lemon/maps.h
author Peter Kovacs <kpeter@inf.elte.hu>
Sat, 16 Mar 2013 16:20:41 +0100
changeset 1070 ee9bac10f58e
parent 877 141f9c0db4a3
child 1092 dceba191c00d
permissions -rw-r--r--
Debug checking for capacity bounds in min cost flow algorithms (#454)
     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) 2003-2010
     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 
    29 ///\file
    30 ///\ingroup maps
    31 ///\brief Miscellaneous property maps
    32 
    33 namespace lemon {
    34 
    35   /// \addtogroup maps
    36   /// @{
    37 
    38   /// Base class of maps.
    39 
    40   /// Base class of maps. It provides the necessary type definitions
    41   /// required by the map %concepts.
    42   template<typename K, typename V>
    43   class MapBase {
    44   public:
    45     /// \brief The key type of the map.
    46     typedef K Key;
    47     /// \brief The value type of the map.
    48     /// (The type of objects associated with the keys).
    49     typedef V Value;
    50   };
    51 
    52 
    53   /// Null map. (a.k.a. DoNothingMap)
    54 
    55   /// This map can be used if you have to provide a map only for
    56   /// its type definitions, or if you have to provide a writable map,
    57   /// but data written to it is not required (i.e. it will be sent to
    58   /// <tt>/dev/null</tt>).
    59   /// It conforms to the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
    60   ///
    61   /// \sa ConstMap
    62   template<typename K, typename V>
    63   class NullMap : public MapBase<K, V> {
    64   public:
    65     ///\e
    66     typedef K Key;
    67     ///\e
    68     typedef V Value;
    69 
    70     /// Gives back a default constructed element.
    71     Value operator[](const Key&) const { return Value(); }
    72     /// Absorbs the value.
    73     void set(const Key&, const Value&) {}
    74   };
    75 
    76   /// Returns a \c NullMap class
    77 
    78   /// This function just returns a \c NullMap class.
    79   /// \relates NullMap
    80   template <typename K, typename V>
    81   NullMap<K, V> nullMap() {
    82     return NullMap<K, V>();
    83   }
    84 
    85 
    86   /// Constant map.
    87 
    88   /// This \ref concepts::ReadMap "readable map" assigns a specified
    89   /// value to each key.
    90   ///
    91   /// In other aspects it is equivalent to \c NullMap.
    92   /// So it conforms to the \ref concepts::ReadWriteMap "ReadWriteMap"
    93   /// concept, but it absorbs the data written to it.
    94   ///
    95   /// The simplest way of using this map is through the constMap()
    96   /// function.
    97   ///
    98   /// \sa NullMap
    99   /// \sa IdentityMap
   100   template<typename K, typename V>
   101   class ConstMap : public MapBase<K, V> {
   102   private:
   103     V _value;
   104   public:
   105     ///\e
   106     typedef K Key;
   107     ///\e
   108     typedef V Value;
   109 
   110     /// Default constructor
   111 
   112     /// Default constructor.
   113     /// The value of the map will be default constructed.
   114     ConstMap() {}
   115 
   116     /// Constructor with specified initial value
   117 
   118     /// Constructor with specified initial value.
   119     /// \param v The initial value of the map.
   120     ConstMap(const Value &v) : _value(v) {}
   121 
   122     /// Gives back the specified value.
   123     Value operator[](const Key&) const { return _value; }
   124 
   125     /// Absorbs the value.
   126     void set(const Key&, const Value&) {}
   127 
   128     /// Sets the value that is assigned to each key.
   129     void setAll(const Value &v) {
   130       _value = v;
   131     }
   132 
   133     template<typename V1>
   134     ConstMap(const ConstMap<K, V1> &, const Value &v) : _value(v) {}
   135   };
   136 
   137   /// Returns a \c ConstMap class
   138 
   139   /// This function just returns a \c ConstMap class.
   140   /// \relates ConstMap
   141   template<typename K, typename V>
   142   inline ConstMap<K, V> constMap(const V &v) {
   143     return ConstMap<K, V>(v);
   144   }
   145 
   146   template<typename K, typename V>
   147   inline ConstMap<K, V> constMap() {
   148     return ConstMap<K, V>();
   149   }
   150 
   151 
   152   template<typename T, T v>
   153   struct Const {};
   154 
   155   /// Constant map with inlined constant value.
   156 
   157   /// This \ref concepts::ReadMap "readable map" assigns a specified
   158   /// value to each key.
   159   ///
   160   /// In other aspects it is equivalent to \c NullMap.
   161   /// So it conforms to the \ref concepts::ReadWriteMap "ReadWriteMap"
   162   /// concept, but it absorbs the data written to it.
   163   ///
   164   /// The simplest way of using this map is through the constMap()
   165   /// function.
   166   ///
   167   /// \sa NullMap
   168   /// \sa IdentityMap
   169   template<typename K, typename V, V v>
   170   class ConstMap<K, Const<V, v> > : public MapBase<K, V> {
   171   public:
   172     ///\e
   173     typedef K Key;
   174     ///\e
   175     typedef V Value;
   176 
   177     /// Constructor.
   178     ConstMap() {}
   179 
   180     /// Gives back the specified value.
   181     Value operator[](const Key&) const { return v; }
   182 
   183     /// Absorbs the value.
   184     void set(const Key&, const Value&) {}
   185   };
   186 
   187   /// Returns a \c ConstMap class with inlined constant value
   188 
   189   /// This function just returns a \c ConstMap class with inlined
   190   /// constant value.
   191   /// \relates ConstMap
   192   template<typename K, typename V, V v>
   193   inline ConstMap<K, Const<V, v> > constMap() {
   194     return ConstMap<K, Const<V, v> >();
   195   }
   196 
   197 
   198   /// Identity map.
   199 
   200   /// This \ref concepts::ReadMap "read-only map" gives back the given
   201   /// key as value without any modification.
   202   ///
   203   /// \sa ConstMap
   204   template <typename T>
   205   class IdentityMap : public MapBase<T, T> {
   206   public:
   207     ///\e
   208     typedef T Key;
   209     ///\e
   210     typedef T Value;
   211 
   212     /// Gives back the given value without any modification.
   213     Value operator[](const Key &k) const {
   214       return k;
   215     }
   216   };
   217 
   218   /// Returns an \c IdentityMap class
   219 
   220   /// This function just returns an \c IdentityMap class.
   221   /// \relates IdentityMap
   222   template<typename T>
   223   inline IdentityMap<T> identityMap() {
   224     return IdentityMap<T>();
   225   }
   226 
   227 
   228   /// \brief Map for storing values for integer keys from the range
   229   /// <tt>[0..size-1]</tt>.
   230   ///
   231   /// This map is essentially a wrapper for \c std::vector. It assigns
   232   /// values to integer keys from the range <tt>[0..size-1]</tt>.
   233   /// It can be used together with some data structures, e.g.
   234   /// heap types and \c UnionFind, when the used items are small
   235   /// integers. This map conforms to the \ref concepts::ReferenceMap
   236   /// "ReferenceMap" concept.
   237   ///
   238   /// The simplest way of using this map is through the rangeMap()
   239   /// function.
   240   template <typename V>
   241   class RangeMap : public MapBase<int, V> {
   242     template <typename V1>
   243     friend class RangeMap;
   244   private:
   245 
   246     typedef std::vector<V> Vector;
   247     Vector _vector;
   248 
   249   public:
   250 
   251     /// Key type
   252     typedef int Key;
   253     /// Value type
   254     typedef V Value;
   255     /// Reference type
   256     typedef typename Vector::reference Reference;
   257     /// Const reference type
   258     typedef typename Vector::const_reference ConstReference;
   259 
   260     typedef True ReferenceMapTag;
   261 
   262   public:
   263 
   264     /// Constructor with specified default value.
   265     RangeMap(int size = 0, const Value &value = Value())
   266       : _vector(size, value) {}
   267 
   268     /// Constructs the map from an appropriate \c std::vector.
   269     template <typename V1>
   270     RangeMap(const std::vector<V1>& vector)
   271       : _vector(vector.begin(), vector.end()) {}
   272 
   273     /// Constructs the map from another \c RangeMap.
   274     template <typename V1>
   275     RangeMap(const RangeMap<V1> &c)
   276       : _vector(c._vector.begin(), c._vector.end()) {}
   277 
   278     /// Returns the size of the map.
   279     int size() {
   280       return _vector.size();
   281     }
   282 
   283     /// Resizes the map.
   284 
   285     /// Resizes the underlying \c std::vector container, so changes the
   286     /// keyset of the map.
   287     /// \param size The new size of the map. The new keyset will be the
   288     /// range <tt>[0..size-1]</tt>.
   289     /// \param value The default value to assign to the new keys.
   290     void resize(int size, const Value &value = Value()) {
   291       _vector.resize(size, value);
   292     }
   293 
   294   private:
   295 
   296     RangeMap& operator=(const RangeMap&);
   297 
   298   public:
   299 
   300     ///\e
   301     Reference operator[](const Key &k) {
   302       return _vector[k];
   303     }
   304 
   305     ///\e
   306     ConstReference operator[](const Key &k) const {
   307       return _vector[k];
   308     }
   309 
   310     ///\e
   311     void set(const Key &k, const Value &v) {
   312       _vector[k] = v;
   313     }
   314   };
   315 
   316   /// Returns a \c RangeMap class
   317 
   318   /// This function just returns a \c RangeMap class.
   319   /// \relates RangeMap
   320   template<typename V>
   321   inline RangeMap<V> rangeMap(int size = 0, const V &value = V()) {
   322     return RangeMap<V>(size, value);
   323   }
   324 
   325   /// \brief Returns a \c RangeMap class created from an appropriate
   326   /// \c std::vector
   327 
   328   /// This function just returns a \c RangeMap class created from an
   329   /// appropriate \c std::vector.
   330   /// \relates RangeMap
   331   template<typename V>
   332   inline RangeMap<V> rangeMap(const std::vector<V> &vector) {
   333     return RangeMap<V>(vector);
   334   }
   335 
   336 
   337   /// Map type based on \c std::map
   338 
   339   /// This map is essentially a wrapper for \c std::map with addition
   340   /// that you can specify a default value for the keys that are not
   341   /// stored actually. This value can be different from the default
   342   /// contructed value (i.e. \c %Value()).
   343   /// This type conforms to the \ref concepts::ReferenceMap "ReferenceMap"
   344   /// concept.
   345   ///
   346   /// This map is useful if a default value should be assigned to most of
   347   /// the keys and different values should be assigned only to a few
   348   /// keys (i.e. the map is "sparse").
   349   /// The name of this type also refers to this important usage.
   350   ///
   351   /// Apart form that, this map can be used in many other cases since it
   352   /// is based on \c std::map, which is a general associative container.
   353   /// However, keep in mind that it is usually not as efficient as other
   354   /// maps.
   355   ///
   356   /// The simplest way of using this map is through the sparseMap()
   357   /// function.
   358   template <typename K, typename V, typename Comp = std::less<K> >
   359   class SparseMap : public MapBase<K, V> {
   360     template <typename K1, typename V1, typename C1>
   361     friend class SparseMap;
   362   public:
   363 
   364     /// Key type
   365     typedef K Key;
   366     /// Value type
   367     typedef V Value;
   368     /// Reference type
   369     typedef Value& Reference;
   370     /// Const reference type
   371     typedef const Value& ConstReference;
   372 
   373     typedef True ReferenceMapTag;
   374 
   375   private:
   376 
   377     typedef std::map<K, V, Comp> Map;
   378     Map _map;
   379     Value _value;
   380 
   381   public:
   382 
   383     /// \brief Constructor with specified default value.
   384     SparseMap(const Value &value = Value()) : _value(value) {}
   385     /// \brief Constructs the map from an appropriate \c std::map, and
   386     /// explicitly specifies a default value.
   387     template <typename V1, typename Comp1>
   388     SparseMap(const std::map<Key, V1, Comp1> &map,
   389               const Value &value = Value())
   390       : _map(map.begin(), map.end()), _value(value) {}
   391 
   392     /// \brief Constructs the map from another \c SparseMap.
   393     template<typename V1, typename Comp1>
   394     SparseMap(const SparseMap<Key, V1, Comp1> &c)
   395       : _map(c._map.begin(), c._map.end()), _value(c._value) {}
   396 
   397   private:
   398 
   399     SparseMap& operator=(const SparseMap&);
   400 
   401   public:
   402 
   403     ///\e
   404     Reference operator[](const Key &k) {
   405       typename Map::iterator it = _map.lower_bound(k);
   406       if (it != _map.end() && !_map.key_comp()(k, it->first))
   407         return it->second;
   408       else
   409         return _map.insert(it, std::make_pair(k, _value))->second;
   410     }
   411 
   412     ///\e
   413     ConstReference operator[](const Key &k) const {
   414       typename Map::const_iterator it = _map.find(k);
   415       if (it != _map.end())
   416         return it->second;
   417       else
   418         return _value;
   419     }
   420 
   421     ///\e
   422     void set(const Key &k, const Value &v) {
   423       typename Map::iterator it = _map.lower_bound(k);
   424       if (it != _map.end() && !_map.key_comp()(k, it->first))
   425         it->second = v;
   426       else
   427         _map.insert(it, std::make_pair(k, v));
   428     }
   429 
   430     ///\e
   431     void setAll(const Value &v) {
   432       _value = v;
   433       _map.clear();
   434     }
   435   };
   436 
   437   /// Returns a \c SparseMap class
   438 
   439   /// This function just returns a \c SparseMap class with specified
   440   /// default value.
   441   /// \relates SparseMap
   442   template<typename K, typename V, typename Compare>
   443   inline SparseMap<K, V, Compare> sparseMap(const V& value = V()) {
   444     return SparseMap<K, V, Compare>(value);
   445   }
   446 
   447   template<typename K, typename V>
   448   inline SparseMap<K, V, std::less<K> > sparseMap(const V& value = V()) {
   449     return SparseMap<K, V, std::less<K> >(value);
   450   }
   451 
   452   /// \brief Returns a \c SparseMap class created from an appropriate
   453   /// \c std::map
   454 
   455   /// This function just returns a \c SparseMap class created from an
   456   /// appropriate \c std::map.
