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

  *

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

  *

  * Copyright (C) 2003-2008

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

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

  *

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

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

  * precise terms see the accompanying LICENSE file.

  *

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

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

  * purpose.

  *

  */

 #ifndef LEMON_DIJKSTRA_H

 #define LEMON_DIJKSTRA_H

 ///\ingroup shortest_path

 ///\file

 ///\brief Dijkstra algorithm.

 #include <limits>

 #include <lemon/list_graph.h>

 #include <lemon/bin_heap.h>

 #include <lemon/bits/path_dump.h>

 #include <lemon/core.h>

 #include <lemon/error.h>

 #include <lemon/maps.h>

 namespace lemon {

   /// \brief Default operation traits for the Dijkstra algorithm class.

   ///

   /// This operation traits class 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 is less than the second.

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

       return left < right;

     }

   };

   /// \brief Widest path operation traits for the Dijkstra algorithm class.

   ///

   /// This operation traits class defines all computational operations and

   /// constants which are used in the Dijkstra algorithm for widest path

   /// computation.

   ///

   /// \see DijkstraDefaultOperationTraits

   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 is 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.

   ///\tparam GR The type of the digraph.

   ///\tparam LM The type of the length map.

   template<class GR, class LM>

   struct DijkstraDefaultTraits

   {

     ///The type of the digraph the algorithm runs on.

     typedef GR Digraph;

     ///The type of the map that stores the arc lengths.

     ///The type of the map that stores the arc lengths.

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

     typedef LM LengthMap;

     ///The type of the length of the arcs.

     typedef typename LM::Value Value;

     /// Operation traits for Dijkstra algorithm.

     /// This class defines the operations that are used in the algorithm.

     /// \see DijkstraDefaultOperationTraits

     typedef DijkstraDefaultOperationTraits<Value> OperationTraits;

     /// The cross reference type used by the heap.

     /// The cross reference type used by the heap.

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

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

     ///Instantiates a \ref HeapCrossRef.

     ///This function instantiates a \ref HeapCrossRef.

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

     /// \ref HeapCrossRef.

     static HeapCrossRef *createHeapCrossRef(const Digraph &g)

     {

       return new HeapCrossRef(g);

     }

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

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

     ///

     ///\sa BinHeap

     ///\sa Dijkstra

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

     ///Instantiates a \ref Heap.

     ///This function instantiates a \ref Heap.

     static Heap *createHeap(HeapCrossRef& r)

     {

       return new Heap(r);

     }

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

     ///arcs of the shortest paths.

     ///

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

     ///arcs of the shortest paths.

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

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

     ///Instantiates a \ref PredMap.

     ///This function instantiates a \ref PredMap.

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

     ///\ref PredMap.

     static PredMap *createPredMap(const Digraph &g)

     {

       return new PredMap(g);

     }

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

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

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

     ///By default it is a NullMap.

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

     ///Instantiates a \ref ProcessedMap.

     ///This function instantiates a \ref ProcessedMap.

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

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

 #ifdef DOXYGEN

     static ProcessedMap *createProcessedMap(const Digraph &g)

 #else

     static ProcessedMap *createProcessedMap(const Digraph &)

 #endif

     {

       return new ProcessedMap();

     }

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

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

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

     typedef typename Digraph::template NodeMap<typename LM::Value> DistMap;

     ///Instantiates a \ref DistMap.

     ///This function instantiates a \ref DistMap.

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

     ///the \ref DistMap

     static DistMap *createDistMap(const Digraph &g)

     {

       return new DistMap(g);

     }

   };

   ///%Dijkstra algorithm class.

   /// \ingroup shortest_path

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

   ///

   ///The arc 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.

   ///

   ///There is also a \ref dijkstra() "function type interface" for the

   ///%Dijkstra algorithm, which is convenient in the simplier cases and

   ///it can be used easier.

   ///

   ///\tparam GR The type of the digraph the algorithm runs on.

   ///The default value is \ref ListDigraph.

   ///The value of GR is not used directly by \ref Dijkstra, it is only

   ///passed to \ref DijkstraDefaultTraits.

