lemon/bellman_ford.h
author hegyi
Mon, 09 Jan 2006 12:41:06 +0000
changeset 1887 22fdc00894aa
parent 1864 1788205e36af
child 1946 17eb3eaad9f8
permissions -rw-r--r--
The tree that is created for evaluation of expression string at new map creation is deleted after usage.
     1 /* -*- C++ -*-
     2  * lemon/bellman_ford.h - Part of LEMON, a generic C++ optimization library
     3  *
     4  * Copyright (C) 2006 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     5  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     6  *
     7  * Permission to use, modify and distribute this software is granted
     8  * provided that this copyright notice appears in all copies. For
     9  * precise terms see the accompanying LICENSE file.
    10  *
    11  * This software is provided "AS IS" with no warranty of any kind,
    12  * express or implied, and with no claim as to its suitability for any
    13  * purpose.
    14  *
    15  */
    16 
    17 #ifndef LEMON_BELMANN_FORD_H
    18 #define LEMON_BELMANN_FORD_H
    19 
    20 /// \ingroup flowalgs
    21 /// \file
    22 /// \brief BellmanFord algorithm.
    23 ///
    24 
    25 #include <lemon/list_graph.h>
    26 #include <lemon/invalid.h>
    27 #include <lemon/error.h>
    28 #include <lemon/maps.h>
    29 
    30 #include <limits>
    31 
    32 namespace lemon {
    33 
    34   /// \brief Default OperationTraits for the BellmanFord algorithm class.
    35   ///  
    36   /// It defines all computational operations and constants which are
    37   /// used in the bellman ford algorithm. The default implementation
    38   /// is based on the numeric_limits class. If the numeric type does not
    39   /// have infinity value then the maximum value is used as extremal
    40   /// infinity value.
    41   template <
    42     typename Value, 
    43     bool has_infinity = std::numeric_limits<Value>::has_infinity>
    44   struct BellmanFordDefaultOperationTraits {
    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 positive infinity value of the type.
    50     static Value infinity() {
    51       return std::numeric_limits<Value>::infinity();
    52     }
    53     /// \brief Gives back the sum of the given two elements.
    54     static Value plus(const Value& left, const Value& right) {
    55       return left + right;
    56     }
    57     /// \brief Gives back true only if the first value less than the second.
    58     static bool less(const Value& left, const Value& right) {
    59       return left < right;
    60     }
    61   };
    62 
    63   template <typename Value>
    64   struct BellmanFordDefaultOperationTraits<Value, false> {
    65     static Value zero() {
    66       return static_cast<Value>(0);
    67     }
    68     static Value infinity() {
    69       return std::numeric_limits<Value>::max();
    70     }
    71     static Value plus(const Value& left, const Value& right) {
    72       if (left == infinity() || right == infinity()) return infinity();
    73       return left + right;
    74     }
    75     static bool less(const Value& left, const Value& right) {
    76       return left < right;
    77     }
    78   };
    79   
    80   /// \brief Default traits class of BellmanFord class.
    81   ///
    82   /// Default traits class of BellmanFord class.
    83   /// \param _Graph Graph type.
    84   /// \param _LegthMap Type of length map.
    85   template<class _Graph, class _LengthMap>
    86   struct BellmanFordDefaultTraits {
    87     /// The graph type the algorithm runs on. 
    88     typedef _Graph Graph;
    89 
    90     /// \brief The type of the map that stores the edge lengths.
    91     ///
    92     /// The type of the map that stores the edge lengths.
    93     /// It must meet the \ref concept::ReadMap "ReadMap" concept.
    94     typedef _LengthMap LengthMap;
    95 
    96     // The type of the length of the edges.
    97     typedef typename _LengthMap::Value Value;
    98 
    99     /// \brief Operation traits for bellman-ford algorithm.
   100     ///
   101     /// It defines the infinity type on the given Value type
   102     /// and the used operation.
   103     /// \see BellmanFordDefaultOperationTraits
   104     typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
   105  
   106     /// \brief The type of the map that stores the last edges of the 
   107     /// shortest paths.
   108     /// 
   109     /// The type of the map that stores the last
   110     /// edges of the shortest paths.
   111     /// It must meet the \ref concept::WriteMap "WriteMap" concept.
   112     ///
   113     typedef typename Graph::template NodeMap<typename _Graph::Edge> PredMap;
   114 
   115     /// \brief Instantiates a PredMap.
   116     /// 
   117     /// This function instantiates a \ref PredMap. 
   118     /// \param graph is the graph, to which we would like to define the PredMap.
   119     static PredMap *createPredMap(const _Graph& graph) {
   120       return new PredMap(graph);
   121     }
   122 
   123     /// \brief The type of the map that stores the dists of the nodes.
