lemon/dijkstra.h
author Akos Ladanyi <ladanyi@tmit.bme.hu>
Wed, 30 Jul 2008 12:07:29 +0100
changeset 245 da1d220b176b
parent 210 81cfc04531e8
child 247 f1158744a112
permissions -rw-r--r--
Update INSTALL file.
     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) 2003-2008
     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 
    34 namespace lemon {
    35 
    36   /// \brief Default OperationTraits for the Dijkstra algorithm class.
    37   ///
    38   /// It defines all computational operations and constants which are
    39   /// used in the Dijkstra algorithm.
    40   template <typename Value>
    41   struct DijkstraDefaultOperationTraits {
    42     /// \brief Gives back the zero value of the type.
    43     static Value zero() {
    44       return static_cast<Value>(0);
    45     }
    46     /// \brief Gives back the sum of the given two elements.
    47     static Value plus(const Value& left, const Value& right) {
    48       return left + right;
    49     }
    50     /// \brief Gives back true only if the first value less than the second.
    51     static bool less(const Value& left, const Value& right) {
    52       return left < right;
    53     }
    54   };
    55 
    56   /// \brief Widest path OperationTraits for the Dijkstra algorithm class.
    57   ///
    58   /// It defines all computational operations and constants which are
    59   /// used in the Dijkstra algorithm for widest path computation.
    60   template <typename Value>
    61   struct DijkstraWidestPathOperationTraits {
    62     /// \brief Gives back the maximum value of the type.
    63     static Value zero() {
    64       return std::numeric_limits<Value>::max();
    65     }
    66     /// \brief Gives back the minimum of the given two elements.
    67     static Value plus(const Value& left, const Value& right) {
    68       return std::min(left, right);
    69     }
    70     /// \brief Gives back true only if the first value less than the second.
    71     static bool less(const Value& left, const Value& right) {
    72       return left < right;
    73     }
    74   };
    75 
    76   ///Default traits class of Dijkstra class.
    77 
    78   ///Default traits class of Dijkstra class.
    79   ///\tparam GR Digraph type.
    80   ///\tparam LM Type of length map.
    81   template<class GR, class LM>
    82   struct DijkstraDefaultTraits
    83   {
    84     ///The digraph type the algorithm runs on.
    85     typedef GR Digraph;
    86     ///The type of the map that stores the arc lengths.
    87 
    88     ///The type of the map that stores the arc lengths.
    89     ///It must meet the \ref concepts::ReadMap "ReadMap" concept.
    90     typedef LM LengthMap;
    91     //The type of the length of the arcs.
    92     typedef typename LM::Value Value;
    93     /// Operation traits for Dijkstra algorithm.
    94 
    95     /// It defines the used operation by the algorithm.
    96     /// \see DijkstraDefaultOperationTraits
    97     typedef DijkstraDefaultOperationTraits<Value> OperationTraits;
    98     /// The cross reference type used by heap.
    99 
   100 
   101     /// The cross reference type used by heap.
   102     /// Usually it is \c Digraph::NodeMap<int>.
   103     typedef typename Digraph::template NodeMap<int> HeapCrossRef;
   104     ///Instantiates a HeapCrossRef.
   105 
   106     ///This function instantiates a \c HeapCrossRef.
   107     /// \param G is the digraph, to which we would like to define the
   108     /// HeapCrossRef.
   109     static HeapCrossRef *createHeapCrossRef(const GR &G)
   110     {
   111       return new HeapCrossRef(G);
   112     }
   113 
   114     ///The heap type used by Dijkstra algorithm.
   115 
   116     ///The heap type used by Dijkstra algorithm.
   117     ///
   118     ///\sa BinHeap
   119     ///\sa Dijkstra
   120     typedef BinHeap<typename LM::Value, HeapCrossRef, std::less<Value> > Heap;
   121 
   122     static Heap *createHeap(HeapCrossRef& R)
   123     {
   124       return new Heap(R);
   125     }
   126 
   127     ///\brief The type of the map that stores the last
   128     ///arcs of the shortest paths.
   129     ///
   130     ///The type of the map that stores the last
   131     ///arcs of the shortest paths.
   132     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   133     ///
   134     typedef typename Digraph::template NodeMap<typename GR::Arc> PredMap;
   135     ///Instantiates a PredMap.
   136 
   137     ///This function instantiates a \c PredMap.
   138     ///\param G is the digraph, to which we would like to define the PredMap.
   139     ///\todo The digraph alone may be insufficient for the initialization
   140     static PredMap *createPredMap(const GR &G)
   141     {
   142       return new PredMap(G);
   143     }
   144 
   145     ///The type of the map that stores whether a nodes is processed.
   146 
   147     ///The type of the map that stores whether a nodes is processed.
   148     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   149     ///By default it is a NullMap.
   150     ///\todo If it is set to a real map,
   151     ///Dijkstra::processed() should read this.
   152     ///\todo named parameter to set this type, function to read and write.
   153     typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
   154     ///Instantiates a ProcessedMap.
   155 
   156     ///This function instantiates a \c ProcessedMap.
   157     ///\param g is the digraph, to which
   158     ///we would like to define the \c ProcessedMap
   159 #ifdef DOXYGEN
   160     static ProcessedMap *createProcessedMap(const GR &g)
   161 #else
   162     static ProcessedMap *createProcessedMap(const GR &)
   163 #endif
   164     {
   165       return new ProcessedMap();
   166     }
   167     ///The type of the map that stores the dists of the nodes.
   168 
   169     ///The type of the map that stores the dists of the nodes.
   170     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   171     ///
   172     typedef typename Digraph::template NodeMap<typename LM::Value> DistMap;
   173     ///Instantiates a DistMap.
