lemon/dijkstra.h
author Peter Kovacs <kpeter@inf.elte.hu>
Wed, 25 Mar 2009 15:58:44 +0100
changeset 605 5232721b3f14
parent 440 88ed40ad0d4f
child 559 c5fd2d996909
permissions -rw-r--r--
Rework the interface of NetworkSimplex (#234)

The parameters of the problem can be set with separate functions
instead of different constructors.
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2009
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #ifndef LEMON_DIJKSTRA_H
    20 #define LEMON_DIJKSTRA_H
    21 
    22 ///\ingroup shortest_path
    23 ///\file
    24 ///\brief Dijkstra algorithm.
    25 
    26 #include <limits>
    27 #include <lemon/list_graph.h>
    28 #include <lemon/bin_heap.h>
    29 #include <lemon/bits/path_dump.h>
    30 #include <lemon/core.h>
    31 #include <lemon/error.h>
    32 #include <lemon/maps.h>
    33 #include <lemon/path.h>
    34 
    35 namespace lemon {
    36 
    37   /// \brief Default operation traits for the Dijkstra algorithm class.
    38   ///
    39   /// This operation traits class defines all computational operations and
    40   /// constants which are used in the Dijkstra algorithm.
    41   template <typename Value>
    42   struct DijkstraDefaultOperationTraits {
    43     /// \brief Gives back the zero value of the type.
    44     static Value zero() {
    45       return static_cast<Value>(0);
    46     }
    47     /// \brief Gives back the sum of the given two elements.
    48     static Value plus(const Value& left, const Value& right) {
    49       return left + right;
    50     }
    51     /// \brief Gives back true only if the first value is less than the second.
    52     static bool less(const Value& left, const Value& right) {
    53       return left < right;
    54     }
    55   };
    56 
    57   ///Default traits class of Dijkstra class.
    58 
    59   ///Default traits class of Dijkstra class.
    60   ///\tparam GR The type of the digraph.
    61   ///\tparam LM The type of the length map.
    62   template<class GR, class LM>
    63   struct DijkstraDefaultTraits
    64   {
    65     ///The type of the digraph the algorithm runs on.
    66     typedef GR Digraph;
    67 
    68     ///The type of the map that stores the arc lengths.
    69 
    70     ///The type of the map that stores the arc lengths.
    71     ///It must meet the \ref concepts::ReadMap "ReadMap" concept.
    72     typedef LM LengthMap;
    73     ///The type of the length of the arcs.
    74     typedef typename LM::Value Value;
    75 
    76     /// Operation traits for %Dijkstra algorithm.
    77 
    78     /// This class defines the operations that are used in the algorithm.
    79     /// \see DijkstraDefaultOperationTraits
    80     typedef DijkstraDefaultOperationTraits<Value> OperationTraits;
    81 
    82     /// The cross reference type used by the heap.
    83 
    84     /// The cross reference type used by the heap.
    85     /// Usually it is \c Digraph::NodeMap<int>.
    86     typedef typename Digraph::template NodeMap<int> HeapCrossRef;
    87     ///Instantiates a \c HeapCrossRef.
    88 
    89     ///This function instantiates a \ref HeapCrossRef.
    90     /// \param g is the digraph, to which we would like to define the
    91     /// \ref HeapCrossRef.
    92     static HeapCrossRef *createHeapCrossRef(const Digraph &g)
    93     {
    94       return new HeapCrossRef(g);
    95     }
    96 
    97     ///The heap type used by the %Dijkstra algorithm.
    98 
    99     ///The heap type used by the Dijkstra algorithm.
   100     ///
   101     ///\sa BinHeap
   102     ///\sa Dijkstra
   103     typedef BinHeap<typename LM::Value, HeapCrossRef, std::less<Value> > Heap;
   104     ///Instantiates a \c Heap.
   105 
   106     ///This function instantiates a \ref Heap.
   107     static Heap *createHeap(HeapCrossRef& r)
   108     {
   109       return new Heap(r);
   110     }
   111 
   112     ///\brief The type of the map that stores the predecessor
   113     ///arcs of the shortest paths.
   114     ///
   115     ///The type of the map that stores the predecessor
   116     ///arcs of the shortest paths.
   117     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   118     typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
   119     ///Instantiates a \c PredMap.
   120 
   121     ///This function instantiates a \ref PredMap.
   122     ///\param g is the digraph, to which we would like to define the
   123     ///\ref PredMap.
   124     static PredMap *createPredMap(const Digraph &g)
   125     {
   126       return new PredMap(g);
   127     }
   128 
   129     ///The type of the map that indicates which nodes are processed.
   130 
   131     ///The type of the map that indicates which nodes are processed.
   132     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   133     ///By default it is a NullMap.
   134     typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
   135     ///Instantiates a \c ProcessedMap.
   136 
   137     ///This function instantiates a \ref ProcessedMap.
   138     ///\param g is the digraph, to which
   139     ///we would like to define the \ref ProcessedMap.
   140 #ifdef DOXYGEN
   141     static ProcessedMap *createProcessedMap(const Digraph &g)
   142 #else
   143     static ProcessedMap *createProcessedMap(const Digraph &)
   144 #endif
   145     {
   146       return new ProcessedMap();
   147     }
   148 
   149     ///The type of the map that stores the distances of the nodes.
   150 
   151     ///The type of the map that stores the distances of the nodes.
   152     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   153     typedef typename Digraph::template NodeMap<typename LM::Value> DistMap;
   154     ///Instantiates a \c DistMap.
   155 
   156     ///This function instantiates a \ref DistMap.
   157     ///\param g is the digraph, to which we would like to define
   158     ///the \ref DistMap.
   159     static DistMap *createDistMap(const Digraph &g)
   160     {
   161       return new DistMap(g);
   162     }
   163   };
   164 
   165   ///%Dijkstra algorithm class.
   166 
   167   /// \ingroup shortest_path
   168   ///This class provides an efficient implementation of the %Dijkstra algorithm.
   169   ///
   170   ///The arc lengths are passed to the algorithm using a
   171   ///\ref concepts::ReadMap "ReadMap",
   172   ///so it is easy to change it to any kind of length.
   173   ///The type of the length is determined by the
   174   ///\ref concepts::ReadMap::Value "Value" of the length map.
