/* -*- C++ -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2003-2007

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * 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_ITERABLE_MAPS_H

 #define LEMON_ITERABLE_MAPS_H

 #include <lemon/bits/traits.h>

 #include <lemon/bits/invalid.h>

 #include <lemon/bits/default_map.h>

 #include <lemon/bits/map_extender.h>

 #include <vector>

 #include <map>

 #include <iterator>

 #include <limits>

 ///\ingroup maps

 ///\file

 ///\brief Maps that makes it possible to iterate through the keys having

 ///a certain value

 ///

 ///

 namespace lemon {

   ///\ingroup graph_maps

   ///

   /// \brief Dynamic iterable bool map.

   ///

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

   /// for each graph item(node, edge, etc.) a bool value. For both 

   /// the true and the false it is possible to iterate on the keys which

   /// mapped to the given value.

   /// 

   /// \param _Graph The graph type.

   /// \param _Item One of the graph's item type, the key of the map.

   template <typename _Graph, typename _Item>

   class IterableBoolMap : protected DefaultMap<_Graph, _Item, int> {

   private:

     typedef _Graph Graph;

     typedef typename ItemSetTraits<Graph, _Item>::ItemIt KeyIt;

     typedef DefaultMap<_Graph, _Item, int> Parent;

     std::vector<_Item> array;

     int sep;

     const Graph& graph;

   public:

     /// Indicates that the map if reference map.

     typedef True ReferenceMapTag;

     /// The key type

     typedef _Item 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 Refernce to the value of the map.

     ///

     /// This class is near to similar to the bool type. It can

     /// be converted to bool and it has 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), graph(_graph) {

       for (KeyIt it(graph); it != INVALID; ++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 true.

     ///

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

     int trueNum() const {

       return sep;

     } 

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

     ///

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

     int falseNum() const {

       return array.size() - sep;

     }

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

     ///

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

     /// like a graph item iterator in the map, it can be converted

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

     /// if the iterator leave 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 which mapped to true.

       /// \param _map The IterableIntMap

       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 key 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 false.

     ///

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

     /// like a graph item iterator in the map, it can be converted

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

     /// if the iterator leave 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 which mapped to false.

       /// \param _map The IterableIntMap

       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 key 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 in the map, it can be converted

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

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

     /// \c INVALID.

     class ItemIt : public Key {

     public:

       typedef Key Parent;

       /// \brief Creates an iterator.

       ///

       /// Creates an iterator. It iterates on the 

       /// keys which mapped to false.

       /// \param _map The IterableIntMap

       /// \param value Which elements should be iterated.

       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 key 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();

       for (KeyIt it(graph); it != INVALID; ++it) {

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

         array.push_back(it);

       }

       sep = 0;      

     }

     virtual void clear() {

       array.clear();

       sep = 0;

       Parent::clear();

     }

   };

   namespace _iterable_maps_bits {

     template <typename Item>

     struct IterableIntMapNode {

       IterableIntMapNode() : value(-1) {}

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

       Item prev, next;

       int value;

     };

   }

   ///\ingroup graph_maps

   ///

   /// \brief Dynamic iterable integer map.

   ///

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

   /// for each graph item(node, edge, etc.) an integer value. For each

   /// non negative value it is possible to iterate on the keys which

   /// mapped to the given value.

   /// 

   /// \param _Graph The graph type.

   /// \param _Item One of the graph's item type, the key of the map.

   template <typename _Graph, typename _Item>

   class IterableIntMap 

     : protected MapExtender<DefaultMap<_Graph, _Item, _iterable_maps_bits::

                                        IterableIntMapNode<_Item> > >{

   public:

     typedef MapExtender<DefaultMap<_Graph, _Item, _iterable_maps_bits::

                                    IterableIntMapNode<_Item> > > Parent;

     /// The key type

     typedef _Item Key;

     /// The value type

     typedef int Value;

     /// The graph type

     typedef _Graph Graph;

     /// \brief Constructor of the Map.

     ///

     /// Constructor of the Map. It set all values -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, _iterable_maps_bits::IterableIntMapNode<_Item>(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 if reference map.

     typedef True ReferenceMapTag;

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

     ///

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

     /// be converted to 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.

     unsigned 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 in the map, it can be converted

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

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

     /// \c INVALID.

     class ItemIt : public _Item {

     public:

       typedef _Item Parent;

       /// \brief Invalid constructor \& conversion.

       ///

       /// This constructor initializes the item 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 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<_Item> first;

   };

   namespace _iterable_maps_bits {

     template <typename Item, typename Value>

     struct IterableValueMapNode {

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

       Item prev, next;

       Value value;

     };

   }

   ///\ingroup graph_maps

   ///

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

   ///

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

   /// for each graph item(node, edge, etc.) a value. For each

   /// value it is possible to iterate on the keys which mapped to the 

   /// given value. The type 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 subscription operator.

   ///

   /// \see InvertableMap

   /// 

   /// \param _Graph The graph type.

   /// \param _Item One of the graph's item type, the key of the map.

   /// \param _Value Any comparable value type.

   template <typename _Graph, typename _Item, typename _Value>

   class IterableValueMap 

     : protected MapExtender<DefaultMap<_Graph, _Item, _iterable_maps_bits::

                                        IterableValueMapNode<_Item, _Value> > >{

   public:

     typedef MapExtender<DefaultMap<_Graph, _Item, _iterable_maps_bits::

                                    IterableValueMapNode<_Item, _Value> > >

     Parent;

     /// The key type

     typedef _Item Key;

     /// The value type

     typedef _Value Value;

     /// The graph type

     typedef _Graph 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, _iterable_maps_bits::

                IterableValueMapNode<_Item, _Value>(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;

         if (node.next != INVALID) {

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

         }

         first.insert(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 [beginValue, endValue) 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 [beginValue, endValue)

     /// 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 [beginValue, endValue)

     /// 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 in the map, it can be converted

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

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

     /// \c INVALID.

     class ItemIt : public _Item {

     public:

       typedef _Item Parent;

       /// \brief Invalid constructor \& conversion.

       ///

       /// This constructor initializes the item 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;

   };

   /// @}

 }

 #endif