   457   /// \relates SparseMap
   458   template<typename K, typename V, typename Compare>
   459   inline SparseMap<K, V, Compare>
   460     sparseMap(const std::map<K, V, Compare> &map, const V& value = V())
   461   {
   462     return SparseMap<K, V, Compare>(map, value);
   463   }
   464 
   465   /// @}
   466 
   467   /// \addtogroup map_adaptors
   468   /// @{
   469 
   470   /// Composition of two maps
   471 
   472   /// This \ref concepts::ReadMap "read-only map" returns the
   473   /// composition of two given maps. That is to say, if \c m1 is of
   474   /// type \c M1 and \c m2 is of \c M2, then for
   475   /// \code
   476   ///   ComposeMap<M1, M2> cm(m1,m2);
   477   /// \endcode
   478   /// <tt>cm[x]</tt> will be equal to <tt>m1[m2[x]]</tt>.
   479   ///
   480   /// The \c Key type of the map is inherited from \c M2 and the
   481   /// \c Value type is from \c M1.
   482   /// \c M2::Value must be convertible to \c M1::Key.
   483   ///
   484   /// The simplest way of using this map is through the composeMap()
   485   /// function.
   486   ///
   487   /// \sa CombineMap
   488   template <typename M1, typename M2>
   489   class ComposeMap : public MapBase<typename M2::Key, typename M1::Value> {
   490     const M1 &_m1;
   491     const M2 &_m2;
   492   public:
   493     ///\e
   494     typedef typename M2::Key Key;
   495     ///\e
   496     typedef typename M1::Value Value;
   497 
   498     /// Constructor
   499     ComposeMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
   500 
   501     ///\e
   502     typename MapTraits<M1>::ConstReturnValue
   503     operator[](const Key &k) const { return _m1[_m2[k]]; }
   504   };
   505 
   506   /// Returns a \c ComposeMap class
   507 
   508   /// This function just returns a \c ComposeMap class.
   509   ///
   510   /// If \c m1 and \c m2 are maps and the \c Value type of \c m2 is
   511   /// convertible to the \c Key of \c m1, then <tt>composeMap(m1,m2)[x]</tt>
   512   /// will be equal to <tt>m1[m2[x]]</tt>.
   513   ///
   514   /// \relates ComposeMap
   515   template <typename M1, typename M2>
   516   inline ComposeMap<M1, M2> composeMap(const M1 &m1, const M2 &m2) {
   517     return ComposeMap<M1, M2>(m1, m2);
   518   }
   519 
   520 
   521   /// Combination of two maps using an STL (binary) functor.
   522 
   523   /// This \ref concepts::ReadMap "read-only map" takes two maps and a
   524   /// binary functor and returns the combination of the two given maps
   525   /// using the functor.
   526   /// That is to say, if \c m1 is of type \c M1 and \c m2 is of \c M2
   527   /// and \c f is of \c F, then for
   528   /// \code
   529   ///   CombineMap<M1,M2,F,V> cm(m1,m2,f);
   530   /// \endcode
   531   /// <tt>cm[x]</tt> will be equal to <tt>f(m1[x],m2[x])</tt>.
   532   ///
   533   /// The \c Key type of the map is inherited from \c M1 (\c M1::Key
   534   /// must be convertible to \c M2::Key) and the \c Value type is \c V.
   535   /// \c M2::Value and \c M1::Value must be convertible to the
   536   /// corresponding input parameter of \c F and the return type of \c F
   537   /// must be convertible to \c V.
   538   ///
   539   /// The simplest way of using this map is through the combineMap()
   540   /// function.
   541   ///
   542   /// \sa ComposeMap
   543   template<typename M1, typename M2, typename F,
   544            typename V = typename F::result_type>
   545   class CombineMap : public MapBase<typename M1::Key, V> {
   546     const M1 &_m1;
   547     const M2 &_m2;
   548     F _f;
   549   public:
   550     ///\e
   551     typedef typename M1::Key Key;
   552     ///\e
   553     typedef V Value;
   554 
   555     /// Constructor
   556     CombineMap(const M1 &m1, const M2 &m2, const F &f = F())
   557       : _m1(m1), _m2(m2), _f(f) {}
   558     ///\e
   559     Value operator[](const Key &k) const { return _f(_m1[k],_m2[k]); }
   560   };
   561 
   562   /// Returns a \c CombineMap class
   563 
   564   /// This function just returns a \c CombineMap class.
   565   ///
   566   /// For example, if \c m1 and \c m2 are both maps with \c double
   567   /// values, then
   568   /// \code
   569   ///   combineMap(m1,m2,std::plus<double>())
   570   /// \endcode
   571   /// is equivalent to
   572   /// \code
   573   ///   addMap(m1,m2)
   574   /// \endcode
   575   ///
   576   /// This function is specialized for adaptable binary function
   577   /// classes and C++ functions.
   578   ///
   579   /// \relates CombineMap
   580   template<typename M1, typename M2, typename F, typename V>
   581   inline CombineMap<M1, M2, F, V>
   582   combineMap(const M1 &m1, const M2 &m2, const F &f) {
   583     return CombineMap<M1, M2, F, V>(m1,m2,f);
   584   }
   585 
   586   template<typename M1, typename M2, typename F>
   587   inline CombineMap<M1, M2, F, typename F::result_type>
   588   combineMap(const M1 &m1, const M2 &m2, const F &f) {
   589     return combineMap<M1, M2, F, typename F::result_type>(m1,m2,f);
   590   }
   591 
   592   template<typename M1, typename M2, typename K1, typename K2, typename V>
   593   inline CombineMap<M1, M2, V (*)(K1, K2), V>
   594   combineMap(const M1 &m1, const M2 &m2, V (*f)(K1, K2)) {
   595     return combineMap<M1, M2, V (*)(K1, K2), V>(m1,m2,f);
   596   }
   597 
   598 
   599   /// Converts an STL style (unary) functor to a map
   600 
   601   /// This \ref concepts::ReadMap "read-only map" returns the value
   602   /// of a given functor. Actually, it just wraps the functor and
   603   /// provides the \c Key and \c Value typedefs.
   604   ///
   605   /// Template parameters \c K and \c V will become its \c Key and
   606   /// \c Value. In most cases they have to be given explicitly because
   607   /// a functor typically does not provide \c argument_type and
   608   /// \c result_type typedefs.
   609   /// Parameter \c F is the type of the used functor.
   610   ///
   611   /// The simplest way of using this map is through the functorToMap()
   612   /// function.
   613   ///
   614   /// \sa MapToFunctor
   615   template<typename F,
   616            typename K = typename F::argument_type,
   617            typename V = typename F::result_type>
   618   class FunctorToMap : public MapBase<K, V> {
   619     F _f;
   620   public:
   621     ///\e
   622     typedef K Key;
   623     ///\e
   624     typedef V Value;
   625 
   626     /// Constructor
   627     FunctorToMap(const F &f = F()) : _f(f) {}
   628     ///\e
   629     Value operator[](const Key &k) const { return _f(k); }
   630   };
   631 
   632   /// Returns a \c FunctorToMap class
   633 
   634   /// This function just returns a \c FunctorToMap class.
   635   ///
   636   /// This function is specialized for adaptable binary function
   637   /// classes and C++ functions.