   175   ///It is also possible to change the underlying priority heap.
   176   ///
   177   ///There is also a \ref dijkstra() "function-type interface" for the
   178   ///%Dijkstra algorithm, which is convenient in the simplier cases and
   179   ///it can be used easier.
   180   ///
   181   ///\tparam GR The type of the digraph the algorithm runs on.
   182   ///The default type is \ref ListDigraph.
   183   ///\tparam LM A \ref concepts::ReadMap "readable" arc map that specifies
   184   ///the lengths of the arcs.
   185   ///It is read once for each arc, so the map may involve in
   186   ///relatively time consuming process to compute the arc lengths if
   187   ///it is necessary. The default map type is \ref
   188   ///concepts::Digraph::ArcMap "GR::ArcMap<int>".
   189 #ifdef DOXYGEN
   190   template <typename GR, typename LM, typename TR>
   191 #else
   192   template <typename GR=ListDigraph,
   193             typename LM=typename GR::template ArcMap<int>,
   194             typename TR=DijkstraDefaultTraits<GR,LM> >
   195 #endif
   196   class Dijkstra {
   197   public:
   198 
   199     ///The type of the digraph the algorithm runs on.
   200     typedef typename TR::Digraph Digraph;
   201 
   202     ///The type of the length of the arcs.
   203     typedef typename TR::LengthMap::Value Value;
   204     ///The type of the map that stores the arc lengths.
   205     typedef typename TR::LengthMap LengthMap;
   206     ///\brief The type of the map that stores the predecessor arcs of the
   207     ///shortest paths.
   208     typedef typename TR::PredMap PredMap;
   209     ///The type of the map that stores the distances of the nodes.
   210     typedef typename TR::DistMap DistMap;
   211     ///The type of the map that indicates which nodes are processed.
   212     typedef typename TR::ProcessedMap ProcessedMap;
   213     ///The type of the paths.
   214     typedef PredMapPath<Digraph, PredMap> Path;
   215     ///The cross reference type used for the current heap.
   216     typedef typename TR::HeapCrossRef HeapCrossRef;
   217     ///The heap type used by the algorithm.
   218     typedef typename TR::Heap Heap;
   219     ///\brief The \ref DijkstraDefaultOperationTraits "operation traits class"
   220     ///of the algorithm.
   221     typedef typename TR::OperationTraits OperationTraits;
   222 
   223     ///The \ref DijkstraDefaultTraits "traits class" of the algorithm.
   224     typedef TR Traits;
   225 
   226   private:
   227 
   228     typedef typename Digraph::Node Node;
   229     typedef typename Digraph::NodeIt NodeIt;
   230     typedef typename Digraph::Arc Arc;
   231     typedef typename Digraph::OutArcIt OutArcIt;
   232 
   233     //Pointer to the underlying digraph.
   234     const Digraph *G;
   235     //Pointer to the length map.
   236     const LengthMap *_length;
   237     //Pointer to the map of predecessors arcs.
   238     PredMap *_pred;
   239     //Indicates if _pred is locally allocated (true) or not.
   240     bool local_pred;
   241     //Pointer to the map of distances.
   242     DistMap *_dist;
   243     //Indicates if _dist is locally allocated (true) or not.
   244     bool local_dist;
   245     //Pointer to the map of processed status of the nodes.
   246     ProcessedMap *_processed;
   247     //Indicates if _processed is locally allocated (true) or not.
   248     bool local_processed;
   249     //Pointer to the heap cross references.
   250     HeapCrossRef *_heap_cross_ref;
   251     //Indicates if _heap_cross_ref is locally allocated (true) or not.
   252     bool local_heap_cross_ref;
   253     //Pointer to the heap.
   254     Heap *_heap;
   255     //Indicates if _heap is locally allocated (true) or not.
   256     bool local_heap;
   257 
   258     //Creates the maps if necessary.
   259     void create_maps()
   260     {
   261       if(!_pred) {
   262         local_pred = true;
   263         _pred = Traits::createPredMap(*G);
   264       }
   265       if(!_dist) {
   266         local_dist = true;
   267         _dist = Traits::createDistMap(*G);
   268       }
   269       if(!_processed) {
   270         local_processed = true;
   271         _processed = Traits::createProcessedMap(*G);
   272       }
   273       if (!_heap_cross_ref) {
   274         local_heap_cross_ref = true;
   275         _heap_cross_ref = Traits::createHeapCrossRef(*G);
   276       }
   277       if (!_heap) {
   278         local_heap = true;
   279         _heap = Traits::createHeap(*_heap_cross_ref);
   280       }
   281     }
   282 
   283   public:
   284 
   285     typedef Dijkstra Create;
   286 
   287     ///\name Named template parameters
   288 
   289     ///@{
   290 
   291     template <class T>
   292     struct SetPredMapTraits : public Traits {
   293       typedef T PredMap;
   294       static PredMap *createPredMap(const Digraph &)
   295       {
   296         LEMON_ASSERT(false, "PredMap is not initialized");
   297         return 0; // ignore warnings
   298       }
   299     };
   300     ///\brief \ref named-templ-param "Named parameter" for setting
   301     ///\c PredMap type.
   302     ///
   303     ///\ref named-templ-param "Named parameter" for setting
   304     ///\c PredMap type.
   305     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   306     template <class T>
   307     struct SetPredMap
   308       : public Dijkstra< Digraph, LengthMap, SetPredMapTraits<T> > {
   309       typedef Dijkstra< Digraph, LengthMap, SetPredMapTraits<T> > Create;
   310     };
   311 
   312     template <class T>
   313     struct SetDistMapTraits : public Traits {
   314       typedef T DistMap;
   315       static DistMap *createDistMap(const Digraph &)
   316       {
   317         LEMON_ASSERT(false, "DistMap is not initialized");
   318         return 0; // ignore warnings
   319       }
   320     };
   321     ///\brief \ref named-templ-param "Named parameter" for setting
   322     ///\c DistMap type.
   323     ///
   324     ///\ref named-templ-param "Named parameter" for setting
   325     ///\c DistMap type.
