deba@1699: /* -*- C++ -*-
deba@1699:  *
alpar@1956:  * This file is a part of LEMON, a generic C++ optimization library
alpar@1956:  *
alpar@2553:  * Copyright (C) 2003-2008
alpar@1956:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@1699:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@1699:  *
deba@1699:  * Permission to use, modify and distribute this software is granted
deba@1699:  * provided that this copyright notice appears in all copies. For
deba@1699:  * precise terms see the accompanying LICENSE file.
deba@1699:  *
deba@1699:  * This software is provided "AS IS" with no warranty of any kind,
deba@1699:  * express or implied, and with no claim as to its suitability for any
deba@1699:  * purpose.
deba@1699:  *
deba@1699:  */
deba@1699: 
deba@1699: #ifndef LEMON_BELMANN_FORD_H
deba@1699: #define LEMON_BELMANN_FORD_H
deba@1699: 
deba@2376: /// \ingroup shortest_path
deba@1699: /// \file
deba@1864: /// \brief BellmanFord algorithm.
deba@1699: ///
deba@1699: 
deba@1699: #include <lemon/list_graph.h>
deba@2335: #include <lemon/bits/path_dump.h>
deba@1993: #include <lemon/bits/invalid.h>
deba@2394: #include <lemon/graph_utils.h>
deba@1699: #include <lemon/error.h>
deba@1699: #include <lemon/maps.h>
deba@1699: 
deba@1699: #include <limits>
deba@1699: 
deba@1699: namespace lemon {
deba@1699: 
deba@1864:   /// \brief Default OperationTraits for the BellmanFord algorithm class.
deba@1699:   ///  
deba@1699:   /// It defines all computational operations and constants which are
alpar@2408:   /// used in the Bellman-Ford algorithm. The default implementation
deba@1699:   /// is based on the numeric_limits class. If the numeric type does not
deba@1699:   /// have infinity value then the maximum value is used as extremal
deba@1699:   /// infinity value.
deba@1699:   template <
deba@1699:     typename Value, 
deba@1699:     bool has_infinity = std::numeric_limits<Value>::has_infinity>
deba@1864:   struct BellmanFordDefaultOperationTraits {
deba@1699:     /// \brief Gives back the zero value of the type.
deba@1699:     static Value zero() {
deba@1699:       return static_cast<Value>(0);
deba@1699:     }
deba@1699:     /// \brief Gives back the positive infinity value of the type.
deba@1699:     static Value infinity() {
deba@1699:       return std::numeric_limits<Value>::infinity();
deba@1699:     }
deba@1699:     /// \brief Gives back the sum of the given two elements.
deba@1699:     static Value plus(const Value& left, const Value& right) {
deba@1699:       return left + right;
deba@1699:     }
deba@1699:     /// \brief Gives back true only if the first value less than the second.
deba@1699:     static bool less(const Value& left, const Value& right) {
deba@1699:       return left < right;
deba@1699:     }
deba@1699:   };
deba@1699: 
deba@1699:   template <typename Value>
deba@1864:   struct BellmanFordDefaultOperationTraits<Value, false> {
deba@1699:     static Value zero() {
deba@1699:       return static_cast<Value>(0);
deba@1699:     }
deba@1699:     static Value infinity() {
deba@1699:       return std::numeric_limits<Value>::max();
deba@1699:     }
deba@1699:     static Value plus(const Value& left, const Value& right) {
deba@1699:       if (left == infinity() || right == infinity()) return infinity();
deba@1699:       return left + right;
deba@1699:     }
deba@1699:     static bool less(const Value& left, const Value& right) {
deba@1699:       return left < right;
deba@1699:     }
deba@1699:   };
deba@1699:   
deba@1864:   /// \brief Default traits class of BellmanFord class.
deba@1699:   ///
deba@1864:   /// Default traits class of BellmanFord class.
deba@1699:   /// \param _Graph Graph type.
deba@1699:   /// \param _LegthMap Type of length map.
deba@1699:   template<class _Graph, class _LengthMap>
deba@1864:   struct BellmanFordDefaultTraits {
deba@1699:     /// The graph type the algorithm runs on. 
deba@1699:     typedef _Graph Graph;
deba@1699: 
deba@1699:     /// \brief The type of the map that stores the edge lengths.
deba@1699:     ///
deba@1699:     /// The type of the map that stores the edge lengths.
alpar@2260:     /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
deba@1699:     typedef _LengthMap LengthMap;
deba@1699: 
deba@1699:     // The type of the length of the edges.
deba@1699:     typedef typename _LengthMap::Value Value;
deba@1699: 
alpar@2408:     /// \brief Operation traits for Bellman-Ford algorithm.
deba@1699:     ///
deba@1699:     /// It defines the infinity type on the given Value type
deba@1699:     /// and the used operation.
deba@1864:     /// \see BellmanFordDefaultOperationTraits
deba@1864:     typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
deba@1699:  
deba@1699:     /// \brief The type of the map that stores the last edges of the 
deba@1699:     /// shortest paths.
deba@1699:     /// 
deba@1699:     /// The type of the map that stores the last
deba@1699:     /// edges of the shortest paths.
alpar@2260:     /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
deba@1699:     ///
deba@1699:     typedef typename Graph::template NodeMap<typename _Graph::Edge> PredMap;
deba@1699: 
deba@1699:     /// \brief Instantiates a PredMap.
deba@1699:     /// 
deba@1699:     /// This function instantiates a \ref PredMap. 
deba@1858:     /// \param graph is the graph, to which we would like to define the PredMap.
deba@1699:     static PredMap *createPredMap(const _Graph& graph) {
deba@1699:       return new PredMap(graph);
deba@1699:     }
deba@1699: 
deba@1699:     /// \brief The type of the map that stores the dists of the nodes.
deba@1699:     ///
deba@1699:     /// The type of the map that stores the dists of the nodes.
alpar@2260:     /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
deba@1699:     ///
deba@1699:     typedef typename Graph::template NodeMap<typename _LengthMap::Value> 
deba@1699:     DistMap;
deba@1699: 
deba@1699:     /// \brief Instantiates a DistMap.
deba@1699:     ///
deba@1699:     /// This function instantiates a \ref DistMap. 
deba@1858:     /// \param graph is the graph, to which we would like to define the 
deba@1699:     /// \ref DistMap
deba@1699:     static DistMap *createDistMap(const _Graph& graph) {
deba@1699:       return new DistMap(graph);
deba@1699:     }
deba@1699: 
deba@1699:   };
deba@1699:   
deba@1864:   /// \brief %BellmanFord algorithm class.
