/* -*- C++ -*-

 *

 * 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_DIJKSTRA_H

#define LEMON_DIJKSTRA_H

///\ingroup shortest_path

///\file

///\brief Dijkstra algorithm.

///

#include <lemon/list_graph.h>

#include <lemon/bin_heap.h>

#include <lemon/bits/path_dump.h>

#include <lemon/bits/invalid.h>

#include <lemon/error.h>

#include <lemon/maps.h>

namespace lemon {

  /// \brief Default OperationTraits for the Dijkstra algorithm class.

  ///  

  /// It defines all computational operations and constants which are

  /// used in the Dijkstra algorithm.

  template <typename Value>

  struct DijkstraDefaultOperationTraits {

    /// \brief Gives back the zero value of the type.

    static Value zero() {

      return static_cast<Value>(0);

    }

    /// \brief Gives back the sum of the given two elements.

    static Value plus(const Value& left, const Value& right) {

      return left + right;

    }

    /// \brief Gives back true only if the first value less than the second.

    static bool less(const Value& left, const Value& right) {

      return left < right;

    }

  };

  /// \brief Widest path OperationTraits for the Dijkstra algorithm class.

  ///  

  /// It defines all computational operations and constants which are

  /// used in the Dijkstra algorithm for widest path computation.

  template <typename Value>

  struct DijkstraWidestPathOperationTraits {

    /// \brief Gives back the maximum value of the type.

    static Value zero() {

      return std::numeric_limits<Value>::max();

    }

    /// \brief Gives back the minimum of the given two elements.

    static Value plus(const Value& left, const Value& right) {

      return std::min(left, right);

    }

    /// \brief Gives back true only if the first value less than the second.

    static bool less(const Value& left, const Value& right) {

      return left < right;

    }

  };

  ///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 concepts::ReadMap "ReadMap" concept.

    typedef LM LengthMap;

    //The type of the length of the edges.

    typedef typename LM::Value Value;

    /// Operation traits for Dijkstra algorithm.

    /// It defines the used operation by the algorithm.

    /// \see DijkstraDefaultOperationTraits

    typedef DijkstraDefaultOperationTraits<Value> OperationTraits;

    /// The cross reference type used by heap.

    /// The cross reference type used by heap.

    /// Usually it is \c Graph::NodeMap<int>.

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

    ///Instantiates a HeapCrossRef.

    ///This function instantiates a \c HeapCrossRef. 

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

    /// HeapCrossRef.

    static HeapCrossRef *createHeapCrossRef(const GR &G) 

    {

      return new HeapCrossRef(G);

    }

    ///The heap type used by Dijkstra algorithm.

    ///The heap type used by Dijkstra algorithm.

    ///

    ///\sa BinHeap

    ///\sa Dijkstra

    typedef BinHeap<typename LM::Value, HeapCrossRef, std::less<Value> > Heap;

    static Heap *createHeap(HeapCrossRef& R) 

    {

      return new Heap(R);

    }

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

    ///edges of the shortest paths.

    /// 

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

    ///edges of the shortest paths.

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

    ///

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

    ///Instantiates a PredMap.

    ///This function instantiates a \c 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);

    }

    ///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 concepts::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 \c ProcessedMap. 

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

    ///we would like to define the \c 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 stores the dists of the nodes.

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

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

    ///

    typedef typename Graph::template NodeMap<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 shortest_path

  ///This class provides an efficient implementation of %Dijkstra algorithm.

  ///The edge lengths are passed to the algorithm using a

  ///\ref concepts::ReadMap "ReadMap",

  ///so it is easy to change it to any kind of length.

  ///

  ///The type of the length is determined by the

  ///\ref concepts::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

  ///concepts::Graph::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

#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* what() const throw() {

	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;

    ///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 cross reference type used for the current heap.

    typedef typename TR::HeapCrossRef HeapCrossRef;

    ///The heap type used by the dijkstra algorithm.

    typedef typename TR::Heap Heap;

    ///The operation traits.

    typedef typename TR::OperationTraits OperationTraits;

  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 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;

    ///Pointer to the heap cross references.

    HeapCrossRef *_heap_cross_ref;

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

    bool local_heap_cross_ref;

    ///Pointer to the heap.

    Heap *_heap;

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

    bool local_heap;

    ///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(!_processed) {

	local_processed = true;

	_processed = Traits::createProcessedMap(*G);

      }

      if (!_heap_cross_ref) {

	local_heap_cross_ref = true;

	_heap_cross_ref = Traits::createHeapCrossRef(*G);

      }

      if (!_heap) {

	local_heap = true;

	_heap = Traits::createHeap(*_heap_cross_ref);

      }

    }

  public :

    typedef Dijkstra Create;

    ///\name Named template parameters

    ///@{

    template <class T>

    struct DefPredMapTraits : public Traits {

      typedef T PredMap;

      static PredMap *createPredMap(const Graph &)

      {

	throw UninitializedParameter();

      }

    };

