/* -*- C++ -*-

 * lemon/belmann_ford.h - Part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_BELMANN_FORD_H

#define LEMON_BELMANN_FORD_H

///\ingroup flowalgs

/// \file

/// \brief BelmannFord algorithm.

///

/// \todo getPath() should be implemented! (also for BFS and DFS)

#include <lemon/list_graph.h>

#include <lemon/invalid.h>

#include <lemon/error.h>

#include <lemon/maps.h>

#include <limits>

namespace lemon {

  /// \brief Default OperationTraits for the BelmannFord algorithm class.

  ///  

  /// It defines all computational operations and constants which are

  /// used in the belmann ford algorithm. The default implementation

  /// is based on the numeric_limits class. If the numeric type does not

  /// have infinity value then the maximum value is used as extremal

  /// infinity value.

  template <

    typename Value, 

    bool has_infinity = std::numeric_limits<Value>::has_infinity>

  struct BelmannFordDefaultOperationTraits {

    /// \brief Gives back the zero value of the type.

    static Value zero() {

      return static_cast<Value>(0);

    }

    /// \brief Gives back the positive infinity value of the type.

    static Value infinity() {

      return std::numeric_limits<Value>::infinity();

    }

    /// \brief Gives back the sum of the given two elements.

    static Value plus(const Value& left, const Value& right) {

      return left + right;

    }

    /// \brief Gives back true only if the first value less than the second.

    static bool less(const Value& left, const Value& right) {

      return left < right;

    }

  };

  template <typename Value>

  struct BelmannFordDefaultOperationTraits<Value, false> {

    static Value zero() {

      return static_cast<Value>(0);

    }

    static Value infinity() {

      return std::numeric_limits<Value>::max();

    }

    static Value plus(const Value& left, const Value& right) {

      if (left == infinity() || right == infinity()) return infinity();

      return left + right;

    }

    static bool less(const Value& left, const Value& right) {

      return left < right;

    }

  };

  /// \brief Default traits class of BelmannFord class.

  ///

  /// Default traits class of BelmannFord class.

  /// \param _Graph Graph type.

  /// \param _LegthMap Type of length map.

  template<class _Graph, class _LengthMap>

  struct BelmannFordDefaultTraits {

    /// The graph type the algorithm runs on. 

    typedef _Graph Graph;

    /// \brief The type of the map that stores the edge lengths.

    ///

    /// The type of the map that stores the edge lengths.

    /// It must meet the \ref concept::ReadMap "ReadMap" concept.

    typedef _LengthMap LengthMap;

    // The type of the length of the edges.

    typedef typename _LengthMap::Value Value;

    /// \brief Operation traits for belmann-ford algorithm.

    ///

    /// It defines the infinity type on the given Value type

    /// and the used operation.

    /// \see BelmannFordDefaultOperationTraits

    typedef BelmannFordDefaultOperationTraits<Value> OperationTraits;

    /// \brief The type of the map that stores the last edges of the 

    /// shortest paths.

    /// 

    /// The type of the map that stores the last

    /// edges of the shortest paths.

    /// It must meet the \ref concept::WriteMap "WriteMap" concept.

    ///

    typedef typename Graph::template NodeMap<typename _Graph::Edge> PredMap;

    /// \brief Instantiates a PredMap.

    /// 

    /// This function instantiates a \ref PredMap. 

    /// \param G is the graph, to which we would like to define the PredMap.

    /// \todo The graph alone may be insufficient for the initialization

    static PredMap *createPredMap(const _Graph& graph) {

      return new PredMap(graph);

    }

    /// \brief The type of the map that stores the dists of the nodes.

    ///

    /// The type of the map that stores the dists of the nodes.

    /// It must meet the \ref concept::WriteMap "WriteMap" concept.

    ///

    typedef typename Graph::template NodeMap<typename _LengthMap::Value> 

    DistMap;

    /// \brief Instantiates a DistMap.

    ///

    /// This function instantiates a \ref DistMap. 

    /// \param G is the graph, to which we would like to define the 

    /// \ref DistMap

    static DistMap *createDistMap(const _Graph& graph) {

      return new DistMap(graph);

    }

  };

  /// \brief BelmannFord algorithm class.

  ///

  /// \ingroup flowalgs

  /// This class provides an efficient implementation of \c BelmannFord 

  /// algorithm. The edge lengths are passed to the algorithm using a

  /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any 

  /// kind of length.

