lemon/maps.h
author Alpar Juttner <alpar@cs.elte.hu>
Wed, 06 May 2015 11:31:43 +0200
changeset 1138 f95b18d99843
parent 1092 dceba191c00d
child 1210 da87dbdf3daf
permissions -rw-r--r--
Merge CMP0026 setting
     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) 2003-2013
     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 #include <map>
    26 
    27 #include <lemon/core.h>
    28 #include <lemon/bits/stl_iterators.h>
    29 
    30 ///\file
    31 ///\ingroup maps
    32 ///\brief Miscellaneous property maps
    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 to 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 to 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 to 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 together with some data structures, e.g.
   235   /// heap types and \c UnionFind, when the used items are small
   236   /// integers. This map conforms to 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 to 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 to 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).processedMap(loggerBoolMap(std::back_inserter(v))).run(s);
  1794   /// \endcode
  1795   /// \code
  1796   ///   std::vector<Node> v(countNodes(g));
  1797   ///   dfs(g).processedMap(loggerBoolMap(v.begin())).run(s);
  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     typedef GR Digraph;
  1842     /// The key type of IdMap (\c Node, \c Arc or \c Edge).
  1843     typedef K Item;
  1844     /// The key type of IdMap (\c Node, \c Arc or \c Edge).
  1845     typedef K Key;
  1846     /// The value type of IdMap.
  1847     typedef int Value;
  1848 
  1849     /// \brief Constructor.
  1850     ///
  1851     /// Constructor of the map.
  1852     explicit IdMap(const Graph& graph) : _graph(&graph) {}
  1853 
  1854     /// \brief Gives back the \e id of the item.
  1855     ///
  1856     /// Gives back the immutable and unique \e id of the item.
  1857     int operator[](const Item& item) const { return _graph->id(item);}
  1858 
  1859     /// \brief Gives back the \e item by its id.
  1860     ///
  1861     /// Gives back the \e item by its id.
  1862     Item operator()(int id) { return _graph->fromId(id, Item()); }
  1863 
  1864   private:
  1865     const Graph* _graph;
  1866 
  1867   public:
  1868 
  1869     /// \brief The inverse map type of IdMap.
  1870     ///
  1871     /// The inverse map type of IdMap. The subscript operator gives back
  1872     /// an item by its id.
  1873     /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
  1874     /// \see inverse()
  1875     class InverseMap {
  1876     public:
  1877 
  1878       /// \brief Constructor.
  1879       ///
  1880       /// Constructor for creating an id-to-item map.
  1881       explicit InverseMap(const Graph& graph) : _graph(&graph) {}
  1882 
  1883       /// \brief Constructor.
  1884       ///
  1885       /// Constructor for creating an id-to-item map.
  1886       explicit InverseMap(const IdMap& map) : _graph(map._graph) {}
  1887 
  1888       /// \brief Gives back an item by its id.
  1889       ///
  1890       /// Gives back an item by its id.
  1891       Item operator[](int id) const { return _graph->fromId(id, Item());}
  1892 
  1893     private:
  1894       const Graph* _graph;
  1895     };
  1896 
  1897     /// \brief Gives back the inverse of the map.
  1898     ///
  1899     /// Gives back the inverse of the IdMap.
  1900     InverseMap inverse() const { return InverseMap(*_graph);}
  1901   };
  1902 
  1903   /// \brief Returns an \c IdMap class.
  1904   ///
  1905   /// This function just returns an \c IdMap class.
  1906   /// \relates IdMap
  1907   template <typename K, typename GR>
  1908   inline IdMap<GR, K> idMap(const GR& graph) {
  1909     return IdMap<GR, K>(graph);
  1910   }
  1911 
  1912   /// \brief General cross reference graph map type.
  1913 
  1914   /// This class provides simple invertable graph maps.
  1915   /// It wraps a standard graph map (\c NodeMap, \c ArcMap or \c EdgeMap)
  1916   /// and if a key is set to a new value, then stores it in the inverse map.
  1917   /// The graph items can be accessed by their values either using
  1918   /// \c InverseMap or \c operator()(), and the values of the map can be
  1919   /// accessed with an STL compatible forward iterator (\c ValueIt).
  1920   ///
  1921   /// This map is intended to be used when all associated values are
  1922   /// different (the map is actually invertable) or there are only a few
  1923   /// items with the same value.
  1924   /// Otherwise consider to use \c IterableValueMap, which is more
  1925   /// suitable and more efficient for such cases. It provides iterators
  1926   /// to traverse the items with the same associated value, but
  1927   /// it does not have \c InverseMap.
  1928   ///
  1929   /// This type is not reference map, so it cannot be modified with
  1930   /// the subscript operator.
  1931   ///
  1932   /// \tparam GR The graph type.
  1933   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  1934   /// \c GR::Edge).
  1935   /// \tparam V The value type of the map.
  1936   ///
  1937   /// \see IterableValueMap
  1938   template <typename GR, typename K, typename V>
  1939   class CrossRefMap
  1940     : protected ItemSetTraits<GR, K>::template Map<V>::Type {
  1941   private:
  1942 
  1943     typedef typename ItemSetTraits<GR, K>::
  1944       template Map<V>::Type Map;
  1945 
  1946     typedef std::multimap<V, K> Container;
  1947     Container _inv_map;
  1948 
  1949   public:
  1950 
  1951     /// The graph type of CrossRefMap.
  1952     typedef GR Graph;
  1953     typedef GR Digraph;
  1954     /// The key type of CrossRefMap (\c Node, \c Arc or \c Edge).
  1955     typedef K Item;
  1956     /// The key type of CrossRefMap (\c Node, \c Arc or \c Edge).
  1957     typedef K Key;
  1958     /// The value type of CrossRefMap.
  1959     typedef V Value;
  1960 
  1961     /// \brief Constructor.
  1962     ///
  1963     /// Construct a new CrossRefMap for the given graph.
  1964     explicit CrossRefMap(const Graph& graph) : Map(graph) {}
  1965 
  1966     /// \brief Forward iterator for values.
  1967     ///
  1968     /// This iterator is an STL compatible forward
  1969     /// iterator on the values of the map. The values can
  1970     /// be accessed in the <tt>[beginValue, endValue)</tt> range.
  1971     /// They are considered with multiplicity, so each value is
  1972     /// traversed for each item it is assigned to.
  1973     class ValueIt
  1974       : public std::iterator<std::forward_iterator_tag, Value> {
  1975       friend class CrossRefMap;
  1976     private:
  1977       ValueIt(typename Container::const_iterator _it)
  1978         : it(_it) {}
  1979     public:
  1980 
  1981       /// Constructor
  1982       ValueIt() {}
  1983 
  1984       /// \e
  1985       ValueIt& operator++() { ++it; return *this; }
  1986       /// \e
  1987       ValueIt operator++(int) {
  1988         ValueIt tmp(*this);
  1989         operator++();
  1990         return tmp;
  1991       }
  1992 
  1993       /// \e
  1994       const Value& operator*() const { return it->first; }
  1995       /// \e
  1996       const Value* operator->() const { return &(it->first); }
  1997 
  1998       /// \e
  1999       bool operator==(ValueIt jt) const { return it == jt.it; }
  2000       /// \e
  2001       bool operator!=(ValueIt jt) const { return it != jt.it; }
  2002 
  2003     private:
  2004       typename Container::const_iterator it;
  2005     };
  2006 
  2007     /// Alias for \c ValueIt
  2008     typedef ValueIt ValueIterator;
  2009 
  2010     /// \brief Returns an iterator to the first value.
  2011     ///
  2012     /// Returns an STL compatible iterator to the
  2013     /// first value of the map. The values of the
  2014     /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  2015     /// range.
  2016     ValueIt beginValue() const {
  2017       return ValueIt(_inv_map.begin());
  2018     }
  2019 
  2020     /// \brief Returns an iterator after the last value.
  2021     ///
  2022     /// Returns an STL compatible iterator after the
  2023     /// last value of the map. The values of the
  2024     /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  2025     /// range.
  2026     ValueIt endValue() const {
  2027       return ValueIt(_inv_map.end());
  2028     }
  2029 
  2030     /// \brief Sets the value associated with the given key.
  2031     ///
  2032     /// Sets the value associated with the given key.
  2033     void set(const Key& key, const Value& val) {
  2034       Value oldval = Map::operator[](key);
  2035       typename Container::iterator it;
  2036       for (it = _inv_map.equal_range(oldval).first;
  2037            it != _inv_map.equal_range(oldval).second; ++it) {
  2038         if (it->second == key) {
  2039           _inv_map.erase(it);
  2040           break;
  2041         }
  2042       }
  2043       _inv_map.insert(std::make_pair(val, key));
  2044       Map::set(key, val);
  2045     }
  2046 
  2047     /// \brief Returns the value associated with the given key.
  2048     ///
  2049     /// Returns the value associated with the given key.
  2050     typename MapTraits<Map>::ConstReturnValue
  2051     operator[](const Key& key) const {
  2052       return Map::operator[](key);
  2053     }
  2054 
  2055     /// \brief Gives back an item by its value.
  2056     ///
  2057     /// This function gives back an item that is assigned to
  2058     /// the given value or \c INVALID if no such item exists.
  2059     /// If there are more items with the same associated value,
  2060     /// only one of them is returned.
  2061     Key operator()(const Value& val) const {
  2062       typename Container::const_iterator it = _inv_map.find(val);
  2063       return it != _inv_map.end() ? it->second : INVALID;
  2064     }
  2065 
  2066     /// \brief Returns the number of items with the given value.
  2067     ///
  2068     /// This function returns the number of items with the given value
  2069     /// associated with it.
  2070     int count(const Value &val) const {
  2071       return _inv_map.count(val);
  2072     }
  2073 
  2074   protected:
  2075 
  2076     /// \brief Erase the key from the map and the inverse map.
  2077     ///
  2078     /// Erase the key from the map and the inverse map. It is called by the
  2079     /// \c AlterationNotifier.
  2080     virtual void erase(const Key& key) {
  2081       Value val = Map::operator[](key);
  2082       typename Container::iterator it;
  2083       for (it = _inv_map.equal_range(val).first;
  2084            it != _inv_map.equal_range(val).second; ++it) {
  2085         if (it->second == key) {
  2086           _inv_map.erase(it);
  2087           break;
  2088         }
  2089       }
  2090       Map::erase(key);
  2091     }
  2092 
  2093     /// \brief Erase more keys from the map and the inverse map.
  2094     ///
  2095     /// Erase more keys from the map and the inverse map. It is called by the
  2096     /// \c AlterationNotifier.