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

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

    ///

    template <class T>

    struct DefPredMap 

      : public Dijkstra< Graph,	LengthMap, DefPredMapTraits<T> > {

      typedef Dijkstra< Graph,	LengthMap, DefPredMapTraits<T> > Create;

    };

    template <class T>

    struct DefDistMapTraits : public Traits {

      typedef T DistMap;

      static DistMap *createDistMap(const Graph &)

      {

	throw UninitializedParameter();

      }

    };

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

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

    ///

    template <class T>

    struct DefDistMap 

      : public Dijkstra< Graph, LengthMap, DefDistMapTraits<T> > { 

      typedef Dijkstra< Graph, LengthMap, DefDistMapTraits<T> > Create;

    };

    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>

    struct DefProcessedMap 

      : public Dijkstra< Graph,	LengthMap, DefProcessedMapTraits<T> > { 

      typedef Dijkstra< Graph,	LengthMap, DefProcessedMapTraits<T> > Create;

    };

    struct DefGraphProcessedMapTraits : public Traits {

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

      static ProcessedMap *createProcessedMap(const Graph &G) 

      {

	return new ProcessedMap(G);

      }

    };

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

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

    ///

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

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

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

    template <class T>

    struct DefProcessedMapToBeDefaultMap 

      : public Dijkstra< Graph, LengthMap, DefGraphProcessedMapTraits> {

      typedef Dijkstra< Graph, LengthMap, DefGraphProcessedMapTraits> Create;

    };

    template <class H, class CR>

    struct DefHeapTraits : public Traits {

      typedef CR HeapCrossRef;

      typedef H Heap;

      static HeapCrossRef *createHeapCrossRef(const Graph &) {

	throw UninitializedParameter();

      }

      static Heap *createHeap(HeapCrossRef &) 

      {

	throw UninitializedParameter();

      }

    };

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

    ///heap and cross reference type

    ///

    ///\ref named-templ-param "Named parameter" for setting heap and cross 

    ///reference type

    ///

    template <class H, class CR = typename Graph::template NodeMap<int> >

    struct DefHeap

      : public Dijkstra< Graph,	LengthMap, DefHeapTraits<H, CR> > { 

      typedef Dijkstra< Graph,	LengthMap, DefHeapTraits<H, CR> > Create;

    };

    template <class H, class CR>

    struct DefStandardHeapTraits : public Traits {

      typedef CR HeapCrossRef;

      typedef H Heap;

      static HeapCrossRef *createHeapCrossRef(const Graph &G) {

	return new HeapCrossRef(G);

      }

      static Heap *createHeap(HeapCrossRef &R) 

      {

	return new Heap(R);

      }

    };

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

    ///heap and cross reference type with automatic allocation

    ///

    ///\ref named-templ-param "Named parameter" for setting heap and cross 

    ///reference type. It can allocate the heap and the cross reference 

    ///object if the cross reference's constructor waits for the graph as 

    ///parameter and the heap's constructor waits for the cross reference.

    template <class H, class CR = typename Graph::template NodeMap<int> >

    struct DefStandardHeap

      : public Dijkstra< Graph,	LengthMap, DefStandardHeapTraits<H, CR> > { 

      typedef Dijkstra< Graph,	LengthMap, DefStandardHeapTraits<H, CR> > 

      Create;

    };

    template <class T>

    struct DefOperationTraitsTraits : public Traits {

      typedef T OperationTraits;

    };

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

    /// OperationTraits type

    ///

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

    /// type

    template <class T>

    struct DefOperationTraits

      : public Dijkstra<Graph, LengthMap, DefOperationTraitsTraits<T> > {

      typedef Dijkstra<Graph, LengthMap, DefOperationTraitsTraits<T> >

      Create;

    };

    ///@}

  protected:

    Dijkstra() {}

  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),

      _dist(NULL), local_dist(false),

      _processed(NULL), local_processed(false),

      _heap_cross_ref(NULL), local_heap_cross_ref(false),

      _heap(NULL), local_heap(false)

    { }

    ///Destructor.

    ~Dijkstra() 

    {

      if(local_pred) delete _pred;

      if(local_dist) delete _dist;

      if(local_processed) delete _processed;

      if(local_heap_cross_ref) delete _heap_cross_ref;

      if(local_heap) delete _heap;

    }

    ///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 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;

    }

    ///Sets the heap and the cross reference used by algorithm.

    ///Sets the heap and the cross reference used by algorithm.

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

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

    ///automatically allocated heap and cross reference, of course.

