/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

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

 *

 * Copyright (C) 2003-2008

 * 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.

  ///\tparam GR Digraph type.

  template<class GR>

  struct BfsDefaultTraits

  {

    ///The digraph type the algorithm runs on.

    typedef GR Digraph;

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

    ///arcs of the shortest paths.

    ///

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

    ///arcs of the shortest paths.

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

    ///

    typedef typename Digraph::template NodeMap<typename GR::Arc> PredMap;

    ///Instantiates a PredMap.

    ///This function instantiates a \ref PredMap.

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

    ///\todo The digraph 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 Digraph::Node,bool> ProcessedMap;

    ///Instantiates a ProcessedMap.

    ///This function instantiates a \ref ProcessedMap.

    ///\param g is the digraph, 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 Digraph::template NodeMap<bool> ReachedMap;

    ///Instantiates a ReachedMap.

    ///This function instantiates a \ref ReachedMap.

    ///\param G is the digraph, 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 Digraph::template NodeMap<int> DistMap;

    ///Instantiates a DistMap.

    ///This function instantiates a \ref DistMap.

    ///\param G is the digraph, 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.

  ///

  ///\tparam GR The digraph type the algorithm runs on. The default value is

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

  ///is only passed to \ref BfsDefaultTraits.

  ///\tparam 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.

#ifdef DOXYGEN

  template <typename GR,

            typename TR>

#else

  template <typename GR=ListDigraph,

            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 digraph.

    typedef typename TR::Digraph Digraph;

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

    ///arcs 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:

    typedef typename Digraph::Node Node;

    typedef typename Digraph::NodeIt NodeIt;

    typedef typename Digraph::Arc Arc;

    typedef typename Digraph::OutArcIt OutArcIt;

    /// Pointer to the underlying digraph.

    const Digraph *G;

    ///Pointer to the map of predecessors arcs.

    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 Digraph::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 Digraph &)

      {

        throw UninitializedParameter();

      }

    };

    ///\brief \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< Digraph, DefPredMapTraits<T> > {

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

    };

    template <class T>

    struct DefDistMapTraits : public Traits {

      typedef T DistMap;

      static DistMap *createDistMap(const Digraph &)

      {

        throw UninitializedParameter();

      }

    };

    ///\brief \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< Digraph, DefDistMapTraits<T> > {

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

    };

    template <class T>

    struct DefReachedMapTraits : public Traits {

      typedef T ReachedMap;

      static ReachedMap *createReachedMap(const Digraph &)

      {

        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 Bfs< Digraph, DefReachedMapTraits<T> > {

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

    };

    template <class T>

    struct DefProcessedMapTraits : public Traits {

      typedef T ProcessedMap;

      static ProcessedMap *createProcessedMap(const Digraph &)

      {

        throw UninitializedParameter();

      }

    };

    ///\brief \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< Digraph, DefProcessedMapTraits<T> > {

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

    };

    struct DefDigraphProcessedMapTraits : public Traits {

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

      static ProcessedMap *createProcessedMap(const Digraph &G)

      {

        return new ProcessedMap(G);

      }

    };

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

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

    ///

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

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

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

    template <class T>

    struct DefProcessedMapToBeDefaultMap :

      public Bfs< Digraph, DefDigraphProcessedMapTraits> {

      typedef Bfs< Digraph, DefDigraphProcessedMapTraits> Create;

    };

    ///@}

  public:

    ///Constructor.

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

    ///

    Bfs(const Digraph& _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 arcs.

    ///Sets the map storing the predecessor arcs.

    ///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.

    ///@{

    ///\brief 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(OutArcIt 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(OutArcIt 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(OutArcIt 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<Digraph, 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 arc' of the shortest path tree.

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

    ///of the shortest path tree,

    ///i.e. it returns the last arc 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.

    Arc predArc(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 predArc().

    ///\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 arcs 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.

  ///\tparam GR Digraph type.

  template<class GR>

  struct BfsWizardDefaultTraits

  {

    ///The digraph type the algorithm runs on.

    typedef GR Digraph;

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

    ///arcs of the shortest paths.

    ///

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

    ///arcs of the shortest paths.

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

    ///

    typedef NullMap<typename Digraph::Node,typename GR::Arc> PredMap;

    ///Instantiates a PredMap.

    ///This function instantiates a \ref PredMap.

    ///\param g is the digraph, to which we would like to define the PredMap.

    ///\todo The digraph 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 Digraph::Node,bool> ProcessedMap;

    ///Instantiates a ProcessedMap.

    ///This function instantiates a \ref ProcessedMap.

    ///\param g is the digraph, 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 Digraph::template NodeMap<bool> ReachedMap;

    ///Instantiates a ReachedMap.

    ///This function instantiates a \ref ReachedMap.

    ///\param G is the digraph, 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 Digraph::Node,int> DistMap;

    ///Instantiates a DistMap.

    ///This function instantiates a \ref DistMap.

    ///\param g is the digraph, 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 digraph.

    typedef typename Base::Digraph::Node Node;

    /// Pointer to the underlying digraph.

    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 arcs.

    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 digraph.

    typedef typename TR::Digraph Digraph;

    //\e

    typedef typename Digraph::Node Node;

    //\e

    typedef typename Digraph::NodeIt NodeIt;

    //\e

    typedef typename Digraph::Arc Arc;

    //\e

    typedef typename Digraph::OutArcIt OutArcIt;

    ///\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

    ///arcs 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 Digraph &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<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(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 Digraph &) { return 0; };

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

    };

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

    ///function for setting PredMap