deba@1699: /* -*- C++ -*-
deba@1699:  * lemon/johnson.h - Part of LEMON, a generic C++ optimization library
deba@1699:  *
deba@1699:  * Copyright (C) 2005 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_JOHNSON_H
deba@1699: #define LEMON_JOHNSON_H
deba@1699: 
deba@1699: ///\ingroup flowalgs
deba@1699: /// \file
deba@1699: /// \brief Johnson algorithm.
deba@1699: ///
deba@1699: 
deba@1699: #include <lemon/list_graph.h>
deba@1699: #include <lemon/graph_utils.h>
deba@1699: #include <lemon/dijkstra.h>
deba@1699: #include <lemon/belmann_ford.h>
deba@1699: #include <lemon/invalid.h>
deba@1699: #include <lemon/error.h>
deba@1699: #include <lemon/maps.h>
deba@1723: #include <lemon/matrix_maps.h>
deba@1699: 
deba@1699: #include <limits>
deba@1699: 
deba@1699: namespace lemon {
deba@1699: 
deba@1699:   /// \brief Default OperationTraits for the Johnson algorithm class.
deba@1699:   ///  
deba@1699:   /// It defines all computational operations and constants which are
deba@1699:   /// used in the Floyd-Warshall 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@1699:   struct JohnsonDefaultOperationTraits {
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@1699:   struct JohnsonDefaultOperationTraits<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@1699:   /// \brief Default traits class of Johnson class.
deba@1699:   ///
deba@1699:   /// Default traits class of Johnson class.
deba@1699:   /// \param _Graph Graph type.
deba@1699:   /// \param _LegthMap Type of length map.
deba@1699:   template<class _Graph, class _LengthMap>
deba@1699:   struct JohnsonDefaultTraits {
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.
deba@1699:     /// It must meet the \ref concept::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: 
deba@1699:     /// \brief Operation traits for belmann-ford algorithm.
deba@1699:     ///
deba@1699:     /// It defines the infinity type on the given Value type
deba@1699:     /// and the used operation.
deba@1699:     /// \see JohnsonDefaultOperationTraits
deba@1699:     typedef JohnsonDefaultOperationTraits<Value> OperationTraits;
deba@1699:  
deba@1723:     /// \brief The type of the matrix map that stores the last edges of the 
deba@1699:     /// shortest paths.
deba@1699:     /// 
deba@1723:     /// The type of the map that stores the last edges of the shortest paths.
deba@1699:     /// It must be a matrix map with \c Graph::Edge value type.
deba@1699:     ///
deba@1723:     typedef DynamicMatrixMap<Graph, typename Graph::Node, 
deba@1723: 			     typename Graph::Edge> PredMap;
deba@1699: 
deba@1699:     /// \brief Instantiates a PredMap.
deba@1699:     /// 
deba@1699:     /// This function instantiates a \ref PredMap. 
deba@1699:     /// \param G is the graph, to which we would like to define the PredMap.
deba@1699:     /// \todo The graph alone may be insufficient for the initialization
deba@1699:     static PredMap *createPredMap(const _Graph& graph) {
deba@1699:       return new PredMap(graph);
deba@1699:     }
deba@1699: 
deba@1723:     /// \brief The type of the matrix map that stores the dists of the nodes.
deba@1699:     ///
deba@1723:     /// The type of the matrix map that stores the dists of the nodes.
deba@1723:     /// It must meet the \ref concept::WriteMatrixMap "WriteMatrixMap" concept.
deba@1699:     ///
deba@1723:     typedef DynamicMatrixMap<Graph, typename Graph::Node, Value> DistMap;
deba@1723:     
deba@1699:     /// \brief Instantiates a DistMap.
deba@1699:     ///
deba@1699:     /// This function instantiates a \ref DistMap. 
deba@1699:     /// \param G 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@1699:   /// \brief Johnson algorithm class.
deba@1699:   ///
deba@1699:   /// \ingroup flowalgs
deba@1699:   /// This class provides an efficient implementation of \c Johnson 
deba@1699:   /// algorithm. The edge lengths are passed to the algorithm using a
deba@1699:   /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any 
deba@1699:   /// kind of length.
deba@1699:   ///
deba@1723:   /// The algorithm solves the shortest path problem for each pairs
deba@1723:   /// of node when the edges can have negative length but the graph should
deba@1723:   /// not contain circle 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 from each node.
deba@1723:   ///
deba@1723:   /// The complexity of this algorithm is $O(n^2 * log(n) + n * log(n) * e)$ or
deba@1723:   /// with fibonacci heap O(n^2 * log(n) + n * e).
deba@1723:   ///
deba@1699:   /// The type of the length is determined by the
deba@1699:   /// \ref concept::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@1699:   /// Johnson, it is only passed to \ref JohnsonDefaultTraits.