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

    Dijkstra &heap(Heap& hp, HeapCrossRef &cr)

    {

      if(local_heap_cross_ref) {

	delete _heap_cross_ref;

	local_heap_cross_ref=false;

      }

      _heap_cross_ref = &cr;

      if(local_heap) {

	delete _heap;

	local_heap=false;

      }

      _heap = &hp;

      return *this;

    }

  private:

    void finalizeNodeData(Node v,Value dst)

    {

      _processed->set(v,true);

      _dist->set(v, dst);

    }

  public:

    typedef PredMapPath<Graph, PredMap> Path;

    ///\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();

      _heap->clear();

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

	_pred->set(u,INVALID);

	_processed->set(u,false);

	_heap_cross_ref->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 shorter than \c dst.

    void addSource(Node s,Value dst=OperationTraits::zero())

    {

      if(_heap->state(s) != Heap::IN_HEAP) {

	_heap->push(s,dst);

      } else if(OperationTraits::less((*_heap)[s], dst)) {

	_heap->set(s,dst);

	_pred->set(s,INVALID);

      }

    }

    ///Processes the next node in the priority heap

    ///Processes the next node in the priority heap.

    ///

    ///\return The processed node.

    ///

    ///\warning The priority heap must not be empty!

    Node processNextNode()

    {

      Node v=_heap->top(); 

      Value oldvalue=_heap->prio();

      _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,OperationTraits::plus(oldvalue, (*length)[e])); 

	  _pred->set(w,e);

	  break;

	case Heap::IN_HEAP:

	  {

	    Value newvalue = OperationTraits::plus(oldvalue, (*length)[e]);

	    if ( OperationTraits::less(newvalue, (*_heap)[w]) ) {

	      _heap->decrease(w, newvalue); 

	      _pred->set(w,e);

	    }

	  }

	  break;

	case Heap::POST_HEAP:

	  break;

	}

      }

      return v;

    }

    ///Next node to be processed.

    ///Next node to be processed.

    ///

    ///\return The next node to be processed or INVALID if the priority heap

    /// is empty.

    Node nextNode()

    { 

      return !_heap->empty()?_heap->top():INVALID;

    }

    ///\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]</tt> true.

    ///

    ///\return The reached node \c v with <tt>nm[v]</tt> true or

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

    template<class NodeBoolMap>

    Node start(const NodeBoolMap &nm)

    {

      while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode();

      if ( _heap->empty() ) return INVALID;

      finalizeNodeData(_heap->top(),_heap->prio());

      return _heap->top();

    }

    ///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?OperationTraits::zero():(*_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.

    ///@{

    ///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.

    ///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]; }

    ///The current distance of a node from the root.

    ///Returns the current distance of a node from the root.

    ///It may be decreased in the following processes.

    ///\pre \c node should be reached but not processed

    Value currentDist(Node v) const { return (*_heap)[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().  \pre \ref run() must be called before using

    ///this function.

    Edge predEdge(Node v) const { return (*_pred)[v]; }

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

    ///For a node \c v it returns the 'previous node' of the shortest path tree,

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

    ///root 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 predEdge().  \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;}

    ///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_cross_ref)[v] != Heap::PRE_HEAP; }

    ///Checks if a node is processed.

    ///Returns \c true if \c v is processed, i.e. the shortest

    ///path to \c v has already found.

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

    ///

    bool processed(Node v) { return (*_heap_cross_ref)[v] == Heap::POST_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 concepts::ReadMap "ReadMap" concept.

    typedef LM LengthMap;

    //The type of the length of the edges.

    typedef typename LM::Value Value;

    /// Operation traits for Dijkstra algorithm.

    /// It defines the used operation by the algorithm.

    /// \see DijkstraDefaultOperationTraits

    typedef DijkstraDefaultOperationTraits<Value> OperationTraits;

    ///The heap type used by Dijkstra algorithm.

    /// The cross reference type used by heap.

    /// The cross reference type used by heap.

    /// Usually it is \c Graph::NodeMap<int>.

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

    ///Instantiates a HeapCrossRef.

    ///This function instantiates a \ref HeapCrossRef. 

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

    /// HeapCrossRef.

    /// \todo The graph alone may be insufficient for the initialization

    static HeapCrossRef *createHeapCrossRef(const GR &G) 

    {

      return new HeapCrossRef(G);

    }

    ///The heap type used by Dijkstra algorithm.

    ///The heap type used by Dijkstra algorithm.

    ///

    ///\sa BinHeap

    ///\sa Dijkstra

    typedef BinHeap<typename LM::Value, typename GR::template NodeMap<int>,

		    std::less<Value> > Heap;

    static Heap *createHeap(HeapCrossRef& R) 

    {

      return new Heap(R);

    }

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

    ///edges of the shortest paths.

    /// 

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

    ///edges of the shortest paths.

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

    ///

    typedef NullMap <typename 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

#ifdef DOXYGEN

    static PredMap *createPredMap(const GR &g) 

#else

    static PredMap *createPredMap(const GR &) 

#endif

    {

      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 concepts::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

#ifdef DOXYGEN

    static ProcessedMap *createProcessedMap(const GR &g)

#else

    static ProcessedMap *createProcessedMap(const GR &)

#endif

    {

      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 concepts::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

#ifdef DOXYGEN

    static DistMap *createDistMap(const GR &g)

#else

    static DistMap *createDistMap(const GR &)

#endif

    {

      return new DistMap();

    }

  };

  /// Default traits used by \ref DijkstraWizard