deba@1699:   ///
deba@2376:   /// \ingroup shortest_path
deba@1864:   /// This class provides an efficient implementation of \c Bellman-Ford 
deba@1699:   /// algorithm. The edge lengths are passed to the algorithm using a
alpar@2260:   /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any 
deba@1699:   /// kind of length.
deba@1699:   ///
deba@1864:   /// The Bellman-Ford algorithm solves the shortest path from one node
deba@1723:   /// problem when the edges can have negative length but the graph should
deba@1754:   /// not contain cycles with negative sum of length. If we can assume
deba@1723:   /// that all edge is non-negative in the graph then the dijkstra algorithm
deba@1723:   /// should be used rather.
deba@1723:   ///
deba@2042:   /// The maximal time complexity of the algorithm is \f$ O(ne) \f$.
deba@1723:   ///
deba@1699:   /// The type of the length is determined by the
alpar@2260:   /// \ref concepts::ReadMap::Value "Value" of the length map.
deba@1699:   ///
deba@1699:   /// \param _Graph The graph type the algorithm runs on. The default value
deba@1699:   /// is \ref ListGraph. The value of _Graph is not used directly by
deba@1864:   /// BellmanFord, it is only passed to \ref BellmanFordDefaultTraits.
deba@1699:   /// \param _LengthMap This read-only EdgeMap determines the lengths of the
alpar@2260:   /// edges. The default map type is \ref concepts::Graph::EdgeMap 
deba@1699:   /// "Graph::EdgeMap<int>".  The value of _LengthMap is not used directly 
deba@1864:   /// by BellmanFord, it is only passed to \ref BellmanFordDefaultTraits.  
deba@1699:   /// \param _Traits Traits class to set various data types used by the 
deba@1864:   /// algorithm.  The default traits class is \ref BellmanFordDefaultTraits
deba@1864:   /// "BellmanFordDefaultTraits<_Graph,_LengthMap>".  See \ref
deba@1864:   /// BellmanFordDefaultTraits for the documentation of a BellmanFord traits
deba@1699:   /// class.
deba@1699:   ///
deba@1699:   /// \author Balazs Dezso
deba@1699: 
deba@1710: #ifdef DOXYGEN
deba@1710:   template <typename _Graph, typename _LengthMap, typename _Traits>
deba@1710: #else
deba@1699:   template <typename _Graph=ListGraph,
deba@1699: 	    typename _LengthMap=typename _Graph::template EdgeMap<int>,
deba@1864: 	    typename _Traits=BellmanFordDefaultTraits<_Graph,_LengthMap> >
deba@1710: #endif
deba@1864:   class BellmanFord {
deba@1699:   public:
deba@1699:     
deba@1699:     /// \brief \ref Exception for uninitialized parameters.
deba@1699:     ///
deba@1699:     /// This error represents problems in the initialization
deba@1699:     /// of the parameters of the algorithms.
deba@1699: 
deba@1699:     class UninitializedParameter : public lemon::UninitializedParameter {
deba@1699:     public:
alpar@2151:       virtual const char* what() const throw() {
deba@1864: 	return "lemon::BellmanFord::UninitializedParameter";
deba@1699:       }
deba@1699:     };
deba@1699: 
deba@1699:     typedef _Traits Traits;
deba@1699:     ///The type of the underlying graph.
deba@1699:     typedef typename _Traits::Graph Graph;
deba@1699: 
deba@1699:     typedef typename Graph::Node Node;
deba@1699:     typedef typename Graph::NodeIt NodeIt;
deba@1699:     typedef typename Graph::Edge Edge;
deba@1781:     typedef typename Graph::OutEdgeIt OutEdgeIt;
deba@1699:     
deba@1699:     /// \brief The type of the length of the edges.
deba@1699:     typedef typename _Traits::LengthMap::Value Value;
deba@1699:     /// \brief The type of the map that stores the edge lengths.
deba@1699:     typedef typename _Traits::LengthMap LengthMap;
deba@1699:     /// \brief The type of the map that stores the last
deba@1699:     /// edges of the shortest paths.
deba@1699:     typedef typename _Traits::PredMap PredMap;
deba@1699:     /// \brief The type of the map that stores the dists of the nodes.
deba@1699:     typedef typename _Traits::DistMap DistMap;
deba@1699:     /// \brief The operation traits.
deba@1699:     typedef typename _Traits::OperationTraits OperationTraits;
deba@1699:   private:
deba@1699:     /// Pointer to the underlying graph.
deba@1699:     const Graph *graph;
deba@1699:     /// Pointer to the length map
deba@1699:     const LengthMap *length;
deba@1699:     ///Pointer to the map of predecessors edges.
deba@1699:     PredMap *_pred;
deba@1699:     ///Indicates if \ref _pred is locally allocated (\c true) or not.
deba@1699:     bool local_pred;
deba@1699:     ///Pointer to the map of distances.
deba@1699:     DistMap *_dist;
deba@1699:     ///Indicates if \ref _dist is locally allocated (\c true) or not.
deba@1699:     bool local_dist;
deba@1699: 
deba@1781:     typedef typename Graph::template NodeMap<bool> MaskMap;
deba@1781:     MaskMap *_mask;
deba@1781: 
deba@1781:     std::vector<Node> _process;
deba@1781: 
deba@1699:     /// Creates the maps if necessary.
