/* -*- C++ -*-
 * src/lemon/dijkstra.h - Part of LEMON, a generic C++ optimization library
 *
 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 * (Egervary Combinatorial Optimization Research Group, 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_DIJKSTRA_H
#define LEMON_DIJKSTRA_H

///\ingroup flowalgs
///\file
///\brief Dijkstra algorithm.
///
///\todo getPath() should be implemented! (also for BFS and DFS)

#include <lemon/list_graph.h>
#include <lemon/bin_heap.h>
#include <lemon/invalid.h>
#include <lemon/error.h>
#include <lemon/maps.h>

namespace lemon {


  
  ///Default traits class of Dijkstra class.

  ///Default traits class of Dijkstra class.
  ///\param GR Graph type.
  ///\param LM Type of length map.
  template<class GR, class LM>
  struct DijkstraDefaultTraits
  {
    ///The graph type the algorithm runs on. 
    typedef GR Graph;
    ///The type of the map that stores the edge lengths.

    ///The type of the map that stores the edge lengths.
    ///It must meet the \ref concept::ReadMap "ReadMap" concept.
    typedef LM LengthMap;
    //The type of the length of the edges.
    typedef typename LM::Value Value;
    ///The heap type used by Dijkstra algorithm.

    ///The heap type used by Dijkstra algorithm.
    ///
    ///\sa BinHeap
    ///\sa Dijkstra
    typedef BinHeap<typename Graph::Node,
		    typename LM::Value,
		    typename GR::template NodeMap<int>,
		    std::less<Value> > Heap;

    ///\brief The type of the map that stores the last
    ///edges of the shortest paths.
    /// 
    ///The type of the map that stores the last
    ///edges of the shortest paths.
    ///It must meet the \ref concept::WriteMap "WriteMap" concept.
    ///
    typedef typename Graph::template NodeMap<typename GR::Edge> PredMap;
    ///Instantiates a PredMap.
 
    ///This function instantiates a \ref PredMap. 
    ///\param G is the graph, to which we would like to define the PredMap.
    ///\todo The graph alone may be insufficient for the initialization
    static PredMap *createPredMap(const GR &G) 
    {
      return new PredMap(G);
    }
//     ///\brief The type of the map that stores the last but one
//     ///nodes of the shortest paths.
//     ///
//     ///The type of the map that stores the last but one
//     ///nodes of the shortest paths.
//     ///It must meet the \ref concept::WriteMap "WriteMap" concept.
//     ///
//     typedef NullMap<typename Graph::Node,typename Graph::Node> PredNodeMap;
//     ///Instantiates a PredNodeMap.
    
//     ///This function instantiates a \ref PredNodeMap. 
//     ///\param G is the graph, to which
//     ///we would like to define the \ref PredNodeMap
//     static PredNodeMap *createPredNodeMap(const GR &G)
//     {
//       return new PredNodeMap();
//     }

    ///The type of the map that stores whether a nodes is processed.
 
    ///The type of the map that stores whether a nodes is processed.
    ///It must meet the \ref concept::WriteMap "WriteMap" concept.
    ///By default it is a NullMap.
    ///\todo If it is set to a real map,
    ///Dijkstra::processed() should read this.
    ///\todo named parameter to set this type, function to read and write.
    typedef NullMap<typename Graph::Node,bool> ProcessedMap;
    ///Instantiates a ProcessedMap.
 
    ///This function instantiates a \ref ProcessedMap. 
    ///\param G is the graph, to which
    ///we would like to define the \ref ProcessedMap
    static ProcessedMap *createProcessedMap(const GR &G)
    {
      return new ProcessedMap();
    }
    ///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<typename LM::Value> 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);
    }
  };
  
  ///%Dijkstra algorithm class.
  
  /// \ingroup flowalgs
  ///This class provides an efficient implementation of %Dijkstra algorithm.
  ///The edge lengths are passed to the algorithm using a
  ///\ref concept::ReadMap "ReadMap",
  ///so it is easy to change it to any kind of length.
  ///
  ///The type of the length is determined by the
  ///\ref concept::ReadMap::Value "Value" of the length map.
  ///
  ///It is also possible to change the underlying priority heap.
  ///
  ///\param GR The graph type the algorithm runs on. The default value
  ///is \ref ListGraph. The value of GR is not used directly by
  ///Dijkstra, it is only passed to \ref DijkstraDefaultTraits.
  ///\param LM This read-only EdgeMap determines the lengths of the
  ///edges. It is read once for each edge, so the map may involve in
  ///relatively time consuming process to compute the edge length if
  ///it is necessary. The default map type is \ref
  ///concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>".  The value
  ///of LM is not used directly by Dijkstra, it is only passed to \ref
  ///DijkstraDefaultTraits.  \param TR Traits class to set
  ///various data types used by the algorithm.  The default traits
  ///class is \ref DijkstraDefaultTraits
  ///"DijkstraDefaultTraits<GR,LM>".  See \ref
  ///DijkstraDefaultTraits for the documentation of a Dijkstra traits
  ///class.
  ///
  ///\author Jacint Szabo and Alpar Juttner
  ///\todo A compare object would be nice.