   326     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   327     template <class T>
   328     struct SetDistMap
   329       : public Dijkstra< Digraph, LengthMap, SetDistMapTraits<T> > {
   330       typedef Dijkstra< Digraph, LengthMap, SetDistMapTraits<T> > Create;
   331     };
   332 
   333     template <class T>
   334     struct SetProcessedMapTraits : public Traits {
   335       typedef T ProcessedMap;
   336       static ProcessedMap *createProcessedMap(const Digraph &)
   337       {
   338         LEMON_ASSERT(false, "ProcessedMap is not initialized");
   339         return 0; // ignore warnings
   340       }
   341     };
   342     ///\brief \ref named-templ-param "Named parameter" for setting
   343     ///\c ProcessedMap type.
   344     ///
   345     ///\ref named-templ-param "Named parameter" for setting
   346     ///\c ProcessedMap type.
   347     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   348     template <class T>
   349     struct SetProcessedMap
   350       : public Dijkstra< Digraph, LengthMap, SetProcessedMapTraits<T> > {
   351       typedef Dijkstra< Digraph, LengthMap, SetProcessedMapTraits<T> > Create;
   352     };
   353 
   354     struct SetStandardProcessedMapTraits : public Traits {
   355       typedef typename Digraph::template NodeMap<bool> ProcessedMap;
   356       static ProcessedMap *createProcessedMap(const Digraph &g)
   357       {
   358         return new ProcessedMap(g);
   359       }
   360     };
   361     ///\brief \ref named-templ-param "Named parameter" for setting
   362     ///\c ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
   363     ///
   364     ///\ref named-templ-param "Named parameter" for setting
   365     ///\c ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
   366     ///If you don't set it explicitly, it will be automatically allocated.
   367     struct SetStandardProcessedMap
   368       : public Dijkstra< Digraph, LengthMap, SetStandardProcessedMapTraits > {
   369       typedef Dijkstra< Digraph, LengthMap, SetStandardProcessedMapTraits >
   370       Create;
   371     };
   372 
   373     template <class H, class CR>
   374     struct SetHeapTraits : public Traits {
   375       typedef CR HeapCrossRef;
   376       typedef H Heap;
   377       static HeapCrossRef *createHeapCrossRef(const Digraph &) {
   378         LEMON_ASSERT(false, "HeapCrossRef is not initialized");
   379         return 0; // ignore warnings
   380       }
   381       static Heap *createHeap(HeapCrossRef &)
   382       {
   383         LEMON_ASSERT(false, "Heap is not initialized");
   384         return 0; // ignore warnings
   385       }
   386     };
   387     ///\brief \ref named-templ-param "Named parameter" for setting
   388     ///heap and cross reference types
   389     ///
   390     ///\ref named-templ-param "Named parameter" for setting heap and cross
   391     ///reference types. If this named parameter is used, then external
   392     ///heap and cross reference objects must be passed to the algorithm
   393     ///using the \ref heap() function before calling \ref run(Node) "run()"
   394     ///or \ref init().
   395     ///\sa SetStandardHeap
   396     template <class H, class CR = typename Digraph::template NodeMap<int> >
   397     struct SetHeap
   398       : public Dijkstra< Digraph, LengthMap, SetHeapTraits<H, CR> > {
   399       typedef Dijkstra< Digraph, LengthMap, SetHeapTraits<H, CR> > Create;
   400     };
   401 
   402     template <class H, class CR>
   403     struct SetStandardHeapTraits : public Traits {
   404       typedef CR HeapCrossRef;
   405       typedef H Heap;
   406       static HeapCrossRef *createHeapCrossRef(const Digraph &G) {
   407         return new HeapCrossRef(G);
   408       }
   409       static Heap *createHeap(HeapCrossRef &R)
   410       {
   411         return new Heap(R);
   412       }
   413     };
   414     ///\brief \ref named-templ-param "Named parameter" for setting
   415     ///heap and cross reference types with automatic allocation
   416     ///
   417     ///\ref named-templ-param "Named parameter" for setting heap and cross
   418     ///reference types with automatic allocation.
   419     ///They should have standard constructor interfaces to be able to
   420     ///automatically created by the algorithm (i.e. the digraph should be
   421     ///passed to the constructor of the cross reference and the cross
   422     ///reference should be passed to the constructor of the heap).
   423     ///However external heap and cross reference objects could also be
   424     ///passed to the algorithm using the \ref heap() function before
   425     ///calling \ref run(Node) "run()" or \ref init().
   426     ///\sa SetHeap
   427     template <class H, class CR = typename Digraph::template NodeMap<int> >
   428     struct SetStandardHeap
   429       : public Dijkstra< Digraph, LengthMap, SetStandardHeapTraits<H, CR> > {
   430       typedef Dijkstra< Digraph, LengthMap, SetStandardHeapTraits<H, CR> >
   431       Create;
   432     };
   433 
   434     template <class T>
   435     struct SetOperationTraitsTraits : public Traits {
   436       typedef T OperationTraits;
   437     };
   438 
   439     /// \brief \ref named-templ-param "Named parameter" for setting
   440     ///\c OperationTraits type
   441     ///
   442     ///\ref named-templ-param "Named parameter" for setting
   443     ///\c OperationTraits type.
   444     template <class T>
   445     struct SetOperationTraits
   446       : public Dijkstra<Digraph, LengthMap, SetOperationTraitsTraits<T> > {
   447       typedef Dijkstra<Digraph, LengthMap, SetOperationTraitsTraits<T> >
   448       Create;
   449     };
   450 
   451     ///@}
   452 
   453   protected:
   454 
   455     Dijkstra() {}
   456 
   457   public:
   458 
   459     ///Constructor.
   460 
   461     ///Constructor.
   462     ///\param g The digraph the algorithm runs on.
   463     ///\param length The length map used by the algorithm.
   464     Dijkstra(const Digraph& g, const LengthMap& length) :
   465       G(&g), _length(&length),
   466       _pred(NULL), local_pred(false),
   467       _dist(NULL), local_dist(false),
   468       _processed(NULL), local_processed(false),
   469       _heap_cross_ref(NULL), local_heap_cross_ref(false),
   470       _heap(NULL), local_heap(false)
   471     { }
   472 
   473     ///Destructor.
   474     ~Dijkstra()
   475     {
   476       if(local_pred) delete _pred;
   477       if(local_dist) delete _dist;
   478       if(local_processed) delete _processed;
   479       if(local_heap_cross_ref) delete _heap_cross_ref;
   480       if(local_heap) delete _heap;
   481     }
   482 
   483     ///Sets the length map.