  ///

  /// The type of the length is determined by the

  /// \ref concept::ReadMap::Value "Value" of the length map.

  ///

  /// \param _Graph The graph type the algorithm runs on. The default value

  /// is \ref ListGraph. The value of _Graph is not used directly by

  /// BelmannFord, it is only passed to \ref BelmannFordDefaultTraits.

  /// \param _LengthMap This read-only EdgeMap determines the lengths of the

  /// edges. The default map type is \ref concept::StaticGraph::EdgeMap 

  /// "Graph::EdgeMap<int>".  The value of _LengthMap is not used directly 

  /// by BelmannFord, it is only passed to \ref BelmannFordDefaultTraits.  

  /// \param _Traits Traits class to set various data types used by the 

  /// algorithm.  The default traits class is \ref BelmannFordDefaultTraits

  /// "BelmannFordDefaultTraits<_Graph,_LengthMap>".  See \ref

  /// BelmannFordDefaultTraits for the documentation of a BelmannFord traits

  /// class.

  ///

  /// \author Balazs Dezso

  template <typename _Graph=ListGraph,

	    typename _LengthMap=typename _Graph::template EdgeMap<int>,

	    typename _Traits=BelmannFordDefaultTraits<_Graph,_LengthMap> >

  class BelmannFord {

  public:

    /// \brief \ref Exception for uninitialized parameters.

    ///

    /// This error represents problems in the initialization

    /// of the parameters of the algorithms.

    class UninitializedParameter : public lemon::UninitializedParameter {

    public:

      virtual const char* exceptionName() const {

	return "lemon::BelmannFord::UninitializedParameter";

      }

    };

    typedef _Traits Traits;

    ///The type of the underlying graph.

    typedef typename _Traits::Graph Graph;

    typedef typename Graph::Node Node;

    typedef typename Graph::NodeIt NodeIt;

    typedef typename Graph::Edge Edge;

    typedef typename Graph::EdgeIt EdgeIt;

    /// \brief The type of the length of the edges.

    typedef typename _Traits::LengthMap::Value Value;

    /// \brief The type of the map that stores the edge lengths.

    typedef typename _Traits::LengthMap LengthMap;

    /// \brief The type of the map that stores the last

    /// edges of the shortest paths.

    typedef typename _Traits::PredMap PredMap;

    /// \brief The type of the map that stores the dists of the nodes.

    typedef typename _Traits::DistMap DistMap;

    /// \brief The operation traits.

    typedef typename _Traits::OperationTraits OperationTraits;

  private:

    /// Pointer to the underlying graph.

    const Graph *graph;

    /// Pointer to the length map

    const LengthMap *length;

    ///Pointer to the map of predecessors edges.

    PredMap *_pred;

    ///Indicates if \ref _pred is locally allocated (\c true) or not.

    bool local_pred;

    ///Pointer to the map of distances.

    DistMap *_dist;

    ///Indicates if \ref _dist is locally allocated (\c true) or not.

    bool local_dist;

    /// Creates the maps if necessary.

    void create_maps() {

      if(!_pred) {

	local_pred = true;

	_pred = Traits::createPredMap(*graph);

      }

      if(!_dist) {

	local_dist = true;

	_dist = Traits::createDistMap(*graph);

      }

    }

  public :

    /// \name Named template parameters

    ///@{

    template <class T>

    struct DefPredMapTraits : public Traits {

      typedef T PredMap;

      static PredMap *createPredMap(const Graph& graph) {

	throw UninitializedParameter();

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for setting PredMap 

    /// type

    /// \ref named-templ-param "Named parameter" for setting PredMap type

    ///

    template <class T>

    class DefPredMap 

      : public BelmannFord< Graph, LengthMap, DefPredMapTraits<T> > {};

    template <class T>

    struct DefDistMapTraits : public Traits {

      typedef T DistMap;

      static DistMap *createDistMap(const Graph& graph) {

	throw UninitializedParameter();

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for setting DistMap 

    /// type

    ///

    /// \ref named-templ-param "Named parameter" for setting DistMap type

    ///

    template <class T>

    class DefDistMap 

      : public BelmannFord< Graph, LengthMap, DefDistMapTraits<T> > {};

    template <class T>

    struct DefOperationTraitsTraits : public Traits {

      typedef T OperationTraits;

    };

    /// \brief \ref named-templ-param "Named parameter" for setting 

    /// OperationTraits type

    ///

    /// \ref named-templ-param "Named parameter" for setting PredMap type

    template <class T>

    class DefOperationTraits

      : public BelmannFord< Graph, LengthMap, DefOperationTraitsTraits<T> > {

    public:

      typedef BelmannFord< Graph, LengthMap, DefOperationTraitsTraits<T> >

      BelmannFord;

    };

    ///@}

  public:      

    /// \brief Constructor.

