RhodeCode

#include <lemon/core.h>

#include <lemon/error.h>

#include <lemon/maps.h>

#include <lemon/path.h>

namespace lemon {

  ///Default traits class of Bfs class.

  ///Default traits class of Bfs class.

  ///\tparam GR Digraph type.

  template<class GR>

  struct BfsDefaultTraits

  {

    ///The type of the digraph the algorithm runs on.

    typedef GR Digraph;

    ///\brief The type of the map that stores the predecessor

    ///arcs of the shortest paths.

    ///

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

    ///arcs of the shortest paths.

    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.

    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;

    ///\param g is the digraph, to which we would like to define the

    static PredMap *createPredMap(const Digraph &g)

    {

      return new PredMap(g);

    }

    ///The type of the map that indicates which nodes are processed.

    ///The type of the map that indicates which nodes are processed.

    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.

    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;

    ///\param g is the digraph, to which

#ifdef DOXYGEN

    static ProcessedMap *createProcessedMap(const Digraph &g)

#else

    static ProcessedMap *createProcessedMap(const Digraph &)

#endif

    {

      return new ProcessedMap();

    }

    ///The type of the map that indicates which nodes are reached.

    ///The type of the map that indicates which nodes are reached.

    ///It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.

    typedef typename Digraph::template NodeMap<bool> ReachedMap;

    ///\param g is the digraph, to which

    static ReachedMap *createReachedMap(const Digraph &g)

    {

      return new ReachedMap(g);

    }

    ///The type of the map that stores the distances of the nodes.

    ///The type of the map that stores the distances of the nodes.

    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.

    typedef typename Digraph::template NodeMap<int> DistMap;

    ///\param g is the digraph, to which we would like to define the

    static DistMap *createDistMap(const Digraph &g)

    {

      return new DistMap(g);

    }

  };

  ///%BFS algorithm class.

  ///\ingroup search

  ///This class provides an efficient implementation of the %BFS algorithm.

  ///

  ///There is also a \ref bfs() "function-type interface" for the BFS

  ///algorithm, which is convenient in the simplier cases and it can be

  ///used easier.

  ///

  ///\tparam GR The type of the digraph the algorithm runs on.

  ///The default type is \ref ListDigraph.

#ifdef DOXYGEN

  template <typename GR,

            typename TR>

#else

  template <typename GR=ListDigraph,

            typename TR=BfsDefaultTraits<GR> >

#endif

    }

  protected:

    Bfs() {}

  public:

    typedef Bfs Create;

    ///\name Named Template Parameters

    ///@{

    template <class T>

    struct SetPredMapTraits : public Traits {

      typedef T PredMap;

      static PredMap *createPredMap(const Digraph &)

      {

        LEMON_ASSERT(false, "PredMap is not initialized");

        return 0; // ignore warnings

      }

    };

    ///\brief \ref named-templ-param "Named parameter" for setting

    ///

    ///\ref named-templ-param "Named parameter" for setting

    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.

    template <class T>

    struct SetPredMap : public Bfs< Digraph, SetPredMapTraits<T> > {

      typedef Bfs< Digraph, SetPredMapTraits<T> > Create;

    };

    template <class T>

    struct SetDistMapTraits : public Traits {

      typedef T DistMap;

      static DistMap *createDistMap(const Digraph &)

      {

        LEMON_ASSERT(false, "DistMap is not initialized");

        return 0; // ignore warnings

      }

    };

    ///\brief \ref named-templ-param "Named parameter" for setting

    ///

    ///\ref named-templ-param "Named parameter" for setting

    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.

    template <class T>

    struct SetDistMap : public Bfs< Digraph, SetDistMapTraits<T> > {

      typedef Bfs< Digraph, SetDistMapTraits<T> > Create;

    };

    template <class T>

    struct SetReachedMapTraits : public Traits {

      typedef T ReachedMap;

      static ReachedMap *createReachedMap(const Digraph &)

      {

        LEMON_ASSERT(false, "ReachedMap is not initialized");

        return 0; // ignore warnings

      }

    };

    ///\brief \ref named-templ-param "Named parameter" for setting

    ///

    ///\ref named-templ-param "Named parameter" for setting

    ///It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.

    template <class T>

    struct SetReachedMap : public Bfs< Digraph, SetReachedMapTraits<T> > {

      typedef Bfs< Digraph, SetReachedMapTraits<T> > Create;

    };

    template <class T>

    struct SetProcessedMapTraits : public Traits {

      typedef T ProcessedMap;

      static ProcessedMap *createProcessedMap(const Digraph &)

      {

        LEMON_ASSERT(false, "ProcessedMap is not initialized");

        return 0; // ignore warnings

      }

    };

    ///\brief \ref named-templ-param "Named parameter" for setting

    ///

    ///\ref named-templ-param "Named parameter" for setting

    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.

    template <class T>

    struct SetProcessedMap : public Bfs< Digraph, SetProcessedMapTraits<T> > {

      typedef Bfs< Digraph, SetProcessedMapTraits<T> > Create;

    };

    struct SetStandardProcessedMapTraits : public Traits {

      typedef typename Digraph::template NodeMap<bool> ProcessedMap;

      static ProcessedMap *createProcessedMap(const Digraph &g)

      {

        return new ProcessedMap(g);

        return 0; // ignore warnings

      }

    };

    ///\brief \ref named-templ-param "Named parameter" for setting

    ///

    ///\ref named-templ-param "Named parameter" for setting

    ///If you don't set it explicitly, it will be automatically allocated.

    struct SetStandardProcessedMap :

      public Bfs< Digraph, SetStandardProcessedMapTraits > {

      typedef Bfs< Digraph, SetStandardProcessedMapTraits > Create;

    };

    ///@}

  public:

    ///Constructor.

    ///Constructor.

    ///\param g The digraph the algorithm runs on.

    Bfs(const Digraph &g) :

      G(&g),

      _pred(NULL), local_pred(false),

      _dist(NULL), local_dist(false),

      _reached(NULL), local_reached(false),

      _processed(NULL), local_processed(false)

    { }

    ///Destructor.

    ~Bfs()

  ///The following examples show how to use these parameters.

  ///\code

  ///  // Compute shortest path from node s to each node

  ///  bfs(g).predMap(preds).distMap(dists).run(s);

  ///

  ///  // Compute shortest path from s to t

  ///  bool reached = bfs(g).path(p).dist(d).run(s,t);

  ///\endcode

  ///\warning Don't forget to put the \ref BfsWizard::run(Node) "run()"

  ///to the end of the parameter list.

  ///\sa BfsWizard

  ///\sa Bfs

  template<class GR>

  BfsWizard<BfsWizardBase<GR> >

  bfs(const GR &digraph)

  {

    return BfsWizard<BfsWizardBase<GR> >(digraph);

  }

#ifdef DOXYGEN

  /// \brief Visitor class for BFS.

  ///

  /// This class defines the interface of the BfsVisit events, and

  /// it could be the base of a real visitor class.

  struct BfsVisitor {

    typedef typename Digraph::Arc Arc;

    typedef typename Digraph::Node Node;

    /// \brief Called for the source node(s) of the BFS.

    ///

    /// This function is called for the source node(s) of the BFS.

    void start(const Node& node) {}

    /// \brief Called when a node is reached first time.

    ///

    /// This function is called when a node is reached first time.

    void reach(const Node& node) {}

    /// \brief Called when a node is processed.

    ///

    /// This function is called when a node is processed.

    void process(const Node& node) {}

    /// \brief Called when an arc reaches a new node.

    ///

    /// This function is called when the BFS finds an arc whose target node

    /// is not reached yet.

    void discover(const Arc& arc) {}

    /// \brief Called when an arc is examined but its target node is

    /// already discovered.

    ///

    /// This function is called when an arc is examined but its target node is

    /// already discovered.

    void examine(const Arc& arc) {}

  };

#else

  struct BfsVisitor {

    typedef typename Digraph::Arc Arc;

    typedef typename Digraph::Node Node;

    void start(const Node&) {}

    void reach(const Node&) {}

    void process(const Node&) {}

    void discover(const Arc&) {}

    void examine(const Arc&) {}

    template <typename _Visitor>

    struct Constraints {

      void constraints() {

        Arc arc;

        Node node;

        visitor.start(node);

        visitor.reach(node);

        visitor.process(node);

        visitor.discover(arc);

        visitor.examine(arc);

      }

      _Visitor& visitor;

    };

  };

#endif

  /// \brief Default traits class of BfsVisit class.

  ///

  /// Default traits class of BfsVisit class.

  struct BfsVisitDefaultTraits {

    /// \brief The type of the digraph the algorithm runs on.

    /// \brief The type of the map that indicates which nodes are reached.

    ///

    /// The type of the map that indicates which nodes are reached.

    /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.

    typedef typename Digraph::template NodeMap<bool> ReachedMap;

    /// \brief Instantiates a ReachedMap.

    ///

    /// This function instantiates a ReachedMap.

    /// \param digraph is the digraph, to which

    /// we would like to define the ReachedMap.

    static ReachedMap *createReachedMap(const Digraph &digraph) {

      return new ReachedMap(digraph);

    }

  };

  /// \ingroup search

  ///

  ///

  /// with visitor interface.

  ///

  /// class. It works with callback mechanism, the BfsVisit object calls

  /// the member functions of the \c Visitor class on every BFS event.

  ///

  /// This interface of the BFS algorithm should be used in special cases

  /// when extra actions have to be performed in connection with certain

  /// events of the BFS algorithm. Otherwise consider to use Bfs or bfs()

  /// instead.

  ///

  /// does not observe the BFS events. If you want to observe the BFS

  /// events, you should implement your own visitor class.

  /// algorithm. The default traits class is

  /// See \ref BfsVisitDefaultTraits for the documentation of

  /// a BFS visit traits class.

#ifdef DOXYGEN

#else

#endif

  class BfsVisit {

  public:

    ///The traits class.

    ///The type of the digraph the algorithm runs on.

    typedef typename Traits::Digraph Digraph;

    ///The visitor type used by the algorithm.

    ///The type of the map that indicates which nodes are reached.

    typedef typename Traits::ReachedMap ReachedMap;

  private:

    typedef typename Digraph::Node Node;

    typedef typename Digraph::NodeIt NodeIt;

    typedef typename Digraph::Arc Arc;

    typedef typename Digraph::OutArcIt OutArcIt;

    //Pointer to the underlying digraph.

    const Digraph *_digraph;

    //Pointer to the visitor object.

    Visitor *_visitor;

    //Pointer to the map of reached status of the nodes.

    ReachedMap *_reached;

    //Indicates if _reached is locally allocated (true) or not.

    bool local_reached;

    std::vector<typename Digraph::Node> _list;

    int _list_front, _list_back;

    //Creates the maps if necessary.

      if (capacity == 0) return;

      values = allocator.allocate(capacity);

      Notifier* nf = Parent::notifier();

      Item it;

      for (nf->first(it); it != INVALID; nf->next(it)) {

        int id = nf->id(it);;

        allocator.construct(&(values[id]), copy.values[id]);

      }

    }

    // \brief Assign operator.

    //

    // This operator assigns for each item in the map the

    // value mapped to the same item in the copied map.

    // The parameter map should be indiced with the same

    // itemset because this assign operator does not change

    // the container of the map.

    ArrayMap& operator=(const ArrayMap& cmap) {

      return operator=<ArrayMap>(cmap);

    }

    // \brief Template assign operator.

    //

    // concecpt and could be indiced by the current item set of

    // the NodeMap. In this case the value for each item

    // is assigned by the value of the given ReadMap.

    template <typename CMap>

    ArrayMap& operator=(const CMap& cmap) {

      checkConcept<concepts::ReadMap<Key, _Value>, CMap>();

      const typename Parent::Notifier* nf = Parent::notifier();

      Item it;

      for (nf->first(it); it != INVALID; nf->next(it)) {

        set(it, cmap[it]);

      }

      return *this;

    }

  public:

    // \brief The destructor of the map.

    //

    // The destructor of the map.

    virtual ~ArrayMap() {

      if (attached()) {

        clear();

        detach();

      }

    }

    // \brief Copy constructor

    //

    // Copy constructor.

    VectorMap(const VectorMap& _copy) : Parent() {

      if (_copy.attached()) {

        Parent::attach(*_copy.notifier());

        container = _copy.container;

      }

    }

    // \brief Assign operator.

    //

    // This operator assigns for each item in the map the

    // value mapped to the same item in the copied map.

    // The parameter map should be indiced with the same

    // itemset because this assign operator does not change

    // the container of the map.

    VectorMap& operator=(const VectorMap& cmap) {

      return operator=<VectorMap>(cmap);

    }

    // \brief Template assign operator.

    //

    // concecpt and could be indiced by the current item set of

    // the NodeMap. In this case the value for each item

    // is assigned by the value of the given ReadMap.

    template <typename CMap>

    VectorMap& operator=(const CMap& cmap) {

      checkConcept<concepts::ReadMap<Key, _Value>, CMap>();

      const typename Parent::Notifier* nf = Parent::notifier();

      Item it;

      for (nf->first(it); it != INVALID; nf->next(it)) {

        set(it, cmap[it]);

      }

      return *this;

    }

  public:

    // \brief The subcript operator.

    //

    // The subscript operator. The map can be subscripted by the

    // actual items of the graph.

    Reference operator[](const Key& key) {

      return container[Parent::notifier()->id(key)];

    }

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_CIRCULATION_H

#define LEMON_CIRCULATION_H

#include <lemon/tolerance.h>

#include <lemon/elevator.h>

///\ingroup max_flow

///\file

///\brief Push-relabel algorithm for finding a feasible circulation.

///

namespace lemon {

  /// \brief Default traits class of Circulation class.

  ///

  /// Default traits class of Circulation class.

  struct CirculationDefaultTraits {

    /// \brief The type of the digraph the algorithm runs on.

    /// \brief The type of the map that stores the circulation lower

    /// bound.

    ///

    /// The type of the map that stores the circulation lower bound.

    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.

    /// \brief The type of the map that stores the circulation upper

    /// bound.

    ///

    /// The type of the map that stores the circulation upper bound.

    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.

    /// \brief The type of the map that stores the lower bound for

    /// the supply of the nodes.

    ///

    /// The type of the map that stores the lower bound for the supply

    /// of the nodes. It must meet the \ref concepts::ReadMap "ReadMap"

    /// concept.

    /// \brief The type of the flow values.

    typedef typename DeltaMap::Value Value;

    /// \brief The type of the map that stores the flow values.

    ///

    /// The type of the map that stores the flow values.

    /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.

    typedef typename Digraph::template ArcMap<Value> FlowMap;

    /// \brief Instantiates a FlowMap.

    ///

    /// This function instantiates a \ref FlowMap.

    /// \param digraph The digraph, to which we would like to define

    /// the flow map.

    static FlowMap* createFlowMap(const Digraph& digraph) {

      return new FlowMap(digraph);

    }

    /// \brief The elevator type used by the algorithm.

    ///

    /// The elevator type used by the algorithm.

    ///

    /// \sa Elevator

     It is to find a feasible circulation when lower and upper bounds

     are given for the flow values on the arcs and lower bounds

     are given for the supply values of the nodes.

     The exact formulation of this problem is the following.

     Let \f$G=(V,A)\f$ be a digraph,

     \f$lower, upper: A\rightarrow\mathbf{R}^+_0\f$,

     \f$delta: V\rightarrow\mathbf{R}\f$. Find a feasible circulation

     \f$f: A\rightarrow\mathbf{R}^+_0\f$ so that

     \f[ \sum_{a\in\delta_{out}(v)} f(a) - \sum_{a\in\delta_{in}(v)} f(a)

     \geq delta(v) \quad \forall v\in V, \f]

     \f[ lower(a)\leq f(a) \leq upper(a) \quad \forall a\in A. \f]

     \note \f$delta(v)\f$ specifies a lower bound for the supply of node

     \f$v\f$. It can be either positive or negative, however note that

     \f$\sum_{v\in V}delta(v)\f$ should be zero or negative in order to

     have a feasible solution.

     \note A special case of this problem is when

     \f$\sum_{v\in V}delta(v) = 0\f$. Then the supply of each node \f$v\f$

     will be \e equal \e to \f$delta(v)\f$, if a circulation can be found.

     Thus a feasible solution for the

     \ref min_cost_flow "minimum cost flow" problem can be calculated

     in this way.

     for the supply of the nodes. The default map type is

  */

#ifdef DOXYGEN

#else

#endif

  class Circulation {

  public:

    ///The \ref CirculationDefaultTraits "traits class" of the algorithm.

    ///The type of the digraph the algorithm runs on.

    typedef typename Traits::Digraph Digraph;

    ///The type of the flow values.

    typedef typename Traits::Value Value;

    /// The type of the lower bound capacity map.

    typedef typename Traits::LCapMap LCapMap;

    /// The type of the upper bound capacity map.

    typedef typename Traits::UCapMap UCapMap;

    /// \brief The type of the map that stores the lower bound for

    /// the supply of the nodes.

    typedef typename Traits::DeltaMap DeltaMap;

    ///The type of the flow map.

    typedef typename Traits::FlowMap FlowMap;

    ///The type of the elevator.

    typedef typename Traits::Elevator Elevator;

    ///The type of the tolerance.

    typedef typename Traits::Tolerance Tolerance;

  private:

    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

      template<typename _GraphItem>

      struct Constraints {

        void constraints() {

          _GraphItem i1;

          _GraphItem i2 = i1;

          _GraphItem i3 = INVALID;

          i1 = i2 = i3;

          bool b;

          //          b = (ia == ib) && (ia != ib) && (ia < ib);

          b = (ia == ib) && (ia != ib);

          b = (ia == INVALID) && (ib != INVALID);

          b = (ia < ib);

        }

        const _GraphItem &ia;

        const _GraphItem &ib;

      };

    };

    /// \brief An empty base directed graph class.

    ///

    /// This class provides the minimal set of features needed for a

    /// conform to this base directed graph. It just provides types

    /// for nodes and arcs and functions to get the source and the

    /// target of the arcs.

    class BaseDigraphComponent {

    public:

      typedef BaseDigraphComponent Digraph;

      /// \brief Node class of the digraph.

      ///

      /// This class represents the Nodes of the digraph.

      ///

      typedef GraphItem<'n'> Node;

      /// \brief Arc class of the digraph.

      ///

      /// This class represents the Arcs of the digraph.

      ///

      typedef GraphItem<'e'> Arc;

      /// \brief Gives back the target node of an arc.

      ///

      /// Gives back the target node of an arc.

      ///

      struct Constraints {

        typedef typename _Digraph::Node Node;

        typedef typename _Digraph::Arc Arc;

        void constraints() {

          checkConcept<GraphItem<'n'>, Node>();

          checkConcept<GraphItem<'a'>, Arc>();

          {

            Node n;

            Arc e(INVALID);

            n = digraph.source(e);

            n = digraph.target(e);

            n = digraph.oppositeNode(n, e);

          }

        }

        const _Digraph& digraph;

      };

    };

    /// \brief An empty base undirected graph class.

    ///

    /// This class provides the minimal set of features needed for an

    /// undirected graph structure. All undirected graph concepts have

    /// nodes, arcs and edges and functions to get the

    /// source and the target of the arcs and edges,

    /// conversion from arcs to edges and function to get

    /// both direction of the edges.

    class BaseGraphComponent : public BaseDigraphComponent {

    public:

      typedef BaseDigraphComponent::Node Node;

      typedef BaseDigraphComponent::Arc Arc;

      /// \brief Undirected arc class of the graph.

      ///

      /// This class represents the edges of the graph.

      /// The undirected graphs can be used as a directed graph which

      /// for each arc contains the opposite arc too so the graph is

      /// bidirected. The edge represents two opposite

      /// directed arcs.

      class Edge : public GraphItem<'u'> {

      public:

        typedef GraphItem<'u'> Parent;

        /// \brief Default constructor.

        ///

        /// \warning The default constructor is not required to set

        /// the item to some well-defined value. So you should consider it

        /// as uninitialized.

        Edge() {}

          {

            Node n;

            Edge ue(INVALID);

            Arc e;

            n = graph.u(ue);

            n = graph.v(ue);

            e = graph.direct(ue, true);

            e = graph.direct(ue, n);

            e = graph.oppositeArc(e);

            ue = e;

            bool d = graph.direction(e);

            ignore_unused_variable_warning(d);

          }

        }

        const _Graph& graph;

      };

    };

    /// \brief An empty idable base digraph class.

    ///

    /// This class provides beside the core digraph features

    /// core id functions for the digraph structure.

    /// The id's are unique and immutable.

    template <typename _Base = BaseDigraphComponent>

    class IDableDigraphComponent : public _Base {

    public:

      typedef _Base Base;

      typedef typename Base::Node Node;

      typedef typename Base::Arc Arc;

      /// \brief Gives back an unique integer id for the Node.

      ///

      /// Gives back an unique integer id for the Node.

      ///

      int id(const Node&) const { return -1;}

      /// \brief Gives back the node by the unique id.

      ///

      /// Gives back the node by the unique id.

      /// If the digraph does not contain node with the given id

      /// then the result of the function is undetermined.

      Node nodeFromId(int) const { return INVALID;}

      /// \brief Gives back an unique integer id for the Arc.

      ///

          checkConcept<Base, _Digraph >();

          typename _Digraph::Node node;

          int nid = digraph.id(node);

          nid = digraph.id(node);

          node = digraph.nodeFromId(nid);

          typename _Digraph::Arc arc;

          int eid = digraph.id(arc);

          eid = digraph.id(arc);

          arc = digraph.arcFromId(eid);

          nid = digraph.maxNodeId();

          ignore_unused_variable_warning(nid);

          eid = digraph.maxArcId();

          ignore_unused_variable_warning(eid);

        }

        const _Digraph& digraph;

      };

    };

    /// \brief An empty idable base undirected graph class.

    ///

    /// This class provides beside the core undirected graph features

    /// core id functions for the undirected graph structure.  The

    /// concept.  The id's are unique and immutable.

    template <typename _Base = BaseGraphComponent>

    class IDableGraphComponent : public IDableDigraphComponent<_Base> {

    public:

      typedef _Base Base;

      typedef typename Base::Edge Edge;

      using IDableDigraphComponent<_Base>::id;

      /// \brief Gives back an unique integer id for the Edge.

      ///

      /// Gives back an unique integer id for the Edge.

      ///

      int id(const Edge&) const { return -1;}

      /// \brief Gives back the edge by the unique id.

      ///

      /// Gives back the edge by the unique id.  If the

      /// graph does not contain arc with the given id then the

      /// result of the function is undetermined.

      Edge edgeFromId(int) const { return INVALID;}

      /// \brief Gives back an integer greater or equal to the maximum

#include <lemon/core.h>

#include <lemon/error.h>

#include <lemon/maps.h>

#include <lemon/path.h>

namespace lemon {

  ///Default traits class of Dfs class.

  ///Default traits class of Dfs class.

  ///\tparam GR Digraph type.

  template<class GR>

  struct DfsDefaultTraits

  {

    ///The type of the digraph the algorithm runs on.

    typedef GR Digraph;

    ///\brief The type of the map that stores the predecessor

    ///arcs of the %DFS paths.

    ///

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

    ///arcs of the %DFS paths.

    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.

    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;

    ///\param g is the digraph, to which we would like to define the

    static PredMap *createPredMap(const Digraph &g)

    {

      return new PredMap(g);

    }

    ///The type of the map that indicates which nodes are processed.

    ///The type of the map that indicates which nodes are processed.

    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.

    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;

    ///\param g is the digraph, to which

#ifdef DOXYGEN

    static ProcessedMap *createProcessedMap(const Digraph &g)

#else

    static ProcessedMap *createProcessedMap(const Digraph &)

#endif

    {

      return new ProcessedMap();

    }

    ///The type of the map that indicates which nodes are reached.

    ///The type of the map that indicates which nodes are reached.

    ///It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.

    typedef typename Digraph::template NodeMap<bool> ReachedMap;

    ///\param g is the digraph, to which

    static ReachedMap *createReachedMap(const Digraph &g)

    {

      return new ReachedMap(g);

    }

    ///The type of the map that stores the distances of the nodes.

    ///The type of the map that stores the distances of the nodes.

    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.

    typedef typename Digraph::template NodeMap<int> DistMap;

    ///\param g is the digraph, to which we would like to define the

    static DistMap *createDistMap(const Digraph &g)

    {

      return new DistMap(g);

    }

  };

  ///%DFS algorithm class.

  ///\ingroup search

  ///This class provides an efficient implementation of the %DFS algorithm.

  ///

  ///There is also a \ref dfs() "function-type interface" for the DFS

  ///algorithm, which is convenient in the simplier cases and it can be

  ///used easier.

  ///

  ///\tparam GR The type of the digraph the algorithm runs on.

  ///The default type is \ref ListDigraph.

#ifdef DOXYGEN

  template <typename GR,

            typename TR>

#else

  template <typename GR=ListDigraph,

            typename TR=DfsDefaultTraits<GR> >

#endif

    }

  protected:

    Dfs() {}

  public:

    typedef Dfs Create;