   124     ///
   125     /// The type of the map that stores the dists of the nodes.
   126     /// It must meet the \ref concept::WriteMap "WriteMap" concept.
   127     ///
   128     typedef typename Graph::template NodeMap<typename _LengthMap::Value> 
   129     DistMap;
   130 
   131     /// \brief Instantiates a DistMap.
   132     ///
   133     /// This function instantiates a \ref DistMap. 
   134     /// \param graph is the graph, to which we would like to define the 
   135     /// \ref DistMap
   136     static DistMap *createDistMap(const _Graph& graph) {
   137       return new DistMap(graph);
   138     }
   139 
   140   };
   141   
   142   /// \brief %BellmanFord algorithm class.
   143   ///
   144   /// \ingroup flowalgs
   145   /// This class provides an efficient implementation of \c Bellman-Ford 
   146   /// algorithm. The edge lengths are passed to the algorithm using a
   147   /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any 
   148   /// kind of length.
   149   ///
   150   /// The Bellman-Ford algorithm solves the shortest path from one node
   151   /// problem when the edges can have negative length but the graph should
   152   /// not contain cycles with negative sum of length. If we can assume
   153   /// that all edge is non-negative in the graph then the dijkstra algorithm
   154   /// should be used rather.
   155   ///
   156   /// The complexity of the algorithm is O(n * e).
   157   ///
   158   /// The type of the length is determined by the
   159   /// \ref concept::ReadMap::Value "Value" of the length map.
   160   ///
   161   /// \param _Graph The graph type the algorithm runs on. The default value
   162   /// is \ref ListGraph. The value of _Graph is not used directly by
   163   /// BellmanFord, it is only passed to \ref BellmanFordDefaultTraits.
   164   /// \param _LengthMap This read-only EdgeMap determines the lengths of the
   165   /// edges. The default map type is \ref concept::StaticGraph::EdgeMap 
   166   /// "Graph::EdgeMap<int>".  The value of _LengthMap is not used directly 
   167   /// by BellmanFord, it is only passed to \ref BellmanFordDefaultTraits.  
   168   /// \param _Traits Traits class to set various data types used by the 
   169   /// algorithm.  The default traits class is \ref BellmanFordDefaultTraits
   170   /// "BellmanFordDefaultTraits<_Graph,_LengthMap>".  See \ref
   171   /// BellmanFordDefaultTraits for the documentation of a BellmanFord traits
   172   /// class.
   173   ///
   174   /// \author Balazs Dezso
   175 
   176 #ifdef DOXYGEN
   177   template <typename _Graph, typename _LengthMap, typename _Traits>
   178 #else
   179   template <typename _Graph=ListGraph,
   180 	    typename _LengthMap=typename _Graph::template EdgeMap<int>,
   181 	    typename _Traits=BellmanFordDefaultTraits<_Graph,_LengthMap> >
   182 #endif
   183   class BellmanFord {
   184   public:
   185     
   186     /// \brief \ref Exception for uninitialized parameters.
   187     ///
   188     /// This error represents problems in the initialization
   189     /// of the parameters of the algorithms.
   190 
   191     class UninitializedParameter : public lemon::UninitializedParameter {
   192     public:
   193       virtual const char* exceptionName() const {
   194 	return "lemon::BellmanFord::UninitializedParameter";
   195       }
   196     };
   197 
   198     typedef _Traits Traits;
   199     ///The type of the underlying graph.
   200     typedef typename _Traits::Graph Graph;
   201 
   202     typedef typename Graph::Node Node;
   203     typedef typename Graph::NodeIt NodeIt;
   204     typedef typename Graph::Edge Edge;
   205     typedef typename Graph::OutEdgeIt OutEdgeIt;
   206     
   207     /// \brief The type of the length of the edges.
   208     typedef typename _Traits::LengthMap::Value Value;
   209     /// \brief The type of the map that stores the edge lengths.
   210     typedef typename _Traits::LengthMap LengthMap;
   211     /// \brief The type of the map that stores the last
   212     /// edges of the shortest paths.
   213     typedef typename _Traits::PredMap PredMap;
   214     /// \brief The type of the map that stores the dists of the nodes.
   215     typedef typename _Traits::DistMap DistMap;
   216     /// \brief The operation traits.
   217     typedef typename _Traits::OperationTraits OperationTraits;
   218   private:
   219     /// Pointer to the underlying graph.
   220     const Graph *graph;
   221     /// Pointer to the length map
   222     const LengthMap *length;
   223     ///Pointer to the map of predecessors edges.
   224     PredMap *_pred;
   225     ///Indicates if \ref _pred is locally allocated (\c true) or not.
   226     bool local_pred;
   227     ///Pointer to the map of distances.
