#include <map>

   ///

   /// This type is not reference map, so it cannot be modified with

   /// the subscript operator.

     /// They are considered with multiplicity, so each value is

     /// traversed for each item it is assigned to.

   /// \brief Dynamic iterable \c bool map.

   ///

   /// This class provides a special graph map type which can store a

   /// \c bool value for graph items (\c Node, \c Arc or \c Edge).

   /// For both \c true and \c false values it is possible to iterate on

   /// the keys.

   ///

   /// This type is a reference map, so it can be modified with the

   /// subscript operator.

   ///

   /// \tparam GR The graph type.

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

   /// \c GR::Edge).

   ///

   /// \see IterableIntMap, IterableValueMap

   /// \see CrossRefMap

   template <typename GR, typename K>

   class IterableBoolMap

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

   private:

     typedef GR Graph;

     typedef typename ItemSetTraits<GR, K>::ItemIt KeyIt;

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

     std::vector<K> _array;

     int _sep;

   public:

     /// Indicates that the map is reference map.

     typedef True ReferenceMapTag;

     /// The key type

     typedef K Key;

     /// The value type

     typedef bool Value;

     /// The const reference type.

     typedef const Value& ConstReference;

   private:

     int position(const Key& key) const {

       return Parent::operator[](key);

     }

   public:

     /// \brief Reference to the value of the map.

     ///

     /// This class is similar to the \c bool type. It can be converted to

     /// \c bool and it provides the same operators.

     class Reference {

       friend class IterableBoolMap;

     private:

       Reference(IterableBoolMap& map, const Key& key)

         : _key(key), _map(map) {}

     public:

       Reference& operator=(const Reference& value) {

         _map.set(_key, static_cast<bool>(value));

          return *this;

       }

       operator bool() const {

         return static_cast<const IterableBoolMap&>(_map)[_key];

       }

       Reference& operator=(bool value) {

         _map.set(_key, value);

         return *this;

       }

       Reference& operator&=(bool value) {

         _map.set(_key, _map[_key] & value);

         return *this;

       }

       Reference& operator|=(bool value) {

         _map.set(_key, _map[_key] | value);

         return *this;

       }

       Reference& operator^=(bool value) {

         _map.set(_key, _map[_key] ^ value);

         return *this;

       }

     private:

       Key _key;

       IterableBoolMap& _map;

     };

     /// \brief Constructor of the map with a default value.

     ///

     /// Constructor of the map with a default value.

     explicit IterableBoolMap(const Graph& graph, bool def = false)

       : Parent(graph) {

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

       Key it;

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

         Parent::set(it, _array.size());

         _array.push_back(it);

       }

       _sep = (def ? _array.size() : 0);

     }

     /// \brief Const subscript operator of the map.

     ///

     /// Const subscript operator of the map.

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

       return position(key) < _sep;

     }

     /// \brief Subscript operator of the map.

     ///

     /// Subscript operator of the map.

     Reference operator[](const Key& key) {

       return Reference(*this, key);

     }

     /// \brief Set operation of the map.

     ///

     /// Set operation of the map.

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

       int pos = position(key);

       if (value) {

         if (pos < _sep) return;

         Key tmp = _array[_sep];

         _array[_sep] = key;

         Parent::set(key, _sep);

         _array[pos] = tmp;

         Parent::set(tmp, pos);

         ++_sep;

       } else {

         if (pos >= _sep) return;

         --_sep;

         Key tmp = _array[_sep];

         _array[_sep] = key;

         Parent::set(key, _sep);

         _array[pos] = tmp;

         Parent::set(tmp, pos);

       }

     }

     /// \brief Set all items.

     ///

     /// Set all items in the map.

     /// \note Constant time operation.

     void setAll(bool value) {

       _sep = (value ? _array.size() : 0);

     }

     /// \brief Returns the number of the keys mapped to \c true.

     ///

     /// Returns the number of the keys mapped to \c true.

     int trueNum() const {

       return _sep;

     }

     /// \brief Returns the number of the keys mapped to \c false.

     ///

     /// Returns the number of the keys mapped to \c false.

     int falseNum() const {

       return _array.size() - _sep;

     }

     /// \brief Iterator for the keys mapped to \c true.

     ///

     /// Iterator for the keys mapped to \c true. It works

     /// like a graph item iterator, it can be converted to

     /// the key type of the map, incremented with \c ++ operator, and

     /// if the iterator leaves the last valid key, it will be equal to

     /// \c INVALID.

     class TrueIt : public Key {

     public:

       typedef Key Parent;

       /// \brief Creates an iterator.

       ///

       /// Creates an iterator. It iterates on the

       /// keys mapped to \c true.

       /// \param map The IterableBoolMap.

       explicit TrueIt(const IterableBoolMap& map)

         : Parent(map._sep > 0 ? map._array[map._sep - 1] : INVALID),

           _map(&map) {}

       /// \brief Invalid constructor \& conversion.

       ///

       /// This constructor initializes the iterator to be invalid.

       /// \sa Invalid for more details.

       TrueIt(Invalid) : Parent(INVALID), _map(0) {}

       /// \brief Increment operator.

       ///

       /// Increment operator.

       TrueIt& operator++() {

         int pos = _map->position(*this);

         Parent::operator=(pos > 0 ? _map->_array[pos - 1] : INVALID);

         return *this;

       }

     private:

       const IterableBoolMap* _map;

     };

     /// \brief Iterator for the keys mapped to \c false.

     ///

     /// Iterator for the keys mapped to \c false. It works

     /// like a graph item iterator, it can be converted to

     /// the key type of the map, incremented with \c ++ operator, and

     /// if the iterator leaves the last valid key, it will be equal to

     /// \c INVALID.

     class FalseIt : public Key {

     public:

       typedef Key Parent;

       /// \brief Creates an iterator.

       ///

       /// Creates an iterator. It iterates on the

       /// keys mapped to \c false.

       /// \param map The IterableBoolMap.

       explicit FalseIt(const IterableBoolMap& map)

         : Parent(map._sep < int(map._array.size()) ?

                  map._array.back() : INVALID), _map(&map) {}

       /// \brief Invalid constructor \& conversion.

       ///

       /// This constructor initializes the iterator to be invalid.

       /// \sa Invalid for more details.

       FalseIt(Invalid) : Parent(INVALID), _map(0) {}

       /// \brief Increment operator.

       ///

       /// Increment operator.

       FalseIt& operator++() {

         int pos = _map->position(*this);

         Parent::operator=(pos > _map->_sep ? _map->_array[pos - 1] : INVALID);

         return *this;

       }

     private:

       const IterableBoolMap* _map;

     };

     /// \brief Iterator for the keys mapped to a given value.

     ///

     /// Iterator for the keys mapped to a given value. It works

     /// like a graph item iterator, it can be converted to

     /// the key type of the map, incremented with \c ++ operator, and

     /// if the iterator leaves the last valid key, it will be equal to

     /// \c INVALID.

     class ItemIt : public Key {

     public:

       typedef Key Parent;

       /// \brief Creates an iterator with a value.

       ///

       /// Creates an iterator with a value. It iterates on the

       /// keys mapped to the given value.

       /// \param map The IterableBoolMap.

       /// \param value The value.

       ItemIt(const IterableBoolMap& map, bool value)

         : Parent(value ? 

                  (map._sep > 0 ?

                   map._array[map._sep - 1] : INVALID) :

                  (map._sep < int(map._array.size()) ?

                   map._array.back() : INVALID)), _map(&map) {}

       /// \brief Invalid constructor \& conversion.

       ///

       /// This constructor initializes the iterator to be invalid.

       /// \sa Invalid for more details.

       ItemIt(Invalid) : Parent(INVALID), _map(0) {}

       /// \brief Increment operator.

       ///

       /// Increment operator.

       ItemIt& operator++() {

         int pos = _map->position(*this);

         int _sep = pos >= _map->_sep ? _map->_sep : 0;

         Parent::operator=(pos > _sep ? _map->_array[pos - 1] : INVALID);

         return *this;

       }

     private:

       const IterableBoolMap* _map;

     };

   protected:

     virtual void add(const Key& key) {

       Parent::add(key);

       Parent::set(key, _array.size());

       _array.push_back(key);

     }

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

       Parent::add(keys);

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

         Parent::set(keys[i], _array.size());

         _array.push_back(keys[i]);

       }

     }

     virtual void erase(const Key& key) {

       int pos = position(key);

       if (pos < _sep) {

         --_sep;

         Parent::set(_array[_sep], pos);

         _array[pos] = _array[_sep];

         Parent::set(_array.back(), _sep);

         _array[_sep] = _array.back();

         _array.pop_back();

       } else {

         Parent::set(_array.back(), pos);

         _array[pos] = _array.back();

         _array.pop_back();

       }

       Parent::erase(key);

     }

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

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

         int pos = position(keys[i]);

         if (pos < _sep) {

           --_sep;

           Parent::set(_array[_sep], pos);

           _array[pos] = _array[_sep];

           Parent::set(_array.back(), _sep);

           _array[_sep] = _array.back();

           _array.pop_back();

         } else {

           Parent::set(_array.back(), pos);

           _array[pos] = _array.back();

           _array.pop_back();

         }

       }

       Parent::erase(keys);

     }

     virtual void build() {

       Parent::build();

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

       Key it;

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

         Parent::set(it, _array.size());

         _array.push_back(it);

       }

       _sep = 0;

     }

     virtual void clear() {

       _array.clear();

       _sep = 0;

       Parent::clear();

     }

   };

   namespace _maps_bits {

     template <typename Item>

     struct IterableIntMapNode {

       IterableIntMapNode() : value(-1) {}

       IterableIntMapNode(int _value) : value(_value) {}

       Item prev, next;

       int value;

     };

   }

   /// \brief Dynamic iterable integer map.

   ///

   /// This class provides a special graph map type which can store an

   /// integer value for graph items (\c Node, \c Arc or \c Edge).

   /// For each non-negative value it is possible to iterate on the keys

   /// mapped to the value.

   ///

   /// This type is a reference map, so it can be modified with the

   /// subscript operator.

   ///

   /// \note The size of the data structure depends on the largest

   /// value in the map.

   ///

   /// \tparam GR The graph type.

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

   /// \c GR::Edge).

   ///

   /// \see IterableBoolMap, IterableValueMap

   /// \see CrossRefMap

   template <typename GR, typename K>

   class IterableIntMap

     : protected ItemSetTraits<GR, K>::

         template Map<_maps_bits::IterableIntMapNode<K> >::Type {

   public:

     typedef typename ItemSetTraits<GR, K>::

       template Map<_maps_bits::IterableIntMapNode<K> >::Type Parent;

     /// The key type

     typedef K Key;

     /// The value type

     typedef int Value;

     /// The graph type

     typedef GR Graph;

     /// \brief Constructor of the map.

     ///

     /// Constructor of the map. It sets all values to -1.

     explicit IterableIntMap(const Graph& graph)

       : Parent(graph) {}

     /// \brief Constructor of the map with a given value.

     ///

     /// Constructor of the map with a given value.

     explicit IterableIntMap(const Graph& graph, int value)

       : Parent(graph, _maps_bits::IterableIntMapNode<K>(value)) {

       if (value >= 0) {

         for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {

           lace(it);

         }

       }

     }

   private:

     void unlace(const Key& key) {

       typename Parent::Value& node = Parent::operator[](key);

       if (node.value < 0) return;

       if (node.prev != INVALID) {

         Parent::operator[](node.prev).next = node.next;

       } else {

         _first[node.value] = node.next;

       }

       if (node.next != INVALID) {

         Parent::operator[](node.next).prev = node.prev;

       }

       while (!_first.empty() && _first.back() == INVALID) {

         _first.pop_back();

       }

     }

     void lace(const Key& key) {

       typename Parent::Value& node = Parent::operator[](key);

       if (node.value < 0) return;

       if (node.value >= int(_first.size())) {

         _first.resize(node.value + 1, INVALID);

       }

       node.prev = INVALID;

       node.next = _first[node.value];

       if (node.next != INVALID) {

         Parent::operator[](node.next).prev = key;

       }

       _first[node.value] = key;

     }

   public:

     /// Indicates that the map is reference map.

     typedef True ReferenceMapTag;

     /// \brief Reference to the value of the map.

     ///

     /// This class is similar to the \c int type. It can

     /// be converted to \c int and it has the same operators.

     class Reference {

       friend class IterableIntMap;

     private:

       Reference(IterableIntMap& map, const Key& key)

         : _key(key), _map(map) {}

     public:

       Reference& operator=(const Reference& value) {

         _map.set(_key, static_cast<const int&>(value));

          return *this;

       }

       operator const int&() const {

         return static_cast<const IterableIntMap&>(_map)[_key];

       }

       Reference& operator=(int value) {

         _map.set(_key, value);

         return *this;

       }

       Reference& operator++() {

         _map.set(_key, _map[_key] + 1);

         return *this;

       }

       int operator++(int) {

         int value = _map[_key];

         _map.set(_key, value + 1);

         return value;

       }

       Reference& operator--() {

         _map.set(_key, _map[_key] - 1);

         return *this;

       }

       int operator--(int) {

         int value = _map[_key];

         _map.set(_key, value - 1);

         return value;

       }

       Reference& operator+=(int value) {

         _map.set(_key, _map[_key] + value);

         return *this;

       }

       Reference& operator-=(int value) {

         _map.set(_key, _map[_key] - value);

         return *this;

       }

       Reference& operator*=(int value) {

         _map.set(_key, _map[_key] * value);

         return *this;

       }

       Reference& operator/=(int value) {

         _map.set(_key, _map[_key] / value);

         return *this;

       }

       Reference& operator%=(int value) {

         _map.set(_key, _map[_key] % value);

         return *this;

       }

       Reference& operator&=(int value) {

         _map.set(_key, _map[_key] & value);

         return *this;

       }

       Reference& operator|=(int value) {

         _map.set(_key, _map[_key] | value);

         return *this;

       }

       Reference& operator^=(int value) {

         _map.set(_key, _map[_key] ^ value);

         return *this;

       }

       Reference& operator<<=(int value) {

         _map.set(_key, _map[_key] << value);

         return *this;

       }

       Reference& operator>>=(int value) {

         _map.set(_key, _map[_key] >> value);

         return *this;

       }

     private:

       Key _key;

       IterableIntMap& _map;

     };

     /// The const reference type.

     typedef const Value& ConstReference;

     /// \brief Gives back the maximal value plus one.

     ///

     /// Gives back the maximal value plus one.

     int size() const {

       return _first.size();

     }

     /// \brief Set operation of the map.

     ///

     /// Set operation of the map.

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

       unlace(key);

       Parent::operator[](key).value = value;

       lace(key);

     }

     /// \brief Const subscript operator of the map.

     ///

     /// Const subscript operator of the map.

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

       return Parent::operator[](key).value;

     }

     /// \brief Subscript operator of the map.

     ///

     /// Subscript operator of the map.

     Reference operator[](const Key& key) {

       return Reference(*this, key);

     }

     /// \brief Iterator for the keys with the same value.

     ///

     /// Iterator for the keys with the same value. It works

     /// like a graph item iterator, it can be converted to

     /// the item type of the map, incremented with \c ++ operator, and

     /// if the iterator leaves the last valid item, it will be equal to

     /// \c INVALID.

     class ItemIt : public Key {

     public:

       typedef Key Parent;

       /// \brief Invalid constructor \& conversion.

       ///

       /// This constructor initializes the iterator to be invalid.

       /// \sa Invalid for more details.

       ItemIt(Invalid) : Parent(INVALID), _map(0) {}

       /// \brief Creates an iterator with a value.

       ///

       /// Creates an iterator with a value. It iterates on the

       /// keys mapped to the given value.

       /// \param map The IterableIntMap.

       /// \param value The value.

       ItemIt(const IterableIntMap& map, int value) : _map(&map) {

         if (value < 0 || value >= int(_map->_first.size())) {

           Parent::operator=(INVALID);

         } else {

           Parent::operator=(_map->_first[value]);

         }

       }

       /// \brief Increment operator.

       ///

       /// Increment operator.

       ItemIt& operator++() {

         Parent::operator=(_map->IterableIntMap::Parent::

                           operator[](static_cast<Parent&>(*this)).next);

         return *this;

       }

     private:

       const IterableIntMap* _map;

     };

   protected:

     virtual void erase(const Key& key) {

       unlace(key);

       Parent::erase(key);

     }

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

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

         unlace(keys[i]);

       }

       Parent::erase(keys);

     }

     virtual void clear() {

       _first.clear();

       Parent::clear();

     }

   private:

     std::vector<Key> _first;

   };

   namespace _maps_bits {

     template <typename Item, typename Value>

     struct IterableValueMapNode {

       IterableValueMapNode(Value _value = Value()) : value(_value) {}

       Item prev, next;

       Value value;

     };

   }

   /// \brief Dynamic iterable map for comparable values.

   ///

   /// This class provides a special graph map type which can store an

   /// comparable value for graph items (\c Node, \c Arc or \c Edge).

   /// For each value it is possible to iterate on the keys mapped to

   /// the value.

   ///

   /// The map stores for each value a linked list with

   /// the items which mapped to the value, and the values are stored

   /// in balanced binary tree. The values of the map can be accessed

   /// with stl compatible forward iterator.

   ///

   /// This type is not reference map, so it cannot be modified with

   /// the subscript operator.

   ///

   /// \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. It can be any comparable

   /// value type.

   ///

   /// \see IterableBoolMap, IterableIntMap

   /// \see CrossRefMap

   template <typename GR, typename K, typename V>

   class IterableValueMap

     : protected ItemSetTraits<GR, K>::

         template Map<_maps_bits::IterableValueMapNode<K, V> >::Type {

   public:

     typedef typename ItemSetTraits<GR, K>::

       template Map<_maps_bits::IterableValueMapNode<K, V> >::Type Parent;

     /// The key type

     typedef K Key;

     /// The value type

     typedef V Value;

     /// The graph type

     typedef GR Graph;

   public:

     /// \brief Constructor of the map with a given value.

     ///

     /// Constructor of the map with a given value.

     explicit IterableValueMap(const Graph& graph,

                               const Value& value = Value())

       : Parent(graph, _maps_bits::IterableValueMapNode<K, V>(value)) {

       for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {

         lace(it);

       }

     }

   protected:

     void unlace(const Key& key) {

       typename Parent::Value& node = Parent::operator[](key);

       if (node.prev != INVALID) {

         Parent::operator[](node.prev).next = node.next;

       } else {

         if (node.next != INVALID) {

           _first[node.value] = node.next;

         } else {

           _first.erase(node.value);

         }

       }

       if (node.next != INVALID) {

         Parent::operator[](node.next).prev = node.prev;

       }

     }

     void lace(const Key& key) {

       typename Parent::Value& node = Parent::operator[](key);

       typename std::map<Value, Key>::iterator it = _first.find(node.value);

       if (it == _first.end()) {

         node.prev = node.next = INVALID;

         _first.insert(std::make_pair(node.value, key));

       } else {

         node.prev = INVALID;

         node.next = it->second;

         if (node.next != INVALID) {

           Parent::operator[](node.next).prev = key;

         }

         it->second = key;

       }

     }

   public:

     /// \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> {

       friend class IterableValueMap;

     private:

       ValueIterator(typename std::map<Value, Key>::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 std::map<Value, Key>::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(_first.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(_first.end());

     }

     /// \brief Set operation of the map.

     ///

     /// Set operation of the map.

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

       unlace(key);

       Parent::operator[](key).value = value;

       lace(key);

     }

     /// \brief Const subscript operator of the map.

     ///

     /// Const subscript operator of the map.

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

       return Parent::operator[](key).value;

     }

     /// \brief Iterator for the keys with the same value.

     ///

     /// Iterator for the keys with the same value. It works

     /// like a graph item iterator, it can be converted to

     /// the item type of the map, incremented with \c ++ operator, and

     /// if the iterator leaves the last valid item, it will be equal to

     /// \c INVALID.

     class ItemIt : public Key {

     public:

       typedef Key Parent;

       /// \brief Invalid constructor \& conversion.

       ///

       /// This constructor initializes the iterator to be invalid.

       /// \sa Invalid for more details.

       ItemIt(Invalid) : Parent(INVALID), _map(0) {}

       /// \brief Creates an iterator with a value.

       ///

       /// Creates an iterator with a value. It iterates on the

       /// keys which have the given value.

       /// \param map The IterableValueMap

       /// \param value The value

       ItemIt(const IterableValueMap& map, const Value& value) : _map(&map) {

         typename std::map<Value, Key>::const_iterator it =

           map._first.find(value);

         if (it == map._first.end()) {

           Parent::operator=(INVALID);

         } else {

           Parent::operator=(it->second);

         }

       }

       /// \brief Increment operator.

       ///

       /// Increment Operator.

       ItemIt& operator++() {

         Parent::operator=(_map->IterableValueMap::Parent::

                           operator[](static_cast<Parent&>(*this)).next);

         return *this;

       }

     private:

       const IterableValueMap* _map;

     };

   protected:

     virtual void add(const Key& key) {

       Parent::add(key);

       unlace(key);

     }

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

       Parent::add(keys);

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

         lace(keys[i]);

       }

     }

     virtual void erase(const Key& key) {

       unlace(key);

       Parent::erase(key);

     }

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

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

         unlace(keys[i]);

       }

       Parent::erase(keys);

     }

     virtual void build() {

       Parent::build();

       for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {

         lace(it);

       }

     }

     virtual void clear() {

       _first.clear();

       Parent::clear();

     }

   private:

     std::map<Value, Key> _first;

   };