/* -*- 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_MAPS_H

 #define LEMON_MAPS_H

 #include <iterator>

 #include <functional>

 #include <vector>

 #include <lemon/bits/utility.h>

 // #include <lemon/bits/traits.h>

 ///\file

 ///\ingroup maps

 ///\brief Miscellaneous property maps

 ///

 #include <map>

 namespace lemon {

   /// \addtogroup maps

   /// @{

   /// Base class of maps.

   /// Base class of maps.

   /// It provides the necessary <tt>typedef</tt>s required by the map concept.

   template<typename K, typename T>

   class MapBase {

   public:

     ///\e

     typedef K Key;

     ///\e

     typedef T Value;

   };

   /// Null map. (a.k.a. DoNothingMap)

   /// If you have to provide a map only for its type definitions,

   /// or if you have to provide a writable map, but

   /// data written to it will sent to <tt>/dev/null</tt>...

   template<typename K, typename T>

   class NullMap : public MapBase<K, T> {

   public:

     typedef MapBase<K, T> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     /// Gives back a default constructed element.

     T operator[](const K&) const { return T(); }

     /// Absorbs the value.

     void set(const K&, const T&) {}

   };

   template <typename K, typename V> 

   NullMap<K, V> nullMap() {

     return NullMap<K, V>();

   }

   /// Constant map.

   /// This is a readable map which assigns a specified value to each key.

   /// In other aspects it is equivalent to the \c NullMap.

   template<typename K, typename T>

   class ConstMap : public MapBase<K, T> {

   private:

     T v;

   public:

     typedef MapBase<K, T> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     /// Default constructor

     /// The value of the map will be uninitialized. 

     /// (More exactly it will be default constructed.)

     ConstMap() {}

     ///\e

     /// \param _v The initial value of the map.

     ///

     ConstMap(const T &_v) : v(_v) {}

     ///\e

     T operator[](const K&) const { return v; }

     ///\e

     void setAll(const T &t) {

       v = t;

     }    

     template<typename T1>

     struct rebind {

       typedef ConstMap<K, T1> other;

     };

     template<typename T1>

     ConstMap(const ConstMap<K, T1> &, const T &_v) : v(_v) {}

   };

   ///Returns a \c ConstMap class

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

   ///\relates ConstMap

   template<typename K, typename V> 

   inline ConstMap<K, V> constMap(const V &v) {

     return ConstMap<K, V>(v);

   }

   template<typename T, T v>

   struct Const { };

   /// Constant map with inlined constant value.

   /// This is a readable map which assigns a specified value to each key.

   /// In other aspects it is equivalent to the \c NullMap.

   template<typename K, typename V, V v>

   class ConstMap<K, Const<V, v> > : public MapBase<K, V> {

   public:

     typedef MapBase<K, V> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ConstMap() { }

     ///\e

     V operator[](const K&) const { return v; }

     ///\e

     void set(const K&, const V&) { }

   };

   ///Returns a \c ConstMap class

   ///This function just returns a \c ConstMap class with inlined value.

   ///\relates ConstMap

   template<typename K, typename V, V v> 

   inline ConstMap<K, Const<V, v> > constMap() {

     return ConstMap<K, Const<V, v> >();

   }

   ///Map based on std::map

   ///This is essentially a wrapper for \c std::map. With addition that

   ///you can specify a default value different from \c Value() .

   template <typename K, typename T, typename Compare = std::less<K> >

   class StdMap {

     template <typename K1, typename T1, typename C1>

     friend class StdMap;

   public:

     typedef True ReferenceMapTag;

     ///\e

     typedef K Key;

     ///\e

     typedef T Value;

     ///\e

     typedef T& Reference;

     ///\e

     typedef const T& ConstReference;

   private:

     typedef std::map<K, T, Compare> Map;

     Value _value;

     Map _map;

   public:

     /// Constructor with specified default value

     StdMap(const T& value = T()) : _value(value) {}

     /// \brief Constructs the map from an appropriate std::map, and explicitly

     /// specifies a default value.

     template <typename T1, typename Comp1>

     StdMap(const std::map<Key, T1, Comp1> &map, const T& value = T()) 

       : _map(map.begin(), map.end()), _value(value) {}

     /// \brief Constructs a map from an other StdMap.

     template<typename T1, typename Comp1>

     StdMap(const StdMap<Key, T1, Comp1> &c) 

       : _map(c._map.begin(), c._map.end()), _value(c._value) {}

   private:

     StdMap& operator=(const StdMap&);

   public:

     ///\e

     Reference operator[](const Key &k) {

       typename Map::iterator it = _map.lower_bound(k);

       if (it != _map.end() && !_map.key_comp()(k, it->first))

 	return it->second;

       else

 	return _map.insert(it, std::make_pair(k, _value))->second;

     }

     /// \e 

     ConstReference operator[](const Key &k) const {

       typename Map::const_iterator it = _map.find(k);

       if (it != _map.end())

 	return it->second;

       else

 	return _value;

     }

     /// \e 

     void set(const Key &k, const T &t) {

       typename Map::iterator it = _map.lower_bound(k);

       if (it != _map.end() && !_map.key_comp()(k, it->first))

 	it->second = t;

       else

 	_map.insert(it, std::make_pair(k, t));

     }

     /// \e

     void setAll(const T &t) {

       _value = t;

       _map.clear();

     }    

     template <typename T1, typename C1 = std::less<T1> >

     struct rebind {

       typedef StdMap<Key, T1, C1> other;

     };

   };

   /// \brief Map for storing values for the range \c [0..size-1] range keys

   ///

   /// The current map has the \c [0..size-1] keyset and the values

   /// are stored in a \c std::vector<T>  container. It can be used with

   /// some data structures, for example \c UnionFind, \c BinHeap, when 

   /// the used items are small integer numbers.

   template <typename T>

   class IntegerMap {

     template <typename T1>

     friend class IntegerMap;

   public:

     typedef True ReferenceMapTag;

     ///\e

     typedef int Key;

     ///\e

     typedef T Value;

     ///\e

     typedef T& Reference;

     ///\e

     typedef const T& ConstReference;

   private:

     typedef std::vector<T> Vector;

     Vector _vector;

   public:

     /// Constructor with specified default value

     IntegerMap(int size = 0, const T& value = T()) : _vector(size, value) {}

     /// \brief Constructs the map from an appropriate std::vector.

     template <typename T1>

     IntegerMap(const std::vector<T1>& vector) 

       : _vector(vector.begin(), vector.end()) {}

     /// \brief Constructs a map from an other IntegerMap.

     template <typename T1>

     IntegerMap(const IntegerMap<T1> &c) 

       : _vector(c._vector.begin(), c._vector.end()) {}

     /// \brief Resize the container

     void resize(int size, const T& value = T()) {

       _vector.resize(size, value);

     }

   private:

     IntegerMap& operator=(const IntegerMap&);

   public:

     ///\e

     Reference operator[](Key k) {

       return _vector[k];

     }

     /// \e 

     ConstReference operator[](Key k) const {

       return _vector[k];

     }

     /// \e 

     void set(const Key &k, const T& t) {

       _vector[k] = t;

     }

   };

   /// @}

   /// \addtogroup map_adaptors

   /// @{

   /// \brief Identity mapping.

   ///

   /// This mapping gives back the given key as value without any

   /// modification. 

   template <typename T>

   class IdentityMap : public MapBase<T, T> {

   public:

     typedef MapBase<T, T> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     /// \e

     const T& operator[](const T& t) const {

       return t;

     }

   };

   ///Returns an \c IdentityMap class

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

   ///\relates IdentityMap

   template<typename T>

   inline IdentityMap<T> identityMap() {

     return IdentityMap<T>();

   }

   ///Convert the \c Value of a map to another type.

   ///This \c concepts::ReadMap "read only map"

   ///converts the \c Value of a maps to type \c T.

   ///Its \c Key is inherited from \c M.

   template <typename M, typename T> 

   class ConvertMap : public MapBase<typename M::Key, T> {

     const M& m;

   public:

     typedef MapBase<typename M::Key, T> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

     ///Constructor

     ///\param _m is the underlying map

     ConvertMap(const M &_m) : m(_m) {};

     /// \brief The subscript operator.

     ///

     /// The subscript operator.

     /// \param k The key

     /// \return The target of the arc 

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

   };

   ///Returns an \c ConvertMap class

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

   ///\relates ConvertMap

   template<typename T, typename M>

   inline ConvertMap<M, T> convertMap(const M &m) {

     return ConvertMap<M, T>(m);

   }

   ///Simple wrapping of the map

   ///This \c concepts::ReadMap "read only map" returns the simple

   ///wrapping of the given map. Sometimes the reference maps cannot be

   ///combined with simple read maps. This map adaptor wraps the given

   ///map to simple read map.

   template<typename M> 

   class SimpleMap : public MapBase<typename M::Key, typename M::Value> {

     const M& m;

   public:

     typedef MapBase<typename M::Key, typename M::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

     SimpleMap(const M &_m) : m(_m) {};

     ///\e

     Value operator[](Key k) const {return m[k];}

   };

   ///Simple writeable wrapping of the map

   ///This \c concepts::ReadMap "read only map" returns the simple

   ///wrapping of the given map. Sometimes the reference maps cannot be

   ///combined with simple read-write maps. This map adaptor wraps the

   ///given map to simple read-write map.

   template<typename M> 

   class SimpleWriteMap : public MapBase<typename M::Key, typename M::Value> {

     M& m;

   public:

     typedef MapBase<typename M::Key, typename M::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

     SimpleWriteMap(M &_m) : m(_m) {};

     ///\e

     Value operator[](Key k) const {return m[k];}

     ///\e

     void set(Key k, const Value& c) { m.set(k, c); }

   };

   ///Sum of two maps

   ///This \c concepts::ReadMap "read only map" returns the sum of the two

   ///given maps. Its \c Key and \c Value will be inherited from \c M1.

   ///The \c Key and \c Value of M2 must be convertible to those of \c M1.

   template<typename M1, typename M2> 

   class AddMap : public MapBase<typename M1::Key, typename M1::Value> {

     const M1& m1;

     const M2& m2;

   public:

     typedef MapBase<typename M1::Key, typename M1::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

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

     ///\e

     Value operator[](Key k) const {return m1[k]+m2[k];}

   };

   ///Returns an \c AddMap class

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

   ///\todo How to call these type of functions?

   ///

   ///\relates AddMap

   template<typename M1, typename M2> 

   inline AddMap<M1, M2> addMap(const M1 &m1,const M2 &m2) {

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

   }

   ///Shift a map with a constant.

   ///This \c concepts::ReadMap "read only map" returns the sum of the

   ///given map and a constant value.

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

   ///

   ///Actually,

   ///\code

   ///  ShiftMap<X> sh(x,v);

   ///\endcode

   ///is equivalent with

   ///\code

   ///  ConstMap<X::Key, X::Value> c_tmp(v);

   ///  AddMap<X, ConstMap<X::Key, X::Value> > sh(x,v);

   ///\endcode

   template<typename M, typename C = typename M::Value> 

   class ShiftMap : public MapBase<typename M::Key, typename M::Value> {

     const M& m;

     C v;

   public:

     typedef MapBase<typename M::Key, typename M::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

     ///Constructor

     ///\param _m is the undelying map

     ///\param _v is the shift value

     ShiftMap(const M &_m, const C &_v ) : m(_m), v(_v) {};

     ///\e

     Value operator[](Key k) const {return m[k] + v;}

   };

   ///Shift a map with a constant.

   ///This \c concepts::ReadWriteMap "read-write map" returns the sum of the

   ///given map and a constant value. It makes also possible to write the map.

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

   ///

   ///Actually,

   ///\code

   ///  ShiftMap<X> sh(x,v);

   ///\endcode

   ///is equivalent with

   ///\code

   ///  ConstMap<X::Key, X::Value> c_tmp(v);

   ///  AddMap<X, ConstMap<X::Key, X::Value> > sh(x,v);

   ///\endcode

   template<typename M, typename C = typename M::Value> 

   class ShiftWriteMap : public MapBase<typename M::Key, typename M::Value> {

     M& m;

     C v;

   public:

     typedef MapBase<typename M::Key, typename M::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

     ///Constructor

     ///\param _m is the undelying map

     ///\param _v is the shift value

     ShiftWriteMap(M &_m, const C &_v ) : m(_m), v(_v) {};

     /// \e

     Value operator[](Key k) const {return m[k] + v;}

     /// \e

     void set(Key k, const Value& c) { m.set(k, c - v); }

   };

   ///Returns an \c ShiftMap class

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

   ///\relates ShiftMap

   template<typename M, typename C> 

   inline ShiftMap<M, C> shiftMap(const M &m,const C &v) {

     return ShiftMap<M, C>(m,v);

   }

   template<typename M, typename C> 

   inline ShiftWriteMap<M, C> shiftMap(M &m,const C &v) {

     return ShiftWriteMap<M, C>(m,v);

   }

   ///Difference of two maps

   ///This \c concepts::ReadMap "read only map" returns the difference

   ///of the values of the two

   ///given maps. Its \c Key and \c Value will be inherited from \c M1.

   ///The \c Key and \c Value of \c M2 must be convertible to those of \c M1.

   template<typename M1, typename M2> 

   class SubMap : public MapBase<typename M1::Key, typename M1::Value> {

     const M1& m1;

     const M2& m2;

   public:

     typedef MapBase<typename M1::Key, typename M1::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

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

     /// \e

     Value operator[](Key k) const {return m1[k]-m2[k];}

   };

   ///Returns a \c SubMap class

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

   ///

   ///\relates SubMap

   template<typename M1, typename M2> 

   inline SubMap<M1, M2> subMap(const M1 &m1, const M2 &m2) {

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

   }

   ///Product of two maps

   ///This \c concepts::ReadMap "read only map" returns the product of the

   ///values of the two

   ///given

   ///maps. Its \c Key and \c Value will be inherited from \c M1.

   ///The \c Key and \c Value of \c M2 must be convertible to those of \c M1.

   template<typename M1, typename M2> 

   class MulMap : public MapBase<typename M1::Key, typename M1::Value> {

     const M1& m1;

     const M2& m2;

   public:

     typedef MapBase<typename M1::Key, typename M1::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

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

     /// \e

     Value operator[](Key k) const {return m1[k]*m2[k];}

   };

   ///Returns a \c MulMap class

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

   ///\relates MulMap

   template<typename M1, typename M2> 

   inline MulMap<M1, M2> mulMap(const M1 &m1,const M2 &m2) {

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

   }

   ///Scales a maps with a constant.

   ///This \c concepts::ReadMap "read only map" returns the value of the

   ///given map multiplied from the left side with a constant value.

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

   ///

   ///Actually,

   ///\code

   ///  ScaleMap<X> sc(x,v);

   ///\endcode

   ///is equivalent with

   ///\code

   ///  ConstMap<X::Key, X::Value> c_tmp(v);

   ///  MulMap<X, ConstMap<X::Key, X::Value> > sc(x,v);

   ///\endcode

   template<typename M, typename C = typename M::Value> 

   class ScaleMap : public MapBase<typename M::Key, typename M::Value> {

     const M& m;

     C v;

   public:

     typedef MapBase<typename M::Key, typename M::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

     ///Constructor

     ///\param _m is the undelying map

     ///\param _v is the scaling value

     ScaleMap(const M &_m, const C &_v ) : m(_m), v(_v) {};

     /// \e

     Value operator[](Key k) const {return v * m[k];}

   };

   ///Scales a maps with a constant.

   ///This \c concepts::ReadWriteMap "read-write map" returns the value of the

   ///given map multiplied from the left side with a constant value. It can

   ///be used as write map also if the given multiplier is not zero.

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

   template<typename M, typename C = typename M::Value> 

   class ScaleWriteMap : public MapBase<typename M::Key, typename M::Value> {

     M& m;

     C v;

   public:

     typedef MapBase<typename M::Key, typename M::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

     ///Constructor

     ///\param _m is the undelying map

     ///\param _v is the scaling value

     ScaleWriteMap(M &_m, const C &_v ) : m(_m), v(_v) {};

     /// \e

     Value operator[](Key k) const {return v * m[k];}

     /// \e

     void set(Key k, const Value& c) { m.set(k, c / v);}

   };

   ///Returns an \c ScaleMap class

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

   ///\relates ScaleMap

   template<typename M, typename C> 

   inline ScaleMap<M, C> scaleMap(const M &m,const C &v) {

     return ScaleMap<M, C>(m,v);

   }

   template<typename M, typename C> 

   inline ScaleWriteMap<M, C> scaleMap(M &m,const C &v) {

     return ScaleWriteMap<M, C>(m,v);

   }

   ///Quotient of two maps

   ///This \c concepts::ReadMap "read only map" returns the quotient of the

   ///values of the two

   ///given maps. Its \c Key and \c Value will be inherited from \c M1.

   ///The \c Key and \c Value of \c M2 must be convertible to those of \c M1.

   template<typename M1, typename M2> 

   class DivMap : public MapBase<typename M1::Key, typename M1::Value> {

     const M1& m1;

     const M2& m2;

   public:

     typedef MapBase<typename M1::Key, typename M1::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

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

     /// \e

     Value operator[](Key k) const {return m1[k]/m2[k];}

   };

   ///Returns a \c DivMap class

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

   ///\relates DivMap

   template<typename M1, typename M2> 

   inline DivMap<M1, M2> divMap(const M1 &m1,const M2 &m2) {

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

   }

   ///Composition of two maps

   ///This \c concepts::ReadMap "read only map" returns the composition of

   ///two

   ///given maps. That is to say, if \c m1 is of type \c M1 and \c m2 is

   ///of \c M2,

   ///then for

   ///\code

   ///  ComposeMap<M1, M2> cm(m1,m2);

   ///\endcode

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

   ///

   ///Its \c Key is inherited from \c M2 and its \c Value is from

   ///\c M1.

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

   ///\todo Check the requirements.

   template <typename M1, typename M2> 

   class ComposeMap : public MapBase<typename M2::Key, typename M1::Value> {

     const M1& m1;

     const M2& m2;

   public:

     typedef MapBase<typename M2::Key, typename M1::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

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

     /// \e

     /// \todo Use the  MapTraits once it is ported.

     ///

     //typename MapTraits<M1>::ConstReturnValue

     typename M1::Value

     operator[](Key k) const {return m1[m2[k]];}

   };

   ///Returns a \c ComposeMap class

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

   ///

   ///\relates ComposeMap

   template <typename M1, typename M2> 

   inline ComposeMap<M1, M2> composeMap(const M1 &m1,const M2 &m2) {

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

   }

   ///Combines of two maps using an STL (binary) functor.

   ///Combines of two maps using an STL (binary) functor.

   ///

   ///

   ///This \c concepts::ReadMap "read only map" takes two maps and a

   ///binary functor and returns the composition of

   ///the two

   ///given maps unsing the functor. 

   ///That is to say, if \c m1 and \c m2 is of type \c M1 and \c M2

   ///and \c f is of \c F,

   ///then for

   ///\code

   ///  CombineMap<M1, M2,F,V> cm(m1,m2,f);

   ///\endcode

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

   ///

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

   ///The \c M2::Value and \c M1::Value must be convertible to the corresponding

   ///input parameter of \c F and the return type of \c F must be convertible

   ///to \c V.

   ///\todo Check the requirements.

   template<typename M1, typename M2, typename F,

 	   typename V = typename F::result_type> 

   class CombineMap : public MapBase<typename M1::Key, V> {

     const M1& m1;

     const M2& m2;

     F f;

   public:

     typedef MapBase<typename M1::Key, V> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

     CombineMap(const M1 &_m1,const M2 &_m2,const F &_f = F())

       : m1(_m1), m2(_m2), f(_f) {};

     /// \e

     Value operator[](Key k) const {return f(m1[k],m2[k]);}

   };

   ///Returns a \c CombineMap class

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

   ///

   ///For example if \c m1 and \c m2 are both \c double valued maps, then 

   ///\code

   ///combineMap<double>(m1,m2,std::plus<double>())

   ///\endcode

   ///is equivalent with

   ///\code

   ///addMap(m1,m2)

   ///\endcode

   ///

   ///This function is specialized for adaptable binary function

   ///classes and c++ functions.

   ///

   ///\relates CombineMap

   template<typename M1, typename M2, typename F, typename V> 

   inline CombineMap<M1, M2, F, V> 

   combineMap(const M1& m1,const M2& m2, const F& f) {

     return CombineMap<M1, M2, F, V>(m1,m2,f);

   }

   template<typename M1, typename M2, typename F> 

   inline CombineMap<M1, M2, F, typename F::result_type> 

   combineMap(const M1& m1, const M2& m2, const F& f) {

     return combineMap<M1, M2, F, typename F::result_type>(m1,m2,f);

   }

   template<typename M1, typename M2, typename K1, typename K2, typename V> 

   inline CombineMap<M1, M2, V (*)(K1, K2), V> 

   combineMap(const M1 &m1, const M2 &m2, V (*f)(K1, K2)) {

     return combineMap<M1, M2, V (*)(K1, K2), V>(m1,m2,f);

   }

   ///Negative value of a map

   ///This \c concepts::ReadMap "read only map" returns the negative

   ///value of the

   ///value returned by the

   ///given map. Its \c Key and \c Value will be inherited from \c M.

   ///The unary \c - operator must be defined for \c Value, of course.

   template<typename M> 

   class NegMap : public MapBase<typename M::Key, typename M::Value> {

     const M& m;

   public:

     typedef MapBase<typename M::Key, typename M::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

     NegMap(const M &_m) : m(_m) {};

     /// \e

     Value operator[](Key k) const {return -m[k];}

   };

   ///Negative value of a map

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

   ///value of the value returned by the

   ///given map. Its \c Key and \c Value will be inherited from \c M.

   ///The unary \c - operator must be defined for \c Value, of course.

   template<typename M> 

   class NegWriteMap : public MapBase<typename M::Key, typename M::Value> {

     M& m;

   public:

     typedef MapBase<typename M::Key, typename M::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

     NegWriteMap(M &_m) : m(_m) {};

     /// \e

     Value operator[](Key k) const {return -m[k];}

     /// \e

     void set(Key k, const Value& v) { m.set(k, -v); }

   };

   ///Returns a \c NegMap class

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

   ///\relates NegMap

   template <typename M> 

   inline NegMap<M> negMap(const M &m) {

     return NegMap<M>(m);

   }

   template <typename M> 

   inline NegWriteMap<M> negMap(M &m) {

     return NegWriteMap<M>(m);

   }

   ///Absolute value of a map

   ///This \c concepts::ReadMap "read only map" returns the absolute value

   ///of the

   ///value returned by the

   ///given map. Its \c Key and \c Value will be inherited

   ///from <tt>M</tt>. <tt>Value</tt>

   ///must be comparable to <tt>0</tt> and the unary <tt>-</tt>

   ///operator must be defined for it, of course.

   ///

   ///\bug We need a unified way to handle the situation below:

   ///\code

   ///  struct _UnConvertible {};

   ///  template<class A> inline A t_abs(A a) {return _UnConvertible();}

   ///  template<> inline int t_abs<>(int n) {return abs(n);}

   ///  template<> inline long int t_abs<>(long int n) {return labs(n);}

   ///  template<> inline long long int t_abs<>(long long int n) {return ::llabs(n);}

   ///  template<> inline float t_abs<>(float n) {return fabsf(n);}

   ///  template<> inline double t_abs<>(double n) {return fabs(n);}

   ///  template<> inline long double t_abs<>(long double n) {return fabsl(n);}

   ///\endcode

   template<typename M> 

   class AbsMap : public MapBase<typename M::Key, typename M::Value> {

     const M& m;

   public:

     typedef MapBase<typename M::Key, typename M::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

     AbsMap(const M &_m) : m(_m) {};

     /// \e

     Value operator[](Key k) const {

       Value tmp = m[k]; 

       return tmp >= 0 ? tmp : -tmp;

     }

   };

   ///Returns a \c AbsMap class

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

   ///\relates AbsMap

   template<typename M> 

   inline AbsMap<M> absMap(const M &m) {

     return AbsMap<M>(m);

   }

   ///Converts an STL style functor to a map

   ///This \c concepts::ReadMap "read only map" returns the value

   ///of a

   ///given map.

   ///

   ///Template parameters \c K and \c V will become its

   ///\c Key and \c Value. They must be given explicitely

   ///because a functor does not provide such typedefs.

   ///

   ///Parameter \c F is the type of the used functor.

   template<typename F, 

 	   typename K = typename F::argument_type, 

 	   typename V = typename F::result_type> 

   class FunctorMap : public MapBase<K, V> {

     F f;

   public:

     typedef MapBase<K, V> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

     FunctorMap(const F &_f = F()) : f(_f) {}

     /// \e

     Value operator[](Key k) const { return f(k);}

   };

   ///Returns a \c FunctorMap class

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

   ///

   ///It is specialized for adaptable function classes and

   ///c++ functions.

   ///\relates FunctorMap

   template<typename K, typename V, typename F> inline 

   FunctorMap<F, K, V> functorMap(const F &f) {

     return FunctorMap<F, K, V>(f);

   }

   template <typename F> inline 

   FunctorMap<F, typename F::argument_type, typename F::result_type> 

   functorMap(const F &f) {

     return FunctorMap<F, typename F::argument_type, 

       typename F::result_type>(f);

   }

   template <typename K, typename V> inline 

   FunctorMap<V (*)(K), K, V> functorMap(V (*f)(K)) {

     return FunctorMap<V (*)(K), K, V>(f);

   }

   ///Converts a map to an STL style (unary) functor

   ///This class Converts a map to an STL style (unary) functor.

   ///that is it provides an <tt>operator()</tt> to read its values.

   ///

   ///For the sake of convenience it also works as

   ///a ususal \c concepts::ReadMap "readable map",

   ///i.e. <tt>operator[]</tt> and the \c Key and \c Value typedefs also exist.

   template <typename M> 

   class MapFunctor : public MapBase<typename M::Key, typename M::Value> {

     const M& m;

   public:

     typedef MapBase<typename M::Key, typename M::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     typedef typename M::Key argument_type;

     typedef typename M::Value result_type;

     ///Constructor

     MapFunctor(const M &_m) : m(_m) {};

     ///\e

     Value operator()(Key k) const {return m[k];}

     ///\e

     Value operator[](Key k) const {return m[k];}

   };

   ///Returns a \c MapFunctor class

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

   ///\relates MapFunctor

   template<typename M> 

   inline MapFunctor<M> mapFunctor(const M &m) {

     return MapFunctor<M>(m);

   }

   ///Applies all map setting operations to two maps

   ///This map has two \c concepts::ReadMap "readable map"

   ///parameters and each read request will be passed just to the

   ///first map. This class is the just readable map type of the ForkWriteMap.

   ///

   ///The \c Key and \c Value will be inherited from \c M1.

   ///The \c Key and \c Value of M2 must be convertible from those of \c M1.

   template<typename  M1, typename M2> 

   class ForkMap : public MapBase<typename M1::Key, typename M1::Value> {

     const M1& m1;

     const M2& m2;

   public:

     typedef MapBase<typename M1::Key, typename M1::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

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

     /// \e

     Value operator[](Key k) const {return m1[k];}

   };

   ///Applies all map setting operations to two maps

   ///This map has two \c concepts::WriteMap "writable map"

   ///parameters and each write request will be passed to both of them.

   ///If \c M1 is also \c concepts::ReadMap "readable",

   ///then the read operations will return the

   ///corresponding values of \c M1.

   ///

   ///The \c Key and \c Value will be inherited from \c M1.

   ///The \c Key and \c Value of M2 must be convertible from those of \c M1.

   template<typename  M1, typename M2> 

   class ForkWriteMap : public MapBase<typename M1::Key, typename M1::Value> {

     M1& m1;

     M2& m2;

   public:

     typedef MapBase<typename M1::Key, typename M1::Value> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     ///Constructor

     ForkWriteMap(M1 &_m1, M2 &_m2) : m1(_m1), m2(_m2) {};

     ///\e

     Value operator[](Key k) const {return m1[k];}

     ///\e

     void set(Key k, const Value &v) {m1.set(k,v); m2.set(k,v);}

   };

   ///Returns an \c ForkMap class

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

   ///

   ///\relates ForkMap

   template <typename M1, typename M2> 

   inline ForkMap<M1, M2> forkMap(const M1 &m1, const M2 &m2) {

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

   }

   template <typename M1, typename M2> 

   inline ForkWriteMap<M1, M2> forkMap(M1 &m1, M2 &m2) {

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

   }

   /* ************* BOOL MAPS ******************* */

   ///Logical 'not' of a map

   ///This bool \c concepts::ReadMap "read only map" returns the 

   ///logical negation of

   ///value returned by the

   ///given map. Its \c Key and will be inherited from \c M,

   ///its Value is <tt>bool</tt>.

   template <typename M> 

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

     const M& m;

   public:

     typedef MapBase<typename M::Key, bool> Parent;

     typedef typename Parent::Key Key;

     typedef typename Parent::Value Value;

     /// Constructor

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

     ///\e

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

   };

   ///Logical 'not' of a map with writing possibility

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

   ///logical negation of value returned by the given map. When it is set,

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

   ///Its \c Key and will be inherited from \c M,

   ///its Value is <tt>bool</tt>.

   template <typename M> 

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

     M& m;