lemon/dijkstra.h
author Alpar Juttner <alpar@cs.elte.hu>
Fri, 15 Apr 2011 09:37:47 +0200
changeset 945 2024bf2ecdd6
parent 559 c5fd2d996909
child 713 4ac30454f1c1
child 716 f47b6c94577e
permissions -rw-r--r--
Build of mip_test and lp_test precede the running of the tests (#419)
     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 V>
    42   struct DijkstraDefaultOperationTraits {
    43     /// \e
    44     typedef V Value;
    45     /// \brief Gives back the zero value of the type.
    46     static Value zero() {
    47       return static_cast<Value>(0);
    48     }
    49     /// \brief Gives back the sum of the given two elements.
    50     static Value plus(const Value& left, const Value& right) {
    51       return left + right;
    52     }
    53     /// \brief Gives back true only if the first value is less than the second.
    54     static bool less(const Value& left, const Value& right) {
    55       return left < right;
    56     }
    57   };
    58 
    59   ///Default traits class of Dijkstra class.
    60 
    61   ///Default traits class of Dijkstra class.
    62   ///\tparam GR The type of the digraph.
    63   ///\tparam LEN The type of the length map.
    64   template<typename GR, typename LEN>
    65   struct DijkstraDefaultTraits
    66   {
    67     ///The type of the digraph the algorithm runs on.
    68     typedef GR Digraph;
    69 
    70     ///The type of the map that stores the arc lengths.
    71 
    72     ///The type of the map that stores the arc lengths.
    73     ///It must meet the \ref concepts::ReadMap "ReadMap" concept.
    74     typedef LEN LengthMap;
    75     ///The type of the length of the arcs.
    76     typedef typename LEN::Value Value;
    77 
    78     /// Operation traits for %Dijkstra algorithm.
    79 
    80     /// This class defines the operations that are used in the algorithm.
    81     /// \see DijkstraDefaultOperationTraits
    82     typedef DijkstraDefaultOperationTraits<Value> OperationTraits;
    83 
    84     /// The cross reference type used by the heap.
    85 
    86     /// The cross reference type used by the heap.
    87     /// Usually it is \c Digraph::NodeMap<int>.
    88     typedef typename Digraph::template NodeMap<int> HeapCrossRef;
    89     ///Instantiates a \c HeapCrossRef.
    90 
    91     ///This function instantiates a \ref HeapCrossRef.
    92     /// \param g is the digraph, to which we would like to define the
    93     /// \ref HeapCrossRef.
    94     static HeapCrossRef *createHeapCrossRef(const Digraph &g)
    95     {
    96       return new HeapCrossRef(g);
    97     }
    98 
    99     ///The heap type used by the %Dijkstra algorithm.
   100 
   101     ///The heap type used by the Dijkstra algorithm.
   102     ///
   103     ///\sa BinHeap
   104     ///\sa Dijkstra
   105     typedef BinHeap<typename LEN::Value, HeapCrossRef, std::less<Value> > Heap;
   106     ///Instantiates a \c Heap.
   107 
   108     ///This function instantiates a \ref Heap.
   109     static Heap *createHeap(HeapCrossRef& r)
   110     {
   111       return new Heap(r);
   112     }
   113 
   114     ///\brief The type of the map that stores the predecessor
   115     ///arcs of the shortest paths.
   116     ///
   117     ///The type of the map that stores the predecessor
   118     ///arcs of the shortest paths.
   119     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   120     typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
   121     ///Instantiates a \c PredMap.
   122 
   123     ///This function instantiates a \ref PredMap.
   124     ///\param g is the digraph, to which we would like to define the
   125     ///\ref PredMap.
   126     static PredMap *createPredMap(const Digraph &g)
   127     {
   128       return new PredMap(g);
   129     }
   130 
   131     ///The type of the map that indicates which nodes are processed.
   132 
   133     ///The type of the map that indicates which nodes are processed.
   134     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   135     ///By default it is a NullMap.
   136     typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
   137     ///Instantiates a \c ProcessedMap.
   138 
   139     ///This function instantiates a \ref ProcessedMap.
   140     ///\param g is the digraph, to which
   141     ///we would like to define the \ref ProcessedMap.
   142 #ifdef DOXYGEN
   143     static ProcessedMap *createProcessedMap(const Digraph &g)
   144 #else
   145     static ProcessedMap *createProcessedMap(const Digraph &)
   146 #endif
   147     {
   148       return new ProcessedMap();
   149     }
   150 
   151     ///The type of the map that stores the distances of the nodes.
   152 
   153     ///The type of the map that stores the distances of the nodes.
   154     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   155     typedef typename Digraph::template NodeMap<typename LEN::Value> DistMap;
   156     ///Instantiates a \c DistMap.
   157 
   158     ///This function instantiates a \ref DistMap.
   159     ///\param g is the digraph, to which we would like to define
   160     ///the \ref DistMap.
   161     static DistMap *createDistMap(const Digraph &g)
   162     {
   163       return new DistMap(g);
   164     }
   165   };
   166 
   167   ///%Dijkstra algorithm class.
   168 
   169   /// \ingroup shortest_path
   170   ///This class provides an efficient implementation of the %Dijkstra algorithm.
   171   ///
   172   ///The arc lengths are passed to the algorithm using a
   173   ///\ref concepts::ReadMap "ReadMap",
   174   ///so it is easy to change it to any kind of length.
   175   ///The type of the length is determined by the
   176   ///\ref concepts::ReadMap::Value "Value" of the length map.
   177   ///It is also possible to change the underlying priority heap.
   178   ///
   179   ///There is also a \ref dijkstra() "function-type interface" for the
   180   ///%Dijkstra algorithm, which is convenient in the simplier cases and
   181   ///it can be used easier.
   182   ///
   183   ///\tparam GR The type of the digraph the algorithm runs on.
   184   ///The default type is \ref ListDigraph.
   185   ///\tparam LEN A \ref concepts::ReadMap "readable" arc map that specifies
   186   ///the lengths of the arcs.
   187   ///It is read once for each arc, so the map may involve in
   188   ///relatively time consuming process to compute the arc lengths if
   189   ///it is necessary. The default map type is \ref
   190   ///concepts::Digraph::ArcMap "GR::ArcMap<int>".
