lemon/maps.h
author Balazs Dezso <deba@inf.elte.hu>
Wed, 08 Apr 2009 22:49:28 +0200
changeset 576 745e182d0139
parent 559 c5fd2d996909
child 584 33c6b6e755cd
permissions -rw-r--r--
Unified message handling for LP and MIP solvers (#9)
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2009
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #ifndef LEMON_MAPS_H
    20 #define LEMON_MAPS_H
    21 
    22 #include <iterator>
    23 #include <functional>
    24 #include <vector>
    25 
    26 #include <lemon/core.h>
    27 
    28 ///\file
    29 ///\ingroup maps
    30 ///\brief Miscellaneous property maps
    31 
    32 #include <map>
    33 
    34 namespace lemon {
    35 
    36   /// \addtogroup maps
    37   /// @{
    38 
    39   /// Base class of maps.
    40 
    41   /// Base class of maps. It provides the necessary type definitions
    42   /// required by the map %concepts.
    43   template<typename K, typename V>
    44   class MapBase {
    45   public:
    46     /// \brief The key type of the map.
    47     typedef K Key;
    48     /// \brief The value type of the map.
    49     /// (The type of objects associated with the keys).
    50     typedef V Value;
    51   };
    52 
    53 
    54   /// Null map. (a.k.a. DoNothingMap)
    55 
    56   /// This map can be used if you have to provide a map only for
    57   /// its type definitions, or if you have to provide a writable map,
    58   /// but data written to it is not required (i.e. it will be sent to
    59   /// <tt>/dev/null</tt>).
    60   /// It conforms the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
    61   ///
    62   /// \sa ConstMap
    63   template<typename K, typename V>
    64   class NullMap : public MapBase<K, V> {
    65   public:
    66     ///\e
    67     typedef K Key;
    68     ///\e
    69     typedef V Value;
    70 
    71     /// Gives back a default constructed element.
    72     Value operator[](const Key&) const { return Value(); }
    73     /// Absorbs the value.
    74     void set(const Key&, const Value&) {}
    75   };
    76 
    77   /// Returns a \c NullMap class
    78 
    79   /// This function just returns a \c NullMap class.
    80   /// \relates NullMap
    81   template <typename K, typename V>
    82   NullMap<K, V> nullMap() {
    83     return NullMap<K, V>();
    84   }
    85 
    86 
    87   /// Constant map.
    88 
    89   /// This \ref concepts::ReadMap "readable map" assigns a specified
    90   /// value to each key.
    91   ///
    92   /// In other aspects it is equivalent to \c NullMap.
    93   /// So it conforms the \ref concepts::ReadWriteMap "ReadWriteMap"
    94   /// concept, but it absorbs the data written to it.
    95   ///
    96   /// The simplest way of using this map is through the constMap()
    97   /// function.
    98   ///
    99   /// \sa NullMap
   100   /// \sa IdentityMap
   101   template<typename K, typename V>
   102   class ConstMap : public MapBase<K, V> {
   103   private:
   104     V _value;
   105   public:
   106     ///\e
   107     typedef K Key;
   108     ///\e
   109     typedef V Value;
   110 
   111     /// Default constructor
   112 
   113     /// Default constructor.
   114     /// The value of the map will be default constructed.
   115     ConstMap() {}
   116 
   117     /// Constructor with specified initial value
   118 
   119     /// Constructor with specified initial value.
   120     /// \param v The initial value of the map.
   121     ConstMap(const Value &v) : _value(v) {}
   122 
   123     /// Gives back the specified value.
   124     Value operator[](const Key&) const { return _value; }
   125 
   126     /// Absorbs the value.
   127     void set(const Key&, const Value&) {}
   128 
   129     /// Sets the value that is assigned to each key.
   130     void setAll(const Value &v) {
   131       _value = v;
   132     }
   133 
   134     template<typename V1>
   135     ConstMap(const ConstMap<K, V1> &, const Value &v) : _value(v) {}
   136   };
   137 
   138   /// Returns a \c ConstMap class
   139 
   140   /// This function just returns a \c ConstMap class.
   141   /// \relates ConstMap
   142   template<typename K, typename V>
   143   inline ConstMap<K, V> constMap(const V &v) {
   144     return ConstMap<K, V>(v);
   145   }
   146 
   147   template<typename K, typename V>
   148   inline ConstMap<K, V> constMap() {
   149     return ConstMap<K, V>();
   150   }
   151 
   152 
   153   template<typename T, T v>
   154   struct Const {};
   155 
   156   /// Constant map with inlined constant value.
   157 
   158   /// This \ref concepts::ReadMap "readable map" assigns a specified
   159   /// value to each key.
   160   ///
   161   /// In other aspects it is equivalent to \c NullMap.
   162   /// So it conforms the \ref concepts::ReadWriteMap "ReadWriteMap"
   163   /// concept, but it absorbs the data written to it.
   164   ///
   165   /// The simplest way of using this map is through the constMap()
   166   /// function.
   167   ///
   168   /// \sa NullMap
   169   /// \sa IdentityMap
   170   template<typename K, typename V, V v>
   171   class ConstMap<K, Const<V, v> > : public MapBase<K, V> {
   172   public:
   173     ///\e
   174     typedef K Key;
   175     ///\e
   176     typedef V Value;
   177 
   178     /// Constructor.
   179     ConstMap() {}
   180 
   181     /// Gives back the specified value.
   182     Value operator[](const Key&) const { return v; }
   183 
   184     /// Absorbs the value.
   185     void set(const Key&, const Value&) {}
   186   };
   187 
   188   /// Returns a \c ConstMap class with inlined constant value
   189 
   190   /// This function just returns a \c ConstMap class with inlined
   191   /// constant value.
   192   /// \relates ConstMap
   193   template<typename K, typename V, V v>
   194   inline ConstMap<K, Const<V, v> > constMap() {
   195     return ConstMap<K, Const<V, v> >();
   196   }
   197 
   198 
   199   /// Identity map.
   200 
   201   /// This \ref concepts::ReadMap "read-only map" gives back the given
   202   /// key as value without any modification.
   203   ///
   204   /// \sa ConstMap
   205   template <typename T>
   206   class IdentityMap : public MapBase<T, T> {
   207   public:
   208     ///\e
   209     typedef T Key;
   210     ///\e
   211     typedef T Value;
   212 
   213     /// Gives back the given value without any modification.
   214     Value operator[](const Key &k) const {
   215       return k;
   216     }
   217   };
   218 
   219   /// Returns an \c IdentityMap class
   220 
   221   /// This function just returns an \c IdentityMap class.
   222   /// \relates IdentityMap
   223   template<typename T>
   224   inline IdentityMap<T> identityMap() {
   225     return IdentityMap<T>();
   226   }
   227 
   228 
   229   /// \brief Map for storing values for integer keys from the range
   230   /// <tt>[0..size-1]</tt>.
   231   ///
   232   /// This map is essentially a wrapper for \c std::vector. It assigns
   233   /// values to integer keys from the range <tt>[0..size-1]</tt>.
   234   /// It can be used with some data structures, for example
   235   /// \c UnionFind, \c BinHeap, when the used items are small
   236   /// integers. This map conforms the \ref concepts::ReferenceMap
   237   /// "ReferenceMap" concept.
   238   ///
   239   /// The simplest way of using this map is through the rangeMap()
   240   /// function.
   241   template <typename V>
   242   class RangeMap : public MapBase<int, V> {
   243     template <typename V1>
   244     friend class RangeMap;
   245   private:
   246 
   247     typedef std::vector<V> Vector;
   248     Vector _vector;
   249 
   250   public:
   251 
   252     /// Key type
   253     typedef int Key;
   254     /// Value type
   255     typedef V Value;
   256     /// Reference type
   257     typedef typename Vector::reference Reference;
   258     /// Const reference type
   259     typedef typename Vector::const_reference ConstReference;
   260 
   261     typedef True ReferenceMapTag;
   262 
   263   public:
   264 
   265     /// Constructor with specified default value.
   266     RangeMap(int size = 0, const Value &value = Value())
   267       : _vector(size, value) {}
   268 
   269     /// Constructs the map from an appropriate \c std::vector.
   270     template <typename V1>
   271     RangeMap(const std::vector<V1>& vector)
   272       : _vector(vector.begin(), vector.end()) {}
   273 
   274     /// Constructs the map from another \c RangeMap.
   275     template <typename V1>
   276     RangeMap(const RangeMap<V1> &c)
   277       : _vector(c._vector.begin(), c._vector.end()) {}
   278 
   279     /// Returns the size of the map.
   280     int size() {
   281       return _vector.size();
   282     }
   283 
   284     /// Resizes the map.
   285 
   286     /// Resizes the underlying \c std::vector container, so changes the
   287     /// keyset of the map.
   288     /// \param size The new size of the map. The new keyset will be the
   289     /// range <tt>[0..size-1]</tt>.
   290     /// \param value The default value to assign to the new keys.
   291     void resize(int size, const Value &value = Value()) {
   292       _vector.resize(size, value);
   293     }
   294 
   295   private:
   296 
   297     RangeMap& operator=(const RangeMap&);
   298 
   299   public:
   300 
   301     ///\e
   302     Reference operator[](const Key &k) {
   303       return _vector[k];
   304     }
   305 
   306     ///\e
   307     ConstReference operator[](const Key &k) const {
   308       return _vector[k];
   309     }
   310 
   311     ///\e
   312     void set(const Key &k, const Value &v) {
   313       _vector[k] = v;
   314     }
   315   };
   316 
   317   /// Returns a \c RangeMap class
   318 
   319   /// This function just returns a \c RangeMap class.
   320   /// \relates RangeMap
   321   template<typename V>
   322   inline RangeMap<V> rangeMap(int size = 0, const V &value = V()) {
   323     return RangeMap<V>(size, value);
   324   }
   325 
   326   /// \brief Returns a \c RangeMap class created from an appropriate
   327   /// \c std::vector
   328 
   329   /// This function just returns a \c RangeMap class created from an
   330   /// appropriate \c std::vector.
   331   /// \relates RangeMap
   332   template<typename V>
   333   inline RangeMap<V> rangeMap(const std::vector<V> &vector) {
   334     return RangeMap<V>(vector);
   335   }
   336 
   337 
   338   /// Map type based on \c std::map
   339 
   340   /// This map is essentially a wrapper for \c std::map with addition
   341   /// that you can specify a default value for the keys that are not
   342   /// stored actually. This value can be different from the default
   343   /// contructed value (i.e. \c %Value()).
   344   /// This type conforms the \ref concepts::ReferenceMap "ReferenceMap"
   345   /// concept.
   346   ///
   347   /// This map is useful if a default value should be assigned to most of
   348   /// the keys and different values should be assigned only to a few
   349   /// keys (i.e. the map is "sparse").
   350   /// The name of this type also refers to this important usage.
   351   ///
   352   /// Apart form that this map can be used in many other cases since it
   353   /// is based on \c std::map, which is a general associative container.
   354   /// However keep in mind that it is usually not as efficient as other
   355   /// maps.
   356   ///
   357   /// The simplest way of using this map is through the sparseMap()
   358   /// function.
   359   template <typename K, typename V, typename Comp = std::less<K> >
   360   class SparseMap : public MapBase<K, V> {
   361     template <typename K1, typename V1, typename C1>
   362     friend class SparseMap;
   363   public:
   364 
   365     /// Key type
   366     typedef K Key;
   367     /// Value type
   368     typedef V Value;
   369     /// Reference type
   370     typedef Value& Reference;
   371     /// Const reference type
   372     typedef const Value& ConstReference;
   373 
   374     typedef True ReferenceMapTag;
   375 
   376   private:
   377 
   378     typedef std::map<K, V, Comp> Map;
   379     Map _map;
   380     Value _value;
   381 
   382   public:
   383 
   384     /// \brief Constructor with specified default value.
   385     SparseMap(const Value &value = Value()) : _value(value) {}
   386     /// \brief Constructs the map from an appropriate \c std::map, and
   387     /// explicitly specifies a default value.
   388     template <typename V1, typename Comp1>
   389     SparseMap(const std::map<Key, V1, Comp1> &map,
   390               const Value &value = Value())
   391       : _map(map.begin(), map.end()), _value(value) {}
   392 
   393     /// \brief Constructs the map from another \c SparseMap.
   394     template<typename V1, typename Comp1>
   395     SparseMap(const SparseMap<Key, V1, Comp1> &c)
   396       : _map(c._map.begin(), c._map.end()), _value(c._value) {}
   397 
   398   private:
   399 
   400     SparseMap& operator=(const SparseMap&);
   401 
   402   public:
   403 
   404     ///\e
   405     Reference operator[](const Key &k) {
   406       typename Map::iterator it = _map.lower_bound(k);
   407       if (it != _map.end() && !_map.key_comp()(k, it->first))
   408         return it->second;
   409       else
   410         return _map.insert(it, std::make_pair(k, _value))->second;
   411     }
   412 
   413     ///\e
   414     ConstReference operator[](const Key &k) const {
   415       typename Map::const_iterator it = _map.find(k);
   416       if (it != _map.end())
   417         return it->second;
   418       else
   419         return _value;
   420     }
   421 
   422     ///\e
   423     void set(const Key &k, const Value &v) {
   424       typename Map::iterator it = _map.lower_bound(k);
   425       if (it != _map.end() && !_map.key_comp()(k, it->first))
   426         it->second = v;
   427       else
   428         _map.insert(it, std::make_pair(k, v));
   429     }
   430 
   431     ///\e
   432     void setAll(const Value &v) {
   433       _value = v;
   434       _map.clear();
   435     }
   436   };
   437 
   438   /// Returns a \c SparseMap class
   439 
   440   /// This function just returns a \c SparseMap class with specified
   441   /// default value.
   442   /// \relates SparseMap
   443   template<typename K, typename V, typename Compare>
   444   inline SparseMap<K, V, Compare> sparseMap(const V& value = V()) {
   445     return SparseMap<K, V, Compare>(value);
   446   }
   447 
   448   template<typename K, typename V>
   449   inline SparseMap<K, V, std::less<K> > sparseMap(const V& value = V()) {
   450     return SparseMap<K, V, std::less<K> >(value);
   451   }
   452 
   453   /// \brief Returns a \c SparseMap class created from an appropriate
   454   /// \c std::map
   455 
   456   /// This function just returns a \c SparseMap class created from an
   457   /// appropriate \c std::map.
   458   /// \relates SparseMap
   459   template<typename K, typename V, typename Compare>
   460   inline SparseMap<K, V, Compare>
   461     sparseMap(const std::map<K, V, Compare> &map, const V& value = V())
   462   {
   463     return SparseMap<K, V, Compare>(map, value);
   464   }
   465 
   466   /// @}
   467 
   468   /// \addtogroup map_adaptors
   469   /// @{
   470 
   471   /// Composition of two maps
   472 
   473   /// This \ref concepts::ReadMap "read-only map" returns the
   474   /// composition of two given maps. That is to say, if \c m1 is of
   475   /// type \c M1 and \c m2 is of \c M2, then for
   476   /// \code
   477   ///   ComposeMap<M1, M2> cm(m1,m2);
   478   /// \endcode
   479   /// <tt>cm[x]</tt> will be equal to <tt>m1[m2[x]]</tt>.
   480   ///
   481   /// The \c Key type of the map is inherited from \c M2 and the
   482   /// \c Value type is from \c M1.
   483   /// \c M2::Value must be convertible to \c M1::Key.
   484   ///
   485   /// The simplest way of using this map is through the composeMap()
   486   /// function.
   487   ///
   488   /// \sa CombineMap
   489   template <typename M1, typename M2>
   490   class ComposeMap : public MapBase<typename M2::Key, typename M1::Value> {
   491     const M1 &_m1;
   492     const M2 &_m2;
   493   public:
   494     ///\e
   495     typedef typename M2::Key Key;
   496     ///\e
   497     typedef typename M1::Value Value;
   498 
   499     /// Constructor
   500     ComposeMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
   501 
   502     ///\e
   503     typename MapTraits<M1>::ConstReturnValue
   504     operator[](const Key &k) const { return _m1[_m2[k]]; }
   505   };
   506 
   507   /// Returns a \c ComposeMap class
   508 
   509   /// This function just returns a \c ComposeMap class.
   510   ///
   511   /// If \c m1 and \c m2 are maps and the \c Value type of \c m2 is
   512   /// convertible to the \c Key of \c m1, then <tt>composeMap(m1,m2)[x]</tt>
   513   /// will be equal to <tt>m1[m2[x]]</tt>.
   514   ///
   515   /// \relates ComposeMap
   516   template <typename M1, typename M2>
   517   inline ComposeMap<M1, M2> composeMap(const M1 &m1, const M2 &m2) {
   518     return ComposeMap<M1, M2>(m1, m2);
   519   }
   520 
   521 
   522   /// Combination of two maps using an STL (binary) functor.
   523 
   524   /// This \ref concepts::ReadMap "read-only map" takes two maps and a
   525   /// binary functor and returns the combination of the two given maps
   526   /// using the functor.
   527   /// That is to say, if \c m1 is of type \c M1 and \c m2 is of \c M2
   528   /// and \c f is of \c F, then for
   529   /// \code
   530   ///   CombineMap<M1,M2,F,V> cm(m1,m2,f);
   531   /// \endcode
   532   /// <tt>cm[x]</tt> will be equal to <tt>f(m1[x],m2[x])</tt>.
   533   ///
   534   /// The \c Key type of the map is inherited from \c M1 (\c M1::Key
   535   /// must be convertible to \c M2::Key) and the \c Value type is \c V.
   536   /// \c M2::Value and \c M1::Value must be convertible to the
   537   /// corresponding input parameter of \c F and the return type of \c F
   538   /// must be convertible to \c V.
   539   ///
   540   /// The simplest way of using this map is through the combineMap()
   541   /// function.
   542   ///
   543   /// \sa ComposeMap
   544   template<typename M1, typename M2, typename F,
   545            typename V = typename F::result_type>
   546   class CombineMap : public MapBase<typename M1::Key, V> {
   547     const M1 &_m1;
   548     const M2 &_m2;
   549     F _f;
   550   public:
   551     ///\e
   552     typedef typename M1::Key Key;
   553     ///\e
   554     typedef V Value;
   555 
   556     /// Constructor
   557     CombineMap(const M1 &m1, const M2 &m2, const F &f = F())
   558       : _m1(m1), _m2(m2), _f(f) {}
   559     ///\e
   560     Value operator[](const Key &k) const { return _f(_m1[k],_m2[k]); }
   561   };
   562 
   563   /// Returns a \c CombineMap class
   564 
   565   /// This function just returns a \c CombineMap class.
   566   ///
   567   /// For example, if \c m1 and \c m2 are both maps with \c double
   568   /// values, then
   569   /// \code
   570   ///   combineMap(m1,m2,std::plus<double>())
   571   /// \endcode
   572   /// is equivalent to
   573   /// \code
   574   ///   addMap(m1,m2)
   575   /// \endcode
   576   ///
   577   /// This function is specialized for adaptable binary function
   578   /// classes and C++ functions.
   579   ///
   580   /// \relates CombineMap
   581   template<typename M1, typename M2, typename F, typename V>
   582   inline CombineMap<M1, M2, F, V>
   583   combineMap(const M1 &m1, const M2 &m2, const F &f) {
   584     return CombineMap<M1, M2, F, V>(m1,m2,f);
   585   }
   586 
   587   template<typename M1, typename M2, typename F>
   588   inline CombineMap<M1, M2, F, typename F::result_type>
   589   combineMap(const M1 &m1, const M2 &m2, const F &f) {
   590     return combineMap<M1, M2, F, typename F::result_type>(m1,m2,f);
   591   }
   592 
   593   template<typename M1, typename M2, typename K1, typename K2, typename V>
   594   inline CombineMap<M1, M2, V (*)(K1, K2), V>
   595   combineMap(const M1 &m1, const M2 &m2, V (*f)(K1, K2)) {
   596     return combineMap<M1, M2, V (*)(K1, K2), V>(m1,m2,f);
   597   }
   598 
   599 
   600   /// Converts an STL style (unary) functor to a map
   601 
   602   /// This \ref concepts::ReadMap "read-only map" returns the value
   603   /// of a given functor. Actually, it just wraps the functor and
   604   /// provides the \c Key and \c Value typedefs.
   605   ///
   606   /// Template parameters \c K and \c V will become its \c Key and
   607   /// \c Value. In most cases they have to be given explicitly because
   608   /// a functor typically does not provide \c argument_type and
   609   /// \c result_type typedefs.
   610   /// Parameter \c F is the type of the used functor.
   611   ///
   612   /// The simplest way of using this map is through the functorToMap()
   613   /// function.
   614   ///
   615   /// \sa MapToFunctor
   616   template<typename F,
   617            typename K = typename F::argument_type,
   618            typename V = typename F::result_type>
   619   class FunctorToMap : public MapBase<K, V> {
   620     F _f;
   621   public:
   622     ///\e
   623     typedef K Key;
   624     ///\e
   625     typedef V Value;
   626 
   627     /// Constructor
   628     FunctorToMap(const F &f = F()) : _f(f) {}
   629     ///\e
   630     Value operator[](const Key &k) const { return _f(k); }
   631   };
   632 
   633   /// Returns a \c FunctorToMap class
   634 
   635   /// This function just returns a \c FunctorToMap class.
   636   ///
   637   /// This function is specialized for adaptable binary function
   638   /// classes and C++ functions.
   639   ///
   640   /// \relates FunctorToMap
   641   template<typename K, typename V, typename F>
   642   inline FunctorToMap<F, K, V> functorToMap(const F &f) {
   643     return FunctorToMap<F, K, V>(f);
   644   }
   645 
   646   template <typename F>
   647   inline FunctorToMap<F, typename F::argument_type, typename F::result_type>
   648     functorToMap(const F &f)
   649   {
   650     return FunctorToMap<F, typename F::argument_type,
   651       typename F::result_type>(f);
   652   }
   653 
   654   template <typename K, typename V>
   655   inline FunctorToMap<V (*)(K), K, V> functorToMap(V (*f)(K)) {
   656     return FunctorToMap<V (*)(K), K, V>(f);
   657   }
   658 
   659 
   660   /// Converts a map to an STL style (unary) functor
   661 
   662   /// This class converts a map to an STL style (unary) functor.
   663   /// That is it provides an <tt>operator()</tt> to read its values.
   664   ///
   665   /// For the sake of convenience it also works as a usual
   666   /// \ref concepts::ReadMap "readable map", i.e. <tt>operator[]</tt>
   667   /// and the \c Key and \c Value typedefs also exist.
   668   ///
   669   /// The simplest way of using this map is through the mapToFunctor()
   670   /// function.
   671   ///
   672   ///\sa FunctorToMap
   673   template <typename M>
   674   class MapToFunctor : public MapBase<typename M::Key, typename M::Value> {
   675     const M &_m;
   676   public:
   677     ///\e
   678     typedef typename M::Key Key;
   679     ///\e
   680     typedef typename M::Value Value;
   681 
   682     typedef typename M::Key argument_type;
   683     typedef typename M::Value result_type;
   684 
   685     /// Constructor
   686     MapToFunctor(const M &m) : _m(m) {}
   687     ///\e
   688     Value operator()(const Key &k) const { return _m[k]; }
   689     ///\e
   690     Value operator[](const Key &k) const { return _m[k]; }
   691   };
   692 
   693   /// Returns a \c MapToFunctor class
   694 
   695   /// This function just returns a \c MapToFunctor class.
   696   /// \relates MapToFunctor
   697   template<typename M>
   698   inline MapToFunctor<M> mapToFunctor(const M &m) {
   699     return MapToFunctor<M>(m);
   700   }
   701 
   702 
   703   /// \brief Map adaptor to convert the \c Value type of a map to
   704   /// another type using the default conversion.
   705 
   706   /// Map adaptor to convert the \c Value type of a \ref concepts::ReadMap
   707   /// "readable map" to another type using the default conversion.
   708   /// The \c Key type of it is inherited from \c M and the \c Value
   709   /// type is \c V.
   710   /// This type conforms the \ref concepts::ReadMap "ReadMap" concept.
   711   ///
   712   /// The simplest way of using this map is through the convertMap()
   713   /// function.
   714   template <typename M, typename V>
   715   class ConvertMap : public MapBase<typename M::Key, V> {
   716     const M &_m;
   717   public:
   718     ///\e
   719     typedef typename M::Key Key;
   720     ///\e
   721     typedef V Value;
   722 
   723     /// Constructor
   724 
   725     /// Constructor.
   726     /// \param m The underlying map.
   727     ConvertMap(const M &m) : _m(m) {}
   728 
   729     ///\e
   730     Value operator[](const Key &k) const { return _m[k]; }
   731   };
   732 
   733   /// Returns a \c ConvertMap class
   734 
   735   /// This function just returns a \c ConvertMap class.
   736   /// \relates ConvertMap
   737   template<typename V, typename M>
   738   inline ConvertMap<M, V> convertMap(const M &map) {
   739     return ConvertMap<M, V>(map);
   740   }
   741 
   742 
   743   /// Applies all map setting operations to two maps
   744 
   745   /// This map has two \ref concepts::WriteMap "writable map" parameters
   746   /// and each write request will be passed to both of them.
   747   /// If \c M1 is also \ref concepts::ReadMap "readable", then the read
   748   /// operations will return the corresponding values of \c M1.
   749   ///
   750   /// The \c Key and \c Value types are inherited from \c M1.
   751   /// The \c Key and \c Value of \c M2 must be convertible from those
   752   /// of \c M1.
   753   ///
   754   /// The simplest way of using this map is through the forkMap()
   755   /// function.
   756   template<typename  M1, typename M2>
   757   class ForkMap : public MapBase<typename M1::Key, typename M1::Value> {
   758     M1 &_m1;
   759     M2 &_m2;
   760   public:
   761     ///\e
   762     typedef typename M1::Key Key;
   763     ///\e
   764     typedef typename M1::Value Value;
   765 
   766     /// Constructor
   767     ForkMap(M1 &m1, M2 &m2) : _m1(m1), _m2(m2) {}
   768     /// Returns the value associated with the given key in the first map.
   769     Value operator[](const Key &k) const { return _m1[k]; }
   770     /// Sets the value associated with the given key in both maps.
   771     void set(const Key &k, const Value &v) { _m1.set(k,v); _m2.set(k,v); }
   772   };
   773 
   774   /// Returns a \c ForkMap class
   775 
   776   /// This function just returns a \c ForkMap class.
   777   /// \relates ForkMap
   778   template <typename M1, typename M2>
   779   inline ForkMap<M1,M2> forkMap(M1 &m1, M2 &m2) {
   780     return ForkMap<M1,M2>(m1,m2);
   781   }
   782 
   783 
   784   /// Sum of two maps
   785 
   786   /// This \ref concepts::ReadMap "read-only map" returns the sum
   787   /// of the values of the two given maps.
   788   /// Its \c Key and \c Value types are inherited from \c M1.
   789   /// The \c Key and \c Value of \c M2 must be convertible to those of
   790   /// \c M1.
   791   ///
   792   /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
   793   /// \code
   794   ///   AddMap<M1,M2> am(m1,m2);
   795   /// \endcode
   796   /// <tt>am[x]</tt> will be equal to <tt>m1[x]+m2[x]</tt>.
   797   ///
   798   /// The simplest way of using this map is through the addMap()
   799   /// function.
   800   ///
   801   /// \sa SubMap, MulMap, DivMap
   802   /// \sa ShiftMap, ShiftWriteMap
   803   template<typename M1, typename M2>
   804   class AddMap : public MapBase<typename M1::Key, typename M1::Value> {
   805     const M1 &_m1;
   806     const M2 &_m2;
   807   public:
   808     ///\e
   809     typedef typename M1::Key Key;
   810     ///\e
   811     typedef typename M1::Value Value;
   812 
   813     /// Constructor
   814     AddMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
   815     ///\e
   816     Value operator[](const Key &k) const { return _m1[k]+_m2[k]; }
   817   };
   818 
   819   /// Returns an \c AddMap class
   820 
   821   /// This function just returns an \c AddMap class.
   822   ///
   823   /// For example, if \c m1 and \c m2 are both maps with \c double
   824   /// values, then <tt>addMap(m1,m2)[x]</tt> will be equal to
   825   /// <tt>m1[x]+m2[x]</tt>.
   826   ///
   827   /// \relates AddMap
   828   template<typename M1, typename M2>
   829   inline AddMap<M1, M2> addMap(const M1 &m1, const M2 &m2) {
   830     return AddMap<M1, M2>(m1,m2);
   831   }
   832 
   833 
   834   /// Difference of two maps
   835 
   836   /// This \ref concepts::ReadMap "read-only map" returns the difference
   837   /// of the values of the two given maps.
   838   /// Its \c Key and \c Value types are inherited from \c M1.
   839   /// The \c Key and \c Value of \c M2 must be convertible to those of
   840   /// \c M1.
   841   ///
   842   /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
   843   /// \code
   844   ///   SubMap<M1,M2> sm(m1,m2);
   845   /// \endcode
   846   /// <tt>sm[x]</tt> will be equal to <tt>m1[x]-m2[x]</tt>.
   847   ///
   848   /// The simplest way of using this map is through the subMap()
   849   /// function.
   850   ///
   851   /// \sa AddMap, MulMap, DivMap
   852   template<typename M1, typename M2>
   853   class SubMap : public MapBase<typename M1::Key, typename M1::Value> {
   854     const M1 &_m1;
   855     const M2 &_m2;
   856   public:
   857     ///\e
   858     typedef typename M1::Key Key;
   859     ///\e
   860     typedef typename M1::Value Value;
   861 
   862     /// Constructor
   863     SubMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
   864     ///\e
   865     Value operator[](const Key &k) const { return _m1[k]-_m2[k]; }
   866   };
   867 
   868   /// Returns a \c SubMap class
   869 
   870   /// This function just returns a \c SubMap class.
   871   ///
   872   /// For example, if \c m1 and \c m2 are both maps with \c double
   873   /// values, then <tt>subMap(m1,m2)[x]</tt> will be equal to
   874   /// <tt>m1[x]-m2[x]</tt>.
   875   ///
   876   /// \relates SubMap
   877   template<typename M1, typename M2>
   878   inline SubMap<M1, M2> subMap(const M1 &m1, const M2 &m2) {
   879     return SubMap<M1, M2>(m1,m2);
   880   }
   881 
   882 
   883   /// Product of two maps
   884 
   885   /// This \ref concepts::ReadMap "read-only map" returns the product
   886   /// of the values of the two given maps.
   887   /// Its \c Key and \c Value types are inherited from \c M1.
   888   /// The \c Key and \c Value of \c M2 must be convertible to those of
   889   /// \c M1.
   890   ///
   891   /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
   892   /// \code
   893   ///   MulMap<M1,M2> mm(m1,m2);
   894   /// \endcode
   895   /// <tt>mm[x]</tt> will be equal to <tt>m1[x]*m2[x]</tt>.
   896   ///
   897   /// The simplest way of using this map is through the mulMap()
   898   /// function.
   899   ///
   900   /// \sa AddMap, SubMap, DivMap
   901   /// \sa ScaleMap, ScaleWriteMap
   902   template<typename M1, typename M2>
   903   class MulMap : public MapBase<typename M1::Key, typename M1::Value> {
   904     const M1 &_m1;
   905     const M2 &_m2;
   906   public:
   907     ///\e
   908     typedef typename M1::Key Key;
   909     ///\e
   910     typedef typename M1::Value Value;
   911 
   912     /// Constructor
   913     MulMap(const M1 &m1,const M2 &m2) : _m1(m1), _m2(m2) {}
   914     ///\e
   915     Value operator[](const Key &k) const { return _m1[k]*_m2[k]; }
   916   };
   917 
   918   /// Returns a \c MulMap class
   919 
   920   /// This function just returns a \c MulMap class.
   921   ///
   922   /// For example, if \c m1 and \c m2 are both maps with \c double
   923   /// values, then <tt>mulMap(m1,m2)[x]</tt> will be equal to
   924   /// <tt>m1[x]*m2[x]</tt>.
   925   ///
   926   /// \relates MulMap
   927   template<typename M1, typename M2>
   928   inline MulMap<M1, M2> mulMap(const M1 &m1,const M2 &m2) {
   929     return MulMap<M1, M2>(m1,m2);
   930   }
   931 
   932 
   933   /// Quotient of two maps
   934 
   935   /// This \ref concepts::ReadMap "read-only map" returns the quotient
   936   /// of the values of the two given maps.
   937   /// Its \c Key and \c Value types are inherited from \c M1.
   938   /// The \c Key and \c Value of \c M2 must be convertible to those of
   939   /// \c M1.
   940   ///
   941   /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
   942   /// \code
   943   ///   DivMap<M1,M2> dm(m1,m2);
   944   /// \endcode
   945   /// <tt>dm[x]</tt> will be equal to <tt>m1[x]/m2[x]</tt>.
   946   ///
   947   /// The simplest way of using this map is through the divMap()
   948   /// function.
   949   ///
   950   /// \sa AddMap, SubMap, MulMap
   951   template<typename M1, typename M2>
   952   class DivMap : public MapBase<typename M1::Key, typename M1::Value> {
   953     const M1 &_m1;
   954     const M2 &_m2;
   955   public:
   956     ///\e
   957     typedef typename M1::Key Key;
   958     ///\e
   959     typedef typename M1::Value Value;
   960 
   961     /// Constructor
   962     DivMap(const M1 &m1,const M2 &m2) : _m1(m1), _m2(m2) {}
   963     ///\e
   964     Value operator[](const Key &k) const { return _m1[k]/_m2[k]; }
   965   };
   966 
   967   /// Returns a \c DivMap class
   968 
   969   /// This function just returns a \c DivMap class.
   970   ///
   971   /// For example, if \c m1 and \c m2 are both maps with \c double
   972   /// values, then <tt>divMap(m1,m2)[x]</tt> will be equal to
   973   /// <tt>m1[x]/m2[x]</tt>.
   974   ///
   975   /// \relates DivMap
   976   template<typename M1, typename M2>
   977   inline DivMap<M1, M2> divMap(const M1 &m1,const M2 &m2) {
   978     return DivMap<M1, M2>(m1,m2);
   979   }
   980 
   981 
   982   /// Shifts a map with a constant.
   983 
   984   /// This \ref concepts::ReadMap "read-only map" returns the sum of
   985   /// the given map and a constant value (i.e. it shifts the map with
   986   /// the constant). Its \c Key and \c Value are inherited from \c M.
   987   ///
   988   /// Actually,
   989   /// \code
   990   ///   ShiftMap<M> sh(m,v);
   991   /// \endcode
   992   /// is equivalent to
   993   /// \code
   994   ///   ConstMap<M::Key, M::Value> cm(v);
   995   ///   AddMap<M, ConstMap<M::Key, M::Value> > sh(m,cm);
   996   /// \endcode
   997   ///
   998   /// The simplest way of using this map is through the shiftMap()
   999   /// function.
  1000   ///
  1001   /// \sa ShiftWriteMap
  1002   template<typename M, typename C = typename M::Value>
  1003   class ShiftMap : public MapBase<typename M::Key, typename M::Value> {
  1004     const M &_m;
  1005     C _v;
  1006   public:
  1007     ///\e
  1008     typedef typename M::Key Key;
  1009     ///\e
  1010     typedef typename M::Value Value;
  1011 
  1012     /// Constructor
  1013 
  1014     /// Constructor.
  1015     /// \param m The undelying map.
  1016     /// \param v The constant value.
  1017     ShiftMap(const M &m, const C &v) : _m(m), _v(v) {}
  1018     ///\e
  1019     Value operator[](const Key &k) const { return _m[k]+_v; }
  1020   };
  1021 
  1022   /// Shifts a map with a constant (read-write version).
  1023 
  1024   /// This \ref concepts::ReadWriteMap "read-write map" returns the sum
  1025   /// of the given map and a constant value (i.e. it shifts the map with
  1026   /// the constant). Its \c Key and \c Value are inherited from \c M.
  1027   /// It makes also possible to write the map.
  1028   ///
  1029   /// The simplest way of using this map is through the shiftWriteMap()
  1030   /// function.
  1031   ///
  1032   /// \sa ShiftMap
  1033   template<typename M, typename C = typename M::Value>
  1034   class ShiftWriteMap : public MapBase<typename M::Key, typename M::Value> {
  1035     M &_m;
  1036     C _v;
  1037   public:
  1038     ///\e
  1039     typedef typename M::Key Key;
  1040     ///\e
  1041     typedef typename M::Value Value;
  1042 
  1043     /// Constructor
  1044 
  1045     /// Constructor.
  1046     /// \param m The undelying map.
  1047     /// \param v The constant value.
  1048     ShiftWriteMap(M &m, const C &v) : _m(m), _v(v) {}
  1049     ///\e
  1050     Value operator[](const Key &k) const { return _m[k]+_v; }
  1051     ///\e
  1052     void set(const Key &k, const Value &v) { _m.set(k, v-_v); }
  1053   };
  1054 
  1055   /// Returns a \c ShiftMap class
  1056 
  1057   /// This function just returns a \c ShiftMap class.
  1058   ///
  1059   /// For example, if \c m is a map with \c double values and \c v is
  1060   /// \c double, then <tt>shiftMap(m,v)[x]</tt> will be equal to
  1061   /// <tt>m[x]+v</tt>.
  1062   ///
  1063   /// \relates ShiftMap
  1064   template<typename M, typename C>
  1065   inline ShiftMap<M, C> shiftMap(const M &m, const C &v) {
  1066     return ShiftMap<M, C>(m,v);
  1067   }
  1068 
  1069   /// Returns a \c ShiftWriteMap class
  1070 
  1071   /// This function just returns a \c ShiftWriteMap class.
  1072   ///
  1073   /// For example, if \c m is a map with \c double values and \c v is
  1074   /// \c double, then <tt>shiftWriteMap(m,v)[x]</tt> will be equal to
  1075   /// <tt>m[x]+v</tt>.
  1076   /// Moreover it makes also possible to write the map.
  1077   ///
  1078   /// \relates ShiftWriteMap
  1079   template<typename M, typename C>
  1080   inline ShiftWriteMap<M, C> shiftWriteMap(M &m, const C &v) {
  1081     return ShiftWriteMap<M, C>(m,v);
  1082   }
  1083 
  1084 
  1085   /// Scales a map with a constant.
  1086 
  1087   /// This \ref concepts::ReadMap "read-only map" returns the value of
  1088   /// the given map multiplied from the left side with a constant value.
  1089   /// Its \c Key and \c Value are inherited from \c M.
  1090   ///
  1091   /// Actually,
  1092   /// \code
  1093   ///   ScaleMap<M> sc(m,v);
  1094   /// \endcode
  1095   /// is equivalent to
  1096   /// \code
  1097   ///   ConstMap<M::Key, M::Value> cm(v);
  1098   ///   MulMap<ConstMap<M::Key, M::Value>, M> sc(cm,m);
  1099   /// \endcode
  1100   ///
  1101   /// The simplest way of using this map is through the scaleMap()
  1102   /// function.
  1103   ///
  1104   /// \sa ScaleWriteMap
  1105   template<typename M, typename C = typename M::Value>
  1106   class ScaleMap : public MapBase<typename M::Key, typename M::Value> {
  1107     const M &_m;
  1108     C _v;
  1109   public:
  1110     ///\e
  1111     typedef typename M::Key Key;
  1112     ///\e
  1113     typedef typename M::Value Value;
  1114 
  1115     /// Constructor
  1116 
  1117     /// Constructor.
  1118     /// \param m The undelying map.
  1119     /// \param v The constant value.
  1120     ScaleMap(const M &m, const C &v) : _m(m), _v(v) {}
  1121     ///\e
  1122     Value operator[](const Key &k) const { return _v*_m[k]; }
  1123   };
  1124 
  1125   /// Scales a map with a constant (read-write version).
  1126 
  1127   /// This \ref concepts::ReadWriteMap "read-write map" returns the value of
  1128   /// the given map multiplied from the left side with a constant value.
  1129   /// Its \c Key and \c Value are inherited from \c M.
  1130   /// It can also be used as write map if the \c / operator is defined
  1131   /// between \c Value and \c C and the given multiplier is not zero.
  1132   ///
  1133   /// The simplest way of using this map is through the scaleWriteMap()
  1134   /// function.
  1135   ///
  1136   /// \sa ScaleMap
  1137   template<typename M, typename C = typename M::Value>
  1138   class ScaleWriteMap : public MapBase<typename M::Key, typename M::Value> {
  1139     M &_m;
  1140     C _v;
  1141   public:
  1142     ///\e
  1143     typedef typename M::Key Key;
  1144     ///\e
  1145     typedef typename M::Value Value;
  1146 
  1147     /// Constructor
  1148 
  1149     /// Constructor.
  1150     /// \param m The undelying map.
  1151     /// \param v The constant value.
  1152     ScaleWriteMap(M &m, const C &v) : _m(m), _v(v) {}
  1153     ///\e
  1154     Value operator[](const Key &k) const { return _v*_m[k]; }
  1155     ///\e
  1156     void set(const Key &k, const Value &v) { _m.set(k, v/_v); }
  1157   };
  1158 
  1159   /// Returns a \c ScaleMap class
  1160 
  1161   /// This function just returns a \c ScaleMap class.
  1162   ///
  1163   /// For example, if \c m is a map with \c double values and \c v is
  1164   /// \c double, then <tt>scaleMap(m,v)[x]</tt> will be equal to
  1165   /// <tt>v*m[x]</tt>.
  1166   ///
  1167   /// \relates ScaleMap
  1168   template<typename M, typename C>
  1169   inline ScaleMap<M, C> scaleMap(const M &m, const C &v) {
  1170     return ScaleMap<M, C>(m,v);
  1171   }
  1172 
  1173   /// Returns a \c ScaleWriteMap class
  1174 
  1175   /// This function just returns a \c ScaleWriteMap class.
  1176   ///
  1177   /// For example, if \c m is a map with \c double values and \c v is
  1178   /// \c double, then <tt>scaleWriteMap(m,v)[x]</tt> will be equal to
  1179   /// <tt>v*m[x]</tt>.
  1180   /// Moreover it makes also possible to write the map.
  1181   ///
  1182   /// \relates ScaleWriteMap
  1183   template<typename M, typename C>
  1184   inline ScaleWriteMap<M, C> scaleWriteMap(M &m, const C &v) {
  1185     return ScaleWriteMap<M, C>(m,v);
  1186   }
  1187 
  1188 
  1189   /// Negative of a map
  1190 
  1191   /// This \ref concepts::ReadMap "read-only map" returns the negative
  1192   /// of the values of the given map (using the unary \c - operator).
  1193   /// Its \c Key and \c Value are inherited from \c M.
  1194   ///
  1195   /// If M::Value is \c int, \c double etc., then
  1196   /// \code
  1197   ///   NegMap<M> neg(m);
  1198   /// \endcode
  1199   /// is equivalent to
  1200   /// \code
  1201   ///   ScaleMap<M> neg(m,-1);
  1202   /// \endcode
  1203   ///
  1204   /// The simplest way of using this map is through the negMap()
  1205   /// function.
  1206   ///
  1207   /// \sa NegWriteMap
  1208   template<typename M>
  1209   class NegMap : public MapBase<typename M::Key, typename M::Value> {
  1210     const M& _m;
  1211   public:
  1212     ///\e
  1213     typedef typename M::Key Key;
  1214     ///\e
  1215     typedef typename M::Value Value;
  1216 
  1217     /// Constructor
  1218     NegMap(const M &m) : _m(m) {}
  1219     ///\e
  1220     Value operator[](const Key &k) const { return -_m[k]; }
  1221   };
  1222 
  1223   /// Negative of a map (read-write version)
  1224 
  1225   /// This \ref concepts::ReadWriteMap "read-write map" returns the
  1226   /// negative of the values of the given map (using the unary \c -
  1227   /// operator).
  1228   /// Its \c Key and \c Value are inherited from \c M.
  1229   /// It makes also possible to write the map.
  1230   ///
  1231   /// If M::Value is \c int, \c double etc., then
  1232   /// \code
  1233   ///   NegWriteMap<M> neg(m);
  1234   /// \endcode
  1235   /// is equivalent to
  1236   /// \code
  1237   ///   ScaleWriteMap<M> neg(m,-1);
  1238   /// \endcode
  1239   ///
  1240   /// The simplest way of using this map is through the negWriteMap()
  1241   /// function.
  1242   ///
  1243   /// \sa NegMap
  1244   template<typename M>
  1245   class NegWriteMap : public MapBase<typename M::Key, typename M::Value> {
  1246     M &_m;
  1247   public:
  1248     ///\e
  1249     typedef typename M::Key Key;
  1250     ///\e
  1251     typedef typename M::Value Value;
  1252 
  1253     /// Constructor
  1254     NegWriteMap(M &m) : _m(m) {}
  1255     ///\e
  1256     Value operator[](const Key &k) const { return -_m[k]; }
  1257     ///\e
  1258     void set(const Key &k, const Value &v) { _m.set(k, -v); }
  1259   };
  1260 
  1261   /// Returns a \c NegMap class
  1262 
  1263   /// This function just returns a \c NegMap class.
  1264   ///
  1265   /// For example, if \c m is a map with \c double values, then
  1266   /// <tt>negMap(m)[x]</tt> will be equal to <tt>-m[x]</tt>.
  1267   ///
  1268   /// \relates NegMap
  1269   template <typename M>
  1270   inline NegMap<M> negMap(const M &m) {
  1271     return NegMap<M>(m);
  1272   }
  1273 
  1274   /// Returns a \c NegWriteMap class
  1275 
  1276   /// This function just returns a \c NegWriteMap class.
  1277   ///
  1278   /// For example, if \c m is a map with \c double values, then
  1279   /// <tt>negWriteMap(m)[x]</tt> will be equal to <tt>-m[x]</tt>.
  1280   /// Moreover it makes also possible to write the map.
  1281   ///
  1282   /// \relates NegWriteMap
  1283   template <typename M>
  1284   inline NegWriteMap<M> negWriteMap(M &m) {
  1285     return NegWriteMap<M>(m);
  1286   }
  1287 
  1288 
  1289   /// Absolute value of a map
  1290 
  1291   /// This \ref concepts::ReadMap "read-only map" returns the absolute
  1292   /// value of the values of the given map.
  1293   /// Its \c Key and \c Value are inherited from \c M.
  1294   /// \c Value must be comparable to \c 0 and the unary \c -
  1295   /// operator must be defined for it, of course.
  1296   ///
  1297   /// The simplest way of using this map is through the absMap()
  1298   /// function.
  1299   template<typename M>
  1300   class AbsMap : public MapBase<typename M::Key, typename M::Value> {
  1301     const M &_m;
  1302   public:
  1303     ///\e
  1304     typedef typename M::Key Key;
  1305     ///\e
  1306     typedef typename M::Value Value;
  1307 
  1308     /// Constructor
  1309     AbsMap(const M &m) : _m(m) {}
  1310     ///\e
  1311     Value operator[](const Key &k) const {
  1312       Value tmp = _m[k];
  1313       return tmp >= 0 ? tmp : -tmp;
  1314     }
  1315 
  1316   };
  1317 
  1318   /// Returns an \c AbsMap class
  1319 
  1320   /// This function just returns an \c AbsMap class.
  1321   ///
  1322   /// For example, if \c m is a map with \c double values, then
  1323   /// <tt>absMap(m)[x]</tt> will be equal to <tt>m[x]</tt> if
  1324   /// it is positive or zero and <tt>-m[x]</tt> if <tt>m[x]</tt> is
  1325   /// negative.
  1326   ///
  1327   /// \relates AbsMap
  1328   template<typename M>
  1329   inline AbsMap<M> absMap(const M &m) {
  1330     return AbsMap<M>(m);
  1331   }
  1332 
  1333   /// @}
  1334 
  1335   // Logical maps and map adaptors:
  1336 
  1337   /// \addtogroup maps
  1338   /// @{
  1339 
  1340   /// Constant \c true map.
  1341 
  1342   /// This \ref concepts::ReadMap "read-only map" assigns \c true to
  1343   /// each key.
  1344   ///
  1345   /// Note that
  1346   /// \code
  1347   ///   TrueMap<K> tm;
  1348   /// \endcode
  1349   /// is equivalent to
  1350   /// \code
  1351   ///   ConstMap<K,bool> tm(true);
  1352   /// \endcode
  1353   ///
  1354   /// \sa FalseMap
  1355   /// \sa ConstMap
  1356   template <typename K>
  1357   class TrueMap : public MapBase<K, bool> {
  1358   public:
  1359     ///\e
  1360     typedef K Key;
  1361     ///\e
  1362     typedef bool Value;
  1363 
  1364     /// Gives back \c true.
  1365     Value operator[](const Key&) const { return true; }
  1366   };
  1367 
  1368   /// Returns a \c TrueMap class
  1369 
  1370   /// This function just returns a \c TrueMap class.
  1371   /// \relates TrueMap
  1372   template<typename K>
  1373   inline TrueMap<K> trueMap() {
  1374     return TrueMap<K>();
  1375   }
  1376 
  1377 
  1378   /// Constant \c false map.
  1379 
  1380   /// This \ref concepts::ReadMap "read-only map" assigns \c false to
  1381   /// each key.
  1382   ///
  1383   /// Note that
  1384   /// \code
  1385   ///   FalseMap<K> fm;
  1386   /// \endcode
  1387   /// is equivalent to
  1388   /// \code
  1389   ///   ConstMap<K,bool> fm(false);
  1390   /// \endcode
  1391   ///
  1392   /// \sa TrueMap
  1393   /// \sa ConstMap
  1394   template <typename K>
  1395   class FalseMap : public MapBase<K, bool> {
  1396   public:
  1397     ///\e
  1398     typedef K Key;
  1399     ///\e
  1400     typedef bool Value;
  1401 
  1402     /// Gives back \c false.
  1403     Value operator[](const Key&) const { return false; }
  1404   };
  1405 
  1406   /// Returns a \c FalseMap class
  1407 
  1408   /// This function just returns a \c FalseMap class.
  1409   /// \relates FalseMap
  1410   template<typename K>
  1411   inline FalseMap<K> falseMap() {
  1412     return FalseMap<K>();
  1413   }
  1414 
  1415   /// @}
  1416 
  1417   /// \addtogroup map_adaptors
  1418   /// @{
  1419 
  1420   /// Logical 'and' of two maps
  1421 
  1422   /// This \ref concepts::ReadMap "read-only map" returns the logical
  1423   /// 'and' of the values of the two given maps.
  1424   /// Its \c Key type is inherited from \c M1 and its \c Value type is
  1425   /// \c bool. \c M2::Key must be convertible to \c M1::Key.
  1426   ///
  1427   /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
  1428   /// \code
  1429   ///   AndMap<M1,M2> am(m1,m2);
  1430   /// \endcode
  1431   /// <tt>am[x]</tt> will be equal to <tt>m1[x]&&m2[x]</tt>.
  1432   ///
  1433   /// The simplest way of using this map is through the andMap()
  1434   /// function.
  1435   ///
  1436   /// \sa OrMap
  1437   /// \sa NotMap, NotWriteMap
  1438   template<typename M1, typename M2>
  1439   class AndMap : public MapBase<typename M1::Key, bool> {
  1440     const M1 &_m1;
  1441     const M2 &_m2;
  1442   public:
  1443     ///\e
  1444     typedef typename M1::Key Key;
  1445     ///\e
  1446     typedef bool Value;
  1447 
  1448     /// Constructor
  1449     AndMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
  1450     ///\e
  1451     Value operator[](const Key &k) const { return _m1[k]&&_m2[k]; }
  1452   };
  1453 
  1454   /// Returns an \c AndMap class
  1455 
  1456   /// This function just returns an \c AndMap class.
  1457   ///
  1458   /// For example, if \c m1 and \c m2 are both maps with \c bool values,
  1459   /// then <tt>andMap(m1,m2)[x]</tt> will be equal to
  1460   /// <tt>m1[x]&&m2[x]</tt>.
  1461   ///
  1462   /// \relates AndMap
  1463   template<typename M1, typename M2>
  1464   inline AndMap<M1, M2> andMap(const M1 &m1, const M2 &m2) {
  1465     return AndMap<M1, M2>(m1,m2);
  1466   }
  1467 
  1468 
  1469   /// Logical 'or' of two maps
  1470 
  1471   /// This \ref concepts::ReadMap "read-only map" returns the logical
  1472   /// 'or' of the values of the two given maps.
  1473   /// Its \c Key type is inherited from \c M1 and its \c Value type is
  1474   /// \c bool. \c M2::Key must be convertible to \c M1::Key.
  1475   ///
  1476   /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
  1477   /// \code
  1478   ///   OrMap<M1,M2> om(m1,m2);
  1479   /// \endcode
  1480   /// <tt>om[x]</tt> will be equal to <tt>m1[x]||m2[x]</tt>.
  1481   ///
  1482   /// The simplest way of using this map is through the orMap()
  1483   /// function.
  1484   ///
  1485   /// \sa AndMap
  1486   /// \sa NotMap, NotWriteMap
  1487   template<typename M1, typename M2>
  1488   class OrMap : public MapBase<typename M1::Key, bool> {
  1489     const M1 &_m1;
  1490     const M2 &_m2;
  1491   public:
  1492     ///\e
  1493     typedef typename M1::Key Key;
  1494     ///\e
  1495     typedef bool Value;
  1496 
  1497     /// Constructor
  1498     OrMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
  1499     ///\e
  1500     Value operator[](const Key &k) const { return _m1[k]||_m2[k]; }
  1501   };
  1502 
  1503   /// Returns an \c OrMap class
  1504 
  1505   /// This function just returns an \c OrMap class.
  1506   ///
  1507   /// For example, if \c m1 and \c m2 are both maps with \c bool values,
  1508   /// then <tt>orMap(m1,m2)[x]</tt> will be equal to
  1509   /// <tt>m1[x]||m2[x]</tt>.
  1510   ///
  1511   /// \relates OrMap
  1512   template<typename M1, typename M2>
  1513   inline OrMap<M1, M2> orMap(const M1 &m1, const M2 &m2) {
  1514     return OrMap<M1, M2>(m1,m2);
  1515   }
  1516 
  1517 
  1518   /// Logical 'not' of a map
  1519 
  1520   /// This \ref concepts::ReadMap "read-only map" returns the logical
  1521   /// negation of the values of the given map.
  1522   /// Its \c Key is inherited from \c M and its \c Value is \c bool.
  1523   ///
  1524   /// The simplest way of using this map is through the notMap()
  1525   /// function.
  1526   ///
  1527   /// \sa NotWriteMap
  1528   template <typename M>
  1529   class NotMap : public MapBase<typename M::Key, bool> {
  1530     const M &_m;
  1531   public:
  1532     ///\e
  1533     typedef typename M::Key Key;
  1534     ///\e
  1535     typedef bool Value;
  1536 
  1537     /// Constructor
  1538     NotMap(const M &m) : _m(m) {}
  1539     ///\e
  1540     Value operator[](const Key &k) const { return !_m[k]; }
  1541   };
  1542 
  1543   /// Logical 'not' of a map (read-write version)
  1544 
  1545   /// This \ref concepts::ReadWriteMap "read-write map" returns the
  1546   /// logical negation of the values of the given map.
  1547   /// Its \c Key is inherited from \c M and its \c Value is \c bool.
  1548   /// It makes also possible to write the map. When a value is set,
  1549   /// the opposite value is set to the original map.
  1550   ///
  1551   /// The simplest way of using this map is through the notWriteMap()
  1552   /// function.
  1553   ///
  1554   /// \sa NotMap
  1555   template <typename M>
  1556   class NotWriteMap : public MapBase<typename M::Key, bool> {
  1557     M &_m;
  1558   public:
  1559     ///\e
  1560     typedef typename M::Key Key;
  1561     ///\e
  1562     typedef bool Value;
  1563 
  1564     /// Constructor
  1565     NotWriteMap(M &m) : _m(m) {}
  1566     ///\e
  1567     Value operator[](const Key &k) const { return !_m[k]; }
  1568     ///\e
  1569     void set(const Key &k, bool v) { _m.set(k, !v); }
  1570   };
  1571 
  1572   /// Returns a \c NotMap class
  1573 
  1574   /// This function just returns a \c NotMap class.
  1575   ///
  1576   /// For example, if \c m is a map with \c bool values, then
  1577   /// <tt>notMap(m)[x]</tt> will be equal to <tt>!m[x]</tt>.
  1578   ///
  1579   /// \relates NotMap
  1580   template <typename M>
  1581   inline NotMap<M> notMap(const M &m) {
  1582     return NotMap<M>(m);
  1583   }
  1584 
  1585   /// Returns a \c NotWriteMap class
  1586 
  1587   /// This function just returns a \c NotWriteMap class.
  1588   ///
  1589   /// For example, if \c m is a map with \c bool values, then
  1590   /// <tt>notWriteMap(m)[x]</tt> will be equal to <tt>!m[x]</tt>.
  1591   /// Moreover it makes also possible to write the map.
  1592   ///
  1593   /// \relates NotWriteMap
  1594   template <typename M>
  1595   inline NotWriteMap<M> notWriteMap(M &m) {
  1596     return NotWriteMap<M>(m);
  1597   }
  1598 
  1599 
  1600   /// Combination of two maps using the \c == operator
  1601 
  1602   /// This \ref concepts::ReadMap "read-only map" assigns \c true to
  1603   /// the keys for which the corresponding values of the two maps are
  1604   /// equal.
  1605   /// Its \c Key type is inherited from \c M1 and its \c Value type is
  1606   /// \c bool. \c M2::Key must be convertible to \c M1::Key.
  1607   ///
  1608   /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
  1609   /// \code
  1610   ///   EqualMap<M1,M2> em(m1,m2);
  1611   /// \endcode
  1612   /// <tt>em[x]</tt> will be equal to <tt>m1[x]==m2[x]</tt>.
  1613   ///
  1614   /// The simplest way of using this map is through the equalMap()
  1615   /// function.
  1616   ///
  1617   /// \sa LessMap
  1618   template<typename M1, typename M2>
  1619   class EqualMap : public MapBase<typename M1::Key, bool> {
  1620     const M1 &_m1;
  1621     const M2 &_m2;
  1622   public:
  1623     ///\e
  1624     typedef typename M1::Key Key;
  1625     ///\e
  1626     typedef bool Value;
  1627 
  1628     /// Constructor
  1629     EqualMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
  1630     ///\e
  1631     Value operator[](const Key &k) const { return _m1[k]==_m2[k]; }
  1632   };
  1633 
  1634   /// Returns an \c EqualMap class
  1635 
  1636   /// This function just returns an \c EqualMap class.
  1637   ///
  1638   /// For example, if \c m1 and \c m2 are maps with keys and values of
  1639   /// the same type, then <tt>equalMap(m1,m2)[x]</tt> will be equal to
  1640   /// <tt>m1[x]==m2[x]</tt>.
  1641   ///
  1642   /// \relates EqualMap
  1643   template<typename M1, typename M2>
  1644   inline EqualMap<M1, M2> equalMap(const M1 &m1, const M2 &m2) {
  1645     return EqualMap<M1, M2>(m1,m2);
  1646   }
  1647 
  1648 
  1649   /// Combination of two maps using the \c < operator
  1650 
  1651   /// This \ref concepts::ReadMap "read-only map" assigns \c true to
  1652   /// the keys for which the corresponding value of the first map is
  1653   /// less then the value of the second map.
  1654   /// Its \c Key type is inherited from \c M1 and its \c Value type is
  1655   /// \c bool. \c M2::Key must be convertible to \c M1::Key.
  1656   ///
  1657   /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
  1658   /// \code
  1659   ///   LessMap<M1,M2> lm(m1,m2);
  1660   /// \endcode
  1661   /// <tt>lm[x]</tt> will be equal to <tt>m1[x]<m2[x]</tt>.
  1662   ///
  1663   /// The simplest way of using this map is through the lessMap()
  1664   /// function.
  1665   ///
  1666   /// \sa EqualMap
  1667   template<typename M1, typename M2>
  1668   class LessMap : public MapBase<typename M1::Key, bool> {
  1669     const M1 &_m1;
  1670     const M2 &_m2;
  1671   public:
  1672     ///\e
  1673     typedef typename M1::Key Key;
  1674     ///\e
  1675     typedef bool Value;
  1676 
  1677     /// Constructor
  1678     LessMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
  1679     ///\e
  1680     Value operator[](const Key &k) const { return _m1[k]<_m2[k]; }
  1681   };
  1682 
  1683   /// Returns an \c LessMap class
  1684 
  1685   /// This function just returns an \c LessMap class.
  1686   ///
  1687   /// For example, if \c m1 and \c m2 are maps with keys and values of
  1688   /// the same type, then <tt>lessMap(m1,m2)[x]</tt> will be equal to
  1689   /// <tt>m1[x]<m2[x]</tt>.
  1690   ///
  1691   /// \relates LessMap
  1692   template<typename M1, typename M2>
  1693   inline LessMap<M1, M2> lessMap(const M1 &m1, const M2 &m2) {
  1694     return LessMap<M1, M2>(m1,m2);
  1695   }
  1696 
  1697   namespace _maps_bits {
  1698 
  1699     template <typename _Iterator, typename Enable = void>
  1700     struct IteratorTraits {
  1701       typedef typename std::iterator_traits<_Iterator>::value_type Value;
  1702     };
  1703 
  1704     template <typename _Iterator>
  1705     struct IteratorTraits<_Iterator,
  1706       typename exists<typename _Iterator::container_type>::type>
  1707     {
  1708       typedef typename _Iterator::container_type::value_type Value;
  1709     };
  1710 
  1711   }
  1712 
  1713   /// @}
  1714 
  1715   /// \addtogroup maps
  1716   /// @{
  1717 
  1718   /// \brief Writable bool map for logging each \c true assigned element
  1719   ///
  1720   /// A \ref concepts::WriteMap "writable" bool map for logging
  1721   /// each \c true assigned element, i.e it copies subsequently each
  1722   /// keys set to \c true to the given iterator.
  1723   /// The most important usage of it is storing certain nodes or arcs
  1724   /// that were marked \c true by an algorithm.
  1725   ///
  1726   /// There are several algorithms that provide solutions through bool
  1727   /// maps and most of them assign \c true at most once for each key.
  1728   /// In these cases it is a natural request to store each \c true
  1729   /// assigned elements (in order of the assignment), which can be
  1730   /// easily done with LoggerBoolMap.
  1731   ///
  1732   /// The simplest way of using this map is through the loggerBoolMap()
  1733   /// function.
  1734   ///
  1735   /// \tparam IT The type of the iterator.
  1736   /// \tparam KEY The key type of the map. The default value set
  1737   /// according to the iterator type should work in most cases.
  1738   ///
  1739   /// \note The container of the iterator must contain enough space
  1740   /// for the elements or the iterator should be an inserter iterator.
  1741 #ifdef DOXYGEN
  1742   template <typename IT, typename KEY>
  1743 #else
  1744   template <typename IT,
  1745             typename KEY = typename _maps_bits::IteratorTraits<IT>::Value>
  1746 #endif
  1747   class LoggerBoolMap : public MapBase<KEY, bool> {
  1748   public:
  1749 
  1750     ///\e
  1751     typedef KEY Key;
  1752     ///\e
  1753     typedef bool Value;
  1754     ///\e
  1755     typedef IT Iterator;
  1756 
  1757     /// Constructor
  1758     LoggerBoolMap(Iterator it)
  1759       : _begin(it), _end(it) {}
  1760 
  1761     /// Gives back the given iterator set for the first key
  1762     Iterator begin() const {
  1763       return _begin;
  1764     }
  1765 
  1766     /// Gives back the the 'after the last' iterator
  1767     Iterator end() const {
  1768       return _end;
  1769     }
  1770 
  1771     /// The set function of the map
  1772     void set(const Key& key, Value value) {
  1773       if (value) {
  1774         *_end++ = key;
  1775       }
  1776     }
  1777 
  1778   private:
  1779     Iterator _begin;
  1780     Iterator _end;
  1781   };
  1782 
  1783   /// Returns a \c LoggerBoolMap class
  1784 
  1785   /// This function just returns a \c LoggerBoolMap class.
  1786   ///
  1787   /// The most important usage of it is storing certain nodes or arcs
  1788   /// that were marked \c true by an algorithm.
  1789   /// For example it makes easier to store the nodes in the processing
  1790   /// order of Dfs algorithm, as the following examples show.
  1791   /// \code
  1792   ///   std::vector<Node> v;
  1793   ///   dfs(g,s).processedMap(loggerBoolMap(std::back_inserter(v))).run();
  1794   /// \endcode
  1795   /// \code
  1796   ///   std::vector<Node> v(countNodes(g));
  1797   ///   dfs(g,s).processedMap(loggerBoolMap(v.begin())).run();
  1798   /// \endcode
  1799   ///
  1800   /// \note The container of the iterator must contain enough space
  1801   /// for the elements or the iterator should be an inserter iterator.
  1802   ///
  1803   /// \note LoggerBoolMap is just \ref concepts::WriteMap "writable", so
  1804   /// it cannot be used when a readable map is needed, for example as
  1805   /// \c ReachedMap for \c Bfs, \c Dfs and \c Dijkstra algorithms.
  1806   ///
  1807   /// \relates LoggerBoolMap
  1808   template<typename Iterator>
  1809   inline LoggerBoolMap<Iterator> loggerBoolMap(Iterator it) {
  1810     return LoggerBoolMap<Iterator>(it);
  1811   }
  1812 
  1813   /// @}
  1814 
  1815   /// \addtogroup graph_maps
  1816   /// @{
  1817 
  1818   /// \brief Provides an immutable and unique id for each item in a graph.
  1819   ///
  1820   /// IdMap provides a unique and immutable id for each item of the
  1821   /// same type (\c Node, \c Arc or \c Edge) in a graph. This id is 
  1822   ///  - \b unique: different items get different ids,
  1823   ///  - \b immutable: the id of an item does not change (even if you
  1824   ///    delete other nodes).
  1825   ///
  1826   /// Using this map you get access (i.e. can read) the inner id values of
  1827   /// the items stored in the graph, which is returned by the \c id()
  1828   /// function of the graph. This map can be inverted with its member
  1829   /// class \c InverseMap or with the \c operator() member.
  1830   ///
  1831   /// \tparam GR The graph type.
  1832   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  1833   /// \c GR::Edge).
  1834   ///
  1835   /// \see RangeIdMap
  1836   template <typename GR, typename K>
  1837   class IdMap : public MapBase<K, int> {
  1838   public:
  1839     /// The graph type of IdMap.
  1840     typedef GR Graph;
  1841     /// The key type of IdMap (\c Node, \c Arc or \c Edge).
  1842     typedef K Item;
  1843     /// The key type of IdMap (\c Node, \c Arc or \c Edge).
  1844     typedef K Key;
  1845     /// The value type of IdMap.
  1846     typedef int Value;
  1847 
  1848     /// \brief Constructor.
  1849     ///
  1850     /// Constructor of the map.
  1851     explicit IdMap(const Graph& graph) : _graph(&graph) {}
  1852 
  1853     /// \brief Gives back the \e id of the item.
  1854     ///
  1855     /// Gives back the immutable and unique \e id of the item.
  1856     int operator[](const Item& item) const { return _graph->id(item);}
  1857 
  1858     /// \brief Gives back the \e item by its id.
  1859     ///
  1860     /// Gives back the \e item by its id.
  1861     Item operator()(int id) { return _graph->fromId(id, Item()); }
  1862 
  1863   private:
  1864     const Graph* _graph;
  1865 
  1866   public:
  1867 
  1868     /// \brief This class represents the inverse of its owner (IdMap).
  1869     ///
  1870     /// This class represents the inverse of its owner (IdMap).
  1871     /// \see inverse()
  1872     class InverseMap {
  1873     public:
  1874 
  1875       /// \brief Constructor.
  1876       ///
  1877       /// Constructor for creating an id-to-item map.
  1878       explicit InverseMap(const Graph& graph) : _graph(&graph) {}
  1879 
  1880       /// \brief Constructor.
  1881       ///
  1882       /// Constructor for creating an id-to-item map.
  1883       explicit InverseMap(const IdMap& map) : _graph(map._graph) {}
  1884 
  1885       /// \brief Gives back the given item from its id.
  1886       ///
  1887       /// Gives back the given item from its id.
  1888       Item operator[](int id) const { return _graph->fromId(id, Item());}
  1889 
  1890     private:
  1891       const Graph* _graph;
  1892     };
  1893 
  1894     /// \brief Gives back the inverse of the map.
  1895     ///
  1896     /// Gives back the inverse of the IdMap.
  1897     InverseMap inverse() const { return InverseMap(*_graph);}
  1898   };
  1899 
  1900 
  1901   /// \brief General cross reference graph map type.
  1902 
  1903   /// This class provides simple invertable graph maps.
  1904   /// It wraps an arbitrary \ref concepts::ReadWriteMap "ReadWriteMap"
  1905   /// and if a key is set to a new value then store it
  1906   /// in the inverse map.
  1907   ///
  1908   /// The values of the map can be accessed
  1909   /// with stl compatible forward iterator.
  1910   ///
  1911   /// \tparam GR The graph type.
  1912   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  1913   /// \c GR::Edge).
  1914   /// \tparam V The value type of the map.
  1915   ///
  1916   /// \see IterableValueMap
  1917   template <typename GR, typename K, typename V>
  1918   class CrossRefMap
  1919     : protected ItemSetTraits<GR, K>::template Map<V>::Type {
  1920   private:
  1921 
  1922     typedef typename ItemSetTraits<GR, K>::
  1923       template Map<V>::Type Map;
  1924 
  1925     typedef std::map<V, K> Container;
  1926     Container _inv_map;
  1927 
  1928   public:
  1929 
  1930     /// The graph type of CrossRefMap.
  1931     typedef GR Graph;
  1932     /// The key type of CrossRefMap (\c Node, \c Arc or \c Edge).
  1933     typedef K Item;
  1934     /// The key type of CrossRefMap (\c Node, \c Arc or \c Edge).
  1935     typedef K Key;
  1936     /// The value type of CrossRefMap.
  1937     typedef V Value;
  1938 
  1939     /// \brief Constructor.
  1940     ///
  1941     /// Construct a new CrossRefMap for the given graph.
  1942     explicit CrossRefMap(const Graph& graph) : Map(graph) {}
  1943 
  1944     /// \brief Forward iterator for values.
  1945     ///
  1946     /// This iterator is an stl compatible forward
  1947     /// iterator on the values of the map. The values can
  1948     /// be accessed in the <tt>[beginValue, endValue)</tt> range.
  1949     class ValueIterator
  1950       : public std::iterator<std::forward_iterator_tag, Value> {
  1951       friend class CrossRefMap;
  1952     private:
  1953       ValueIterator(typename Container::const_iterator _it)
  1954         : it(_it) {}
  1955     public:
  1956 
  1957       ValueIterator() {}
  1958 
  1959       ValueIterator& operator++() { ++it; return *this; }
  1960       ValueIterator operator++(int) {
  1961         ValueIterator tmp(*this);
  1962         operator++();
  1963         return tmp;
  1964       }
  1965 
  1966       const Value& operator*() const { return it->first; }
  1967       const Value* operator->() const { return &(it->first); }
  1968 
  1969       bool operator==(ValueIterator jt) const { return it == jt.it; }
  1970       bool operator!=(ValueIterator jt) const { return it != jt.it; }
  1971 
  1972     private:
  1973       typename Container::const_iterator it;
  1974     };
  1975 
  1976     /// \brief Returns an iterator to the first value.
  1977     ///
  1978     /// Returns an stl compatible iterator to the
  1979     /// first value of the map. The values of the
  1980     /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  1981     /// range.
  1982     ValueIterator beginValue() const {
  1983       return ValueIterator(_inv_map.begin());
  1984     }
  1985 
  1986     /// \brief Returns an iterator after the last value.
  1987     ///
  1988     /// Returns an stl compatible iterator after the
  1989     /// last value of the map. The values of the
  1990     /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  1991     /// range.
  1992     ValueIterator endValue() const {
  1993       return ValueIterator(_inv_map.end());
  1994     }
  1995 
  1996     /// \brief Sets the value associated with the given key.
  1997     ///
  1998     /// Sets the value associated with the given key.
  1999     void set(const Key& key, const Value& val) {
  2000       Value oldval = Map::operator[](key);
  2001       typename Container::iterator it = _inv_map.find(oldval);
  2002       if (it != _inv_map.end() && it->second == key) {
  2003         _inv_map.erase(it);
  2004       }
  2005       _inv_map.insert(make_pair(val, key));
  2006       Map::set(key, val);
  2007     }
  2008 
  2009     /// \brief Returns the value associated with the given key.
  2010     ///
  2011     /// Returns the value associated with the given key.
  2012     typename MapTraits<Map>::ConstReturnValue
  2013     operator[](const Key& key) const {
  2014       return Map::operator[](key);
  2015     }
  2016 
  2017     /// \brief Gives back the item by its value.
  2018     ///
  2019     /// Gives back the item by its value.
  2020     Key operator()(const Value& key) const {
  2021       typename Container::const_iterator it = _inv_map.find(key);
  2022       return it != _inv_map.end() ? it->second : INVALID;
  2023     }
  2024 
  2025   protected:
  2026 
  2027     /// \brief Erase the key from the map and the inverse map.
  2028     ///
  2029     /// Erase the key from the map and the inverse map. It is called by the
  2030     /// \c AlterationNotifier.
  2031     virtual void erase(const Key& key) {
  2032       Value val = Map::operator[](key);
  2033       typename Container::iterator it = _inv_map.find(val);
  2034       if (it != _inv_map.end() && it->second == key) {
  2035         _inv_map.erase(it);
  2036       }
  2037       Map::erase(key);
  2038     }
  2039 
  2040     /// \brief Erase more keys from the map and the inverse map.
  2041     ///
  2042     /// Erase more keys from the map and the inverse map. It is called by the
  2043     /// \c AlterationNotifier.
  2044     virtual void erase(const std::vector<Key>& keys) {
  2045       for (int i = 0; i < int(keys.size()); ++i) {
  2046         Value val = Map::operator[](keys[i]);
  2047         typename Container::iterator it = _inv_map.find(val);
  2048         if (it != _inv_map.end() && it->second == keys[i]) {
  2049           _inv_map.erase(it);
  2050         }
  2051       }
  2052       Map::erase(keys);
  2053     }
  2054 
  2055     /// \brief Clear the keys from the map and the inverse map.
  2056     ///
  2057     /// Clear the keys from the map and the inverse map. It is called by the
  2058     /// \c AlterationNotifier.
  2059     virtual void clear() {
  2060       _inv_map.clear();
  2061       Map::clear();
  2062     }
  2063 
  2064   public:
  2065 
  2066     /// \brief The inverse map type.
  2067     ///
  2068     /// The inverse of this map. The subscript operator of the map
  2069     /// gives back the item that was last assigned to the value.
  2070     class InverseMap {
  2071     public:
  2072       /// \brief Constructor
  2073       ///
  2074       /// Constructor of the InverseMap.
  2075       explicit InverseMap(const CrossRefMap& inverted)
  2076         : _inverted(inverted) {}
  2077 
  2078       /// The value type of the InverseMap.
  2079       typedef typename CrossRefMap::Key Value;
  2080       /// The key type of the InverseMap.
  2081       typedef typename CrossRefMap::Value Key;
  2082 
  2083       /// \brief Subscript operator.
  2084       ///
  2085       /// Subscript operator. It gives back the item
  2086       /// that was last assigned to the given value.
  2087       Value operator[](const Key& key) const {
  2088         return _inverted(key);
  2089       }
  2090 
  2091     private:
  2092       const CrossRefMap& _inverted;
  2093     };
  2094 
  2095     /// \brief It gives back the read-only inverse map.
  2096     ///
  2097     /// It gives back the read-only inverse map.
  2098     InverseMap inverse() const {
  2099       return InverseMap(*this);
  2100     }
  2101 
  2102   };
  2103 
  2104   /// \brief Provides continuous and unique ID for the
  2105   /// items of a graph.
  2106   ///
  2107   /// RangeIdMap provides a unique and continuous
  2108   /// ID for each item of a given type (\c Node, \c Arc or
  2109   /// \c Edge) in a graph. This id is
  2110   ///  - \b unique: different items get different ids,
  2111   ///  - \b continuous: the range of the ids is the set of integers
  2112   ///    between 0 and \c n-1, where \c n is the number of the items of
  2113   ///    this type (\c Node, \c Arc or \c Edge).
  2114   ///  - So, the ids can change when deleting an item of the same type.
  2115   ///
  2116   /// Thus this id is not (necessarily) the same as what can get using
  2117   /// the \c id() function of the graph or \ref IdMap.
  2118   /// This map can be inverted with its member class \c InverseMap,
  2119   /// or with the \c operator() member.
  2120   ///
  2121   /// \tparam GR The graph type.
  2122   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  2123   /// \c GR::Edge).
  2124   ///
  2125   /// \see IdMap
  2126   template <typename GR, typename K>
  2127   class RangeIdMap
  2128     : protected ItemSetTraits<GR, K>::template Map<int>::Type {
  2129 
  2130     typedef typename ItemSetTraits<GR, K>::template Map<int>::Type Map;
  2131 
  2132   public:
  2133     /// The graph type of RangeIdMap.
  2134     typedef GR Graph;
  2135     /// The key type of RangeIdMap (\c Node, \c Arc or \c Edge).
  2136     typedef K Item;
  2137     /// The key type of RangeIdMap (\c Node, \c Arc or \c Edge).
  2138     typedef K Key;
  2139     /// The value type of RangeIdMap.
  2140     typedef int Value;
  2141 
  2142     /// \brief Constructor.
  2143     ///
  2144     /// Constructor.
  2145     explicit RangeIdMap(const Graph& gr) : Map(gr) {
  2146       Item it;
  2147       const typename Map::Notifier* nf = Map::notifier();
  2148       for (nf->first(it); it != INVALID; nf->next(it)) {
  2149         Map::set(it, _inv_map.size());
  2150         _inv_map.push_back(it);
  2151       }
  2152     }
  2153 
  2154   protected:
  2155 
  2156     /// \brief Adds a new key to the map.
  2157     ///
  2158     /// Add a new key to the map. It is called by the
  2159     /// \c AlterationNotifier.
  2160     virtual void add(const Item& item) {
  2161       Map::add(item);
  2162       Map::set(item, _inv_map.size());
  2163       _inv_map.push_back(item);
  2164     }
  2165 
  2166     /// \brief Add more new keys to the map.
  2167     ///
  2168     /// Add more new keys to the map. It is called by the
  2169     /// \c AlterationNotifier.
  2170     virtual void add(const std::vector<Item>& items) {
  2171       Map::add(items);
  2172       for (int i = 0; i < int(items.size()); ++i) {
  2173         Map::set(items[i], _inv_map.size());
  2174         _inv_map.push_back(items[i]);
  2175       }
  2176     }
  2177 
  2178     /// \brief Erase the key from the map.
  2179     ///
  2180     /// Erase the key from the map. It is called by the
  2181     /// \c AlterationNotifier.
  2182     virtual void erase(const Item& item) {
  2183       Map::set(_inv_map.back(), Map::operator[](item));
  2184       _inv_map[Map::operator[](item)] = _inv_map.back();
  2185       _inv_map.pop_back();
  2186       Map::erase(item);
  2187     }
  2188 
  2189     /// \brief Erase more keys from the map.
  2190     ///
  2191     /// Erase more keys from the map. It is called by the
  2192     /// \c AlterationNotifier.
  2193     virtual void erase(const std::vector<Item>& items) {
  2194       for (int i = 0; i < int(items.size()); ++i) {
  2195         Map::set(_inv_map.back(), Map::operator[](items[i]));
  2196         _inv_map[Map::operator[](items[i])] = _inv_map.back();
  2197         _inv_map.pop_back();
  2198       }
  2199       Map::erase(items);
  2200     }
  2201 
  2202     /// \brief Build the unique map.
  2203     ///
  2204     /// Build the unique map. It is called by the
  2205     /// \c AlterationNotifier.
  2206     virtual void build() {
  2207       Map::build();
  2208       Item it;
  2209       const typename Map::Notifier* nf = Map::notifier();
  2210       for (nf->first(it); it != INVALID; nf->next(it)) {
  2211         Map::set(it, _inv_map.size());
  2212         _inv_map.push_back(it);
  2213       }
  2214     }
  2215 
  2216     /// \brief Clear the keys from the map.
  2217     ///
  2218     /// Clear the keys from the map. It is called by the
  2219     /// \c AlterationNotifier.
  2220     virtual void clear() {
  2221       _inv_map.clear();
  2222       Map::clear();
  2223     }
  2224 
  2225   public:
  2226 
  2227     /// \brief Returns the maximal value plus one.
  2228     ///
  2229     /// Returns the maximal value plus one in the map.
  2230     unsigned int size() const {
  2231       return _inv_map.size();
  2232     }
  2233 
  2234     /// \brief Swaps the position of the two items in the map.
  2235     ///
  2236     /// Swaps the position of the two items in the map.
  2237     void swap(const Item& p, const Item& q) {
  2238       int pi = Map::operator[](p);
  2239       int qi = Map::operator[](q);
  2240       Map::set(p, qi);
  2241       _inv_map[qi] = p;
  2242       Map::set(q, pi);
  2243       _inv_map[pi] = q;
  2244     }
  2245 
  2246     /// \brief Gives back the \e RangeId of the item
  2247     ///
  2248     /// Gives back the \e RangeId of the item.
  2249     int operator[](const Item& item) const {
  2250       return Map::operator[](item);
  2251     }
  2252 
  2253     /// \brief Gives back the item belonging to a \e RangeId
  2254     /// 
  2255     /// Gives back the item belonging to a \e RangeId.
  2256     Item operator()(int id) const {
  2257       return _inv_map[id];
  2258     }
  2259 
  2260   private:
  2261 
  2262     typedef std::vector<Item> Container;
  2263     Container _inv_map;
  2264 
  2265   public:
  2266 
  2267     /// \brief The inverse map type of RangeIdMap.
  2268     ///
  2269     /// The inverse map type of RangeIdMap.
  2270     class InverseMap {
  2271     public:
  2272       /// \brief Constructor
  2273       ///
  2274       /// Constructor of the InverseMap.
  2275       explicit InverseMap(const RangeIdMap& inverted)
  2276         : _inverted(inverted) {}
  2277 
  2278 
  2279       /// The value type of the InverseMap.
  2280       typedef typename RangeIdMap::Key Value;
  2281       /// The key type of the InverseMap.
  2282       typedef typename RangeIdMap::Value Key;
  2283 
  2284       /// \brief Subscript operator.
  2285       ///
  2286       /// Subscript operator. It gives back the item
  2287       /// that the descriptor currently belongs to.
  2288       Value operator[](const Key& key) const {
  2289         return _inverted(key);
  2290       }
  2291 
  2292       /// \brief Size of the map.
  2293       ///
  2294       /// Returns the size of the map.
  2295       unsigned int size() const {
  2296         return _inverted.size();
  2297       }
  2298 
  2299     private:
  2300       const RangeIdMap& _inverted;
  2301     };
  2302 
  2303     /// \brief Gives back the inverse of the map.
  2304     ///
  2305     /// Gives back the inverse of the map.
  2306     const InverseMap inverse() const {
  2307       return InverseMap(*this);
  2308     }
  2309   };
  2310 
  2311   /// \brief Map of the source nodes of arcs in a digraph.
  2312   ///
  2313   /// SourceMap provides access for the source node of each arc in a digraph,
  2314   /// which is returned by the \c source() function of the digraph.
  2315   /// \tparam GR The digraph type.
  2316   /// \see TargetMap
  2317   template <typename GR>
  2318   class SourceMap {
  2319   public:
  2320 
  2321     ///\e
  2322     typedef typename GR::Arc Key;
  2323     ///\e
  2324     typedef typename GR::Node Value;
  2325 
  2326     /// \brief Constructor
  2327     ///
  2328     /// Constructor.
  2329     /// \param digraph The digraph that the map belongs to.
  2330     explicit SourceMap(const GR& digraph) : _graph(digraph) {}
  2331 
  2332     /// \brief Returns the source node of the given arc.
  2333     ///
  2334     /// Returns the source node of the given arc.
  2335     Value operator[](const Key& arc) const {
  2336       return _graph.source(arc);
  2337     }
  2338 
  2339   private:
  2340     const GR& _graph;
  2341   };
  2342 
  2343   /// \brief Returns a \c SourceMap class.
  2344   ///
  2345   /// This function just returns an \c SourceMap class.
  2346   /// \relates SourceMap
  2347   template <typename GR>
  2348   inline SourceMap<GR> sourceMap(const GR& graph) {
  2349     return SourceMap<GR>(graph);
  2350   }
  2351 
  2352   /// \brief Map of the target nodes of arcs in a digraph.
  2353   ///
  2354   /// TargetMap provides access for the target node of each arc in a digraph,
  2355   /// which is returned by the \c target() function of the digraph.
  2356   /// \tparam GR The digraph type.
  2357   /// \see SourceMap
  2358   template <typename GR>
  2359   class TargetMap {
  2360   public:
  2361 
  2362     ///\e
  2363     typedef typename GR::Arc Key;
  2364     ///\e
  2365     typedef typename GR::Node Value;
  2366 
  2367     /// \brief Constructor
  2368     ///
  2369     /// Constructor.
  2370     /// \param digraph The digraph that the map belongs to.
  2371     explicit TargetMap(const GR& digraph) : _graph(digraph) {}
  2372 
  2373     /// \brief Returns the target node of the given arc.
  2374     ///
  2375     /// Returns the target node of the given arc.
  2376     Value operator[](const Key& e) const {
  2377       return _graph.target(e);
  2378     }
  2379 
  2380   private:
  2381     const GR& _graph;
  2382   };
  2383 
  2384   /// \brief Returns a \c TargetMap class.
  2385   ///
  2386   /// This function just returns a \c TargetMap class.
  2387   /// \relates TargetMap
  2388   template <typename GR>
  2389   inline TargetMap<GR> targetMap(const GR& graph) {
  2390     return TargetMap<GR>(graph);
  2391   }
  2392 
  2393   /// \brief Map of the "forward" directed arc view of edges in a graph.
  2394   ///
  2395   /// ForwardMap provides access for the "forward" directed arc view of
  2396   /// each edge in a graph, which is returned by the \c direct() function
  2397   /// of the graph with \c true parameter.
  2398   /// \tparam GR The graph type.
  2399   /// \see BackwardMap
  2400   template <typename GR>
  2401   class ForwardMap {
  2402   public:
  2403 
  2404     typedef typename GR::Arc Value;
  2405     typedef typename GR::Edge Key;
  2406 
  2407     /// \brief Constructor
  2408     ///
  2409     /// Constructor.
  2410     /// \param graph The graph that the map belongs to.
  2411     explicit ForwardMap(const GR& graph) : _graph(graph) {}
  2412 
  2413     /// \brief Returns the "forward" directed arc view of the given edge.
  2414     ///
  2415     /// Returns the "forward" directed arc view of the given edge.
  2416     Value operator[](const Key& key) const {
  2417       return _graph.direct(key, true);
  2418     }
  2419 
  2420   private:
  2421     const GR& _graph;
  2422   };
  2423 
  2424   /// \brief Returns a \c ForwardMap class.
  2425   ///
  2426   /// This function just returns an \c ForwardMap class.
  2427   /// \relates ForwardMap
  2428   template <typename GR>
  2429   inline ForwardMap<GR> forwardMap(const GR& graph) {
  2430     return ForwardMap<GR>(graph);
  2431   }
  2432 
  2433   /// \brief Map of the "backward" directed arc view of edges in a graph.
  2434   ///
  2435   /// BackwardMap provides access for the "backward" directed arc view of
  2436   /// each edge in a graph, which is returned by the \c direct() function
  2437   /// of the graph with \c false parameter.
  2438   /// \tparam GR The graph type.
  2439   /// \see ForwardMap
  2440   template <typename GR>
  2441   class BackwardMap {
  2442   public:
  2443 
  2444     typedef typename GR::Arc Value;
  2445     typedef typename GR::Edge Key;
  2446 
  2447     /// \brief Constructor
  2448     ///
  2449     /// Constructor.
  2450     /// \param graph The graph that the map belongs to.
  2451     explicit BackwardMap(const GR& graph) : _graph(graph) {}
  2452 
  2453     /// \brief Returns the "backward" directed arc view of the given edge.
  2454     ///
  2455     /// Returns the "backward" directed arc view of the given edge.
  2456     Value operator[](const Key& key) const {
  2457       return _graph.direct(key, false);
  2458     }
  2459 
  2460   private:
  2461     const GR& _graph;
  2462   };
  2463 
  2464   /// \brief Returns a \c BackwardMap class
  2465 
  2466   /// This function just returns a \c BackwardMap class.
  2467   /// \relates BackwardMap
  2468   template <typename GR>
  2469   inline BackwardMap<GR> backwardMap(const GR& graph) {
  2470     return BackwardMap<GR>(graph);
  2471   }
  2472 
  2473   /// \brief Map of the in-degrees of nodes in a digraph.
  2474   ///
  2475   /// This map returns the in-degree of a node. Once it is constructed,
  2476   /// the degrees are stored in a standard \c NodeMap, so each query is done
  2477   /// in constant time. On the other hand, the values are updated automatically
  2478   /// whenever the digraph changes.
  2479   ///
  2480   /// \warning Besides \c addNode() and \c addArc(), a digraph structure 
  2481   /// may provide alternative ways to modify the digraph.
  2482   /// The correct behavior of InDegMap is not guarantied if these additional
  2483   /// features are used. For example the functions
  2484   /// \ref ListDigraph::changeSource() "changeSource()",
  2485   /// \ref ListDigraph::changeTarget() "changeTarget()" and
  2486   /// \ref ListDigraph::reverseArc() "reverseArc()"
  2487   /// of \ref ListDigraph will \e not update the degree values correctly.
  2488   ///
  2489   /// \sa OutDegMap
  2490   template <typename GR>
  2491   class InDegMap
  2492     : protected ItemSetTraits<GR, typename GR::Arc>
  2493       ::ItemNotifier::ObserverBase {
  2494 
  2495   public:
  2496     
  2497     /// The digraph type
  2498     typedef GR Digraph;
  2499     /// The key type
  2500     typedef typename Digraph::Node Key;
  2501     /// The value type
  2502     typedef int Value;
  2503 
  2504     typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
  2505     ::ItemNotifier::ObserverBase Parent;
  2506 
  2507   private:
  2508 
  2509     class AutoNodeMap
  2510       : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {
  2511     public:
  2512 
  2513       typedef typename ItemSetTraits<Digraph, Key>::
  2514       template Map<int>::Type Parent;
  2515 
  2516       AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
  2517 
  2518       virtual void add(const Key& key) {
  2519         Parent::add(key);
  2520         Parent::set(key, 0);
  2521       }
  2522 
  2523       virtual void add(const std::vector<Key>& keys) {
  2524         Parent::add(keys);
  2525         for (int i = 0; i < int(keys.size()); ++i) {
  2526           Parent::set(keys[i], 0);
  2527         }
  2528       }
  2529 
  2530       virtual void build() {
  2531         Parent::build();
  2532         Key it;
  2533         typename Parent::Notifier* nf = Parent::notifier();
  2534         for (nf->first(it); it != INVALID; nf->next(it)) {
  2535           Parent::set(it, 0);
  2536         }
  2537       }
  2538     };
  2539 
  2540   public:
  2541 
  2542     /// \brief Constructor.
  2543     ///
  2544     /// Constructor for creating an in-degree map.
  2545     explicit InDegMap(const Digraph& graph)
  2546       : _digraph(graph), _deg(graph) {
  2547       Parent::attach(_digraph.notifier(typename Digraph::Arc()));
  2548 
  2549       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  2550         _deg[it] = countInArcs(_digraph, it);
  2551       }
  2552     }
  2553 
  2554     /// \brief Gives back the in-degree of a Node.
  2555     ///
  2556     /// Gives back the in-degree of a Node.
  2557     int operator[](const Key& key) const {
  2558       return _deg[key];
  2559     }
  2560 
  2561   protected:
  2562 
  2563     typedef typename Digraph::Arc Arc;
  2564 
  2565     virtual void add(const Arc& arc) {
  2566       ++_deg[_digraph.target(arc)];
  2567     }
  2568 
  2569     virtual void add(const std::vector<Arc>& arcs) {
  2570       for (int i = 0; i < int(arcs.size()); ++i) {
  2571         ++_deg[_digraph.target(arcs[i])];
  2572       }
  2573     }
  2574 
  2575     virtual void erase(const Arc& arc) {
  2576       --_deg[_digraph.target(arc)];
  2577     }
  2578 
  2579     virtual void erase(const std::vector<Arc>& arcs) {
  2580       for (int i = 0; i < int(arcs.size()); ++i) {
  2581         --_deg[_digraph.target(arcs[i])];
  2582       }
  2583     }
  2584 
  2585     virtual void build() {
  2586       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  2587         _deg[it] = countInArcs(_digraph, it);
  2588       }
  2589     }
  2590 
  2591     virtual void clear() {
  2592       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  2593         _deg[it] = 0;
  2594       }
  2595     }
  2596   private:
  2597 
  2598     const Digraph& _digraph;
  2599     AutoNodeMap _deg;
  2600   };
  2601 
  2602   /// \brief Map of the out-degrees of nodes in a digraph.
  2603   ///
  2604   /// This map returns the out-degree of a node. Once it is constructed,
  2605   /// the degrees are stored in a standard \c NodeMap, so each query is done
  2606   /// in constant time. On the other hand, the values are updated automatically
  2607   /// whenever the digraph changes.
  2608   ///
  2609   /// \warning Besides \c addNode() and \c addArc(), a digraph structure 
  2610   /// may provide alternative ways to modify the digraph.
  2611   /// The correct behavior of OutDegMap is not guarantied if these additional
  2612   /// features are used. For example the functions
  2613   /// \ref ListDigraph::changeSource() "changeSource()",
  2614   /// \ref ListDigraph::changeTarget() "changeTarget()" and
  2615   /// \ref ListDigraph::reverseArc() "reverseArc()"
  2616   /// of \ref ListDigraph will \e not update the degree values correctly.
  2617   ///
  2618   /// \sa InDegMap
  2619   template <typename GR>
  2620   class OutDegMap
  2621     : protected ItemSetTraits<GR, typename GR::Arc>
  2622       ::ItemNotifier::ObserverBase {
  2623 
  2624   public:
  2625 
  2626     /// The digraph type
  2627     typedef GR Digraph;
  2628     /// The key type
  2629     typedef typename Digraph::Node Key;
  2630     /// The value type
  2631     typedef int Value;
  2632 
  2633     typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
  2634     ::ItemNotifier::ObserverBase Parent;
  2635 
  2636   private:
  2637 
  2638     class AutoNodeMap
  2639       : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {
  2640     public:
  2641 
  2642       typedef typename ItemSetTraits<Digraph, Key>::
  2643       template Map<int>::Type Parent;
  2644 
  2645       AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
  2646 
  2647       virtual void add(const Key& key) {
  2648         Parent::add(key);
  2649         Parent::set(key, 0);
  2650       }
  2651       virtual void add(const std::vector<Key>& keys) {
  2652         Parent::add(keys);
  2653         for (int i = 0; i < int(keys.size()); ++i) {
  2654           Parent::set(keys[i], 0);
  2655         }
  2656       }
  2657       virtual void build() {
  2658         Parent::build();
  2659         Key it;
  2660         typename Parent::Notifier* nf = Parent::notifier();
  2661         for (nf->first(it); it != INVALID; nf->next(it)) {
  2662           Parent::set(it, 0);
  2663         }
  2664       }
  2665     };
  2666 
  2667   public:
  2668 
  2669     /// \brief Constructor.
  2670     ///
  2671     /// Constructor for creating an out-degree map.
  2672     explicit OutDegMap(const Digraph& graph)
  2673       : _digraph(graph), _deg(graph) {
  2674       Parent::attach(_digraph.notifier(typename Digraph::Arc()));
  2675 
  2676       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  2677         _deg[it] = countOutArcs(_digraph, it);
  2678       }
  2679     }
  2680 
  2681     /// \brief Gives back the out-degree of a Node.
  2682     ///
  2683     /// Gives back the out-degree of a Node.
  2684     int operator[](const Key& key) const {
  2685       return _deg[key];
  2686     }
  2687 
  2688   protected:
  2689 
  2690     typedef typename Digraph::Arc Arc;
  2691 
  2692     virtual void add(const Arc& arc) {
  2693       ++_deg[_digraph.source(arc)];
  2694     }
  2695 
  2696     virtual void add(const std::vector<Arc>& arcs) {
  2697       for (int i = 0; i < int(arcs.size()); ++i) {
  2698         ++_deg[_digraph.source(arcs[i])];
  2699       }
  2700     }
  2701 
  2702     virtual void erase(const Arc& arc) {
  2703       --_deg[_digraph.source(arc)];
  2704     }
  2705 
  2706     virtual void erase(const std::vector<Arc>& arcs) {
  2707       for (int i = 0; i < int(arcs.size()); ++i) {
  2708         --_deg[_digraph.source(arcs[i])];
  2709       }
  2710     }
  2711 
  2712     virtual void build() {
  2713       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  2714         _deg[it] = countOutArcs(_digraph, it);
  2715       }
  2716     }
  2717 
  2718     virtual void clear() {
  2719       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  2720         _deg[it] = 0;
  2721       }
  2722     }
  2723   private:
  2724 
  2725     const Digraph& _digraph;
  2726     AutoNodeMap _deg;
  2727   };
  2728 
  2729   /// \brief Potential difference map
  2730   ///
  2731   /// PotentialMap returns the difference between the potentials of the
  2732   /// source and target nodes of each arc in a digraph, i.e. it returns
  2733   /// \code
  2734   ///   potential[gr.target(arc)] - potential[gr.source(arc)].
  2735   /// \endcode
  2736   /// \tparam GR The digraph type.
  2737   /// \tparam POT A node map storing the potentials.
  2738   template <typename GR, typename POT>
  2739   class PotentialDifferenceMap {
  2740   public:
  2741     /// Key type
  2742     typedef typename GR::Arc Key;
  2743     /// Value type
  2744     typedef typename POT::Value Value;
  2745 
  2746     /// \brief Constructor
  2747     ///
  2748     /// Contructor of the map.
  2749     explicit PotentialDifferenceMap(const GR& gr,
  2750                                     const POT& potential)
  2751       : _digraph(gr), _potential(potential) {}
  2752 
  2753     /// \brief Returns the potential difference for the given arc.
  2754     ///
  2755     /// Returns the potential difference for the given arc, i.e.
  2756     /// \code
  2757     ///   potential[gr.target(arc)] - potential[gr.source(arc)].
  2758     /// \endcode
  2759     Value operator[](const Key& arc) const {
  2760       return _potential[_digraph.target(arc)] -
  2761         _potential[_digraph.source(arc)];
  2762     }
  2763 
  2764   private:
  2765     const GR& _digraph;
  2766     const POT& _potential;
  2767   };
  2768 
  2769   /// \brief Returns a PotentialDifferenceMap.
  2770   ///
  2771   /// This function just returns a PotentialDifferenceMap.
  2772   /// \relates PotentialDifferenceMap
  2773   template <typename GR, typename POT>
  2774   PotentialDifferenceMap<GR, POT>
  2775   potentialDifferenceMap(const GR& gr, const POT& potential) {
  2776     return PotentialDifferenceMap<GR, POT>(gr, potential);
  2777   }
  2778 
  2779   /// @}
  2780 }
  2781 
  2782 #endif // LEMON_MAPS_H