source: lemon-0.x/lemon/belmann_ford.h @ 1707:39496e5482af

/* -*- 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