   638   ///
   639   /// \relates FunctorToMap
   640   template<typename K, typename V, typename F>
   641   inline FunctorToMap<F, K, V> functorToMap(const F &f) {
   642     return FunctorToMap<F, K, V>(f);
   643   }
   644 
   645   template <typename F>
   646   inline FunctorToMap<F, typename F::argument_type, typename F::result_type>
   647     functorToMap(const F &f)
   648   {
   649     return FunctorToMap<F, typename F::argument_type,
   650       typename F::result_type>(f);
   651   }
   652 
   653   template <typename K, typename V>
   654   inline FunctorToMap<V (*)(K), K, V> functorToMap(V (*f)(K)) {
   655     return FunctorToMap<V (*)(K), K, V>(f);
   656   }
   657 
   658 
   659   /// Converts a map to an STL style (unary) functor
   660 
   661   /// This class converts a map to an STL style (unary) functor.
   662   /// That is it provides an <tt>operator()</tt> to read its values.
   663   ///
   664   /// For the sake of convenience it also works as a usual
   665   /// \ref concepts::ReadMap "readable map", i.e. <tt>operator[]</tt>
   666   /// and the \c Key and \c Value typedefs also exist.
   667   ///
   668   /// The simplest way of using this map is through the mapToFunctor()
   669   /// function.
   670   ///
   671   ///\sa FunctorToMap
   672   template <typename M>
   673   class MapToFunctor : public MapBase<typename M::Key, typename M::Value> {
   674     const M &_m;
   675   public:
   676     ///\e
   677     typedef typename M::Key Key;
   678     ///\e
   679     typedef typename M::Value Value;
   680 
   681     typedef typename M::Key argument_type;
   682     typedef typename M::Value result_type;
   683 
   684     /// Constructor
   685     MapToFunctor(const M &m) : _m(m) {}
   686     ///\e
   687     Value operator()(const Key &k) const { return _m[k]; }
   688     ///\e
   689     Value operator[](const Key &k) const { return _m[k]; }
   690   };
   691 
   692   /// Returns a \c MapToFunctor class
   693 
   694   /// This function just returns a \c MapToFunctor class.
   695   /// \relates MapToFunctor
   696   template<typename M>
   697   inline MapToFunctor<M> mapToFunctor(const M &m) {
   698     return MapToFunctor<M>(m);
   699   }
   700 
   701 
   702   /// \brief Map adaptor to convert the \c Value type of a map to
   703   /// another type using the default conversion.
   704 
   705   /// Map adaptor to convert the \c Value type of a \ref concepts::ReadMap
   706   /// "readable map" to another type using the default conversion.
   707   /// The \c Key type of it is inherited from \c M and the \c Value
   708   /// type is \c V.
   709   /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
   710   ///
   711   /// The simplest way of using this map is through the convertMap()
   712   /// function.
   713   template <typename M, typename V>
   714   class ConvertMap : public MapBase<typename M::Key, V> {
   715     const M &_m;
   716   public:
   717     ///\e
   718     typedef typename M::Key Key;
   719     ///\e
   720     typedef V Value;
   721 
   722     /// Constructor
   723 
   724     /// Constructor.
   725     /// \param m The underlying map.
   726     ConvertMap(const M &m) : _m(m) {}
   727 
   728     ///\e
   729     Value operator[](const Key &k) const { return _m[k]; }
   730   };
   731 
   732   /// Returns a \c ConvertMap class
   733 
   734   /// This function just returns a \c ConvertMap class.
   735   /// \relates ConvertMap
   736   template<typename V, typename M>
   737   inline ConvertMap<M, V> convertMap(const M &map) {
   738     return ConvertMap<M, V>(map);
   739   }
   740 
   741 
   742   /// Applies all map setting operations to two maps
   743 
   744   /// This map has two \ref concepts::WriteMap "writable map" parameters
   745   /// and each write request will be passed to both of them.
   746   /// If \c M1 is also \ref concepts::ReadMap "readable", then the read
   747   /// operations will return the corresponding values of \c M1.
   748   ///
   749   /// The \c Key and \c Value types are inherited from \c M1.
   750   /// The \c Key and \c Value of \c M2 must be convertible from those
   751   /// of \c M1.
   752   ///
   753   /// The simplest way of using this map is through the forkMap()
   754   /// function.
   755   template<typename  M1, typename M2>
   756   class ForkMap : public MapBase<typename M1::Key, typename M1::Value> {
   757     M1 &_m1;
   758     M2 &_m2;
   759   public:
   760     ///\e
   761     typedef typename M1::Key Key;
   762     ///\e
   763     typedef typename M1::Value Value;
   764 
   765     /// Constructor
   766     ForkMap(M1 &m1, M2 &m2) : _m1(m1), _m2(m2) {}
   767     /// Returns the value associated with the given key in the first map.
   768     Value operator[](const Key &k) const { return _m1[k]; }
   769     /// Sets the value associated with the given key in both maps.
   770     void set(const Key &k, const Value &v) { _m1.set(k,v); _m2.set(k,v); }
   771   };
   772 
   773   /// Returns a \c ForkMap class
   774 
   775   /// This function just returns a \c ForkMap class.
   776   /// \relates ForkMap
   777   template <typename M1, typename M2>
   778   inline ForkMap<M1,M2> forkMap(M1 &m1, M2 &m2) {
   779     return ForkMap<M1,M2>(m1,m2);
   780   }
   781 
   782 
   783   /// Sum of two maps
   784 
   785   /// This \ref concepts::ReadMap "read-only map" returns the sum
   786   /// of the values of the two given maps.
   787   /// Its \c Key and \c Value types are inherited from \c M1.
   788   /// The \c Key and \c Value of \c M2 must be convertible to those of
   789   /// \c M1.
   790   ///
   791   /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
   792   /// \code
   793   ///   AddMap<M1,M2> am(m1,m2);
   794   /// \endcode
   795   /// <tt>am[x]</tt> will be equal to <tt>m1[x]+m2[x]</tt>.
   796   ///
   797   /// The simplest way of using this map is through the addMap()
   798   /// function.
   799   ///
   800   /// \sa SubMap, MulMap, DivMap
   801   /// \sa ShiftMap, ShiftWriteMap
   802   template<typename M1, typename M2>
   803   class AddMap : public MapBase<typename M1::Key, typename M1::Value> {
   804     const M1 &_m1;
   805     const M2 &_m2;
   806   public:
   807     ///\e
   808     typedef typename M1::Key Key;
   809     ///\e
   810     typedef typename M1::Value Value;
   811 
   812     /// Constructor
   813     AddMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
   814     ///\e
   815     Value operator[](const Key &k) const { return _m1[k]+_m2[k]; }
   816   };
   817 
   818   /// Returns an \c AddMap class
   819 
   820   /// This function just returns an \c AddMap class.
   821   ///
   822   /// For example, if \c m1 and \c m2 are both maps with \c double
   823   /// values, then <tt>addMap(m1,m2)[x]</tt> will be equal to
   824   /// <tt>m1[x]+m2[x]</tt>.
   825   ///
   826   /// \relates AddMap
   827   template<typename M1, typename M2>
   828   inline AddMap<M1, M2> addMap(const M1 &m1, const M2 &m2) {
   829     return AddMap<M1, M2>(m1,m2);
   830   }
   831 
   832 
   833   /// Difference of two maps
   834 
   835   /// This \ref concepts::ReadMap "read-only map" returns the difference
   836   /// of the values of the two given maps.
   837   /// Its \c Key and \c Value types are inherited from \c M1.
   838   /// The \c Key and \c Value of \c M2 must be convertible to those of
   839   /// \c M1.
   840   ///
   841   /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
   842   /// \code
   843   ///   SubMap<M1,M2> sm(m1,m2);
   844   /// \endcode
   845   /// <tt>sm[x]</tt> will be equal to <tt>m1[x]-m2[x]</tt>.