deba@1699:     void create_maps() {
deba@1699:       if(!_pred) {
deba@1699: 	local_pred = true;
deba@1699: 	_pred = Traits::createPredMap(*graph);
deba@1699:       }
deba@1699:       if(!_dist) {
deba@1699: 	local_dist = true;
deba@1699: 	_dist = Traits::createDistMap(*graph);
deba@1699:       }
deba@1781:       _mask = new MaskMap(*graph, false);
deba@1699:     }
deba@1699:     
deba@1699:   public :
deba@1699:  
deba@1864:     typedef BellmanFord Create;
deba@1710: 
deba@1699:     /// \name Named template parameters
deba@1699: 
deba@1699:     ///@{
deba@1699: 
deba@1699:     template <class T>
deba@1699:     struct DefPredMapTraits : public Traits {
deba@1699:       typedef T PredMap;
deba@1710:       static PredMap *createPredMap(const Graph&) {
deba@1699: 	throw UninitializedParameter();
deba@1699:       }
deba@1699:     };
deba@1699: 
deba@1699:     /// \brief \ref named-templ-param "Named parameter" for setting PredMap 
deba@1699:     /// type
deba@1699:     /// \ref named-templ-param "Named parameter" for setting PredMap type
deba@1699:     ///
deba@1699:     template <class T>
deba@1858:     struct DefPredMap 
deba@1864:       : public BellmanFord< Graph, LengthMap, DefPredMapTraits<T> > {
deba@1864:       typedef BellmanFord< Graph, LengthMap, DefPredMapTraits<T> > Create;
deba@1710:     };
deba@1699:     
deba@1699:     template <class T>
deba@1699:     struct DefDistMapTraits : public Traits {
deba@1699:       typedef T DistMap;
klao@2010:       static DistMap *createDistMap(const Graph&) {
deba@1699: 	throw UninitializedParameter();
deba@1699:       }
deba@1699:     };
deba@1699: 
deba@1699:     /// \brief \ref named-templ-param "Named parameter" for setting DistMap 
deba@1699:     /// type
deba@1699:     ///
deba@1699:     /// \ref named-templ-param "Named parameter" for setting DistMap type
deba@1699:     ///
deba@1699:     template <class T>
deba@1710:     struct DefDistMap 
deba@1864:       : public BellmanFord< Graph, LengthMap, DefDistMapTraits<T> > {
deba@1864:       typedef BellmanFord< Graph, LengthMap, DefDistMapTraits<T> > Create;
deba@1710:     };
deba@1699:     
deba@1699:     template <class T>
deba@1699:     struct DefOperationTraitsTraits : public Traits {
deba@1699:       typedef T OperationTraits;
deba@1699:     };
deba@1699:     
deba@1699:     /// \brief \ref named-templ-param "Named parameter" for setting 
deba@1699:     /// OperationTraits type
deba@1699:     ///
deba@1710:     /// \ref named-templ-param "Named parameter" for setting OperationTraits
deba@1710:     /// type
deba@1699:     template <class T>
deba@1710:     struct DefOperationTraits
deba@1864:       : public BellmanFord< Graph, LengthMap, DefOperationTraitsTraits<T> > {
deba@1864:       typedef BellmanFord< Graph, LengthMap, DefOperationTraitsTraits<T> >
deba@1710:       Create;
deba@1699:     };
deba@1699:     
deba@1699:     ///@}
deba@1699: 
deba@1710:   protected:
deba@1710:     
deba@1864:     BellmanFord() {}
deba@1710: 
deba@1699:   public:      
deba@1699:     
deba@1699:     /// \brief Constructor.
deba@1699:     ///
deba@1699:     /// \param _graph the graph the algorithm will run on.
deba@1699:     /// \param _length the length map used by the algorithm.
deba@1864:     BellmanFord(const Graph& _graph, const LengthMap& _length) :
deba@1699:       graph(&_graph), length(&_length),
deba@1699:       _pred(0), local_pred(false),
deba@2074:       _dist(0), local_dist(false), _mask(0) {}
deba@1699:     
deba@1699:     ///Destructor.
deba@1864:     ~BellmanFord() {
deba@1699:       if(local_pred) delete _pred;
deba@1699:       if(local_dist) delete _dist;
deba@2074:       if(_mask) delete _mask;
deba@1699:     }
deba@1699: 
deba@1699:     /// \brief Sets the length map.
deba@1699:     ///
deba@1699:     /// Sets the length map.
deba@1699:     /// \return \c (*this)
deba@1864:     BellmanFord &lengthMap(const LengthMap &m) {
deba@1699:       length = &m;
deba@1699:       return *this;
deba@1699:     }
deba@1699: 
deba@1699:     /// \brief Sets the map storing the predecessor edges.
deba@1699:     ///
deba@1699:     /// Sets the map storing the predecessor edges.
deba@1699:     /// If you don't use this function before calling \ref run(),
deba@1699:     /// it will allocate one. The destuctor deallocates this
deba@1699:     /// automatically allocated map, of course.
deba@1699:     /// \return \c (*this)
deba@1864:     BellmanFord &predMap(PredMap &m) {
deba@1699:       if(local_pred) {
deba@1699: 	delete _pred;
deba@1699: 	local_pred=false;
deba@1699:       }
deba@1699:       _pred = &m;
deba@1699:       return *this;
deba@1699:     }
deba@1699: 
deba@1699:     /// \brief Sets the map storing the distances calculated by the algorithm.
deba@1699:     ///
deba@1699:     /// Sets the map storing the distances calculated by the algorithm.
deba@1699:     /// If you don't use this function before calling \ref run(),
deba@1699:     /// it will allocate one. The destuctor deallocates this
deba@1699:     /// automatically allocated map, of course.
deba@1699:     /// \return \c (*this)
deba@1864:     BellmanFord &distMap(DistMap &m) {
deba@1699:       if(local_dist) {
deba@1699: 	delete _dist;
deba@1699: 	local_dist=false;
deba@1699:       }
deba@1699:       _dist = &m;
deba@1699:       return *this;
deba@1699:     }
deba@1699: 
deba@1699:     /// \name Execution control
deba@1699:     /// The simplest way to execute the algorithm is to use
deba@1699:     /// one of the member functions called \c run(...).
deba@1699:     /// \n
deba@1699:     /// If you need more control on the execution,
deba@1699:     /// first you must call \ref init(), then you can add several source nodes
deba@1699:     /// with \ref addSource().
deba@1699:     /// Finally \ref start() will perform the actual path
deba@1699:     /// computation.
deba@1699: 
deba@1699:     ///@{
deba@1699: 
deba@1699:     /// \brief Initializes the internal data structures.
deba@1699:     /// 
deba@1699:     /// Initializes the internal data structures.
deba@1710:     void init(const Value value = OperationTraits::infinity()) {
deba@1699:       create_maps();
deba@1699:       for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1699: 	_pred->set(it, INVALID);
deba@1710: 	_dist->set(it, value);
deba@1699:       }
deba@1781:       _process.clear();
deba@1781:       if (OperationTraits::less(value, OperationTraits::infinity())) {
deba@1781: 	for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1781: 	  _process.push_back(it);
deba@1783: 	  _mask->set(it, true);
deba@1781: 	}
deba@1781:       }
deba@1699:     }
deba@1699:     
deba@1699:     /// \brief Adds a new source node.