   484 
   485     ///Sets the length map.
   486     ///\return <tt> (*this) </tt>
   487     Dijkstra &lengthMap(const LengthMap &m)
   488     {
   489       _length = &m;
   490       return *this;
   491     }
   492 
   493     ///Sets the map that stores the predecessor arcs.
   494 
   495     ///Sets the map that stores the predecessor arcs.
   496     ///If you don't use this function before calling \ref run(Node) "run()"
   497     ///or \ref init(), an instance will be allocated automatically.
   498     ///The destructor deallocates this automatically allocated map,
   499     ///of course.
   500     ///\return <tt> (*this) </tt>
   501     Dijkstra &predMap(PredMap &m)
   502     {
   503       if(local_pred) {
   504         delete _pred;
   505         local_pred=false;
   506       }
   507       _pred = &m;
   508       return *this;
   509     }
   510 
   511     ///Sets the map that indicates which nodes are processed.
   512 
   513     ///Sets the map that indicates which nodes are processed.
   514     ///If you don't use this function before calling \ref run(Node) "run()"
   515     ///or \ref init(), an instance will be allocated automatically.
   516     ///The destructor deallocates this automatically allocated map,
   517     ///of course.
   518     ///\return <tt> (*this) </tt>
   519     Dijkstra &processedMap(ProcessedMap &m)
   520     {
   521       if(local_processed) {
   522         delete _processed;
   523         local_processed=false;
   524       }
   525       _processed = &m;
   526       return *this;
   527     }
   528 
   529     ///Sets the map that stores the distances of the nodes.
   530 
   531     ///Sets the map that stores the distances of the nodes calculated by the
   532     ///algorithm.
   533     ///If you don't use this function before calling \ref run(Node) "run()"
   534     ///or \ref init(), an instance will be allocated automatically.
   535     ///The destructor deallocates this automatically allocated map,
   536     ///of course.
   537     ///\return <tt> (*this) </tt>
   538     Dijkstra &distMap(DistMap &m)
   539     {
   540       if(local_dist) {
   541         delete _dist;
   542         local_dist=false;
   543       }
   544       _dist = &m;
   545       return *this;
   546     }
   547 
   548     ///Sets the heap and the cross reference used by algorithm.
   549 
   550     ///Sets the heap and the cross reference used by algorithm.
   551     ///If you don't use this function before calling \ref run(Node) "run()"
   552     ///or \ref init(), heap and cross reference instances will be
   553     ///allocated automatically.
   554     ///The destructor deallocates these automatically allocated objects,
   555     ///of course.
   556     ///\return <tt> (*this) </tt>
   557     Dijkstra &heap(Heap& hp, HeapCrossRef &cr)
   558     {
   559       if(local_heap_cross_ref) {
   560         delete _heap_cross_ref;
   561         local_heap_cross_ref=false;
   562       }
   563       _heap_cross_ref = &cr;
   564       if(local_heap) {
   565         delete _heap;
   566         local_heap=false;
   567       }
   568       _heap = &hp;
   569       return *this;
   570     }
   571 
   572   private:
   573 
   574     void finalizeNodeData(Node v,Value dst)
   575     {
   576       _processed->set(v,true);
   577       _dist->set(v, dst);
   578     }
   579 
   580   public:
   581 
   582     ///\name Execution Control
   583     ///The simplest way to execute the %Dijkstra algorithm is to use
   584     ///one of the member functions called \ref run(Node) "run()".\n
   585     ///If you need more control on the execution, first you have to call
   586     ///\ref init(), then you can add several source nodes with
   587     ///\ref addSource(). Finally the actual path computation can be
   588     ///performed with one of the \ref start() functions.
   589 
   590     ///@{
   591 
   592     ///\brief Initializes the internal data structures.
   593     ///
   594     ///Initializes the internal data structures.
   595     void init()
   596     {
   597       create_maps();
   598       _heap->clear();
   599       for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
   600         _pred->set(u,INVALID);
   601         _processed->set(u,false);
   602         _heap_cross_ref->set(u,Heap::PRE_HEAP);
   603       }
   604     }
   605 
   606     ///Adds a new source node.
   607 
   608     ///Adds a new source node to the priority heap.
   609     ///The optional second parameter is the initial distance of the node.
   610     ///
   611     ///The function checks if the node has already been added to the heap and
   612     ///it is pushed to the heap only if either it was not in the heap
   613     ///or the shortest path found till then is shorter than \c dst.
   614     void addSource(Node s,Value dst=OperationTraits::zero())
   615     {
   616       if(_heap->state(s) != Heap::IN_HEAP) {
   617         _heap->push(s,dst);
   618       } else if(OperationTraits::less((*_heap)[s], dst)) {
   619         _heap->set(s,dst);
   620         _pred->set(s,INVALID);
   621       }
   622     }
   623 
   624     ///Processes the next node in the priority heap
   625 
   626     ///Processes the next node in the priority heap.
   627     ///
   628     ///\return The processed node.
   629     ///
   630     ///\warning The priority heap must not be empty.
   631     Node processNextNode()
   632     {
   633       Node v=_heap->top();
   634       Value oldvalue=_heap->prio();
   635       _heap->pop();
   636       finalizeNodeData(v,oldvalue);
   637 
   638       for(OutArcIt e(*G,v); e!=INVALID; ++e) {
   639         Node w=G->target(e);
   640         switch(_heap->state(w)) {
   641         case Heap::PRE_HEAP:
   642           _heap->push(w,OperationTraits::plus(oldvalue, (*_length)[e]));
   643           _pred->set(w,e);
   644           break;
   645         case Heap::IN_HEAP:
   646           {
   647             Value newvalue = OperationTraits::plus(oldvalue, (*_length)[e]);
   648             if ( OperationTraits::less(newvalue, (*_heap)[w]) ) {
   649               _heap->decrease(w, newvalue);
   650               _pred->set(w,e);
   651             }
   652           }
   653           break;
   654         case Heap::POST_HEAP:
   655           break;
   656         }
   657       }
   658       return v;
   659     }
   660 
   661     ///The next node to be processed.
   662 
   663     ///Returns the next node to be processed or \c INVALID if the
   664     ///priority heap is empty.
