/* -*- C++ -*-

  * lemon/dfs.h - Part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

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

  *

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

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

  * precise terms see the accompanying LICENSE file.

  *

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

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

  * purpose.

  *

  */

 #ifndef LEMON_DFS_H

 #define LEMON_DFS_H

 ///\ingroup flowalgs

 ///\file

 ///\brief Dfs algorithm.

 #include <lemon/list_graph.h>

 #include <lemon/graph_utils.h>

 #include <lemon/invalid.h>

 #include <lemon/error.h>

 #include <lemon/maps.h>

 namespace lemon {

   ///Default traits class of Dfs class.

   ///Default traits class of Dfs class.

   ///\param GR Graph type.

   template<class GR>

   struct DfsDefaultTraits

   {

     ///The graph type the algorithm runs on. 

     typedef GR Graph;

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

     ///edges of the %DFS paths.

     /// 

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

     ///edges of the %DFS paths.

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

     ///

     typedef typename Graph::template NodeMap<typename GR::Edge> PredMap;

     ///Instantiates a PredMap.

     ///This function instantiates a \ref PredMap. 

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

     ///\todo The graph alone may be insufficient to initialize

     static PredMap *createPredMap(const GR &G) 

     {

       return new PredMap(G);

     }

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

 //     ///nodes of the %DFS paths.

 //     ///

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

 //     ///nodes of the %DFS paths.

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

 //     ///

 //     typedef NullMap<typename Graph::Node,typename Graph::Node> PredNodeMap;

 //     ///Instantiates a PredNodeMap.

 //     ///This function instantiates a \ref PredNodeMap. 

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

 //     ///we would like to define the \ref PredNodeMap

 //     static PredNodeMap *createPredNodeMap(const GR &G)

 //     {

 //       return new PredNodeMap();

 //     }

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

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

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

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

     typedef NullMap<typename Graph::Node,bool> ProcessedMap;

     ///Instantiates a ProcessedMap.

     ///This function instantiates a \ref ProcessedMap. 

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

     ///we would like to define the \ref ProcessedMap

 #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 concept::WriteMap "WriteMap" concept.

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

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

     ///Instantiates a ReachedMap.

     ///This function instantiates a \ref ReachedMap. 

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

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

     static ReachedMap *createReachedMap(const GR &G)

     {

       return new ReachedMap(G);

     }

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

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

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

     ///

     typedef typename Graph::template NodeMap<int> DistMap;

     ///Instantiates a DistMap.

     ///This function instantiates a \ref DistMap. 

     ///\param G is the graph, to which we would like to define the \ref DistMap

     static DistMap *createDistMap(const GR &G)

     {

       return new DistMap(G);

     }

   };

   ///%DFS algorithm class.

   ///\ingroup flowalgs

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

   ///is only passed to \ref DfsDefaultTraits.

   ///\param 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.

   ///

   ///\author Jacint Szabo and Alpar Juttner

   ///\todo A compare object would be nice.

 #ifdef DOXYGEN

   template <typename GR,

 	    typename TR>

 #else

   template <typename GR=ListGraph,

 	    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* exceptionName() const {

 	return "lemon::Dfs::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 %DFS paths.

     typedef typename TR::PredMap PredMap;

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

 //     ///nodes of the %DFS paths.

 //     typedef typename TR::PredNodeMap PredNodeMap;

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

     typedef typename TR::ReachedMap ReachedMap;

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

     typedef typename TR::ProcessedMap ProcessedMap;

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

     typedef typename TR::DistMap DistMap;

   private:

     /// Pointer to the underlying graph.

     const Graph *G;

     ///Pointer to the map of predecessors edges.

     PredMap *_pred;

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

     bool local_pred;

 //     ///Pointer to the map of predecessors nodes.

 //     PredNodeMap *_predNode;

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

 //     bool local_predNode;

     ///Pointer to the map of distances.

     DistMap *_dist;

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

     bool local_dist;

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

     ReachedMap *_reached;

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

     bool local_reached;

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

     ProcessedMap *_processed;

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

     bool local_processed;

     std::vector<typename Graph::OutEdgeIt> _stack;

     int _stack_head;

 //     ///The source node of the last execution.

 //     Node source;

     ///Creates the maps if necessary.

     ///\todo Error if \c G are \c NULL.

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

     void create_maps() 

     {

       if(!_pred) {

 	local_pred = true;

 	_pred = Traits::createPredMap(*G);

       }

 //       if(!_predNode) {

 // 	local_predNode = true;

 // 	_predNode = Traits::createPredNodeMap(*G);

 //       }

       if(!_dist) {

 	local_dist = true;

 	_dist = Traits::createDistMap(*G);

       }

       if(!_reached) {

 	local_reached = true;

 	_reached = Traits::createReachedMap(*G);

       }

       if(!_processed) {

 	local_processed = true;

 	_processed = Traits::createProcessedMap(*G);

       }

     }

   public :

     ///\name Named template parameters

     ///@{

     template <class T>

     struct DefPredMapTraits : public Traits {

       typedef T PredMap;

       static PredMap *createPredMap(const Graph &G) 

       {

 	throw UninitializedParameter();

       }

     };

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

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

     ///

     template <class T>

     class DefPredMap : public Dfs< Graph,

 					DefPredMapTraits<T> > { };

 //     template <class T>

 //     struct DefPredNodeMapTraits : public Traits {

 //       typedef T PredNodeMap;

 //       static PredNodeMap *createPredNodeMap(const Graph &G) 

 //       {

 // 	throw UninitializedParameter();

 //       }

 //     };

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

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

 //     ///

 //     template <class T>

 //     class DefPredNodeMap : public Dfs< Graph,

 // 					    LengthMap,

 // 					    DefPredNodeMapTraits<T> > { };

     template <class T>

     struct DefDistMapTraits : public Traits {

       typedef T DistMap;

       static DistMap *createDistMap(const Graph &G) 

       {

 	throw UninitializedParameter();

       }

     };

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

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

     ///

     template <class T>

     class DefDistMap : public Dfs< Graph,

 				   DefDistMapTraits<T> > { };

     template <class T>

     struct DefReachedMapTraits : public Traits {

       typedef T ReachedMap;

       static ReachedMap *createReachedMap(const Graph &G) 

       {

 	throw UninitializedParameter();

       }

     };

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

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

     ///

     template <class T>

     class DefReachedMap : public Dfs< Graph,

 				      DefReachedMapTraits<T> > { };

     struct DefGraphReachedMapTraits : public Traits {

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

       static ReachedMap *createReachedMap(const Graph &G) 

       {

 	return new ReachedMap(G);

       }

     };

     template <class T>

     struct DefProcessedMapTraits : public Traits {

       typedef T ProcessedMap;

       static ProcessedMap *createProcessedMap(const Graph &G) 

       {

 	throw UninitializedParameter();

       }

     };

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

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

     ///

     template <class T>

     class DefProcessedMap : public Dfs< Graph,

 					DefProcessedMapTraits<T> > { };

     struct DefGraphProcessedMapTraits : public Traits {

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

       static ProcessedMap *createProcessedMap(const Graph &G) 

       {

 	return new ProcessedMap(G);

       }

     };

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

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

     ///

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

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

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

     template <class T>

     class DefProcessedMapToBeDefaultMap :

       public Dfs< Graph,

 		  DefGraphProcessedMapTraits> { };

     ///@}

   public:      

     ///Constructor.

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

     ///

     Dfs(const Graph& _G) :

       G(&_G),

       _pred(NULL), local_pred(false),

 //       _predNode(NULL), local_predNode(false),

       _dist(NULL), local_dist(false),

       _reached(NULL), local_reached(false),

       _processed(NULL), local_processed(false)

     { }

     ///Destructor.

     ~Dfs() 

     {

       if(local_pred) delete _pred;

 //       if(local_predNode) delete _predNode;

       if(local_dist) delete _dist;

       if(local_reached) delete _reached;

       if(local_processed) delete _processed;

     }

     ///Sets the map storing the predecessor edges.

     ///Sets the map storing the predecessor edges.

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

     ///it will allocate one. The 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 predecessor nodes.

 //     ///Sets the map storing the predecessor nodes.

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

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

 //     ///automatically allocated map, of course.

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

 //     Dfs &predNodeMap(PredNodeMap &m) 

 //     {

 //       if(local_predNode) {

 // 	delete _predNode;

 // 	local_predNode=false;

 //       }

 //       _predNode = &m;

 //       return *this;

 //     }

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

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

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

     ///it will allocate one. The 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 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();

       _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.

