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

     /// ReachedMap type

     ///

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

     template <class T>

     struct DefReachedMap : public BfsVisit< Graph, Visitor,

 					    DefReachedMapTraits<T> > {

       typedef BfsVisit< Graph, Visitor, DefReachedMapTraits<T> > Create;

     };

     ///@}

   public:      

     /// \brief Constructor.

     ///

     /// Constructor.

     ///

     /// \param graph the graph the algorithm will run on.

     /// \param visitor The visitor of the algorithm.

     ///

     BfsVisit(const Graph& graph, Visitor& visitor) 

       : _graph(&graph), _visitor(&visitor),

 	_reached(0), local_reached(false) {}

     /// \brief Destructor.

     ///

     /// Destructor.

     ~BfsVisit() {

       if(local_reached) delete _reached;

     }

     /// \brief Sets the map indicating if a node is reached.

     ///

     /// Sets the map indicating if a node is reached.

     /// If you don't use this function before calling \ref run(),

     /// it will allocate one. The destuctor deallocates this

     /// automatically allocated map, of course.

     /// \return <tt> (*this) </tt>

     BfsVisit &reachedMap(ReachedMap &m) {

       if(local_reached) {

 	delete _reached;

 	local_reached = false;

       }

       _reached = &m;

       return *this;

     }

   public:

     /// \name Execution control

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

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

     /// \n

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

     /// first you must call \ref init(), then you can adda source node

     /// with \ref addSource().

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

     /// computation.

     /// @{

     /// \brief Initializes the internal data structures.

     ///

     /// Initializes the internal data structures.

     ///

     void init() {

       create_maps();

       _list.resize(countNodes(*_graph));

       _list_front = _list_back = -1;

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

 	_reached->set(u, false);

       }

     }

     /// \brief 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);

 	  _visitor->start(s);

 	  _visitor->reach(s);

           _list[++_list_back] = s;

 	}

     }

     /// \brief Processes the next node.

     ///

     /// Processes the next node.

     ///

     /// \return The processed node.

     ///

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

     Node processNextNode() { 

       Node n = _list[++_list_front];

       _visitor->process(n);

       Edge e;

       for (_graph->firstOut(e, n); e != INVALID; _graph->nextOut(e)) {

         Node m = _graph->target(e);

         if (!(*_reached)[m]) {

           _visitor->discover(e);

           _visitor->reach(m);

           _reached->set(m, true);

           _list[++_list_back] = m;

         } else {

           _visitor->examine(e);

         }

       }

       return n;

     }

     /// \brief Processes the next node.

     ///

     /// Processes the next node. And checks that the given target node

     /// is reached. If the target node is reachable from the processed

     /// node then the reached parameter will be set true. The reached

     /// parameter should be initially false.

     ///

     /// \param target The target node.

     /// \retval reach Indicates that the target node is reached.

     /// \return The processed node.

     ///

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

     Node processNextNode(Node target, bool& reach) {

       Node n = _list[++_list_front];

       _visitor->process(n);

       Edge e;

       for (_graph->firstOut(e, n); e != INVALID; _graph->nextOut(e)) {

         Node m = _graph->target(e);

         if (!(*_reached)[m]) {

           _visitor->discover(e);

           _visitor->reach(m);

           _reached->set(m, true);

           _list[++_list_back] = m;

           reach = reach || (target == m);

         } else {

           _visitor->examine(e);

         }

       }

       return n;

     }

     /// \brief Processes the next node.

     ///

     /// Processes the next node. And checks that at least one of

     /// reached node has true value in the \c nm node map. If one node

     /// with true value is reachable from the processed node then the

     /// rnode parameter will be set to the first of such nodes.

     ///

     /// \param nm The node map of possible targets.

     /// \retval rnode The reached target node.

     /// \return The processed node.

     ///

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

     template <typename NM>

     Node processNextNode(const NM& nm, Node& rnode) {

       Node n = _list[++_list_front];

       _visitor->process(n);

       Edge e;

       for (_graph->firstOut(e, n); e != INVALID; _graph->nextOut(e)) {

         Node m = _graph->target(e);

         if (!(*_reached)[m]) {

           _visitor->discover(e);

           _visitor->reach(m);

           _reached->set(m, true);

           _list[++_list_back] = m;

           if (nm[m] && rnode == INVALID) rnode = m;

         } else {

           _visitor->examine(e);

         }

       }

       return n;

     }

     /// \brief Next node to be processed.

     ///

     /// Next node to be processed.

     ///

     /// \return The next node to be processed or INVALID if the stack is

     /// empty.

     Node nextNode() { 

       return _list_front != _list_back ? _list[_list_front + 1] : INVALID;

     }

     /// \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 _list_front == _list_back; }

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

     ///

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

     int queueSize() { return _list_back - _list_front; }

     /// \brief 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.

     void start() {

       while ( !emptyQueue() ) processNextNode();

     }

     /// \brief 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.

     void start(Node dest) {

       bool reach = false;

       while ( !emptyQueue() && !reach ) processNextNode(dest, reach);

     }

     /// \brief 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]</tt> true.

     ///

     ///\return The reached node \c v with <tt>nm[v]</tt> true or

     ///\c INVALID if no such node was found.

     template <typename NM>

     Node start(const NM &nm) {

       Node rnode = INVALID;

       while ( !emptyQueue() && rnode == INVALID ) {

 	processNextNode(nm, rnode);

       }

       return rnode;

     }

     /// \brief Runs %BFSVisit algorithm from node \c s.

     ///

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

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

     ///\code

     ///   b.init();

     ///   b.addSource(s);

     ///   b.start();

     ///\endcode

     void run(Node s) {

       init();

       addSource(s);

       start();

     }

     /// \brief Runs %BFSVisit algorithm to visit all nodes in the graph.

     ///    

     /// This method runs the %BFS algorithm in order to

     /// compute the %BFS path to each node. The algorithm computes

     /// - The %BFS tree.

     /// - The distance of each node from the root in the %BFS tree.

     ///

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

     ///\code

     ///  b.init();

     ///  for (NodeIt it(graph); it != INVALID; ++it) {

     ///    if (!b.reached(it)) {

     ///      b.addSource(it);

     ///      b.start();

     ///    }

     ///  }

     ///\endcode

     void run() {

       init();

       for (NodeIt it(*_graph); it != INVALID; ++it) {

         if (!reached(it)) {

           addSource(it);

           start();

         }

       }

     }

     ///@}

     /// \name Query Functions

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

     /// functions.\n

     /// Before the use of these functions,

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

     ///@{

     /// \brief Checks if a node is reachable from the root.

     ///

     /// Returns \c true if \c v is reachable from the root(s).

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

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

     /// must be called before using this function.

     ///

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

     ///@}

   };

 } //END OF NAMESPACE LEMON

 #endif