   846   ///
   847   /// The simplest way of using this map is through the subMap()
   848   /// function.
   849   ///
   850   /// \sa AddMap, MulMap, DivMap
   851   template<typename M1, typename M2>
   852   class SubMap : public MapBase<typename M1::Key, typename M1::Value> {
   853     const M1 &_m1;
   854     const M2 &_m2;
   855   public:
   856     ///\e
   857     typedef typename M1::Key Key;
   858     ///\e
   859     typedef typename M1::Value Value;
   860 
   861     /// Constructor
   862     SubMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
   863     ///\e
   864     Value operator[](const Key &k) const { return _m1[k]-_m2[k]; }
   865   };
   866 
   867   /// Returns a \c SubMap class
   868 
   869   /// This function just returns a \c SubMap class.
   870   ///
   871   /// For example, if \c m1 and \c m2 are both maps with \c double
   872   /// values, then <tt>subMap(m1,m2)[x]</tt> will be equal to
   873   /// <tt>m1[x]-m2[x]</tt>.
   874   ///
   875   /// \relates SubMap
   876   template<typename M1, typename M2>
   877   inline SubMap<M1, M2> subMap(const M1 &m1, const M2 &m2) {
   878     return SubMap<M1, M2>(m1,m2);
   879   }
   880 
   881 
   882   /// Product of two maps
   883 
   884   /// This \ref concepts::ReadMap "read-only map" returns the product
   885   /// of the values of the two given maps.
   886   /// Its \c Key and \c Value types are inherited from \c M1.
   887   /// The \c Key and \c Value of \c M2 must be convertible to those of
   888   /// \c M1.
   889   ///
   890   /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
   891   /// \code
   892   ///   MulMap<M1,M2> mm(m1,m2);
   893   /// \endcode
   894   /// <tt>mm[x]</tt> will be equal to <tt>m1[x]*m2[x]</tt>.
   895   ///
   896   /// The simplest way of using this map is through the mulMap()
   897   /// function.
   898   ///
   899   /// \sa AddMap, SubMap, DivMap
   900   /// \sa ScaleMap, ScaleWriteMap
   901   template<typename M1, typename M2>
   902   class MulMap : public MapBase<typename M1::Key, typename M1::Value> {
   903     const M1 &_m1;
   904     const M2 &_m2;
   905   public:
   906     ///\e
   907     typedef typename M1::Key Key;
   908     ///\e
   909     typedef typename M1::Value Value;
   910 
   911     /// Constructor
   912     MulMap(const M1 &m1,const M2 &m2) : _m1(m1), _m2(m2) {}
   913     ///\e
   914     Value operator[](const Key &k) const { return _m1[k]*_m2[k]; }
   915   };
   916 
   917   /// Returns a \c MulMap class
   918 
   919   /// This function just returns a \c MulMap class.
   920   ///
   921   /// For example, if \c m1 and \c m2 are both maps with \c double
   922   /// values, then <tt>mulMap(m1,m2)[x]</tt> will be equal to
   923   /// <tt>m1[x]*m2[x]</tt>.
   924   ///
   925   /// \relates MulMap
   926   template<typename M1, typename M2>
   927   inline MulMap<M1, M2> mulMap(const M1 &m1,const M2 &m2) {
   928     return MulMap<M1, M2>(m1,m2);
   929   }
   930 
   931 
   932   /// Quotient of two maps
   933 
   934   /// This \ref concepts::ReadMap "read-only map" returns the quotient
   935   /// of the values of the two given maps.
   936   /// Its \c Key and \c Value types are inherited from \c M1.
   937   /// The \c Key and \c Value of \c M2 must be convertible to those of
   938   /// \c M1.
   939   ///
   940   /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
   941   /// \code
   942   ///   DivMap<M1,M2> dm(m1,m2);
   943   /// \endcode
   944   /// <tt>dm[x]</tt> will be equal to <tt>m1[x]/m2[x]</tt>.
   945   ///
   946   /// The simplest way of using this map is through the divMap()
   947   /// function.
   948   ///
   949   /// \sa AddMap, SubMap, MulMap
   950   template<typename M1, typename M2>
   951   class DivMap : public MapBase<typename M1::Key, typename M1::Value> {
   952     const M1 &_m1;
   953     const M2 &_m2;
   954   public:
   955     ///\e
   956     typedef typename M1::Key Key;
   957     ///\e
   958     typedef typename M1::Value Value;
   959 
   960     /// Constructor
   961     DivMap(const M1 &m1,const M2 &m2) : _m1(m1), _m2(m2) {}
   962     ///\e
   963     Value operator[](const Key &k) const { return _m1[k]/_m2[k]; }
   964   };
   965 
   966   /// Returns a \c DivMap class
   967 
   968   /// This function just returns a \c DivMap class.
   969   ///
   970   /// For example, if \c m1 and \c m2 are both maps with \c double
   971   /// values, then <tt>divMap(m1,m2)[x]</tt> will be equal to
   972   /// <tt>m1[x]/m2[x]</tt>.
   973   ///
   974   /// \relates DivMap
   975   template<typename M1, typename M2>
   976   inline DivMap<M1, M2> divMap(const M1 &m1,const M2 &m2) {
   977     return DivMap<M1, M2>(m1,m2);
   978   }
   979 
   980 
   981   /// Shifts a map with a constant.
   982 
   983   /// This \ref concepts::ReadMap "read-only map" returns the sum of
   984   /// the given map and a constant value (i.e. it shifts the map with
   985   /// the constant). Its \c Key and \c Value are inherited from \c M.
   986   ///
   987   /// Actually,
   988   /// \code
   989   ///   ShiftMap<M> sh(m,v);
   990   /// \endcode
   991   /// is equivalent to
   992   /// \code
   993   ///   ConstMap<M::Key, M::Value> cm(v);
   994   ///   AddMap<M, ConstMap<M::Key, M::Value> > sh(m,cm);
   995   /// \endcode
   996   ///
   997   /// The simplest way of using this map is through the shiftMap()
   998   /// function.
   999   ///
  1000   /// \sa ShiftWriteMap
  1001   template<typename M, typename C = typename M::Value>
  1002   class ShiftMap : public MapBase<typename M::Key, typename M::Value> {
  1003     const M &_m;
  1004     C _v;
  1005   public:
  1006     ///\e
  1007     typedef typename M::Key Key;
  1008     ///\e
  1009     typedef typename M::Value Value;
  1010 
  1011     /// Constructor
  1012 
  1013     /// Constructor.
  1014     /// \param m The undelying map.
  1015     /// \param v The constant value.
  1016     ShiftMap(const M &m, const C &v) : _m(m), _v(v) {}
  1017     ///\e
  1018     Value operator[](const Key &k) const { return _m[k]+_v; }
  1019   };
  1020 
  1021   /// Shifts a map with a constant (read-write version).
  1022 
  1023   /// This \ref concepts::ReadWriteMap "read-write map" returns the sum
  1024   /// of the given map and a constant value (i.e. it shifts the map with
  1025   /// the constant). Its \c Key and \c Value are inherited from \c M.
  1026   /// It makes also possible to write the map.
  1027   ///
  1028   /// The simplest way of using this map is through the shiftWriteMap()
  1029   /// function.
