/* -*- 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_DFS_H

 #define LEMON_DFS_H

 ///\ingroup search

 ///\file

 ///\brief Dfs algorithm.

 #include <lemon/list_graph.h>

 #include <lemon/bits/path_dump.h>

 #include <lemon/core.h>

 #include <lemon/error.h>

 #include <lemon/maps.h>

 #include <lemon/concept_check.h>

 namespace lemon {

   ///Default traits class of Dfs class.

   ///Default traits class of Dfs class.

   ///\tparam GR Digraph type.

   template<class GR>

   struct DfsDefaultTraits

   {

     ///The digraph type the algorithm runs on.

     typedef GR Digraph;

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

     ///arcs of the %DFS paths.

     ///

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

     ///arcs of the %DFS 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);

     }

   };

   ///%DFS algorithm class.

   ///\ingroup search

   ///This class provides an efficient implementation of the %DFS 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 Dfs, it

   ///is only passed to \ref DfsDefaultTraits.

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

   ///The default traits class is

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

   ///See \ref DfsDefaultTraits for the documentation of

   ///a Dfs traits class.

 #ifdef DOXYGEN

   template <typename GR,

             typename TR>

 #else

   template <typename GR=ListDigraph,

             typename TR=DfsDefaultTraits<GR> >

 #endif

   class Dfs {

   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::Dfs::UninitializedParameter";

       }

     };

     typedef TR Traits;

     ///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 last

     ///arcs of the %DFS 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 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::OutArcIt> _stack;

     int _stack_head;

     ///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:

     Dfs() {}

   public:

     typedef Dfs Create;

     ///\name Named template parameters

     ///@{

     template <class T>

     struct DefPredMapTraits : public Traits {

       typedef T PredMap;

       static PredMap *createPredMap(const Digraph &G)

       {

         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 Dfs<Digraph, DefPredMapTraits<T> > {

       typedef Dfs<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 {

       typedef Dfs<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 Dfs< Digraph, DefReachedMapTraits<T> > {

       typedef Dfs< 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 Dfs< Digraph, DefProcessedMapTraits<T> > {

       typedef Dfs< 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 explicitely, it will be automatically allocated.

     template <class T>

     class DefProcessedMapToBeDefaultMap :

       public Dfs< Digraph, DefDigraphProcessedMapTraits> {

       typedef Dfs< Digraph, DefDigraphProcessedMapTraits> Create;

     };

     ///@}

   public:

     ///Constructor.

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

     ///

     Dfs(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.

     ~Dfs()

     {

       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 destuctor deallocates this

     ///automatically allocated map, of course.

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

     Dfs &predMap(PredMap &m)

     {

       if(local_pred) {

         delete _pred;

         local_pred=false;

       }

       _pred = &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 destuctor deallocates this

     ///automatically allocated map, of course.

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

     Dfs &distMap(DistMap &m)

     {

       if(local_dist) {

         delete _dist;

         local_dist=false;

       }

       _dist = &m;

       return *this;

     }

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

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

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

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

     ///automatically allocated map, of course.

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

     Dfs &reachedMap(ReachedMap &m)

     {

       if(local_reached) {

         delete _reached;

         local_reached=false;

       }

       _reached = &m;

       return *this;

     }

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

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

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

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

     ///automatically allocated map, of course.

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

     Dfs &processedMap(ProcessedMap &m)

     {

       if(local_processed) {

         delete _processed;

         local_processed=false;

       }

       _processed = &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 a source node

     ///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();

       _stack.resize(countNodes(*G));

       _stack_head=-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.

     ///

     ///\warning dists are wrong (or at least strange)

     ///in case of multiple sources.

     void addSource(Node s)

     {

       if(!(*_reached)[s])

         {

           _reached->set(s,true);

           _pred->set(s,INVALID);

           OutArcIt e(*G,s);

           if(e!=INVALID) {

             _stack[++_stack_head]=e;

             _dist->set(s,_stack_head);

           }

           else {

             _processed->set(s,true);

             _dist->set(s,0);

           }

         }

     }

     ///Processes the next arc.