   191 #ifdef DOXYGEN
   192   template <typename GR, typename LEN, typename TR>
   193 #else
   194   template <typename GR=ListDigraph,
   195             typename LEN=typename GR::template ArcMap<int>,
   196             typename TR=DijkstraDefaultTraits<GR,LEN> >
   197 #endif
   198   class Dijkstra {
   199   public:
   200 
   201     ///The type of the digraph the algorithm runs on.
   202     typedef typename TR::Digraph Digraph;
   203 
   204     ///The type of the length of the arcs.
   205     typedef typename TR::LengthMap::Value Value;
   206     ///The type of the map that stores the arc lengths.
   207     typedef typename TR::LengthMap LengthMap;
   208     ///\brief The type of the map that stores the predecessor arcs of the
   209     ///shortest paths.
   210     typedef typename TR::PredMap PredMap;
   211     ///The type of the map that stores the distances of the nodes.
   212     typedef typename TR::DistMap DistMap;
   213     ///The type of the map that indicates which nodes are processed.
   214     typedef typename TR::ProcessedMap ProcessedMap;
   215     ///The type of the paths.
   216     typedef PredMapPath<Digraph, PredMap> Path;
   217     ///The cross reference type used for the current heap.
   218     typedef typename TR::HeapCrossRef HeapCrossRef;
   219     ///The heap type used by the algorithm.
   220     typedef typename TR::Heap Heap;
   221     ///\brief The \ref DijkstraDefaultOperationTraits "operation traits class"
   222     ///of the algorithm.
   223     typedef typename TR::OperationTraits OperationTraits;
   224 
   225     ///The \ref DijkstraDefaultTraits "traits class" of the algorithm.
   226     typedef TR Traits;
   227 
   228   private:
   229 
   230     typedef typename Digraph::Node Node;
   231     typedef typename Digraph::NodeIt NodeIt;
   232     typedef typename Digraph::Arc Arc;
   233     typedef typename Digraph::OutArcIt OutArcIt;
   234 
   235     //Pointer to the underlying digraph.
   236     const Digraph *G;
   237     //Pointer to the length map.
   238     const LengthMap *_length;
   239     //Pointer to the map of predecessors arcs.
   240     PredMap *_pred;
   241     //Indicates if _pred is locally allocated (true) or not.
   242     bool local_pred;
   243     //Pointer to the map of distances.
   244     DistMap *_dist;
   245     //Indicates if _dist is locally allocated (true) or not.
   246     bool local_dist;
   247     //Pointer to the map of processed status of the nodes.
   248     ProcessedMap *_processed;
   249     //Indicates if _processed is locally allocated (true) or not.
   250     bool local_processed;
   251     //Pointer to the heap cross references.
   252     HeapCrossRef *_heap_cross_ref;
   253     //Indicates if _heap_cross_ref is locally allocated (true) or not.
   254     bool local_heap_cross_ref;
   255     //Pointer to the heap.
   256     Heap *_heap;
   257     //Indicates if _heap is locally allocated (true) or not.
   258     bool local_heap;
   259 
   260     //Creates the maps if necessary.
   261     void create_maps()
   262     {
   263       if(!_pred) {
   264         local_pred = true;
   265         _pred = Traits::createPredMap(*G);
   266       }
   267       if(!_dist) {
   268         local_dist = true;
   269         _dist = Traits::createDistMap(*G);
   270       }
   271       if(!_processed) {
   272         local_processed = true;
   273         _processed = Traits::createProcessedMap(*G);
   274       }
   275       if (!_heap_cross_ref) {
   276         local_heap_cross_ref = true;
   277         _heap_cross_ref = Traits::createHeapCrossRef(*G);
   278       }
   279       if (!_heap) {
   280         local_heap = true;
   281         _heap = Traits::createHeap(*_heap_cross_ref);
   282       }
   283     }
   284 
   285   public:
   286 
   287     typedef Dijkstra Create;
   288 
   289     ///\name Named Template Parameters
   290 
   291     ///@{
   292 
   293     template <class T>
   294     struct SetPredMapTraits : public Traits {
   295       typedef T PredMap;
   296       static PredMap *createPredMap(const Digraph &)
   297       {
   298         LEMON_ASSERT(false, "PredMap is not initialized");
   299         return 0; // ignore warnings
   300       }
   301     };
   302     ///\brief \ref named-templ-param "Named parameter" for setting
   303     ///\c PredMap type.
   304     ///
   305     ///\ref named-templ-param "Named parameter" for setting
   306     ///\c PredMap type.
   307     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   308     template <class T>
   309     struct SetPredMap
   310       : public Dijkstra< Digraph, LengthMap, SetPredMapTraits<T> > {
   311       typedef Dijkstra< Digraph, LengthMap, SetPredMapTraits<T> > Create;
   312     };
   313 
   314     template <class T>
   315     struct SetDistMapTraits : public Traits {
   316       typedef T DistMap;
   317       static DistMap *createDistMap(const Digraph &)
   318       {
   319         LEMON_ASSERT(false, "DistMap is not initialized");
   320         return 0; // ignore warnings
   321       }
   322     };
   323     ///\brief \ref named-templ-param "Named parameter" for setting
   324     ///\c DistMap type.
   325     ///
   326     ///\ref named-templ-param "Named parameter" for setting
   327     ///\c DistMap type.
   328     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   329     template <class T>
   330     struct SetDistMap
   331       : public Dijkstra< Digraph, LengthMap, SetDistMapTraits<T> > {
   332       typedef Dijkstra< Digraph, LengthMap, SetDistMapTraits<T> > Create;
   333     };
   334 
   335     template <class T>
   336     struct SetProcessedMapTraits : public Traits {
   337       typedef T ProcessedMap;
   338       static ProcessedMap *createProcessedMap(const Digraph &)
   339       {
   340         LEMON_ASSERT(false, "ProcessedMap is not initialized");
   341         return 0; // ignore warnings
   342       }
   343     };
   344     ///\brief \ref named-templ-param "Named parameter" for setting
   345     ///\c ProcessedMap type.
   346     ///
   347     ///\ref named-templ-param "Named parameter" for setting
   348     ///\c ProcessedMap type.
   349     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   350     template <class T>
   351     struct SetProcessedMap
   352       : public Dijkstra< Digraph, LengthMap, SetProcessedMapTraits<T> > {
   353       typedef Dijkstra< Digraph, LengthMap, SetProcessedMapTraits<T> > Create;
   354     };
   355 
   356     struct SetStandardProcessedMapTraits : public Traits {
   357       typedef typename Digraph::template NodeMap<bool> ProcessedMap;
   358       static ProcessedMap *createProcessedMap(const Digraph &g)
   359       {
   360         return new ProcessedMap(g);
   361       }
   362     };
   363     ///\brief \ref named-templ-param "Named parameter" for setting
   364     ///\c ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
   365     ///
   366     ///\ref named-templ-param "Named parameter" for setting
   367     ///\c ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
   368     ///If you don't set it explicitly, it will be automatically allocated.
   369     struct SetStandardProcessedMap
   370       : public Dijkstra< Digraph, LengthMap, SetStandardProcessedMapTraits > {
   371       typedef Dijkstra< Digraph, LengthMap, SetStandardProcessedMapTraits >
   372       Create;
   373     };
   374 
   375     template <class H, class CR>
   376     struct SetHeapTraits : public Traits {
   377       typedef CR HeapCrossRef;
   378       typedef H Heap;
   379       static HeapCrossRef *createHeapCrossRef(const Digraph &) {
   380         LEMON_ASSERT(false, "HeapCrossRef is not initialized");
   381         return 0; // ignore warnings
   382       }
   383       static Heap *createHeap(HeapCrossRef &)
   384       {
   385         LEMON_ASSERT(false, "Heap is not initialized");
   386         return 0; // ignore warnings
   387       }
   388     };
   389     ///\brief \ref named-templ-param "Named parameter" for setting
   390     ///heap and cross reference types
   391     ///
   392     ///\ref named-templ-param "Named parameter" for setting heap and cross
   393     ///reference types. If this named parameter is used, then external
   394     ///heap and cross reference objects must be passed to the algorithm
   395     ///using the \ref heap() function before calling \ref run(Node) "run()"
   396     ///or \ref init().
   397     ///\sa SetStandardHeap
   398     template <class H, class CR = typename Digraph::template NodeMap<int> >
   399     struct SetHeap
   400       : public Dijkstra< Digraph, LengthMap, SetHeapTraits<H, CR> > {
   401       typedef Dijkstra< Digraph, LengthMap, SetHeapTraits<H, CR> > Create;
   402     };
   403 
   404     template <class H, class CR>
   405     struct SetStandardHeapTraits : public Traits {
   406       typedef CR HeapCrossRef;
   407       typedef H Heap;
   408       static HeapCrossRef *createHeapCrossRef(const Digraph &G) {
   409         return new HeapCrossRef(G);
   410       }
   411       static Heap *createHeap(HeapCrossRef &R)
   412       {
   413         return new Heap(R);
   414       }
   415     };
   416     ///\brief \ref named-templ-param "Named parameter" for setting
   417     ///heap and cross reference types with automatic allocation
   418     ///
   419     ///\ref named-templ-param "Named parameter" for setting heap and cross
   420     ///reference types with automatic allocation.
   421     ///They should have standard constructor interfaces to be able to
   422     ///automatically created by the algorithm (i.e. the digraph should be
   423     ///passed to the constructor of the cross reference and the cross
   424     ///reference should be passed to the constructor of the heap).
   425     ///However external heap and cross reference objects could also be
   426     ///passed to the algorithm using the \ref heap() function before
   427     ///calling \ref run(Node) "run()" or \ref init().
   428     ///\sa SetHeap
   429     template <class H, class CR = typename Digraph::template NodeMap<int> >
   430     struct SetStandardHeap
   431       : public Dijkstra< Digraph, LengthMap, SetStandardHeapTraits<H, CR> > {
   432       typedef Dijkstra< Digraph, LengthMap, SetStandardHeapTraits<H, CR> >
   433       Create;
   434     };
   435 
   436     template <class T>
   437     struct SetOperationTraitsTraits : public Traits {
   438       typedef T OperationTraits;
   439     };
   440 
   441     /// \brief \ref named-templ-param "Named parameter" for setting
   442     ///\c OperationTraits type
   443     ///
   444     ///\ref named-templ-param "Named parameter" for setting
   445     ///\c OperationTraits type.
   446     template <class T>
   447     struct SetOperationTraits
   448       : public Dijkstra<Digraph, LengthMap, SetOperationTraitsTraits<T> > {
   449       typedef Dijkstra<Digraph, LengthMap, SetOperationTraitsTraits<T> >
   450       Create;
   451     };
   452 
   453     ///@}
   454 
   455   protected:
   456 
   457     Dijkstra() {}
   458 
   459   public:
   460 
   461     ///Constructor.
   462 
   463     ///Constructor.
   464     ///\param g The digraph the algorithm runs on.
   465     ///\param length The length map used by the algorithm.
   466     Dijkstra(const Digraph& g, const LengthMap& length) :
   467       G(&g), _length(&length),
   468       _pred(NULL), local_pred(false),
   469       _dist(NULL), local_dist(false),
   470       _processed(NULL), local_processed(false),
   471       _heap_cross_ref(NULL), local_heap_cross_ref(false),
   472       _heap(NULL), local_heap(false)
   473     { }
   474 
   475     ///Destructor.
   476     ~Dijkstra()
   477     {
   478       if(local_pred) delete _pred;
   479       if(local_dist) delete _dist;
   480       if(local_processed) delete _processed;
   481       if(local_heap_cross_ref) delete _heap_cross_ref;
   482       if(local_heap) delete _heap;
   483     }
   484 
   485     ///Sets the length map.
   486 
   487     ///Sets the length map.
   488     ///\return <tt> (*this) </tt>
   489     Dijkstra &lengthMap(const LengthMap &m)
   490     {
   491       _length = &m;
   492       return *this;
   493     }
   494 
   495     ///Sets the map that stores the predecessor arcs.
   496 
   497     ///Sets the map that stores the predecessor arcs.