deba@1699:   /// \param _LengthMap This read-only EdgeMap determines the lengths of the
deba@1699:   /// edges. It is read once for each edge, so the map may involve in
deba@1699:   /// relatively time consuming process to compute the edge length if
deba@1699:   /// it is necessary. The default map type is \ref
deba@1699:   /// concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>".  The value
deba@1699:   /// of _LengthMap is not used directly by Johnson, it is only passed 
deba@1699:   /// to \ref JohnsonDefaultTraits.  \param _Traits Traits class to set
deba@1699:   /// various data types used by the algorithm.  The default traits
deba@1699:   /// class is \ref JohnsonDefaultTraits
deba@1699:   /// "JohnsonDefaultTraits<_Graph,_LengthMap>".  See \ref
deba@1699:   /// JohnsonDefaultTraits for the documentation of a Johnson 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@1699: 	    typename _Traits=JohnsonDefaultTraits<_Graph,_LengthMap> >
deba@1710: #endif
deba@1699:   class Johnson {
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:
deba@1699:       virtual const char* exceptionName() const {
deba@1699: 	return "lemon::Johnson::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@1699:     typedef typename Graph::EdgeIt EdgeIt;
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. The type of the PredMap
deba@1699:     /// is a matrix map for Edges
deba@1699:     typedef typename _Traits::PredMap PredMap;
deba@1699:     /// \brief The type of the map that stores the dists of the nodes.
deba@1699:     /// The type of the DistMap is a matrix map for Values
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@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@1699:     }
deba@1699:     
deba@1699:   public :
deba@1699:  
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@1699:       static PredMap *createPredMap(const Graph& 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@1710:     struct DefPredMap 
deba@1710:       : public Johnson< Graph, LengthMap, DefPredMapTraits<T> > {
deba@1710:       typedef Johnson< 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;
deba@1699:       static DistMap *createDistMap(const Graph& graph) {
deba@1699: 	throw UninitializedParameter();
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@1710:       : public Johnson< Graph, LengthMap, DefDistMapTraits<T> > {
deba@1710:       typedef Johnson< 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 
deba@1710:     /// OperationTraits type
deba@1699:     template <class T>
deba@1710:     struct DefOperationTraits
deba@1710:       : public Johnson< Graph, LengthMap, DefOperationTraitsTraits<T> > {
deba@1710:       typedef Johnson< Graph, LengthMap, DefOperationTraitsTraits<T> > Create;
deba@1710:     };
deba@1699:     
deba@1699:     ///@}
deba@1699: 
deba@1710:   protected:
deba@1710: 
deba@1710:     Johnson() {}
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@1699:     Johnson(const Graph& _graph, const LengthMap& _length) :
deba@1699:       graph(&_graph), length(&_length),
deba@1699:       _pred(0), local_pred(false),
deba@1699:       _dist(0), local_dist(false) {}
deba@1699:     
deba@1699:     ///Destructor.
deba@1699:     ~Johnson() {
deba@1699:       if(local_pred) delete _pred;
deba@1699:       if(local_dist) delete _dist;
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@1699:     Johnson &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@1699:     Johnson &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@1699:     Johnson &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:     /// 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@1699:     void init() {
deba@1699:       create_maps();
deba@1699:     }
deba@1699:     
deba@1699:     /// \brief Executes the algorithm.
deba@1699:     ///
deba@1699:     /// This method runs the %Johnson algorithm in order to compute 
deba@1699:     /// the shortest path to each node pairs. The algorithm 
deba@1699:     /// computes 
deba@1699:     /// - The shortest path tree for each node.
deba@1699:     /// - The distance between each node pairs.
deba@1699:     void start() {
deba@1710:       typedef typename BelmannFord<Graph, LengthMap>::
deba@1699:       template DefOperationTraits<OperationTraits>::
deba@1710:       template DefPredMap<NullMap<Node, Edge> >::
deba@1710:       Create BelmannFordType;
deba@1710: 
deba@1710:       BelmannFordType belmannford(*graph, *length);
deba@1710: 
deba@1710:       NullMap<Node, Edge> predMap;
deba@1710: 
deba@1710:       belmannford.predMap(predMap);
deba@1699:       
deba@1710:       belmannford.init(OperationTraits::zero());
deba@1699:       belmannford.start();
deba@1699: 
deba@1699:       for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1699: 	typedef PotentialDifferenceMap<Graph, 
deba@1710: 	  typename BelmannFordType::DistMap> PotDiffMap;
deba@1699: 	PotDiffMap potdiff(*graph, belmannford.distMap());
deba@1699: 	typedef SubMap<LengthMap, PotDiffMap> ShiftLengthMap;
deba@1699: 	ShiftLengthMap shiftlen(*length, potdiff);
deba@1699: 	Dijkstra<Graph, ShiftLengthMap> dijkstra(*graph, shiftlen); 
deba@1699: 	dijkstra.run(it);
deba@1699: 	for (NodeIt jt(*graph); jt != INVALID; ++jt) {
deba@1699: 	  if (dijkstra.reached(jt)) {
deba@1699: 	    _dist->set(it, jt, dijkstra.dist(jt) + 
deba@1699: 		       belmannford.dist(jt) - belmannford.dist(it));
deba@1699: 	    _pred->set(it, jt, dijkstra.pred(jt));
deba@1699: 	  } else {
deba@1699: 	    _dist->set(it, jt, OperationTraits::infinity());
deba@1699: 	    _pred->set(it, jt, INVALID);
deba@1699: 	  }
deba@1699: 	}
deba@1699:       }
deba@1699:     }
deba@1699:     
deba@1699:     /// \brief Runs %Johnson algorithm.
