lemon/bfs.h
changeset 2306 42cce226b87b
parent 2300 69330d717235
child 2307 558cc308a4bd
     1.1 --- a/lemon/bfs.h	Tue Nov 21 17:28:08 2006 +0000
     1.2 +++ b/lemon/bfs.h	Tue Nov 21 18:22:08 2006 +0000
     1.3 @@ -587,9 +587,9 @@
     1.4        while ( !emptyQueue() ) processNextNode();
     1.5      }
     1.6      
     1.7 -    ///Executes the algorithm until \c dest is reached.
     1.8 +    ///Executes the algorithm until \c dest is the next node to processed.
     1.9  
    1.10 -    ///Executes the algorithm until \c dest is reached.
    1.11 +    ///Executes the algorithm until \c dest is the next node to processed.
    1.12      ///
    1.13      ///\pre init() must be called and at least one node should be added
    1.14      ///with addSource() before using this function.
    1.15 @@ -614,8 +614,9 @@
    1.16      ///\pre init() must be called and at least one node should be added
    1.17      ///with addSource() before using this function.
    1.18      ///
    1.19 -    ///\param nm must be a bool (or convertible) node map. The algorithm
    1.20 -    ///will stop when it reaches a node \c v with <tt>nm[v]==true</tt>.
    1.21 +    ///\param nm must be a bool (or convertible) node map. The
    1.22 +    ///algorithm will stop when for the next processable node \c v is
    1.23 +    ///<tt>nm[v]</tt> true.
    1.24      ///\todo query the reached target
    1.25      template<class NM>
    1.26      void start(const NM &nm)
    1.27 @@ -633,11 +634,11 @@
    1.28      ///- The shortest path tree.
    1.29      ///- The distance of each node from the root.
    1.30      ///
    1.31 -    ///\note d.run(s) is just a shortcut of the following code.
    1.32 +    ///\note b.run(s) is just a shortcut of the following code.
    1.33      ///\code
    1.34 -    ///  d.init();
    1.35 -    ///  d.addSource(s);
    1.36 -    ///  d.start();
    1.37 +    ///  b.init();
    1.38 +    ///  b.addSource(s);
    1.39 +    ///  b.start();
    1.40      ///\endcode
    1.41      void run(Node s) {
    1.42        init();
    1.43 @@ -651,12 +652,12 @@
    1.44      ///
    1.45      ///\return The length of the shortest s---t path if there exists one,
    1.46      ///0 otherwise.
    1.47 -    ///\note Apart from the return value, d.run(s) is
    1.48 +    ///\note Apart from the return value, b.run(s) is
    1.49      ///just a shortcut of the following code.
    1.50      ///\code
    1.51 -    ///  d.init();
    1.52 -    ///  d.addSource(s);
    1.53 -    ///  d.start(t);
    1.54 +    ///  b.init();
    1.55 +    ///  b.addSource(s);
    1.56 +    ///  b.start(t);
    1.57      ///\endcode
    1.58      int run(Node s,Node t) {
    1.59        init();
    1.60 @@ -671,7 +672,7 @@
    1.61      ///The result of the %BFS algorithm can be obtained using these
    1.62      ///functions.\n
    1.63      ///Before the use of these functions,
    1.64 -    ///either run() or start() must be called.
    1.65 +    ///either run() or start() must be calleb.
    1.66      
    1.67      ///@{
    1.68  
    1.69 @@ -943,7 +944,7 @@
    1.70      ///The type of the map that stores the dists of the nodes.
    1.71      typedef typename TR::DistMap DistMap;
    1.72  
    1.73 -public:
    1.74 +  public:
    1.75      /// Constructor.
    1.76      BfsWizard() : TR() {}
    1.77  
    1.78 @@ -1104,6 +1105,495 @@
    1.79      return BfsWizard<BfsWizardBase<GR> >(g,s);
    1.80    }
    1.81  
    1.82 +#ifdef DOXYGEN
    1.83 +  /// \brief Visitor class for bfs.
    1.84 +  ///  
    1.85 +  /// It gives a simple interface for a functional interface for bfs 
    1.86 +  /// traversal. The traversal on a linear data structure. 
    1.87 +  template <typename _Graph>
    1.88 +  struct BfsVisitor {
    1.89 +    typedef _Graph Graph;
    1.90 +    typedef typename Graph::Edge Edge;
    1.91 +    typedef typename Graph::Node Node;
    1.92 +    /// \brief Called when the edge reach a node.