   665     Node nextNode() const
   666     {
   667       return !_heap->empty()?_heap->top():INVALID;
   668     }
   669 
   670     ///Returns \c false if there are nodes to be processed.
   671 
   672     ///Returns \c false if there are nodes to be processed
   673     ///in the priority heap.
   674     bool emptyQueue() const { return _heap->empty(); }
   675 
   676     ///Returns the number of the nodes to be processed.
   677 
   678     ///Returns the number of the nodes to be processed
   679     ///in the priority heap.
   680     int queueSize() const { return _heap->size(); }
   681 
   682     ///Executes the algorithm.
   683 
   684     ///Executes the algorithm.
   685     ///
   686     ///This method runs the %Dijkstra algorithm from the root node(s)
   687     ///in order to compute the shortest path to each node.
   688     ///
   689     ///The algorithm computes
   690     ///- the shortest path tree (forest),
   691     ///- the distance of each node from the root(s).
   692     ///
   693     ///\pre init() must be called and at least one root node should be
   694     ///added with addSource() before using this function.
   695     ///
   696     ///\note <tt>d.start()</tt> is just a shortcut of the following code.
   697     ///\code
   698     ///  while ( !d.emptyQueue() ) {
   699     ///    d.processNextNode();
   700     ///  }
   701     ///\endcode
   702     void start()
   703     {
   704       while ( !emptyQueue() ) processNextNode();
   705     }
   706 
   707     ///Executes the algorithm until the given target node is processed.
   708 
   709     ///Executes the algorithm until the given target node is processed.
   710     ///
   711     ///This method runs the %Dijkstra algorithm from the root node(s)
   712     ///in order to compute the shortest path to \c t.
   713     ///
   714     ///The algorithm computes
   715     ///- the shortest path to \c t,
   716     ///- the distance of \c t from the root(s).
   717     ///
   718     ///\pre init() must be called and at least one root node should be
   719     ///added with addSource() before using this function.
   720     void start(Node t)
   721     {
   722       while ( !_heap->empty() && _heap->top()!=t ) processNextNode();
   723       if ( !_heap->empty() ) {
   724         finalizeNodeData(_heap->top(),_heap->prio());
   725         _heap->pop();
   726       }
   727     }
   728 
   729     ///Executes the algorithm until a condition is met.
   730 
   731     ///Executes the algorithm until a condition is met.
   732     ///
   733     ///This method runs the %Dijkstra algorithm from the root node(s) in
   734     ///order to compute the shortest path to a node \c v with
   735     /// <tt>nm[v]</tt> true, if such a node can be found.
   736     ///
   737     ///\param nm A \c bool (or convertible) node map. The algorithm
   738     ///will stop when it reaches a node \c v with <tt>nm[v]</tt> true.
   739     ///
   740     ///\return The reached node \c v with <tt>nm[v]</tt> true or
   741     ///\c INVALID if no such node was found.
   742     ///
   743     ///\pre init() must be called and at least one root node should be
   744     ///added with addSource() before using this function.
   745     template<class NodeBoolMap>
   746     Node start(const NodeBoolMap &nm)
   747     {
   748       while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode();
   749       if ( _heap->empty() ) return INVALID;
   750       finalizeNodeData(_heap->top(),_heap->prio());
   751       return _heap->top();
   752     }
   753 
   754     ///Runs the algorithm from the given source node.
   755 
   756     ///This method runs the %Dijkstra algorithm from node \c s
   757     ///in order to compute the shortest path to each node.
   758     ///
   759     ///The algorithm computes
   760     ///- the shortest path tree,
   761     ///- the distance of each node from the root.
   762     ///
   763     ///\note <tt>d.run(s)</tt> is just a shortcut of the following code.
   764     ///\code
   765     ///  d.init();
   766     ///  d.addSource(s);
   767     ///  d.start();
   768     ///\endcode
   769     void run(Node s) {
   770       init();
   771       addSource(s);
   772       start();
   773     }
   774 
   775     ///Finds the shortest path between \c s and \c t.
   776 
   777     ///This method runs the %Dijkstra algorithm from node \c s
   778     ///in order to compute the shortest path to node \c t
   779     ///(it stops searching when \c t is processed).
   780     ///
   781     ///\return \c true if \c t is reachable form \c s.
   782     ///
   783     ///\note Apart from the return value, <tt>d.run(s,t)</tt> is just a
   784     ///shortcut of the following code.
   785     ///\code
   786     ///  d.init();
   787     ///  d.addSource(s);
   788     ///  d.start(t);
   789     ///\endcode
   790     bool run(Node s,Node t) {
   791       init();
   792       addSource(s);
   793       start(t);
   794       return (*_heap_cross_ref)[t] == Heap::POST_HEAP;
   795     }
   796 
   797     ///@}
   798 
   799     ///\name Query Functions
   800     ///The results of the %Dijkstra algorithm can be obtained using these
   801     ///functions.\n
   802     ///Either \ref run(Node) "run()" or \ref start() should be called
   803     ///before using them.
   804 
   805     ///@{
   806 
   807     ///The shortest path to a node.
   808 
   809     ///Returns the shortest path to a node.
   810     ///
   811     ///\warning \c t should be reached from the root(s).
   812     ///
   813     ///\pre Either \ref run(Node) "run()" or \ref init()
   814     ///must be called before using this function.
   815     Path path(Node t) const { return Path(*G, *_pred, t); }
   816 
   817     ///The distance of a node from the root(s).
   818 
   819     ///Returns the distance of a node from the root(s).
   820     ///
   821     ///\warning If node \c v is not reached from the root(s), then
   822     ///the return value of this function is undefined.
   823     ///
   824     ///\pre Either \ref run(Node) "run()" or \ref init()
   825     ///must be called before using this function.
   826     Value dist(Node v) const { return (*_dist)[v]; }
   827 
   828     ///Returns the 'previous arc' of the shortest path tree for a node.
   829 
   830     ///This function returns the 'previous arc' of the shortest path
   831     ///tree for the node \c v, i.e. it returns the last arc of a
   832     ///shortest path from a root to \c v. It is \c INVALID if \c v
   833     ///is not reached from the root(s) or if \c v is a root.
   834     ///
   835     ///The shortest path tree used here is equal to the shortest path
   836     ///tree used in \ref predNode().