#ifdef DOXYGEN
  template <typename GR,
	    typename LM,
	    typename TR>
#else
  template <typename GR=ListGraph,
	    typename LM=typename GR::template EdgeMap<int>,
	    typename TR=DijkstraDefaultTraits<GR,LM> >
#endif
  class Dijkstra {
  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::Dijkstra::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;
    
    ///The type of the length of the edges.
    typedef typename TR::LengthMap::Value Value;
    ///The type of the map that stores the edge lengths.
    typedef typename TR::LengthMap LengthMap;
    ///\brief The type of the map that stores the last
    ///edges of the shortest paths.
    typedef typename TR::PredMap PredMap;
//     ///\brief The type of the map that stores the last but one
//     ///nodes of the shortest paths.
//     typedef typename TR::PredNodeMap PredNodeMap;
    ///The type of the map indicating if a node is processed.
    typedef typename TR::ProcessedMap ProcessedMap;
    ///The type of the map that stores the dists of the nodes.
    typedef typename TR::DistMap DistMap;
    ///The heap type used by the dijkstra algorithm.
    typedef typename TR::Heap Heap;
  private:
    /// Pointer to the underlying graph.
    const Graph *G;
    /// Pointer to the length map
    const LengthMap *length;
    ///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 processed status of the nodes.
    ProcessedMap *_processed;
    ///Indicates if \ref _processed is locally allocated (\c true) or not.
    bool local_processed;

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

    ///Creates the maps if necessary.
    
    ///\todo Error if \c G or are \c NULL. What about \c length?
    ///\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(!_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 Dijkstra< Graph,
					LengthMap,
					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 Dijkstra< 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 Dijkstra< Graph,
					LengthMap,
					DefDistMapTraits<T> > { };
    
    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 Dijkstra< Graph,
					LengthMap,
					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 Dijkstra< Graph,
		       LengthMap,
		       DefGraphProcessedMapTraits> { };
    
    ///@}


  private:
    typename Graph::template NodeMap<int> _heap_map;
    Heap _heap;
  public:      
    
    ///Constructor.
    
    ///\param _G the graph the algorithm will run on.
    ///\param _length the length map used by the algorithm.
    Dijkstra(const Graph& _G, const LengthMap& _length) :
      G(&_G), length(&_length),
      _pred(NULL), local_pred(false),
//       _predNode(NULL), local_predNode(false),
      _dist(NULL), local_dist(false),
      _processed(NULL), local_processed(false),
      _heap_map(*G,-1),_heap(_heap_map)
    { }
    
    ///Destructor.
    ~Dijkstra() 
    {
      if(local_pred) delete _pred;
//       if(local_predNode) delete _predNode;
      if(local_dist) delete _dist;
      if(local_processed) delete _processed;
    }

    ///Sets the length map.

    ///Sets the length map.
    ///\return <tt> (*this) </tt>
    Dijkstra &lengthMap(const LengthMap &m) 
    {
      length = &m;
      return *this;
    }

    ///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>
    Dijkstra &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>
//     Dijkstra &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>
    Dijkstra &distMap(DistMap &m) 
    {
      if(local_dist) {
	delete _dist;
	local_dist=false;
      }
      _dist = &m;
      return *this;
    }

  private:
    void finalizeNodeData(Node v,Value dst)
    {
      _processed->set(v,true);
      _dist->set(v, dst);
//       if((*_pred)[v]!=INVALID)
//       _predNode->set(v,G->source((*_pred)[v])); ///\todo What to do?
    }

  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.
    ///
    ///\todo _heap_map's type could also be in the traits class.
    ///\todo The heaps should be able to make themselves empty directly.
    void init()
    {
      create_maps();
      while(!_heap.empty()) _heap.pop();
      for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
	_pred->set(u,INVALID);
// 	_predNode->set(u,INVALID);
	_processed->set(u,false);
	_heap_map.set(u,Heap::PRE_HEAP);
      }
    }
    
    ///Adds a new source node.