deba@1699:     ///
alpar@2408:     /// Adds a new source node. The optional second parameter is the 
alpar@2408:     /// initial distance of the node. It just sets the distance of the 
alpar@2408:     /// node to the given value.
deba@1699:     void addSource(Node source, Value dst = OperationTraits::zero()) {
deba@1699:       _dist->set(source, dst);
deba@1781:       if (!(*_mask)[source]) {
deba@1781: 	_process.push_back(source);
deba@1781: 	_mask->set(source, true);
deba@1781:       }
deba@1781:     }
deba@1781: 
alpar@2408:     /// \brief Executes one round from the Bellman-Ford algorithm.
deba@1781:     ///
deba@2059:     /// If the algoritm calculated the distances in the previous round
deba@2059:     /// exactly for all at most \f$ k \f$ length path lengths then it will
deba@2059:     /// calculate the distances exactly for all at most \f$ k + 1 \f$
deba@2059:     /// length path lengths. With \f$ k \f$ iteration this function
deba@2059:     /// calculates the at most \f$ k \f$ length path lengths.
deba@2059:     ///
deba@2059:     /// \warning The paths with limited edge number cannot be retrieved
deba@2335:     /// easily with \ref path() or \ref predEdge() functions. If you
deba@2059:     /// need the shortest path and not just the distance you should store
kpeter@2476:     /// after each iteration the \ref predMap() map and manually build
deba@2059:     /// the path.
deba@2059:     ///
kpeter@2517:     /// \return \c true when the algorithm have not found more shorter
deba@2059:     /// paths.
deba@1781:     bool processNextRound() {
deba@2386:       for (int i = 0; i < int(_process.size()); ++i) {
deba@1781: 	_mask->set(_process[i], false);
deba@1781:       }
deba@1781:       std::vector<Node> nextProcess;
deba@1781:       std::vector<Value> values(_process.size());
deba@2386:       for (int i = 0; i < int(_process.size()); ++i) {
klao@1857: 	values[i] = (*_dist)[_process[i]];
deba@1781:       }
deba@2386:       for (int i = 0; i < int(_process.size()); ++i) {
deba@1781: 	for (OutEdgeIt it(*graph, _process[i]); it != INVALID; ++it) {
deba@1781: 	  Node target = graph->target(it);
deba@1781: 	  Value relaxed = OperationTraits::plus(values[i], (*length)[it]);
deba@1781: 	  if (OperationTraits::less(relaxed, (*_dist)[target])) {
deba@1781: 	    _pred->set(target, it);
deba@1781: 	    _dist->set(target, relaxed);
deba@1781: 	    if (!(*_mask)[target]) {
deba@1781: 	      _mask->set(target, true);
deba@1781: 	      nextProcess.push_back(target);
deba@1781: 	    }
deba@1781: 	  }	  
deba@1781: 	}
deba@1781:       }
deba@1781:       _process.swap(nextProcess);
deba@1781:       return _process.empty();
deba@1781:     }
deba@1781: 
alpar@2408:     /// \brief Executes one weak round from the Bellman-Ford algorithm.
deba@1781:     ///
deba@1781:     /// If the algorithm calculated the distances in the
alpar@1816:     /// previous round at least for all at most k length paths then it will
alpar@1816:     /// calculate the distances at least for all at most k + 1 length paths.
alpar@1816:     /// This function does not make it possible to calculate strictly the
alpar@1816:     /// at most k length minimal paths, this is why it is
alpar@1816:     /// called just weak round.
kpeter@2517:     /// \return \c true when the algorithm have not found more shorter paths.
deba@1781:     bool processNextWeakRound() {
deba@2386:       for (int i = 0; i < int(_process.size()); ++i) {
deba@1781: 	_mask->set(_process[i], false);
deba@1781:       }
deba@1781:       std::vector<Node> nextProcess;
deba@2386:       for (int i = 0; i < int(_process.size()); ++i) {
deba@1781: 	for (OutEdgeIt it(*graph, _process[i]); it != INVALID; ++it) {
deba@1781: 	  Node target = graph->target(it);
deba@1781: 	  Value relaxed = 
deba@1781: 	    OperationTraits::plus((*_dist)[_process[i]], (*length)[it]);
deba@1781: 	  if (OperationTraits::less(relaxed, (*_dist)[target])) {
deba@1781: 	    _pred->set(target, it);
deba@1781: 	    _dist->set(target, relaxed);
deba@1781: 	    if (!(*_mask)[target]) {
deba@1781: 	      _mask->set(target, true);
deba@1781: 	      nextProcess.push_back(target);
deba@1781: 	    }
deba@1781: 	  }	  
deba@1781: 	}
deba@1781:       }
deba@1781:       _process.swap(nextProcess);
deba@1781:       return _process.empty();
deba@1699:     }
deba@1699: 
deba@1699:     /// \brief Executes the algorithm.
deba@1699:     ///
deba@1699:     /// \pre init() must be called and at least one node should be added
deba@1699:     /// with addSource() before using this function.
deba@1699:     ///
deba@1864:     /// This method runs the %BellmanFord algorithm from the root node(s)
deba@1699:     /// in order to compute the shortest path to each node. The algorithm 
deba@1699:     /// computes 
deba@1699:     /// - The shortest path tree.
deba@1699:     /// - The distance of each node from the root(s).
deba@1699:     void start() {
deba@1723:       int num = countNodes(*graph) - 1;
deba@1723:       for (int i = 0; i < num; ++i) {
deba@1781: 	if (processNextWeakRound()) break;
deba@1699:       }
deba@1699:     }
deba@1723: 
deba@1754:     /// \brief Executes the algorithm and checks the negative cycles.
deba@1723:     ///
deba@1723:     /// \pre init() must be called and at least one node should be added
kpeter@2517:     /// with addSource() before using this function. 
deba@1723:     ///
deba@1864:     /// This method runs the %BellmanFord algorithm from the root node(s)
deba@1723:     /// in order to compute the shortest path to each node. The algorithm 
deba@1723:     /// computes 
deba@1723:     /// - The shortest path tree.
deba@1723:     /// - The distance of each node from the root(s).
kpeter@2517:     /// 
kpeter@2517:     /// \return \c false if there is a negative cycle in the graph.