   ///\tparam LM A readable arc map that determines the lengths of the

   ///arcs. It is read once for each arc, so the map may involve in

   ///relatively time consuming process to compute the arc lengths if

   ///it is necessary. The default map type is \ref

   ///concepts::Digraph::ArcMap "Digraph::ArcMap<int>".

   ///The value of LM is not used directly by \ref Dijkstra, it is only

   ///passed to \ref DijkstraDefaultTraits.

   ///\tparam 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.

 #ifdef DOXYGEN

   template <typename GR, typename LM, typename TR>

 #else

   template <typename GR=ListDigraph,

             typename LM=typename GR::template ArcMap<int>,

             typename TR=DijkstraDefaultTraits<GR,LM> >

 #endif

   class Dijkstra {

   public:

     ///\ref Exception for uninitialized parameters.

     ///This error represents problems in the initialization of the

     ///parameters of the algorithm.

     class UninitializedParameter : public lemon::UninitializedParameter {

     public:

       virtual const char* what() const throw() {

         return "lemon::Dijkstra::UninitializedParameter";

       }

     };

     ///The type of the digraph the algorithm runs on.

     typedef typename TR::Digraph Digraph;

     ///The type of the length of the arcs.

     typedef typename TR::LengthMap::Value Value;

     ///The type of the map that stores the arc lengths.

     typedef typename TR::LengthMap LengthMap;

     ///\brief The type of the map that stores the predecessor arcs of the

     ///shortest paths.

     typedef typename TR::PredMap PredMap;

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

     typedef typename TR::DistMap DistMap;

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

     typedef typename TR::ProcessedMap ProcessedMap;

     ///The type of the paths.

     typedef PredMapPath<Digraph, PredMap> Path;

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

     typedef typename TR::HeapCrossRef HeapCrossRef;

     ///The heap type used by the algorithm.

     typedef typename TR::Heap Heap;

     ///The operation traits class.

     typedef typename TR::OperationTraits OperationTraits;

     ///The traits class.

     typedef TR Traits;

   private:

     typedef typename Digraph::Node Node;

     typedef typename Digraph::NodeIt NodeIt;

     typedef typename Digraph::Arc Arc;

     typedef typename Digraph::OutArcIt OutArcIt;

     //Pointer to the underlying digraph.

     const Digraph *G;

     //Pointer to the length map.

     const LengthMap *length;

     //Pointer to the map of predecessors arcs.

     PredMap *_pred;

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

     bool local_pred;

     //Pointer to the map of distances.

     DistMap *_dist;

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

     bool local_dist;

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

     ProcessedMap *_processed;

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

     bool local_processed;

     //Pointer to the heap cross references.

     HeapCrossRef *_heap_cross_ref;

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

     bool local_heap_cross_ref;

     //Pointer to the heap.

     Heap *_heap;

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

     bool local_heap;

     //Creates the maps if necessary.

     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 SetPredMapTraits : public Traits {

       typedef T PredMap;

       static PredMap *createPredMap(const Digraph &)

       {

         throw UninitializedParameter();

       }

     };

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

     ///\ref PredMap type.

     ///

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

     ///\ref PredMap type.

     template <class T>

     struct SetPredMap

       : public Dijkstra< Digraph, LengthMap, SetPredMapTraits<T> > {

       typedef Dijkstra< Digraph, LengthMap, SetPredMapTraits<T> > Create;

     };

     template <class T>

     struct SetDistMapTraits : public Traits {

       typedef T DistMap;

       static DistMap *createDistMap(const Digraph &)

       {

         throw UninitializedParameter();

       }

     };

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

     ///\ref DistMap type.

     ///

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

     ///\ref DistMap type.

     template <class T>

     struct SetDistMap

       : public Dijkstra< Digraph, LengthMap, SetDistMapTraits<T> > {

       typedef Dijkstra< Digraph, LengthMap, SetDistMapTraits<T> > Create;

     };

     template <class T>

     struct SetProcessedMapTraits : public Traits {

       typedef T ProcessedMap;

       static ProcessedMap *createProcessedMap(const Digraph &)

       {

         throw UninitializedParameter();

       }

     };

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

     ///\ref ProcessedMap type.

     ///

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

     ///\ref ProcessedMap type.

     template <class T>

     struct SetProcessedMap

       : public Dijkstra< Digraph, LengthMap, SetProcessedMapTraits<T> > {

       typedef Dijkstra< Digraph, LengthMap, SetProcessedMapTraits<T> > Create;

     };

     struct SetStandardProcessedMapTraits : public Traits {

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

       static ProcessedMap *createProcessedMap(const Digraph &g)

       {

         return new ProcessedMap(g);

       }

     };

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

     ///\ref ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.

     ///

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

     ///\ref ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.

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

     struct SetStandardProcessedMap

       : public Dijkstra< Digraph, LengthMap, SetStandardProcessedMapTraits > {

       typedef Dijkstra< Digraph, LengthMap, SetStandardProcessedMapTraits >

       Create;

     };

     template <class H, class CR>

     struct SetHeapTraits : public Traits {

       typedef CR HeapCrossRef;

       typedef H Heap;

       static HeapCrossRef *createHeapCrossRef(const Digraph &) {

         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 Digraph::template NodeMap<int> >

     struct SetHeap

       : public Dijkstra< Digraph, LengthMap, SetHeapTraits<H, CR> > {

       typedef Dijkstra< Digraph, LengthMap, SetHeapTraits<H, CR> > Create;

     };

     template <class H, class CR>

     struct SetStandardHeapTraits : public Traits {

       typedef CR HeapCrossRef;

       typedef H Heap;

       static HeapCrossRef *createHeapCrossRef(const Digraph &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 digraph as

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

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

     struct SetStandardHeap

       : public Dijkstra< Digraph, LengthMap, SetStandardHeapTraits<H, CR> > {

       typedef Dijkstra< Digraph, LengthMap, SetStandardHeapTraits<H, CR> >

       Create;

     };

     template <class T>

     struct SetOperationTraitsTraits : public Traits {

       typedef T OperationTraits;

     };

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

     ///\ref OperationTraits type

     ///

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

     ///\ref OperationTraits type.

     template <class T>

     struct SetOperationTraits

       : public Dijkstra<Digraph, LengthMap, SetOperationTraitsTraits<T> > {

       typedef Dijkstra<Digraph, LengthMap, SetOperationTraitsTraits<T> >

       Create;

     };

     ///@}

   protected:

     Dijkstra() {}

   public:

     ///Constructor.

     ///Constructor.

     ///\param _g The digraph the algorithm runs on.

     ///\param _length The length map used by the algorithm.

     Dijkstra(const Digraph& _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 that stores the predecessor arcs.

     ///Sets the map that stores the predecessor arcs.

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

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

     ///automatically allocated map, of course.

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

     Dijkstra &predMap(PredMap &m)

     {

       if(local_pred) {

         delete _pred;

         local_pred=false;

       }

       _pred = &m;

       return *this;

     }

     ///Sets the map that indicates which nodes are processed.

     ///Sets the map that indicates which nodes are processed.

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

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

     ///automatically allocated map, of course.

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

     Dijkstra &processedMap(ProcessedMap &m)

     {

       if(local_processed) {

         delete _processed;

         local_processed=false;

       }

       _processed = &m;

       return *this;

     }

     ///Sets the map that stores the distances of the nodes.

     ///Sets the map that stores the distances of the nodes calculated by the

     ///algorithm.

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

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

     ///automatically allocated map, of course.

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

     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 destructor 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:

     ///\name Execution control

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

     ///member functions called \ref lemon::Dijkstra::run() "run()".

     ///\n

     ///If you need more control on the execution, first you must call

     ///\ref lemon::Dijkstra::init() "init()", then you can add several

     ///source nodes with \ref lemon::Dijkstra::addSource() "addSource()".

     ///Finally \ref lemon::Dijkstra::start() "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.

     ///

     ///The function 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(OutArcIt 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;

     }

     ///The next node to be processed.