   228     DistMap *_dist;
   229     ///Indicates if \ref _dist is locally allocated (\c true) or not.
   230     bool local_dist;
   231 
   232     typedef typename Graph::template NodeMap<bool> MaskMap;
   233     MaskMap *_mask;
   234 
   235     std::vector<Node> _process;
   236 
   237     /// Creates the maps if necessary.
   238     void create_maps() {
   239       if(!_pred) {
   240 	local_pred = true;
   241 	_pred = Traits::createPredMap(*graph);
   242       }
   243       if(!_dist) {
   244 	local_dist = true;
   245 	_dist = Traits::createDistMap(*graph);
   246       }
   247       _mask = new MaskMap(*graph, false);
   248     }
   249     
   250   public :
   251  
   252     typedef BellmanFord Create;
   253 
   254     /// \name Named template parameters
   255 
   256     ///@{
   257 
   258     template <class T>
   259     struct DefPredMapTraits : public Traits {
   260       typedef T PredMap;
   261       static PredMap *createPredMap(const Graph&) {
   262 	throw UninitializedParameter();
   263       }
   264     };
   265 
   266     /// \brief \ref named-templ-param "Named parameter" for setting PredMap 
   267     /// type
   268     /// \ref named-templ-param "Named parameter" for setting PredMap type
   269     ///
   270     template <class T>
   271     struct DefPredMap 
   272       : public BellmanFord< Graph, LengthMap, DefPredMapTraits<T> > {
   273       typedef BellmanFord< Graph, LengthMap, DefPredMapTraits<T> > Create;
   274     };
   275     
   276     template <class T>
   277     struct DefDistMapTraits : public Traits {
   278       typedef T DistMap;
   279       static DistMap *createDistMap(const Graph& graph) {
   280 	throw UninitializedParameter();
   281       }
   282     };
   283 
   284     /// \brief \ref named-templ-param "Named parameter" for setting DistMap 
   285     /// type
   286     ///
   287     /// \ref named-templ-param "Named parameter" for setting DistMap type
   288     ///
   289     template <class T>
   290     struct DefDistMap 
   291       : public BellmanFord< Graph, LengthMap, DefDistMapTraits<T> > {
   292       typedef BellmanFord< Graph, LengthMap, DefDistMapTraits<T> > Create;
   293     };
   294     
   295     template <class T>
   296     struct DefOperationTraitsTraits : public Traits {
   297       typedef T OperationTraits;
   298     };
   299     
   300     /// \brief \ref named-templ-param "Named parameter" for setting 
   301     /// OperationTraits type
   302     ///
   303     /// \ref named-templ-param "Named parameter" for setting OperationTraits
   304     /// type
   305     template <class T>
   306     struct DefOperationTraits
   307       : public BellmanFord< Graph, LengthMap, DefOperationTraitsTraits<T> > {
   308       typedef BellmanFord< Graph, LengthMap, DefOperationTraitsTraits<T> >
   309       Create;
   310     };
   311     
   312     ///@}
   313 
   314   protected:
   315     
   316     BellmanFord() {}
   317 
   318   public:      
   319     
   320     /// \brief Constructor.
   321     ///
   322     /// \param _graph the graph the algorithm will run on.
   323     /// \param _length the length map used by the algorithm.
   324     BellmanFord(const Graph& _graph, const LengthMap& _length) :
   325       graph(&_graph), length(&_length),
   326       _pred(0), local_pred(false),
   327       _dist(0), local_dist(false) {}
   328     
   329     ///Destructor.
   330     ~BellmanFord() {
   331       if(local_pred) delete _pred;
   332       if(local_dist) delete _dist;
   333       delete _mask;
   334     }
   335 
   336     /// \brief Sets the length map.
   337     ///
   338     /// Sets the length map.
   339     /// \return \c (*this)
   340     BellmanFord &lengthMap(const LengthMap &m) {
   341       length = &m;
   342       return *this;
   343     }
   344 
   345     /// \brief Sets the map storing the predecessor edges.
   346     ///
   347     /// Sets the map storing the predecessor edges.
   348     /// If you don't use this function before calling \ref run(),
   349     /// it will allocate one. The destuctor deallocates this
   350     /// automatically allocated map, of course.
   351     /// \return \c (*this)
   352     BellmanFord &predMap(PredMap &m) {
   353       if(local_pred) {
   354 	delete _pred;
   355 	local_pred=false;
   356       }
   357       _pred = &m;
   358       return *this;
   359     }
   360 
   361     /// \brief Sets the map storing the distances calculated by the algorithm.
   362     ///
   363     /// Sets the map storing the distances calculated by the algorithm.
   364     /// If you don't use this function before calling \ref run(),
   365     /// it will allocate one. The destuctor deallocates this
   366     /// automatically allocated map, of course.