   174 
   175     ///This function instantiates a \ref DistMap.
   176     ///\param G is the digraph, to which we would like to define
   177     ///the \ref DistMap
   178     static DistMap *createDistMap(const GR &G)
   179     {
   180       return new DistMap(G);
   181     }
   182   };
   183 
   184   ///%Dijkstra algorithm class.
   185 
   186   /// \ingroup shortest_path
   187   ///This class provides an efficient implementation of %Dijkstra algorithm.
   188   ///The arc lengths are passed to the algorithm using a
   189   ///\ref concepts::ReadMap "ReadMap",
   190   ///so it is easy to change it to any kind of length.
   191   ///
   192   ///The type of the length is determined by the
   193   ///\ref concepts::ReadMap::Value "Value" of the length map.
   194   ///
   195   ///It is also possible to change the underlying priority heap.
   196   ///
   197   ///\tparam GR The digraph type the algorithm runs on. The default value
   198   ///is \ref ListDigraph. The value of GR is not used directly by
   199   ///Dijkstra, it is only passed to \ref DijkstraDefaultTraits.
   200   ///\tparam LM This read-only ArcMap determines the lengths of the
   201   ///arcs. It is read once for each arc, so the map may involve in
   202   ///relatively time consuming process to compute the arc length if
   203   ///it is necessary. The default map type is \ref
   204   ///concepts::Digraph::ArcMap "Digraph::ArcMap<int>".  The value
   205   ///of LM is not used directly by Dijkstra, it is only passed to \ref
   206   ///DijkstraDefaultTraits.
   207   ///\tparam TR Traits class to set
   208   ///various data types used by the algorithm.  The default traits
   209   ///class is \ref DijkstraDefaultTraits
   210   ///"DijkstraDefaultTraits<GR,LM>".  See \ref
   211   ///DijkstraDefaultTraits for the documentation of a Dijkstra traits
   212   ///class.
   213 
   214 #ifdef DOXYGEN
   215   template <typename GR, typename LM, typename TR>
   216 #else
   217   template <typename GR=ListDigraph,
   218             typename LM=typename GR::template ArcMap<int>,
   219             typename TR=DijkstraDefaultTraits<GR,LM> >
   220 #endif
   221   class Dijkstra {
   222   public:
   223     /**
   224      * \brief \ref Exception for uninitialized parameters.
   225      *
   226      * This error represents problems in the initialization
   227      * of the parameters of the algorithms.
   228      */
   229     class UninitializedParameter : public lemon::UninitializedParameter {
   230     public:
   231       virtual const char* what() const throw() {
   232         return "lemon::Dijkstra::UninitializedParameter";
   233       }
   234     };
   235 
   236     typedef TR Traits;
   237     ///The type of the underlying digraph.
   238     typedef typename TR::Digraph Digraph;
   239     ///\e
   240     typedef typename Digraph::Node Node;
   241     ///\e
   242     typedef typename Digraph::NodeIt NodeIt;
   243     ///\e
   244     typedef typename Digraph::Arc Arc;
   245     ///\e
   246     typedef typename Digraph::OutArcIt OutArcIt;
   247 
   248     ///The type of the length of the arcs.
   249     typedef typename TR::LengthMap::Value Value;
   250     ///The type of the map that stores the arc lengths.
   251     typedef typename TR::LengthMap LengthMap;
   252     ///\brief The type of the map that stores the last
   253     ///arcs of the shortest paths.
   254     typedef typename TR::PredMap PredMap;
   255     ///The type of the map indicating if a node is processed.
   256     typedef typename TR::ProcessedMap ProcessedMap;
   257     ///The type of the map that stores the dists of the nodes.
   258     typedef typename TR::DistMap DistMap;
   259     ///The cross reference type used for the current heap.
   260     typedef typename TR::HeapCrossRef HeapCrossRef;
   261     ///The heap type used by the dijkstra algorithm.
   262     typedef typename TR::Heap Heap;
   263     ///The operation traits.
   264     typedef typename TR::OperationTraits OperationTraits;
   265   private:
   266     /// Pointer to the underlying digraph.
   267     const Digraph *G;
   268     /// Pointer to the length map
   269     const LengthMap *length;
   270     ///Pointer to the map of predecessors arcs.
   271     PredMap *_pred;
   272     ///Indicates if \ref _pred is locally allocated (\c true) or not.
   273     bool local_pred;
   274     ///Pointer to the map of distances.
   275     DistMap *_dist;
   276     ///Indicates if \ref _dist is locally allocated (\c true) or not.
   277     bool local_dist;
   278     ///Pointer to the map of processed status of the nodes.
   279     ProcessedMap *_processed;
   280     ///Indicates if \ref _processed is locally allocated (\c true) or not.
   281     bool local_processed;
   282     ///Pointer to the heap cross references.
   283     HeapCrossRef *_heap_cross_ref;
   284     ///Indicates if \ref _heap_cross_ref is locally allocated (\c true) or not.
   285     bool local_heap_cross_ref;
   286     ///Pointer to the heap.
   287     Heap *_heap;
   288     ///Indicates if \ref _heap is locally allocated (\c true) or not.
   289     bool local_heap;
   290 
   291     ///Creates the maps if necessary.
   292 
   293     ///\todo Better memory allocation (instead of new).