   498     ///If you don't use this function before calling \ref run(Node) "run()"
   499     ///or \ref init(), an instance will be allocated automatically.
   500     ///The destructor deallocates this automatically allocated map,
   501     ///of course.
   502     ///\return <tt> (*this) </tt>
   503     Dijkstra &predMap(PredMap &m)
   504     {
   505       if(local_pred) {
   506         delete _pred;
   507         local_pred=false;
   508       }
   509       _pred = &m;
   510       return *this;
   511     }
   512 
   513     ///Sets the map that indicates which nodes are processed.
   514 
   515     ///Sets the map that indicates which nodes are processed.
   516     ///If you don't use this function before calling \ref run(Node) "run()"
   517     ///or \ref init(), an instance will be allocated automatically.
   518     ///The destructor deallocates this automatically allocated map,
   519     ///of course.
   520     ///\return <tt> (*this) </tt>
   521     Dijkstra &processedMap(ProcessedMap &m)
   522     {
   523       if(local_processed) {
   524         delete _processed;
   525         local_processed=false;
   526       }
   527       _processed = &m;
   528       return *this;
   529     }
   530 
   531     ///Sets the map that stores the distances of the nodes.
   532 
   533     ///Sets the map that stores the distances of the nodes calculated by the
   534     ///algorithm.
   535     ///If you don't use this function before calling \ref run(Node) "run()"
   536     ///or \ref init(), an instance will be allocated automatically.
   537     ///The destructor deallocates this automatically allocated map,
   538     ///of course.
   539     ///\return <tt> (*this) </tt>
   540     Dijkstra &distMap(DistMap &m)
   541     {
   542       if(local_dist) {
   543         delete _dist;
   544         local_dist=false;
   545       }
   546       _dist = &m;
   547       return *this;
   548     }
   549 
   550     ///Sets the heap and the cross reference used by algorithm.
   551 
   552     ///Sets the heap and the cross reference used by algorithm.
   553     ///If you don't use this function before calling \ref run(Node) "run()"
   554     ///or \ref init(), heap and cross reference instances will be
   555     ///allocated automatically.
   556     ///The destructor deallocates these automatically allocated objects,
   557     ///of course.
   558     ///\return <tt> (*this) </tt>
   559     Dijkstra &heap(Heap& hp, HeapCrossRef &cr)
   560     {
   561       if(local_heap_cross_ref) {
   562         delete _heap_cross_ref;
   563         local_heap_cross_ref=false;
   564       }
   565       _heap_cross_ref = &cr;
   566       if(local_heap) {
   567         delete _heap;
   568         local_heap=false;
   569       }
   570       _heap = &hp;
   571       return *this;
   572     }
   573 
   574   private:
   575 
   576     void finalizeNodeData(Node v,Value dst)
   577     {
   578       _processed->set(v,true);
   579       _dist->set(v, dst);
   580     }
   581 
   582   public:
   583 
   584     ///\name Execution Control
   585     ///The simplest way to execute the %Dijkstra algorithm is to use
   586     ///one of the member functions called \ref run(Node) "run()".\n
   587     ///If you need more control on the execution, first you have to call
   588     ///\ref init(), then you can add several source nodes with
   589     ///\ref addSource(). Finally the actual path computation can be
   590     ///performed with one of the \ref start() functions.
   591 
   592     ///@{
   593 
   594     ///\brief Initializes the internal data structures.
   595     ///
   596     ///Initializes the internal data structures.
   597     void init()
   598     {
   599       create_maps();
   600       _heap->clear();
   601       for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
   602         _pred->set(u,INVALID);
   603         _processed->set(u,false);
   604         _heap_cross_ref->set(u,Heap::PRE_HEAP);
   605       }
   606     }
   607 
   608     ///Adds a new source node.
   609 
   610     ///Adds a new source node to the priority heap.
   611     ///The optional second parameter is the initial distance of the node.
   612     ///
   613     ///The function checks if the node has already been added to the heap and
   614     ///it is pushed to the heap only if either it was not in the heap
   615     ///or the shortest path found till then is shorter than \c dst.
   616     void addSource(Node s,Value dst=OperationTraits::zero())
   617     {
   618       if(_heap->state(s) != Heap::IN_HEAP) {
   619         _heap->push(s,dst);
   620       } else if(OperationTraits::less((*_heap)[s], dst)) {
   621         _heap->set(s,dst);
   622         _pred->set(s,INVALID);
   623       }
   624     }
   625 
   626     ///Processes the next node in the priority heap
   627 
   628     ///Processes the next node in the priority heap.
   629     ///
   630     ///\return The processed node.
   631     ///
   632     ///\warning The priority heap must not be empty.
   633     Node processNextNode()
   634     {
   635       Node v=_heap->top();
   636       Value oldvalue=_heap->prio();
   637       _heap->pop();
   638       finalizeNodeData(v,oldvalue);
   639 
   640       for(OutArcIt e(*G,v); e!=INVALID; ++e) {
   641         Node w=G->target(e);
   642         switch(_heap->state(w)) {
   643         case Heap::PRE_HEAP:
   644           _heap->push(w,OperationTraits::plus(oldvalue, (*_length)[e]));
   645           _pred->set(w,e);
   646           break;
   647         case Heap::IN_HEAP:
   648           {
   649             Value newvalue = OperationTraits::plus(oldvalue, (*_length)[e]);
   650             if ( OperationTraits::less(newvalue, (*_heap)[w]) ) {
   651               _heap->decrease(w, newvalue);
   652               _pred->set(w,e);
   653             }
   654           }
   655           break;
   656         case Heap::POST_HEAP:
   657           break;
   658         }
   659       }
   660       return v;
   661     }
   662 
   663     ///The next node to be processed.
   664 
   665     ///Returns the next node to be processed or \c INVALID if the
   666     ///priority heap is empty.
   667     Node nextNode() const
   668     {
   669       return !_heap->empty()?_heap->top():INVALID;
   670     }
   671 
   672     ///Returns \c false if there are nodes to be processed.
   673 
   674     ///Returns \c false if there are nodes to be processed
   675     ///in the priority heap.
   676     bool emptyQueue() const { return _heap->empty(); }
   677 
   678     ///Returns the number of the nodes to be processed.