  2097     virtual void erase(const std::vector<Key>& keys) {
  2098       for (int i = 0; i < int(keys.size()); ++i) {
  2099         Value val = Map::operator[](keys[i]);
  2100         typename Container::iterator it;
  2101         for (it = _inv_map.equal_range(val).first;
  2102              it != _inv_map.equal_range(val).second; ++it) {
  2103           if (it->second == keys[i]) {
  2104             _inv_map.erase(it);
  2105             break;
  2106           }
  2107         }
  2108       }
  2109       Map::erase(keys);
  2110     }
  2111 
  2112     /// \brief Clear the keys from the map and the inverse map.
  2113     ///
  2114     /// Clear the keys from the map and the inverse map. It is called by the
  2115     /// \c AlterationNotifier.
  2116     virtual void clear() {
  2117       _inv_map.clear();
  2118       Map::clear();
  2119     }
  2120 
  2121   public:
  2122 
  2123     /// \brief The inverse map type of CrossRefMap.
  2124     ///
  2125     /// The inverse map type of CrossRefMap. The subscript operator gives
  2126     /// back an item by its value.
  2127     /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
  2128     /// \see inverse()
  2129     class InverseMap {
  2130     public:
  2131       /// \brief Constructor
  2132       ///
  2133       /// Constructor of the InverseMap.
  2134       explicit InverseMap(const CrossRefMap& inverted)
  2135         : _inverted(inverted) {}
  2136 
  2137       /// The value type of the InverseMap.
  2138       typedef typename CrossRefMap::Key Value;
  2139       /// The key type of the InverseMap.
  2140       typedef typename CrossRefMap::Value Key;
  2141 
  2142       /// \brief Subscript operator.
  2143       ///
  2144       /// Subscript operator. It gives back an item
  2145       /// that is assigned to the given value or \c INVALID
  2146       /// if no such item exists.
  2147       Value operator[](const Key& key) const {
  2148         return _inverted(key);
  2149       }
  2150 
  2151     private:
  2152       const CrossRefMap& _inverted;
  2153     };
  2154 
  2155     /// \brief Gives back the inverse of the map.
  2156     ///
  2157     /// Gives back the inverse of the CrossRefMap.
  2158     InverseMap inverse() const {
  2159       return InverseMap(*this);
  2160     }
  2161 
  2162   };
  2163 
  2164   /// \brief Provides continuous and unique id for the
  2165   /// items of a graph.
  2166   ///
  2167   /// RangeIdMap provides a unique and continuous
  2168   /// id for each item of a given type (\c Node, \c Arc or
  2169   /// \c Edge) in a graph. This id is
  2170   ///  - \b unique: different items get different ids,
  2171   ///  - \b continuous: the range of the ids is the set of integers
  2172   ///    between 0 and \c n-1, where \c n is the number of the items of
  2173   ///    this type (\c Node, \c Arc or \c Edge).
  2174   ///  - So, the ids can change when deleting an item of the same type.
  2175   ///
  2176   /// Thus this id is not (necessarily) the same as what can get using
  2177   /// the \c id() function of the graph or \ref IdMap.
  2178   /// This map can be inverted with its member class \c InverseMap,
  2179   /// or with the \c operator()() member.
  2180   ///
  2181   /// \tparam GR The graph type.
  2182   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  2183   /// \c GR::Edge).
  2184   ///
  2185   /// \see IdMap
  2186   template <typename GR, typename K>
  2187   class RangeIdMap
  2188     : protected ItemSetTraits<GR, K>::template Map<int>::Type {
  2189 
  2190     typedef typename ItemSetTraits<GR, K>::template Map<int>::Type Map;
  2191 
  2192   public:
  2193     /// The graph type of RangeIdMap.
  2194     typedef GR Graph;
  2195     typedef GR Digraph;
  2196     /// The key type of RangeIdMap (\c Node, \c Arc or \c Edge).
  2197     typedef K Item;
  2198     /// The key type of RangeIdMap (\c Node, \c Arc or \c Edge).
  2199     typedef K Key;
  2200     /// The value type of RangeIdMap.
  2201     typedef int Value;
  2202 
  2203     /// \brief Constructor.
  2204     ///
  2205     /// Constructor.
  2206     explicit RangeIdMap(const Graph& gr) : Map(gr) {
  2207       Item it;
  2208       const typename Map::Notifier* nf = Map::notifier();
  2209       for (nf->first(it); it != INVALID; nf->next(it)) {
  2210         Map::set(it, _inv_map.size());
  2211         _inv_map.push_back(it);
  2212       }
  2213     }
  2214 
  2215   protected:
  2216 
  2217     /// \brief Adds a new key to the map.
  2218     ///
  2219     /// Add a new key to the map. It is called by the
  2220     /// \c AlterationNotifier.
  2221     virtual void add(const Item& item) {
  2222       Map::add(item);
  2223       Map::set(item, _inv_map.size());
  2224       _inv_map.push_back(item);
  2225     }
  2226 
  2227     /// \brief Add more new keys to the map.
  2228     ///
  2229     /// Add more new keys to the map. It is called by the
  2230     /// \c AlterationNotifier.
  2231     virtual void add(const std::vector<Item>& items) {
  2232       Map::add(items);
  2233       for (int i = 0; i < int(items.size()); ++i) {
  2234         Map::set(items[i], _inv_map.size());
  2235         _inv_map.push_back(items[i]);
  2236       }
  2237     }
  2238 
  2239     /// \brief Erase the key from the map.
  2240     ///
  2241     /// Erase the key from the map. It is called by the
  2242     /// \c AlterationNotifier.
  2243     virtual void erase(const Item& item) {
  2244       Map::set(_inv_map.back(), Map::operator[](item));
  2245       _inv_map[Map::operator[](item)] = _inv_map.back();
  2246       _inv_map.pop_back();
  2247       Map::erase(item);
  2248     }
  2249 
  2250     /// \brief Erase more keys from the map.
  2251     ///
  2252     /// Erase more keys from the map. It is called by the
  2253     /// \c AlterationNotifier.
  2254     virtual void erase(const std::vector<Item>& items) {
  2255       for (int i = 0; i < int(items.size()); ++i) {
  2256         Map::set(_inv_map.back(), Map::operator[](items[i]));
  2257         _inv_map[Map::operator[](items[i])] = _inv_map.back();
  2258         _inv_map.pop_back();
  2259       }
  2260       Map::erase(items);
  2261     }
  2262 
  2263     /// \brief Build the unique map.
  2264     ///
  2265     /// Build the unique map. It is called by the
  2266     /// \c AlterationNotifier.
  2267     virtual void build() {
  2268       Map::build();
  2269       Item it;
  2270       const typename Map::Notifier* nf = Map::notifier();
  2271       for (nf->first(it); it != INVALID; nf->next(it)) {
  2272         Map::set(it, _inv_map.size());
  2273         _inv_map.push_back(it);
  2274       }
  2275     }
  2276 
  2277     /// \brief Clear the keys from the map.
  2278     ///
  2279     /// Clear the keys from the map. It is called by the
  2280     /// \c AlterationNotifier.
  2281     virtual void clear() {
  2282       _inv_map.clear();
  2283       Map::clear();
  2284     }
  2285 
  2286   public:
  2287 
  2288     /// \brief Returns the maximal value plus one.
  2289     ///
  2290     /// Returns the maximal value plus one in the map.
  2291     unsigned int size() const {
  2292       return _inv_map.size();
  2293     }
  2294 
  2295     /// \brief Swaps the position of the two items in the map.
  2296     ///
  2297     /// Swaps the position of the two items in the map.
  2298     void swap(const Item& p, const Item& q) {
  2299       int pi = Map::operator[](p);
  2300       int qi = Map::operator[](q);
  2301       Map::set(p, qi);
  2302       _inv_map[qi] = p;
  2303       Map::set(q, pi);
  2304       _inv_map[pi] = q;
  2305     }
  2306 
  2307     /// \brief Gives back the \e range \e id of the item
  2308     ///
  2309     /// Gives back the \e range \e id of the item.
  2310     int operator[](const Item& item) const {
  2311       return Map::operator[](item);
  2312     }
  2313 
  2314     /// \brief Gives back the item belonging to a \e range \e id
  2315     ///
  2316     /// Gives back the item belonging to the given \e range \e id.
  2317     Item operator()(int id) const {
  2318       return _inv_map[id];
  2319     }
  2320 
  2321   private:
  2322 
  2323     typedef std::vector<Item> Container;
  2324     Container _inv_map;
  2325 
  2326   public:
  2327 
  2328     /// \brief The inverse map type of RangeIdMap.
  2329     ///
  2330     /// The inverse map type of RangeIdMap. The subscript operator gives
  2331     /// back an item by its \e range \e id.
  2332     /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
  2333     class InverseMap {
  2334     public:
  2335       /// \brief Constructor
  2336       ///
  2337       /// Constructor of the InverseMap.
  2338       explicit InverseMap(const RangeIdMap& inverted)
  2339         : _inverted(inverted) {}
  2340 
  2341 
  2342       /// The value type of the InverseMap.
  2343       typedef typename RangeIdMap::Key Value;
  2344       /// The key type of the InverseMap.
  2345       typedef typename RangeIdMap::Value Key;
  2346 
  2347       /// \brief Subscript operator.
  2348       ///
  2349       /// Subscript operator. It gives back the item
  2350       /// that the given \e range \e id currently belongs to.
  2351       Value operator[](const Key& key) const {
  2352         return _inverted(key);
  2353       }
  2354 
  2355       /// \brief Size of the map.
  2356       ///
  2357       /// Returns the size of the map.
  2358       unsigned int size() const {
  2359         return _inverted.size();
  2360       }
  2361 
  2362     private:
  2363       const RangeIdMap& _inverted;
  2364     };
  2365 
  2366     /// \brief Gives back the inverse of the map.
  2367     ///
  2368     /// Gives back the inverse of the RangeIdMap.
  2369     const InverseMap inverse() const {
  2370       return InverseMap(*this);
  2371     }
  2372   };
  2373 
  2374   /// \brief Returns a \c RangeIdMap class.
  2375   ///
  2376   /// This function just returns an \c RangeIdMap class.
  2377   /// \relates RangeIdMap
  2378   template <typename K, typename GR>
  2379   inline RangeIdMap<GR, K> rangeIdMap(const GR& graph) {
  2380     return RangeIdMap<GR, K>(graph);
  2381   }
  2382 
  2383   /// \brief Dynamic iterable \c bool map.
  2384   ///
  2385   /// This class provides a special graph map type which can store a
  2386   /// \c bool value for graph items (\c Node, \c Arc or \c Edge).
  2387   /// For both \c true and \c false values it is possible to iterate on
  2388   /// the keys mapped to the value.
  2389   ///
  2390   /// This type is a reference map, so it can be modified with the
  2391   /// subscript operator.
  2392   ///
  2393   /// \tparam GR The graph type.
  2394   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  2395   /// \c GR::Edge).
  2396   ///
  2397   /// \see IterableIntMap, IterableValueMap
  2398   /// \see CrossRefMap
  2399   template <typename GR, typename K>
  2400   class IterableBoolMap
  2401     : protected ItemSetTraits<GR, K>::template Map<int>::Type {
  2402   private:
  2403     typedef GR Graph;
  2404 
  2405     typedef typename ItemSetTraits<GR, K>::ItemIt KeyIt;
  2406     typedef typename ItemSetTraits<GR, K>::template Map<int>::Type Parent;
  2407 
  2408     std::vector<K> _array;
  2409     int _sep;
  2410 
  2411   public:
  2412 
  2413     /// Indicates that the map is reference map.
  2414     typedef True ReferenceMapTag;
  2415 
  2416     /// The key type
  2417     typedef K Key;
  2418     /// The value type
  2419     typedef bool Value;
  2420     /// The const reference type.
  2421     typedef const Value& ConstReference;
  2422 
  2423   private:
  2424 
  2425     int position(const Key& key) const {
  2426       return Parent::operator[](key);
  2427     }
  2428 
  2429   public:
  2430 
  2431     /// \brief Reference to the value of the map.
  2432     ///
  2433     /// This class is similar to the \c bool type. It can be converted to
  2434     /// \c bool and it provides the same operators.
  2435     class Reference {
  2436       friend class IterableBoolMap;
  2437     private:
  2438       Reference(IterableBoolMap& map, const Key& key)
  2439         : _key(key), _map(map) {}
  2440     public:
  2441 
  2442       Reference& operator=(const Reference& value) {
  2443         _map.set(_key, static_cast<bool>(value));
  2444          return *this;
  2445       }
  2446 
  2447       operator bool() const {
  2448         return static_cast<const IterableBoolMap&>(_map)[_key];
  2449       }
  2450 
  2451       Reference& operator=(bool value) {
  2452         _map.set(_key, value);
  2453         return *this;
  2454       }
  2455       Reference& operator&=(bool value) {
  2456         _map.set(_key, _map[_key] & value);
  2457         return *this;
  2458       }
  2459       Reference& operator|=(bool value) {
  2460         _map.set(_key, _map[_key] | value);
  2461         return *this;
  2462       }
  2463       Reference& operator^=(bool value) {
  2464         _map.set(_key, _map[_key] ^ value);
  2465         return *this;
  2466       }
  2467     private:
  2468       Key _key;
  2469       IterableBoolMap& _map;
  2470     };
  2471 
  2472     /// \brief Constructor of the map with a default value.
  2473     ///
  2474     /// Constructor of the map with a default value.
  2475     explicit IterableBoolMap(const Graph& graph, bool def = false)
  2476       : Parent(graph) {
  2477       typename Parent::Notifier* nf = Parent::notifier();
  2478       Key it;
  2479       for (nf->first(it); it != INVALID; nf->next(it)) {
  2480         Parent::set(it, _array.size());
  2481         _array.push_back(it);
  2482       }
  2483       _sep = (def ? _array.size() : 0);
  2484     }
  2485 
  2486     /// \brief Const subscript operator of the map.
  2487     ///
  2488     /// Const subscript operator of the map.
  2489     bool operator[](const Key& key) const {
  2490       return position(key) < _sep;
  2491     }
  2492 
  2493     /// \brief Subscript operator of the map.
  2494     ///
  2495     /// Subscript operator of the map.
  2496     Reference operator[](const Key& key) {
  2497       return Reference(*this, key);
  2498     }
  2499 
  2500     /// \brief Set operation of the map.
  2501     ///
  2502     /// Set operation of the map.
  2503     void set(const Key& key, bool value) {
  2504       int pos = position(key);
  2505       if (value) {
  2506         if (pos < _sep) return;
  2507         Key tmp = _array[_sep];
  2508         _array[_sep] = key;
  2509         Parent::set(key, _sep);
  2510         _array[pos] = tmp;
  2511         Parent::set(tmp, pos);
  2512         ++_sep;
  2513       } else {
  2514         if (pos >= _sep) return;
  2515         --_sep;
  2516         Key tmp = _array[_sep];
  2517         _array[_sep] = key;
  2518         Parent::set(key, _sep);
  2519         _array[pos] = tmp;
  2520         Parent::set(tmp, pos);
  2521       }
  2522     }
  2523 
  2524     /// \brief Set all items.
  2525     ///
  2526     /// Set all items in the map.
  2527     /// \note Constant time operation.
  2528     void setAll(bool value) {
  2529       _sep = (value ? _array.size() : 0);
  2530     }
  2531 
  2532     /// \brief Returns the number of the keys mapped to \c true.
  2533     ///
  2534     /// Returns the number of the keys mapped to \c true.
  2535     int trueNum() const {
  2536       return _sep;
  2537     }
  2538 
  2539     /// \brief Returns the number of the keys mapped to \c false.
  2540     ///
  2541     /// Returns the number of the keys mapped to \c false.
  2542     int falseNum() const {
  2543       return _array.size() - _sep;
  2544     }
  2545 
  2546     /// \brief Iterator for the keys mapped to \c true.
  2547     ///
  2548     /// Iterator for the keys mapped to \c true. It works
  2549     /// like a graph item iterator, it can be converted to
  2550     /// the key type of the map, incremented with \c ++ operator, and
  2551     /// if the iterator leaves the last valid key, it will be equal to
  2552     /// \c INVALID.
  2553     class TrueIt : public Key {
  2554     public:
  2555       typedef Key Parent;
  2556 
  2557       /// \brief Creates an iterator.
  2558       ///
  2559       /// Creates an iterator. It iterates on the
  2560       /// keys mapped to \c true.
  2561       /// \param map The IterableBoolMap.
  2562       explicit TrueIt(const IterableBoolMap& map)
  2563         : Parent(map._sep > 0 ? map._array[map._sep - 1] : INVALID),
  2564           _map(&map) {}
  2565 
  2566       /// \brief Invalid constructor \& conversion.
  2567       ///
  2568       /// This constructor initializes the iterator to be invalid.
  2569       /// \sa Invalid for more details.
  2570       TrueIt(Invalid) : Parent(INVALID), _map(0) {}
  2571 
  2572       /// \brief Increment operator.
  2573       ///
  2574       /// Increment operator.
  2575       TrueIt& operator++() {
  2576         int pos = _map->position(*this);
  2577         Parent::operator=(pos > 0 ? _map->_array[pos - 1] : INVALID);
  2578         return *this;
  2579       }
  2580 
  2581     private:
  2582       const IterableBoolMap* _map;
  2583     };
  2584 
  2585     /// \brief STL style iterator for the keys mapped to \c true.
  2586     ///
  2587     /// This is an STL style wrapper for \ref TrueIt.
  2588     /// It can be used in range-based for loops, STL algorithms, etc.
  2589     LemonRangeWrapper1<TrueIt, IterableBoolMap>
  2590     trueKeys() {
  2591       return LemonRangeWrapper1<TrueIt, IterableBoolMap>(*this);
  2592     }
  2593 
  2594 
  2595     /// \brief Iterator for the keys mapped to \c false.
  2596     ///
  2597     /// Iterator for the keys mapped to \c false. It works
  2598     /// like a graph item iterator, it can be converted to
  2599     /// the key type of the map, incremented with \c ++ operator, and
  2600     /// if the iterator leaves the last valid key, it will be equal to
  2601     /// \c INVALID.
  2602     class FalseIt : public Key {
  2603     public:
  2604       typedef Key Parent;
  2605 
  2606       /// \brief Creates an iterator.
  2607       ///
  2608       /// Creates an iterator. It iterates on the
  2609       /// keys mapped to \c false.
  2610       /// \param map The IterableBoolMap.
  2611       explicit FalseIt(const IterableBoolMap& map)
  2612         : Parent(map._sep < int(map._array.size()) ?
  2613                  map._array.back() : INVALID), _map(&map) {}
  2614 
  2615       /// \brief Invalid constructor \& conversion.
  2616       ///
  2617       /// This constructor initializes the iterator to be invalid.
  2618       /// \sa Invalid for more details.
  2619       FalseIt(Invalid) : Parent(INVALID), _map(0) {}
  2620 
  2621       /// \brief Increment operator.
  2622       ///
  2623       /// Increment operator.
  2624       FalseIt& operator++() {
  2625         int pos = _map->position(*this);
  2626         Parent::operator=(pos > _map->_sep ? _map->_array[pos - 1] : INVALID);
  2627         return *this;
  2628       }
  2629 
  2630     private:
  2631       const IterableBoolMap* _map;
  2632     };
  2633 
  2634     /// \brief STL style iterator for the keys mapped to \c false.
  2635     ///
  2636     /// This is an STL style wrapper for \ref FalseIt.
  2637     /// It can be used in range-based for loops, STL algorithms, etc.
  2638     LemonRangeWrapper1<FalseIt, IterableBoolMap>
  2639     falseKeys() {
  2640       return LemonRangeWrapper1<FalseIt, IterableBoolMap>(*this);
  2641     }
  2642 
  2643 
  2644     /// \brief Iterator for the keys mapped to a given value.
  2645     ///
  2646     /// Iterator for the keys mapped to a given value. It works
  2647     /// like a graph item iterator, it can be converted to
  2648     /// the key type of the map, incremented with \c ++ operator, and
  2649     /// if the iterator leaves the last valid key, it will be equal to
  2650     /// \c INVALID.
  2651     class ItemIt : public Key {
  2652     public:
  2653       typedef Key Parent;
  2654 
  2655       /// \brief Creates an iterator with a value.
  2656       ///
  2657       /// Creates an iterator with a value. It iterates on the
  2658       /// keys mapped to the given value.
  2659       /// \param map The IterableBoolMap.
  2660       /// \param value The value.
  2661       ItemIt(const IterableBoolMap& map, bool value)
  2662         : Parent(value ?
  2663                  (map._sep > 0 ?
  2664                   map._array[map._sep - 1] : INVALID) :
  2665                  (map._sep < int(map._array.size()) ?
