Index: mon/belmann_ford.h
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--- lemon/belmann_ford.h	(revision 1858)
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-/* -*- 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.
-///
-
-#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 graph is the graph, to which we would like to define the PredMap.
-    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 graph 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 Belmann-Ford 
-  /// 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 Belmann-Ford algorithm solves the shortest path from one node
-  /// problem when the edges can have negative length but the graph should
-  /// not contain cycles with negative sum of length. If we can assume
-  /// that all edge is non-negative in the graph then the dijkstra algorithm
-  /// should be used rather.
-  ///
-  /// The complexity of the algorithm is O(n * e).
-  ///
-  /// 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
-
-#ifdef DOXYGEN
-  template <typename _Graph, typename _LengthMap, typename _Traits>
-#else
-  template <typename _Graph=ListGraph,
-	    typename _LengthMap=typename _Graph::template EdgeMap<int>,
-	    typename _Traits=BelmannFordDefaultTraits<_Graph,_LengthMap> >
-#endif
-  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::OutEdgeIt OutEdgeIt;
-    
-    /// \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;
-
-    typedef typename Graph::template NodeMap<bool> MaskMap;
-    MaskMap *_mask;
-
-    std::vector<Node> _process;
-
-    /// 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);
-      }
-      _mask = new MaskMap(*graph, false);
-    }
-    
-  public :
- 
-    typedef BelmannFord Create;
-
-    /// \name Named template parameters
-
-    ///@{
-
-    template <class T>
-    struct DefPredMapTraits : public Traits {
-      typedef T PredMap;
-      static PredMap *createPredMap(const 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>
-    struct DefPredMap 
-      : public BelmannFord< Graph, LengthMap, DefPredMapTraits<T> > {
-      typedef BelmannFord< Graph, LengthMap, DefPredMapTraits<T> > Create;
-    };
-    
-    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>
-    struct DefDistMap 
-      : public BelmannFord< Graph, LengthMap, DefDistMapTraits<T> > {
-      typedef BelmannFord< Graph, LengthMap, DefDistMapTraits<T> > Create;
-    };
-    
-    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 OperationTraits
-    /// type
-    template <class T>
-    struct DefOperationTraits
-      : public BelmannFord< Graph, LengthMap, DefOperationTraitsTraits<T> > {
-      typedef BelmannFord< Graph, LengthMap, DefOperationTraitsTraits<T> >
-      Create;
-    };
-    
-    ///@}
-
-  protected:
-    
-    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;
-      delete _mask;
-    }
-
-    /// \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(const Value value = OperationTraits::infinity()) {
-      create_maps();
-      for (NodeIt it(*graph); it != INVALID; ++it) {
-	_pred->set(it, INVALID);
-	_dist->set(it, value);
-      }
-      _process.clear();
-      if (OperationTraits::less(value, OperationTraits::infinity())) {
-	for (NodeIt it(*graph); it != INVALID; ++it) {
-	  _process.push_back(it);
-	  _mask->set(it, true);
-	}
-      }
-    }
-    
-    /// \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);
-      if (!(*_mask)[source]) {
-	_process.push_back(source);
-	_mask->set(source, true);
-      }
-    }
-
-    /// \brief Executes one round from the belmann ford algorithm.
-    ///
-    /// If the algoritm calculated the distances in the previous round 
-    /// strictly for all at most k length paths then it will calculate the 
-    /// distances strictly for all at most k + 1 length paths. With k
-    /// iteration this function calculates the at most k length paths.
-    /// \return %True when the algorithm have not found more shorter paths.
-    bool processNextRound() {
-      for (int i = 0; i < (int)_process.size(); ++i) {
-	_mask->set(_process[i], false);
-      }
-      std::vector<Node> nextProcess;
-      std::vector<Value> values(_process.size());
-      for (int i = 0; i < (int)_process.size(); ++i) {
-	values[i] = (*_dist)[_process[i]];
-      }
-      for (int i = 0; i < (int)_process.size(); ++i) {
-	for (OutEdgeIt it(*graph, _process[i]); it != INVALID; ++it) {
-	  Node target = graph->target(it);
-	  Value relaxed = OperationTraits::plus(values[i], (*length)[it]);
-	  if (OperationTraits::less(relaxed, (*_dist)[target])) {
-	    _pred->set(target, it);
-	    _dist->set(target, relaxed);
-	    if (!(*_mask)[target]) {
-	      _mask->set(target, true);
-	      nextProcess.push_back(target);
-	    }
-	  }	  
-	}
-      }
-      _process.swap(nextProcess);
-      return _process.empty();
-    }
-
-    /// \brief Executes one weak round from the belmann ford algorithm.
