diff -r dbaa96cc1013 -r 4f754b4cf82b lemon/dijkstra.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/dijkstra.h	Thu Feb 07 21:37:07 2008 +0000
@@ -0,0 +1,1209 @@
+/* -*- 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_digraph.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 Digraph type.
+  ///\param LM Type of length map.
+  template<class GR, class LM>
+  struct DijkstraDefaultTraits
+  {
+    ///The digraph type 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.
+
+    /// 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 Digraph::NodeMap<int>.
+    typedef typename Digraph::template NodeMap<int> HeapCrossRef;
+    ///Instantiates a HeapCrossRef.
+
+    ///This function instantiates a \c HeapCrossRef. 
+    /// \param G is the digraph, 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
+    ///arcs of the shortest paths.
+    /// 
+    ///The type of the map that stores the last
+    ///arcs of the shortest paths.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef typename Digraph::template NodeMap<typename GR::Arc> PredMap;
+    ///Instantiates a PredMap.
+ 
+    ///This function instantiates a \c PredMap. 
+    ///\param G is the digraph, to which we would like to define the PredMap.
+    ///\todo The digraph 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 Digraph::Node,bool> ProcessedMap;
+    ///Instantiates a ProcessedMap.
+ 
+    ///This function instantiates a \c ProcessedMap. 
+    ///\param g is the digraph, 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 Digraph::template NodeMap<typename LM::Value> DistMap;
+    ///Instantiates a DistMap.
+ 
+    ///This function instantiates a \ref DistMap. 
+    ///\param G is the digraph, to which we would like to define the \ref DistMap
+    static DistMap *createDistMap(const GR &G)
+    {
+      return new DistMap(G);
+    }
+  };
+  
+  ///%Dijkstra algorithm class.
+  
+  /// \ingroup shortest_path
+  ///This class provides an efficient implementation of %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.
+  ///
+  ///\param GR The digraph type the algorithm runs on. The default value
+  ///is \ref ListDigraph. The value of GR is not used directly by
+  ///Dijkstra, it is only passed to \ref DijkstraDefaultTraits.
+  ///\param LM This read-only ArcMap 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 length 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 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=ListDigraph,
+	    typename LM=typename GR::template ArcMap<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 digraph.
+    typedef typename TR::Digraph Digraph;
+    ///\e
+    typedef typename Digraph::Node Node;
+    ///\e
+    typedef typename Digraph::NodeIt NodeIt;
+    ///\e
+    typedef typename Digraph::Arc Arc;
+    ///\e
+    typedef typename Digraph::OutArcIt OutArcIt;
+    
+    ///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 last
+    ///arcs 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 digraph.
+    const Digraph *G;
+    /// Pointer to the length map
+    const LengthMap *length;
+    ///Pointer to the map of predecessors arcs.
+    PredMap *_pred;
+    ///Indicates if \ref _pred is locally allocated (\c true) or not.
+    bool local_pred;
+    ///Pointer to the map of distances.
+    DistMap *_dist;
+    ///Indicates if \ref _dist is locally allocated (\c true) or not.
+    bool local_dist;
+    ///Pointer to the map of 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 Digraph &)
+      {
+	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< Digraph,	LengthMap, DefPredMapTraits<T> > {
+      typedef Dijkstra< Digraph,	LengthMap, DefPredMapTraits<T> > Create;
+    };
+    
+    template <class T>
+    struct DefDistMapTraits : public Traits {
+      typedef T DistMap;
+      static DistMap *createDistMap(const Digraph &)
+      {
+	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< Digraph, LengthMap, DefDistMapTraits<T> > { 
+      typedef Dijkstra< Digraph, LengthMap, DefDistMapTraits<T> > Create;
+    };
+    
+    template <class T>
+    struct DefProcessedMapTraits : public Traits {
+      typedef T ProcessedMap;
+      static ProcessedMap *createProcessedMap(const Digraph &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< Digraph,	LengthMap, DefProcessedMapTraits<T> > { 
+      typedef Dijkstra< Digraph,	LengthMap, DefProcessedMapTraits<T> > Create;
+    };
+    
+    struct DefDigraphProcessedMapTraits : public Traits {
+      typedef typename Digraph::template NodeMap<bool> ProcessedMap;
+      static ProcessedMap *createProcessedMap(const Digraph &G) 
+      {
+	return new ProcessedMap(G);
+      }
+    };
+    ///\brief \ref named-templ-param "Named parameter"
+    ///for setting the ProcessedMap type to be Digraph::NodeMap<bool>.
+    ///
+    ///\ref named-templ-param "Named parameter"
+    ///for setting the ProcessedMap type to be Digraph::NodeMap<bool>.
+    ///If you don't set it explicitely, it will be automatically allocated.
+    template <class T>
+    struct DefProcessedMapToBeDefaultMap 
+      : public Dijkstra< Digraph, LengthMap, DefDigraphProcessedMapTraits> {
+      typedef Dijkstra< Digraph, LengthMap, DefDigraphProcessedMapTraits> Create;
+    };
+
+    template <class H, class CR>
+    struct DefHeapTraits : 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 DefHeap
+      : public Dijkstra< Digraph,	LengthMap, DefHeapTraits<H, CR> > { 
+      typedef Dijkstra< Digraph,	LengthMap, DefHeapTraits<H, CR> > Create;
+    };
+
+    template <class H, class CR>
+    struct DefStandardHeapTraits : 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 DefStandardHeap
+      : public Dijkstra< Digraph,	LengthMap, DefStandardHeapTraits<H, CR> > { 
+      typedef Dijkstra< Digraph,	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<Digraph, LengthMap, DefOperationTraitsTraits<T> > {
+      typedef Dijkstra<Digraph, LengthMap, DefOperationTraitsTraits<T> >
+      Create;
+    };
+    
+    ///@}
+
+
+  protected:
+
+    Dijkstra() {}
+
+  public:      
+    
+    ///Constructor.