  2666                   map._array.back() : INVALID)), _map(&map) {}
  2667 
  2668       /// \brief Invalid constructor \& conversion.
  2669       ///
  2670       /// This constructor initializes the iterator to be invalid.
  2671       /// \sa Invalid for more details.
  2672       ItemIt(Invalid) : Parent(INVALID), _map(0) {}
  2673 
  2674       /// \brief Increment operator.
  2675       ///
  2676       /// Increment operator.
  2677       ItemIt& operator++() {
  2678         int pos = _map->position(*this);
  2679         int _sep = pos >= _map->_sep ? _map->_sep : 0;
  2680         Parent::operator=(pos > _sep ? _map->_array[pos - 1] : INVALID);
  2681         return *this;
  2682       }
  2683 
  2684     private:
  2685       const IterableBoolMap* _map;
  2686     };
  2687 
  2688     /// \brief STL style iterator for the keys mapped to a given value.
  2689     ///
  2690     /// This is an STL style wrapper for \ref ItemIt.
  2691     /// It can be used in range-based for loops, STL algorithms, etc.
  2692     LemonRangeWrapper2<ItemIt, IterableBoolMap, bool>
  2693     items(bool value) {
  2694       return LemonRangeWrapper2<ItemIt, IterableBoolMap, bool>(*this, value);
  2695     }
  2696 
  2697   protected:
  2698 
  2699     virtual void add(const Key& key) {
  2700       Parent::add(key);
  2701       Parent::set(key, _array.size());
  2702       _array.push_back(key);
  2703     }
  2704 
  2705     virtual void add(const std::vector<Key>& keys) {
  2706       Parent::add(keys);
  2707       for (int i = 0; i < int(keys.size()); ++i) {
  2708         Parent::set(keys[i], _array.size());
  2709         _array.push_back(keys[i]);
  2710       }
  2711     }
  2712 
  2713     virtual void erase(const Key& key) {
  2714       int pos = position(key);
  2715       if (pos < _sep) {
  2716         --_sep;
  2717         Parent::set(_array[_sep], pos);
  2718         _array[pos] = _array[_sep];
  2719         Parent::set(_array.back(), _sep);
  2720         _array[_sep] = _array.back();
  2721         _array.pop_back();
  2722       } else {
  2723         Parent::set(_array.back(), pos);
  2724         _array[pos] = _array.back();
  2725         _array.pop_back();
  2726       }
  2727       Parent::erase(key);
  2728     }
  2729 
  2730     virtual void erase(const std::vector<Key>& keys) {
  2731       for (int i = 0; i < int(keys.size()); ++i) {
  2732         int pos = position(keys[i]);
  2733         if (pos < _sep) {
  2734           --_sep;
  2735           Parent::set(_array[_sep], pos);
  2736           _array[pos] = _array[_sep];
  2737           Parent::set(_array.back(), _sep);
  2738           _array[_sep] = _array.back();
  2739           _array.pop_back();
  2740         } else {
  2741           Parent::set(_array.back(), pos);
  2742           _array[pos] = _array.back();
  2743           _array.pop_back();
  2744         }
  2745       }
  2746       Parent::erase(keys);
  2747     }
  2748 
  2749     virtual void build() {
  2750       Parent::build();
  2751       typename Parent::Notifier* nf = Parent::notifier();
  2752       Key it;
  2753       for (nf->first(it); it != INVALID; nf->next(it)) {
  2754         Parent::set(it, _array.size());
  2755         _array.push_back(it);
  2756       }
  2757       _sep = 0;
  2758     }
  2759 
  2760     virtual void clear() {
  2761       _array.clear();
  2762       _sep = 0;
  2763       Parent::clear();
  2764     }
  2765 
  2766   };
  2767 
  2768 
  2769   namespace _maps_bits {
  2770     template <typename Item>
  2771     struct IterableIntMapNode {
  2772       IterableIntMapNode() : value(-1) {}
  2773       IterableIntMapNode(int _value) : value(_value) {}
  2774       Item prev, next;
  2775       int value;
  2776     };
  2777   }
  2778 
  2779   /// \brief Dynamic iterable integer map.
  2780   ///
  2781   /// This class provides a special graph map type which can store an
  2782   /// integer value for graph items (\c Node, \c Arc or \c Edge).
  2783   /// For each non-negative value it is possible to iterate on the keys
  2784   /// mapped to the value.
  2785   ///
  2786   /// This map is intended to be used with small integer values, for which
  2787   /// it is efficient, and supports iteration only for non-negative values.
  2788   /// If you need large values and/or iteration for negative integers,
  2789   /// consider to use \ref IterableValueMap instead.
  2790   ///
  2791   /// This type is a reference map, so it can be modified with the
  2792   /// subscript operator.
  2793   ///
  2794   /// \note The size of the data structure depends on the largest
  2795   /// value in the map.
  2796   ///
  2797   /// \tparam GR The graph type.
  2798   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  2799   /// \c GR::Edge).
  2800   ///
  2801   /// \see IterableBoolMap, IterableValueMap
  2802   /// \see CrossRefMap
  2803   template <typename GR, typename K>
  2804   class IterableIntMap
  2805     : protected ItemSetTraits<GR, K>::
  2806         template Map<_maps_bits::IterableIntMapNode<K> >::Type {
  2807   public:
  2808     typedef typename ItemSetTraits<GR, K>::
  2809       template Map<_maps_bits::IterableIntMapNode<K> >::Type Parent;
  2810 
  2811     /// The key type
  2812     typedef K Key;
  2813     /// The value type
  2814     typedef int Value;
  2815     /// The graph type
  2816     typedef GR Graph;
  2817 
  2818     /// \brief Constructor of the map.
  2819     ///
  2820     /// Constructor of the map. It sets all values to -1.
  2821     explicit IterableIntMap(const Graph& graph)
  2822       : Parent(graph) {}
  2823 
  2824     /// \brief Constructor of the map with a given value.
  2825     ///
  2826     /// Constructor of the map with a given value.
  2827     explicit IterableIntMap(const Graph& graph, int value)
  2828       : Parent(graph, _maps_bits::IterableIntMapNode<K>(value)) {
  2829       if (value >= 0) {
  2830         for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
  2831           lace(it);
  2832         }
  2833       }
  2834     }
  2835 
  2836   private:
  2837 
  2838     void unlace(const Key& key) {
  2839       typename Parent::Value& node = Parent::operator[](key);
  2840       if (node.value < 0) return;
  2841       if (node.prev != INVALID) {
  2842         Parent::operator[](node.prev).next = node.next;
  2843       } else {
  2844         _first[node.value] = node.next;
  2845       }
  2846       if (node.next != INVALID) {
  2847         Parent::operator[](node.next).prev = node.prev;
  2848       }
  2849       while (!_first.empty() && _first.back() == INVALID) {
  2850         _first.pop_back();
  2851       }
  2852     }
  2853 
  2854     void lace(const Key& key) {
  2855       typename Parent::Value& node = Parent::operator[](key);
  2856       if (node.value < 0) return;
  2857       if (node.value >= int(_first.size())) {
  2858         _first.resize(node.value + 1, INVALID);
  2859       }
  2860       node.prev = INVALID;
  2861       node.next = _first[node.value];
  2862       if (node.next != INVALID) {
  2863         Parent::operator[](node.next).prev = key;
  2864       }
  2865       _first[node.value] = key;
  2866     }
  2867 
  2868   public:
  2869 
  2870     /// Indicates that the map is reference map.
  2871     typedef True ReferenceMapTag;
  2872 
  2873     /// \brief Reference to the value of the map.
  2874     ///
  2875     /// This class is similar to the \c int type. It can
  2876     /// be converted to \c int and it has the same operators.
  2877     class Reference {
  2878       friend class IterableIntMap;
  2879     private:
  2880       Reference(IterableIntMap& map, const Key& key)
  2881         : _key(key), _map(map) {}
  2882     public:
  2883 
  2884       Reference& operator=(const Reference& value) {
  2885         _map.set(_key, static_cast<const int&>(value));
  2886          return *this;
  2887       }
  2888 
  2889       operator const int&() const {
  2890         return static_cast<const IterableIntMap&>(_map)[_key];
  2891       }
  2892 
  2893       Reference& operator=(int value) {
  2894         _map.set(_key, value);
  2895         return *this;
  2896       }
  2897       Reference& operator++() {
  2898         _map.set(_key, _map[_key] + 1);
  2899         return *this;
  2900       }
  2901       int operator++(int) {
  2902         int value = _map[_key];
  2903         _map.set(_key, value + 1);
  2904         return value;
  2905       }
  2906       Reference& operator--() {
  2907         _map.set(_key, _map[_key] - 1);
  2908         return *this;
  2909       }
  2910       int operator--(int) {
  2911         int value = _map[_key];
  2912         _map.set(_key, value - 1);
  2913         return value;
  2914       }
  2915       Reference& operator+=(int value) {
  2916         _map.set(_key, _map[_key] + value);
  2917         return *this;
  2918       }
  2919       Reference& operator-=(int value) {
  2920         _map.set(_key, _map[_key] - value);
  2921         return *this;
  2922       }
  2923       Reference& operator*=(int value) {
  2924         _map.set(_key, _map[_key] * value);
  2925         return *this;
  2926       }
  2927       Reference& operator/=(int value) {
  2928         _map.set(_key, _map[_key] / value);
  2929         return *this;
  2930       }
  2931       Reference& operator%=(int value) {
  2932         _map.set(_key, _map[_key] % value);
  2933         return *this;
  2934       }
  2935       Reference& operator&=(int value) {
  2936         _map.set(_key, _map[_key] & value);
  2937         return *this;
  2938       }
  2939       Reference& operator|=(int value) {
  2940         _map.set(_key, _map[_key] | value);
  2941         return *this;
  2942       }
  2943       Reference& operator^=(int value) {
  2944         _map.set(_key, _map[_key] ^ value);
  2945         return *this;
  2946       }
  2947       Reference& operator<<=(int value) {
  2948         _map.set(_key, _map[_key] << value);
  2949         return *this;
  2950       }
  2951       Reference& operator>>=(int value) {
  2952         _map.set(_key, _map[_key] >> value);
  2953         return *this;
  2954       }
  2955 
  2956     private:
  2957       Key _key;
  2958       IterableIntMap& _map;
  2959     };
  2960 
  2961     /// The const reference type.
  2962     typedef const Value& ConstReference;
  2963 
  2964     /// \brief Gives back the maximal value plus one.
  2965     ///
  2966     /// Gives back the maximal value plus one.