   679 
   680     ///Returns the number of the nodes to be processed
   681     ///in the priority heap.
   682     int queueSize() const { return _heap->size(); }
   683 
   684     ///Executes the algorithm.
   685 
   686     ///Executes the algorithm.
   687     ///
   688     ///This method runs the %Dijkstra algorithm from the root node(s)
   689     ///in order to compute the shortest path to each node.
   690     ///
   691     ///The algorithm computes
   692     ///- the shortest path tree (forest),
   693     ///- the distance of each node from the root(s).
   694     ///
   695     ///\pre init() must be called and at least one root node should be
   696     ///added with addSource() before using this function.
   697     ///
   698     ///\note <tt>d.start()</tt> is just a shortcut of the following code.
   699     ///\code
   700     ///  while ( !d.emptyQueue() ) {
   701     ///    d.processNextNode();
   702     ///  }
   703     ///\endcode
   704     void start()
   705     {
   706       while ( !emptyQueue() ) processNextNode();
   707     }
   708 
   709     ///Executes the algorithm until the given target node is processed.
   710 
   711     ///Executes the algorithm until the given target node is processed.
   712     ///
   713     ///This method runs the %Dijkstra algorithm from the root node(s)
   714     ///in order to compute the shortest path to \c t.
   715     ///
   716     ///The algorithm computes
   717     ///- the shortest path to \c t,
   718     ///- the distance of \c t from the root(s).
   719     ///
   720     ///\pre init() must be called and at least one root node should be
   721     ///added with addSource() before using this function.
   722     void start(Node t)
   723     {
   724       while ( !_heap->empty() && _heap->top()!=t ) processNextNode();
   725       if ( !_heap->empty() ) {
   726         finalizeNodeData(_heap->top(),_heap->prio());
   727         _heap->pop();
   728       }
   729     }
   730 
   731     ///Executes the algorithm until a condition is met.
   732 
   733     ///Executes the algorithm until a condition is met.
   734     ///
   735     ///This method runs the %Dijkstra algorithm from the root node(s) in
   736     ///order to compute the shortest path to a node \c v with
   737     /// <tt>nm[v]</tt> true, if such a node can be found.
   738     ///
   739     ///\param nm A \c bool (or convertible) node map. The algorithm
   740     ///will stop when it reaches a node \c v with <tt>nm[v]</tt> true.
   741     ///
   742     ///\return The reached node \c v with <tt>nm[v]</tt> true or
   743     ///\c INVALID if no such node was found.
   744     ///
   745     ///\pre init() must be called and at least one root node should be
   746     ///added with addSource() before using this function.
   747     template<class NodeBoolMap>
   748     Node start(const NodeBoolMap &nm)
   749     {
   750       while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode();
   751       if ( _heap->empty() ) return INVALID;
   752       finalizeNodeData(_heap->top(),_heap->prio());
   753       return _heap->top();
   754     }
   755 
   756     ///Runs the algorithm from the given source node.
   757 
   758     ///This method runs the %Dijkstra algorithm from node \c s
   759     ///in order to compute the shortest path to each node.
   760     ///
   761     ///The algorithm computes
   762     ///- the shortest path tree,
   763     ///- the distance of each node from the root.
   764     ///
   765     ///\note <tt>d.run(s)</tt> is just a shortcut of the following code.
   766     ///\code
   767     ///  d.init();
   768     ///  d.addSource(s);
   769     ///  d.start();
   770     ///\endcode
   771     void run(Node s) {
   772       init();
   773       addSource(s);
   774       start();
   775     }
   776 
   777     ///Finds the shortest path between \c s and \c t.
   778 
   779     ///This method runs the %Dijkstra algorithm from node \c s
   780     ///in order to compute the shortest path to node \c t
   781     ///(it stops searching when \c t is processed).
   782     ///
   783     ///\return \c true if \c t is reachable form \c s.
   784     ///
   785     ///\note Apart from the return value, <tt>d.run(s,t)</tt> is just a
   786     ///shortcut of the following code.
   787     ///\code
   788     ///  d.init();
   789     ///  d.addSource(s);
   790     ///  d.start(t);
   791     ///\endcode
   792     bool run(Node s,Node t) {
   793       init();
   794       addSource(s);
   795       start(t);
   796       return (*_heap_cross_ref)[t] == Heap::POST_HEAP;
   797     }
   798 
   799     ///@}
   800 
   801     ///\name Query Functions
   802     ///The results of the %Dijkstra algorithm can be obtained using these
   803     ///functions.\n
   804     ///Either \ref run(Node) "run()" or \ref start() should be called
   805     ///before using them.
   806 
   807     ///@{
   808 
   809     ///The shortest path to a node.
   810 
   811     ///Returns the shortest path to a node.
   812     ///
   813     ///\warning \c t should be reached from the root(s).
   814     ///
   815     ///\pre Either \ref run(Node) "run()" or \ref init()
   816     ///must be called before using this function.
   817     Path path(Node t) const { return Path(*G, *_pred, t); }
   818 
   819     ///The distance of a node from the root(s).
   820 
   821     ///Returns the distance of a node from the root(s).
   822     ///
   823     ///\warning If node \c v is not reached from the root(s), then
   824     ///the return value of this function is undefined.
   825     ///
   826     ///\pre Either \ref run(Node) "run()" or \ref init()
   827     ///must be called before using this function.
   828     Value dist(Node v) const { return (*_dist)[v]; }
   829 
   830     ///Returns the 'previous arc' of the shortest path tree for a node.
   831 
   832     ///This function returns the 'previous arc' of the shortest path
   833     ///tree for the node \c v, i.e. it returns the last arc of a
   834     ///shortest path from a root to \c v. It is \c INVALID if \c v
   835     ///is not reached from the root(s) or if \c v is a root.
   836     ///
   837     ///The shortest path tree used here is equal to the shortest path
   838     ///tree used in \ref predNode().
   839     ///
   840     ///\pre Either \ref run(Node) "run()" or \ref init()
   841     ///must be called before using this function.
   842     Arc predArc(Node v) const { return (*_pred)[v]; }
   843 
   844     ///Returns the 'previous node' of the shortest path tree for a node.