deba@1723:     bool checkedStart() {
deba@2393:       int num = countNodes(*graph);
deba@1723:       for (int i = 0; i < num; ++i) {
deba@1781: 	if (processNextWeakRound()) return true;
deba@1723:       }
deba@2362:       return _process.empty();
deba@1723:     }
deba@1781: 
deba@1781:     /// \brief Executes the algorithm with path length limit.
deba@1781:     ///
deba@1781:     /// \pre init() must be called and at least one node should be added
deba@1781:     /// with addSource() before using this function.
deba@1781:     ///
deba@2059:     /// This method runs the %BellmanFord algorithm from the root
deba@2059:     /// node(s) in order to compute the shortest path lengths with at
deba@2059:     /// most \c num edge.
deba@2059:     ///
deba@2059:     /// \warning The paths with limited edge number cannot be retrieved
deba@2335:     /// easily with \ref path() or \ref predEdge() functions. If you
deba@2059:     /// need the shortest path and not just the distance you should store
kpeter@2476:     /// after each iteration the \ref predMap() map and manually build
deba@2059:     /// the path.
deba@2059:     ///
deba@2059:     /// The algorithm computes
deba@2059:     /// - The predecessor edge from each node.
deba@1781:     /// - The limited distance of each node from the root(s).
deba@2059:     void limitedStart(int num) {
deba@2059:       for (int i = 0; i < num; ++i) {
deba@1781: 	if (processNextRound()) break;
deba@1781:       }
deba@1781:     }
deba@1699:     
deba@1864:     /// \brief Runs %BellmanFord algorithm from node \c s.
deba@1699:     ///    
deba@1864:     /// This method runs the %BellmanFord algorithm from a root node \c s
deba@1699:     /// in order to compute the shortest path to each node. The algorithm 
deba@1699:     /// computes
deba@1699:     /// - The shortest path tree.
deba@1699:     /// - The distance of each node from the root.
deba@1699:     ///
deba@1699:     /// \note d.run(s) is just a shortcut of the following code.
alpar@1946:     ///\code
deba@1699:     ///  d.init();
deba@1699:     ///  d.addSource(s);
deba@1699:     ///  d.start();
alpar@1946:     ///\endcode
deba@1699:     void run(Node s) {
deba@1699:       init();
deba@1699:       addSource(s);
deba@1699:       start();
deba@1699:     }
deba@1699:     
deba@1864:     /// \brief Runs %BellmanFord algorithm with limited path length 
klao@1857:     /// from node \c s.
klao@1857:     ///    
deba@1864:     /// This method runs the %BellmanFord algorithm from a root node \c s
klao@1857:     /// in order to compute the shortest path with at most \c len edges 
klao@1857:     /// to each node. The algorithm computes
klao@1857:     /// - The shortest path tree.
klao@1857:     /// - The distance of each node from the root.
klao@1857:     ///
deba@2362:     /// \note d.run(s, num) is just a shortcut of the following code.
alpar@1946:     ///\code
klao@1857:     ///  d.init();
klao@1857:     ///  d.addSource(s);
deba@2362:     ///  d.limitedStart(num);
alpar@1946:     ///\endcode
deba@2362:     void run(Node s, int num) {
klao@1857:       init();
klao@1857:       addSource(s);
deba@2362:       limitedStart(num);
klao@1857:     }
klao@1857:     
deba@1699:     ///@}
deba@1699: 
deba@1699:     /// \name Query Functions
deba@1864:     /// The result of the %BellmanFord algorithm can be obtained using these
deba@1699:     /// functions.\n
deba@1699:     /// Before the use of these functions,
deba@1699:     /// either run() or start() must be called.
deba@1699:     
deba@1699:     ///@{
deba@1699: 
alpar@2408:     /// \brief Lemon iterator for get the active nodes.
deba@2070:     ///
deba@2362:     /// Lemon iterator for get the active nodes. This class provides a
deba@2070:     /// common style lemon iterator which gives back a subset of the
deba@2070:     /// nodes. The iterated nodes are active in the algorithm after
deba@2070:     /// the last phase so these should be checked in the next phase to
deba@2070:     /// find augmenting edges from these.
deba@2070:     class ActiveIt {
deba@2070:     public:
deba@2070: 
deba@2070:       /// \brief Constructor.
deba@2070:       ///
deba@2070:       /// Constructor for get the nodeset of the variable. 
deba@2070:       ActiveIt(const BellmanFord& algorithm) : _algorithm(&algorithm)
deba@2070:       {
deba@2070:         _index = _algorithm->_process.size() - 1;
deba@2070:       }
deba@2070: 
deba@2070:       /// \brief Invalid constructor.
deba@2070:       ///
deba@2070:       /// Invalid constructor.
deba@2070:       ActiveIt(Invalid) : _algorithm(0), _index(-1) {}
deba@2070: 
deba@2070:       /// \brief Conversion to node.
deba@2070:       ///
deba@2070:       /// Conversion to node.
deba@2070:       operator Node() const { 
deba@2070:         return _index >= 0 ? _algorithm->_process[_index] : INVALID;
deba@2070:       }
deba@2070: 
deba@2070:       /// \brief Increment operator.
deba@2070:       ///
deba@2070:       /// Increment operator.
deba@2070:       ActiveIt& operator++() {
deba@2070:         --_index;
deba@2070:         return *this; 
deba@2070:       }
deba@2070: 
deba@2070:       bool operator==(const ActiveIt& it) const { 
deba@2386:         return static_cast<Node>(*this) == static_cast<Node>(it); 
deba@2070:       }
deba@2070:       bool operator!=(const ActiveIt& it) const { 
deba@2386:         return static_cast<Node>(*this) != static_cast<Node>(it); 
deba@2070:       }
deba@2070:       bool operator<(const ActiveIt& it) const { 
deba@2386:         return static_cast<Node>(*this) < static_cast<Node>(it); 
deba@2070:       }
deba@2070:       
deba@2070:     private:
deba@2070:       const BellmanFord* _algorithm;
deba@2070:       int _index;
deba@2070:     };
deba@2070: 
deba@2335:     typedef PredMapPath<Graph, PredMap> Path;
deba@2335: 
deba@2335:     /// \brief Gives back the shortest path.
deba@1699:     ///    
deba@2335:     /// Gives back the shortest path.
deba@2335:     /// \pre The \c t should be reachable from the source.
deba@2335:     Path path(Node t) 
deba@2335:     {
deba@2335:       return Path(*graph, *_pred, t);
deba@1699:     }
deba@2070: 
deba@2335: 
deba@2335:     // TODO : implement negative cycle
deba@2335: //     /// \brief Gives back a negative cycle.
deba@2335: //     ///    
deba@2335: //     /// This function gives back a negative cycle.
deba@2335: //     /// If the algorithm have not found yet negative cycle it will give back
deba@2335: //     /// an empty path.
deba@2335: //     Path negativeCycle() {
deba@2335: //       typename Graph::template NodeMap<int> state(*graph, 0);
deba@2335: //       for (ActiveIt it(*this); it != INVALID; ++it) {
deba@2335: //         if (state[it] == 0) {
deba@2335: //           for (Node t = it; predEdge(t) != INVALID; t = predNode(t)) {
deba@2335: //             if (state[t] == 0) {
deba@2335: //               state[t] = 1;
deba@2335: //             } else if (state[t] == 2) {
deba@2335: //               break;
deba@2335: //             } else {
deba@2335: //               p.clear();
deba@2335: //               typename Path::Builder b(p);
deba@2335: //               b.setStartNode(t);
deba@2335: //               b.pushFront(predEdge(t));
deba@2335: //               for(Node s = predNode(t); s != t; s = predNode(s)) {
deba@2335: //                 b.pushFront(predEdge(s));
deba@2335: //               }
deba@2335: //               b.commit();
deba@2335: //               return true;
deba@2335: //             }
deba@2335: //           }
deba@2335: //           for (Node t = it; predEdge(t) != INVALID; t = predNode(t)) {
deba@2335: //             if (state[t] == 1) {
deba@2335: //               state[t] = 2;
deba@2335: //             } else {
deba@2335: //               break;
deba@2335: //             }
deba@2335: //           }
deba@2335: //         }
deba@2335: //       }
deba@2335: //       return false;
deba@2335: //     }
deba@1699: 	  
deba@1699:     /// \brief The distance of a node from the root.
deba@1699:     ///
deba@1699:     /// Returns the distance of a node from the root.
deba@1699:     /// \pre \ref run() must be called before using this function.
deba@1699:     /// \warning If node \c v in unreachable from the root the return value
deba@1699:     /// of this funcion is undefined.
deba@1699:     Value dist(Node v) const { return (*_dist)[v]; }
deba@1699: 
deba@1699:     /// \brief Returns the 'previous edge' of the shortest path tree.
deba@1699:     ///
deba@1699:     /// For a node \c v it returns the 'previous edge' of the shortest path 
deba@1699:     /// tree, i.e. it returns the last edge of a shortest path from the root 
deba@1699:     /// to \c v. It is \ref INVALID if \c v is unreachable from the root or 
deba@1699:     /// if \c v=s. The shortest path tree used here is equal to the shortest 
deba@1699:     /// path tree used in \ref predNode(). 
deba@1699:     /// \pre \ref run() must be called before using
deba@1699:     /// this function.
deba@1763:     Edge predEdge(Node v) const { return (*_pred)[v]; }
deba@1699: 
deba@1699:     /// \brief Returns the 'previous node' of the shortest path tree.
deba@1699:     ///
deba@1699:     /// For a node \c v it returns the 'previous node' of the shortest path 
deba@1699:     /// tree, i.e. it returns the last but one node from a shortest path from 
deba@1699:     /// the root to \c /v. It is INVALID if \c v is unreachable from the root 
deba@1699:     /// or if \c v=s. The shortest path tree used here is equal to the 
deba@1763:     /// shortest path tree used in \ref predEdge().  \pre \ref run() must be 
deba@1699:     /// called before using this function.
deba@1699:     Node predNode(Node v) const { 
deba@1699:       return (*_pred)[v] == INVALID ? INVALID : graph->source((*_pred)[v]); 
deba@1699:     }
deba@1699:     
deba@1699:     /// \brief Returns a reference to the NodeMap of distances.
deba@1699:     ///
deba@1699:     /// Returns a reference to the NodeMap of distances. \pre \ref run() must
deba@1699:     /// be called before using this function.
deba@1699:     const DistMap &distMap() const { return *_dist;}
deba@1699:  
deba@1699:     /// \brief Returns a reference to the shortest path tree map.
deba@1699:     ///
deba@1699:     /// Returns a reference to the NodeMap of the edges of the
deba@1699:     /// shortest path tree.
deba@1699:     /// \pre \ref run() must be called before using this function.
deba@1699:     const PredMap &predMap() const { return *_pred; }
deba@1699:  
deba@1699:     /// \brief Checks if a node is reachable from the root.
deba@1699:     ///
deba@1699:     /// Returns \c true if \c v is reachable from the root.
deba@1699:     /// \pre \ref run() must be called before using this function.
deba@1699:     ///
deba@1699:     bool reached(Node v) { return (*_dist)[v] != OperationTraits::infinity(); }
deba@1699:     
deba@1699:     ///@}
deba@1699:   };
deba@1699:  
deba@1864:   /// \brief Default traits class of BellmanFord function.
deba@1699:   ///
deba@1864:   /// Default traits class of BellmanFord function.
deba@1699:   /// \param _Graph Graph type.
deba@1699:   /// \param _LengthMap Type of length map.
deba@1699:   template <typename _Graph, typename _LengthMap>
deba@1864:   struct BellmanFordWizardDefaultTraits {
deba@1699:     /// \brief The graph type the algorithm runs on. 
deba@1699:     typedef _Graph Graph;
deba@1699: 
deba@1699:     /// \brief The type of the map that stores the edge lengths.
deba@1699:     ///
deba@1699:     /// The type of the map that stores the edge lengths.
alpar@2260:     /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
deba@1699:     typedef _LengthMap LengthMap;
deba@1699: 
deba@1699:     /// \brief The value type of the length map.
deba@1699:     typedef typename _LengthMap::Value Value;
deba@1699: 
alpar@2408:     /// \brief Operation traits for Bellman-Ford algorithm.
deba@1699:     ///
deba@1699:     /// It defines the infinity type on the given Value type
deba@1699:     /// and the used operation.
deba@1864:     /// \see BellmanFordDefaultOperationTraits
deba@1864:     typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
deba@1699: 
deba@1699:     /// \brief The type of the map that stores the last
deba@1699:     /// edges of the shortest paths.
deba@1699:     /// 
deba@1699:     /// The type of the map that stores the last
deba@1699:     /// edges of the shortest paths.