  1030   ///
  1031   /// \sa ShiftMap
  1032   template<typename M, typename C = typename M::Value>
  1033   class ShiftWriteMap : public MapBase<typename M::Key, typename M::Value> {
  1034     M &_m;
  1035     C _v;
  1036   public:
  1037     ///\e
  1038     typedef typename M::Key Key;
  1039     ///\e
  1040     typedef typename M::Value Value;
  1041 
  1042     /// Constructor
  1043 
  1044     /// Constructor.
  1045     /// \param m The undelying map.
  1046     /// \param v The constant value.
  1047     ShiftWriteMap(M &m, const C &v) : _m(m), _v(v) {}
  1048     ///\e
  1049     Value operator[](const Key &k) const { return _m[k]+_v; }
  1050     ///\e
  1051     void set(const Key &k, const Value &v) { _m.set(k, v-_v); }
  1052   };
  1053 
  1054   /// Returns a \c ShiftMap class
  1055 
  1056   /// This function just returns a \c ShiftMap class.
  1057   ///
  1058   /// For example, if \c m is a map with \c double values and \c v is
  1059   /// \c double, then <tt>shiftMap(m,v)[x]</tt> will be equal to
  1060   /// <tt>m[x]+v</tt>.
  1061   ///
  1062   /// \relates ShiftMap
  1063   template<typename M, typename C>
  1064   inline ShiftMap<M, C> shiftMap(const M &m, const C &v) {
  1065     return ShiftMap<M, C>(m,v);
  1066   }
  1067 
  1068   /// Returns a \c ShiftWriteMap class
  1069 
  1070   /// This function just returns a \c ShiftWriteMap class.
  1071   ///
  1072   /// For example, if \c m is a map with \c double values and \c v is
  1073   /// \c double, then <tt>shiftWriteMap(m,v)[x]</tt> will be equal to
  1074   /// <tt>m[x]+v</tt>.
  1075   /// Moreover it makes also possible to write the map.
  1076   ///
  1077   /// \relates ShiftWriteMap
  1078   template<typename M, typename C>
  1079   inline ShiftWriteMap<M, C> shiftWriteMap(M &m, const C &v) {
  1080     return ShiftWriteMap<M, C>(m,v);
  1081   }
  1082 
  1083 
  1084   /// Scales a map with a constant.
  1085 
  1086   /// This \ref concepts::ReadMap "read-only map" returns the value of
  1087   /// the given map multiplied from the left side with a constant value.
  1088   /// Its \c Key and \c Value are inherited from \c M.
  1089   ///
  1090   /// Actually,
  1091   /// \code
  1092   ///   ScaleMap<M> sc(m,v);
  1093   /// \endcode
  1094   /// is equivalent to
  1095   /// \code
  1096   ///   ConstMap<M::Key, M::Value> cm(v);
  1097   ///   MulMap<ConstMap<M::Key, M::Value>, M> sc(cm,m);
  1098   /// \endcode
  1099   ///
  1100   /// The simplest way of using this map is through the scaleMap()
  1101   /// function.
  1102   ///
  1103   /// \sa ScaleWriteMap
  1104   template<typename M, typename C = typename M::Value>
  1105   class ScaleMap : public MapBase<typename M::Key, typename M::Value> {
  1106     const M &_m;
  1107     C _v;
  1108   public:
  1109     ///\e
  1110     typedef typename M::Key Key;
  1111     ///\e
  1112     typedef typename M::Value Value;
  1113 
  1114     /// Constructor
  1115 
  1116     /// Constructor.
  1117     /// \param m The undelying map.
  1118     /// \param v The constant value.
  1119     ScaleMap(const M &m, const C &v) : _m(m), _v(v) {}
  1120     ///\e
  1121     Value operator[](const Key &k) const { return _v*_m[k]; }
  1122   };
  1123 
  1124   /// Scales a map with a constant (read-write version).
  1125 
  1126   /// This \ref concepts::ReadWriteMap "read-write map" returns the value of
  1127   /// the given map multiplied from the left side with a constant value.
  1128   /// Its \c Key and \c Value are inherited from \c M.
  1129   /// It can also be used as write map if the \c / operator is defined
  1130   /// between \c Value and \c C and the given multiplier is not zero.
  1131   ///
  1132   /// The simplest way of using this map is through the scaleWriteMap()
  1133   /// function.
  1134   ///
  1135   /// \sa ScaleMap
  1136   template<typename M, typename C = typename M::Value>
  1137   class ScaleWriteMap : public MapBase<typename M::Key, typename M::Value> {
  1138     M &_m;
  1139     C _v;
  1140   public:
  1141     ///\e
  1142     typedef typename M::Key Key;
  1143     ///\e
  1144     typedef typename M::Value Value;
  1145 
  1146     /// Constructor
  1147 
  1148     /// Constructor.
  1149     /// \param m The undelying map.
  1150     /// \param v The constant value.
  1151     ScaleWriteMap(M &m, const C &v) : _m(m), _v(v) {}
  1152     ///\e
  1153     Value operator[](const Key &k) const { return _v*_m[k]; }
  1154     ///\e
  1155     void set(const Key &k, const Value &v) { _m.set(k, v/_v); }
  1156   };
  1157 
  1158   /// Returns a \c ScaleMap class
  1159 
  1160   /// This function just returns a \c ScaleMap class.
  1161   ///
  1162   /// For example, if \c m is a map with \c double values and \c v is
  1163   /// \c double, then <tt>scaleMap(m,v)[x]</tt> will be equal to
  1164   /// <tt>v*m[x]</tt>.
  1165   ///
  1166   /// \relates ScaleMap
  1167   template<typename M, typename C>
  1168   inline ScaleMap<M, C> scaleMap(const M &m, const C &v) {
  1169     return ScaleMap<M, C>(m,v);
  1170   }
  1171 
  1172   /// Returns a \c ScaleWriteMap class
  1173 
  1174   /// This function just returns a \c ScaleWriteMap class.
  1175   ///
  1176   /// For example, if \c m is a map with \c double values and \c v is
  1177   /// \c double, then <tt>scaleWriteMap(m,v)[x]</tt> will be equal to
  1178   /// <tt>v*m[x]</tt>.
  1179   /// Moreover it makes also possible to write the map.
  1180   ///
  1181   /// \relates ScaleWriteMap
  1182   template<typename M, typename C>
  1183   inline ScaleWriteMap<M, C> scaleWriteMap(M &m, const C &v) {
  1184     return ScaleWriteMap<M, C>(m,v);
  1185   }
  1186 
  1187 
  1188   /// Negative of a map
  1189 
  1190   /// This \ref concepts::ReadMap "read-only map" returns the negative
  1191   /// of the values of the given map (using the unary \c - operator).
  1192   /// Its \c Key and \c Value are inherited from \c M.
  1193   ///
  1194   /// If M::Value is \c int, \c double etc., then
  1195   /// \code
  1196   ///   NegMap<M> neg(m);
  1197   /// \endcode
  1198   /// is equivalent to
  1199   /// \code
  1200   ///   ScaleMap<M> neg(m,-1);
  1201   /// \endcode
  1202   ///
  1203   /// The simplest way of using this map is through the negMap()
  1204   /// function.
  1205   ///
  1206   /// \sa NegWriteMap
  1207   template<typename M>
  1208   class NegMap : public MapBase<typename M::Key, typename M::Value> {
  1209     const M& _m;
  1210   public:
  1211     ///\e
  1212     typedef typename M::Key Key;
  1213     ///\e
  1214     typedef typename M::Value Value;
  1215 
  1216     /// Constructor
  1217     NegMap(const M &m) : _m(m) {}
  1218     ///\e
  1219     Value operator[](const Key &k) const { return -_m[k]; }
  1220   };
  1221 
  1222   /// Negative of a map (read-write version)
  1223 
  1224   /// This \ref concepts::ReadWriteMap "read-write map" returns the
  1225   /// negative of the values of the given map (using the unary \c -
  1226   /// operator).
  1227   /// Its \c Key and \c Value are inherited from \c M.
  1228   /// It makes also possible to write the map.
  1229   ///
  1230   /// If M::Value is \c int, \c double etc., then
  1231   /// \code
  1232   ///   NegWriteMap<M> neg(m);
  1233   /// \endcode
  1234   /// is equivalent to
  1235   /// \code
  1236   ///   ScaleWriteMap<M> neg(m,-1);
  1237   /// \endcode
  1238   ///
  1239   /// The simplest way of using this map is through the negWriteMap()
  1240   /// function.
  1241   ///
  1242   /// \sa NegMap
  1243   template<typename M>
  1244   class NegWriteMap : public MapBase<typename M::Key, typename M::Value> {
  1245     M &_m;
  1246   public:
  1247     ///\e
  1248     typedef typename M::Key Key;
  1249     ///\e
  1250     typedef typename M::Value Value;
  1251 
  1252     /// Constructor
  1253     NegWriteMap(M &m) : _m(m) {}
  1254     ///\e
  1255     Value operator[](const Key &k) const { return -_m[k]; }
  1256     ///\e
  1257     void set(const Key &k, const Value &v) { _m.set(k, -v); }
  1258   };
  1259 
  1260   /// Returns a \c NegMap class
  1261 
  1262   /// This function just returns a \c NegMap class.
  1263   ///
  1264   /// For example, if \c m is a map with \c double values, then
  1265   /// <tt>negMap(m)[x]</tt> will be equal to <tt>-m[x]</tt>.
  1266   ///
  1267   /// \relates NegMap
  1268   template <typename M>
  1269   inline NegMap<M> negMap(const M &m) {
  1270     return NegMap<M>(m);
  1271   }
  1272 
  1273   /// Returns a \c NegWriteMap class
  1274 
  1275   /// This function just returns a \c NegWriteMap class.
  1276   ///
  1277   /// For example, if \c m is a map with \c double values, then
  1278   /// <tt>negWriteMap(m)[x]</tt> will be equal to <tt>-m[x]</tt>.
  1279   /// Moreover it makes also possible to write the map.
  1280   ///
  1281   /// \relates NegWriteMap
  1282   template <typename M>
  1283   inline NegWriteMap<M> negWriteMap(M &m) {
  1284     return NegWriteMap<M>(m);
  1285   }
  1286 
  1287 
  1288   /// Absolute value of a map
  1289 
  1290   /// This \ref concepts::ReadMap "read-only map" returns the absolute
  1291   /// value of the values of the given map.
  1292   /// Its \c Key and \c Value are inherited from \c M.
  1293   /// \c Value must be comparable to \c 0 and the unary \c -
  1294   /// operator must be defined for it, of course.
  1295   ///
  1296   /// The simplest way of using this map is through the absMap()
  1297   /// function.
  1298   template<typename M>
  1299   class AbsMap : public MapBase<typename M::Key, typename M::Value> {
  1300     const M &_m;
  1301   public:
  1302     ///\e
  1303     typedef typename M::Key Key;
  1304     ///\e
  1305     typedef typename M::Value Value;
  1306 
  1307     /// Constructor
  1308     AbsMap(const M &m) : _m(m) {}
  1309     ///\e
  1310     Value operator[](const Key &k) const {
  1311       Value tmp = _m[k];
  1312       return tmp >= 0 ? tmp : -tmp;
  1313     }
  1314 
  1315   };
  1316 
  1317   /// Returns an \c AbsMap class
  1318 
  1319   /// This function just returns an \c AbsMap class.
  1320   ///
  1321   /// For example, if \c m is a map with \c double values, then
  1322   /// <tt>absMap(m)[x]</tt> will be equal to <tt>m[x]</tt> if
  1323   /// it is positive or zero and <tt>-m[x]</tt> if <tt>m[x]</tt> is
  1324   /// negative.
  1325   ///
  1326   /// \relates AbsMap
  1327   template<typename M>
  1328   inline AbsMap<M> absMap(const M &m) {
  1329     return AbsMap<M>(m);
  1330   }
  1331 
  1332   /// @}
  1333 
  1334   // Logical maps and map adaptors:
  1335 
  1336   /// \addtogroup maps
  1337   /// @{
  1338 
  1339   /// Constant \c true map.
  1340 
  1341   /// This \ref concepts::ReadMap "read-only map" assigns \c true to
  1342   /// each key.
  1343   ///
  1344   /// Note that
  1345   /// \code
  1346   ///   TrueMap<K> tm;
  1347   /// \endcode
  1348   /// is equivalent to
  1349   /// \code
  1350   ///   ConstMap<K,bool> tm(true);
  1351   /// \endcode
  1352   ///
  1353   /// \sa FalseMap
  1354   /// \sa ConstMap
  1355   template <typename K>
  1356   class TrueMap : public MapBase<K, bool> {
  1357   public:
  1358     ///\e
  1359     typedef K Key;
  1360     ///\e
  1361     typedef bool Value;
  1362 
  1363     /// Gives back \c true.
  1364     Value operator[](const Key&) const { return true; }
  1365   };
  1366 
  1367   /// Returns a \c TrueMap class
  1368 
  1369   /// This function just returns a \c TrueMap class.
  1370   /// \relates TrueMap
  1371   template<typename K>
  1372   inline TrueMap<K> trueMap() {
  1373     return TrueMap<K>();
  1374   }
  1375 
  1376 
  1377   /// Constant \c false map.
  1378 
  1379   /// This \ref concepts::ReadMap "read-only map" assigns \c false to
  1380   /// each key.
  1381   ///
  1382   /// Note that
  1383   /// \code
  1384   ///   FalseMap<K> fm;
  1385   /// \endcode
  1386   /// is equivalent to
  1387   /// \code
  1388   ///   ConstMap<K,bool> fm(false);
  1389   /// \endcode
  1390   ///
  1391   /// \sa TrueMap
  1392   /// \sa ConstMap
  1393   template <typename K>
  1394   class FalseMap : public MapBase<K, bool> {
  1395   public:
  1396     ///\e
  1397     typedef K Key;
  1398     ///\e
  1399     typedef bool Value;
  1400 
  1401     /// Gives back \c false.
  1402     Value operator[](const Key&) const { return false; }
  1403   };
  1404 
  1405   /// Returns a \c FalseMap class
  1406 
  1407   /// This function just returns a \c FalseMap class.
  1408   /// \relates FalseMap
  1409   template<typename K>
  1410   inline FalseMap<K> falseMap() {
  1411     return FalseMap<K>();
  1412   }
  1413 
  1414   /// @}
  1415 
  1416   /// \addtogroup map_adaptors
  1417   /// @{
  1418 
  1419   /// Logical 'and' of two maps
  1420 
  1421   /// This \ref concepts::ReadMap "read-only map" returns the logical
  1422   /// 'and' of the values of the two given maps.