    ///

    /// \param _graph the graph the algorithm will run on.

    /// \param _length the length map used by the algorithm.

    BelmannFord(const Graph& _graph, const LengthMap& _length) :

      graph(&_graph), length(&_length),

      _pred(0), local_pred(false),

      _dist(0), local_dist(false) {}

    ///Destructor.

    ~BelmannFord() {

      if(local_pred) delete _pred;

      if(local_dist) delete _dist;

    }

    /// \brief Sets the length map.

    ///

    /// Sets the length map.

    /// \return \c (*this)

    BelmannFord &lengthMap(const LengthMap &m) {

      length = &m;

      return *this;

    }

    /// \brief Sets the map storing the predecessor edges.

    ///

    /// Sets the map storing the predecessor edges.

    /// If you don't use this function before calling \ref run(),

    /// it will allocate one. The destuctor deallocates this

    /// automatically allocated map, of course.

    /// \return \c (*this)

    BelmannFord &predMap(PredMap &m) {

      if(local_pred) {

	delete _pred;

	local_pred=false;

      }

      _pred = &m;

      return *this;

    }

    /// \brief Sets the map storing the distances calculated by the algorithm.

    ///

    /// Sets the map storing the distances calculated by the algorithm.

    /// If you don't use this function before calling \ref run(),

    /// it will allocate one. The destuctor deallocates this

    /// automatically allocated map, of course.

    /// \return \c (*this)

    BelmannFord &distMap(DistMap &m) {

      if(local_dist) {

	delete _dist;

	local_dist=false;

      }

      _dist = &m;

      return *this;

    }

    /// \name Execution control

    /// The simplest way to execute the algorithm is to use

    /// one of the member functions called \c run(...).

    /// \n

    /// If you need more control on the execution,

    /// first you must call \ref init(), then you can add several source nodes

    /// with \ref addSource().

    /// Finally \ref start() will perform the actual path

    /// computation.

    ///@{

    /// \brief Initializes the internal data structures.

    /// 

    /// Initializes the internal data structures.

    void init() {

      create_maps();

      for (NodeIt it(*graph); it != INVALID; ++it) {

	_pred->set(it, INVALID);

	_dist->set(it, OperationTraits::infinity());

      }

    }

    /// \brief Adds a new source node.

    ///

    /// The optional second parameter is the initial distance of the node.

    /// It just sets the distance of the node to the given value.

    void addSource(Node source, Value dst = OperationTraits::zero()) {

      _dist->set(source, dst);

    }

    /// \brief Executes the algorithm.

    ///

    /// \pre init() must be called and at least one node should be added

    /// with addSource() before using this function.

    ///

    /// This method runs the %BelmannFord algorithm from the root node(s)

    /// in order to compute the shortest path to each node. The algorithm 

    /// computes 

    /// - The shortest path tree.

    /// - The distance of each node from the root(s).

    void start() {

      bool ready = false;

      while (!ready) {

	ready = true;

	for (EdgeIt it(*graph); it != INVALID; ++it) {

	  Node source = graph->source(it);

	  Node target = graph->target(it);

	  Value relaxed = 

	    OperationTraits::plus((*_dist)[source], (*length)[it]);

	  if (OperationTraits::less(relaxed, (*_dist)[target])) {

	    _pred->set(target, it);

	    _dist->set(target, relaxed);

	    ready = false; 

	  }

	}

      }

    }

    /// \brief Runs %BelmannFord algorithm from node \c s.

    ///    

    /// This method runs the %BelmannFord algorithm from a root node \c s

    /// in order to compute the shortest path to each node. The algorithm 

    /// computes

    /// - The shortest path tree.

    /// - The distance of each node from the root.

    ///

    /// \note d.run(s) is just a shortcut of the following code.

