/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2007

 * 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 BellmanFord algorithm.

///

#include <lemon/list_graph.h>

#include <lemon/bits/path_dump.h>

#include <lemon/bits/invalid.h>

#include <lemon/graph_utils.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 concepts::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 concepts::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 concepts::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 shortest_path

  /// This class provides an efficient implementation of \c Bellman-Ford 

  /// algorithm. The edge 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 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 concepts::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 concepts::Graph::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* what() const throw() {

	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.

    ///

    /// 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 path() or \ref predEdge() 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 %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 cycle 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 _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 edge.

    ///

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

    /// easily with \ref path() or \ref predEdge() 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 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, 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 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 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<Graph, 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(*graph, *_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 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 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

    /// edges of the shortest paths.

    /// 

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

    /// edges of the shortest paths.

    /// It must meet the \ref concepts::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 concepts::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(reinterpret_cast<void*>(const_cast<_Graph*>(&graph))), 

      _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 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 src = INVALID) 

      : _Traits(graph, 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() {

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

      BellmanFord<Graph,LengthMap,_Traits> 

	bf(*reinterpret_cast<const Graph*>(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 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=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 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>