     ///Returns the next node to be processed or \c INVALID if the

     ///priority heap is empty.

     Node nextNode() const

     {

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

     }

     ///\brief Returns \c false if there are nodes

     ///to be processed.

     ///

     ///Returns \c false if there are nodes

     ///to be processed in the priority heap.

     bool emptyQueue() const { 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() const { return _heap->size(); }

     ///Executes the algorithm.

     ///Executes the algorithm.

     ///

     ///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 (forest),

     ///- the distance of each node from the root(s).

     ///

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

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

     ///

     ///\note <tt>d.start()</tt> is just a shortcut of the following code.

     ///\code

     ///  while ( !d.emptyQueue() ) {

     ///    d.processNextNode();

     ///  }

     ///\endcode

     void start()

     {

       while ( !emptyQueue() ) processNextNode();

     }

     ///Executes the algorithm until the given target node is reached.

     ///Executes the algorithm until the given target node is reached.

     ///

     ///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).

     ///

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

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

     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.

     ///

     ///This method runs the %Dijkstra algorithm from the root node(s) in

     ///order to compute the shortest path to a node \c v with

     /// <tt>nm[v]</tt> true, if such a node can be found.

     ///

     ///\param nm A \c 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.

     ///

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

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

     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 the algorithm from the given node.

     ///This method runs the %Dijkstra algorithm from 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 <tt>d.run(s)</tt> 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.

     ///This method runs the %Dijkstra algorithm from node \c s

     ///in order to compute the shortest path to \c t.

     ///

     ///\return The length of the shortest <tt>s</tt>--<tt>t</tt> path,

     ///if \c t is reachable form \c s, \c 0 otherwise.

     ///

     ///\note Apart from the return value, <tt>d.run(s,t)</tt> 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

     ///Either \ref lemon::Dijkstra::run() "run()" or

     ///\ref lemon::Dijkstra::start() "start()" must be called before

     ///using them.

     ///@{

     ///The shortest path to a node.

     ///Returns the shortest path to a node.

     ///

     ///\warning \c t should be reachable from the root(s).

     ///

     ///\pre Either \ref run() or \ref start() must be called before

     ///using this function.

     Path path(Node t) const { return Path(*G, *_pred, t); }

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

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

     ///

     ///\warning If node \c v is not reachable from the root(s), then

     ///the return value of this function is undefined.

     ///

     ///\pre Either \ref run() or \ref start() must be called before

     ///using this function.

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

     ///Returns the 'previous arc' of the shortest path tree for a node.

     ///This function returns the 'previous arc' of the shortest path

     ///tree for the node \c v, i.e. it returns the last arc of a

     ///shortest path from the root(s) to \c v. It is \c INVALID if \c v

     ///is not reachable from the root(s) or if \c v is a root.

     ///

     ///The shortest path tree used here is equal to the shortest path

     ///tree used in \ref predNode().

     ///

     ///\pre Either \ref run() or \ref start() must be called before

     ///using this function.

     Arc predArc(Node v) const { return (*_pred)[v]; }

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

     ///This function returns the 'previous node' of the shortest path

     ///tree for the node \c v, i.e. it returns the last but one node

     ///from a shortest path from the root(s) to \c v. It is \c INVALID

     ///if \c v is not reachable from the root(s) or if \c v is a root.

     ///

     ///The shortest path tree used here is equal to the shortest path

     ///tree used in \ref predArc().

     ///

     ///\pre Either \ref run() or \ref start() must be called before

     ///using this function.

     Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:

                                   G->source((*_pred)[v]); }

     ///\brief Returns a const reference to the node map that stores the

     ///distances of the nodes.

     ///

     ///Returns a const reference to the node map that stores the distances

     ///of the nodes calculated by the algorithm.

     ///

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

     ///must be called before using this function.

     const DistMap &distMap() const { return *_dist;}

     ///\brief Returns a const reference to the node map that stores the

     ///predecessor arcs.

     ///

     ///Returns a const reference to the node map that stores the predecessor

     ///arcs, which form the shortest path tree.