    ///Adds a new source node to the priority heap.
    ///
    ///The optional second parameter is the initial distance of the node.
    ///
    ///It checks if the node has already been added to the heap and
    ///It is pushed to the heap only if either it was not in the heap
    ///or the shortest path found till then is longer then \c dst.
    void addSource(Node s,Value dst=0)
    {
//       source = s;
      if(_heap.state(s) != Heap::IN_HEAP) _heap.push(s,dst);
      else if(_heap[s]<dst) {
	_heap.push(s,dst);
	_pred->set(s,INVALID);
      }
    }
    
    ///Processes the next node in the priority heap

    ///Processes the next node in the priority heap.
    ///
    ///\warning The priority heap must not be empty!
    void processNextNode()
    {
      Node v=_heap.top(); 
      Value oldvalue=_heap[v];
      _heap.pop();
      finalizeNodeData(v,oldvalue);
      
      for(OutEdgeIt e(*G,v); e!=INVALID; ++e) {
	Node w=G->target(e); 
	switch(_heap.state(w)) {
	case Heap::PRE_HEAP:
	  _heap.push(w,oldvalue+(*length)[e]); 
	  _pred->set(w,e);
//  	  _predNode->set(w,v);
	  break;
	case Heap::IN_HEAP:
	  if ( oldvalue+(*length)[e] < _heap[w] ) {
	    _heap.decrease(w, oldvalue+(*length)[e]); 
	    _pred->set(w,e);
// 	    _predNode->set(w,v);
	  }
	  break;
	case Heap::POST_HEAP:
	  break;
	}
      }
    }

    ///\brief Returns \c false if there are nodes
    ///to be processed in the priority heap
    ///
    ///Returns \c false if there are nodes
    ///to be processed in the priority heap
    bool emptyQueue() { return _heap.empty(); }
    ///Returns the number of the nodes to be processed in the priority heap

    ///Returns the number of the nodes to be processed in the priority heap
    ///
    int queueSize() { return _heap.size(); }
    
    ///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 %Dijkstra 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 ( !_heap.empty() ) 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 %Dijkstra algorithm from the root node(s)
    ///in order to
    ///compute the
    ///shortest path to \c dest. The algorithm computes
    ///- The shortest path to \c  dest.
    ///- The distance of \c dest from the root(s).
    ///
    void start(Node dest)
    {
      while ( !_heap.empty() && _heap.top()!=dest ) processNextNode();
      if ( !_heap.empty() ) finalizeNodeData(_heap.top(),_heap.prio());
    }
    
    ///Executes the algorithm until a condition is met.

    ///Executes the algorithm until a condition is met.
    ///
    ///\pre init() must be called and at least one node should be added
    ///with addSource() before using this function.
    ///
    ///\param nm must be a bool (or convertible) node map. The algorithm
    ///will stop when it reaches a node \c v with <tt>nm[v]==true</tt>.
    template<class NM>
    void start(const NM &nm)
    {
      while ( !_heap.empty() && !nm[_heap.top()] ) processNextNode();
      if ( !_heap.empty() ) finalizeNodeData(_heap.top(),_heap.prio());
    }
    
    ///Runs %Dijkstra algorithm from node \c s.
    
    ///This method runs the %Dijkstra algorithm from a root node \c s
    ///in order to
    ///compute the
    ///shortest path to each node. The algorithm computes
    ///- The shortest path tree.
    ///- The distance of each node from the root.
    ///
    ///\note d.run(s) is just a shortcut of the following code.
    ///\code
    ///  d.init();
    ///  d.addSource(s);
    ///  d.start();
    ///\endcode
    void run(Node s) {
      init();
      addSource(s);
      start();
    }
    
    ///Finds the shortest path between \c s and \c t.
    
    ///Finds the shortest path between \c s and \c t.
    ///
    ///\return The length of the shortest s---t path if there exists one,
    ///0 otherwise.
    ///\note Apart from the return value, d.run(s) is
    ///just a shortcut of the following code.
    ///\code
    ///  d.init();
    ///  d.addSource(s);
    ///  d.start(t);
    ///\endcode
    Value run(Node s,Node t) {
      init();
      addSource(s);
      start(t);
      return (*_pred)[t]==INVALID?0:(*_dist)[t];
    }
    
    ///@}

    ///\name Query Functions
    ///The result of the %Dijkstra algorithm can be obtained using these
    ///functions.\n
    ///Before the use of these functions,
    ///either run() or start() must be called.
    
    ///@{

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

    ///Returns the distance of a node from the root.
    ///\pre \ref run() must be called before using this function.
    ///\warning If node \c v in unreachable from the root the return value
    ///of this funcion is undefined.
    Value dist(Node v) const { return (*_dist)[v]; }

    ///Returns the 'previous edge' of the shortest path tree.