    1.93 +    /// 
    1.94 +    /// It is called when the bfs find an edge which target is not
    1.95 +    /// reached yet.
    1.96 +    void discover(const Edge& edge) {}
    1.97 +    /// \brief Called when the node reached first time.
    1.98 +    /// 
    1.99 +    /// It is Called when the node reached first time.
   1.100 +    void reach(const Node& node) {}
   1.101 +    /// \brief Called when the edge examined but target of the edge 
   1.102 +    /// already discovered.
   1.103 +    /// 
   1.104 +    /// It called when the edge examined but the target of the edge 
   1.105 +    /// already discovered.
   1.106 +    void examine(const Edge& edge) {}
   1.107 +    /// \brief Called for the source node of the bfs.
   1.108 +    /// 
   1.109 +    /// It is called for the source node of the bfs.
   1.110 +    void start(const Node& node) {}
   1.111 +    /// \brief Called when the node processed.
   1.112 +    /// 
   1.113 +    /// It is Called when the node processed.
   1.114 +    void process(const Node& node) {}
   1.115 +  };
   1.116 +#else
   1.117 +  template <typename _Graph>
   1.118 +  struct BfsVisitor {
   1.119 +    typedef _Graph Graph;
   1.120 +    typedef typename Graph::Edge Edge;
   1.121 +    typedef typename Graph::Node Node;
   1.122 +    void discover(const Edge&) {}
   1.123 +    void reach(const Node&) {}
   1.124 +    void examine(const Edge&) {}
   1.125 +    void start(const Node&) {}
   1.126 +    void process(const Node&) {}
   1.127 +
   1.128 +    template <typename _Visitor>
   1.129 +    struct Constraints {
   1.130 +      void constraints() {
   1.131 +	Edge edge;
   1.132 +	Node node;
   1.133 +	visitor.discover(edge);
   1.134 +	visitor.reach(node);
   1.135 +	visitor.examine(edge);
   1.136 +	visitor.start(node);
   1.137 +        visitor.process(node);
   1.138 +      }
   1.139 +      _Visitor& visitor;
   1.140 +    };
   1.141 +  };
   1.142 +#endif
   1.143 +
   1.144 +  /// \brief Default traits class of BfsVisit class.
   1.145 +  ///
   1.146 +  /// Default traits class of BfsVisit class.
   1.147 +  /// \param _Graph Graph type.
   1.148 +  template<class _Graph>
   1.149 +  struct BfsVisitDefaultTraits {
   1.150 +
   1.151 +    /// \brief The graph type the algorithm runs on. 
   1.152 +    typedef _Graph Graph;
   1.153 +
   1.154 +    /// \brief The type of the map that indicates which nodes are reached.
   1.155 +    /// 
   1.156 +    /// The type of the map that indicates which nodes are reached.
   1.157 +    /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
   1.158 +    /// \todo named parameter to set this type, function to read and write.
   1.159 +    typedef typename Graph::template NodeMap<bool> ReachedMap;
   1.160 +
   1.161 +    /// \brief Instantiates a ReachedMap.
   1.162 +    ///
   1.163 +    /// This function instantiates a \ref ReachedMap. 
   1.164 +    /// \param graph is the graph, to which
   1.165 +    /// we would like to define the \ref ReachedMap.
   1.166 +    static ReachedMap *createReachedMap(const Graph &graph) {
   1.167 +      return new ReachedMap(graph);
   1.168 +    }
   1.169 +
   1.170 +  };
   1.171 +  
   1.172 +  /// %BFS Visit algorithm class.
   1.173 +  
   1.174 +  /// \ingroup flowalgs
   1.175 +  /// This class provides an efficient implementation of the %BFS algorithm
   1.176 +  /// with visitor interface.
   1.177 +  ///
   1.178 +  /// The %BfsVisit class provides an alternative interface to the Bfs
   1.179 +  /// class. It works with callback mechanism, the BfsVisit object calls
   1.180 +  /// on every bfs event the \c Visitor class member functions. 
   1.181 +  ///
   1.182 +  /// \param _Graph The graph type the algorithm runs on. The default value is
   1.183 +  /// \ref ListGraph. The value of _Graph is not used directly by Bfs, it
   1.184 +  /// is only passed to \ref BfsDefaultTraits.
   1.185 +  /// \param _Visitor The Visitor object for the algorithm. The 
   1.186 +  /// \ref BfsVisitor "BfsVisitor<_Graph>" is an empty Visitor which
   1.187 +  /// does not observe the Bfs events. If you want to observe the bfs
   1.188 +  /// events you should implement your own Visitor class.
   1.189 +  /// \param _Traits Traits class to set various data types used by the 
   1.190 +  /// algorithm. The default traits class is
   1.191 +  /// \ref BfsVisitDefaultTraits "BfsVisitDefaultTraits<_Graph>".
   1.192 +  /// See \ref BfsVisitDefaultTraits for the documentation of
   1.193 +  /// a Bfs visit traits class.
   1.194 +  ///
   1.195 +  /// \author Jacint Szabo, Alpar Juttner and Balazs Dezso
   1.196 +#ifdef DOXYGEN
   1.197 +  template <typename _Graph, typename _Visitor, typename _Traits>
   1.198 +#else
   1.199 +  template <typename _Graph = ListGraph,
   1.200 +	    typename _Visitor = BfsVisitor<_Graph>,
   1.201 +	    typename _Traits = BfsDefaultTraits<_Graph> >
   1.202 +#endif
   1.203 +  class BfsVisit {
   1.204 +  public:
   1.205 +    
   1.206 +    /// \brief \ref Exception for uninitialized parameters.
   1.207 +    ///
   1.208 +    /// This error represents problems in the initialization
   1.209 +    /// of the parameters of the algorithms.
   1.210 +    class UninitializedParameter : public lemon::UninitializedParameter {
   1.211 +    public:
   1.212 +      virtual const char* what() const throw() 
   1.213 +      {
   1.214 +	return "lemon::BfsVisit::UninitializedParameter";
   1.215 +      }
   1.216 +    };
   1.217 +
   1.218 +    typedef _Traits Traits;
   1.219 +
   1.220 +    typedef typename Traits::Graph Graph;
   1.221 +
   1.222 +    typedef _Visitor Visitor;
   1.223 +
   1.224 +    ///The type of the map indicating which nodes are reached.
   1.225 +    typedef typename Traits::ReachedMap ReachedMap;
   1.226 +
   1.227 +  private:
   1.228 +
   1.229 +    typedef typename Graph::Node Node;
   1.230 +    typedef typename Graph::NodeIt NodeIt;
   1.231 +    typedef typename Graph::Edge Edge;
   1.232 +    typedef typename Graph::OutEdgeIt OutEdgeIt;
   1.233 +
   1.234 +    /// Pointer to the underlying graph.
   1.235 +    const Graph *_graph;
   1.236 +    /// Pointer to the visitor object.
   1.237 +    Visitor *_visitor;
   1.238 +    ///Pointer to the map of reached status of the nodes.
   1.239 +    ReachedMap *_reached;
   1.240 +    ///Indicates if \ref _reached is locally allocated (\c true) or not.
   1.241 +    bool local_reached;
   1.242 +
   1.243 +    std::vector<typename Graph::Node> _list;
   1.244 +    int _list_front, _list_back;
   1.245 +
   1.246 +    /// \brief Creates the maps if necessary.
   1.247 +    ///
   1.248 +    /// Creates the maps if necessary.
   1.249 +    void create_maps() {
   1.250 +      if(!_reached) {
   1.251 +	local_reached = true;
   1.252 +	_reached = Traits::createReachedMap(*_graph);
   1.253 +      }
   1.254 +    }
   1.255 +
   1.256 +  protected:
   1.257 +
   1.258 +    BfsVisit() {}
   1.259 +    
   1.260 +  public:
   1.261 +
   1.262 +    typedef BfsVisit Create;
   1.263 +
   1.264 +    /// \name Named template parameters
   1.265 +
   1.266 +    ///@{
   1.267 +    template <class T>
   1.268 +    struct DefReachedMapTraits : public Traits {
   1.269 +      typedef T ReachedMap;
   1.270 +      static ReachedMap *createReachedMap(const Graph &graph) {
   1.271 +	throw UninitializedParameter();
   1.272 +      }
   1.273 +    };
   1.274 +    /// \brief \ref named-templ-param "Named parameter" for setting 
   1.275 +    /// ReachedMap type
   1.276 +    ///
   1.277 +    /// \ref named-templ-param "Named parameter" for setting ReachedMap type
   1.278 +    template <class T>
   1.279 +    struct DefReachedMap : public BfsVisit< Graph, Visitor,
   1.280 +					    DefReachedMapTraits<T> > {
   1.281 +      typedef BfsVisit< Graph, Visitor, DefReachedMapTraits<T> > Create;
   1.282 +    };
   1.283 +    ///@}
   1.284 +
   1.285 +  public:      
   1.286 +    
   1.287 +    /// \brief Constructor.
   1.288 +    ///
   1.289 +    /// Constructor.
   1.290 +    ///
   1.291 +    /// \param graph the graph the algorithm will run on.
   1.292 +    /// \param visitor The visitor of the algorithm.
   1.293 +    ///
   1.294 +    BfsVisit(const Graph& graph, Visitor& visitor) 
   1.295 +      : _graph(&graph), _visitor(&visitor),
   1.296 +	_reached(0), local_reached(false) {}
   1.297 +    
   1.298 +    /// \brief Destructor.
   1.299 +    ///
   1.300 +    /// Destructor.
   1.301 +    ~BfsVisit() {
   1.302 +      if(local_reached) delete _reached;
   1.303 +    }
   1.304 +
   1.305 +    /// \brief Sets the map indicating if a node is reached.
   1.306 +    ///
   1.307 +    /// Sets the map indicating if a node is reached.
   1.308 +    /// If you don't use this function before calling \ref run(),
   1.309 +    /// it will allocate one. The destuctor deallocates this
   1.310 +    /// automatically allocated map, of course.
   1.311 +    /// \return <tt> (*this) </tt>
   1.312 +    BfsVisit &reachedMap(ReachedMap &m) {
   1.313 +      if(local_reached) {
   1.314 +	delete _reached;
   1.315 +	local_reached = false;
   1.316 +      }
   1.317 +      _reached = &m;
   1.318 +      return *this;
   1.319 +    }
   1.320 +
   1.321 +  public:
   1.322 +    /// \name Execution control
   1.323 +    /// The simplest way to execute the algorithm is to use
   1.324 +    /// one of the member functions called \c run(...).
   1.325 +    /// \n
   1.326 +    /// If you need more control on the execution,
   1.327 +    /// first you must call \ref init(), then you can adda source node
   1.328 +    /// with \ref addSource().
   1.329 +    /// Finally \ref start() will perform the actual path
   1.330 +    /// computation.
   1.331 +
   1.332 +    /// @{
   1.333 +    /// \brief Initializes the internal data structures.
   1.334 +    ///
   1.335 +    /// Initializes the internal data structures.
   1.336 +    ///
   1.337 +    void init() {
   1.338 +      create_maps();
   1.339 +      _list.resize(countNodes(*_graph));
   1.340 +      _list_front = _list_back = -1;
   1.341 +      for (NodeIt u(*_graph) ; u != INVALID ; ++u) {
   1.342 +	_reached->set(u, false);
   1.343 +      }
   1.344 +    }
   1.345 +    
   1.346 +    /// \brief Adds a new source node.
   1.347 +    ///
   1.348 +    /// Adds a new source node to the set of nodes to be processed.
   1.349 +    void addSource(Node s) {
   1.350 +      if(!(*_reached)[s]) {
   1.351 +	  _reached->set(s,true);
   1.352 +	  _visitor->start(s);
   1.353 +	  _visitor->reach(s);
   1.354 +          _list[++_list_back] = s;
   1.355 +	}
   1.356 +    }
   1.357 +    
   1.358 +    /// \brief Processes the next node.
   1.359 +    ///
   1.360 +    /// Processes the next node.
   1.361 +    ///
   1.362 +    /// \return The processed node.
   1.363 +    ///
   1.364 +    /// \pre The queue must not be empty!
   1.365 +    Node processNextNode() { 
   1.366 +      Node n = _list[++_list_front];
   1.367 +      _visitor->process(n);
   1.368 +      Edge e;
   1.369 +      for (_graph->firstOut(e, n); e != INVALID; _graph->nextOut(e)) {
   1.370 +        Node m = _graph->target(e);
   1.371 +        if (!(*_reached)[m]) {
   1.372 +          _visitor->discover(e);
   1.373 +          _visitor->reach(m);
   1.374 +          _reached->set(m, true);
   1.375 +          _list[++_list_back] = m;
   1.376 +        } else {
   1.377 +          _visitor->examine(e);
   1.378 +        }
   1.379 +      }
   1.380 +      return n;
   1.381 +    }
   1.382 +
   1.383 +    /// \brief Processes the next node.
   1.384 +    ///
   1.385 +    /// Processes the next node. And checks that the given target node
   1.386 +    /// is reached. If the target node is reachable from the processed
   1.387 +    /// node then the reached parameter will be set true. The reached
   1.388 +    /// parameter should be initially false.
   1.389 +    ///
   1.390 +    /// \param target The target node.
   1.391 +    /// \retval reached Indicates that the target node is reached.
   1.392 +    /// \return The processed node.
   1.393 +    ///
   1.394 +    /// \warning The queue must not be empty!
   1.395 +    Node processNextNode(Node target, bool& reached) {
   1.396 +      Node n = _list[++_list_front];
   1.397 +      _visitor->process(n);
   1.398 +      Edge e;
   1.399 +      for (_graph->firstOut(e, n); e != INVALID; _graph->nextOut(e)) {
   1.400 +        Node m = _graph->target(e);
   1.401 +        if (!(*_reached)[m]) {
   1.402 +          _visitor->discover(e);
   1.403 +          _visitor->reach(m);
   1.404 +          _reached->set(m, true);
   1.405 +          _list[++_list_back] = m;
   1.406 +          reached = reached || (target == m);
   1.407 +        } else {
   1.408 +          _visitor->examine(e);
   1.409 +        }
   1.410 +      }
   1.411 +      return n;
   1.412 +    }
   1.413 +
   1.414 +    /// \brief Processes the next node.
   1.415 +    ///
   1.416 +    /// Processes the next node. And checks that at least one of
   1.417 +    /// reached node has true value in the \c nm nodemap. If one node
   1.418 +    /// with true value is reachable from the processed node then the
   1.419 +    /// reached parameter will be set true. The reached parameter
   1.420 +    /// should be initially false.
   1.421 +    ///
   1.422 +    /// \param target The nodemaps of possible targets.
   1.423 +    /// \retval reached Indicates that one of the target nodes is reached.
   1.424 +    /// \return The processed node.
   1.425 +    ///
   1.426 +    /// \warning The queue must not be empty!
   1.427 +    template <typename NM>
   1.428 +    Node processNextNode(const NM& nm, bool& reached) {
   1.429 +      Node n = _list[++_list_front];
   1.430 +      _visitor->process(n);
   1.431 +      Edge e;
   1.432 +      for (_graph->firstOut(e, n); e != INVALID; _graph->nextOut(e)) {
   1.433 +        Node m = _graph->target(e);
   1.434 +        if (!(*_reached)[m]) {
   1.435 +          _visitor->discover(e);
   1.436 +          _visitor->reach(m);
   1.437 +          _reached->set(m, true);
   1.438 +          _list[++_list_back] = m;
   1.439 +          reached = reached || nm[m];
   1.440 +        } else {
   1.441 +          _visitor->examine(e);
   1.442 +        }
   1.443 +      }
   1.444 +      return n;
   1.445 +    }
   1.446 +
   1.447 +    /// \brief Next node to be processed.
   1.448 +    ///
   1.449 +    /// Next node to be processed.
   1.450 +    ///
   1.451 +    /// \return The next node to be processed or INVALID if the stack is
   1.452 +    /// empty.
   1.453 +    Node nextNode() { 
   1.454 +      return _list_front != _list_back ? _list[_list_front + 1] : INVALID;
   1.455 +    }
   1.456 +
   1.457 +    /// \brief Returns \c false if there are nodes
   1.458 +    /// to be processed in the queue
   1.459 +    ///
   1.460 +    /// Returns \c false if there are nodes
   1.461 +    /// to be processed in the queue
   1.462 +    bool emptyQueue() { return _list_front == _list_back; }
   1.463 +
   1.464 +    /// \brief Returns the number of the nodes to be processed.
   1.465 +    ///
   1.466 +    /// Returns the number of the nodes to be processed in the queue.
   1.467 +    int queueSize() { return _list_back - _list_front; }
   1.468 +    
   1.469 +    /// \brief Executes the algorithm.
   1.470 +    ///
   1.471 +    /// Executes the algorithm.
   1.472 +    ///
   1.473 +    /// \pre init() must be called and at least one node should be added
   1.474 +    /// with addSource() before using this function.
   1.475 +    void start() {
   1.476 +      while ( !emptyQueue() ) processNextNode();
   1.477 +    }
   1.478 +    
   1.479 +    /// \brief Executes the algorithm until \c dest will be next processed.
   1.480 +    ///
   1.481 +    /// Executes the algorithm until \c dest will be next processed.
   1.482 +    ///
   1.483 +    /// \pre init() must be called and at least one node should be added
   1.484 +    /// with addSource() before using this function.
   1.485 +    void start(Node dest) {
   1.486 +      bool reached = false;
   1.487 +      while (!emptyQueue() && !reached) { 
   1.488 +	processNextNode(dest, reached);
   1.489 +      }
   1.490 +    }
   1.491 +    
   1.492 +    /// \brief Executes the algorithm until a condition is met.
   1.493 +    ///
   1.494 +    /// Executes the algorithm until a condition is met.
   1.495 +    ///
   1.496 +    /// \pre init() must be called and at least one node should be added
   1.497 +    /// with addSource() before using this function.
   1.498 +    ///
   1.499 +    ///\param nm must be a bool (or convertible) node map. The
   1.500 +    ///algorithm will stop when it reaches a node \c v with
   1.501 +    ///<tt>nm[v]</tt> true.
   1.502 +    template <typename NM>
   1.503 +    void start(const NM &nm) {
   1.504 +      bool reached = false;
   1.505 +      while (!emptyQueue() && !reached) {
   1.506 +        processNextNode(nm, reached);
   1.507 +      }
   1.508 +    }
   1.509 +
   1.510 +    /// \brief Runs %BFSVisit algorithm from node \c s.
   1.511 +    ///
   1.512 +    /// This method runs the %BFS algorithm from a root node \c s.
   1.513 +    /// \note b.run(s) is just a shortcut of the following code.
   1.514 +    ///\code
   1.515 +    ///   b.init();
   1.516 +    ///   b.addSource(s);
   1.517 +    ///   b.start();
   1.518 +    ///\endcode
   1.519 +    void run(Node s) {
   1.520 +      init();
   1.521 +      addSource(s);
   1.522 +      start();
   1.523 +    }
   1.524 +
   1.525 +    /// \brief Runs %BFSVisit algorithm to visit all nodes in the graph.
   1.526 +    ///    
   1.527 +    /// This method runs the %BFS algorithm in order to
   1.528 +    /// compute the %BFS path to each node. The algorithm computes
   1.529 +    /// - The %BFS tree.
   1.530 +    /// - The distance of each node from the root in the %BFS tree.
   1.531 +    ///
   1.532 +    ///\note b.run() is just a shortcut of the following code.
   1.533 +    ///\code
   1.534 +    ///  b.init();
   1.535 +    ///  for (NodeIt it(graph); it != INVALID; ++it) {
   1.536 +    ///    if (!b.reached(it)) {
   1.537 +    ///      b.addSource(it);
   1.538 +    ///      b.start();
   1.539 +    ///    }
   1.540 +    ///  }
   1.541 +    ///\endcode
   1.542 +    void run() {
   1.543 +      init();
   1.544 +      for (NodeIt it(*_graph); it != INVALID; ++it) {
   1.545 +        if (!reached(it)) {
   1.546 +          addSource(it);
   1.547 +          start();
   1.548 +        }
   1.549 +      }
   1.550 +    }
   1.551 +    ///@}
   1.552 +
   1.553 +    /// \name Query Functions
   1.554 +    /// The result of the %BFS algorithm can be obtained using these
   1.555 +    /// functions.\n
   1.556 +    /// Before the use of these functions,
   1.557 +    /// either run() or start() must be called.
   1.558 +    ///@{
   1.559 +
   1.560 +    /// \brief Checks if a node is reachable from the root.
   1.561 +    ///
   1.562 +    /// Returns \c true if \c v is reachable from the root(s).
   1.563 +    /// \warning The source nodes are inditated as unreachable.
   1.564 +    /// \pre Either \ref run() or \ref start()
   1.565 +    /// must be called before using this function.
   1.566 +    ///
   1.567 +    bool reached(Node v) { return (*_reached)[v]; }
   1.568 +    ///@}
   1.569 +  };
   1.570 +
   1.571  } //END OF NAMESPACE LEMON
   1.572  
   1.573  #endif