   294     void create_maps()
   295     {
   296       if(!_pred) {
   297         local_pred = true;
   298         _pred = Traits::createPredMap(*G);
   299       }
   300       if(!_dist) {
   301         local_dist = true;
   302         _dist = Traits::createDistMap(*G);
   303       }
   304       if(!_processed) {
   305         local_processed = true;
   306         _processed = Traits::createProcessedMap(*G);
   307       }
   308       if (!_heap_cross_ref) {
   309         local_heap_cross_ref = true;
   310         _heap_cross_ref = Traits::createHeapCrossRef(*G);
   311       }
   312       if (!_heap) {
   313         local_heap = true;
   314         _heap = Traits::createHeap(*_heap_cross_ref);
   315       }
   316     }
   317 
   318   public :
   319 
   320     typedef Dijkstra Create;
   321 
   322     ///\name Named template parameters
   323 
   324     ///@{
   325 
   326     template <class T>
   327     struct DefPredMapTraits : public Traits {
   328       typedef T PredMap;
   329       static PredMap *createPredMap(const Digraph &)
   330       {
   331         throw UninitializedParameter();
   332       }
   333     };
   334     ///\ref named-templ-param "Named parameter" for setting PredMap type
   335 
   336     ///\ref named-templ-param "Named parameter" for setting PredMap type
   337     ///
   338     template <class T>
   339     struct DefPredMap
   340       : public Dijkstra< Digraph, LengthMap, DefPredMapTraits<T> > {
   341       typedef Dijkstra< Digraph, LengthMap, DefPredMapTraits<T> > Create;
   342     };
   343 
   344     template <class T>
   345     struct DefDistMapTraits : public Traits {
   346       typedef T DistMap;
   347       static DistMap *createDistMap(const Digraph &)
   348       {
   349         throw UninitializedParameter();
   350       }
   351     };
   352     ///\ref named-templ-param "Named parameter" for setting DistMap type
   353 
   354     ///\ref named-templ-param "Named parameter" for setting DistMap type
   355     ///
   356     template <class T>
   357     struct DefDistMap
   358       : public Dijkstra< Digraph, LengthMap, DefDistMapTraits<T> > {
   359       typedef Dijkstra< Digraph, LengthMap, DefDistMapTraits<T> > Create;
   360     };
   361 
   362     template <class T>
   363     struct DefProcessedMapTraits : public Traits {
   364       typedef T ProcessedMap;
   365       static ProcessedMap *createProcessedMap(const Digraph &G)
   366       {
   367         throw UninitializedParameter();
   368       }
   369     };
   370     ///\ref named-templ-param "Named parameter" for setting ProcessedMap type
   371 
   372     ///\ref named-templ-param "Named parameter" for setting ProcessedMap type
   373     ///
   374     template <class T>
   375     struct DefProcessedMap
   376       : public Dijkstra< Digraph, LengthMap, DefProcessedMapTraits<T> > {
   377       typedef Dijkstra< Digraph, LengthMap, DefProcessedMapTraits<T> > Create;
   378     };
   379 
   380     struct DefDigraphProcessedMapTraits : public Traits {
   381       typedef typename Digraph::template NodeMap<bool> ProcessedMap;
   382       static ProcessedMap *createProcessedMap(const Digraph &G)
   383       {
   384         return new ProcessedMap(G);
   385       }
   386     };
   387     ///\brief \ref named-templ-param "Named parameter"
   388     ///for setting the ProcessedMap type to be Digraph::NodeMap<bool>.
   389     ///
   390     ///\ref named-templ-param "Named parameter"
   391     ///for setting the ProcessedMap type to be Digraph::NodeMap<bool>.
   392     ///If you don't set it explicitely, it will be automatically allocated.
   393     template <class T>
   394     struct DefProcessedMapToBeDefaultMap
   395       : public Dijkstra< Digraph, LengthMap, DefDigraphProcessedMapTraits> {
   396       typedef Dijkstra< Digraph, LengthMap, DefDigraphProcessedMapTraits>
   397       Create;
   398     };
   399 
   400     template <class H, class CR>
   401     struct DefHeapTraits : public Traits {
   402       typedef CR HeapCrossRef;
   403       typedef H Heap;
   404       static HeapCrossRef *createHeapCrossRef(const Digraph &) {
   405         throw UninitializedParameter();
   406       }
   407       static Heap *createHeap(HeapCrossRef &)
   408       {
   409         throw UninitializedParameter();
   410       }
   411     };
   412     ///\brief \ref named-templ-param "Named parameter" for setting
   413     ///heap and cross reference type
   414     ///
   415     ///\ref named-templ-param "Named parameter" for setting heap and cross
   416     ///reference type
   417     ///
   418     template <class H, class CR = typename Digraph::template NodeMap<int> >
   419     struct DefHeap
   420       : public Dijkstra< Digraph, LengthMap, DefHeapTraits<H, CR> > {
   421       typedef Dijkstra< Digraph, LengthMap, DefHeapTraits<H, CR> > Create;
   422     };
   423 
   424     template <class H, class CR>
   425     struct DefStandardHeapTraits : public Traits {
   426       typedef CR HeapCrossRef;
   427       typedef H Heap;
   428       static HeapCrossRef *createHeapCrossRef(const Digraph &G) {
   429         return new HeapCrossRef(G);
   430       }
   431       static Heap *createHeap(HeapCrossRef &R)
   432       {
   433         return new Heap(R);
   434       }
   435     };
   436     ///\brief \ref named-templ-param "Named parameter" for setting
   437     ///heap and cross reference type with automatic allocation
   438     ///
   439     ///\ref named-templ-param "Named parameter" for setting heap and cross
   440     ///reference type. It can allocate the heap and the cross reference
   441     ///object if the cross reference's constructor waits for the digraph as
   442     ///parameter and the heap's constructor waits for the cross reference.