     ///

     ///\bug 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);

 	  // _predNode->set(u,INVALID);

 	  OutEdgeIt e(*G,s);

 	  if(e!=INVALID) _stack[++_stack_head]=e;

 	  else _processed->set(s,true);

 	  _dist->set(s,_stack_head);

 	}

     }

     ///Processes the next edge.

     ///Processes the next edge.

     ///

     ///\return The processed edge.

     ///

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

     Edge processNextEdge()

     { 

       Node m;

       Edge e=_stack[_stack_head];

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

 	_pred->set(m,e);

 	_reached->set(m,true);

 	//	  _pred_node->set(m,G->source(e));

 	++_stack_head;

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

 	_dist->set(m,_stack_head);

       }

       else {

 	m=G->source(e);

 	++_stack[_stack_head];

       }

       //'m' is now the (original) source of the _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 edge to be processed.

     ///Next edge to be processed.

     ///

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

     /// empty.

     OutEdgeIt NextEdge()

     { 

       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

     ///

     ///\todo This should be called emptyStack() or some "neutral" name.

     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.

     ///

     ///\todo This should be called stackSize() or some "neutral" name.

     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() ) processNextEdge();

     }

     ///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 ) 

 	processNextEdge();

     }

     ///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) edge map. The algorithm

     ///will stop when it reaches an edge \c e with <tt>nm[e]==true</tt>.

     ///

     ///\warning Contrary to \ref Dfs and \ref Dijkstra, \c nm is an edge map,

     ///not a node map.

     template<class NM>

       void start(const NM &nm)

       {

 	while ( !emptyQueue() && !nm[_stack[_stack_head]] ) processNextEdge();

       }

     ///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.

     ///@{

     ///Copies the path to \c t on the DFS tree into \c p

     ///This function copies the path to \c t on the DFS tree  into \c p.

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

     ///alter \c p.

     ///\todo Is this the right way to handle unreachable nodes?

     ///

     ///\return Returns \c true if a path to \c t was actually copied to \c p,

     ///\c false otherwise.

     ///\sa DirPath

     template<class P>

     bool getPath(P &p,Node t) 

     {

       if(reached(t)) {

 	p.clear();

 	typename P::Builder b(p);

 	for(b.setStartNode(t);pred(t)!=INVALID;t=predNode(t))

 	  b.pushFront(pred(t));

 	b.commit();

 	return true;

       }

       return false;

     }

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

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

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

     ///\warning If node \c v 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 edge' of the %DFS tree.

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

     ///of the %DFS path,

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

     ///\todo predEdge could be a better name.

     Edge pred(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(a) 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 pred().

     ///\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 edge-tree map.

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

     ///%DFS tree.

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

     ///must be called before using this function.

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

 //     ///Returns a reference to the map of nodes of %DFS paths.

 //     ///Returns a reference to the NodeMap of the last but one nodes of the

 //     ///%DFS tree.

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

 //     const PredNodeMap &predNodeMap() const { return *_predNode;}

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

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

   ///\param GR Graph type.

   template<class GR>

   struct DfsWizardDefaultTraits

   {

     ///The graph type the algorithm runs on. 

     typedef GR Graph;

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

     ///edges of the %DFS paths.

     /// 

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

     ///edges of the %DFS paths.

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

     ///

     typedef NullMap<typename Graph::Node,typename GR::Edge> PredMap;

     ///Instantiates a PredMap.

     ///This function instantiates a \ref PredMap. 

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

     ///\todo The graph alone may be insufficient to initialize

 #ifdef DOXYGEN

     static PredMap *createPredMap(const GR &g) 

 #else

     static PredMap *createPredMap(const GR &) 

 #endif

     {

       return new PredMap();

     }

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

 //     ///nodes of the %DFS paths.

 //     ///

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

 //     ///nodes of the %DFS paths.

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

 //     ///

 //     typedef NullMap<typename Graph::Node,typename Graph::Node> PredNodeMap;

 //     ///Instantiates a PredNodeMap.

 //     ///This function instantiates a \ref PredNodeMap. 

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

 //     ///we would like to define the \ref PredNodeMap

 //     static PredNodeMap *createPredNodeMap(const GR &G)

 //     {

 //       return new PredNodeMap();

 //     }

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

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

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

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

     typedef NullMap<typename Graph::Node,bool> ProcessedMap;

     ///Instantiates a ProcessedMap.