    ///For a node \c v it returns the 'previous edge' of the shortest path tree,
    ///i.e. it returns the last edge of a shortest path from the root to \c
    ///v. It is \ref INVALID
    ///if \c v is unreachable from the root or if \c v=s. The
    ///shortest path tree used here is equal to the shortest path tree used in
    ///\ref predNode(Node v).  \pre \ref run() must be called before using
    ///this function.
    ///\todo predEdge could be a better name.
    Edge pred(Node v) const { return (*_pred)[v]; }

    ///Returns the 'previous node' of the shortest path tree.

    ///For a node \c v it returns the 'previous node' of the shortest path tree,
    ///i.e. it returns the last but one node from a shortest path from the
    ///root to \c /v. It is INVALID if \c v is unreachable from the root or if
    ///\c v=s. The shortest path tree used here is equal to the shortest path
    ///tree used in \ref pred(Node v).  \pre \ref run() 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 \ref run() must
    ///be called before using this function.
    const DistMap &distMap() const { return *_dist;}
 
    ///Returns a reference to the shortest path tree map.

    ///Returns a reference to the NodeMap of the edges of the
    ///shortest path tree.
    ///\pre \ref run() must be called before using this function.
    const PredMap &predMap() const { return *_pred;}
 
//     ///Returns a reference to the map of nodes of shortest paths.

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

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

    ///Returns \c true if \c v is reachable from the root.
    ///\warning The source nodes are inditated as unreached.
    ///\pre \ref run() must be called before using this function.
    ///
    bool reached(Node v) { return _heap_map[v]!=Heap::PRE_HEAP; }
    
    ///@}
  };




 
  ///Default traits class of Dijkstra function.

  ///Default traits class of Dijkstra function.
  ///\param GR Graph type.
  ///\param LM Type of length map.
  template<class GR, class LM>
  struct DijkstraWizardDefaultTraits
  {
    ///The graph type the algorithm runs on. 
    typedef GR Graph;
    ///The type of the map that stores the edge lengths.

    ///The type of the map that stores the edge lengths.
    ///It must meet the \ref concept::ReadMap "ReadMap" concept.
    typedef LM LengthMap;
    //The type of the length of the edges.
    typedef typename LM::Value Value;
    ///The heap type used by Dijkstra algorithm.

    ///The heap type used by Dijkstra algorithm.
    ///
    ///\sa BinHeap
    ///\sa Dijkstra
    typedef BinHeap<typename Graph::Node,
		    typename LM::Value,
		    typename GR::template NodeMap<int>,
		    std::less<Value> > Heap;

    ///\brief The type of the map that stores the last
    ///edges of the shortest paths.
    /// 
    ///The type of the map that stores the last
    ///edges of the shortest paths.
    ///It must meet the \ref concept::WriteMap "WriteMap" concept.
    ///
    typedef NullMap <typename GR::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 for the initialization
    static PredMap *createPredMap(const GR &G) 
    {
      return new PredMap();
    }
    ///The type of the map that stores whether a nodes is processed.
 
    ///The type of the map that stores whether a nodes is processed.
    ///It must meet the \ref concept::WriteMap "WriteMap" concept.
    ///By default it is a NullMap.
    ///\todo If it is set to a real map,
    ///Dijkstra::processed() should read this.
    ///\todo named parameter to set this type, function to read and write.
    typedef NullMap<typename Graph::Node,bool> ProcessedMap;
    ///Instantiates a ProcessedMap.
 
    ///This function instantiates a \ref ProcessedMap. 
    ///\param G is the graph, to which
    ///we would like to define the \ref ProcessedMap
    static ProcessedMap *createProcessedMap(const GR &G)
    {
      return new ProcessedMap();
    }
    ///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,typename LM::Value> 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();
    }
  };
  
  /// Default traits used by \ref DijkstraWizard

  /// To make it easier to use Dijkstra algorithm
  ///we have created a wizard class.
  /// This \ref DijkstraWizard class needs default traits,
  ///as well as the \ref Dijkstra class.
  /// The \ref DijkstraWizardBase is a class to be the default traits of the
  /// \ref DijkstraWizard class.
  /// \todo More named parameters are required...
  template<class GR,class LM>
  class DijkstraWizardBase : public DijkstraWizardDefaultTraits<GR,LM>
  {

    typedef DijkstraWizardDefaultTraits<GR,LM> 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 length map
    void *_length;
    ///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).
    DijkstraWizardBase() : _g(0), _length(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 l is the initial value of  \ref _length
    /// \param s is the initial value of  \ref _source
    DijkstraWizardBase(const GR &g,const LM &l, Node s=INVALID) :
      _g((void *)&g), _length((void *)&l), _pred(0),
//       _predNode(0),
      _dist(0), _source(s) {}