    /// \code

    ///  d.init();

    ///  d.addSource(s);

    ///  d.start();

    /// \endcode

    void run(Node s) {

      init();

      addSource(s);

      start();

    }

    ///@}

    /// \name Query Functions

    /// The result of the %BelmannFord algorithm can be obtained using these

    /// functions.\n

    /// Before the use of these functions,

    /// either run() or start() must be called.

    ///@{

    /// \brief Copies the shortest path to \c t into \c p

    ///    

    /// This function copies the shortest path to \c t into \c p.

    /// If it \c t is a source itself or unreachable, then it does not

    /// alter \c p.

    /// \todo Is it the right way to handle unreachable nodes?

    /// \return Returns \c true if a path to \c t was actually copied to \c p,

    /// \c false otherwise.

    /// \sa DirPath

    template <typename Path>

    bool getPath(Path &p, Node t) {

      if(reached(t)) {

	p.clear();

	typename Path::Builder b(p);

	for(b.setStartNode(t);pred(t)!=INVALID;t=predNode(t))

	  b.pushFront(pred(t));

	b.commit();

	return true;

      }

      return false;

    }

    /// \brief The distance of a node from the root.

    ///

    /// Returns the distance of a node from the root.

    /// \pre \ref run() must be called before using this function.

    /// \warning If node \c v in unreachable from the root the return value

    /// of this funcion is undefined.

    Value dist(Node v) const { return (*_dist)[v]; }

    /// \brief Returns the 'previous edge' of the shortest path tree.

    ///

    /// For a node \c v it returns the 'previous edge' of the shortest path 

    /// tree, i.e. it returns the last edge of a shortest path from the root 

    /// to \c v. It is \ref INVALID if \c v is unreachable from the root or 

    /// if \c v=s. The shortest path tree used here is equal to the shortest 

    /// path tree used in \ref predNode(). 

    /// \pre \ref run() must be called before using

    /// this function.

    /// \todo predEdge could be a better name.

    Edge pred(Node v) const { return (*_pred)[v]; }

    /// \brief Returns the 'previous node' of the shortest path tree.

    ///

    /// For a node \c v it returns the 'previous node' of the shortest path 

    /// tree, i.e. it returns the last but one node from a shortest path from 

    /// the root to \c /v. It is INVALID if \c v is unreachable from the root 

    /// or if \c v=s. The shortest path tree used here is equal to the 

    /// shortest path tree used in \ref pred().  \pre \ref run() must be 

    /// called before using this function.

    Node predNode(Node v) const { 

      return (*_pred)[v] == INVALID ? INVALID : graph->source((*_pred)[v]); 

    }

    /// \brief Returns a reference to the NodeMap of distances.

    ///

    /// Returns a reference to the NodeMap of distances. \pre \ref run() must

    /// be called before using this function.

    const DistMap &distMap() const { return *_dist;}

    /// \brief Returns a reference to the shortest path tree map.

    ///

    /// Returns a reference to the NodeMap of the edges of the

    /// shortest path tree.

    /// \pre \ref run() must be called before using this function.

    const PredMap &predMap() const { return *_pred; }

    /// \brief Checks if a node is reachable from the root.

    ///

    /// Returns \c true if \c v is reachable from the root.

    /// \pre \ref run() must be called before using this function.

    ///

    bool reached(Node v) { return (*_dist)[v] != OperationTraits::infinity(); }

    ///@}

  };

  /// \brief Default traits class of BelmannFord function.

  ///

  /// Default traits class of BelmannFord function.

  /// \param _Graph Graph type.

  /// \param _LengthMap Type of length map.

  template <typename _Graph, typename _LengthMap>

  struct BelmannFordWizardDefaultTraits {

    /// \brief The graph type the algorithm runs on. 

    typedef _Graph Graph;

    /// \brief The type of the map that stores the edge lengths.

    ///

    /// The type of the map that stores the edge lengths.

    /// It must meet the \ref concept::ReadMap "ReadMap" concept.

    typedef _LengthMap LengthMap;

    /// \brief The value type of the length map.

    typedef typename _LengthMap::Value Value;

    /// \brief Operation traits for belmann-ford algorithm.

    ///

    /// It defines the infinity type on the given Value type

    /// and the used operation.

    /// \see BelmannFordDefaultOperationTraits

    typedef BelmannFordDefaultOperationTraits<Value> OperationTraits;

    /// \brief The type of the map that stores the last

    /// edges of the shortest paths.

    /// 

    /// The type of the map that stores the last

    /// edges of the shortest paths.

    /// It must meet the \ref concept::WriteMap "WriteMap" concept.

    typedef NullMap <typename _Graph::Node,typename _Graph::Edge> PredMap;

    /// \brief Instantiates a PredMap.

    /// 

    /// This function instantiates a \ref PredMap. 

    static PredMap *createPredMap(const _Graph &) {

      return new PredMap();

    }

    /// \brief The type of the map that stores the dists of the nodes.

    ///

    /// The type of the map that stores the dists of the nodes.

    /// It must meet the \ref concept::WriteMap "WriteMap" concept.

    typedef NullMap<typename Graph::Node, Value> DistMap;

    /// \brief Instantiates a DistMap.

    ///

    /// This function instantiates a \ref DistMap. 

    static DistMap *createDistMap(const _Graph &) {

      return new DistMap();

    }

  };

  /// \brief Default traits used by \ref BelmannFordWizard

  ///

  /// To make it easier to use BelmannFord algorithm

  /// we have created a wizard class.

  /// This \ref BelmannFordWizard class needs default traits,

  /// as well as the \ref BelmannFord class.

  /// The \ref BelmannFordWizardBase is a class to be the default traits of the

  /// \ref BelmannFordWizard class.

  /// \todo More named parameters are required...

  template<class _Graph,class _LengthMap>

  class BelmannFordWizardBase 

    : public BelmannFordWizardDefaultTraits<_Graph,_LengthMap> {

    typedef BelmannFordWizardDefaultTraits<_Graph,_LengthMap> Base;

  protected:

    /// Type of the nodes in the graph.

    typedef typename Base::Graph::Node Node;

    /// Pointer to the underlying graph.

    void *_graph;

    /// Pointer to the length map

    void *_length;

    ///Pointer to the map of predecessors edges.

    void *_pred;

    ///Pointer to the map of distances.

    void *_dist;

    ///Pointer to the source node.

    Node _source;

    public:

    /// Constructor.

    /// This constructor does not require parameters, therefore it initiates

    /// all of the attributes to default values (0, INVALID).

    BelmannFordWizardBase() : _graph(0), _length(0), _pred(0),

			   _dist(0), _source(INVALID) {}

    /// Constructor.

    /// This constructor requires some parameters,

    /// listed in the parameters list.

    /// Others are initiated to 0.

    /// \param graph is the initial value of  \ref _graph

    /// \param length is the initial value of  \ref _length

    /// \param source is the initial value of  \ref _source

    BelmannFordWizardBase(const _Graph& graph, 

			  const _LengthMap& length, 

			  Node source = INVALID) :

      _graph((void *)&graph), _length((void *)&length), _pred(0),

      _dist(0), _source(source) {}

  };

  /// A class to make the usage of BelmannFord algorithm easier

  /// This class is created to make it easier to use BelmannFord algorithm.

  /// It uses the functions and features of the plain \ref BelmannFord,

  /// but it is much simpler to use it.

  ///

  /// Simplicity means that the way to change the types defined

  /// in the traits class is based on functions that returns the new class

  /// and not on templatable built-in classes.

  /// When using the plain \ref BelmannFord

  /// the new class with the modified type comes from

  /// the original class by using the ::

  /// operator. In the case of \ref BelmannFordWizard only

  /// a function have to be called and it will

  /// return the needed class.

  ///

  /// It does not have own \ref run method. When its \ref run method is called

  /// it initiates a plain \ref BelmannFord class, and calls the \ref 

  /// BelmannFord::run method of it.

  template<class _Traits>

  class BelmannFordWizard : public _Traits {

    typedef _Traits Base;

    ///The type of the underlying graph.

    typedef typename _Traits::Graph Graph;

    typedef typename Graph::Node Node;

    typedef typename Graph::NodeIt NodeIt;

    typedef typename Graph::Edge Edge;

    typedef typename Graph::OutEdgeIt EdgeIt;

    ///The type of the map that stores the edge lengths.

    typedef typename _Traits::LengthMap LengthMap;

    ///The type of the length of the edges.

    typedef typename LengthMap::Value Value;

    ///\brief The type of the map that stores the last

    ///edges of the shortest paths.

    typedef typename _Traits::PredMap PredMap;

    ///The type of the map that stores the dists of the nodes.

    typedef typename _Traits::DistMap DistMap;

  public:

    /// Constructor.