     ///Processes the next arc.

     ///

     ///\return The processed arc.

     ///

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

     Arc processNextArc()

     {

       Node m;

       Arc e=_stack[_stack_head];

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

         _pred->set(m,e);

         _reached->set(m,true);

         ++_stack_head;

         _stack[_stack_head] = OutArcIt(*G, m);

         _dist->set(m,_stack_head);

       }

       else {

         m=G->source(e);

         ++_stack[_stack_head];

       }

       while(_stack_head>=0 && _stack[_stack_head]==INVALID) {

         _processed->set(m,true);

         --_stack_head;

         if(_stack_head>=0) {

           m=G->source(_stack[_stack_head]);

           ++_stack[_stack_head];

         }

       }

       return e;

     }

     ///Next arc to be processed.

     ///Next arc to be processed.

     ///

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

     /// empty.

     OutArcIt nextArc()

     {

       return _stack_head>=0?_stack[_stack_head]: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 _stack_head<0; }

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

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

     int queueSize() { return _stack_head+1; }

     ///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 %DFS algorithm from the root node(s)

     ///in order to

     ///compute the

     ///%DFS path to each node. The algorithm computes

     ///- The %DFS tree.

     ///- The distance of each node from the root(s) in the %DFS tree.

     ///

     void start()

     {

       while ( !emptyQueue() ) processNextArc();

     }

     ///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 %DFS algorithm from the root node(s)

     ///in order to

     ///compute the

     ///%DFS path to \c dest. The algorithm computes

     ///- The %DFS path to \c  dest.

     ///- The distance of \c dest from the root(s) in the %DFS tree.

     ///

     void start(Node dest)

     {

       while ( !emptyQueue() && G->target(_stack[_stack_head])!=dest )

         processNextArc();

     }

     ///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 em must be a bool (or convertible) arc map. The algorithm

     ///will stop when it reaches an arc \c e with <tt>em[e]</tt> true.

     ///

     ///\return The reached arc \c e with <tt>em[e]</tt> true or

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

     ///

     ///\warning Contrary to \ref Bfs and \ref Dijkstra, \c em is an arc map,

     ///not a node map.

     template<class EM>

     Arc start(const EM &em)

     {

       while ( !emptyQueue() && !em[_stack[_stack_head]] )

         processNextArc();

       return emptyQueue() ? INVALID : _stack[_stack_head];

     }

     ///Runs %DFS algorithm to visit all nodes in the digraph.

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

     ///compute the

     ///%DFS path to each node. The algorithm computes

     ///- The %DFS tree.

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

     ///

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

     ///\code

     ///  d.init();

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

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

     ///      d.addSource(it);

     ///      d.start();

     ///    }

     ///  }

     ///\endcode

     void run() {

       init();

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

         if (!reached(it)) {

           addSource(it);

           start();

         }

       }

     }

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

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

     ///in order to

     ///compute the

     ///%DFS path to each node. The algorithm computes

     ///- The %DFS tree.

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

     ///

     ///\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 %DFS path between \c s and \c t.

     ///Finds the %DFS path between \c s and \c t.

     ///

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

     ///0 otherwise.

     ///\note Apart from the return value, d.run(s,t) 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)?_stack_head+1:0;

     }

     ///@}

     ///\name Query Functions

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

     ///functions.\n

     ///Before the use of these functions,

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

     ///@{

     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 is unreachable from the root(s) then the return

     ///value of this funcion is undefined.

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

     ///Returns the 'previous arc' of the %DFS tree.

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

     ///of the %DFS path,

     ///i.e. it returns the last arc of a %DFS 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

     ///%DFS tree used here is equal to the %DFS 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 %DFS tree.

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

     ///of the %DFS tree,

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

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

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

     ///if \c v itself a root.

     ///The %DFS tree used here is equal to the %DFS

     ///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 %DFS arc-tree map.

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

     ///%DFS 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(s).

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

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

     ///must be called before using this function.

     ///

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

     ///@}

   };

   ///Default traits class of Dfs function.

   ///Default traits class of Dfs function.