   845 
   846     ///This function returns the 'previous node' of the shortest path
   847     ///tree for the node \c v, i.e. it returns the last but one node
   848     ///from a shortest path from a root to \c v. It is \c INVALID
   849     ///if \c v is not reached from the root(s) or if \c v is a root.
   850     ///
   851     ///The shortest path tree used here is equal to the shortest path
   852     ///tree used in \ref predArc().
   853     ///
   854     ///\pre Either \ref run(Node) "run()" or \ref init()
   855     ///must be called before using this function.
   856     Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
   857                                   G->source((*_pred)[v]); }
   858 
   859     ///\brief Returns a const reference to the node map that stores the
   860     ///distances of the nodes.
   861     ///
   862     ///Returns a const reference to the node map that stores the distances
   863     ///of the nodes calculated by the algorithm.
   864     ///
   865     ///\pre Either \ref run(Node) "run()" or \ref init()
   866     ///must be called before using this function.
   867     const DistMap &distMap() const { return *_dist;}
   868 
   869     ///\brief Returns a const reference to the node map that stores the
   870     ///predecessor arcs.
   871     ///
   872     ///Returns a const reference to the node map that stores the predecessor
   873     ///arcs, which form the shortest path tree.
   874     ///
   875     ///\pre Either \ref run(Node) "run()" or \ref init()
   876     ///must be called before using this function.
   877     const PredMap &predMap() const { return *_pred;}
   878 
   879     ///Checks if a node is reached from the root(s).
   880 
   881     ///Returns \c true if \c v is reached from the root(s).
   882     ///
   883     ///\pre Either \ref run(Node) "run()" or \ref init()
   884     ///must be called before using this function.
   885     bool reached(Node v) const { return (*_heap_cross_ref)[v] !=
   886                                         Heap::PRE_HEAP; }
   887 
   888     ///Checks if a node is processed.
   889 
   890     ///Returns \c true if \c v is processed, i.e. the shortest
   891     ///path to \c v has already found.
   892     ///
   893     ///\pre Either \ref run(Node) "run()" or \ref init()
   894     ///must be called before using this function.
   895     bool processed(Node v) const { return (*_heap_cross_ref)[v] ==
   896                                           Heap::POST_HEAP; }
   897 
   898     ///The current distance of a node from the root(s).
   899 
   900     ///Returns the current distance of a node from the root(s).
   901     ///It may be decreased in the following processes.
   902     ///
   903     ///\pre Either \ref run(Node) "run()" or \ref init()
   904     ///must be called before using this function and
   905     ///node \c v must be reached but not necessarily processed.
   906     Value currentDist(Node v) const {
   907       return processed(v) ? (*_dist)[v] : (*_heap)[v];
   908     }
   909 
   910     ///@}
   911   };
   912 
   913 
   914   ///Default traits class of dijkstra() function.
   915 
   916   ///Default traits class of dijkstra() function.
   917   ///\tparam GR The type of the digraph.
   918   ///\tparam LEN The type of the length map.
   919   template<class GR, class LEN>
   920   struct DijkstraWizardDefaultTraits
   921   {
   922     ///The type of the digraph the algorithm runs on.
   923     typedef GR Digraph;
   924     ///The type of the map that stores the arc lengths.
   925 
   926     ///The type of the map that stores the arc lengths.
   927     ///It must meet the \ref concepts::ReadMap "ReadMap" concept.
   928     typedef LEN LengthMap;
   929     ///The type of the length of the arcs.
   930     typedef typename LEN::Value Value;
   931 
   932     /// Operation traits for Dijkstra algorithm.
   933 
   934     /// This class defines the operations that are used in the algorithm.
   935     /// \see DijkstraDefaultOperationTraits
   936     typedef DijkstraDefaultOperationTraits<Value> OperationTraits;
   937 
   938     /// The cross reference type used by the heap.
   939 
   940     /// The cross reference type used by the heap.
   941     /// Usually it is \c Digraph::NodeMap<int>.
   942     typedef typename Digraph::template NodeMap<int> HeapCrossRef;
   943     ///Instantiates a \ref HeapCrossRef.
   944 
   945     ///This function instantiates a \ref HeapCrossRef.
   946     /// \param g is the digraph, to which we would like to define the
   947     /// HeapCrossRef.
   948     static HeapCrossRef *createHeapCrossRef(const Digraph &g)
   949     {
   950       return new HeapCrossRef(g);
   951     }
   952 
   953     ///The heap type used by the Dijkstra algorithm.
   954 
   955     ///The heap type used by the Dijkstra algorithm.
   956     ///
   957     ///\sa BinHeap
   958     ///\sa Dijkstra
   959     typedef BinHeap<Value, typename Digraph::template NodeMap<int>,
   960                     std::less<Value> > Heap;
   961 
   962     ///Instantiates a \ref Heap.
   963 
   964     ///This function instantiates a \ref Heap.
   965     /// \param r is the HeapCrossRef which is used.
   966     static Heap *createHeap(HeapCrossRef& r)
   967     {
   968       return new Heap(r);
   969     }
   970 
   971     ///\brief The type of the map that stores the predecessor
   972     ///arcs of the shortest paths.
   973     ///
   974     ///The type of the map that stores the predecessor
   975     ///arcs of the shortest paths.
   976     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   977     typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
   978     ///Instantiates a PredMap.
   979 
   980     ///This function instantiates a PredMap.
   981     ///\param g is the digraph, to which we would like to define the
   982     ///PredMap.
   983     static PredMap *createPredMap(const Digraph &g)
   984     {
   985       return new PredMap(g);
   986     }
   987 
   988     ///The type of the map that indicates which nodes are processed.
   989 
   990     ///The type of the map that indicates which nodes are processed.
   991     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   992     ///By default it is a NullMap.
   993     typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
   994     ///Instantiates a ProcessedMap.
   995 
   996     ///This function instantiates a ProcessedMap.
   997     ///\param g is the digraph, to which
   998     ///we would like to define the ProcessedMap.
   999 #ifdef DOXYGEN
  1000     static ProcessedMap *createProcessedMap(const Digraph &g)
  1001 #else
  1002     static ProcessedMap *createProcessedMap(const Digraph &)
  1003 #endif
  1004     {
  1005       return new ProcessedMap();
  1006     }
  1007 
  1008     ///The type of the map that stores the distances of the nodes.