     ///This function instantiates a \ref ProcessedMap. 

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

     ///we would like to define the \ref ProcessedMap

 #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 concept::WriteMap "WriteMap" concept.

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

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

     ///Instantiates a ReachedMap.

     ///This function instantiates a \ref ReachedMap. 

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

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

     static ReachedMap *createReachedMap(const GR &G)

     {

       return new ReachedMap(G);

     }

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

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

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

     ///

     typedef NullMap<typename Graph::Node,int> DistMap;

     ///Instantiates a DistMap.

     ///This function instantiates a \ref DistMap. 

     ///\param g is the graph, to which we would like to define the \ref DistMap

 #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 graph.

     typedef typename Base::Graph::Node Node;

     /// Pointer to the underlying graph.

     void *_g;

     ///Pointer to the map of reached nodes.

     void *_reached;

     ///Pointer to the map of processed nodes.

     void *_processed;

     ///Pointer to the map of predecessors edges.

     void *_pred;

 //     ///Pointer to the map of predecessors nodes.

 //     void *_predNode;

     ///Pointer to the map of distances.

     void *_dist;

     ///Pointer to the source node.

     Node _source;

     public:

     /// Constructor.

     /// This constructor does not require parameters, therefore it initiates

     /// all of the attributes to default values (0, INVALID).

     DfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0),

 // 			   _predNode(0),

 			   _dist(0), _source(INVALID) {}

     /// Constructor.

     /// This constructor requires some parameters,

     /// listed in the parameters list.

     /// Others are initiated to 0.

     /// \param g is the initial value of  \ref _g

     /// \param s is the initial value of  \ref _source

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

       _g((void *)&g), _reached(0), _processed(0), _pred(0),

 //       _predNode(0),

       _dist(0), _source(s) {}

   };

   /// A class to make the usage of 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 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 %DFS paths.

     typedef typename TR::PredMap PredMap;

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

 //     ///nodes of the %DFS paths.

 //     typedef typename TR::PredNodeMap PredNodeMap;

     ///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 Graph &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<Graph,TR> alg(*(Graph*)Base::_g);

       if(Base::_reached) alg.reachedMap(*(ReachedMap*)Base::_reached);

       if(Base::_processed) alg.processedMap(*(ProcessedMap*)Base::_processed);

       if(Base::_pred) alg.predMap(*(PredMap*)Base::_pred);

 //       if(Base::_predNode) alg.predNodeMap(*(PredNodeMap*)Base::_predNode);

       if(Base::_dist) alg.distMap(*(DistMap*)Base::_dist);

       alg.run(Base::_source);

     }

     ///Runs 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 Graph &) { 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=(void *)&t;

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

     }

     template<class T>

     struct DefReachedMapBase : public Base {

       typedef T ReachedMap;

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

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

     };

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

     ///function for setting ReachedMap

     ///

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

     ///function for setting ReachedMap

     ///

     template<class T>

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

     {

       Base::_pred=(void *)&t;

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

     }

     template<class T>

     struct DefProcessedMapBase : public Base {

       typedef T ProcessedMap;

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

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

     };

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

     ///function for setting ProcessedMap

     ///

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

     ///function for setting ProcessedMap

     ///

     template<class T>

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

     {

       Base::_pred=(void *)&t;

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

     }

 //     template<class T>

 //     struct DefPredNodeMapBase : public Base {

 //       typedef T PredNodeMap;

 //       static PredNodeMap *createPredNodeMap(const Graph &G) { return 0; };

 //       DefPredNodeMapBase(const TR &b) : TR(b) {}

 //     };

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

 //     ///function for setting PredNodeMap type

 //     ///

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

 //     ///function for setting PredNodeMap type

 //     ///

 //     template<class T>

 //     DfsWizard<DefPredNodeMapBase<T> > predNodeMap(const T &t) 

 //     {

 //       Base::_predNode=(void *)&t;

 //       return DfsWizard<DefPredNodeMapBase<T> >(*this);

 //     }

     template<class T>

     struct DefDistMapBase : public Base {

       typedef T DistMap;

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

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

     };

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

     ///function for setting DistMap type

     ///

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

     ///function for setting DistMap type

     ///

     template<class T>

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

     {

       Base::_dist=(void *)&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 flowalgs

   ///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);

   }

 } //END OF NAMESPACE LEMON

 #endif