     ///

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

     ///must be called before using this function.

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

     ///Checks if a node is reachable from the root(s).

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

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

     ///must be called before using this function.

     bool reached(Node v) const { 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 Either \ref run() or \ref start()

     ///must be called before using this function.

     bool processed(Node v) const { return (*_heap_cross_ref)[v] ==

                                           Heap::POST_HEAP; }

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

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

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

     ///\pre \c v should be reached but not processed.

     Value currentDist(Node v) const { return (*_heap)[v]; }

     ///@}

   };

   ///Default traits class of dijkstra() function.

   ///Default traits class of dijkstra() function.

   ///\tparam GR The type of the digraph.

   ///\tparam LM The type of the length map.

   template<class GR, class LM>

   struct DijkstraWizardDefaultTraits

   {

     ///The type of the digraph the algorithm runs on.

     typedef GR Digraph;

     ///The type of the map that stores the arc lengths.

     ///The type of the map that stores the arc lengths.

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

     typedef LM LengthMap;

     ///The type of the length of the arcs.

     typedef typename LM::Value Value;

     /// Operation traits for Dijkstra algorithm.

     /// This class defines the operations that are used in the algorithm.

     /// \see DijkstraDefaultOperationTraits

     typedef DijkstraDefaultOperationTraits<Value> OperationTraits;

     /// The cross reference type used by the heap.

     /// The cross reference type used by the heap.

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

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

     ///Instantiates a \ref HeapCrossRef.

     ///This function instantiates a \ref HeapCrossRef.

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

     /// HeapCrossRef.

     static HeapCrossRef *createHeapCrossRef(const Digraph &g)

     {

       return new HeapCrossRef(g);

     }

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

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

     ///

     ///\sa BinHeap

     ///\sa Dijkstra

     typedef BinHeap<Value, typename Digraph::template NodeMap<int>,

                     std::less<Value> > Heap;

     ///Instantiates a \ref Heap.

     ///This function instantiates a \ref Heap.

     /// \param r is the HeapCrossRef which is used.

     static Heap *createHeap(HeapCrossRef& r)

     {

       return new Heap(r);

     }

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

     ///arcs of the shortest paths.

     ///

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

     ///arcs of the shortest paths.

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

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

     ///Instantiates a \ref PredMap.

     ///This function instantiates a \ref PredMap.

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

     ///\ref PredMap.

 #ifdef DOXYGEN

     static PredMap *createPredMap(const Digraph &g)

 #else

     static PredMap *createPredMap(const Digraph &)

 #endif

     {

       return new PredMap();

     }

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

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

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

     ///By default it is a NullMap.

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

     ///Instantiates a \ref ProcessedMap.

     ///This function instantiates a \ref ProcessedMap.

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

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

 #ifdef DOXYGEN

     static ProcessedMap *createProcessedMap(const Digraph &g)

 #else

     static ProcessedMap *createProcessedMap(const Digraph &)

 #endif

     {

       return new ProcessedMap();

     }

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

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

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

     typedef NullMap<typename Digraph::Node,Value> DistMap;

     ///Instantiates a \ref DistMap.

     ///This function instantiates a \ref DistMap.

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

     ///the \ref DistMap

 #ifdef DOXYGEN

     static DistMap *createDistMap(const Digraph &g)

 #else

     static DistMap *createDistMap(const Digraph &)

 #endif

     {

       return new DistMap();

     }

   };

   /// Default traits class 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.

   template<class GR,class LM>

   class DijkstraWizardBase : public DijkstraWizardDefaultTraits<GR,LM>

   {

     typedef DijkstraWizardDefaultTraits<GR,LM> Base;

   protected:

     //The type of the nodes in the digraph.

     typedef typename Base::Digraph::Node Node;

     //Pointer to the digraph the algorithm runs on.

     void *_g;

     //Pointer to the length map

     void *_length;

     //Pointer to the map of processed nodes.

     void *_processed;

     //Pointer to the map of predecessors arcs.

     void *_pred;

     //Pointer to the map of distances.

     void *_dist;

     //Pointer to the source node.