  1009 
  1010     ///The type of the map that stores the distances of the nodes.
  1011     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
  1012     typedef typename Digraph::template NodeMap<typename LEN::Value> DistMap;
  1013     ///Instantiates a DistMap.
  1014 
  1015     ///This function instantiates a DistMap.
  1016     ///\param g is the digraph, to which we would like to define
  1017     ///the DistMap
  1018     static DistMap *createDistMap(const Digraph &g)
  1019     {
  1020       return new DistMap(g);
  1021     }
  1022 
  1023     ///The type of the shortest paths.
  1024 
  1025     ///The type of the shortest paths.
  1026     ///It must meet the \ref concepts::Path "Path" concept.
  1027     typedef lemon::Path<Digraph> Path;
  1028   };
  1029 
  1030   /// Default traits class used by DijkstraWizard
  1031 
  1032   /// To make it easier to use Dijkstra algorithm
  1033   /// we have created a wizard class.
  1034   /// This \ref DijkstraWizard class needs default traits,
  1035   /// as well as the \ref Dijkstra class.
  1036   /// The \ref DijkstraWizardBase is a class to be the default traits of the
  1037   /// \ref DijkstraWizard class.
  1038   template<typename GR, typename LEN>
  1039   class DijkstraWizardBase : public DijkstraWizardDefaultTraits<GR,LEN>
  1040   {
  1041     typedef DijkstraWizardDefaultTraits<GR,LEN> Base;
  1042   protected:
  1043     //The type of the nodes in the digraph.
  1044     typedef typename Base::Digraph::Node Node;
  1045 
  1046     //Pointer to the digraph the algorithm runs on.
  1047     void *_g;
  1048     //Pointer to the length map.
  1049     void *_length;
  1050     //Pointer to the map of processed nodes.
  1051     void *_processed;
  1052     //Pointer to the map of predecessors arcs.
  1053     void *_pred;
  1054     //Pointer to the map of distances.
  1055     void *_dist;
  1056     //Pointer to the shortest path to the target node.
  1057     void *_path;
  1058     //Pointer to the distance of the target node.
  1059     void *_di;
  1060 
  1061   public:
  1062     /// Constructor.
  1063 
  1064     /// This constructor does not require parameters, therefore it initiates
  1065     /// all of the attributes to \c 0.
  1066     DijkstraWizardBase() : _g(0), _length(0), _processed(0), _pred(0),
  1067                            _dist(0), _path(0), _di(0) {}
  1068 
  1069     /// Constructor.
  1070 
  1071     /// This constructor requires two parameters,
  1072     /// others are initiated to \c 0.
  1073     /// \param g The digraph the algorithm runs on.
  1074     /// \param l The length map.
  1075     DijkstraWizardBase(const GR &g,const LEN &l) :
  1076       _g(reinterpret_cast<void*>(const_cast<GR*>(&g))),
  1077       _length(reinterpret_cast<void*>(const_cast<LEN*>(&l))),
  1078       _processed(0), _pred(0), _dist(0), _path(0), _di(0) {}
  1079 
  1080   };
  1081 
  1082   /// Auxiliary class for the function-type interface of Dijkstra algorithm.
  1083 
  1084   /// This auxiliary class is created to implement the
  1085   /// \ref dijkstra() "function-type interface" of \ref Dijkstra algorithm.
  1086   /// It does not have own \ref run(Node) "run()" method, it uses the
  1087   /// functions and features of the plain \ref Dijkstra.
  1088   ///
  1089   /// This class should only be used through the \ref dijkstra() function,
  1090   /// which makes it easier to use the algorithm.
  1091   template<class TR>
  1092   class DijkstraWizard : public TR
  1093   {
  1094     typedef TR Base;
  1095 
  1096     ///The type of the digraph the algorithm runs on.
  1097     typedef typename TR::Digraph Digraph;
  1098 
  1099     typedef typename Digraph::Node Node;
  1100     typedef typename Digraph::NodeIt NodeIt;
  1101     typedef typename Digraph::Arc Arc;
  1102     typedef typename Digraph::OutArcIt OutArcIt;
  1103 
  1104     ///The type of the map that stores the arc lengths.
  1105     typedef typename TR::LengthMap LengthMap;
  1106     ///The type of the length of the arcs.
  1107     typedef typename LengthMap::Value Value;
  1108     ///\brief The type of the map that stores the predecessor
  1109     ///arcs of the shortest paths.
  1110     typedef typename TR::PredMap PredMap;
  1111     ///The type of the map that stores the distances of the nodes.
  1112     typedef typename TR::DistMap DistMap;
  1113     ///The type of the map that indicates which nodes are processed.
  1114     typedef typename TR::ProcessedMap ProcessedMap;
  1115     ///The type of the shortest paths
  1116     typedef typename TR::Path Path;
  1117     ///The heap type used by the dijkstra algorithm.
  1118     typedef typename TR::Heap Heap;
  1119 
  1120   public:
  1121 
  1122     /// Constructor.
  1123     DijkstraWizard() : TR() {}
  1124 
  1125     /// Constructor that requires parameters.
  1126 
  1127     /// Constructor that requires parameters.
  1128     /// These parameters will be the default values for the traits class.
  1129     /// \param g The digraph the algorithm runs on.
  1130     /// \param l The length map.
  1131     DijkstraWizard(const Digraph &g, const LengthMap &l) :
  1132       TR(g,l) {}
  1133 
  1134     ///Copy constructor
  1135     DijkstraWizard(const TR &b) : TR(b) {}
  1136 
  1137     ~DijkstraWizard() {}
  1138 
  1139     ///Runs Dijkstra algorithm from the given source node.
  1140 
  1141     ///This method runs %Dijkstra algorithm from the given source node
  1142     ///in order to compute the shortest path to each node.
  1143     void run(Node s)
  1144     {
  1145       Dijkstra<Digraph,LengthMap,TR>
  1146         dijk(*reinterpret_cast<const Digraph*>(Base::_g),
  1147              *reinterpret_cast<const LengthMap*>(Base::_length));
  1148       if (Base::_pred)
  1149         dijk.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
  1150       if (Base::_dist)
  1151         dijk.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
  1152       if (Base::_processed)
  1153         dijk.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
  1154       dijk.run(s);
  1155     }
  1156 
  1157     ///Finds the shortest path between \c s and \c t.