alpar@2260:     /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
deba@1699:     typedef NullMap <typename _Graph::Node,typename _Graph::Edge> PredMap;
deba@1699: 
deba@1699:     /// \brief Instantiates a PredMap.
deba@1699:     /// 
deba@1699:     /// This function instantiates a \ref PredMap. 
deba@1699:     static PredMap *createPredMap(const _Graph &) {
deba@1699:       return new PredMap();
deba@1699:     }
deba@1699:     /// \brief The type of the map that stores the dists of the nodes.
deba@1699:     ///
deba@1699:     /// The type of the map that stores the dists of the nodes.
alpar@2260:     /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
deba@1699:     typedef NullMap<typename Graph::Node, Value> DistMap;
deba@1699:     /// \brief Instantiates a DistMap.
deba@1699:     ///
deba@1699:     /// This function instantiates a \ref DistMap. 
deba@1699:     static DistMap *createDistMap(const _Graph &) {
deba@1699:       return new DistMap();
deba@1699:     }
deba@1699:   };
deba@1699:   
deba@1864:   /// \brief Default traits used by \ref BellmanFordWizard
deba@1699:   ///
deba@1864:   /// To make it easier to use BellmanFord algorithm
deba@1699:   /// we have created a wizard class.
deba@1864:   /// This \ref BellmanFordWizard class needs default traits,
deba@1864:   /// as well as the \ref BellmanFord class.
deba@1864:   /// The \ref BellmanFordWizardBase is a class to be the default traits of the
deba@1864:   /// \ref BellmanFordWizard class.
deba@1699:   /// \todo More named parameters are required...
deba@1699:   template<class _Graph,class _LengthMap>
deba@1864:   class BellmanFordWizardBase 
deba@1864:     : public BellmanFordWizardDefaultTraits<_Graph,_LengthMap> {
deba@1699: 
deba@1864:     typedef BellmanFordWizardDefaultTraits<_Graph,_LengthMap> Base;
deba@1699:   protected:
deba@1699:     /// Type of the nodes in the graph.
deba@1699:     typedef typename Base::Graph::Node Node;
deba@1699: 
deba@1699:     /// Pointer to the underlying graph.
deba@1699:     void *_graph;
deba@1699:     /// Pointer to the length map
deba@1699:     void *_length;
deba@1699:     ///Pointer to the map of predecessors edges.
deba@1699:     void *_pred;
deba@1699:     ///Pointer to the map of distances.
deba@1699:     void *_dist;
deba@1699:     ///Pointer to the source node.
deba@1699:     Node _source;
deba@1699: 
deba@1699:     public:
deba@1699:     /// Constructor.
deba@1699:     
deba@1699:     /// This constructor does not require parameters, therefore it initiates
deba@1699:     /// all of the attributes to default values (0, INVALID).
deba@1864:     BellmanFordWizardBase() : _graph(0), _length(0), _pred(0),
deba@1699: 			   _dist(0), _source(INVALID) {}
deba@1699: 
deba@1699:     /// Constructor.
deba@1699:     
deba@1699:     /// This constructor requires some parameters,
deba@1699:     /// listed in the parameters list.
deba@1699:     /// Others are initiated to 0.
deba@1699:     /// \param graph is the initial value of  \ref _graph
deba@1699:     /// \param length is the initial value of  \ref _length
deba@1699:     /// \param source is the initial value of  \ref _source
deba@1864:     BellmanFordWizardBase(const _Graph& graph, 
deba@1699: 			  const _LengthMap& length, 
deba@1699: 			  Node source = INVALID) :
deba@2386:       _graph(reinterpret_cast<void*>(const_cast<_Graph*>(&graph))), 
deba@2386:       _length(reinterpret_cast<void*>(const_cast<_LengthMap*>(&length))), 
deba@2386:       _pred(0), _dist(0), _source(source) {}
deba@1699: 
deba@1699:   };
deba@1699:   
deba@1864:   /// A class to make the usage of BellmanFord algorithm easier
deba@1699: 
deba@1864:   /// This class is created to make it easier to use BellmanFord algorithm.
deba@1864:   /// It uses the functions and features of the plain \ref BellmanFord,
deba@1699:   /// but it is much simpler to use it.
deba@1699:   ///
deba@1699:   /// Simplicity means that the way to change the types defined
deba@1699:   /// in the traits class is based on functions that returns the new class
deba@1699:   /// and not on templatable built-in classes.
deba@1864:   /// When using the plain \ref BellmanFord
deba@1699:   /// the new class with the modified type comes from
deba@1699:   /// the original class by using the ::
deba@1864:   /// operator. In the case of \ref BellmanFordWizard only
deba@1699:   /// a function have to be called and it will
deba@1699:   /// return the needed class.
deba@1699:   ///
deba@1699:   /// It does not have own \ref run method. When its \ref run method is called
deba@1864:   /// it initiates a plain \ref BellmanFord class, and calls the \ref 
deba@1864:   /// BellmanFord::run method of it.
deba@1699:   template<class _Traits>
deba@1864:   class BellmanFordWizard : public _Traits {
deba@1699:     typedef _Traits Base;
deba@1699: 
deba@1699:     ///The type of the underlying graph.
deba@1699:     typedef typename _Traits::Graph Graph;
deba@1699: 
deba@1699:     typedef typename Graph::Node Node;
deba@1699:     typedef typename Graph::NodeIt NodeIt;
deba@1699:     typedef typename Graph::Edge Edge;
deba@1699:     typedef typename Graph::OutEdgeIt EdgeIt;
deba@1699:     
deba@1699:     ///The type of the map that stores the edge lengths.
deba@1699:     typedef typename _Traits::LengthMap LengthMap;
deba@1699: 
deba@1699:     ///The type of the length of the edges.
deba@1699:     typedef typename LengthMap::Value Value;
deba@1699: 
deba@1699:     ///\brief The type of the map that stores the last
deba@1699:     ///edges of the shortest paths.
deba@1699:     typedef typename _Traits::PredMap PredMap;
deba@1699: 
deba@1699:     ///The type of the map that stores the dists of the nodes.
deba@1699:     typedef typename _Traits::DistMap DistMap;
deba@1699: 
deba@1699:   public:
deba@1699:     /// Constructor.
deba@1864:     BellmanFordWizard() : _Traits() {}
deba@1699: 
deba@1699:     /// \brief Constructor that requires parameters.
deba@1699:     ///
deba@1699:     /// Constructor that requires parameters.
