RhodeCode

    Value operator[](const Key &k) const { return _m1[k]&&_m2[k]; }

  };

  /// Returns an \c AndMap class

  /// This function just returns an \c AndMap class.

  ///

  /// For example, if \c m1 and \c m2 are both maps with \c bool values,

  /// then <tt>andMap(m1,m2)[x]</tt> will be equal to

  /// <tt>m1[x]&&m2[x]</tt>.

  ///

  /// \relates AndMap

  template<typename M1, typename M2>

  inline AndMap<M1, M2> andMap(const M1 &m1, const M2 &m2) {

    return AndMap<M1, M2>(m1,m2);

  }

  /// Logical 'or' of two maps

  /// This \ref concepts::ReadMap "read-only map" returns the logical

  /// 'or' of the values of the two given maps.

  /// Its \c Key type is inherited from \c M1 and its \c Value type is

  /// \c bool. \c M2::Key must be convertible to \c M1::Key.

  ///

  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for

  /// \code

  ///   OrMap<M1,M2> om(m1,m2);

  /// \endcode

  /// <tt>om[x]</tt> will be equal to <tt>m1[x]||m2[x]</tt>.

  ///

  /// The simplest way of using this map is through the orMap()

  /// function.

  ///

  /// \sa AndMap

  /// \sa NotMap, NotWriteMap

  template<typename M1, typename M2>

  class OrMap : public MapBase<typename M1::Key, bool> {

    const M1 &_m1;

    const M2 &_m2;

  public:

    ///\e

    typedef typename M1::Key Key;

    ///\e

    typedef bool Value;

    /// Constructor

    OrMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}

    ///\e

    Value operator[](const Key &k) const { return _m1[k]||_m2[k]; }

  };

  /// Returns an \c OrMap class

  /// This function just returns an \c OrMap class.

  ///

  /// For example, if \c m1 and \c m2 are both maps with \c bool values,

  /// then <tt>orMap(m1,m2)[x]</tt> will be equal to

  /// <tt>m1[x]||m2[x]</tt>.

  ///

  /// \relates OrMap

  template<typename M1, typename M2>

  inline OrMap<M1, M2> orMap(const M1 &m1, const M2 &m2) {

    return OrMap<M1, M2>(m1,m2);

  }

  /// Logical 'not' of a map

  /// This \ref concepts::ReadMap "read-only map" returns the logical

  /// negation of the values of the given map.

  /// Its \c Key is inherited from \c M and its \c Value is \c bool.

  ///

  /// The simplest way of using this map is through the notMap()

  /// function.

  ///

  /// \sa NotWriteMap

  template <typename M>

  class NotMap : public MapBase<typename M::Key, bool> {

    const M &_m;

  public:

    ///\e

    typedef typename M::Key Key;

    ///\e

    typedef bool Value;

    /// Constructor

    NotMap(const M &m) : _m(m) {}

    ///\e

    Value operator[](const Key &k) const { return !_m[k]; }

  };

  /// Logical 'not' of a map (read-write version)

  /// This \ref concepts::ReadWriteMap "read-write map" returns the

  /// logical negation of the values of the given map.

  /// Its \c Key is inherited from \c M and its \c Value is \c bool.

  /// It makes also possible to write the map. When a value is set,

  /// the opposite value is set to the original map.

  ///

  /// The simplest way of using this map is through the notWriteMap()

  /// function.

  ///

  /// \sa NotMap

  template <typename M>

  class NotWriteMap : public MapBase<typename M::Key, bool> {

    M &_m;

  public:

    ///\e

    typedef typename M::Key Key;

    ///\e

    typedef bool Value;

    /// Constructor

    NotWriteMap(M &m) : _m(m) {}

    ///\e

    Value operator[](const Key &k) const { return !_m[k]; }

    ///\e

    void set(const Key &k, bool v) { _m.set(k, !v); }

  };

  /// Returns a \c NotMap class

  /// This function just returns a \c NotMap class.

  ///

  /// For example, if \c m is a map with \c bool values, then

  /// <tt>notMap(m)[x]</tt> will be equal to <tt>!m[x]</tt>.

  ///

  /// \relates NotMap

  template <typename M>

  inline NotMap<M> notMap(const M &m) {

    return NotMap<M>(m);

  }

  /// Returns a \c NotWriteMap class

  /// This function just returns a \c NotWriteMap class.

  ///

  /// For example, if \c m is a map with \c bool values, then

  /// <tt>notWriteMap(m)[x]</tt> will be equal to <tt>!m[x]</tt>.

  /// Moreover it makes also possible to write the map.

  ///

  /// \relates NotWriteMap

  template <typename M>

  inline NotWriteMap<M> notWriteMap(M &m) {

    return NotWriteMap<M>(m);

  }

  /// Combination of two maps using the \c == operator

  /// This \ref concepts::ReadMap "read-only map" assigns \c true to

  /// the keys for which the corresponding values of the two maps are

  /// equal.

  /// Its \c Key type is inherited from \c M1 and its \c Value type is

  /// \c bool. \c M2::Key must be convertible to \c M1::Key.

  ///

  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for

  /// \code

  ///   EqualMap<M1,M2> em(m1,m2);

  /// \endcode

  /// <tt>em[x]</tt> will be equal to <tt>m1[x]==m2[x]</tt>.

  ///

  /// The simplest way of using this map is through the equalMap()

  /// function.

  ///

  /// \sa LessMap

  template<typename M1, typename M2>

  class EqualMap : public MapBase<typename M1::Key, bool> {

    const M1 &_m1;

    const M2 &_m2;

  public:

    ///\e

    typedef typename M1::Key Key;

    ///\e

    typedef bool Value;

    /// Constructor

    EqualMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}

    ///\e

    Value operator[](const Key &k) const { return _m1[k]==_m2[k]; }

  };

  /// Returns an \c EqualMap class

  /// This function just returns an \c EqualMap class.

  ///

  /// For example, if \c m1 and \c m2 are maps with keys and values of

  /// the same type, then <tt>equalMap(m1,m2)[x]</tt> will be equal to

  /// <tt>m1[x]==m2[x]</tt>.

  ///

  /// \relates EqualMap

  template<typename M1, typename M2>

  inline EqualMap<M1, M2> equalMap(const M1 &m1, const M2 &m2) {

    return EqualMap<M1, M2>(m1,m2);

  }

  /// Combination of two maps using the \c < operator

  /// This \ref concepts::ReadMap "read-only map" assigns \c true to

  /// the keys for which the corresponding value of the first map is

  /// less then the value of the second map.

  /// Its \c Key type is inherited from \c M1 and its \c Value type is

  /// \c bool. \c M2::Key must be convertible to \c M1::Key.

  ///

  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for

  /// \code

  ///   LessMap<M1,M2> lm(m1,m2);

  /// \endcode

  /// <tt>lm[x]</tt> will be equal to <tt>m1[x]<m2[x]</tt>.

  ///

  /// The simplest way of using this map is through the lessMap()

  /// function.

  ///

  /// \sa EqualMap

  template<typename M1, typename M2>

  class LessMap : public MapBase<typename M1::Key, bool> {

    const M1 &_m1;

    const M2 &_m2;

  public:

    ///\e

    typedef typename M1::Key Key;

    ///\e

    typedef bool Value;

    /// Constructor

    LessMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}

    ///\e

    Value operator[](const Key &k) const { return _m1[k]<_m2[k]; }

  };

  /// Returns an \c LessMap class

  /// This function just returns an \c LessMap class.

  ///

  /// For example, if \c m1 and \c m2 are maps with keys and values of

  /// the same type, then <tt>lessMap(m1,m2)[x]</tt> will be equal to

  /// <tt>m1[x]<m2[x]</tt>.

  ///

  /// \relates LessMap

  template<typename M1, typename M2>

  inline LessMap<M1, M2> lessMap(const M1 &m1, const M2 &m2) {

    return LessMap<M1, M2>(m1,m2);

  }

  namespace _maps_bits {

    template <typename _Iterator, typename Enable = void>

    struct IteratorTraits {

      typedef typename std::iterator_traits<_Iterator>::value_type Value;

    };

    template <typename _Iterator>

    struct IteratorTraits<_Iterator,

      typename exists<typename _Iterator::container_type>::type>

    {

      typedef typename _Iterator::container_type::value_type Value;

    };

  }

  /// @}

  /// \addtogroup maps

  /// @{

  /// \brief Writable bool map for logging each \c true assigned element

  ///

  /// A \ref concepts::WriteMap "writable" bool map for logging

  /// each \c true assigned element, i.e it copies subsequently each

  /// keys set to \c true to the given iterator.

  /// The most important usage of it is storing certain nodes or arcs

  /// that were marked \c true by an algorithm.

  ///

  /// There are several algorithms that provide solutions through bool

  /// maps and most of them assign \c true at most once for each key.

  /// In these cases it is a natural request to store each \c true

  /// assigned elements (in order of the assignment), which can be

  /// easily done with LoggerBoolMap.

  ///

  /// The simplest way of using this map is through the loggerBoolMap()

  /// function.

  ///

  /// \tparam IT The type of the iterator.

  /// \tparam KEY The key type of the map. The default value set

  /// according to the iterator type should work in most cases.

  ///

  /// \note The container of the iterator must contain enough space

  /// for the elements or the iterator should be an inserter iterator.

#ifdef DOXYGEN

  template <typename IT, typename KEY>

#else

  template <typename IT,

            typename KEY = typename _maps_bits::IteratorTraits<IT>::Value>

#endif

  class LoggerBoolMap : public MapBase<KEY, bool> {

  public:

    ///\e

    typedef KEY Key;

    ///\e

    typedef bool Value;

    ///\e

    typedef IT Iterator;

    /// Constructor

    LoggerBoolMap(Iterator it)

      : _begin(it), _end(it) {}

    /// Gives back the given iterator set for the first key

    Iterator begin() const {

      return _begin;

    }

    /// Gives back the the 'after the last' iterator

    Iterator end() const {

      return _end;

    }

    /// The set function of the map

    void set(const Key& key, Value value) {

      if (value) {

        *_end++ = key;

      }

    }

  private:

    Iterator _begin;

    Iterator _end;

  };

  /// Returns a \c LoggerBoolMap class

  /// This function just returns a \c LoggerBoolMap class.

  ///

  /// The most important usage of it is storing certain nodes or arcs

  /// that were marked \c true by an algorithm.

  /// For example it makes easier to store the nodes in the processing

  /// order of Dfs algorithm, as the following examples show.

  /// \code

  ///   std::vector<Node> v;

  ///   dfs(g,s).processedMap(loggerBoolMap(std::back_inserter(v))).run();

  /// \endcode

  /// \code

  ///   std::vector<Node> v(countNodes(g));

  ///   dfs(g,s).processedMap(loggerBoolMap(v.begin())).run();

  /// \endcode

  ///

  /// \note The container of the iterator must contain enough space

  /// for the elements or the iterator should be an inserter iterator.

  ///

  /// \note LoggerBoolMap is just \ref concepts::WriteMap "writable", so

  /// it cannot be used when a readable map is needed, for example as

  /// \c ReachedMap for \c Bfs, \c Dfs and \c Dijkstra algorithms.

  ///

  /// \relates LoggerBoolMap

  template<typename Iterator>

  inline LoggerBoolMap<Iterator> loggerBoolMap(Iterator it) {

    return LoggerBoolMap<Iterator>(it);

  }

  /// @}

  /// \addtogroup graph_maps

  /// @{

  /// \brief Provides an immutable and unique id for each item in a graph.

  ///

  /// IdMap provides a unique and immutable id for each item of the

  /// same type (\c Node, \c Arc or \c Edge) in a graph. This id is 

  ///  - \b unique: different items get different ids,

  ///  - \b immutable: the id of an item does not change (even if you

  ///    delete other nodes).

  ///

  /// Using this map you get access (i.e. can read) the inner id values of

  /// the items stored in the graph, which is returned by the \c id()

  /// function of the graph. This map can be inverted with its member

  /// class \c InverseMap or with the \c operator() member.

  ///

  /// \tparam GR The graph type.

  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or

  /// \c GR::Edge).

  ///

  template <typename GR, typename K>

  class IdMap : public MapBase<K, int> {

  public:

    /// The graph type of IdMap.

    typedef GR Graph;

    /// The key type of IdMap (\c Node, \c Arc or \c Edge).

    typedef K Item;

    /// The key type of IdMap (\c Node, \c Arc or \c Edge).

    typedef K Key;

    /// The value type of IdMap.

    typedef int Value;

    /// \brief Constructor.

    ///

    /// Constructor of the map.

    explicit IdMap(const Graph& graph) : _graph(&graph) {}

    /// \brief Gives back the \e id of the item.

    ///

    /// Gives back the immutable and unique \e id of the item.

    int operator[](const Item& item) const { return _graph->id(item);}

    /// \brief Gives back the \e item by its id.

    ///

    /// Gives back the \e item by its id.

    Item operator()(int id) { return _graph->fromId(id, Item()); }

  private:

    const Graph* _graph;

  public:

    /// \brief This class represents the inverse of its owner (IdMap).

    ///

    /// This class represents the inverse of its owner (IdMap).

    /// \see inverse()

    class InverseMap {

    public:

      /// \brief Constructor.

      ///

      /// Constructor for creating an id-to-item map.

      explicit InverseMap(const Graph& graph) : _graph(&graph) {}

      /// \brief Constructor.

      ///

      /// Constructor for creating an id-to-item map.

      explicit InverseMap(const IdMap& map) : _graph(map._graph) {}

      /// \brief Gives back the given item from its id.

      ///

      /// Gives back the given item from its id.

      Item operator[](int id) const { return _graph->fromId(id, Item());}

    private:

      const Graph* _graph;

    };

    /// \brief Gives back the inverse of the map.

    ///

    /// Gives back the inverse of the IdMap.

    InverseMap inverse() const { return InverseMap(*_graph);}

  };

  /// This class provides simple invertable graph maps.

  /// It wraps an arbitrary \ref concepts::ReadWriteMap "ReadWriteMap"

  /// and if a key is set to a new value then store it

  /// in the inverse map.

  ///

  /// The values of the map can be accessed

  /// with stl compatible forward iterator.

  ///

  /// \tparam GR The graph type.

  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or

  /// \c GR::Edge).

  /// \tparam V The value type of the map.

  ///

  /// \see IterableValueMap

  template <typename GR, typename K, typename V>

    : protected ItemSetTraits<GR, K>::template Map<V>::Type {

  private:

    typedef typename ItemSetTraits<GR, K>::

      template Map<V>::Type Map;

    typedef std::map<V, K> Container;

    Container _inv_map;

  public:

    typedef GR Graph;

    typedef K Item;

    typedef K Key;

    typedef V Value;

    /// \brief Constructor.

    ///

    /// \brief Forward iterator for values.

    ///

    /// This iterator is an stl compatible forward

    /// iterator on the values of the map. The values can

    /// be accessed in the <tt>[beginValue, endValue)</tt> range.

    class ValueIterator

      : public std::iterator<std::forward_iterator_tag, Value> {

    private:

      ValueIterator(typename Container::const_iterator _it)

        : it(_it) {}

    public:

      ValueIterator() {}

      ValueIterator& operator++() { ++it; return *this; }

      ValueIterator operator++(int) {

        ValueIterator tmp(*this);

        operator++();

        return tmp;

      }

      const Value& operator*() const { return it->first; }

      const Value* operator->() const { return &(it->first); }

      bool operator==(ValueIterator jt) const { return it == jt.it; }

      bool operator!=(ValueIterator jt) const { return it != jt.it; }

    private:

      typename Container::const_iterator it;

    };

    /// \brief Returns an iterator to the first value.

    ///

    /// Returns an stl compatible iterator to the

    /// first value of the map. The values of the

    /// map can be accessed in the <tt>[beginValue, endValue)</tt>

    /// range.

    ValueIterator beginValue() const {

      return ValueIterator(_inv_map.begin());

    }

    /// \brief Returns an iterator after the last value.

    ///

    /// Returns an stl compatible iterator after the

    /// last value of the map. The values of the

    /// map can be accessed in the <tt>[beginValue, endValue)</tt>

    /// range.

    ValueIterator endValue() const {

      return ValueIterator(_inv_map.end());

    }

    /// \brief Sets the value associated with the given key.

    ///

    /// Sets the value associated with the given key.

    void set(const Key& key, const Value& val) {

      Value oldval = Map::operator[](key);

      typename Container::iterator it = _inv_map.find(oldval);

      if (it != _inv_map.end() && it->second == key) {

        _inv_map.erase(it);

      }

      _inv_map.insert(make_pair(val, key));

      Map::set(key, val);

    }

    /// \brief Returns the value associated with the given key.

    ///

    /// Returns the value associated with the given key.

    typename MapTraits<Map>::ConstReturnValue

    operator[](const Key& key) const {

      return Map::operator[](key);

    }

    /// \brief Gives back the item by its value.

    ///

    /// Gives back the item by its value.

    Key operator()(const Value& key) const {

      typename Container::const_iterator it = _inv_map.find(key);

      return it != _inv_map.end() ? it->second : INVALID;

    }

  protected:

    /// \brief Erase the key from the map and the inverse map.

    ///

    /// Erase the key from the map and the inverse map. It is called by the

    /// \c AlterationNotifier.

    virtual void erase(const Key& key) {

      Value val = Map::operator[](key);

      typename Container::iterator it = _inv_map.find(val);

      if (it != _inv_map.end() && it->second == key) {

        _inv_map.erase(it);

      }

      Map::erase(key);

    }

    /// \brief Erase more keys from the map and the inverse map.

    ///

    /// Erase more keys from the map and the inverse map. It is called by the

    /// \c AlterationNotifier.

    virtual void erase(const std::vector<Key>& keys) {

      for (int i = 0; i < int(keys.size()); ++i) {

        Value val = Map::operator[](keys[i]);

        typename Container::iterator it = _inv_map.find(val);

        if (it != _inv_map.end() && it->second == keys[i]) {

          _inv_map.erase(it);

        }

      }

      Map::erase(keys);

    }

    /// \brief Clear the keys from the map and the inverse map.

    ///

    /// Clear the keys from the map and the inverse map. It is called by the

    /// \c AlterationNotifier.

    virtual void clear() {

      _inv_map.clear();

      Map::clear();

    }

  public:

    /// \brief The inverse map type.

    ///

    /// The inverse of this map. The subscript operator of the map

    /// gives back the item that was last assigned to the value.

    class InverseMap {

    public:

      /// \brief Constructor

      ///

      /// Constructor of the InverseMap.

        : _inverted(inverted) {}

      /// The value type of the InverseMap.

      /// The key type of the InverseMap.

      /// \brief Subscript operator.

      ///

      /// Subscript operator. It gives back the item

      /// that was last assigned to the given value.

      Value operator[](const Key& key) const {

        return _inverted(key);

      }

    private:

    };

    /// \brief It gives back the read-only inverse map.

    ///

    /// It gives back the read-only inverse map.

    InverseMap inverse() const {

      return InverseMap(*this);

    }

  };

  ///

  /// \c Edge) in a graph. This id is

  ///  - \b unique: different items get different ids,

  ///  - \b continuous: the range of the ids is the set of integers

  ///    between 0 and \c n-1, where \c n is the number of the items of

  ///

  /// Thus this id is not (necessarily) the same as what can get using

  /// the \c id() function of the graph or \ref IdMap.

  /// This map can be inverted with its member class \c InverseMap,

  /// or with the \c operator() member.

  ///

  /// \tparam GR The graph type.

  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or

  /// \c GR::Edge).

  ///

  /// \see IdMap

  template <typename GR, typename K>

    : protected ItemSetTraits<GR, K>::template Map<int>::Type {

    typedef typename ItemSetTraits<GR, K>::template Map<int>::Type Map;

  public:

    typedef GR Graph;

    typedef K Item;

    typedef K Key;

    typedef int Value;

    /// \brief Constructor.

    ///

      Item it;

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

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

        Map::set(it, _inv_map.size());

        _inv_map.push_back(it);

      }

    }

  protected:

    /// \brief Adds a new key to the map.

    ///

    /// Add a new key to the map. It is called by the

    /// \c AlterationNotifier.

    virtual void add(const Item& item) {

      Map::add(item);

      Map::set(item, _inv_map.size());

      _inv_map.push_back(item);

    }

    /// \brief Add more new keys to the map.

    ///

    /// Add more new keys to the map. It is called by the

    /// \c AlterationNotifier.

    virtual void add(const std::vector<Item>& items) {

      Map::add(items);

      for (int i = 0; i < int(items.size()); ++i) {

        Map::set(items[i], _inv_map.size());

        _inv_map.push_back(items[i]);

      }

    }

    /// \brief Erase the key from the map.

    ///

    /// Erase the key from the map. It is called by the

    /// \c AlterationNotifier.

    virtual void erase(const Item& item) {

      Map::set(_inv_map.back(), Map::operator[](item));

      _inv_map[Map::operator[](item)] = _inv_map.back();

      _inv_map.pop_back();

      Map::erase(item);

    }

    /// \brief Erase more keys from the map.

    ///

    /// Erase more keys from the map. It is called by the

    /// \c AlterationNotifier.

    virtual void erase(const std::vector<Item>& items) {

      for (int i = 0; i < int(items.size()); ++i) {

        Map::set(_inv_map.back(), Map::operator[](items[i]));

        _inv_map[Map::operator[](items[i])] = _inv_map.back();

        _inv_map.pop_back();

      }

      Map::erase(items);

    }

    /// \brief Build the unique map.

    ///

    /// Build the unique map. It is called by the

    /// \c AlterationNotifier.

    virtual void build() {

      Map::build();

      Item it;

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

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

        Map::set(it, _inv_map.size());

        _inv_map.push_back(it);

      }

    }

    /// \brief Clear the keys from the map.

    ///

    /// Clear the keys from the map. It is called by the

    /// \c AlterationNotifier.

    virtual void clear() {

      _inv_map.clear();

      Map::clear();

    }

  public:

    /// \brief Returns the maximal value plus one.

    ///

    /// Returns the maximal value plus one in the map.

    unsigned int size() const {

      return _inv_map.size();

    }

    /// \brief Swaps the position of the two items in the map.

    ///

    /// Swaps the position of the two items in the map.

    void swap(const Item& p, const Item& q) {

      int pi = Map::operator[](p);

      int qi = Map::operator[](q);

      Map::set(p, qi);

      _inv_map[qi] = p;

      Map::set(q, pi);

      _inv_map[pi] = q;

    }

    ///

    int operator[](const Item& item) const {

      return Map::operator[](item);

    }

    ///

    Item operator()(int id) const {

      return _inv_map[id];

    }

  private:

    typedef std::vector<Item> Container;

    Container _inv_map;

  public:

    ///

    class InverseMap {

    public:

      /// \brief Constructor

      ///

      /// Constructor of the InverseMap.

        : _inverted(inverted) {}

      /// The value type of the InverseMap.

      /// The key type of the InverseMap.

      /// \brief Subscript operator.

      ///

      /// Subscript operator. It gives back the item

      /// that the descriptor currently belongs to.

      Value operator[](const Key& key) const {

        return _inverted(key);

      }

      /// \brief Size of the map.

      ///

      /// Returns the size of the map.

      unsigned int size() const {

        return _inverted.size();

      }

    private:

    };

    /// \brief Gives back the inverse of the map.

    ///

    /// Gives back the inverse of the map.

    const InverseMap inverse() const {

      return InverseMap(*this);

    }

  };

  /// \brief Map of the source nodes of arcs in a digraph.

  ///

  /// SourceMap provides access for the source node of each arc in a digraph,

  /// which is returned by the \c source() function of the digraph.

  /// \tparam GR The digraph type.

  /// \see TargetMap

  template <typename GR>

  class SourceMap {

  public:

    ///\e

    typedef typename GR::Arc Key;

    ///\e

    typedef typename GR::Node Value;

    /// \brief Constructor

    ///

    /// Constructor.

    /// \param digraph The digraph that the map belongs to.

    explicit SourceMap(const GR& digraph) : _graph(digraph) {}

    /// \brief Returns the source node of the given arc.

    ///

    /// Returns the source node of the given arc.

    Value operator[](const Key& arc) const {

      return _graph.source(arc);

    }

  private:

    const GR& _graph;

  };

  /// \brief Returns a \c SourceMap class.

  ///

  /// This function just returns an \c SourceMap class.

  /// \relates SourceMap

  template <typename GR>

  inline SourceMap<GR> sourceMap(const GR& graph) {

    return SourceMap<GR>(graph);

  }

  /// \brief Map of the target nodes of arcs in a digraph.

  ///

  /// TargetMap provides access for the target node of each arc in a digraph,

  /// which is returned by the \c target() function of the digraph.

  /// \tparam GR The digraph type.

  /// \see SourceMap

  template <typename GR>

  class TargetMap {

  public:

    ///\e

    typedef typename GR::Arc Key;

    ///\e

    typedef typename GR::Node Value;

    /// \brief Constructor

    ///

    /// Constructor.

    /// \param digraph The digraph that the map belongs to.

    explicit TargetMap(const GR& digraph) : _graph(digraph) {}

    /// \brief Returns the target node of the given arc.

    ///

    /// Returns the target node of the given arc.

    Value operator[](const Key& e) const {

      return _graph.target(e);

    }

  private:

    const GR& _graph;

  };

  /// \brief Returns a \c TargetMap class.

  ///

  /// This function just returns a \c TargetMap class.

  /// \relates TargetMap

  template <typename GR>

  inline TargetMap<GR> targetMap(const GR& graph) {

    return TargetMap<GR>(graph);

  }

  /// \brief Map of the "forward" directed arc view of edges in a graph.

  ///

  /// ForwardMap provides access for the "forward" directed arc view of

  /// each edge in a graph, which is returned by the \c direct() function

  /// of the graph with \c true parameter.

  /// \tparam GR The graph type.

  /// \see BackwardMap

  template <typename GR>

  class ForwardMap {

  public:

    typedef typename GR::Arc Value;

    typedef typename GR::Edge Key;

    /// \brief Constructor

    ///

    /// Constructor.

    /// \param graph The graph that the map belongs to.

    explicit ForwardMap(const GR& graph) : _graph(graph) {}

    /// \brief Returns the "forward" directed arc view of the given edge.

    ///

    /// Returns the "forward" directed arc view of the given edge.

    Value operator[](const Key& key) const {

      return _graph.direct(key, true);

    }

  private:

    const GR& _graph;

  };

  /// \brief Returns a \c ForwardMap class.

  ///

  /// This function just returns an \c ForwardMap class.

  /// \relates ForwardMap

  template <typename GR>

  inline ForwardMap<GR> forwardMap(const GR& graph) {

    return ForwardMap<GR>(graph);

  }

  /// \brief Map of the "backward" directed arc view of edges in a graph.

  ///

  /// BackwardMap provides access for the "backward" directed arc view of

  /// each edge in a graph, which is returned by the \c direct() function

  /// of the graph with \c false parameter.

  /// \tparam GR The graph type.

  /// \see ForwardMap

  template <typename GR>

  class BackwardMap {

  public:

    typedef typename GR::Arc Value;

    typedef typename GR::Edge Key;

    /// \brief Constructor

    ///

    /// Constructor.

    /// \param graph The graph that the map belongs to.

    explicit BackwardMap(const GR& graph) : _graph(graph) {}

    /// \brief Returns the "backward" directed arc view of the given edge.

    ///

    /// Returns the "backward" directed arc view of the given edge.

    Value operator[](const Key& key) const {

      return _graph.direct(key, false);

    }

  private:

    const GR& _graph;

  };

  /// \brief Returns a \c BackwardMap class

  /// This function just returns a \c BackwardMap class.

  /// \relates BackwardMap

  template <typename GR>

  inline BackwardMap<GR> backwardMap(const GR& graph) {

    return BackwardMap<GR>(graph);

  }

  /// \brief Map of the in-degrees of nodes in a digraph.

  ///

  /// This map returns the in-degree of a node. Once it is constructed,

  /// the degrees are stored in a standard \c NodeMap, so each query is done

  /// in constant time. On the other hand, the values are updated automatically

  /// whenever the digraph changes.

  ///

  /// \warning Besides \c addNode() and \c addArc(), a digraph structure 

  /// may provide alternative ways to modify the digraph.

  /// The correct behavior of InDegMap is not guarantied if these additional

  /// features are used. For example the functions

  /// \ref ListDigraph::changeSource() "changeSource()",

  /// \ref ListDigraph::changeTarget() "changeTarget()" and

  /// \ref ListDigraph::reverseArc() "reverseArc()"

  /// of \ref ListDigraph will \e not update the degree values correctly.

  ///

  /// \sa OutDegMap

  template <typename GR>

  class InDegMap

    : protected ItemSetTraits<GR, typename GR::Arc>

      ::ItemNotifier::ObserverBase {

  public:

    /// The digraph type

    typedef GR Digraph;

    /// The key type

    typedef typename Digraph::Node Key;

    /// The value type

    typedef int Value;

    typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>

    ::ItemNotifier::ObserverBase Parent;

  private:

    class AutoNodeMap

      : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {

    public:

      typedef typename ItemSetTraits<Digraph, Key>::

      template Map<int>::Type Parent;

      AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}