/* -*- C++ -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2003-2006

  * 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 BellmanFord algorithm.

 ///

 #include <lemon/list_graph.h>

 #include <lemon/bits/invalid.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 _Graph Graph type.

   /// \param _LegthMap Type of length map.

   template<class _Graph, class _LengthMap>

   struct BellmanFordDefaultTraits {

     /// 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 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 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 %BellmanFord algorithm class.

   ///

   /// \ingroup flowalgs

   /// This class provides an efficient implementation of \c Bellman-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 Bellman-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 maximal time complexity of the algorithm is \f$ O(ne) \f$.

   ///

   /// 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

   /// BellmanFord, it is only passed to \ref BellmanFordDefaultTraits.

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

   /// BellmanFordDefaultTraits for the documentation of a BellmanFord 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=BellmanFordDefaultTraits<_Graph,_LengthMap> >

 #endif

   class BellmanFord {

   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::BellmanFord::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 BellmanFord 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 BellmanFord< Graph, LengthMap, DefPredMapTraits<T> > {

       typedef BellmanFord< Graph, LengthMap, DefPredMapTraits<T> > Create;

     };

     template <class T>

     struct DefDistMapTraits : public Traits {

       typedef T DistMap;

       static DistMap *createDistMap(const 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 BellmanFord< Graph, LengthMap, DefDistMapTraits<T> > {

       typedef BellmanFord< 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 BellmanFord< Graph, LengthMap, DefOperationTraitsTraits<T> > {

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

       Create;

     };

     ///@}

   protected:

     BellmanFord() {}

   public:      

     /// \brief Constructor.

     ///

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

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

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

       graph(&_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 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)

     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(*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 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 edge number cannot be retrieved

     /// easily with \ref getPath() or \ref predEdge() functions. If you

     /// need the shortest path and not just the distance you should store

     /// after each iteration the \ref predEdgeMap() map and manually build

     /// the path.

     ///

     /// \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 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 %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 %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(*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 %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).

     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 %BellmanFord algorithm from the root

     /// node(s) in order to compute the shortest path lengths with at

     /// most \c num edge.

     ///

     /// \warning The paths with limited edge number cannot be retrieved

     /// easily with \ref getPath() or \ref predEdge() functions. If you

     /// need the shortest path and not just the distance you should store

     /// after each iteration the \ref predEdgeMap() map and manually build

     /// the path.

     ///

     /// The algorithm computes

     /// - The predecessor edge 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 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 %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 a active nodes.

     ///

     /// Lemon iterator for get a 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 edges 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 (Node)(*this) == (Node)it; 

       }

       bool operator!=(const ActiveIt& it) const { 

         return (Node)(*this) != (Node)it; 

       }

       bool operator<(const ActiveIt& it) const { 

         return (Node)(*this) < (Node)it; 

       }

     private:

       const BellmanFord* _algorithm;

       int _index;

     };

     /// \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 Copies a negative cycle into path \c p.

     ///    

     /// This function copies a negative cycle into path \c p.

     /// If the algorithm have not found yet negative cycle it will not change

     /// the given path and gives back false.

     ///

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

     /// \c false otherwise.

     /// \sa DirPath

     template <typename Path>

     bool getNegativeCycle(Path& p) {

       typename Graph::template NodeMap<int> state(*graph, 0);

       for (ActiveIt it(*this); it != INVALID; ++it) {

         if (state[it] == 0) {

           for (Node t = it; predEdge(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(predEdge(t));

               for(Node s = predNode(t); s != t; s = predNode(s)) {

                 b.pushFront(predEdge(s));

               }

               b.commit();

               return true;

             }

           }

           for (Node t = it; predEdge(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 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 BellmanFord function.

   ///

   /// Default traits class of BellmanFord function.

   /// \param _Graph Graph type.

   /// \param _LengthMap Type of length map.

   template <typename _Graph, typename _LengthMap>

   struct BellmanFordWizardDefaultTraits {

     /// \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 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

     /// 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 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 _Graph,class _LengthMap>

   class BellmanFordWizardBase 

     : public BellmanFordWizardDefaultTraits<_Graph,_LengthMap> {

     typedef BellmanFordWizardDefaultTraits<_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).

     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 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

     BellmanFordWizardBase(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 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 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.

     BellmanFordWizard() : _Traits() {}

     /// \brief Constructor that requires parameters.

     ///

     /// Constructor that requires parameters.

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

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

 		      Node source = INVALID) 

       : _Traits(graph, length, source) {}

     /// \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() {

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

       BellmanFord<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 BellmanFord algorithm from the given node.

     ///

     /// Runs BellmanFord 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>

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

     {

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

       return BellmanFordWizard<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>

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

       Base::_dist=(void *)&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 source is the source node.

     BellmanFordWizard<_Traits>& source(Node source) {

       Base::_source = source;

       return *this;

     }

   };

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

   ///

   /// \ingroup flowalgs

   /// 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 _Graph, class _LengthMap>

   BellmanFordWizard<BellmanFordWizardBase<_Graph,_LengthMap> >

   bellmanFord(const _Graph& graph,

 	      const _LengthMap& length, 

 	      typename _Graph::Node source = INVALID) {

     return BellmanFordWizard<BellmanFordWizardBase<_Graph,_LengthMap> >

       (graph, length, source);

   }

 } //END OF NAMESPACE LEMON

 #endif