deba@1699:     /// These parameters will be the default values for the traits class.
deba@1864:     BellmanFordWizard(const Graph& graph, const LengthMap& length, 
deba@2386: 		      Node src = INVALID) 
deba@2386:       : _Traits(graph, length, src) {}
deba@1699: 
deba@1699:     /// \brief Copy constructor
deba@1864:     BellmanFordWizard(const _Traits &b) : _Traits(b) {}
deba@1699: 
deba@1864:     ~BellmanFordWizard() {}
deba@1699: 
deba@1864:     /// \brief Runs BellmanFord algorithm from a given node.
deba@1699:     ///    
deba@1864:     /// Runs BellmanFord algorithm from a given node.
deba@1699:     /// The node can be given by the \ref source function.
deba@1699:     void run() {
deba@1699:       if(Base::_source == INVALID) throw UninitializedParameter();
deba@1864:       BellmanFord<Graph,LengthMap,_Traits> 
deba@2386: 	bf(*reinterpret_cast<const Graph*>(Base::_graph), 
deba@2386:            *reinterpret_cast<const LengthMap*>(Base::_length));
deba@2386:       if (Base::_pred) bf.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
deba@2386:       if (Base::_dist) bf.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
deba@1699:       bf.run(Base::_source);
deba@1699:     }
deba@1699: 
deba@1864:     /// \brief Runs BellmanFord algorithm from the given node.
deba@1699:     ///
deba@1864:     /// Runs BellmanFord algorithm from the given node.
kpeter@2476:     /// \param src is the given source.
deba@2386:     void run(Node src) {
deba@2386:       Base::_source = src;
deba@1699:       run();
deba@1699:     }
deba@1699: 
deba@1699:     template<class T>
deba@1699:     struct DefPredMapBase : public Base {
deba@1699:       typedef T PredMap;
deba@1699:       static PredMap *createPredMap(const Graph &) { return 0; };
deba@1699:       DefPredMapBase(const _Traits &b) : _Traits(b) {}
deba@1699:     };
deba@1699:     
deba@1699:     ///\brief \ref named-templ-param "Named parameter"
deba@1699:     ///function for setting PredMap type
deba@1699:     ///
deba@1699:     /// \ref named-templ-param "Named parameter"
deba@1699:     ///function for setting PredMap type
deba@1699:     ///
deba@1699:     template<class T>
deba@1864:     BellmanFordWizard<DefPredMapBase<T> > predMap(const T &t) 
deba@1699:     {
deba@2386:       Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
deba@1864:       return BellmanFordWizard<DefPredMapBase<T> >(*this);
deba@1699:     }
deba@1699:     
deba@1699:     template<class T>
deba@1699:     struct DefDistMapBase : public Base {
deba@1699:       typedef T DistMap;
deba@1699:       static DistMap *createDistMap(const Graph &) { return 0; };
deba@1699:       DefDistMapBase(const _Traits &b) : _Traits(b) {}
deba@1699:     };
deba@1699:     
deba@1699:     ///\brief \ref named-templ-param "Named parameter"
deba@1699:     ///function for setting DistMap type
deba@1699:     ///
deba@1699:     /// \ref named-templ-param "Named parameter"
deba@1699:     ///function for setting DistMap type
deba@1699:     ///
deba@1699:     template<class T>
deba@1864:     BellmanFordWizard<DefDistMapBase<T> > distMap(const T &t) {
deba@2386:       Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
deba@1864:       return BellmanFordWizard<DefDistMapBase<T> >(*this);
deba@1699:     }
deba@1710: 
deba@1710:     template<class T>
deba@1710:     struct DefOperationTraitsBase : public Base {
deba@1710:       typedef T OperationTraits;
deba@1710:       DefOperationTraitsBase(const _Traits &b) : _Traits(b) {}
deba@1710:     };
deba@1710:     
deba@1710:     ///\brief \ref named-templ-param "Named parameter"
deba@1710:     ///function for setting OperationTraits type
deba@1710:     ///
deba@1710:     /// \ref named-templ-param "Named parameter"
deba@1710:     ///function for setting OperationTraits type
deba@1710:     ///
deba@1710:     template<class T>
deba@1864:     BellmanFordWizard<DefOperationTraitsBase<T> > distMap() {
deba@1864:       return BellmanFordWizard<DefDistMapBase<T> >(*this);
deba@1710:     }
deba@1699:     
deba@1864:     /// \brief Sets the source node, from which the BellmanFord algorithm runs.
deba@1699:     ///
deba@1864:     /// Sets the source node, from which the BellmanFord algorithm runs.
kpeter@2476:     /// \param src is the source node.
deba@2386:     BellmanFordWizard<_Traits>& source(Node src) {
deba@2386:       Base::_source = src;
deba@1699:       return *this;
deba@1699:     }
deba@1699:     
deba@1699:   };
deba@1699:   
deba@1864:   /// \brief Function type interface for BellmanFord algorithm.
deba@1699:   ///
deba@2376:   /// \ingroup shortest_path
deba@1864:   /// Function type interface for BellmanFord algorithm.
deba@1699:   ///
deba@1699:   /// This function also has several \ref named-templ-func-param 
deba@1699:   /// "named parameters", they are declared as the members of class 
deba@1864:   /// \ref BellmanFordWizard.
deba@1699:   /// The following
deba@1699:   /// example shows how to use these parameters.
alpar@1946:   ///\code
deba@1864:   /// bellmanford(g,length,source).predMap(preds).run();
alpar@1946:   ///\endcode
deba@1864:   /// \warning Don't forget to put the \ref BellmanFordWizard::run() "run()"
deba@1699:   /// to the end of the parameter list.
deba@1864:   /// \sa BellmanFordWizard
deba@1864:   /// \sa BellmanFord
deba@1699:   template<class _Graph, class _LengthMap>
deba@1864:   BellmanFordWizard<BellmanFordWizardBase<_Graph,_LengthMap> >
deba@1864:   bellmanFord(const _Graph& graph,
deba@1699: 	      const _LengthMap& length, 
deba@1699: 	      typename _Graph::Node source = INVALID) {
deba@1864:     return BellmanFordWizard<BellmanFordWizardBase<_Graph,_LengthMap> >
deba@1699:       (graph, length, source);
deba@1699:   }
deba@1699: 
deba@1699: } //END OF NAMESPACE LEMON
deba@1699: 
deba@1699: #endif
deba@1699: