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_FLOYD_WARSHALL_H
deba@1699: #define LEMON_FLOYD_WARSHALL_H
deba@1699:
deba@2376: ///\ingroup shortest_path
deba@1699: /// \file
deba@1699: /// \brief FloydWarshall algorithm.
deba@1699: ///
deba@1699:
deba@1699: #include <lemon/list_graph.h>
deba@1699: #include <lemon/graph_utils.h>
deba@2335: #include <lemon/bits/path_dump.h>
deba@1993: #include <lemon/bits/invalid.h>
deba@1699: #include <lemon/error.h>
deba@1723: #include <lemon/matrix_maps.h>
deba@1699: #include <lemon/maps.h>
deba@1699:
deba@1699: #include <limits>
deba@1699:
deba@1699: namespace lemon {
deba@1699:
deba@1699: /// \brief Default OperationTraits for the FloydWarshall 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 FloydWarshallDefaultOperationTraits {
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 FloydWarshallDefaultOperationTraits<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 FloydWarshall class.
deba@1699: ///
deba@1699: /// Default traits class of FloydWarshall 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 FloydWarshallDefaultTraits {
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:
deba@1865: /// \brief Operation traits for floyd-warshall algorithm.
deba@1699: ///
deba@1699: /// It defines the infinity type on the given Value type
deba@1699: /// and the used operation.
deba@1699: /// \see FloydWarshallDefaultOperationTraits
deba@1699: typedef FloydWarshallDefaultOperationTraits<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.
alpar@1946: /// \param graph is the graph,
alpar@1946: /// 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@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::WriteMatrixMap "WriteMatrixMap" concept.
deba@1699: ///
deba@1723: typedef DynamicMatrixMap<Graph, typename Graph::Node, Value> DistMap;
deba@1699:
deba@1699: /// \brief Instantiates a DistMap.
deba@1699: ///
deba@1699: /// This function instantiates a \ref DistMap.
alpar@1946: /// \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@1754: /// \brief %FloydWarshall algorithm class.
deba@1699: ///
deba@2376: /// \ingroup shortest_path
deba@1754: /// This class provides an efficient implementation of \c Floyd-Warshall
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: ///
alpar@1757: /// The algorithm solves the shortest path problem for each pair
deba@1723: /// of node 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 from each node rather and if the graph is sparse and
deba@1754: /// there are negative circles then the johnson algorithm.
deba@1723: ///
deba@2042: /// The complexity of this algorithm is \f$ O(n^3+e) \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@1699: /// FloydWarshall, it is only passed to \ref FloydWarshallDefaultTraits.
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
alpar@2260: /// concepts::Graph::EdgeMap "Graph::EdgeMap<int>". The value
deba@1699: /// of _LengthMap is not used directly by FloydWarshall, it is only passed
deba@1699: /// to \ref FloydWarshallDefaultTraits. \param _Traits Traits class to set
deba@1699: /// various data types used by the algorithm. The default traits
deba@1699: /// class is \ref FloydWarshallDefaultTraits
deba@1699: /// "FloydWarshallDefaultTraits<_Graph,_LengthMap>". See \ref
deba@1699: /// FloydWarshallDefaultTraits for the documentation of a FloydWarshall
deba@1699: /// traits class.
deba@1699: ///
deba@1699: /// \author Balazs Dezso
alpar@2184: /// \todo A function type interface would be nice.
alpar@2184: /// \todo Implement \c nextNode() and \c nextEdge()
deba@1710: #ifdef DOXYGEN
alpar@2184: 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=FloydWarshallDefaultTraits<_Graph,_LengthMap> >
deba@1710: #endif
deba@1699: class FloydWarshall {
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@1699: return "lemon::FloydWarshall::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
alpar@2184: ///
alpar@2184: /// \todo It should rather be
alpar@2184: /// called \c DistMatrix
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 FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > {
deba@1710: typedef FloydWarshall< 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 FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > {
deba@1710: typedef FloydWarshall< 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@1699: /// \ref named-templ-param "Named parameter" for setting PredMap type
deba@1699: template <class T>
deba@1710: struct DefOperationTraits
deba@1699: : public FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> > {
deba@1710: typedef FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> >
deba@1710: Create;
deba@1699: };
deba@1699:
deba@1699: ///@}
deba@1699:
deba@1710: protected:
deba@1710:
deba@1710: FloydWarshall() {}
deba@1710:
deba@1699: public:
deba@1710:
deba@1710: typedef FloydWarshall Create;
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: FloydWarshall(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: ~FloydWarshall() {
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: FloydWarshall &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: FloydWarshall &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: FloydWarshall &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: for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1699: for (NodeIt jt(*graph); jt != INVALID; ++jt) {
deba@1699: _pred->set(it, jt, INVALID);
deba@1741: _dist->set(it, jt, OperationTraits::infinity());
deba@1699: }
deba@1741: _dist->set(it, it, OperationTraits::zero());
deba@1699: }
deba@1699: for (EdgeIt it(*graph); it != INVALID; ++it) {
deba@1699: Node source = graph->source(it);
deba@1699: Node target = graph->target(it);
deba@1699: if (OperationTraits::less((*length)[it], (*_dist)(source, target))) {
deba@1699: _dist->set(source, target, (*length)[it]);
deba@1699: _pred->set(source, target, it);
deba@1699: }
deba@1699: }
deba@1699: }
deba@1699:
deba@1699: /// \brief Executes the algorithm.
deba@1699: ///
deba@1699: /// This method runs the %FloydWarshall 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@1699: for (NodeIt kt(*graph); kt != INVALID; ++kt) {
deba@1699: for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1699: for (NodeIt jt(*graph); jt != INVALID; ++jt) {
deba@1699: Value relaxed = OperationTraits::plus((*_dist)(it, kt),
deba@1699: (*_dist)(kt, jt));
deba@1699: if (OperationTraits::less(relaxed, (*_dist)(it, jt))) {
deba@1699: _dist->set(it, jt, relaxed);
deba@1699: _pred->set(it, jt, (*_pred)(kt, jt));
deba@1699: }
deba@1699: }
deba@1699: }
deba@1699: }
deba@1699: }
deba@1741:
deba@1754: /// \brief Executes the algorithm and checks the negative cycles.
deba@1741: ///
deba@1741: /// This method runs the %FloydWarshall algorithm in order to compute
deba@1754: /// the shortest path to each node pairs. If there is a negative cycle
deba@1741: /// in the graph it gives back false.
deba@1741: /// The algorithm computes
deba@1741: /// - The shortest path tree for each node.
deba@1741: /// - The distance between each node pairs.
deba@1741: bool checkedStart() {
deba@1741: start();
deba@1741: for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1741: if (OperationTraits::less((*dist)(it, it), OperationTraits::zero())) {
deba@1741: return false;
deba@1741: }
deba@1741: }
deba@1741: return true;
deba@1741: }
deba@1699:
deba@1699: /// \brief Runs %FloydWarshall algorithm.
deba@1699: ///
deba@1699: /// This method runs the %FloydWarshall 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.
alpar@1946: ///\code
deba@1699: /// d.init();
deba@1699: /// d.start();
alpar@1946: ///\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 %FloydWarshall 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@2335: typedef PredMatrixMapPath<Graph, PredMap> Path;
deba@2335:
deba@2335: ///Gives back the shortest path.
deba@2335:
deba@2335: ///Gives back the shortest path.
deba@2335: ///\pre The \c t should be reachable from the \c t.
deba@2335: Path path(Node s, Node t)
deba@2335: {
deba@2335: return Path(*graph, *_pred, s, t);
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@1763: Edge predEdge(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@1763: /// shortest path tree used in \ref predEdge().
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
deba@1699: