Ticket #51: 51-1-port-c9b9da1a90a0.patch

lemon/Makefile.am

@@ -57 +57 @@
         lemon/adaptors.h \
         lemon/arg_parser.h \
         lemon/assert.h \
+        lemon/bellman_ford.h \
         lemon/bfs.h \
         lemon/bin_heap.h \
         lemon/bucket_heap.h \

new file lemon/bellman_ford.h

@@ +1 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2008
+ * 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 shortest_path
+/// \file
+/// \brief Bellman-Ford algorithm.
+///
+
+#include <lemon/bits/path_dump.h>
+#include <lemon/core.h>
+#include <lemon/error.h>
+#include <lemon/maps.h>
+
+#include <limits>
+
+namespace lemon {
+
+  /// \brief Default OperationTraits for the BellmanFord algorithm class.
+  ///  
+  /// It defines all computational operations and constants which are
+  /// used in the Bellman-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 BellmanFordDefaultOperationTraits {
+    /// \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 BellmanFordDefaultOperationTraits<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 BellmanFord class.
+  ///
+  /// Default traits class of BellmanFord class.
+  /// \param _Digraph Digraph type.
+  /// \param _LegthMap Type of length map.
+  template<class _Digraph, class _LengthMap>
+  struct BellmanFordDefaultTraits {
+    /// The digraph type the algorithm runs on. 
+    typedef _Digraph Digraph;
+
+    /// \brief The type of the map that stores the arc lengths.
+    ///
+    /// The type of the map that stores the arc lengths.
+    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
+    typedef _LengthMap LengthMap;
+
+    // The type of the length of the arcs.
+    typedef typename _LengthMap::Value Value;
+
+    /// \brief Operation traits for Bellman-Ford algorithm.
+    ///
+    /// It defines the infinity type on the given Value type
+    /// and the used operation.
+    /// \see BellmanFordDefaultOperationTraits
+    typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
+ 
+    /// \brief The type of the map that stores the last arcs of the 
+    /// shortest paths.
+    /// 
+    /// The type of the map that stores the last
+    /// arcs of the shortest paths.
+    /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef typename Digraph::template NodeMap<typename _Digraph::Arc> PredMap;
+
+    /// \brief Instantiates a PredMap.
+    /// 
+    /// This function instantiates a \ref PredMap. 
+    /// \param digraph is the digraph, to which we would like to define the PredMap.
+    static PredMap *createPredMap(const _Digraph& digraph) {
+      return new PredMap(digraph);
+    }
+
+    /// \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 concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef typename Digraph::template NodeMap<typename _LengthMap::Value> 
+    DistMap;
+
+    /// \brief Instantiates a DistMap.
+    ///
+    /// This function instantiates a \ref DistMap. 
+    /// \param digraph is the digraph, to which we would like to define the 
+    /// \ref DistMap
+    static DistMap *createDistMap(const _Digraph& digraph) {
+      return new DistMap(digraph);
+    }
+
+  };
+  
+  /// \brief %BellmanFord algorithm class.
+  ///
+  /// \ingroup shortest_path
+  /// This class provides an efficient implementation of \c Bellman-Ford 
+  /// algorithm. The arc lengths are passed to the algorithm using a
+  /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any 
+  /// kind of length.
+  ///
+  /// The Bellman-Ford algorithm solves the shortest path from one node
+  /// problem when the arcs can have negative length but the digraph should
+  /// not contain cycles with negative sum of length. If we can assume
+  /// that all arc is non-negative in the digraph then the dijkstra algorithm
+  /// should be used rather.
+  ///
+  /// The maximal time complexity of the algorithm is \f$ O(ne) \f$.
+  ///
+  /// The type of the length is determined by the
+  /// \ref concepts::ReadMap::Value "Value" of the length map.
+  ///
+  /// \param _Digraph The digraph type the algorithm runs on. The default value
+  /// is \ref ListDigraph. The value of _Digraph is not used directly by
+  /// BellmanFord, it is only passed to \ref BellmanFordDefaultTraits.
+  /// \param _LengthMap This read-only ArcMap determines the lengths of the
+  /// arcs. The default map type is \ref concepts::Digraph::ArcMap 
+  /// "Digraph::ArcMap<int>".  The value of _LengthMap is not used directly 
+  /// by BellmanFord, it is only passed to \ref BellmanFordDefaultTraits.  
+  /// \param _Traits Traits class to set various data types used by the 
+  /// algorithm.  The default traits class is \ref BellmanFordDefaultTraits
+  /// "BellmanFordDefaultTraits<_Digraph,_LengthMap>".  See \ref
+  /// BellmanFordDefaultTraits for the documentation of a BellmanFord traits
+  /// class.
+#ifdef DOXYGEN
+  template <typename _Digraph, typename _LengthMap, typename _Traits>
+#else
+  template <typename _Digraph,
+            typename _LengthMap=typename _Digraph::template ArcMap<int>,
+            typename _Traits=BellmanFordDefaultTraits<_Digraph,_LengthMap> >
+#endif
+  class BellmanFord {
+  public:
+
+    typedef _Traits Traits;
+    ///The type of the underlying digraph.
+    typedef typename _Traits::Digraph Digraph;
+
+    typedef typename Digraph::Node Node;
+    typedef typename Digraph::NodeIt NodeIt;
+    typedef typename Digraph::Arc Arc;
+    typedef typename Digraph::OutArcIt OutArcIt;
+    
+    /// \brief The type of the length of the arcs.
+    typedef typename _Traits::LengthMap::Value Value;
+    /// \brief The type of the map that stores the arc lengths.
+    typedef typename _Traits::LengthMap LengthMap;
+    /// \brief The type of the map that stores the last
+    /// arcs 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 digraph.
+    const Digraph *digraph;
+    /// Pointer to the length map
+    const LengthMap *length;
+    ///Pointer to the map of predecessors arcs.
+    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 Digraph::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(*digraph);
+      }
+      if(!_dist) {
+        local_dist = true;
+        _dist = Traits::createDistMap(*digraph);
+      }
+      _mask = new MaskMap(*digraph, false);
+    }
+    
+  public :
+ 
+    typedef BellmanFord Create;
+
+    /// \name Named template parameters
+
+    ///@{
+
+    template <class T>
+    struct DefPredMapTraits : public Traits {
+      typedef T PredMap;
+      static PredMap *createPredMap(const Digraph&) {
+        LEMON_ASSERT(false, "PredMap is not initialized");
+        return 0; // ignore warnings
+      }
+    };
+
+    /// \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 SetPredMap 
+      : public BellmanFord< Digraph, LengthMap, DefPredMapTraits<T> > {
+      typedef BellmanFord< Digraph, LengthMap, DefPredMapTraits<T> > Create;
+    };
+    
+    template <class T>
+    struct DefDistMapTraits : public Traits {
+      typedef T DistMap;
+      static DistMap *createDistMap(const Digraph&) {
+        LEMON_ASSERT(false, "DistMap is not initialized");
+        return 0; // ignore warnings
+      }
+    };
+
+    /// \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 SetDistMap 
+      : public BellmanFord< Digraph, LengthMap, DefDistMapTraits<T> > {
+      typedef BellmanFord< Digraph, 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 SetOperationTraits
+      : public BellmanFord< Digraph, LengthMap, DefOperationTraitsTraits<T> > {
+      typedef BellmanFord< Digraph, LengthMap, DefOperationTraitsTraits<T> >
+      Create;
+    };
+    
+    ///@}
+
+  protected:
+    
+    BellmanFord() {}
+
+  public:      
+    
+    /// \brief Constructor.
+    ///
+    /// \param _graph the digraph the algorithm will run on.
+    /// \param _length the length map used by the algorithm.
+    BellmanFord(const Digraph& _graph, const LengthMap& _length) :
+      digraph(&_graph), length(&_length),
+      _pred(0), local_pred(false),
+      _dist(0), local_dist(false), _mask(0) {}
+    
+    ///Destructor.
+    ~BellmanFord() {
+      if(local_pred) delete _pred;
+      if(local_dist) delete _dist;
+      if(_mask) delete _mask;
+    }
+
+    /// \brief Sets the length map.
+    ///
+    /// Sets the length map.
+    /// \return \c (*this)
+    BellmanFord &lengthMap(const LengthMap &m) {
+      length = &m;
+      return *this;
+    }
+
+    /// \brief Sets the map storing the predecessor arcs.
+    ///
+    /// Sets the map storing the predecessor arcs.
+    /// 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)
+    BellmanFord &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)
+    BellmanFord &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(*digraph); it != INVALID; ++it) {
+        _pred->set(it, INVALID);
+        _dist->set(it, value);
+      }
+      _process.clear();
+      if (OperationTraits::less(value, OperationTraits::infinity())) {
+        for (NodeIt it(*digraph); it != INVALID; ++it) {
+          _process.push_back(it);
+          _mask->set(it, true);
+        }
+      }
+    }
+    
+    /// \brief Adds a new source node.
+    ///
+    /// 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 Bellman-Ford algorithm.
+    ///
+    /// If the algoritm calculated the distances in the previous round
+    /// exactly for all at most \f$ k \f$ length path lengths then it will
+    /// calculate the distances exactly for all at most \f$ k + 1 \f$
+    /// length path lengths. With \f$ k \f$ iteration this function
+    /// calculates the at most \f$ k \f$ length path lengths.
+    ///
+    /// \warning The paths with limited arc number cannot be retrieved
+    /// easily with \ref path() or \ref predArc() functions. If you
+    /// need the shortest path and not just the distance you should store
+    /// after each iteration the \ref predMap() map and manually build
+    /// the path.
+    ///
+    /// \return \c 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 (OutArcIt it(*digraph, _process[i]); it != INVALID; ++it) {
+          Node target = digraph->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 Bellman-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 \c 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 (OutArcIt it(*digraph, _process[i]); it != INVALID; ++it) {
+          Node target = digraph->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 %BellmanFord 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(*digraph) - 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. 
+    ///
+    /// This method runs the %BellmanFord 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).
+    /// 
+    /// \return \c false if there is a negative cycle in the digraph.
+    bool checkedStart() {
+      int num = countNodes(*digraph);
+      for (int i = 0; i < num; ++i) {
+        if (processNextWeakRound()) return true;
+      }
+      return _process.empty();
+    }
+
+    /// \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 %BellmanFord algorithm from the root
+    /// node(s) in order to compute the shortest path lengths with at
+    /// most \c num arc.
+    ///
+    /// \warning The paths with limited arc number cannot be retrieved
+    /// easily with \ref path() or \ref predArc() functions. If you
+    /// need the shortest path and not just the distance you should store
+    /// after each iteration the \ref predMap() map and manually build
+    /// the path.
+    ///
+    /// The algorithm computes
+    /// - The predecessor arc from each node.
+    /// - The limited distance of each node from the root(s).
+    void limitedStart(int num) {
+      for (int i = 0; i < num; ++i) {
+        if (processNextRound()) break;
+      }
+    }
+    
+    /// \brief Runs %BellmanFord algorithm from node \c s.
+    ///    
+    /// This method runs the %BellmanFord 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 %BellmanFord algorithm with limited path length 
+    /// from node \c s.
+    ///    
+    /// This method runs the %BellmanFord algorithm from a root node \c s
+    /// in order to compute the shortest path with at most \c len arcs 
+    /// to each node. The algorithm computes
+    /// - The shortest path tree.
+    /// - The distance of each node from the root.
+    ///
+    /// \note d.run(s, num) is just a shortcut of the following code.
+    ///\code
+    ///  d.init();
+    ///  d.addSource(s);
+    ///  d.limitedStart(num);
+    ///\endcode
+    void run(Node s, int num) {
+      init();
+      addSource(s);
+      limitedStart(num);
+    }
+    
+    ///@}
+
+    /// \name Query Functions
+    /// The result of the %BellmanFord algorithm can be obtained using these
+    /// functions.\n
+    /// Before the use of these functions,
+    /// either run() or start() must be called.
+    
+    ///@{
+
+    /// \brief Lemon iterator for get the active nodes.
+    ///
+    /// Lemon iterator for get the active nodes. This class provides a
+    /// common style lemon iterator which gives back a subset of the
+    /// nodes. The iterated nodes are active in the algorithm after
+    /// the last phase so these should be checked in the next phase to
+    /// find augmenting arcs from these.
+    class ActiveIt {
+    public:
+
+      /// \brief Constructor.
+      ///
+      /// Constructor for get the nodeset of the variable. 
+      ActiveIt(const BellmanFord& algorithm) : _algorithm(&algorithm)
+      {
+        _index = _algorithm->_process.size() - 1;
+      }
+
+      /// \brief Invalid constructor.
+      ///
+      /// Invalid constructor.
+      ActiveIt(Invalid) : _algorithm(0), _index(-1) {}
+
+      /// \brief Conversion to node.
+      ///
+      /// Conversion to node.
+      operator Node() const { 
+        return _index >= 0 ? _algorithm->_process[_index] : INVALID;
+      }
+
+      /// \brief Increment operator.
+      ///
+      /// Increment operator.
+      ActiveIt& operator++() {
+        --_index;
+        return *this; 
+      }
+
+      bool operator==(const ActiveIt& it) const { 
+        return static_cast<Node>(*this) == static_cast<Node>(it); 
+      }
+      bool operator!=(const ActiveIt& it) const { 
+        return static_cast<Node>(*this) != static_cast<Node>(it); 
+      }
+      bool operator<(const ActiveIt& it) const { 
+        return static_cast<Node>(*this) < static_cast<Node>(it); 
+      }
+      
+    private:
+      const BellmanFord* _algorithm;
+      int _index;
+    };
+
+    typedef PredMapPath<Digraph, PredMap> Path;
+
+    /// \brief Gives back the shortest path.
+    ///    
+    /// Gives back the shortest path.
+    /// \pre The \c t should be reachable from the source.
+    Path path(Node t) 
+    {
+      return Path(*digraph, *_pred, t);
+    }
+
+
+    // TODO : implement negative cycle
+//     /// \brief Gives back a negative cycle.
+//     ///    
+//     /// This function gives back a negative cycle.
+//     /// If the algorithm have not found yet negative cycle it will give back
+//     /// an empty path.
+//     Path negativeCycle() {
+//       typename Digraph::template NodeMap<int> state(*digraph, 0);
+//       for (ActiveIt it(*this); it != INVALID; ++it) {
+//         if (state[it] == 0) {
+//           for (Node t = it; predArc(t) != INVALID; t = predNode(t)) {
+//             if (state[t] == 0) {
+//               state[t] = 1;
+//             } else if (state[t] == 2) {
+//               break;
+//             } else {
+//               p.clear();
+//               typename Path::Builder b(p);
+//               b.setStartNode(t);
+//               b.pushFront(predArc(t));
+//               for(Node s = predNode(t); s != t; s = predNode(s)) {
+//                 b.pushFront(predArc(s));
+//               }
+//               b.commit();
+//               return true;
+//             }
+//           }
+//           for (Node t = it; predArc(t) != INVALID; t = predNode(t)) {
+//             if (state[t] == 1) {
+//               state[t] = 2;
+//             } else {
+//               break;
+//             }
+//           }
+//         }
+//       }
+//       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 arc' of the shortest path tree.
+    ///
+    /// For a node \c v it returns the 'previous arc' of the shortest path 
+    /// tree, i.e. it returns the last arc 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.
+    Arc predArc(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 predArc().  \pre \ref run() must be 
+    /// called before using this function.
+    Node predNode(Node v) const { 
+      return (*_pred)[v] == INVALID ? INVALID : digraph->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 arcs 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 BellmanFord function.
+  ///
+  /// Default traits class of BellmanFord function.
+  /// \param _Digraph Digraph type.
+  /// \param _LengthMap Type of length map.
+  template <typename _Digraph, typename _LengthMap>
+  struct BellmanFordWizardDefaultTraits {
+    /// \brief The digraph type the algorithm runs on. 
+    typedef _Digraph Digraph;
+
+    /// \brief The type of the map that stores the arc lengths.
+    ///
+    /// The type of the map that stores the arc lengths.
+    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
+    typedef _LengthMap LengthMap;
+
+    /// \brief The value type of the length map.
+    typedef typename _LengthMap::Value Value;
+
+    /// \brief Operation traits for Bellman-Ford algorithm.
+    ///
+    /// It defines the infinity type on the given Value type
+    /// and the used operation.
+    /// \see BellmanFordDefaultOperationTraits
+    typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
+
+    /// \brief The type of the map that stores the last
+    /// arcs of the shortest paths.
+    /// 
+    /// The type of the map that stores the last
+    /// arcs of the shortest paths.
+    /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    typedef NullMap <typename _Digraph::Node,typename _Digraph::Arc> PredMap;
+
+    /// \brief Instantiates a PredMap.
+    /// 
+    /// This function instantiates a \ref PredMap. 
+    static PredMap *createPredMap(const _Digraph &) {
+      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 concepts::WriteMap "WriteMap" concept.
+    typedef NullMap<typename Digraph::Node, Value> DistMap;
+    /// \brief Instantiates a DistMap.
+    ///
+    /// This function instantiates a \ref DistMap. 
+    static DistMap *createDistMap(const _Digraph &) {
+      return new DistMap();
+    }
+  };
+  
+  /// \brief Default traits used by \ref BellmanFordWizard
+  ///
+  /// To make it easier to use BellmanFord algorithm
+  /// we have created a wizard class.
+  /// This \ref BellmanFordWizard class needs default traits,
+  /// as well as the \ref BellmanFord class.
+  /// The \ref BellmanFordWizardBase is a class to be the default traits of the
+  /// \ref BellmanFordWizard class.
+  /// \todo More named parameters are required...
+  template<class _Digraph,class _LengthMap>
+  class BellmanFordWizardBase 
+    : public BellmanFordWizardDefaultTraits<_Digraph,_LengthMap> {
+
+    typedef BellmanFordWizardDefaultTraits<_Digraph,_LengthMap> Base;
+  protected:
+    /// Type of the nodes in the digraph.
+    typedef typename Base::Digraph::Node Node;
+
+    /// Pointer to the underlying digraph.
+    void *_graph;
+    /// Pointer to the length map
+    void *_length;
+    ///Pointer to the map of predecessors arcs.
+    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).
+    BellmanFordWizardBase() : _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 digraph 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
+    BellmanFordWizardBase(const _Digraph& digraph, 
+                          const _LengthMap& length, 
+                          Node source = INVALID) :
+      _graph(reinterpret_cast<void*>(const_cast<_Digraph*>(&digraph))), 
+      _length(reinterpret_cast<void*>(const_cast<_LengthMap*>(&length))), 
+      _pred(0), _dist(0), _source(source) {}
+
+  };
+  
+  /// A class to make the usage of BellmanFord algorithm easier
+
+  /// This class is created to make it easier to use BellmanFord algorithm.
+  /// It uses the functions and features of the plain \ref BellmanFord,
+  /// 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 BellmanFord
+  /// the new class with the modified type comes from
+  /// the original class by using the ::
+  /// operator. In the case of \ref BellmanFordWizard 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 BellmanFord class, and calls the \ref 
+  /// BellmanFord::run method of it.
+  template<class _Traits>
+  class BellmanFordWizard : public _Traits {
+    typedef _Traits Base;
+
+    ///The type of the underlying digraph.
+    typedef typename _Traits::Digraph Digraph;
+
+    typedef typename Digraph::Node Node;
+    typedef typename Digraph::NodeIt NodeIt;
+    typedef typename Digraph::Arc Arc;
+    typedef typename Digraph::OutArcIt ArcIt;
+    
+    ///The type of the map that stores the arc lengths.
+    typedef typename _Traits::LengthMap LengthMap;
+
+    ///The type of the length of the arcs.
+    typedef typename LengthMap::Value Value;
+
+    ///\brief The type of the map that stores the last
+    ///arcs 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.
+    BellmanFordWizard() : _Traits() {}
+
+    /// \brief Constructor that requires parameters.
+    ///
+    /// Constructor that requires parameters.
+    /// These parameters will be the default values for the traits class.
+    BellmanFordWizard(const Digraph& digraph, const LengthMap& length, 
+                      Node src = INVALID) 
+      : _Traits(digraph, length, src) {}
+
+    /// \brief Copy constructor
+    BellmanFordWizard(const _Traits &b) : _Traits(b) {}
+
+    ~BellmanFordWizard() {}
+
+    /// \brief Runs BellmanFord algorithm from a given node.
+    ///    
+    /// Runs BellmanFord algorithm from a given node.
+    /// The node can be given by the \ref source function.
+    void run() {
+      LEMON_ASSERT(Base::_source != INVALID, "Source node is not given");
+      BellmanFord<Digraph,LengthMap,_Traits> 
+        bf(*reinterpret_cast<const Digraph*>(Base::_graph), 
+           *reinterpret_cast<const LengthMap*>(Base::_length));
+      if (Base::_pred) bf.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
+      if (Base::_dist) bf.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
+      bf.run(Base::_source);
+    }
+
+    /// \brief Runs BellmanFord algorithm from the given node.
+    ///
+    /// Runs BellmanFord algorithm from the given node.
+    /// \param src is the given source.
+    void run(Node src) {
+      Base::_source = src;
+      run();
+    }
+
+    template<class T>
+    struct DefPredMapBase : public Base {
+      typedef T PredMap;
+      static PredMap *createPredMap(const Digraph &) { 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>
+    BellmanFordWizard<DefPredMapBase<T> > predMap(const T &t) 
+    {
+      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
+      return BellmanFordWizard<DefPredMapBase<T> >(*this);
+    }
+    
+    template<class T>
+    struct DefDistMapBase : public Base {
+      typedef T DistMap;
+      static DistMap *createDistMap(const Digraph &) { 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>
+    BellmanFordWizard<DefDistMapBase<T> > distMap(const T &t) {
+      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
+      return BellmanFordWizard<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>
+    BellmanFordWizard<DefOperationTraitsBase<T> > distMap() {
+      return BellmanFordWizard<DefDistMapBase<T> >(*this);
+    }
+    
+    /// \brief Sets the source node, from which the BellmanFord algorithm runs.
+    ///
+    /// Sets the source node, from which the BellmanFord algorithm runs.
+    /// \param src is the source node.
+    BellmanFordWizard<_Traits>& source(Node src) {
+      Base::_source = src;
+      return *this;
+    }
+    
+  };
+  
+  /// \brief Function type interface for BellmanFord algorithm.
+  ///
+  /// \ingroup shortest_path
+  /// Function type interface for BellmanFord algorithm.
+  ///
+  /// This function also has several \ref named-templ-func-param 
+  /// "named parameters", they are declared as the members of class 
+  /// \ref BellmanFordWizard.
+  /// The following
+  /// example shows how to use these parameters.
+  ///\code
+  /// bellmanford(g,length,source).predMap(preds).run();
+  ///\endcode
+  /// \warning Don't forget to put the \ref BellmanFordWizard::run() "run()"
+  /// to the end of the parameter list.
+  /// \sa BellmanFordWizard
+  /// \sa BellmanFord
+  template<class _Digraph, class _LengthMap>
+  BellmanFordWizard<BellmanFordWizardBase<_Digraph,_LengthMap> >
+  bellmanFord(const _Digraph& digraph,
+              const _LengthMap& length, 
+              typename _Digraph::Node source = INVALID) {
+    return BellmanFordWizard<BellmanFordWizardBase<_Digraph,_LengthMap> >
+      (digraph, length, source);
+  }
+
+} //END OF NAMESPACE LEMON
+
+#endif
+