/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2008

 * 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:

    /// The key type of the map.

    typedef K Key;

    /// The value type of the map. (The type of objects associated with the keys).

    typedef T Value;

  };

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

  /// This map can be used 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 is not required (i.e. it will be 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&) {}

  };

  ///Returns a \c NullMap class

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

  ///\relates NullMap

  template <typename K, typename V> 

  NullMap<K, V> nullMap() {

    return NullMap<K, V>();

  }

  /// Constant map.

  /// This is a \ref concepts::ReadMap "readable" map which assigns a 

  /// specified value to each key.

  /// In other aspects it is equivalent to \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

    /// Default constructor.

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

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

    ConstMap() {}

    /// Constructor with specified initial value

    /// Constructor with specified initial value.

    /// \param _v is 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 \ref concepts::ReadMap "readable" map which assigns a 

  /// specified value to each key.

  /// In other aspects it is equivalent to \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 with inlined value

  ///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 \c std::map

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

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

  ///It meets the \ref concepts::ReferenceMap "ReferenceMap" concept.

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

  class StdMap : public MapBase<K, T> {

    template <typename K1, typename T1, typename C1>

    friend class StdMap;

  public:

    typedef MapBase<K, T> Parent;

    ///Key type

    typedef typename Parent::Key Key;

    ///Value type

    typedef typename Parent::Value Value;

    ///Reference Type

    typedef T& Reference;

    ///Const reference type

    typedef const T& ConstReference;

    typedef True ReferenceMapTag;

  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 \c 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 \ref 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;

    };

  };

  ///Returns a \c StdMap class

  ///This function just returns a \c StdMap class with specified 

  ///default value.

  ///\relates StdMap

  template<typename K, typename V, typename Compare> 

  inline StdMap<K, V, Compare> stdMap(const V& value = V()) {

    return StdMap<K, V, Compare>(value);

  }

  template<typename K, typename V> 

  inline StdMap<K, V, std::less<K> > stdMap(const V& value = V()) {

    return StdMap<K, V, std::less<K> >(value);

  }

  ///Returns a \c StdMap class created from an appropriate \c std::map

  ///This function just returns a \c StdMap class created from an 

  ///appropriate \c std::map.

  ///\relates StdMap

  template<typename K, typename V, typename Compare> 

  inline StdMap<K, V, Compare> stdMap( const std::map<K, V, Compare> &map, 

                                       const V& value = V() ) {

    return StdMap<K, V, Compare>(map, value);

  }

  /// \brief Map for storing values for keys from the range <tt>[0..size-1]</tt>

  ///

  /// This map has the <tt>[0..size-1]</tt> 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 : public MapBase<int, T> {

    template <typename T1>

    friend class IntegerMap;

  public:

    typedef MapBase<int, T> Parent;

    ///\e

    typedef typename Parent::Key Key;

    ///\e

    typedef typename Parent::Value Value;

    ///\e

    typedef T& Reference;

    ///\e

    typedef const T& ConstReference;

    typedef True ReferenceMapTag;

  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 \c std::vector.

    template <typename T1>

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

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

    /// \brief Constructs a map from an other \ref 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;

    }

  };

  ///Returns an \c IntegerMap class

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

  ///\relates IntegerMap

  template<typename T>

  inline IntegerMap<T> integerMap(int size = 0, const T& value = T()) {

    return IntegerMap<T>(size, value);

  }

  /// @}

  /// \addtogroup map_adaptors

  /// @{

  /// \brief Identity map.

  ///

  /// This map 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>();

  }

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

  ///the default conversion.

  ///

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

  ///converts the \c Value of a map 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) {};

    ///\e

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

  };

  ///Returns a \c ConvertMap class

  ///This function just returns a \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 a map

  ///This \ref 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.

  ///

  ///\sa SimpleWriteMap

  ///

  /// \todo Revise the misleading name 

  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];}

  };

  ///Returns a \c SimpleMap class

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

  ///\relates SimpleMap

  template<typename M>

  inline SimpleMap<M> simpleMap(const M &m) {

    return SimpleMap<M>(m);

  }

  ///Simple writable wrapping of a map

  ///This \ref concepts::ReadWriteMap "read-write 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.

  ///

  ///\sa SimpleMap

  ///

  /// \todo Revise the misleading name

  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); }

  };

  ///Returns a \c SimpleWriteMap class

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

  ///\relates SimpleWriteMap

  template<typename M>

  inline SimpleWriteMap<M> simpleWriteMap(M &m) {

    return SimpleWriteMap<M>(m);

  }

  ///Sum of two maps

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

  ///given maps.

  ///Its \c Key and \c Value are 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 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 \ref 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 to

  ///\code

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

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

  ///\endcode

  ///

  ///\sa ShiftWriteMap

  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 (ReadWrite version).

  ///This \ref 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 are inherited from \c M.

  ///

  ///\sa ShiftMap

  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 a \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);

  }

  ///Returns a \c ShiftWriteMap class

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

  ///\relates ShiftWriteMap

  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 \ref concepts::ReadMap "read only map" returns the difference

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

  ///Its \c Key and \c Value are 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 \ref concepts::ReadMap "read only map" returns the product of the

  ///values of the two given maps.

  ///Its \c Key and \c Value are 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 map with a constant.

  ///This \ref 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 are inherited from \c M.

  ///

  ///Actually,

  ///\code

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

  ///\endcode

  ///is equivalent to

  ///\code

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

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

  ///\endcode

  ///

  ///\sa ScaleWriteMap

  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 map with a constant (ReadWrite version).

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

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

  ///also be used as write map if the \c / operator is defined between

  ///\c Value and \c C and the given multiplier is not zero.

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

  ///

  ///\sa ScaleMap

  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 a \c ScaleMap class

  ///This function just returns a \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);

  }

  ///Returns a \c ScaleWriteMap class

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

  ///\relates ScaleWriteMap

  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 \ref concepts::ReadMap "read only map" returns the quotient of the

  ///values of the two given maps.

  ///Its \c Key and \c Value are 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 \ref 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.

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

  ///

  ///\sa CombineMap

  ///

  ///\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) {};

    typename MapTraits<M1>::ConstReturnValue

    /// \e

    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);

  }

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

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

  ///

  ///This \ref 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.

  ///\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.

  ///

  ///\sa ComposeMap

  ///

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

  ///\endcode

  ///is equivalent to

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

  ///value of the value returned by the given map.

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

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

  ///

  ///\sa NegWriteMap

  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 (ReadWrite version)

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

  ///value of the value returned by the given map.

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

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

  ///

  /// \sa NegMap

  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);

  }

  ///Returns a \c NegWriteMap class

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

  ///\relates NegWriteMap

  template <typename M> 

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

    return NegWriteMap<M>(m);

  }

  ///Absolute value of a map

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

  ///of the value returned by the given map.

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

  ///\c Value must be comparable to \c 0 and the unary \c -

  ///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