   367     /// \return \c (*this)
   368     BellmanFord &distMap(DistMap &m) {
   369       if(local_dist) {
   370 	delete _dist;
   371 	local_dist=false;
   372       }
   373       _dist = &m;
   374       return *this;
   375     }
   376 
   377     /// \name Execution control
   378     /// The simplest way to execute the algorithm is to use
   379     /// one of the member functions called \c run(...).
   380     /// \n
   381     /// If you need more control on the execution,
   382     /// first you must call \ref init(), then you can add several source nodes
   383     /// with \ref addSource().
   384     /// Finally \ref start() will perform the actual path
   385     /// computation.
   386 
   387     ///@{
   388 
   389     /// \brief Initializes the internal data structures.
   390     /// 
   391     /// Initializes the internal data structures.
   392     void init(const Value value = OperationTraits::infinity()) {
   393       create_maps();
   394       for (NodeIt it(*graph); it != INVALID; ++it) {
   395 	_pred->set(it, INVALID);
   396 	_dist->set(it, value);
   397       }
   398       _process.clear();
   399       if (OperationTraits::less(value, OperationTraits::infinity())) {
   400 	for (NodeIt it(*graph); it != INVALID; ++it) {
   401 	  _process.push_back(it);
   402 	  _mask->set(it, true);
   403 	}
   404       }
   405     }
   406     
   407     /// \brief Adds a new source node.
   408     ///
   409     /// The optional second parameter is the initial distance of the node.
   410     /// It just sets the distance of the node to the given value.
   411     void addSource(Node source, Value dst = OperationTraits::zero()) {
   412       _dist->set(source, dst);
   413       if (!(*_mask)[source]) {
   414 	_process.push_back(source);
   415 	_mask->set(source, true);
   416       }
   417     }
   418 
   419     /// \brief Executes one round from the bellman ford algorithm.
   420     ///
   421     /// If the algoritm calculated the distances in the previous round 
   422     /// strictly for all at most k length paths then it will calculate the 
   423     /// distances strictly for all at most k + 1 length paths. With k
   424     /// iteration this function calculates the at most k length paths.
   425     /// \return %True when the algorithm have not found more shorter paths.
   426     bool processNextRound() {
   427       for (int i = 0; i < (int)_process.size(); ++i) {
   428 	_mask->set(_process[i], false);
   429       }
   430       std::vector<Node> nextProcess;
   431       std::vector<Value> values(_process.size());
   432       for (int i = 0; i < (int)_process.size(); ++i) {
   433 	values[i] = (*_dist)[_process[i]];
   434       }
   435       for (int i = 0; i < (int)_process.size(); ++i) {
   436 	for (OutEdgeIt it(*graph, _process[i]); it != INVALID; ++it) {
   437 	  Node target = graph->target(it);
   438 	  Value relaxed = OperationTraits::plus(values[i], (*length)[it]);
   439 	  if (OperationTraits::less(relaxed, (*_dist)[target])) {
   440 	    _pred->set(target, it);
   441 	    _dist->set(target, relaxed);
   442 	    if (!(*_mask)[target]) {
   443 	      _mask->set(target, true);
   444 	      nextProcess.push_back(target);
   445 	    }
   446 	  }	  
   447 	}
   448       }
   449       _process.swap(nextProcess);
   450       return _process.empty();
   451     }
   452 
   453     /// \brief Executes one weak round from the bellman ford algorithm.
   454     ///
   455     /// If the algorithm calculated the distances in the
   456     /// previous round at least for all at most k length paths then it will
   457     /// calculate the distances at least for all at most k + 1 length paths.
   458     /// This function does not make it possible to calculate strictly the
   459     /// at most k length minimal paths, this is why it is
   460     /// called just weak round.
   461     /// \return %True when the algorithm have not found more shorter paths.
   462     bool processNextWeakRound() {
   463       for (int i = 0; i < (int)_process.size(); ++i) {
   464 	_mask->set(_process[i], false);
   465       }
   466       std::vector<Node> nextProcess;
   467       for (int i = 0; i < (int)_process.size(); ++i) {
   468 	for (OutEdgeIt it(*graph, _process[i]); it != INVALID; ++it) {
   469 	  Node target = graph->target(it);
   470 	  Value relaxed = 
   471 	    OperationTraits::plus((*_dist)[_process[i]], (*length)[it]);
   472 	  if (OperationTraits::less(relaxed, (*_dist)[target])) {
   473 	    _pred->set(target, it);
   474 	    _dist->set(target, relaxed);
   475 	    if (!(*_mask)[target]) {
   476 	      _mask->set(target, true);
   477 	      nextProcess.push_back(target);
   478 	    }
   479 	  }	  
   480 	}
   481       }
   482       _process.swap(nextProcess);
   483       return _process.empty();
   484     }
   485 
   486     /// \brief Executes the algorithm.
   487     ///
   488     /// \pre init() must be called and at least one node should be added
   489     /// with addSource() before using this function.
   490     ///
   491     /// This method runs the %BellmanFord algorithm from the root node(s)
   492     /// in order to compute the shortest path to each node. The algorithm 
   493     /// computes 
   494     /// - The shortest path tree.
   495     /// - The distance of each node from the root(s).
   496     void start() {
   497       int num = countNodes(*graph) - 1;
   498       for (int i = 0; i < num; ++i) {
   499 	if (processNextWeakRound()) break;
   500       }
   501     }
   502 
   503     /// \brief Executes the algorithm and checks the negative cycles.
   504     ///
   505     /// \pre init() must be called and at least one node should be added
   506     /// with addSource() before using this function. If there is
   507     /// a negative cycles in the graph it gives back false.
   508     ///
   509     /// This method runs the %BellmanFord algorithm from the root node(s)
   510     /// in order to compute the shortest path to each node. The algorithm 
   511     /// computes 
   512     /// - The shortest path tree.
   513     /// - The distance of each node from the root(s).
   514     bool checkedStart() {
   515       int num = countNodes(*graph);
   516       for (int i = 0; i < num; ++i) {
   517 	if (processNextWeakRound()) return true;
   518       }
   519       return false;
   520     }
   521 
   522     /// \brief Executes the algorithm with path length limit.
   523     ///
   524     /// \pre init() must be called and at least one node should be added
   525     /// with addSource() before using this function.
   526     ///
   527     /// This method runs the %BellmanFord algorithm from the root node(s)
   528     /// in order to compute the shortest path with at most \c length edge 
   529     /// long paths to each node. The algorithm computes 
   530     /// - The shortest path tree.
   531     /// - The limited distance of each node from the root(s).
   532     void limitedStart(int length) {
   533       for (int i = 0; i < length; ++i) {
   534 	if (processNextRound()) break;
   535       }
   536     }
   537     
   538     /// \brief Runs %BellmanFord algorithm from node \c s.
   539     ///    
   540     /// This method runs the %BellmanFord algorithm from a root node \c s
   541     /// in order to compute the shortest path to each node. The algorithm 
   542     /// computes
   543     /// - The shortest path tree.
   544     /// - The distance of each node from the root.
   545     ///
   546     /// \note d.run(s) is just a shortcut of the following code.
   547     /// \code
   548     ///  d.init();
   549     ///  d.addSource(s);
   550     ///  d.start();
   551     /// \endcode
   552     void run(Node s) {
   553       init();
   554       addSource(s);
   555       start();
   556     }
   557     
   558     /// \brief Runs %BellmanFord algorithm with limited path length 
   559     /// from node \c s.
   560     ///    
   561     /// This method runs the %BellmanFord algorithm from a root node \c s
   562     /// in order to compute the shortest path with at most \c len edges 
   563     /// to each node. The algorithm computes
   564     /// - The shortest path tree.
   565     /// - The distance of each node from the root.
   566     ///
   567     /// \note d.run(s, len) is just a shortcut of the following code.
   568     /// \code
   569     ///  d.init();
   570     ///  d.addSource(s);
   571     ///  d.limitedStart(len);
   572     /// \endcode
   573     void run(Node s, int len) {
   574       init();
   575       addSource(s);
   576       limitedStart(len);
   577     }
   578     
   579     ///@}
   580 
   581     /// \name Query Functions
   582     /// The result of the %BellmanFord algorithm can be obtained using these
   583     /// functions.\n
   584     /// Before the use of these functions,
   585     /// either run() or start() must be called.
   586     
   587     ///@{
   588 
   589     /// \brief Copies the shortest path to \c t into \c p
   590     ///    
   591     /// This function copies the shortest path to \c t into \c p.
   592     /// If it \c t is a source itself or unreachable, then it does not
   593     /// alter \c p.
   594     ///
   595     /// \return Returns \c true if a path to \c t was actually copied to \c p,
   596     /// \c false otherwise.
   597     /// \sa DirPath
   598     template <typename Path>
   599     bool getPath(Path &p, Node t) {
   600       if(reached(t)) {
   601 	p.clear();
   602 	typename Path::Builder b(p);
   603 	for(b.setStartNode(t);predEdge(t)!=INVALID;t=predNode(t))
   604 	  b.pushFront(predEdge(t));
   605 	b.commit();
   606 	return true;
   607       }
   608       return false;
   609     }
   610 	  
   611     /// \brief The distance of a node from the root.
   612     ///
   613     /// Returns the distance of a node from the root.
   614     /// \pre \ref run() must be called before using this function.
   615     /// \warning If node \c v in unreachable from the root the return value
   616     /// of this funcion is undefined.
   617     Value dist(Node v) const { return (*_dist)[v]; }
   618 
   619     /// \brief Returns the 'previous edge' of the shortest path tree.
   620     ///
   621     /// For a node \c v it returns the 'previous edge' of the shortest path 
   622     /// tree, i.e. it returns the last edge of a shortest path from the root 
   623     /// to \c v. It is \ref INVALID if \c v is unreachable from the root or 
   624     /// if \c v=s. The shortest path tree used here is equal to the shortest 
   625     /// path tree used in \ref predNode(). 
   626     /// \pre \ref run() must be called before using
   627     /// this function.
   628     Edge predEdge(Node v) const { return (*_pred)[v]; }
   629 
   630     /// \brief Returns the 'previous node' of the shortest path tree.
   631     ///
   632     /// For a node \c v it returns the 'previous node' of the shortest path 
   633     /// tree, i.e. it returns the last but one node from a shortest path from 
   634     /// the root to \c /v. It is INVALID if \c v is unreachable from the root 
   635     /// or if \c v=s. The shortest path tree used here is equal to the 
   636     /// shortest path tree used in \ref predEdge().  \pre \ref run() must be 
   637     /// called before using this function.
   638     Node predNode(Node v) const { 
   639       return (*_pred)[v] == INVALID ? INVALID : graph->source((*_pred)[v]); 
   640     }
   641     
   642     /// \brief Returns a reference to the NodeMap of distances.
   643     ///
   644     /// Returns a reference to the NodeMap of distances. \pre \ref run() must
   645     /// be called before using this function.
   646     const DistMap &distMap() const { return *_dist;}
   647  
   648     /// \brief Returns a reference to the shortest path tree map.
   649     ///
   650     /// Returns a reference to the NodeMap of the edges of the
   651     /// shortest path tree.
   652     /// \pre \ref run() must be called before using this function.
   653     const PredMap &predMap() const { return *_pred; }
   654  
   655     /// \brief Checks if a node is reachable from the root.
   656     ///
   657     /// Returns \c true if \c v is reachable from the root.
   658     /// \pre \ref run() must be called before using this function.
   659     ///
   660     bool reached(Node v) { return (*_dist)[v] != OperationTraits::infinity(); }
   661     
   662     ///@}
   663   };
   664  
   665   /// \brief Default traits class of BellmanFord function.
   666   ///
   667   /// Default traits class of BellmanFord function.
   668   /// \param _Graph Graph type.
   669   /// \param _LengthMap Type of length map.
   670   template <typename _Graph, typename _LengthMap>
   671   struct BellmanFordWizardDefaultTraits {
   672     /// \brief The graph type the algorithm runs on. 
   673     typedef _Graph Graph;
   674 
   675     /// \brief The type of the map that stores the edge lengths.
   676     ///
   677     /// The type of the map that stores the edge lengths.
   678     /// It must meet the \ref concept::ReadMap "ReadMap" concept.
   679     typedef _LengthMap LengthMap;
   680 
   681     /// \brief The value type of the length map.
   682     typedef typename _LengthMap::Value Value;
   683 
   684     /// \brief Operation traits for bellman-ford algorithm.
   685     ///
   686     /// It defines the infinity type on the given Value type
   687     /// and the used operation.
   688     /// \see BellmanFordDefaultOperationTraits
   689     typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
   690 
   691     /// \brief The type of the map that stores the last
   692     /// edges of the shortest paths.
   693     /// 
   694     /// The type of the map that stores the last
   695     /// edges of the shortest paths.
   696     /// It must meet the \ref concept::WriteMap "WriteMap" concept.
   697     typedef NullMap <typename _Graph::Node,typename _Graph::Edge> PredMap;
   698 
   699     /// \brief Instantiates a PredMap.
   700     /// 
   701     /// This function instantiates a \ref PredMap. 
   702     static PredMap *createPredMap(const _Graph &) {
   703       return new PredMap();
   704     }
   705     /// \brief The type of the map that stores the dists of the nodes.
   706     ///
   707     /// The type of the map that stores the dists of the nodes.
   708     /// It must meet the \ref concept::WriteMap "WriteMap" concept.
   709     typedef NullMap<typename Graph::Node, Value> DistMap;
   710     /// \brief Instantiates a DistMap.
   711     ///
   712     /// This function instantiates a \ref DistMap. 
   713     static DistMap *createDistMap(const _Graph &) {
   714       return new DistMap();
   715     }
   716   };
   717   
   718   /// \brief Default traits used by \ref BellmanFordWizard
   719   ///
   720   /// To make it easier to use BellmanFord algorithm
   721   /// we have created a wizard class.