   ///\tparam GR Digraph type.

   template<class GR>

   struct DfsWizardDefaultTraits

   {

     ///The digraph type the algorithm runs on.

     typedef GR Digraph;

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

     ///arcs of the %DFS paths.

     ///

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

     ///arcs of the %DFS 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 DfsWizard

   /// To make it easier to use Dfs algorithm

   ///we have created a wizard class.

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

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

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

   /// \ref DfsWizard class.

   template<class GR>

   class DfsWizardBase : public DfsWizardDefaultTraits<GR>

   {

     typedef DfsWizardDefaultTraits<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).

     DfsWizardBase() : _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

     DfsWizardBase(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 the Dfs algorithm easier

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

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

   /// 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 Dfs

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

   /// the original class by using the ::

   /// operator. In the case of \ref DfsWizard 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 Dfs object, and calls the \ref Dfs::run

   /// method of it.

   template<class TR>

   class DfsWizard : 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 %DFS paths.

     typedef typename TR::PredMap PredMap;

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

     typedef typename TR::DistMap DistMap;

   public:

     /// Constructor.

     DfsWizard() : TR() {}

     /// Constructor that requires parameters.

     /// Constructor that requires parameters.

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

     DfsWizard(const Digraph &g, Node s=INVALID) :

       TR(g,s) {}

     ///Copy constructor

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

     ~DfsWizard() {}

     ///Runs Dfs algorithm from a given node.

     ///Runs Dfs algorithm from a given node.

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

     void run()

     {

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

       Dfs<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 Dfs algorithm from the given node.

     ///Runs Dfs 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 type

     ///

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

     ///function for setting PredMap type

     ///

     template<class T>

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

     {

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

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

     }

     template<class T>

     struct DefReachedMapBase : public Base {

       typedef T ReachedMap;

       static ReachedMap *createReachedMap(const Digraph &) { 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>

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

     {

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

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

     }

     template<class T>

     struct DefProcessedMapBase : public Base {

       typedef T ProcessedMap;

       static ProcessedMap *createProcessedMap(const Digraph &) { 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>

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

     {

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

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

     }

     template<class T>

     struct DefDistMapBase : public Base {

       typedef T DistMap;

       static DistMap *createDistMap(const Digraph &) { 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>

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

     {

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

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

     }

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

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

     /// \param s is the source node.

     DfsWizard<TR> &source(Node s)

     {

       Base::_source=s;

       return *this;

     }

   };

   ///Function type interface for Dfs algorithm.

   ///\ingroup search

   ///Function type interface for Dfs algorithm.

   ///

   ///This function also has several

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

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

   ///The following

   ///example shows how to use these parameters.

   ///\code

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

   ///\endcode

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

   ///to the end of the parameter list.

   ///\sa DfsWizard

   ///\sa Dfs

   template<class GR>

   DfsWizard<DfsWizardBase<GR> >

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

   {

     return DfsWizard<DfsWizardBase<GR> >(g,s);

   }

 #ifdef DOXYGEN

   /// \brief Visitor class for dfs.

   ///

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

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

   template <typename _Digraph>

   struct DfsVisitor {

     typedef _Digraph Digraph;

     typedef typename Digraph::Arc Arc;

     typedef typename Digraph::Node Node;

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

     ///

     /// It is called when the dfs find an arc which target is not

     /// reached yet.

     void discover(const Arc& arc) {}

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

     ///

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

     void reach(const Node& node) {}

     /// \brief Called when we step back on an arc.

     ///

     /// It is called when the dfs should step back on the arc.

     void backtrack(const Arc& arc) {}

     /// \brief Called when we step back from the node.

     ///

     /// It is called when we step back from the node.

     void leave(const Node& node) {}

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

     /// already discovered.

     ///

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

     /// already discovered.

     void examine(const Arc& arc) {}

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

     ///

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

     void start(const Node& node) {}

     /// \brief Called when we leave the source node of the dfs.

