/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2006

 * 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/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 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

#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 reached Indicates that the target node is reached.

    ///\return The processed node.

    ///

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

    Node processNextNode(Node target, bool& reached)

    {

      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);

          reached = reached || (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 nodemap. If one node

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

    ///reached parameter will be set true. The reached parameter

    ///should be initially false.

    ///

    ///\param target The nodemaps of possible targets.

    ///\retval reached Indicates that one of the target nodes is reached.

    ///\return The processed node.

    ///

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

    template<class NM>

    Node processNextNode(const NM& nm, bool& reached)

    {

      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);

          reached = reached || nm[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 reached = false;

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

    }

    ///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>.

    ///\todo query the reached target

    template<class NM>

    void start(const NM &nm)

    {

      bool reached = false;

      while ( !emptyQueue() && !reached) processNextNode(nm, reached);

    }

    ///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 : 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 \c t is a source itself or unreachable, then it does not

    ///alter \c p.

    ///\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);predEdge(t)!=INVALID;t=predNode(t))

	  b.pushFront(predEdge(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().

    ///\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((void *)&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(*(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::_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) {}

    };