/* -*- C++ -*-
 * lemon/bfs.h - Part of LEMON, a generic C++ optimization library
 *
 * Copyright (C) 2005 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 flowalgs
///\file
///\brief Bfs algorithm.

#include <lemon/list_graph.h>
#include <lemon/graph_utils.h>
#include <lemon/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 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 &)
    {
      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);
    }
  };
  
  ///%BFS algorithm class.
  
  ///\ingroup flowalgs
  ///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
  ///\todo A compare object would be nice.

#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* exceptionName() const {
	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;
//     ///\brief The type of the map that stores the last but one
//     ///nodes of the shortest paths.
//     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;
    ///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 predecessors nodes.
//     PredNodeMap *_predNode;
//     ///Indicates if \ref _predNode is locally allocated (\c true) or not.
//     bool local_predNode;
    ///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;
//     ///The source node of the last execution.
//     Node source;

    ///Creates the maps if necessary.
    
    ///\todo Error if \c G are \c NULL.
    ///\todo Better memory allocation (instead of new).
    void create_maps() 
    {
      if(!_pred) {
	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 explicitly, it will be automatically allocated.
    template <class T>
    class DefProcessedMapToBeDefaultMap :
      public Bfs< Graph,
		  DefGraphProcessedMapTraits> { };
    
    ///@}

  public:      
    
    ///Constructor.
    
    ///\param _G the graph the algorithm will run on.
    ///
    Bfs(const Graph& _G) :
      G(&_G),
      _pred(NULL), local_pred(false),
//       _predNode(NULL), local_predNode(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_predNode) delete _predNode;
      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 predecessor nodes.

//     ///Sets the map storing the predecessor 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 &predNodeMap(PredNodeMap &m) 
//     {
//       if(local_predNode) {
// 	delete _predNode;
// 	local_predNode=false;
//       }
//       _predNode = &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);
// 	_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.
    ///
    ///\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);
// 	  _pred_node->set(m,n);
	  _dist->set(m,_curr_dist);
	}
      return n;
    }
      
    ///\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
    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, d.run(s) is
    ///just a shortcut of the following code.
    ///\code
    ///  d.init();
    ///  d.addSource(s);
    ///  d.start(t);
    ///\endcode
    int run(Node s,Node t) {
      init();
      addSource(s);
      start(t);
      return reached(t)?_curr_dist-1+(_queue_tail==_queue_next_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 called.
    
    ///@{

    ///Copies the shortest path to \c t into \c p
    
    ///This function copies the shortest path to \c t into \c p.
    ///If it \c \t is a source itself or unreachable, then it does not
    ///alter \c p.
    ///\todo Is it the right way to handle unreachable nodes?
    ///\return Returns \c true if a path to \c t was actually copied to \c p,
    ///\c false otherwise.
    ///\sa DirPath
    template<class P>
    bool getPath(P &p,Node t) 
    {
      if(reached(t)) {
	p.clear();
	typename P::Builder b(p);
	for(b.setStartNode(t);pred(t)!=INVALID;t=predNode(t))
	  b.pushFront(pred(t));
	b.commit();
	return true;
      }
      return false;
    }

    ///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(Node v).
    ///\pre Either \ref run() or \ref start() must be called before using
    ///this function.
    ///\todo predEdge could be a better name.
    Edge pred(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 pred(Node v).
    ///\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;}
 
//     ///Returns a reference to the map of nodes of shortest paths.

//     ///Returns a reference to the NodeMap of the last but one nodes of the
//     ///shortest path tree.
//     ///\pre \ref run() must be called before using this function.
//     const PredNodeMap &predNodeMap() const { return *_predNode;}

    ///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 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 &) 
    {
      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 &)
    {
      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 &)
    {
      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) {}

  };
  
  /// 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;
//     ///\brief The type of the map that stores the last but one
//     ///nodes of the shortest paths.
//     typedef typename TR::PredNodeMap PredNodeMap;
    ///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(*(Graph*)Base::_g);
      if(Base::_reached)
	alg.reachedMap(*(ReachedMap*)Base::_reached);
      if(Base::_processed) alg.processedMap(*(ProcessedMap*)Base::_processed);
      if(Base::_pred) alg.predMap(*(PredMap*)Base::_pred);
//       if(Base::_predNode) alg.predNodeMap(*(PredNodeMap*)Base::_predNode);
      if(Base::_dist) alg.distMap(*(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=(void *)&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=(void *)&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=(void *)&t;
      return BfsWizard<DefProcessedMapBase<T> >(*this);
    }
    

//     template<class T>
//     struct DefPredNodeMapBase : public Base {
//       typedef T PredNodeMap;
//       static PredNodeMap *createPredNodeMap(const Graph &G) { return 0; };
//       DefPredNodeMapBase(const TR &b) : TR(b) {}
//     };
    
//     ///\brief \ref named-templ-param "Named parameter"
//     ///function for setting PredNodeMap type
//     ///
//     /// \ref named-templ-param "Named parameter"
//     ///function for setting PredNodeMap type
//     ///
//     template<class T>
//     BfsWizard<DefPredNodeMapBase<T> > predNodeMap(const T &t) 
//     {
//       Base::_predNode=(void *)&t;
//       return BfsWizard<DefPredNodeMapBase<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=(void *)&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 flowalgs
  ///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);
  }

} //END OF NAMESPACE LEMON

#endif