     ///

     /// It is called when we leave the source node of the dfs.

     void stop(const Node& node) {}

   };

 #else

   template <typename _Digraph>

   struct DfsVisitor {

     typedef _Digraph Digraph;

     typedef typename Digraph::Arc Arc;

     typedef typename Digraph::Node Node;

     void discover(const Arc&) {}

     void reach(const Node&) {}

     void backtrack(const Arc&) {}

     void leave(const Node&) {}

     void examine(const Arc&) {}

     void start(const Node&) {}

     void stop(const Node&) {}

     template <typename _Visitor>

     struct Constraints {

       void constraints() {

         Arc arc;

         Node node;

         visitor.discover(arc);

         visitor.reach(node);

         visitor.backtrack(arc);

         visitor.leave(node);

         visitor.examine(arc);

         visitor.start(node);

         visitor.stop(arc);

       }

       _Visitor& visitor;

     };

   };

 #endif

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

   ///

   /// Default traits class of DfsVisit class.

   /// \tparam _Digraph Digraph type.

   template<class _Digraph>

   struct DfsVisitDefaultTraits {

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

     typedef _Digraph Digraph;

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

     ///

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

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

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

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

     /// \brief Instantiates a ReachedMap.

     ///

     /// This function instantiates a \ref ReachedMap.

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

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

     static ReachedMap *createReachedMap(const Digraph &digraph) {

       return new ReachedMap(digraph);

     }

   };

   /// %DFS Visit algorithm class.

   /// \ingroup search

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

   /// with visitor interface.

   ///

   /// The %DfsVisit class provides an alternative interface to the Dfs

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

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

   ///

   /// \tparam _Digraph The digraph type the algorithm runs on.

   /// The default value is

   /// \ref ListDigraph. The value of _Digraph is not used directly by Dfs, it

   /// is only passed to \ref DfsDefaultTraits.

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

   /// \ref DfsVisitor "DfsVisitor<_Digraph>" is an empty Visitor which

   /// does not observe the Dfs events. If you want to observe the dfs

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

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

   /// algorithm. The default traits class is

   /// \ref DfsVisitDefaultTraits "DfsVisitDefaultTraits<_Digraph>".

   /// See \ref DfsVisitDefaultTraits for the documentation of

   /// a Dfs visit traits class.

   ///

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

 #ifdef DOXYGEN

   template <typename _Digraph, typename _Visitor, typename _Traits>

 #else

   template <typename _Digraph = ListDigraph,

             typename _Visitor = DfsVisitor<_Digraph>,

             typename _Traits = DfsDefaultTraits<_Digraph> >

 #endif

   class DfsVisit {

   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::DfsVisit::UninitializedParameter";

       }

     };

     typedef _Traits Traits;

     typedef typename Traits::Digraph Digraph;

     typedef _Visitor Visitor;

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

     typedef typename Traits::ReachedMap ReachedMap;

   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 *_digraph;

     /// Pointer to the visitor object.

     Visitor *_visitor;

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

     ReachedMap *_reached;

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

     bool local_reached;

     std::vector<typename Digraph::Arc> _stack;

     int _stack_head;

     /// \brief Creates the maps if necessary.

     ///

     /// Creates the maps if necessary.

     void create_maps() {

       if(!_reached) {

         local_reached = true;

         _reached = Traits::createReachedMap(*_digraph);

       }

     }

   protected:

     DfsVisit() {}

   public:

     typedef DfsVisit Create;

     /// \name Named template parameters

     ///@{

     template <class T>

     struct DefReachedMapTraits : public Traits {

       typedef T ReachedMap;

       static ReachedMap *createReachedMap(const Digraph &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 DfsVisit< Digraph, Visitor,

                                             DefReachedMapTraits<T> > {

       typedef DfsVisit< Digraph, Visitor, DefReachedMapTraits<T> > Create;

     };

     ///@}

   public:

     /// \brief Constructor.

     ///

     /// Constructor.

     ///

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

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

     ///

     DfsVisit(const Digraph& digraph, Visitor& visitor)

       : _digraph(&digraph), _visitor(&visitor),

         _reached(0), local_reached(false) {}

     /// \brief Destructor.

     ///

     /// Destructor.