  2967     int size() const {
  2968       return _first.size();
  2969     }
  2970 
  2971     /// \brief Set operation of the map.
  2972     ///
  2973     /// Set operation of the map.
  2974     void set(const Key& key, const Value& value) {
  2975       unlace(key);
  2976       Parent::operator[](key).value = value;
  2977       lace(key);
  2978     }
  2979 
  2980     /// \brief Const subscript operator of the map.
  2981     ///
  2982     /// Const subscript operator of the map.
  2983     const Value& operator[](const Key& key) const {
  2984       return Parent::operator[](key).value;
  2985     }
  2986 
  2987     /// \brief Subscript operator of the map.
  2988     ///
  2989     /// Subscript operator of the map.
  2990     Reference operator[](const Key& key) {
  2991       return Reference(*this, key);
  2992     }
  2993 
  2994     /// \brief Iterator for the keys with the same value.
  2995     ///
  2996     /// Iterator for the keys with the same value. It works
  2997     /// like a graph item iterator, it can be converted to
  2998     /// the item type of the map, incremented with \c ++ operator, and
  2999     /// if the iterator leaves the last valid item, it will be equal to
  3000     /// \c INVALID.
  3001     class ItemIt : public Key {
  3002     public:
  3003       typedef Key Parent;
  3004 
  3005       /// \brief Invalid constructor \& conversion.
  3006       ///
  3007       /// This constructor initializes the iterator to be invalid.
  3008       /// \sa Invalid for more details.
  3009       ItemIt(Invalid) : Parent(INVALID), _map(0) {}
  3010 
  3011       /// \brief Creates an iterator with a value.
  3012       ///
  3013       /// Creates an iterator with a value. It iterates on the
  3014       /// keys mapped to the given value.
  3015       /// \param map The IterableIntMap.
  3016       /// \param value The value.
  3017       ItemIt(const IterableIntMap& map, int value) : _map(&map) {
  3018         if (value < 0 || value >= int(_map->_first.size())) {
  3019           Parent::operator=(INVALID);
  3020         } else {
  3021           Parent::operator=(_map->_first[value]);
  3022         }
  3023       }
  3024 
  3025       /// \brief Increment operator.
  3026       ///
  3027       /// Increment operator.
  3028       ItemIt& operator++() {
  3029         Parent::operator=(_map->IterableIntMap::Parent::
  3030                           operator[](static_cast<Parent&>(*this)).next);
  3031         return *this;
  3032       }
  3033 
  3034     private:
  3035       const IterableIntMap* _map;
  3036     };
  3037 
  3038     /// \brief STL style iterator for the keys with the same value.
  3039     ///
  3040     /// This is an STL style wrapper for \ref ItemIt.
  3041     /// It can be used in range-based for loops, STL algorithms, etc.
  3042     LemonRangeWrapper2<ItemIt, IterableIntMap, int>
  3043     items(int value) {
  3044       return LemonRangeWrapper2<ItemIt, IterableIntMap, int>(*this, value);
  3045     }
  3046 
  3047 
  3048   protected:
  3049 
  3050     virtual void erase(const Key& key) {
  3051       unlace(key);
  3052       Parent::erase(key);
  3053     }
  3054 
  3055     virtual void erase(const std::vector<Key>& keys) {
  3056       for (int i = 0; i < int(keys.size()); ++i) {
  3057         unlace(keys[i]);
  3058       }
  3059       Parent::erase(keys);
  3060     }
  3061 
  3062     virtual void clear() {
  3063       _first.clear();
  3064       Parent::clear();
  3065     }
  3066 
  3067   private:
  3068     std::vector<Key> _first;
  3069   };
  3070 
  3071   namespace _maps_bits {
  3072     template <typename Item, typename Value>
  3073     struct IterableValueMapNode {
  3074       IterableValueMapNode(Value _value = Value()) : value(_value) {}
  3075       Item prev, next;
  3076       Value value;
  3077     };
  3078   }
  3079 
  3080   /// \brief Dynamic iterable map for comparable values.
  3081   ///
  3082   /// This class provides a special graph map type which can store a
  3083   /// comparable value for graph items (\c Node, \c Arc or \c Edge).
  3084   /// For each value it is possible to iterate on the keys mapped to
  3085   /// the value (\c ItemIt), and the values of the map can be accessed
  3086   /// with an STL compatible forward iterator (\c ValueIt).
  3087   /// The map stores a linked list for each value, which contains
  3088   /// the items mapped to the value, and the used values are stored
  3089   /// in balanced binary tree (\c std::map).
  3090   ///
  3091   /// \ref IterableBoolMap and \ref IterableIntMap are similar classes
  3092   /// specialized for \c bool and \c int values, respectively.
  3093   ///
  3094   /// This type is not reference map, so it cannot be modified with
  3095   /// the subscript operator.
  3096   ///
  3097   /// \tparam GR The graph type.
  3098   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  3099   /// \c GR::Edge).
  3100   /// \tparam V The value type of the map. It can be any comparable
  3101   /// value type.
  3102   ///
  3103   /// \see IterableBoolMap, IterableIntMap
  3104   /// \see CrossRefMap
  3105   template <typename GR, typename K, typename V>
  3106   class IterableValueMap
  3107     : protected ItemSetTraits<GR, K>::
  3108         template Map<_maps_bits::IterableValueMapNode<K, V> >::Type {
  3109   public:
  3110     typedef typename ItemSetTraits<GR, K>::
  3111       template Map<_maps_bits::IterableValueMapNode<K, V> >::Type Parent;
  3112 
  3113     /// The key type
  3114     typedef K Key;
  3115     /// The value type
  3116     typedef V Value;
  3117     /// The graph type
  3118     typedef GR Graph;
  3119 
  3120   public:
  3121 
  3122     /// \brief Constructor of the map with a given value.
  3123     ///
  3124     /// Constructor of the map with a given value.
  3125     explicit IterableValueMap(const Graph& graph,
  3126                               const Value& value = Value())
  3127       : Parent(graph, _maps_bits::IterableValueMapNode<K, V>(value)) {
  3128       for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
  3129         lace(it);
  3130       }
  3131     }
  3132 
  3133   protected:
  3134 
  3135     void unlace(const Key& key) {
  3136       typename Parent::Value& node = Parent::operator[](key);
  3137       if (node.prev != INVALID) {
  3138         Parent::operator[](node.prev).next = node.next;
  3139       } else {
  3140         if (node.next != INVALID) {
  3141           _first[node.value] = node.next;
  3142         } else {
  3143           _first.erase(node.value);
  3144         }
  3145       }
  3146       if (node.next != INVALID) {
  3147         Parent::operator[](node.next).prev = node.prev;
  3148       }
  3149     }
  3150 
  3151     void lace(const Key& key) {
  3152       typename Parent::Value& node = Parent::operator[](key);
  3153       typename std::map<Value, Key>::iterator it = _first.find(node.value);
  3154       if (it == _first.end()) {
  3155         node.prev = node.next = INVALID;
  3156         _first.insert(std::make_pair(node.value, key));
  3157       } else {
  3158         node.prev = INVALID;
  3159         node.next = it->second;
  3160         if (node.next != INVALID) {
  3161           Parent::operator[](node.next).prev = key;
  3162         }
  3163         it->second = key;
  3164       }
  3165     }
  3166 
  3167   public:
  3168 
  3169     /// \brief Forward iterator for values.
  3170     ///
  3171     /// This iterator is an STL compatible forward
  3172     /// iterator on the values of the map. The values can
  3173     /// be accessed in the <tt>[beginValue, endValue)</tt> range.
  3174     class ValueIt
  3175       : public std::iterator<std::forward_iterator_tag, Value> {
  3176       friend class IterableValueMap;
  3177     private:
  3178       ValueIt(typename std::map<Value, Key>::const_iterator _it)
  3179         : it(_it) {}
  3180     public:
  3181 
  3182       /// Constructor
  3183       ValueIt() {}
  3184 
  3185       /// \e
  3186       ValueIt& operator++() { ++it; return *this; }
  3187       /// \e
  3188       ValueIt operator++(int) {
  3189         ValueIt tmp(*this);
  3190         operator++();
  3191         return tmp;
  3192       }
  3193 
  3194       /// \e
  3195       const Value& operator*() const { return it->first; }
  3196       /// \e
  3197       const Value* operator->() const { return &(it->first); }
  3198 
  3199       /// \e
  3200       bool operator==(ValueIt jt) const { return it == jt.it; }
  3201       /// \e
  3202       bool operator!=(ValueIt jt) const { return it != jt.it; }
  3203 
  3204     private:
  3205       typename std::map<Value, Key>::const_iterator it;
  3206     };
  3207 
  3208     /// \brief Returns an iterator to the first value.
  3209     ///
  3210     /// Returns an STL compatible iterator to the
  3211     /// first value of the map. The values of the
  3212     /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  3213     /// range.
  3214     ValueIt beginValue() const {
  3215       return ValueIt(_first.begin());
  3216     }
  3217 
  3218     /// \brief Returns an iterator after the last value.
  3219     ///
  3220     /// Returns an STL compatible iterator after the
  3221     /// last value of the map. The values of the
  3222     /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  3223     /// range.
  3224     ValueIt endValue() const {
  3225       return ValueIt(_first.end());
  3226     }
  3227 
  3228     /// \brief Set operation of the map.
  3229     ///
  3230     /// Set operation of the map.
  3231     void set(const Key& key, const Value& value) {
  3232       unlace(key);
  3233       Parent::operator[](key).value = value;
  3234       lace(key);
  3235     }
  3236 
  3237     /// \brief Const subscript operator of the map.
  3238     ///
  3239     /// Const subscript operator of the map.
  3240     const Value& operator[](const Key& key) const {
  3241       return Parent::operator[](key).value;
  3242     }
  3243 
  3244     /// \brief Iterator for the keys with the same value.
  3245     ///
  3246     /// Iterator for the keys with the same value. It works
  3247     /// like a graph item iterator, it can be converted to
  3248     /// the item type of the map, incremented with \c ++ operator, and
  3249     /// if the iterator leaves the last valid item, it will be equal to
  3250     /// \c INVALID.
  3251     class ItemIt : public Key {
  3252     public:
  3253       typedef Key Parent;
  3254 
  3255       /// \brief Invalid constructor \& conversion.
  3256       ///
  3257       /// This constructor initializes the iterator to be invalid.
  3258       /// \sa Invalid for more details.
  3259       ItemIt(Invalid) : Parent(INVALID), _map(0) {}
  3260 
  3261       /// \brief Creates an iterator with a value.