    BelmannFordWizard() : _Traits() {}

    /// \brief Constructor that requires parameters.

    ///

    /// Constructor that requires parameters.

    /// These parameters will be the default values for the traits class.

    BelmannFordWizard(const Graph& graph, const LengthMap& length, 

		      Node source = INVALID) 

      : _Traits(graph, length, source) {}

    /// \brief Copy constructor

    BelmannFordWizard(const _Traits &b) : _Traits(b) {}

    ~BelmannFordWizard() {}

    /// \brief Runs BelmannFord algorithm from a given node.

    ///    

    /// Runs BelmannFord algorithm from a given node.

    /// The node can be given by the \ref source function.

    void run() {

      if(Base::_source == INVALID) throw UninitializedParameter();

      BelmannFord<Graph,LengthMap,_Traits> 

	bf(*(Graph*)Base::_graph, *(LengthMap*)Base::_length);

      if (Base::_pred) bf.predMap(*(PredMap*)Base::_pred);

      if (Base::_dist) bf.distMap(*(DistMap*)Base::_dist);

      bf.run(Base::_source);

    }

    /// \brief Runs BelmannFord algorithm from the given node.

    ///

    /// Runs BelmannFord algorithm from the given node.

    /// \param s is the given source.

    void run(Node source) {

      Base::_source = source;

      run();

    }

    template<class T>

    struct DefPredMapBase : public Base {

      typedef T PredMap;

      static PredMap *createPredMap(const Graph &) { return 0; };

      DefPredMapBase(const _Traits &b) : _Traits(b) {}

    };

    ///\brief \ref named-templ-param "Named parameter"

    ///function for setting PredMap type

    ///

    /// \ref named-templ-param "Named parameter"

    ///function for setting PredMap type

    ///

    template<class T>

    BelmannFordWizard<DefPredMapBase<T> > predMap(const T &t) 

    {

      Base::_pred=(void *)&t;

      return BelmannFordWizard<DefPredMapBase<T> >(*this);

    }

    template<class T>

    struct DefDistMapBase : public Base {

      typedef T DistMap;

      static DistMap *createDistMap(const Graph &) { return 0; };

      DefDistMapBase(const _Traits &b) : _Traits(b) {}

    };

    ///\brief \ref named-templ-param "Named parameter"

    ///function for setting DistMap type

    ///

    /// \ref named-templ-param "Named parameter"

    ///function for setting DistMap type

    ///

    template<class T>

    BelmannFordWizard<DefDistMapBase<T> > distMap(const T &t) {

      Base::_dist=(void *)&t;

      return BelmannFordWizard<DefDistMapBase<T> >(*this);

    }

    /// \brief Sets the source node, from which the BelmannFord algorithm runs.

    ///

    /// Sets the source node, from which the BelmannFord algorithm runs.

    /// \param s is the source node.

    BelmannFordWizard<_Traits>& source(Node source) {

      Base::_source = source;

      return *this;

    }

  };

  /// \brief Function type interface for BelmannFord algorithm.

  ///

  /// \ingroup flowalgs

  /// Function type interface for BelmannFord algorithm.

  ///

  /// This function also has several \ref named-templ-func-param 

  /// "named parameters", they are declared as the members of class 

  /// \ref BelmannFordWizard.

  /// The following

  /// example shows how to use these parameters.

  /// \code

  /// belmannford(g,length,source).predMap(preds).run();

  /// \endcode

  /// \warning Don't forget to put the \ref BelmannFordWizard::run() "run()"

  /// to the end of the parameter list.

  /// \sa BelmannFordWizard

  /// \sa BelmannFord

  template<class _Graph, class _LengthMap>

  BelmannFordWizard<BelmannFordWizardBase<_Graph,_LengthMap> >

  belmannFord(const _Graph& graph,

	      const _LengthMap& length, 

	      typename _Graph::Node source = INVALID) {

    return BelmannFordWizard<BelmannFordWizardBase<_Graph,_LengthMap> >

      (graph, length, source);

  }

} //END OF NAMESPACE LEMON

#endif