+    
+    ///\param _G the digraph the algorithm will run 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 storing the predecessor arcs.
+
+    ///Sets the map storing the predecessor arcs.
+    ///If you don't use this function before calling \ref run(),
+    ///it will allocate one. The destuctor deallocates this
+    ///automatically allocated map, of course.
+    ///\return <tt> (*this) </tt>
+    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<Digraph, 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(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;
+    }
+
+    ///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 arc' of the shortest path tree.
+
+    ///For a node \c v it returns the 'previous arc' of the shortest path tree,
+    ///i.e. it returns the last arc 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.
+    Arc predArc(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 predArc().  \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 arcs 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 Digraph type.
+  ///\param LM Type of length map.
+  template<class GR, class LM>
+  struct DijkstraWizardDefaultTraits
+  {
+    ///The digraph type 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.
+
+    /// 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 Digraph::NodeMap<int>.
+    typedef typename Digraph::template NodeMap<int> HeapCrossRef;
+    ///Instantiates a HeapCrossRef.
+
+    ///This function instantiates a \ref HeapCrossRef. 
+    /// \param G is the digraph, to which we would like to define the 
+    /// HeapCrossRef.
+    /// \todo The digraph 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
+    ///arcs of the shortest paths.
+    /// 
+    ///The type of the map that stores the last
+    ///arcs of the shortest paths.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef NullMap <typename GR::Node,typename GR::Arc> PredMap;
+    ///Instantiates a PredMap.
+ 
+    ///This function instantiates a \ref PredMap. 
+    ///\param g is the digraph, to which we would like to define the PredMap.
+    ///\todo The digraph alone may be insufficient 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 Digraph::Node,bool> ProcessedMap;
+    ///Instantiates a ProcessedMap.
+ 
+    ///This function instantiates a \ref ProcessedMap. 
+    ///\param g is the digraph, to which
+    ///we would like to define the \ref ProcessedMap
+#ifdef DOXYGEN
+    static ProcessedMap *createProcessedMap(const GR &g)
+#else
+    static ProcessedMap *createProcessedMap(const GR &)
+#endif
+    {
+      return new ProcessedMap();
+    }
+    ///The type of the map that stores the dists of the nodes.
+ 
+    ///The type of the map that stores the dists of the nodes.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef NullMap<typename Digraph::Node,typename LM::Value> DistMap;
+    ///Instantiates a DistMap.
+ 
+    ///This function instantiates a \ref DistMap. 
+    ///\param g is the digraph, to which we would like to define the \ref DistMap
+#ifdef DOXYGEN
+    static DistMap *createDistMap(const GR &g)
+#else
+    static DistMap *createDistMap(const GR &)
+#endif
+    {
+      return new DistMap();
+    }
+  };
+  
+  /// Default traits used by \ref 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 digraph.
+    typedef typename Base::Digraph::Node Node;
+
+    /// Pointer to the underlying digraph.
+    void *_g;
+    /// Pointer to the length map
+    void *_length;
+    ///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), _pred(0),
+			   _dist(0), _source(INVALID) {}
+
+    /// Constructor.
+    
+    /// This constructor requires some parameters,
+    /// listed in the parameters list.
+    /// Others are initiated to 0.
+    /// \param g is the initial value of  \ref _g
+    /// \param 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(reinterpret_cast<void*>(const_cast<GR*>(&g))), 
+      _length(reinterpret_cast<void*>(const_cast<LM*>(&l))), 
+      _pred(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 digraph.
+    typedef typename TR::Digraph Digraph;
+    //\e
+    typedef typename Digraph::Node Node;
+    //\e
+    typedef typename Digraph::NodeIt NodeIt;
+    //\e
+    typedef typename Digraph::Arc Arc;
+    //\e
+    typedef typename Digraph::OutArcIt OutArcIt;
+    
+    ///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 last
+    ///arcs of the shortest paths.
+    typedef typename TR::PredMap PredMap;
+    ///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 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 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<Digraph,LengthMap,TR> 
+	dij(*reinterpret_cast<const Digraph*>(Base::_g),
+            *reinterpret_cast<const LengthMap*>(Base::_length));
+      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();
+    }
+
+    template<class T>
+    struct DefPredMapBase : public Base {
+      typedef T PredMap;
+      static PredMap *createPredMap(const Digraph &) { return 0; };
+      DefPredMapBase(const TR &b) : TR(b) {}
+    };
+    
+    ///\brief \ref named-templ-param "Named parameter"
+    ///function for setting PredMap type
+    ///
+    /// \ref named-templ-param "Named parameter"
+    ///function for setting PredMap type
+    ///
+    template<class T>
+    DijkstraWizard<DefPredMapBase<T> > predMap(const T &t) 
+    {
+      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
+      return DijkstraWizard<DefPredMapBase<T> >(*this);
+    }
+    
+    template<class T>
+    struct DefDistMapBase : public Base {
+      typedef T DistMap;
+      static DistMap *createDistMap(const Digraph &) { return 0; };
+      DefDistMapBase(const TR &b) : TR(b) {}
+    };
+    
+    ///\brief \ref named-templ-param "Named parameter"
+    ///function for setting DistMap type
+    ///
+    /// \ref named-templ-param "Named parameter"
+    ///function for setting DistMap type
+    ///
+    template<class T>
+    DijkstraWizard<DefDistMapBase<T> > distMap(const T &t) 
+    {
+      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&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 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