   837     ///
   838     ///\pre Either \ref run(Node) "run()" or \ref init()
   839     ///must be called before using this function.
   840     Arc predArc(Node v) const { return (*_pred)[v]; }
   841 
   842     ///Returns the 'previous node' of the shortest path tree for a node.
   843 
   844     ///This function returns the 'previous node' of the shortest path
   845     ///tree for the node \c v, i.e. it returns the last but one node
   846     ///from a shortest path from a root to \c v. It is \c INVALID
   847     ///if \c v is not reached from the root(s) or if \c v is a root.
   848     ///
   849     ///The shortest path tree used here is equal to the shortest path
   850     ///tree used in \ref predArc().
   851     ///
   852     ///\pre Either \ref run(Node) "run()" or \ref init()
   853     ///must be called before using this function.
   854     Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
   855                                   G->source((*_pred)[v]); }
   856 
   857     ///\brief Returns a const reference to the node map that stores the
   858     ///distances of the nodes.
   859     ///
   860     ///Returns a const reference to the node map that stores the distances
   861     ///of the nodes calculated by the algorithm.
   862     ///
   863     ///\pre Either \ref run(Node) "run()" or \ref init()
   864     ///must be called before using this function.
   865     const DistMap &distMap() const { return *_dist;}
   866 
   867     ///\brief Returns a const reference to the node map that stores the
   868     ///predecessor arcs.
   869     ///
   870     ///Returns a const reference to the node map that stores the predecessor
   871     ///arcs, which form the shortest path tree.
   872     ///
   873     ///\pre Either \ref run(Node) "run()" or \ref init()
   874     ///must be called before using this function.
   875     const PredMap &predMap() const { return *_pred;}
   876 
   877     ///Checks if a node is reached from the root(s).
   878 
   879     ///Returns \c true if \c v is reached from the root(s).
   880     ///
   881     ///\pre Either \ref run(Node) "run()" or \ref init()
   882     ///must be called before using this function.
   883     bool reached(Node v) const { return (*_heap_cross_ref)[v] !=
   884                                         Heap::PRE_HEAP; }
   885 
   886     ///Checks if a node is processed.
   887 
   888     ///Returns \c true if \c v is processed, i.e. the shortest
   889     ///path to \c v has already found.
   890     ///
   891     ///\pre Either \ref run(Node) "run()" or \ref init()
   892     ///must be called before using this function.
   893     bool processed(Node v) const { return (*_heap_cross_ref)[v] ==
   894                                           Heap::POST_HEAP; }
   895 
   896     ///The current distance of a node from the root(s).
   897 
   898     ///Returns the current distance of a node from the root(s).
   899     ///It may be decreased in the following processes.
   900     ///
   901     ///\pre Either \ref run(Node) "run()" or \ref init()
   902     ///must be called before using this function and
   903     ///node \c v must be reached but not necessarily processed.
   904     Value currentDist(Node v) const {
   905       return processed(v) ? (*_dist)[v] : (*_heap)[v];
   906     }
   907 
   908     ///@}
   909   };
   910 
   911 
   912   ///Default traits class of dijkstra() function.
   913 
   914   ///Default traits class of dijkstra() function.
   915   ///\tparam GR The type of the digraph.
   916   ///\tparam LM The type of the length map.
   917   template<class GR, class LM>
   918   struct DijkstraWizardDefaultTraits
   919   {
   920     ///The type of the digraph the algorithm runs on.
   921     typedef GR Digraph;
   922     ///The type of the map that stores the arc lengths.
   923 
   924     ///The type of the map that stores the arc lengths.
   925     ///It must meet the \ref concepts::ReadMap "ReadMap" concept.
   926     typedef LM LengthMap;
   927     ///The type of the length of the arcs.
   928     typedef typename LM::Value Value;
   929 
   930     /// Operation traits for Dijkstra algorithm.
   931 
   932     /// This class defines the operations that are used in the algorithm.
   933     /// \see DijkstraDefaultOperationTraits
   934     typedef DijkstraDefaultOperationTraits<Value> OperationTraits;
   935 
   936     /// The cross reference type used by the heap.
   937 
   938     /// The cross reference type used by the heap.
   939     /// Usually it is \c Digraph::NodeMap<int>.
   940     typedef typename Digraph::template NodeMap<int> HeapCrossRef;
   941     ///Instantiates a \ref HeapCrossRef.
   942 
   943     ///This function instantiates a \ref HeapCrossRef.
   944     /// \param g is the digraph, to which we would like to define the
   945     /// HeapCrossRef.
   946     static HeapCrossRef *createHeapCrossRef(const Digraph &g)
   947     {
   948       return new HeapCrossRef(g);
   949     }
   950 
   951     ///The heap type used by the Dijkstra algorithm.
   952 
   953     ///The heap type used by the Dijkstra algorithm.
   954     ///
   955     ///\sa BinHeap
   956     ///\sa Dijkstra
   957     typedef BinHeap<Value, typename Digraph::template NodeMap<int>,
   958                     std::less<Value> > Heap;
   959 
   960     ///Instantiates a \ref Heap.
   961 
   962     ///This function instantiates a \ref Heap.
   963     /// \param r is the HeapCrossRef which is used.
   964     static Heap *createHeap(HeapCrossRef& r)
   965     {
   966       return new Heap(r);
   967     }
   968 
   969     ///\brief The type of the map that stores the predecessor
   970     ///arcs of the shortest paths.
   971     ///
   972     ///The type of the map that stores the predecessor
   973     ///arcs of the shortest paths.
   974     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   975     typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
   976     ///Instantiates a PredMap.
   977 
   978     ///This function instantiates a PredMap.
   979     ///\param g is the digraph, to which we would like to define the
   980     ///PredMap.
   981     static PredMap *createPredMap(const Digraph &g)
   982     {
   983       return new PredMap(g);
   984     }
   985 
   986     ///The type of the map that indicates which nodes are processed.
   987 
   988     ///The type of the map that indicates which nodes are processed.
   989     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   990     ///By default it is a NullMap.
   991     typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
   992     ///Instantiates a ProcessedMap.
   993 
   994     ///This function instantiates a ProcessedMap.
   995     ///\param g is the digraph, to which
   996     ///we would like to define the ProcessedMap.