   443     template <class H, class CR = typename Digraph::template NodeMap<int> >
   444     struct DefStandardHeap
   445       : public Dijkstra< Digraph, LengthMap, DefStandardHeapTraits<H, CR> > {
   446       typedef Dijkstra< Digraph, LengthMap, DefStandardHeapTraits<H, CR> >
   447       Create;
   448     };
   449 
   450     template <class T>
   451     struct DefOperationTraitsTraits : public Traits {
   452       typedef T OperationTraits;
   453     };
   454 
   455     /// \brief \ref named-templ-param "Named parameter" for setting
   456     /// OperationTraits type
   457     ///
   458     /// \ref named-templ-param "Named parameter" for setting OperationTraits
   459     /// type
   460     template <class T>
   461     struct DefOperationTraits
   462       : public Dijkstra<Digraph, LengthMap, DefOperationTraitsTraits<T> > {
   463       typedef Dijkstra<Digraph, LengthMap, DefOperationTraitsTraits<T> >
   464       Create;
   465     };
   466 
   467     ///@}
   468 
   469 
   470   protected:
   471 
   472     Dijkstra() {}
   473 
   474   public:
   475 
   476     ///Constructor.
   477 
   478     ///\param _G the digraph the algorithm will run on.
   479     ///\param _length the length map used by the algorithm.
   480     Dijkstra(const Digraph& _G, const LengthMap& _length) :
   481       G(&_G), length(&_length),
   482       _pred(NULL), local_pred(false),
   483       _dist(NULL), local_dist(false),
   484       _processed(NULL), local_processed(false),
   485       _heap_cross_ref(NULL), local_heap_cross_ref(false),
   486       _heap(NULL), local_heap(false)
   487     { }
   488 
   489     ///Destructor.
   490     ~Dijkstra()
   491     {
   492       if(local_pred) delete _pred;
   493       if(local_dist) delete _dist;
   494       if(local_processed) delete _processed;
   495       if(local_heap_cross_ref) delete _heap_cross_ref;
   496       if(local_heap) delete _heap;
   497     }
   498 
   499     ///Sets the length map.
   500 
   501     ///Sets the length map.
   502     ///\return <tt> (*this) </tt>
   503     Dijkstra &lengthMap(const LengthMap &m)
   504     {
   505       length = &m;
   506       return *this;
   507     }
   508 
   509     ///Sets the map storing the predecessor arcs.
   510 
   511     ///Sets the map storing the predecessor arcs.
   512     ///If you don't use this function before calling \ref run(),
   513     ///it will allocate one. The destuctor deallocates this
   514     ///automatically allocated map, of course.
   515     ///\return <tt> (*this) </tt>
   516     Dijkstra &predMap(PredMap &m)
   517     {
   518       if(local_pred) {
   519         delete _pred;
   520         local_pred=false;
   521       }
   522       _pred = &m;
   523       return *this;
   524     }
   525 
   526     ///Sets the map storing the distances calculated by the algorithm.
   527 
   528     ///Sets the map storing the distances calculated by the algorithm.
   529     ///If you don't use this function before calling \ref run(),
   530     ///it will allocate one. The destuctor deallocates this
   531     ///automatically allocated map, of course.
   532     ///\return <tt> (*this) </tt>
   533     Dijkstra &distMap(DistMap &m)
   534     {
   535       if(local_dist) {
   536         delete _dist;
   537         local_dist=false;
   538       }
   539       _dist = &m;
   540       return *this;
   541     }
   542 
   543     ///Sets the heap and the cross reference used by algorithm.
   544 
   545     ///Sets the heap and the cross reference used by algorithm.
   546     ///If you don't use this function before calling \ref run(),
   547     ///it will allocate one. The destuctor deallocates this
   548     ///automatically allocated heap and cross reference, of course.
   549     ///\return <tt> (*this) </tt>
   550     Dijkstra &heap(Heap& hp, HeapCrossRef &cr)
   551     {
   552       if(local_heap_cross_ref) {
   553         delete _heap_cross_ref;
   554         local_heap_cross_ref=false;
   555       }
   556       _heap_cross_ref = &cr;
   557       if(local_heap) {
   558         delete _heap;
   559         local_heap=false;
   560       }
   561       _heap = &hp;
   562       return *this;
   563     }
   564 
   565   private:
   566     void finalizeNodeData(Node v,Value dst)
   567     {
   568       _processed->set(v,true);
   569       _dist->set(v, dst);
   570     }
   571 
   572   public:
   573 
   574     typedef PredMapPath<Digraph, PredMap> Path;
   575 
   576     ///\name Execution control
   577     ///The simplest way to execute the algorithm is to use
   578     ///one of the member functions called \c run(...).
   579     ///\n
   580     ///If you need more control on the execution,
   581     ///first you must call \ref init(), then you can add several source nodes
   582     ///with \ref addSource().
   583     ///Finally \ref start() will perform the actual path
   584     ///computation.
   585 
   586     ///@{
   587 
   588     ///Initializes the internal data structures.
   589 
   590     ///Initializes the internal data structures.
   591     ///
   592     void init()
   593     {
   594       create_maps();
   595       _heap->clear();
   596       for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
   597         _pred->set(u,INVALID);
   598         _processed->set(u,false);
   599         _heap_cross_ref->set(u,Heap::PRE_HEAP);
   600       }
   601     }
   602 
   603     ///Adds a new source node.
   604 
   605     ///Adds a new source node to the priority heap.
   606     ///
   607     ///The optional second parameter is the initial distance of the node.
   608     ///
   609     ///It checks if the node has already been added to the heap and
   610     ///it is pushed to the heap only if either it was not in the heap
   611     ///or the shortest path found till then is shorter than \c dst.
   612     void addSource(Node s,Value dst=OperationTraits::zero())
   613     {
   614       if(_heap->state(s) != Heap::IN_HEAP) {
   615         _heap->push(s,dst);
   616       } else if(OperationTraits::less((*_heap)[s], dst)) {
   617         _heap->set(s,dst);
   618         _pred->set(s,INVALID);
   619       }
   620     }
   621 
   622     ///Processes the next node in the priority heap
   623 
   624     ///Processes the next node in the priority heap.
   625     ///
   626     ///\return The processed node.
   627     ///
   628     ///\warning The priority heap must not be empty!
   629     Node processNextNode()
   630     {
   631       Node v=_heap->top();
   632       Value oldvalue=_heap->prio();
   633       _heap->pop();
   634       finalizeNodeData(v,oldvalue);
   635 
   636       for(OutArcIt e(*G,v); e!=INVALID; ++e) {
   637         Node w=G->target(e);
   638         switch(_heap->state(w)) {
   639         case Heap::PRE_HEAP:
   640           _heap->push(w,OperationTraits::plus(oldvalue, (*length)[e]));
   641           _pred->set(w,e);
   642           break;
   643         case Heap::IN_HEAP:
   644           {
   645             Value newvalue = OperationTraits::plus(oldvalue, (*length)[e]);
   646             if ( OperationTraits::less(newvalue, (*_heap)[w]) ) {
   647               _heap->decrease(w, newvalue);
   648               _pred->set(w,e);
   649             }
   650           }
   651           break;
   652         case Heap::POST_HEAP:
   653           break;
   654         }
   655       }
   656       return v;
   657     }
   658 
   659     ///Next node to be processed.
   660 
   661     ///Next node to be processed.
   662     ///
   663     ///\return The next node to be processed or INVALID if the priority heap
   664     /// is empty.
   665     Node nextNode()
   666     {
   667       return !_heap->empty()?_heap->top():INVALID;
   668     }
   669 
   670     ///\brief Returns \c false if there are nodes
   671     ///to be processed in the priority heap
   672     ///
   673     ///Returns \c false if there are nodes
   674     ///to be processed in the priority heap
   675     bool emptyQueue() { return _heap->empty(); }
   676     ///Returns the number of the nodes to be processed in the priority heap
   677 
   678     ///Returns the number of the nodes to be processed in the priority heap
   679     ///
   680     int queueSize() { return _heap->size(); }
   681 
   682     ///Executes the algorithm.
   683 
   684     ///Executes the algorithm.
   685     ///
   686     ///\pre init() must be called and at least one node should be added
   687     ///with addSource() before using this function.
   688     ///
   689     ///This method runs the %Dijkstra algorithm from the root node(s)
   690     ///in order to
   691     ///compute the
   692     ///shortest path to each node. The algorithm computes
   693     ///- The shortest path tree.
   694     ///- The distance of each node from the root(s).
   695     ///
   696     void start()
   697     {
   698       while ( !_heap->empty() ) processNextNode();
   699     }
   700 
   701     ///Executes the algorithm until \c dest is reached.
   702 
   703     ///Executes the algorithm until \c dest is reached.
   704     ///
   705     ///\pre init() must be called and at least one node should be added
   706     ///with addSource() before using this function.
   707     ///
   708     ///This method runs the %Dijkstra algorithm from the root node(s)
   709     ///in order to
   710     ///compute the
   711     ///shortest path to \c dest. The algorithm computes
   712     ///- The shortest path to \c  dest.
   713     ///- The distance of \c dest from the root(s).
   714     ///
   715     void start(Node dest)
   716     {
   717       while ( !_heap->empty() && _heap->top()!=dest ) processNextNode();
   718       if ( !_heap->empty() ) finalizeNodeData(_heap->top(),_heap->prio());
   719     }
   720 
   721     ///Executes the algorithm until a condition is met.
   722 
   723     ///Executes the algorithm until a condition is met.
   724     ///
   725     ///\pre init() must be called and at least one node should be added
   726     ///with addSource() before using this function.
   727     ///
   728     ///\param nm must be a bool (or convertible) node map. The algorithm
   729     ///will stop when it reaches a node \c v with <tt>nm[v]</tt> true.
   730     ///
   731     ///\return The reached node \c v with <tt>nm[v]</tt> true or
   732     ///\c INVALID if no such node was found.
   733     template<class NodeBoolMap>
   734     Node start(const NodeBoolMap &nm)
   735     {
   736       while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode();
   737       if ( _heap->empty() ) return INVALID;
   738       finalizeNodeData(_heap->top(),_heap->prio());
   739       return _heap->top();
   740     }
   741 
   742     ///Runs %Dijkstra algorithm from node \c s.
   743 
   744     ///This method runs the %Dijkstra algorithm from a root node \c s
   745     ///in order to
   746     ///compute the
   747     ///shortest path to each node. The algorithm computes
   748     ///- The shortest path tree.
   749     ///- The distance of each node from the root.
   750     ///
   751     ///\note d.run(s) is just a shortcut of the following code.
   752     ///\code
   753     ///  d.init();
   754     ///  d.addSource(s);
   755     ///  d.start();
   756     ///\endcode
   757     void run(Node s) {
   758       init();
   759       addSource(s);
   760       start();
   761     }
   762 
   763     ///Finds the shortest path between \c s and \c t.
   764 
   765     ///Finds the shortest path between \c s and \c t.
   766     ///
   767     ///\return The length of the shortest s---t path if there exists one,
   768     ///0 otherwise.
   769     ///\note Apart from the return value, d.run(s) is
   770     ///just a shortcut of the following code.
   771     ///\code
   772     ///  d.init();
   773     ///  d.addSource(s);
   774     ///  d.start(t);
   775     ///\endcode
   776     Value run(Node s,Node t) {
   777       init();
   778       addSource(s);
   779       start(t);
   780       return (*_pred)[t]==INVALID?OperationTraits::zero():(*_dist)[t];
   781     }
   782 
   783     ///@}
   784 
   785     ///\name Query Functions
   786     ///The result of the %Dijkstra algorithm can be obtained using these
   787     ///functions.\n
   788     ///Before the use of these functions,
   789     ///either run() or start() must be called.
   790 
   791     ///@{
   792 
   793     ///Gives back the shortest path.
   794 
   795     ///Gives back the shortest path.
   796     ///\pre The \c t should be reachable from the source.
   797     Path path(Node t)
   798     {
   799       return Path(*G, *_pred, t);
   800     }
   801 
   802     ///The distance of a node from the root.
   803 
   804     ///Returns the distance of a node from the root.
   805     ///\pre \ref run() must be called before using this function.
   806     ///\warning If node \c v in unreachable from the root the return value
   807     ///of this funcion is undefined.
   808     Value dist(Node v) const { return (*_dist)[v]; }
   809 
   810     ///The current distance of a node from the root.
   811 
   812     ///Returns the current distance of a node from the root.
   813     ///It may be decreased in the following processes.
   814     ///\pre \c node should be reached but not processed
   815     Value currentDist(Node v) const { return (*_heap)[v]; }
   816 
   817     ///Returns the 'previous arc' of the shortest path tree.
   818 
   819     ///For a node \c v it returns the 'previous arc' of the shortest path tree,
   820     ///i.e. it returns the last arc of a shortest path from the root to \c
   821     ///v. It is \ref INVALID
   822     ///if \c v is unreachable from the root or if \c v=s. The
   823     ///shortest path tree used here is equal to the shortest path tree used in
   824     ///\ref predNode().  \pre \ref run() must be called before using
   825     ///this function.
   826     Arc predArc(Node v) const { return (*_pred)[v]; }
   827 
   828     ///Returns the 'previous node' of the shortest path tree.
   829 
   830     ///For a node \c v it returns the 'previous node' of the shortest path tree,
   831     ///i.e. it returns the last but one node from a shortest path from the
   832     ///root to \c /v. It is INVALID if \c v is unreachable from the root or if
   833     ///\c v=s. The shortest path tree used here is equal to the shortest path
   834     ///tree used in \ref predArc().  \pre \ref run() must be called before
   835     ///using this function.
   836     Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
   837                                   G->source((*_pred)[v]); }
   838 
   839     ///Returns a reference to the NodeMap of distances.
   840 
   841     ///Returns a reference to the NodeMap of distances. \pre \ref run() must
   842     ///be called before using this function.
   843     const DistMap &distMap() const { return *_dist;}
   844 
   845     ///Returns a reference to the shortest path tree map.
   846 
   847     ///Returns a reference to the NodeMap of the arcs of the
   848     ///shortest path tree.
   849     ///\pre \ref run() must be called before using this function.
   850     const PredMap &predMap() const { return *_pred;}
   851 
   852     ///Checks if a node is reachable from the root.
   853 
   854     ///Returns \c true if \c v is reachable from the root.
   855     ///\warning The source nodes are inditated as unreached.
   856     ///\pre \ref run() must be called before using this function.
   857     ///
   858     bool reached(Node v) { return (*_heap_cross_ref)[v] != Heap::PRE_HEAP; }
   859 
   860     ///Checks if a node is processed.
   861 
   862     ///Returns \c true if \c v is processed, i.e. the shortest
   863     ///path to \c v has already found.
   864     ///\pre \ref run() must be called before using this function.
   865     ///
   866     bool processed(Node v) { return (*_heap_cross_ref)[v] == Heap::POST_HEAP; }
   867 
   868     ///@}
   869   };
   870 
   871 
   872 
   873 
   874 
   875   ///Default traits class of Dijkstra function.
   876 
   877   ///Default traits class of Dijkstra function.
   878   ///\tparam GR Digraph type.
   879   ///\tparam LM Type of length map.
   880   template<class GR, class LM>
   881   struct DijkstraWizardDefaultTraits
   882   {
   883     ///The digraph type the algorithm runs on.
   884     typedef GR Digraph;
   885     ///The type of the map that stores the arc lengths.
   886 
   887     ///The type of the map that stores the arc lengths.
   888     ///It must meet the \ref concepts::ReadMap "ReadMap" concept.
   889     typedef LM LengthMap;
   890     //The type of the length of the arcs.
   891     typedef typename LM::Value Value;
   892     /// Operation traits for Dijkstra algorithm.
   893 
   894     /// It defines the used operation by the algorithm.
   895     /// \see DijkstraDefaultOperationTraits
   896     typedef DijkstraDefaultOperationTraits<Value> OperationTraits;
   897     ///The heap type used by Dijkstra algorithm.
   898 
   899     /// The cross reference type used by heap.
   900 
   901     /// The cross reference type used by heap.
   902     /// Usually it is \c Digraph::NodeMap<int>.
   903     typedef typename Digraph::template NodeMap<int> HeapCrossRef;
   904     ///Instantiates a HeapCrossRef.
   905 
   906     ///This function instantiates a \ref HeapCrossRef.
   907     /// \param G is the digraph, to which we would like to define the
   908     /// HeapCrossRef.
   909     /// \todo The digraph alone may be insufficient for the initialization
   910     static HeapCrossRef *createHeapCrossRef(const GR &G)
   911     {
   912       return new HeapCrossRef(G);
   913     }
   914 
   915     ///The heap type used by Dijkstra algorithm.
   916 
   917     ///The heap type used by Dijkstra algorithm.
   918     ///
   919     ///\sa BinHeap
   920     ///\sa Dijkstra
   921     typedef BinHeap<typename LM::Value, typename GR::template NodeMap<int>,
   922                     std::less<Value> > Heap;
   923 
   924     static Heap *createHeap(HeapCrossRef& R)
   925     {
   926       return new Heap(R);
   927     }
   928 
   929     ///\brief The type of the map that stores the last
   930     ///arcs of the shortest paths.
   931     ///
   932     ///The type of the map that stores the last
   933     ///arcs of the shortest paths.
   934     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   935     ///
   936     typedef NullMap <typename GR::Node,typename GR::Arc> PredMap;
   937     ///Instantiates a PredMap.
   938 
   939     ///This function instantiates a \ref PredMap.
   940     ///\param g is the digraph, to which we would like to define the PredMap.
   941     ///\todo The digraph alone may be insufficient for the initialization
   942 #ifdef DOXYGEN
   943     static PredMap *createPredMap(const GR &g)
   944 #else
   945     static PredMap *createPredMap(const GR &)
   946 #endif
   947     {
   948       return new PredMap();
   949     }
   950     ///The type of the map that stores whether a nodes is processed.
   951 
   952     ///The type of the map that stores whether a nodes is processed.
   953     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   954     ///By default it is a NullMap.
   955     ///\todo If it is set to a real map,
   956     ///Dijkstra::processed() should read this.
   957     ///\todo named parameter to set this type, function to read and write.
   958     typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
   959     ///Instantiates a ProcessedMap.
   960 
   961     ///This function instantiates a \ref ProcessedMap.
   962     ///\param g is the digraph, to which
   963     ///we would like to define the \ref ProcessedMap
   964 #ifdef DOXYGEN
   965     static ProcessedMap *createProcessedMap(const GR &g)
   966 #else
   967     static ProcessedMap *createProcessedMap(const GR &)
   968 #endif
   969     {
   970       return new ProcessedMap();
   971     }
   972     ///The type of the map that stores the dists of the nodes.
   973 
   974     ///The type of the map that stores the dists of the nodes.
   975     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   976     ///
   977     typedef NullMap<typename Digraph::Node,typename LM::Value> DistMap;
   978     ///Instantiates a DistMap.
   979 
   980     ///This function instantiates a \ref DistMap.
   981     ///\param g is the digraph, to which we would like to define
   982     ///the \ref DistMap
   983 #ifdef DOXYGEN
   984     static DistMap *createDistMap(const GR &g)
   985 #else
   986     static DistMap *createDistMap(const GR &)
   987 #endif
   988     {
   989       return new DistMap();
   990     }
   991   };
   992 
   993   /// Default traits used by \ref DijkstraWizard
   994 
   995   /// To make it easier to use Dijkstra algorithm
   996   ///we have created a wizard class.
   997   /// This \ref DijkstraWizard class needs default traits,
   998   ///as well as the \ref Dijkstra class.
   999   /// The \ref DijkstraWizardBase is a class to be the default traits of the
  1000   /// \ref DijkstraWizard class.
  1001   /// \todo More named parameters are required...
  1002   template<class GR,class LM>
  1003   class DijkstraWizardBase : public DijkstraWizardDefaultTraits<GR,LM>
  1004   {
  1005 
  1006     typedef DijkstraWizardDefaultTraits<GR,LM> Base;
  1007   protected:
  1008     /// Type of the nodes in the digraph.
  1009     typedef typename Base::Digraph::Node Node;
  1010 
  1011     /// Pointer to the underlying digraph.
  1012     void *_g;
  1013     /// Pointer to the length map
  1014     void *_length;
  1015     ///Pointer to the map of predecessors arcs.
  1016     void *_pred;
  1017     ///Pointer to the map of distances.
  1018     void *_dist;
  1019     ///Pointer to the source node.
  1020     Node _source;
  1021 
  1022     public:
  1023     /// Constructor.
  1024 
  1025     /// This constructor does not require parameters, therefore it initiates
  1026     /// all of the attributes to default values (0, INVALID).
  1027     DijkstraWizardBase() : _g(0), _length(0), _pred(0),
  1028                            _dist(0), _source(INVALID) {}
  1029 
  1030     /// Constructor.
  1031 
  1032     /// This constructor requires some parameters,
  1033     /// listed in the parameters list.
  1034     /// Others are initiated to 0.
  1035     /// \param g is the initial value of  \ref _g
  1036     /// \param l is the initial value of  \ref _length
  1037     /// \param s is the initial value of  \ref _source
  1038     DijkstraWizardBase(const GR &g,const LM &l, Node s=INVALID) :
  1039       _g(reinterpret_cast<void*>(const_cast<GR*>(&g))),
  1040       _length(reinterpret_cast<void*>(const_cast<LM*>(&l))),
  1041       _pred(0), _dist(0), _source(s) {}
  1042 
  1043   };
  1044 
  1045   /// A class to make the usage of Dijkstra algorithm easier
  1046 
  1047   /// This class is created to make it easier to use Dijkstra algorithm.
  1048   /// It uses the functions and features of the plain \ref Dijkstra,
  1049   /// but it is much simpler to use it.
  1050   ///
  1051   /// Simplicity means that the way to change the types defined
  1052   /// in the traits class is based on functions that returns the new class
  1053   /// and not on templatable built-in classes.
  1054   /// When using the plain \ref Dijkstra
  1055   /// the new class with the modified type comes from
  1056   /// the original class by using the ::
  1057   /// operator. In the case of \ref DijkstraWizard only
  1058   /// a function have to be called and it will
  1059   /// return the needed class.
  1060   ///
  1061   /// It does not have own \ref run method. When its \ref run method is called
  1062   /// it initiates a plain \ref Dijkstra class, and calls the \ref
  1063   /// Dijkstra::run method of it.
  1064   template<class TR>
  1065   class DijkstraWizard : public TR
  1066   {
  1067     typedef TR Base;
  1068 
  1069     ///The type of the underlying digraph.
  1070     typedef typename TR::Digraph Digraph;
  1071     //\e
  1072     typedef typename Digraph::Node Node;
  1073     //\e
  1074     typedef typename Digraph::NodeIt NodeIt;
  1075     //\e
  1076     typedef typename Digraph::Arc Arc;
  1077     //\e
  1078     typedef typename Digraph::OutArcIt OutArcIt;
  1079 
  1080     ///The type of the map that stores the arc lengths.
  1081     typedef typename TR::LengthMap LengthMap;
  1082     ///The type of the length of the arcs.
  1083     typedef typename LengthMap::Value Value;
  1084     ///\brief The type of the map that stores the last
  1085     ///arcs of the shortest paths.
  1086     typedef typename TR::PredMap PredMap;
  1087     ///The type of the map that stores the dists of the nodes.
  1088     typedef typename TR::DistMap DistMap;
  1089     ///The heap type used by the dijkstra algorithm.
  1090     typedef typename TR::Heap Heap;
  1091   public:
  1092     /// Constructor.
  1093     DijkstraWizard() : TR() {}
  1094 
  1095     /// Constructor that requires parameters.
  1096 
  1097     /// Constructor that requires parameters.
  1098     /// These parameters will be the default values for the traits class.
  1099     DijkstraWizard(const Digraph &g,const LengthMap &l, Node s=INVALID) :
  1100       TR(g,l,s) {}
  1101 
  1102     ///Copy constructor
  1103     DijkstraWizard(const TR &b) : TR(b) {}
  1104 
  1105     ~DijkstraWizard() {}
  1106 
  1107     ///Runs Dijkstra algorithm from a given node.
  1108 
  1109     ///Runs Dijkstra algorithm from a given node.
  1110     ///The node can be given by the \ref source function.
  1111     void run()
  1112     {
  1113       if(Base::_source==INVALID) throw UninitializedParameter();
  1114       Dijkstra<Digraph,LengthMap,TR>
  1115         dij(*reinterpret_cast<const Digraph*>(Base::_g),
  1116             *reinterpret_cast<const LengthMap*>(Base::_length));
  1117       if(Base::_pred) dij.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
  1118       if(Base::_dist) dij.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
  1119       dij.run(Base::_source);
  1120     }
  1121 
  1122     ///Runs Dijkstra algorithm from the given node.
  1123 
  1124     ///Runs Dijkstra algorithm from the given node.
  1125     ///\param s is the given source.
  1126     void run(Node s)
  1127     {
  1128       Base::_source=s;
  1129       run();
  1130     }
  1131 
  1132     template<class T>
  1133     struct DefPredMapBase : public Base {
  1134       typedef T PredMap;
  1135       static PredMap *createPredMap(const Digraph &) { return 0; };
  1136       DefPredMapBase(const TR &b) : TR(b) {}
  1137     };
  1138 
  1139     ///\brief \ref named-templ-param "Named parameter"
  1140     ///function for setting PredMap type
  1141     ///
  1142     /// \ref named-templ-param "Named parameter"
  1143     ///function for setting PredMap type
  1144     ///
  1145     template<class T>
  1146     DijkstraWizard<DefPredMapBase<T> > predMap(const T &t)
  1147     {
  1148       Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
  1149       return DijkstraWizard<DefPredMapBase<T> >(*this);
  1150     }
  1151 
  1152     template<class T>
  1153     struct DefDistMapBase : public Base {
  1154       typedef T DistMap;
  1155       static DistMap *createDistMap(const Digraph &) { return 0; };
  1156       DefDistMapBase(const TR &b) : TR(b) {}
  1157     };
  1158 
  1159     ///\brief \ref named-templ-param "Named parameter"
  1160     ///function for setting DistMap type
  1161     ///
  1162     /// \ref named-templ-param "Named parameter"
  1163     ///function for setting DistMap type
  1164     ///
  1165     template<class T>
  1166     DijkstraWizard<DefDistMapBase<T> > distMap(const T &t)
  1167     {
  1168       Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
  1169       return DijkstraWizard<DefDistMapBase<T> >(*this);
  1170     }
  1171 
  1172     /// Sets the source node, from which the Dijkstra algorithm runs.
  1173 
  1174     /// Sets the source node, from which the Dijkstra algorithm runs.
  1175     /// \param s is the source node.
  1176     DijkstraWizard<TR> &source(Node s)
  1177     {
  1178       Base::_source=s;
  1179       return *this;
  1180     }
  1181 
  1182   };
  1183 
  1184   ///Function type interface for Dijkstra algorithm.
  1185 
  1186   /// \ingroup shortest_path
  1187   ///Function type interface for Dijkstra algorithm.
  1188   ///
  1189   ///This function also has several
  1190   ///\ref named-templ-func-param "named parameters",
  1191   ///they are declared as the members of class \ref DijkstraWizard.
  1192   ///The following
  1193   ///example shows how to use these parameters.
  1194   ///\code
  1195   ///  dijkstra(g,length,source).predMap(preds).run();
  1196   ///\endcode
  1197   ///\warning Don't forget to put the \ref DijkstraWizard::run() "run()"
  1198   ///to the end of the parameter list.
  1199   ///\sa DijkstraWizard
  1200   ///\sa Dijkstra
  1201   template<class GR, class LM>
  1202   DijkstraWizard<DijkstraWizardBase<GR,LM> >
  1203   dijkstra(const GR &g,const LM &l,typename GR::Node s=INVALID)
  1204   {
  1205     return DijkstraWizard<DijkstraWizardBase<GR,LM> >(g,l,s);
  1206   }
  1207 
  1208 } //END OF NAMESPACE LEMON
  1209 
  1210 #endif