  };
  
  /// A class to make the usage of Dijkstra algorithm easier

  /// This class is created to make it easier to use Dijkstra algorithm.
  /// It uses the functions and features of the plain \ref Dijkstra,
  /// 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 Dijkstra
  /// the new class with the modified type comes from
  /// the original class by using the ::
  /// operator. In the case of \ref DijkstraWizard 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 Dijkstra class, and calls the \ref Dijkstra::run
  /// method of it.
  template<class TR>
  class DijkstraWizard : 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;
    
    ///The type of the map that stores the edge lengths.
    typedef typename TR::LengthMap LengthMap;
    ///The type of the length of the edges.
    typedef typename LengthMap::Value Value;
    ///\brief The type of the map that stores the last
    ///edges of the shortest paths.
    typedef typename TR::PredMap PredMap;
//     ///\brief The type of the map that stores the last but one
//     ///nodes of the shortest paths.
//     typedef typename TR::PredNodeMap PredNodeMap;
    ///The type of the map that stores the dists of the nodes.
    typedef typename TR::DistMap DistMap;

    ///The heap type used by the dijkstra algorithm.
    typedef typename TR::Heap Heap;
public:
    /// Constructor.
    DijkstraWizard() : TR() {}

    /// Constructor that requires parameters.

    /// Constructor that requires parameters.
    /// These parameters will be the default values for the traits class.
    DijkstraWizard(const Graph &g,const LengthMap &l, Node s=INVALID) :
      TR(g,l,s) {}

    ///Copy constructor
    DijkstraWizard(const TR &b) : TR(b) {}

    ~DijkstraWizard() {}

    ///Runs Dijkstra algorithm from a given node.
    
    ///Runs Dijkstra algorithm from a given node.
    ///The node can be given by the \ref source function.
    void run()
    {
      if(Base::_source==INVALID) throw UninitializedParameter();
      Dijkstra<Graph,LengthMap,TR> 
	Dij(*(Graph*)Base::_g,*(LengthMap*)Base::_length);
      if(Base::_pred) Dij.predMap(*(PredMap*)Base::_pred);
//       if(Base::_predNode) Dij.predNodeMap(*(PredNodeMap*)Base::_predNode);
      if(Base::_dist) Dij.distMap(*(DistMap*)Base::_dist);
      Dij.run(Base::_source);
    }

    ///Runs Dijkstra algorithm from the given node.

    ///Runs Dijkstra 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 &G) { 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>
    DijkstraWizard<DefPredMapBase<T> > predMap(const T &t) 
    {
      Base::_pred=(void *)&t;
      return DijkstraWizard<DefPredMapBase<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>
//     DijkstraWizard<DefPredNodeMapBase<T> > predNodeMap(const T &t) 
//     {
//       Base::_predNode=(void *)&t;
//       return DijkstraWizard<DefPredNodeMapBase<T> >(*this);
//     }
   
    template<class T>
    struct DefDistMapBase : public Base {
      typedef T DistMap;
      static DistMap *createDistMap(const Graph &G) { 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>
    DijkstraWizard<DefDistMapBase<T> > distMap(const T &t) 
    {
      Base::_dist=(void *)&t;
      return DijkstraWizard<DefDistMapBase<T> >(*this);
    }
    
    /// Sets the source node, from which the Dijkstra algorithm runs.

    /// Sets the source node, from which the Dijkstra algorithm runs.
    /// \param s is the source node.
    DijkstraWizard<TR> &source(Node s) 
    {
      Base::_source=s;
      return *this;
    }
    
  };
  
  ///Function type interface for Dijkstra algorithm.

  /// \ingroup flowalgs
  ///Function type interface for Dijkstra algorithm.
  ///
  ///This function also has several
  ///\ref named-templ-func-param "named parameters",
  ///they are declared as the members of class \ref DijkstraWizard.
  ///The following
  ///example shows how to use these parameters.
  ///\code
  ///  dijkstra(g,length,source).predMap(preds).run();
  ///\endcode
  ///\warning Don't forget to put the \ref DijkstraWizard::run() "run()"
  ///to the end of the parameter list.
  ///\sa DijkstraWizard
  ///\sa Dijkstra
  template<class GR, class LM>
  DijkstraWizard<DijkstraWizardBase<GR,LM> >
  dijkstra(const GR &g,const LM &l,typename GR::Node s=INVALID)
  {
    return DijkstraWizard<DijkstraWizardBase<GR,LM> >(g,l,s);
  }

} //END OF NAMESPACE LEMON

#endif