   997 #ifdef DOXYGEN
   998     static ProcessedMap *createProcessedMap(const Digraph &g)
   999 #else
  1000     static ProcessedMap *createProcessedMap(const Digraph &)
  1001 #endif
  1002     {
  1003       return new ProcessedMap();
  1004     }
  1005 
  1006     ///The type of the map that stores the distances of the nodes.
  1007 
  1008     ///The type of the map that stores the distances of the nodes.
  1009     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
  1010     typedef typename Digraph::template NodeMap<typename LM::Value> DistMap;
  1011     ///Instantiates a DistMap.
  1012 
  1013     ///This function instantiates a DistMap.
  1014     ///\param g is the digraph, to which we would like to define
  1015     ///the DistMap
  1016     static DistMap *createDistMap(const Digraph &g)
  1017     {
  1018       return new DistMap(g);
  1019     }
  1020 
  1021     ///The type of the shortest paths.
  1022 
  1023     ///The type of the shortest paths.
  1024     ///It must meet the \ref concepts::Path "Path" concept.
  1025     typedef lemon::Path<Digraph> Path;
  1026   };
  1027 
  1028   /// Default traits class used by DijkstraWizard
  1029 
  1030   /// To make it easier to use Dijkstra algorithm
  1031   /// we have created a wizard class.
  1032   /// This \ref DijkstraWizard class needs default traits,
  1033   /// as well as the \ref Dijkstra class.
  1034   /// The \ref DijkstraWizardBase is a class to be the default traits of the
  1035   /// \ref DijkstraWizard class.
  1036   template<class GR,class LM>
  1037   class DijkstraWizardBase : public DijkstraWizardDefaultTraits<GR,LM>
  1038   {
  1039     typedef DijkstraWizardDefaultTraits<GR,LM> Base;
  1040   protected:
  1041     //The type of the nodes in the digraph.
  1042     typedef typename Base::Digraph::Node Node;
  1043 
  1044     //Pointer to the digraph the algorithm runs on.
  1045     void *_g;
  1046     //Pointer to the length map.
  1047     void *_length;
  1048     //Pointer to the map of processed nodes.
  1049     void *_processed;
  1050     //Pointer to the map of predecessors arcs.
  1051     void *_pred;
  1052     //Pointer to the map of distances.
  1053     void *_dist;
  1054     //Pointer to the shortest path to the target node.
  1055     void *_path;
  1056     //Pointer to the distance of the target node.
  1057     void *_di;
  1058 
  1059   public:
  1060     /// Constructor.
  1061 
  1062     /// This constructor does not require parameters, therefore it initiates
  1063     /// all of the attributes to \c 0.
  1064     DijkstraWizardBase() : _g(0), _length(0), _processed(0), _pred(0),
  1065                            _dist(0), _path(0), _di(0) {}
  1066 
  1067     /// Constructor.
  1068 
  1069     /// This constructor requires two parameters,
  1070     /// others are initiated to \c 0.
  1071     /// \param g The digraph the algorithm runs on.
  1072     /// \param l The length map.
  1073     DijkstraWizardBase(const GR &g,const LM &l) :
  1074       _g(reinterpret_cast<void*>(const_cast<GR*>(&g))),
  1075       _length(reinterpret_cast<void*>(const_cast<LM*>(&l))),
  1076       _processed(0), _pred(0), _dist(0), _path(0), _di(0) {}
  1077 
  1078   };
  1079 
  1080   /// Auxiliary class for the function-type interface of Dijkstra algorithm.
  1081 
  1082   /// This auxiliary class is created to implement the
  1083   /// \ref dijkstra() "function-type interface" of \ref Dijkstra algorithm.
  1084   /// It does not have own \ref run(Node) "run()" method, it uses the
  1085   /// functions and features of the plain \ref Dijkstra.
  1086   ///
  1087   /// This class should only be used through the \ref dijkstra() function,
  1088   /// which makes it easier to use the algorithm.
  1089   template<class TR>
  1090   class DijkstraWizard : public TR
  1091   {
  1092     typedef TR Base;
  1093 
  1094     ///The type of the digraph the algorithm runs on.
  1095     typedef typename TR::Digraph Digraph;
  1096 
  1097     typedef typename Digraph::Node Node;
  1098     typedef typename Digraph::NodeIt NodeIt;
  1099     typedef typename Digraph::Arc Arc;
  1100     typedef typename Digraph::OutArcIt OutArcIt;
  1101 
  1102     ///The type of the map that stores the arc lengths.
  1103     typedef typename TR::LengthMap LengthMap;
  1104     ///The type of the length of the arcs.
  1105     typedef typename LengthMap::Value Value;
  1106     ///\brief The type of the map that stores the predecessor
  1107     ///arcs of the shortest paths.
  1108     typedef typename TR::PredMap PredMap;
  1109     ///The type of the map that stores the distances of the nodes.
  1110     typedef typename TR::DistMap DistMap;
  1111     ///The type of the map that indicates which nodes are processed.
  1112     typedef typename TR::ProcessedMap ProcessedMap;
  1113     ///The type of the shortest paths
  1114     typedef typename TR::Path Path;
  1115     ///The heap type used by the dijkstra algorithm.
  1116     typedef typename TR::Heap Heap;
  1117 
  1118   public:
  1119 
  1120     /// Constructor.
  1121     DijkstraWizard() : TR() {}
  1122 
  1123     /// Constructor that requires parameters.
  1124 
  1125     /// Constructor that requires parameters.
  1126     /// These parameters will be the default values for the traits class.
  1127     /// \param g The digraph the algorithm runs on.
  1128     /// \param l The length map.
  1129     DijkstraWizard(const Digraph &g, const LengthMap &l) :
  1130       TR(g,l) {}
  1131 
  1132     ///Copy constructor
  1133     DijkstraWizard(const TR &b) : TR(b) {}
  1134 
  1135     ~DijkstraWizard() {}
  1136 
  1137     ///Runs Dijkstra algorithm from the given source node.
  1138 
  1139     ///This method runs %Dijkstra algorithm from the given source node
  1140     ///in order to compute the shortest path to each node.