-    ///
-    /// If the algorithm calculated the distances in the
-    /// previous round at least for all at most k length paths then it will
-    /// calculate the distances at least for all at most k + 1 length paths.
-    /// This function does not make it possible to calculate strictly the
-    /// at most k length minimal paths, this is why it is
-    /// called just weak round.
-    /// \return %True when the algorithm have not found more shorter paths.
-    bool processNextWeakRound() {
-      for (int i = 0; i < (int)_process.size(); ++i) {
-	_mask->set(_process[i], false);
-      }
-      std::vector<Node> nextProcess;
-      for (int i = 0; i < (int)_process.size(); ++i) {
-	for (OutEdgeIt it(*graph, _process[i]); it != INVALID; ++it) {
-	  Node target = graph->target(it);
-	  Value relaxed = 
-	    OperationTraits::plus((*_dist)[_process[i]], (*length)[it]);
-	  if (OperationTraits::less(relaxed, (*_dist)[target])) {
-	    _pred->set(target, it);
-	    _dist->set(target, relaxed);
-	    if (!(*_mask)[target]) {
-	      _mask->set(target, true);
-	      nextProcess.push_back(target);
-	    }
-	  }	  
-	}
-      }
-      _process.swap(nextProcess);
-      return _process.empty();
-    }
-
-    /// \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() {
-      int num = countNodes(*graph) - 1;
-      for (int i = 0; i < num; ++i) {
-	if (processNextWeakRound()) break;
-      }
-    }
-
-    /// \brief Executes the algorithm and checks the negative cycles.
-    ///
-    /// \pre init() must be called and at least one node should be added
-    /// with addSource() before using this function. If there is
-    /// a negative cycles in the graph it gives back false.
-    ///
-    /// 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).
-    bool checkedStart() {
-      int num = countNodes(*graph);
-      for (int i = 0; i < num; ++i) {
-	if (processNextWeakRound()) return true;
-      }
-      return false;
-    }
-
-    /// \brief Executes the algorithm with path length limit.
-    ///
-    /// \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 with at most \c length edge 
-    /// long paths to each node. The algorithm computes 
-    /// - The shortest path tree.
-    /// - The limited distance of each node from the root(s).
-    void limitedStart(int length) {
-      for (int i = 0; i < length; ++i) {
-	if (processNextRound()) break;
-      }
-    }
-    
-    /// \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();
-    }
-    
-    /// \brief Runs %BelmannFord algorithm with limited path length 
-    /// from node \c s.
-    ///    
-    /// This method runs the %BelmannFord algorithm from a root node \c s
-    /// in order to compute the shortest path with at most \c len edges 
-    /// to each node. The algorithm computes
-    /// - The shortest path tree.
-    /// - The distance of each node from the root.
-    ///
-    /// \note d.run(s, len) is just a shortcut of the following code.
-    /// \code
-    ///  d.init();
-    ///  d.addSource(s);
-    ///  d.limitedStart(len);
-    /// \endcode
-    void run(Node s, int len) {
-      init();
-      addSource(s);
-      limitedStart(len);
-    }
-    
-    ///@}
-
-    /// \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.
-    ///
-    /// \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);predEdge(t)!=INVALID;t=predNode(t))
-	  b.pushFront(predEdge(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.
-    Edge predEdge(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 predEdge().  \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 source 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);
-    }
-
-    template<class T>
-    struct DefOperationTraitsBase : public Base {
-      typedef T OperationTraits;
-      DefOperationTraitsBase(const _Traits &b) : _Traits(b) {}
-    };
-    
-    ///\brief \ref named-templ-param "Named parameter"
-    ///function for setting OperationTraits type
-    ///
-    /// \ref named-templ-param "Named parameter"
-    ///function for setting OperationTraits type
-    ///
-    template<class T>
-    BelmannFordWizard<DefOperationTraitsBase<T> > distMap() {
-      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 source 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
-