   722   /// This \ref BellmanFordWizard class needs default traits,
   723   /// as well as the \ref BellmanFord class.
   724   /// The \ref BellmanFordWizardBase is a class to be the default traits of the
   725   /// \ref BellmanFordWizard class.
   726   /// \todo More named parameters are required...
   727   template<class _Graph,class _LengthMap>
   728   class BellmanFordWizardBase 
   729     : public BellmanFordWizardDefaultTraits<_Graph,_LengthMap> {
   730 
   731     typedef BellmanFordWizardDefaultTraits<_Graph,_LengthMap> Base;
   732   protected:
   733     /// Type of the nodes in the graph.
   734     typedef typename Base::Graph::Node Node;
   735 
   736     /// Pointer to the underlying graph.
   737     void *_graph;
   738     /// Pointer to the length map
   739     void *_length;
   740     ///Pointer to the map of predecessors edges.
   741     void *_pred;
   742     ///Pointer to the map of distances.
   743     void *_dist;
   744     ///Pointer to the source node.
   745     Node _source;
   746 
   747     public:
   748     /// Constructor.
   749     
   750     /// This constructor does not require parameters, therefore it initiates
   751     /// all of the attributes to default values (0, INVALID).
   752     BellmanFordWizardBase() : _graph(0), _length(0), _pred(0),
   753 			   _dist(0), _source(INVALID) {}
   754 
   755     /// Constructor.
   756     
   757     /// This constructor requires some parameters,
   758     /// listed in the parameters list.
   759     /// Others are initiated to 0.
   760     /// \param graph is the initial value of  \ref _graph
   761     /// \param length is the initial value of  \ref _length
   762     /// \param source is the initial value of  \ref _source
   763     BellmanFordWizardBase(const _Graph& graph, 
   764 			  const _LengthMap& length, 
   765 			  Node source = INVALID) :
   766       _graph((void *)&graph), _length((void *)&length), _pred(0),
   767       _dist(0), _source(source) {}
   768 
   769   };
   770   
   771   /// A class to make the usage of BellmanFord algorithm easier
   772 
   773   /// This class is created to make it easier to use BellmanFord algorithm.
   774   /// It uses the functions and features of the plain \ref BellmanFord,
   775   /// but it is much simpler to use it.
   776   ///
   777   /// Simplicity means that the way to change the types defined
   778   /// in the traits class is based on functions that returns the new class
   779   /// and not on templatable built-in classes.
   780   /// When using the plain \ref BellmanFord
   781   /// the new class with the modified type comes from
   782   /// the original class by using the ::
   783   /// operator. In the case of \ref BellmanFordWizard only
   784   /// a function have to be called and it will
   785   /// return the needed class.
   786   ///
   787   /// It does not have own \ref run method. When its \ref run method is called
   788   /// it initiates a plain \ref BellmanFord class, and calls the \ref 
   789   /// BellmanFord::run method of it.
   790   template<class _Traits>
   791   class BellmanFordWizard : public _Traits {
   792     typedef _Traits Base;
   793 
   794     ///The type of the underlying graph.
   795     typedef typename _Traits::Graph Graph;
   796 
   797     typedef typename Graph::Node Node;
   798     typedef typename Graph::NodeIt NodeIt;
   799     typedef typename Graph::Edge Edge;
   800     typedef typename Graph::OutEdgeIt EdgeIt;
   801     
   802     ///The type of the map that stores the edge lengths.
   803     typedef typename _Traits::LengthMap LengthMap;
   804 
   805     ///The type of the length of the edges.
   806     typedef typename LengthMap::Value Value;
   807 
   808     ///\brief The type of the map that stores the last
   809     ///edges of the shortest paths.
   810     typedef typename _Traits::PredMap PredMap;
   811 
   812     ///The type of the map that stores the dists of the nodes.
   813     typedef typename _Traits::DistMap DistMap;
   814 
   815   public:
   816     /// Constructor.
   817     BellmanFordWizard() : _Traits() {}
   818 
   819     /// \brief Constructor that requires parameters.
   820     ///
   821     /// Constructor that requires parameters.
   822     /// These parameters will be the default values for the traits class.
   823     BellmanFordWizard(const Graph& graph, const LengthMap& length, 
   824 		      Node source = INVALID) 
   825       : _Traits(graph, length, source) {}
   826 
   827     /// \brief Copy constructor
   828     BellmanFordWizard(const _Traits &b) : _Traits(b) {}
   829 
   830     ~BellmanFordWizard() {}
   831 
   832     /// \brief Runs BellmanFord algorithm from a given node.