  1141     void run(Node s)
  1142     {
  1143       Dijkstra<Digraph,LengthMap,TR>
  1144         dijk(*reinterpret_cast<const Digraph*>(Base::_g),
  1145              *reinterpret_cast<const LengthMap*>(Base::_length));
  1146       if (Base::_pred)
  1147         dijk.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
  1148       if (Base::_dist)
  1149         dijk.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
  1150       if (Base::_processed)
  1151         dijk.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
  1152       dijk.run(s);
  1153     }
  1154 
  1155     ///Finds the shortest path between \c s and \c t.
  1156 
  1157     ///This method runs the %Dijkstra algorithm from node \c s
  1158     ///in order to compute the shortest path to node \c t
  1159     ///(it stops searching when \c t is processed).
  1160     ///
  1161     ///\return \c true if \c t is reachable form \c s.
  1162     bool run(Node s, Node t)
  1163     {
  1164       Dijkstra<Digraph,LengthMap,TR>
  1165         dijk(*reinterpret_cast<const Digraph*>(Base::_g),
  1166              *reinterpret_cast<const LengthMap*>(Base::_length));
  1167       if (Base::_pred)
  1168         dijk.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
  1169       if (Base::_dist)
  1170         dijk.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
  1171       if (Base::_processed)
  1172         dijk.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
  1173       dijk.run(s,t);
  1174       if (Base::_path)
  1175         *reinterpret_cast<Path*>(Base::_path) = dijk.path(t);
  1176       if (Base::_di)
  1177         *reinterpret_cast<Value*>(Base::_di) = dijk.dist(t);
  1178       return dijk.reached(t);
  1179     }
  1180 
  1181     template<class T>
  1182     struct SetPredMapBase : public Base {
  1183       typedef T PredMap;
  1184       static PredMap *createPredMap(const Digraph &) { return 0; };
  1185       SetPredMapBase(const TR &b) : TR(b) {}
  1186     };
  1187     ///\brief \ref named-func-param "Named parameter"
  1188     ///for setting PredMap object.
  1189     ///
  1190     ///\ref named-func-param "Named parameter"
  1191     ///for setting PredMap object.
  1192     template<class T>
  1193     DijkstraWizard<SetPredMapBase<T> > predMap(const T &t)
  1194     {
  1195       Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
  1196       return DijkstraWizard<SetPredMapBase<T> >(*this);
  1197     }
  1198 
  1199     template<class T>
  1200     struct SetDistMapBase : public Base {
  1201       typedef T DistMap;
  1202       static DistMap *createDistMap(const Digraph &) { return 0; };
  1203       SetDistMapBase(const TR &b) : TR(b) {}
  1204     };
  1205     ///\brief \ref named-func-param "Named parameter"
  1206     ///for setting DistMap object.
  1207     ///
  1208     ///\ref named-func-param "Named parameter"
  1209     ///for setting DistMap object.
  1210     template<class T>
  1211     DijkstraWizard<SetDistMapBase<T> > distMap(const T &t)
  1212     {
  1213       Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
  1214       return DijkstraWizard<SetDistMapBase<T> >(*this);
  1215     }
  1216 
  1217     template<class T>
  1218     struct SetProcessedMapBase : public Base {
  1219       typedef T ProcessedMap;
  1220       static ProcessedMap *createProcessedMap(const Digraph &) { return 0; };
  1221       SetProcessedMapBase(const TR &b) : TR(b) {}
  1222     };
  1223     ///\brief \ref named-func-param "Named parameter"
  1224     ///for setting ProcessedMap object.
  1225     ///
  1226     /// \ref named-func-param "Named parameter"
  1227     ///for setting ProcessedMap object.
  1228     template<class T>
  1229     DijkstraWizard<SetProcessedMapBase<T> > processedMap(const T &t)
  1230     {
  1231       Base::_processed=reinterpret_cast<void*>(const_cast<T*>(&t));
  1232       return DijkstraWizard<SetProcessedMapBase<T> >(*this);
  1233     }
  1234 
  1235     template<class T>
  1236     struct SetPathBase : public Base {
  1237       typedef T Path;
  1238       SetPathBase(const TR &b) : TR(b) {}
  1239     };
  1240     ///\brief \ref named-func-param "Named parameter"
  1241     ///for getting the shortest path to the target node.
  1242     ///
  1243     ///\ref named-func-param "Named parameter"
  1244     ///for getting the shortest path to the target node.
  1245     template<class T>
  1246     DijkstraWizard<SetPathBase<T> > path(const T &t)
  1247     {
  1248       Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t));
  1249       return DijkstraWizard<SetPathBase<T> >(*this);
  1250     }
  1251 
  1252     ///\brief \ref named-func-param "Named parameter"
  1253     ///for getting the distance of the target node.
  1254     ///
  1255     ///\ref named-func-param "Named parameter"
  1256     ///for getting the distance of the target node.
  1257     DijkstraWizard dist(const Value &d)
  1258     {
  1259       Base::_di=reinterpret_cast<void*>(const_cast<Value*>(&d));
  1260       return *this;
  1261     }
  1262 
  1263   };
  1264 
  1265   ///Function-type interface for Dijkstra algorithm.
  1266 
  1267   /// \ingroup shortest_path
  1268   ///Function-type interface for Dijkstra algorithm.
  1269   ///
  1270   ///This function also has several \ref named-func-param "named parameters",
  1271   ///they are declared as the members of class \ref DijkstraWizard.
  1272   ///The following examples show how to use these parameters.
  1273   ///\code
  1274   ///  // Compute shortest path from node s to each node
  1275   ///  dijkstra(g,length).predMap(preds).distMap(dists).run(s);
  1276   ///
  1277   ///  // Compute shortest path from s to t
  1278   ///  bool reached = dijkstra(g,length).path(p).dist(d).run(s,t);
  1279   ///\endcode
  1280   ///\warning Don't forget to put the \ref DijkstraWizard::run(Node) "run()"
  1281   ///to the end of the parameter list.
  1282   ///\sa DijkstraWizard
  1283   ///\sa Dijkstra
  1284   template<class GR, class LM>
  1285   DijkstraWizard<DijkstraWizardBase<GR,LM> >
  1286   dijkstra(const GR &digraph, const LM &length)
  1287   {
  1288     return DijkstraWizard<DijkstraWizardBase<GR,LM> >(digraph,length);
  1289   }
  1290 
  1291 } //END OF NAMESPACE LEMON
  1292 
  1293 #endif