  1158 
  1159     ///This method runs the %Dijkstra algorithm from node \c s
  1160     ///in order to compute the shortest path to node \c t
  1161     ///(it stops searching when \c t is processed).
  1162     ///
  1163     ///\return \c true if \c t is reachable form \c s.
  1164     bool run(Node s, Node t)
  1165     {
  1166       Dijkstra<Digraph,LengthMap,TR>
  1167         dijk(*reinterpret_cast<const Digraph*>(Base::_g),
  1168              *reinterpret_cast<const LengthMap*>(Base::_length));
  1169       if (Base::_pred)
  1170         dijk.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
  1171       if (Base::_dist)
  1172         dijk.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
  1173       if (Base::_processed)
  1174         dijk.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
  1175       dijk.run(s,t);
  1176       if (Base::_path)
  1177         *reinterpret_cast<Path*>(Base::_path) = dijk.path(t);
  1178       if (Base::_di)
  1179         *reinterpret_cast<Value*>(Base::_di) = dijk.dist(t);
  1180       return dijk.reached(t);
  1181     }
  1182 
  1183     template<class T>
  1184     struct SetPredMapBase : public Base {
  1185       typedef T PredMap;
  1186       static PredMap *createPredMap(const Digraph &) { return 0; };
  1187       SetPredMapBase(const TR &b) : TR(b) {}
  1188     };
  1189     ///\brief \ref named-func-param "Named parameter"
  1190     ///for setting PredMap object.
  1191     ///
  1192     ///\ref named-func-param "Named parameter"
  1193     ///for setting PredMap object.
  1194     template<class T>
  1195     DijkstraWizard<SetPredMapBase<T> > predMap(const T &t)
  1196     {
  1197       Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
  1198       return DijkstraWizard<SetPredMapBase<T> >(*this);
  1199     }
  1200 
  1201     template<class T>
  1202     struct SetDistMapBase : public Base {
  1203       typedef T DistMap;
  1204       static DistMap *createDistMap(const Digraph &) { return 0; };
  1205       SetDistMapBase(const TR &b) : TR(b) {}
  1206     };
  1207     ///\brief \ref named-func-param "Named parameter"
  1208     ///for setting DistMap object.
  1209     ///
  1210     ///\ref named-func-param "Named parameter"
  1211     ///for setting DistMap object.
  1212     template<class T>
  1213     DijkstraWizard<SetDistMapBase<T> > distMap(const T &t)
  1214     {
  1215       Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
  1216       return DijkstraWizard<SetDistMapBase<T> >(*this);
  1217     }
  1218 
  1219     template<class T>
  1220     struct SetProcessedMapBase : public Base {
  1221       typedef T ProcessedMap;
  1222       static ProcessedMap *createProcessedMap(const Digraph &) { return 0; };
  1223       SetProcessedMapBase(const TR &b) : TR(b) {}
  1224     };
  1225     ///\brief \ref named-func-param "Named parameter"
  1226     ///for setting ProcessedMap object.
  1227     ///
  1228     /// \ref named-func-param "Named parameter"
  1229     ///for setting ProcessedMap object.
  1230     template<class T>
  1231     DijkstraWizard<SetProcessedMapBase<T> > processedMap(const T &t)
  1232     {
  1233       Base::_processed=reinterpret_cast<void*>(const_cast<T*>(&t));
  1234       return DijkstraWizard<SetProcessedMapBase<T> >(*this);
  1235     }
  1236 
  1237     template<class T>
  1238     struct SetPathBase : public Base {
  1239       typedef T Path;
  1240       SetPathBase(const TR &b) : TR(b) {}
  1241     };
  1242     ///\brief \ref named-func-param "Named parameter"
  1243     ///for getting the shortest path to the target node.
  1244     ///
  1245     ///\ref named-func-param "Named parameter"
  1246     ///for getting the shortest path to the target node.
  1247     template<class T>
  1248     DijkstraWizard<SetPathBase<T> > path(const T &t)
  1249     {
  1250       Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t));
  1251       return DijkstraWizard<SetPathBase<T> >(*this);
  1252     }
  1253 
  1254     ///\brief \ref named-func-param "Named parameter"
  1255     ///for getting the distance of the target node.
  1256     ///
  1257     ///\ref named-func-param "Named parameter"
  1258     ///for getting the distance of the target node.
  1259     DijkstraWizard dist(const Value &d)
  1260     {
  1261       Base::_di=reinterpret_cast<void*>(const_cast<Value*>(&d));
  1262       return *this;
  1263     }
  1264 
  1265   };
  1266 
  1267   ///Function-type interface for Dijkstra algorithm.
  1268 
  1269   /// \ingroup shortest_path
  1270   ///Function-type interface for Dijkstra algorithm.
  1271   ///
  1272   ///This function also has several \ref named-func-param "named parameters",
  1273   ///they are declared as the members of class \ref DijkstraWizard.
  1274   ///The following examples show how to use these parameters.
  1275   ///\code
  1276   ///  // Compute shortest path from node s to each node
  1277   ///  dijkstra(g,length).predMap(preds).distMap(dists).run(s);
  1278   ///
  1279   ///  // Compute shortest path from s to t
  1280   ///  bool reached = dijkstra(g,length).path(p).dist(d).run(s,t);
  1281   ///\endcode
  1282   ///\warning Don't forget to put the \ref DijkstraWizard::run(Node) "run()"
  1283   ///to the end of the parameter list.
  1284   ///\sa DijkstraWizard
  1285   ///\sa Dijkstra
  1286   template<typename GR, typename LEN>
  1287   DijkstraWizard<DijkstraWizardBase<GR,LEN> >
  1288   dijkstra(const GR &digraph, const LEN &length)
  1289   {
  1290     return DijkstraWizard<DijkstraWizardBase<GR,LEN> >(digraph,length);
  1291   }
  1292 
  1293 } //END OF NAMESPACE LEMON
  1294 
  1295 #endif