     ~DfsVisit() {

       if(local_reached) delete _reached;

     }

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

     ///

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

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

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

     /// automatically allocated map, of course.

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

     DfsVisit &reachedMap(ReachedMap &m) {

       if(local_reached) {

         delete _reached;

         local_reached=false;

       }

       _reached = &m;

       return *this;

     }

   public:

     /// \name Execution control

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

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

     /// \n

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

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

     /// with \ref addSource().

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

     /// computation.

     /// @{

     /// \brief Initializes the internal data structures.

     ///

     /// Initializes the internal data structures.

     ///

     void init() {

       create_maps();

       _stack.resize(countNodes(*_digraph));

       _stack_head = -1;

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

         _reached->set(u, false);

       }

     }

     /// \brief Adds a new source node.

     ///

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

     void addSource(Node s) {

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

           _reached->set(s,true);

           _visitor->start(s);

           _visitor->reach(s);

           Arc e;

           _digraph->firstOut(e, s);

           if (e != INVALID) {

             _stack[++_stack_head] = e;

           } else {

             _visitor->leave(s);

           }

         }

     }

     /// \brief Processes the next arc.

     ///

     /// Processes the next arc.

     ///

     /// \return The processed arc.

     ///

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

     Arc processNextArc() {

       Arc e = _stack[_stack_head];

       Node m = _digraph->target(e);

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

         _visitor->discover(e);

         _visitor->reach(m);

         _reached->set(m, true);

         _digraph->firstOut(_stack[++_stack_head], m);

       } else {

         _visitor->examine(e);

         m = _digraph->source(e);

         _digraph->nextOut(_stack[_stack_head]);

       }

       while (_stack_head>=0 && _stack[_stack_head] == INVALID) {

         _visitor->leave(m);

         --_stack_head;

         if (_stack_head >= 0) {

           _visitor->backtrack(_stack[_stack_head]);

           m = _digraph->source(_stack[_stack_head]);

           _digraph->nextOut(_stack[_stack_head]);

         } else {

           _visitor->stop(m);

         }

       }

       return e;

     }

     /// \brief Next arc to be processed.

     ///

     /// Next arc to be processed.

     ///

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

     /// empty.

     Arc nextArc() {

       return _stack_head >= 0 ? _stack[_stack_head] : 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 _stack_head < 0; }

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

     ///

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

     int queueSize() { return _stack_head + 1; }

     /// \brief Executes the algorithm.

     ///

     /// Executes the algorithm.

     ///

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

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

     void start() {

       while ( !emptyQueue() ) processNextArc();

     }

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

     ///

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

     ///

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

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

     void start(Node dest) {

       while ( !emptyQueue() && _digraph->target(_stack[_stack_head]) != dest )

         processNextArc();

     }

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

     ///

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

     ///

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

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

     ///

     /// \param em must be a bool (or convertible) arc map. The algorithm

     /// will stop when it reaches an arc \c e with <tt>em[e]</tt> true.

     ///

     ///\return The reached arc \c e with <tt>em[e]</tt> true or

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

     ///

     /// \warning Contrary to \ref Bfs and \ref Dijkstra, \c em is an arc map,

     /// not a node map.

     template <typename EM>

     Arc start(const EM &em) {

       while ( !emptyQueue() && !em[_stack[_stack_head]] )

         processNextArc();

       return emptyQueue() ? INVALID : _stack[_stack_head];

     }

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

     ///

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

     /// \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();

     }

     /// \brief Runs %DFSVisit algorithm to visit all nodes in the digraph.

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

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

     /// - The %DFS tree.

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

     ///

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

     ///\code

     ///  d.init();

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

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

     ///      d.addSource(it);

     ///      d.start();

     ///    }

     ///  }

     ///\endcode

     void run() {

       init();

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

         if (!reached(it)) {

           addSource(it);

           start();

         }

       }

     }

     ///@}

     /// \name Query Functions

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

     /// functions.\n

     /// Before the use of these functions,

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

     ///@{

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

     ///

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

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

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

     /// must be called before using this function.

     ///

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

     ///@}

   };

 } //END OF NAMESPACE LEMON

 #endif