     Node _source;

   public:

     /// Constructor.

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

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

     DijkstraWizardBase() : _g(0), _length(0), _processed(0), _pred(0),

                            _dist(0), _source(INVALID) {}

     /// Constructor.

     /// This constructor requires some parameters,

     /// listed in the parameters list.

     /// Others are initiated to 0.

     /// \param g The digraph the algorithm runs on.

     /// \param l The length map.

     /// \param s The source node.

     DijkstraWizardBase(const GR &g,const LM &l, Node s=INVALID) :

       _g(reinterpret_cast<void*>(const_cast<GR*>(&g))),

       _length(reinterpret_cast<void*>(const_cast<LM*>(&l))),

       _processed(0), _pred(0), _dist(0), _source(s) {}

   };

   /// Auxiliary class for the function type interface of Dijkstra algorithm.

   /// This auxiliary class is created to implement the function type

   /// interface of \ref Dijkstra algorithm. It uses the functions and features

   /// of the plain \ref Dijkstra, but it is much simpler to use it.

   /// It should only be used through the \ref dijkstra() function, which makes

   /// it easier to use the algorithm.

   ///

   /// 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 object, and calls the

   /// \ref Dijkstra::run() method of it.

   template<class TR>

   class DijkstraWizard : public TR

   {

     typedef TR Base;

     ///The type of the digraph the algorithm runs on.

     typedef typename TR::Digraph Digraph;

     typedef typename Digraph::Node Node;

     typedef typename Digraph::NodeIt NodeIt;

     typedef typename Digraph::Arc Arc;

     typedef typename Digraph::OutArcIt OutArcIt;

     ///The type of the map that stores the arc lengths.

     typedef typename TR::LengthMap LengthMap;

     ///The type of the length of the arcs.

     typedef typename LengthMap::Value Value;

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

     ///arcs of the shortest paths.

     typedef typename TR::PredMap PredMap;

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

     typedef typename TR::DistMap DistMap;

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

     typedef typename TR::ProcessedMap ProcessedMap;

     ///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 Digraph &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 source node.

     ///Runs Dijkstra algorithm from a source node.

     ///The node can be given with the \ref source() function.

     void run()

     {

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

       Dijkstra<Digraph,LengthMap,TR>

         dij(*reinterpret_cast<const Digraph*>(Base::_g),

             *reinterpret_cast<const LengthMap*>(Base::_length));

       if(Base::_processed)

         dij.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));

       if(Base::_pred)

         dij.predMap(*reinterpret_cast<PredMap*>(Base::_pred));

       if(Base::_dist)

         dij.distMap(*reinterpret_cast<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();

     }

     /// 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;

     }

     template<class T>

     struct SetPredMapBase : public Base {

       typedef T PredMap;

       static PredMap *createPredMap(const Digraph &) { return 0; };

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

     };

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

     ///for setting \ref PredMap object.

     ///

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

     ///for setting \ref PredMap object.

     template<class T>

     DijkstraWizard<SetPredMapBase<T> > predMap(const T &t)

     {

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

       return DijkstraWizard<SetPredMapBase<T> >(*this);

     }

     template<class T>

     struct SetProcessedMapBase : public Base {

       typedef T ProcessedMap;

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

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

     };

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

     ///for setting \ref ProcessedMap object.

     ///

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

     ///for setting \ref ProcessedMap object.

     template<class T>

     DijkstraWizard<SetProcessedMapBase<T> > processedMap(const T &t)

     {

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

       return DijkstraWizard<SetProcessedMapBase<T> >(*this);

     }

     template<class T>

     struct SetDistMapBase : public Base {

       typedef T DistMap;

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

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

     };

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

     ///for setting \ref DistMap object.

     ///

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

     ///for setting \ref DistMap object.

     template<class T>

     DijkstraWizard<SetDistMapBase<T> > distMap(const T &t)

     {

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

       return DijkstraWizard<SetDistMapBase<T> >(*this);

     }

   };

   ///Function type interface for Dijkstra algorithm.

   /// \ingroup shortest_path

   ///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