  3262       ///
  3263       /// Creates an iterator with a value. It iterates on the
  3264       /// keys which have the given value.
  3265       /// \param map The IterableValueMap
  3266       /// \param value The value
  3267       ItemIt(const IterableValueMap& map, const Value& value) : _map(&map) {
  3268         typename std::map<Value, Key>::const_iterator it =
  3269           map._first.find(value);
  3270         if (it == map._first.end()) {
  3271           Parent::operator=(INVALID);
  3272         } else {
  3273           Parent::operator=(it->second);
  3274         }
  3275       }
  3276 
  3277       /// \brief Increment operator.
  3278       ///
  3279       /// Increment Operator.
  3280       ItemIt& operator++() {
  3281         Parent::operator=(_map->IterableValueMap::Parent::
  3282                           operator[](static_cast<Parent&>(*this)).next);
  3283         return *this;
  3284       }
  3285 
  3286 
  3287     private:
  3288       const IterableValueMap* _map;
  3289     };
  3290 
  3291     /// \brief STL style iterator for the keys with the same value.
  3292     ///
  3293     /// This is an STL style wrapper for \ref ItemIt.
  3294     /// It can be used in range-based for loops, STL algorithms, etc.
  3295     LemonRangeWrapper2<ItemIt, IterableValueMap, V>
  3296     items(const V& value) {
  3297       return LemonRangeWrapper2<ItemIt, IterableValueMap, V>(*this, value);
  3298     }
  3299 
  3300 
  3301   protected:
  3302 
  3303     virtual void add(const Key& key) {
  3304       Parent::add(key);
  3305       lace(key);
  3306     }
  3307 
  3308     virtual void add(const std::vector<Key>& keys) {
  3309       Parent::add(keys);
  3310       for (int i = 0; i < int(keys.size()); ++i) {
  3311         lace(keys[i]);
  3312       }
  3313     }
  3314 
  3315     virtual void erase(const Key& key) {
  3316       unlace(key);
  3317       Parent::erase(key);
  3318     }
  3319 
  3320     virtual void erase(const std::vector<Key>& keys) {
  3321       for (int i = 0; i < int(keys.size()); ++i) {
  3322         unlace(keys[i]);
  3323       }
  3324       Parent::erase(keys);
  3325     }
  3326 
  3327     virtual void build() {
  3328       Parent::build();
  3329       for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
  3330         lace(it);
  3331       }
  3332     }
  3333 
  3334     virtual void clear() {
  3335       _first.clear();
  3336       Parent::clear();
  3337     }
  3338 
  3339   private:
  3340     std::map<Value, Key> _first;
  3341   };
  3342 
  3343   /// \brief Map of the source nodes of arcs in a digraph.
  3344   ///
  3345   /// SourceMap provides access for the source node of each arc in a digraph,
  3346   /// which is returned by the \c source() function of the digraph.
  3347   /// \tparam GR The digraph type.
  3348   /// \see TargetMap
  3349   template <typename GR>
  3350   class SourceMap {
  3351   public:
  3352 
  3353     /// The key type (the \c Arc type of the digraph).
  3354     typedef typename GR::Arc Key;
  3355     /// The value type (the \c Node type of the digraph).
  3356     typedef typename GR::Node Value;
  3357 
  3358     /// \brief Constructor
  3359     ///
  3360     /// Constructor.
  3361     /// \param digraph The digraph that the map belongs to.
  3362     explicit SourceMap(const GR& digraph) : _graph(digraph) {}
  3363 
  3364     /// \brief Returns the source node of the given arc.
  3365     ///
  3366     /// Returns the source node of the given arc.
  3367     Value operator[](const Key& arc) const {
  3368       return _graph.source(arc);
  3369     }
  3370 
  3371   private:
  3372     const GR& _graph;
  3373   };
  3374 
  3375   /// \brief Returns a \c SourceMap class.
  3376   ///
  3377   /// This function just returns an \c SourceMap class.
  3378   /// \relates SourceMap
  3379   template <typename GR>
  3380   inline SourceMap<GR> sourceMap(const GR& graph) {
  3381     return SourceMap<GR>(graph);
  3382   }
  3383 
  3384   /// \brief Map of the target nodes of arcs in a digraph.
  3385   ///
  3386   /// TargetMap provides access for the target node of each arc in a digraph,
  3387   /// which is returned by the \c target() function of the digraph.
  3388   /// \tparam GR The digraph type.
  3389   /// \see SourceMap
  3390   template <typename GR>
  3391   class TargetMap {
  3392   public:
  3393 
  3394     /// The key type (the \c Arc type of the digraph).
  3395     typedef typename GR::Arc Key;
  3396     /// The value type (the \c Node type of the digraph).
  3397     typedef typename GR::Node Value;
  3398 
  3399     /// \brief Constructor
  3400     ///
  3401     /// Constructor.
  3402     /// \param digraph The digraph that the map belongs to.
  3403     explicit TargetMap(const GR& digraph) : _graph(digraph) {}
  3404 
  3405     /// \brief Returns the target node of the given arc.
  3406     ///
  3407     /// Returns the target node of the given arc.
  3408     Value operator[](const Key& e) const {
  3409       return _graph.target(e);
  3410     }
  3411 
  3412   private:
  3413     const GR& _graph;
  3414   };
  3415 
  3416   /// \brief Returns a \c TargetMap class.
  3417   ///
  3418   /// This function just returns a \c TargetMap class.
  3419   /// \relates TargetMap
  3420   template <typename GR>
  3421   inline TargetMap<GR> targetMap(const GR& graph) {
  3422     return TargetMap<GR>(graph);
  3423   }
  3424 
  3425   /// \brief Map of the "forward" directed arc view of edges in a graph.
  3426   ///
  3427   /// ForwardMap provides access for the "forward" directed arc view of
  3428   /// each edge in a graph, which is returned by the \c direct() function
  3429   /// of the graph with \c true parameter.
  3430   /// \tparam GR The graph type.
  3431   /// \see BackwardMap
  3432   template <typename GR>
  3433   class ForwardMap {
  3434   public:
  3435 
  3436     /// The key type (the \c Edge type of the digraph).
  3437     typedef typename GR::Edge Key;
  3438     /// The value type (the \c Arc type of the digraph).
  3439     typedef typename GR::Arc Value;
  3440 
  3441     /// \brief Constructor
  3442     ///
  3443     /// Constructor.
  3444     /// \param graph The graph that the map belongs to.
  3445     explicit ForwardMap(const GR& graph) : _graph(graph) {}
  3446 
  3447     /// \brief Returns the "forward" directed arc view of the given edge.
  3448     ///
  3449     /// Returns the "forward" directed arc view of the given edge.
  3450     Value operator[](const Key& key) const {
  3451       return _graph.direct(key, true);
  3452     }
  3453 
  3454   private:
  3455     const GR& _graph;
  3456   };
  3457 
  3458   /// \brief Returns a \c ForwardMap class.
  3459   ///
  3460   /// This function just returns an \c ForwardMap class.
  3461   /// \relates ForwardMap
  3462   template <typename GR>
  3463   inline ForwardMap<GR> forwardMap(const GR& graph) {
  3464     return ForwardMap<GR>(graph);
  3465   }
  3466 
  3467   /// \brief Map of the "backward" directed arc view of edges in a graph.
  3468   ///
  3469   /// BackwardMap provides access for the "backward" directed arc view of
  3470   /// each edge in a graph, which is returned by the \c direct() function
  3471   /// of the graph with \c false parameter.
  3472   /// \tparam GR The graph type.
  3473   /// \see ForwardMap
  3474   template <typename GR>
  3475   class BackwardMap {
  3476   public:
  3477 
  3478     /// The key type (the \c Edge type of the digraph).
  3479     typedef typename GR::Edge Key;
  3480     /// The value type (the \c Arc type of the digraph).
  3481     typedef typename GR::Arc Value;
  3482 
  3483     /// \brief Constructor
  3484     ///
  3485     /// Constructor.
  3486     /// \param graph The graph that the map belongs to.
  3487     explicit BackwardMap(const GR& graph) : _graph(graph) {}
  3488 
  3489     /// \brief Returns the "backward" directed arc view of the given edge.
  3490     ///
  3491     /// Returns the "backward" directed arc view of the given edge.
  3492     Value operator[](const Key& key) const {
  3493       return _graph.direct(key, false);
  3494     }
  3495 
  3496   private:
  3497     const GR& _graph;
  3498   };
  3499 
  3500   /// \brief Returns a \c BackwardMap class
  3501 
  3502   /// This function just returns a \c BackwardMap class.
  3503   /// \relates BackwardMap
  3504   template <typename GR>
  3505   inline BackwardMap<GR> backwardMap(const GR& graph) {
  3506     return BackwardMap<GR>(graph);
  3507   }
  3508 
  3509   /// \brief Map of the in-degrees of nodes in a digraph.
  3510   ///
  3511   /// This map returns the in-degree of a node. Once it is constructed,
  3512   /// the degrees are stored in a standard \c NodeMap, so each query is done
  3513   /// in constant time. On the other hand, the values are updated automatically
  3514   /// whenever the digraph changes.
  3515   ///
  3516   /// \warning Besides \c addNode() and \c addArc(), a digraph structure
  3517   /// may provide alternative ways to modify the digraph.
  3518   /// The correct behavior of InDegMap is not guarantied if these additional
  3519   /// features are used. For example, the functions
  3520   /// \ref ListDigraph::changeSource() "changeSource()",
  3521   /// \ref ListDigraph::changeTarget() "changeTarget()" and
  3522   /// \ref ListDigraph::reverseArc() "reverseArc()"
  3523   /// of \ref ListDigraph will \e not update the degree values correctly.
  3524   ///
  3525   /// \sa OutDegMap
  3526   template <typename GR>
  3527   class InDegMap
  3528     : protected ItemSetTraits<GR, typename GR::Arc>
  3529       ::ItemNotifier::ObserverBase {
  3530 
  3531   public:
  3532 
  3533     /// The graph type of InDegMap
  3534     typedef GR Graph;
  3535     typedef GR Digraph;
  3536     /// The key type
  3537     typedef typename Digraph::Node Key;
  3538     /// The value type
  3539     typedef int Value;
  3540 
  3541     typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
  3542     ::ItemNotifier::ObserverBase Parent;
  3543 
  3544   private:
  3545 
  3546     class AutoNodeMap
  3547       : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {
  3548     public:
  3549 
  3550       typedef typename ItemSetTraits<Digraph, Key>::
  3551       template Map<int>::Type Parent;
  3552 
  3553       AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
  3554 
  3555       virtual void add(const Key& key) {
  3556         Parent::add(key);
  3557         Parent::set(key, 0);
  3558       }
  3559 
  3560       virtual void add(const std::vector<Key>& keys) {
  3561         Parent::add(keys);
  3562         for (int i = 0; i < int(keys.size()); ++i) {
  3563           Parent::set(keys[i], 0);
  3564         }
  3565       }
  3566 
  3567       virtual void build() {
  3568         Parent::build();
  3569         Key it;
  3570         typename Parent::Notifier* nf = Parent::notifier();
  3571         for (nf->first(it); it != INVALID; nf->next(it)) {
  3572           Parent::set(it, 0);
  3573         }
  3574       }
  3575     };
  3576 
  3577   public:
  3578 
  3579     /// \brief Constructor.
  3580     ///
  3581     /// Constructor for creating an in-degree map.
  3582     explicit InDegMap(const Digraph& graph)
  3583       : _digraph(graph), _deg(graph) {
  3584       Parent::attach(_digraph.notifier(typename Digraph::Arc()));
  3585 
  3586       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3587         _deg[it] = countInArcs(_digraph, it);
  3588       }
  3589     }
  3590 
  3591     /// \brief Gives back the in-degree of a Node.
  3592     ///
  3593     /// Gives back the in-degree of a Node.
  3594     int operator[](const Key& key) const {
  3595       return _deg[key];
  3596     }
  3597 
  3598   protected:
  3599 
  3600     typedef typename Digraph::Arc Arc;
  3601 
  3602     virtual void add(const Arc& arc) {
  3603       ++_deg[_digraph.target(arc)];
  3604     }
  3605 
  3606     virtual void add(const std::vector<Arc>& arcs) {
  3607       for (int i = 0; i < int(arcs.size()); ++i) {
  3608         ++_deg[_digraph.target(arcs[i])];
  3609       }
  3610     }
  3611 
  3612     virtual void erase(const Arc& arc) {
  3613       --_deg[_digraph.target(arc)];
  3614     }
  3615 
  3616     virtual void erase(const std::vector<Arc>& arcs) {
  3617       for (int i = 0; i < int(arcs.size()); ++i) {
  3618         --_deg[_digraph.target(arcs[i])];
  3619       }
  3620     }
  3621 
  3622     virtual void build() {
  3623       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3624         _deg[it] = countInArcs(_digraph, it);
  3625       }
  3626     }
  3627 
  3628     virtual void clear() {
  3629       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3630         _deg[it] = 0;
  3631       }
  3632     }
  3633   private:
  3634 
  3635     const Digraph& _digraph;
  3636     AutoNodeMap _deg;
  3637   };
  3638 
  3639   /// \brief Map of the out-degrees of nodes in a digraph.
  3640   ///
  3641   /// This map returns the out-degree of a node. Once it is constructed,
  3642   /// the degrees are stored in a standard \c NodeMap, so each query is done
  3643   /// in constant time. On the other hand, the values are updated automatically
  3644   /// whenever the digraph changes.
  3645   ///
  3646   /// \warning Besides \c addNode() and \c addArc(), a digraph structure
  3647   /// may provide alternative ways to modify the digraph.
  3648   /// The correct behavior of OutDegMap is not guarantied if these additional
  3649   /// features are used. For example, the functions
  3650   /// \ref ListDigraph::changeSource() "changeSource()",
  3651   /// \ref ListDigraph::changeTarget() "changeTarget()" and
  3652   /// \ref ListDigraph::reverseArc() "reverseArc()"
  3653   /// of \ref ListDigraph will \e not update the degree values correctly.
  3654   ///
  3655   /// \sa InDegMap
  3656   template <typename GR>
  3657   class OutDegMap
  3658     : protected ItemSetTraits<GR, typename GR::Arc>
  3659       ::ItemNotifier::ObserverBase {
  3660 
  3661   public:
  3662 
  3663     /// The graph type of OutDegMap
  3664     typedef GR Graph;
  3665     typedef GR Digraph;
  3666     /// The key type
  3667     typedef typename Digraph::Node Key;
  3668     /// The value type
  3669     typedef int Value;
  3670 
  3671     typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
  3672     ::ItemNotifier::ObserverBase Parent;
  3673 
  3674   private:
  3675 
  3676     class AutoNodeMap
  3677       : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {
  3678     public:
  3679 
  3680       typedef typename ItemSetTraits<Digraph, Key>::
  3681       template Map<int>::Type Parent;
  3682 
  3683       AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
  3684 
  3685       virtual void add(const Key& key) {
  3686         Parent::add(key);
  3687         Parent::set(key, 0);
  3688       }
  3689       virtual void add(const std::vector<Key>& keys) {
  3690         Parent::add(keys);
  3691         for (int i = 0; i < int(keys.size()); ++i) {
  3692           Parent::set(keys[i], 0);
  3693         }
  3694       }
  3695       virtual void build() {
  3696         Parent::build();
  3697         Key it;
  3698         typename Parent::Notifier* nf = Parent::notifier();
  3699         for (nf->first(it); it != INVALID; nf->next(it)) {
  3700           Parent::set(it, 0);
  3701         }
  3702       }
  3703     };
  3704 
  3705   public:
  3706 
  3707     /// \brief Constructor.
  3708     ///
  3709     /// Constructor for creating an out-degree map.
  3710     explicit OutDegMap(const Digraph& graph)
  3711       : _digraph(graph), _deg(graph) {
  3712       Parent::attach(_digraph.notifier(typename Digraph::Arc()));
  3713 
  3714       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3715         _deg[it] = countOutArcs(_digraph, it);
  3716       }
  3717     }
  3718 
  3719     /// \brief Gives back the out-degree of a Node.
  3720     ///
  3721     /// Gives back the out-degree of a Node.
  3722     int operator[](const Key& key) const {
  3723       return _deg[key];
  3724     }
  3725 
  3726   protected:
  3727 
  3728     typedef typename Digraph::Arc Arc;
  3729 
  3730     virtual void add(const Arc& arc) {
  3731       ++_deg[_digraph.source(arc)];
  3732     }
  3733 
  3734     virtual void add(const std::vector<Arc>& arcs) {
  3735       for (int i = 0; i < int(arcs.size()); ++i) {
  3736         ++_deg[_digraph.source(arcs[i])];
  3737       }
  3738     }
  3739 
  3740     virtual void erase(const Arc& arc) {
  3741       --_deg[_digraph.source(arc)];
  3742     }
  3743 
  3744     virtual void erase(const std::vector<Arc>& arcs) {
  3745       for (int i = 0; i < int(arcs.size()); ++i) {
  3746         --_deg[_digraph.source(arcs[i])];
  3747       }
  3748     }
  3749 
  3750     virtual void build() {
  3751       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3752         _deg[it] = countOutArcs(_digraph, it);
  3753       }
  3754     }
  3755 
  3756     virtual void clear() {
  3757       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3758         _deg[it] = 0;
  3759       }
  3760     }
  3761   private:
  3762 
  3763     const Digraph& _digraph;
  3764     AutoNodeMap _deg;
  3765   };
  3766 
  3767   /// \brief Potential difference map
  3768   ///
  3769   /// PotentialDifferenceMap returns the difference between the potentials of
  3770   /// the source and target nodes of each arc in a digraph, i.e. it returns
  3771   /// \code
  3772   ///   potential[gr.target(arc)] - potential[gr.source(arc)].
  3773   /// \endcode
  3774   /// \tparam GR The digraph type.
  3775   /// \tparam POT A node map storing the potentials.
  3776   template <typename GR, typename POT>
  3777   class PotentialDifferenceMap {
  3778   public:
  3779     /// Key type
  3780     typedef typename GR::Arc Key;
  3781     /// Value type
  3782     typedef typename POT::Value Value;
  3783 
  3784     /// \brief Constructor
  3785     ///
  3786     /// Contructor of the map.
  3787     explicit PotentialDifferenceMap(const GR& gr,
  3788                                     const POT& potential)
  3789       : _digraph(gr), _potential(potential) {}
  3790 
  3791     /// \brief Returns the potential difference for the given arc.
  3792     ///
  3793     /// Returns the potential difference for the given arc, i.e.
  3794     /// \code
  3795     ///   potential[gr.target(arc)] - potential[gr.source(arc)].
  3796     /// \endcode
  3797     Value operator[](const Key& arc) const {
  3798       return _potential[_digraph.target(arc)] -
  3799         _potential[_digraph.source(arc)];
  3800     }
  3801 
  3802   private:
  3803     const GR& _digraph;
  3804     const POT& _potential;
  3805   };
  3806 
  3807   /// \brief Returns a PotentialDifferenceMap.
  3808   ///
  3809   /// This function just returns a PotentialDifferenceMap.
  3810   /// \relates PotentialDifferenceMap
  3811   template <typename GR, typename POT>
  3812   PotentialDifferenceMap<GR, POT>
  3813   potentialDifferenceMap(const GR& gr, const POT& potential) {
  3814     return PotentialDifferenceMap<GR, POT>(gr, potential);
  3815   }
  3816 
  3817 
  3818   /// \brief Copy the values of a graph map to another map.
  3819   ///
  3820   /// This function copies the values of a graph map to another graph map.
  3821   /// \c To::Key must be equal or convertible to \c From::Key and
  3822   /// \c From::Value must be equal or convertible to \c To::Value.
  3823   ///
  3824   /// For example, an edge map of \c int value type can be copied to
  3825   /// an arc map of \c double value type in an undirected graph, but
  3826   /// an arc map cannot be copied to an edge map.
  3827   /// Note that even a \ref ConstMap can be copied to a standard graph map,
  3828   /// but \ref mapFill() can also be used for this purpose.
  3829   ///
  3830   /// \param gr The graph for which the maps are defined.
  3831   /// \param from The map from which the values have to be copied.
  3832   /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
  3833   /// \param to The map to which the values have to be copied.
  3834   /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
  3835   template <typename GR, typename From, typename To>
  3836   void mapCopy(const GR& gr, const From& from, To& to) {
  3837     typedef typename To::Key Item;
  3838     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  3839 
  3840     for (ItemIt it(gr); it != INVALID; ++it) {
  3841       to.set(it, from[it]);
  3842     }
  3843   }
  3844 
  3845   /// \brief Compare two graph maps.
  3846   ///
  3847   /// This function compares the values of two graph maps. It returns
  3848   /// \c true if the maps assign the same value for all items in the graph.