deba@1699:     ///    
deba@1699:     /// This method runs the %Johnson algorithm from a each node
deba@1699:     /// in order to compute the shortest path to each node pairs. 
deba@1699:     /// The algorithm computes
deba@1699:     /// - The shortest path tree for each node.
deba@1699:     /// - The distance between each node pairs.
deba@1699:     ///
deba@1699:     /// \note d.run(s) is just a shortcut of the following code.
deba@1699:     /// \code
deba@1699:     ///  d.init();
deba@1699:     ///  d.start();
deba@1699:     /// \endcode
deba@1699:     void run() {
deba@1699:       init();
deba@1699:       start();
deba@1699:     }
deba@1699:     
deba@1699:     ///@}
deba@1699: 
deba@1699:     /// \name Query Functions
deba@1699:     /// The result of the %Johnson 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: 
deba@1699:     /// \brief Copies the shortest path to \c t into \c p
deba@1699:     ///    
deba@1699:     /// This function copies the shortest path to \c t into \c p.
deba@1699:     /// If it \c t is a source itself or unreachable, then it does not
deba@1699:     /// alter \c p.
deba@1699:     /// \todo Is it the right way to handle unreachable nodes?
deba@1699:     /// \return Returns \c true if a path to \c t was actually copied to \c p,
deba@1699:     /// \c false otherwise.
deba@1699:     /// \sa DirPath
deba@1699:     template <typename Path>
deba@1699:     bool getPath(Path &p, Node source, Node target) {
deba@1699:       if (connected(source, target)) {
deba@1699: 	p.clear();
deba@1699: 	typename Path::Builder b(target);
deba@1699: 	for(b.setStartNode(target); pred(source, target) != INVALID;
deba@1699: 	    target = predNode(target)) {
deba@1699: 	  b.pushFront(pred(source, target));
deba@1699: 	}
deba@1699: 	b.commit();
deba@1699: 	return true;
deba@1699:       }
deba@1699:       return false;
deba@1699:     }
deba@1699: 	  
deba@1699:     /// \brief The distance between two nodes.
deba@1699:     ///
deba@1699:     /// Returns the distance between two nodes.
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 source, Node target) const { 
deba@1699:       return (*_dist)(source, target); 
deba@1699:     }
deba@1699: 
deba@1699:     /// \brief Returns the 'previous edge' of the shortest path tree.
deba@1699:     ///
deba@1699:     /// For the node \c node it returns the 'previous edge' of the shortest 
deba@1699:     /// path tree to direction of the node \c root 
deba@1699:     /// i.e. it returns the last edge of a shortest path from the node \c root 
deba@1699:     /// to \c node. It is \ref INVALID if \c node is unreachable from the root
deba@1699:     /// or if \c node=root. The shortest path tree used here is equal to the 
deba@1699:     /// shortest path tree used in \ref predNode(). 
deba@1699:     /// \pre \ref run() must be called before using this function.
deba@1699:     /// \todo predEdge could be a better name.
deba@1699:     Edge pred(Node root, Node node) const { 
deba@1699:       return (*_pred)(root, node); 
deba@1699:     }
deba@1699: 
deba@1699:     /// \brief Returns the 'previous node' of the shortest path tree.
deba@1699:     ///
deba@1699:     /// For a node \c node it returns the 'previous node' of the shortest path 
deba@1699:     /// tree to direction of the node \c root, i.e. it returns the last but 
deba@1699:     /// one node from a shortest path from the \c root to \c node. It is 
deba@1699:     /// INVALID if \c node is unreachable from the root or if \c node=root. 
deba@1699:     /// The shortest path tree used here is equal to the 
deba@1699:     /// shortest path tree used in \ref pred().  
deba@1699:     /// \pre \ref run() must be called before using this function.
deba@1699:     Node predNode(Node root, Node node) const { 
deba@1699:       return (*_pred)(root, node) == INVALID ? 
deba@1699:       INVALID : graph->source((*_pred)(root, node)); 
deba@1699:     }
deba@1699:     
deba@1699:     /// \brief Returns a reference to the matrix node map of distances.
deba@1699:     ///
deba@1699:     /// Returns a reference to the matrix node map of distances. 
deba@1699:     ///
deba@1699:     /// \pre \ref run() must 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 matrix node map 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 connected(Node source, Node target) { 
deba@1699:       return (*_dist)(source, target) != OperationTraits::infinity(); 
deba@1699:     }
deba@1699:     
deba@1699:     ///@}
deba@1699:   };
deba@1699:  
deba@1699: } //END OF NAMESPACE LEMON
deba@1699: 
deba@1699: #endif