   833     ///    
   834     /// Runs BellmanFord algorithm from a given node.
   835     /// The node can be given by the \ref source function.
   836     void run() {
   837       if(Base::_source == INVALID) throw UninitializedParameter();
   838       BellmanFord<Graph,LengthMap,_Traits> 
   839 	bf(*(Graph*)Base::_graph, *(LengthMap*)Base::_length);
   840       if (Base::_pred) bf.predMap(*(PredMap*)Base::_pred);
   841       if (Base::_dist) bf.distMap(*(DistMap*)Base::_dist);
   842       bf.run(Base::_source);
   843     }
   844 
   845     /// \brief Runs BellmanFord algorithm from the given node.
   846     ///
   847     /// Runs BellmanFord algorithm from the given node.
   848     /// \param source is the given source.
   849     void run(Node source) {
   850       Base::_source = source;
   851       run();
   852     }
   853 
   854     template<class T>
   855     struct DefPredMapBase : public Base {
   856       typedef T PredMap;
   857       static PredMap *createPredMap(const Graph &) { return 0; };
   858       DefPredMapBase(const _Traits &b) : _Traits(b) {}
   859     };
   860     
   861     ///\brief \ref named-templ-param "Named parameter"
   862     ///function for setting PredMap type
   863     ///
   864     /// \ref named-templ-param "Named parameter"
   865     ///function for setting PredMap type
   866     ///
   867     template<class T>
   868     BellmanFordWizard<DefPredMapBase<T> > predMap(const T &t) 
   869     {
   870       Base::_pred=(void *)&t;
   871       return BellmanFordWizard<DefPredMapBase<T> >(*this);
   872     }
   873     
   874     template<class T>
   875     struct DefDistMapBase : public Base {
   876       typedef T DistMap;
   877       static DistMap *createDistMap(const Graph &) { return 0; };
   878       DefDistMapBase(const _Traits &b) : _Traits(b) {}
   879     };
   880     
   881     ///\brief \ref named-templ-param "Named parameter"
   882     ///function for setting DistMap type
   883     ///
   884     /// \ref named-templ-param "Named parameter"
   885     ///function for setting DistMap type
   886     ///
   887     template<class T>
   888     BellmanFordWizard<DefDistMapBase<T> > distMap(const T &t) {
   889       Base::_dist=(void *)&t;
   890       return BellmanFordWizard<DefDistMapBase<T> >(*this);
   891     }
   892 
   893     template<class T>
   894     struct DefOperationTraitsBase : public Base {
   895       typedef T OperationTraits;
   896       DefOperationTraitsBase(const _Traits &b) : _Traits(b) {}
   897     };
   898     
   899     ///\brief \ref named-templ-param "Named parameter"
   900     ///function for setting OperationTraits type
   901     ///
   902     /// \ref named-templ-param "Named parameter"
   903     ///function for setting OperationTraits type
   904     ///
   905     template<class T>
   906     BellmanFordWizard<DefOperationTraitsBase<T> > distMap() {
   907       return BellmanFordWizard<DefDistMapBase<T> >(*this);
   908     }
   909     
   910     /// \brief Sets the source node, from which the BellmanFord algorithm runs.
   911     ///
   912     /// Sets the source node, from which the BellmanFord algorithm runs.
   913     /// \param source is the source node.
   914     BellmanFordWizard<_Traits>& source(Node source) {
   915       Base::_source = source;
   916       return *this;
   917     }
   918     
   919   };
   920   
   921   /// \brief Function type interface for BellmanFord algorithm.
   922   ///
   923   /// \ingroup flowalgs
   924   /// Function type interface for BellmanFord algorithm.
   925   ///
   926   /// This function also has several \ref named-templ-func-param 
   927   /// "named parameters", they are declared as the members of class 
   928   /// \ref BellmanFordWizard.
   929   /// The following
   930   /// example shows how to use these parameters.
   931   /// \code
   932   /// bellmanford(g,length,source).predMap(preds).run();
   933   /// \endcode
   934   /// \warning Don't forget to put the \ref BellmanFordWizard::run() "run()"
   935   /// to the end of the parameter list.
   936   /// \sa BellmanFordWizard
   937   /// \sa BellmanFord
   938   template<class _Graph, class _LengthMap>
   939   BellmanFordWizard<BellmanFordWizardBase<_Graph,_LengthMap> >
   940   bellmanFord(const _Graph& graph,
   941 	      const _LengthMap& length, 
   942 	      typename _Graph::Node source = INVALID) {
   943     return BellmanFordWizard<BellmanFordWizardBase<_Graph,_LengthMap> >
   944       (graph, length, source);
   945   }
   946 
   947 } //END OF NAMESPACE LEMON
   948 
   949 #endif
   950