  3849   /// The \c Key type of the maps (\c Node, \c Arc or \c Edge) must be equal
  3850   /// and their \c Value types must be comparable using \c %operator==().
  3851   ///
  3852   /// \param gr The graph for which the maps are defined.
  3853   /// \param map1 The first map.
  3854   /// \param map2 The second map.
  3855   template <typename GR, typename Map1, typename Map2>
  3856   bool mapCompare(const GR& gr, const Map1& map1, const Map2& map2) {
  3857     typedef typename Map2::Key Item;
  3858     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  3859 
  3860     for (ItemIt it(gr); it != INVALID; ++it) {
  3861       if (!(map1[it] == map2[it])) return false;
  3862     }
  3863     return true;
  3864   }
  3865 
  3866   /// \brief Return an item having minimum value of a graph map.
  3867   ///
  3868   /// This function returns an item (\c Node, \c Arc or \c Edge) having
  3869   /// minimum value of the given graph map.
  3870   /// If the item set is empty, it returns \c INVALID.
  3871   ///
  3872   /// \param gr The graph for which the map is defined.
  3873   /// \param map The graph map.
  3874   template <typename GR, typename Map>
  3875   typename Map::Key mapMin(const GR& gr, const Map& map) {
  3876     return mapMin(gr, map, std::less<typename Map::Value>());
  3877   }
  3878 
  3879   /// \brief Return an item having minimum value of a graph map.
  3880   ///
  3881   /// This function returns an item (\c Node, \c Arc or \c Edge) having
  3882   /// minimum value of the given graph map.
  3883   /// If the item set is empty, it returns \c INVALID.
  3884   ///
  3885   /// \param gr The graph for which the map is defined.
  3886   /// \param map The graph map.
  3887   /// \param comp Comparison function object.
  3888   template <typename GR, typename Map, typename Comp>
  3889   typename Map::Key mapMin(const GR& gr, const Map& map, const Comp& comp) {
  3890     typedef typename Map::Key Item;
  3891     typedef typename Map::Value Value;
  3892     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  3893 
  3894     ItemIt min_item(gr);
  3895     if (min_item == INVALID) return INVALID;
  3896     Value min = map[min_item];
  3897     for (ItemIt it(gr); it != INVALID; ++it) {
  3898       if (comp(map[it], min)) {
  3899         min = map[it];
  3900         min_item = it;
  3901       }
  3902     }
  3903     return min_item;
  3904   }
  3905 
  3906   /// \brief Return an item having maximum value of a graph map.
  3907   ///
  3908   /// This function returns an item (\c Node, \c Arc or \c Edge) having
  3909   /// maximum value of the given graph map.
  3910   /// If the item set is empty, it returns \c INVALID.
  3911   ///
  3912   /// \param gr The graph for which the map is defined.
  3913   /// \param map The graph map.
  3914   template <typename GR, typename Map>
  3915   typename Map::Key mapMax(const GR& gr, const Map& map) {
  3916     return mapMax(gr, map, std::less<typename Map::Value>());
  3917   }
  3918 
  3919   /// \brief Return an item having maximum value of a graph map.
  3920   ///
  3921   /// This function returns an item (\c Node, \c Arc or \c Edge) having
  3922   /// maximum value of the given graph map.
  3923   /// If the item set is empty, it returns \c INVALID.
  3924   ///
  3925   /// \param gr The graph for which the map is defined.
  3926   /// \param map The graph map.
  3927   /// \param comp Comparison function object.
  3928   template <typename GR, typename Map, typename Comp>
  3929   typename Map::Key mapMax(const GR& gr, const Map& map, const Comp& comp) {
  3930     typedef typename Map::Key Item;
  3931     typedef typename Map::Value Value;
  3932     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  3933 
  3934     ItemIt max_item(gr);
  3935     if (max_item == INVALID) return INVALID;
  3936     Value max = map[max_item];
  3937     for (ItemIt it(gr); it != INVALID; ++it) {
  3938       if (comp(max, map[it])) {
  3939         max = map[it];
  3940         max_item = it;
  3941       }
  3942     }
  3943     return max_item;
  3944   }
  3945 
  3946   /// \brief Return the minimum value of a graph map.
  3947   ///
  3948   /// This function returns the minimum value of the given graph map.
  3949   /// The corresponding item set of the graph must not be empty.
  3950   ///
  3951   /// \param gr The graph for which the map is defined.
  3952   /// \param map The graph map.
  3953   template <typename GR, typename Map>
  3954   typename Map::Value mapMinValue(const GR& gr, const Map& map) {
  3955     return map[mapMin(gr, map, std::less<typename Map::Value>())];
  3956   }
  3957 
  3958   /// \brief Return the minimum value of a graph map.
  3959   ///
  3960   /// This function returns the minimum value of the given graph map.
  3961   /// The corresponding item set of the graph must not be empty.
  3962   ///
  3963   /// \param gr The graph for which the map is defined.
  3964   /// \param map The graph map.
  3965   /// \param comp Comparison function object.
  3966   template <typename GR, typename Map, typename Comp>
  3967   typename Map::Value
  3968   mapMinValue(const GR& gr, const Map& map, const Comp& comp) {
  3969     return map[mapMin(gr, map, comp)];
  3970   }
  3971 
  3972   /// \brief Return the maximum value of a graph map.
  3973   ///
  3974   /// This function returns the maximum value of the given graph map.
  3975   /// The corresponding item set of the graph must not be empty.
  3976   ///
  3977   /// \param gr The graph for which the map is defined.
  3978   /// \param map The graph map.
  3979   template <typename GR, typename Map>
  3980   typename Map::Value mapMaxValue(const GR& gr, const Map& map) {
  3981     return map[mapMax(gr, map, std::less<typename Map::Value>())];
  3982   }
  3983 
  3984   /// \brief Return the maximum value of a graph map.
  3985   ///
  3986   /// This function returns the maximum value of the given graph map.
  3987   /// The corresponding item set of the graph must not be empty.
  3988   ///
  3989   /// \param gr The graph for which the map is defined.
  3990   /// \param map The graph map.
  3991   /// \param comp Comparison function object.
  3992   template <typename GR, typename Map, typename Comp>
  3993   typename Map::Value
  3994   mapMaxValue(const GR& gr, const Map& map, const Comp& comp) {
  3995     return map[mapMax(gr, map, comp)];
  3996   }
  3997 
  3998   /// \brief Return an item having a specified value in a graph map.
  3999   ///
  4000   /// This function returns an item (\c Node, \c Arc or \c Edge) having
  4001   /// the specified assigned value in the given graph map.
  4002   /// If no such item exists, it returns \c INVALID.
  4003   ///
  4004   /// \param gr The graph for which the map is defined.
  4005   /// \param map The graph map.
  4006   /// \param val The value that have to be found.
  4007   template <typename GR, typename Map>
  4008   typename Map::Key
  4009   mapFind(const GR& gr, const Map& map, const typename Map::Value& val) {
  4010     typedef typename Map::Key Item;
  4011     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  4012 
  4013     for (ItemIt it(gr); it != INVALID; ++it) {
  4014       if (map[it] == val) return it;
  4015     }
  4016     return INVALID;
  4017   }
  4018 
  4019   /// \brief Return an item having value for which a certain predicate is
  4020   /// true in a graph map.
  4021   ///
  4022   /// This function returns an item (\c Node, \c Arc or \c Edge) having
  4023   /// such assigned value for which the specified predicate is true
  4024   /// in the given graph map.
  4025   /// If no such item exists, it returns \c INVALID.
  4026   ///
  4027   /// \param gr The graph for which the map is defined.
  4028   /// \param map The graph map.
  4029   /// \param pred The predicate function object.
  4030   template <typename GR, typename Map, typename Pred>
  4031   typename Map::Key
  4032   mapFindIf(const GR& gr, const Map& map, const Pred& pred) {
  4033     typedef typename Map::Key Item;
  4034     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  4035 
  4036     for (ItemIt it(gr); it != INVALID; ++it) {
  4037       if (pred(map[it])) return it;
  4038     }
  4039     return INVALID;
  4040   }
  4041 
  4042   /// \brief Return the number of items having a specified value in a
  4043   /// graph map.
  4044   ///
  4045   /// This function returns the number of items (\c Node, \c Arc or \c Edge)
  4046   /// having the specified assigned value in the given graph map.
  4047   ///
  4048   /// \param gr The graph for which the map is defined.
  4049   /// \param map The graph map.
  4050   /// \param val The value that have to be counted.
  4051   template <typename GR, typename Map>
  4052   int mapCount(const GR& gr, const Map& map, const typename Map::Value& val) {
  4053     typedef typename Map::Key Item;
  4054     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  4055 
  4056     int cnt = 0;
  4057     for (ItemIt it(gr); it != INVALID; ++it) {
  4058       if (map[it] == val) ++cnt;
  4059     }
  4060     return cnt;
  4061   }
  4062 
  4063   /// \brief Return the number of items having values for which a certain
  4064   /// predicate is true in a graph map.
  4065   ///
  4066   /// This function returns the number of items (\c Node, \c Arc or \c Edge)
  4067   /// having such assigned values for which the specified predicate is true
  4068   /// in the given graph map.
  4069   ///
  4070   /// \param gr The graph for which the map is defined.
  4071   /// \param map The graph map.
  4072   /// \param pred The predicate function object.
  4073   template <typename GR, typename Map, typename Pred>
  4074   int mapCountIf(const GR& gr, const Map& map, const Pred& pred) {
  4075     typedef typename Map::Key Item;
  4076     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  4077 
  4078     int cnt = 0;
  4079     for (ItemIt it(gr); it != INVALID; ++it) {
  4080       if (pred(map[it])) ++cnt;
  4081     }
  4082     return cnt;
  4083   }
  4084 
  4085   /// \brief Fill a graph map with a certain value.
  4086   ///
  4087   /// This function sets the specified value for all items (\c Node,
  4088   /// \c Arc or \c Edge) in the given graph map.
  4089   ///
  4090   /// \param gr The graph for which the map is defined.
  4091   /// \param map The graph map. It must conform to the
  4092   /// \ref concepts::WriteMap "WriteMap" concept.
  4093   /// \param val The value.
  4094   template <typename GR, typename Map>
  4095   void mapFill(const GR& gr, Map& map, const typename Map::Value& val) {
  4096     typedef typename Map::Key Item;
  4097     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  4098 
  4099     for (ItemIt it(gr); it != INVALID; ++it) {
  4100       map.set(it, val);
  4101     }
  4102   }
  4103 
  4104   /// @}
  4105 }
  4106 
  4107 #endif // LEMON_MAPS_H