  1423   /// Its \c Key type is inherited from \c M1 and its \c Value type is
  1424   /// \c bool. \c M2::Key must be convertible to \c M1::Key.
  1425   ///
  1426   /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
  1427   /// \code
  1428   ///   AndMap<M1,M2> am(m1,m2);
  1429   /// \endcode
  1430   /// <tt>am[x]</tt> will be equal to <tt>m1[x]&&m2[x]</tt>.
  1431   ///
  1432   /// The simplest way of using this map is through the andMap()
  1433   /// function.
  1434   ///
  1435   /// \sa OrMap
  1436   /// \sa NotMap, NotWriteMap
  1437   template<typename M1, typename M2>
  1438   class AndMap : public MapBase<typename M1::Key, bool> {
  1439     const M1 &_m1;
  1440     const M2 &_m2;
  1441   public:
  1442     ///\e
  1443     typedef typename M1::Key Key;
  1444     ///\e
  1445     typedef bool Value;
  1446 
  1447     /// Constructor
  1448     AndMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
  1449     ///\e
  1450     Value operator[](const Key &k) const { return _m1[k]&&_m2[k]; }
  1451   };
  1452 
  1453   /// Returns an \c AndMap class
  1454 
  1455   /// This function just returns an \c AndMap class.
  1456   ///
  1457   /// For example, if \c m1 and \c m2 are both maps with \c bool values,
  1458   /// then <tt>andMap(m1,m2)[x]</tt> will be equal to
  1459   /// <tt>m1[x]&&m2[x]</tt>.
  1460   ///
  1461   /// \relates AndMap
  1462   template<typename M1, typename M2>
  1463   inline AndMap<M1, M2> andMap(const M1 &m1, const M2 &m2) {
  1464     return AndMap<M1, M2>(m1,m2);
  1465   }
  1466 
  1467 
  1468   /// Logical 'or' of two maps
  1469 
  1470   /// This \ref concepts::ReadMap "read-only map" returns the logical
  1471   /// 'or' of the values of the two given maps.
  1472   /// Its \c Key type is inherited from \c M1 and its \c Value type is
  1473   /// \c bool. \c M2::Key must be convertible to \c M1::Key.
  1474   ///
  1475   /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
  1476   /// \code
  1477   ///   OrMap<M1,M2> om(m1,m2);
  1478   /// \endcode
  1479   /// <tt>om[x]</tt> will be equal to <tt>m1[x]||m2[x]</tt>.
  1480   ///
  1481   /// The simplest way of using this map is through the orMap()
  1482   /// function.
  1483   ///
  1484   /// \sa AndMap
  1485   /// \sa NotMap, NotWriteMap
  1486   template<typename M1, typename M2>
  1487   class OrMap : public MapBase<typename M1::Key, bool> {
  1488     const M1 &_m1;
  1489     const M2 &_m2;
  1490   public:
  1491     ///\e
  1492     typedef typename M1::Key Key;
  1493     ///\e
  1494     typedef bool Value;
  1495 
  1496     /// Constructor
  1497     OrMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
  1498     ///\e
  1499     Value operator[](const Key &k) const { return _m1[k]||_m2[k]; }
  1500   };
  1501 
  1502   /// Returns an \c OrMap class
  1503 
  1504   /// This function just returns an \c OrMap class.
  1505   ///
  1506   /// For example, if \c m1 and \c m2 are both maps with \c bool values,
  1507   /// then <tt>orMap(m1,m2)[x]</tt> will be equal to
  1508   /// <tt>m1[x]||m2[x]</tt>.
  1509   ///
  1510   /// \relates OrMap
  1511   template<typename M1, typename M2>
  1512   inline OrMap<M1, M2> orMap(const M1 &m1, const M2 &m2) {
  1513     return OrMap<M1, M2>(m1,m2);
  1514   }
  1515 
  1516 
  1517   /// Logical 'not' of a map
  1518 
  1519   /// This \ref concepts::ReadMap "read-only map" returns the logical
  1520   /// negation of the values of the given map.
  1521   /// Its \c Key is inherited from \c M and its \c Value is \c bool.
  1522   ///
  1523   /// The simplest way of using this map is through the notMap()
  1524   /// function.
  1525   ///
  1526   /// \sa NotWriteMap
  1527   template <typename M>
  1528   class NotMap : public MapBase<typename M::Key, bool> {
  1529     const M &_m;
  1530   public:
  1531     ///\e
  1532     typedef typename M::Key Key;
  1533     ///\e
  1534     typedef bool Value;
  1535 
  1536     /// Constructor
  1537     NotMap(const M &m) : _m(m) {}
  1538     ///\e
  1539     Value operator[](const Key &k) const { return !_m[k]; }
  1540   };
  1541 
  1542   /// Logical 'not' of a map (read-write version)
  1543 
  1544   /// This \ref concepts::ReadWriteMap "read-write map" returns the
  1545   /// logical negation of the values of the given map.
  1546   /// Its \c Key is inherited from \c M and its \c Value is \c bool.
  1547   /// It makes also possible to write the map. When a value is set,
  1548   /// the opposite value is set to the original map.
  1549   ///
  1550   /// The simplest way of using this map is through the notWriteMap()
  1551   /// function.
  1552   ///
  1553   /// \sa NotMap
  1554   template <typename M>
  1555   class NotWriteMap : public MapBase<typename M::Key, bool> {
  1556     M &_m;
  1557   public:
  1558     ///\e
  1559     typedef typename M::Key Key;
  1560     ///\e
  1561     typedef bool Value;
  1562 
  1563     /// Constructor
  1564     NotWriteMap(M &m) : _m(m) {}
  1565     ///\e
  1566     Value operator[](const Key &k) const { return !_m[k]; }
  1567     ///\e
  1568     void set(const Key &k, bool v) { _m.set(k, !v); }
  1569   };
  1570 
  1571   /// Returns a \c NotMap class
  1572 
  1573   /// This function just returns a \c NotMap class.
  1574   ///
  1575   /// For example, if \c m is a map with \c bool values, then
  1576   /// <tt>notMap(m)[x]</tt> will be equal to <tt>!m[x]</tt>.
  1577   ///
  1578   /// \relates NotMap
  1579   template <typename M>
  1580   inline NotMap<M> notMap(const M &m) {
  1581     return NotMap<M>(m);
  1582   }
  1583 
  1584   /// Returns a \c NotWriteMap class
  1585 
  1586   /// This function just returns a \c NotWriteMap class.
  1587   ///
  1588   /// For example, if \c m is a map with \c bool values, then
  1589   /// <tt>notWriteMap(m)[x]</tt> will be equal to <tt>!m[x]</tt>.
  1590   /// Moreover it makes also possible to write the map.
  1591   ///
  1592   /// \relates NotWriteMap
  1593   template <typename M>
  1594   inline NotWriteMap<M> notWriteMap(M &m) {
  1595     return NotWriteMap<M>(m);
  1596   }
  1597 
  1598 
  1599   /// Combination of two maps using the \c == operator
  1600 
  1601   /// This \ref concepts::ReadMap "read-only map" assigns \c true to
  1602   /// the keys for which the corresponding values of the two maps are
  1603   /// equal.
  1604   /// Its \c Key type is inherited from \c M1 and its \c Value type is
  1605   /// \c bool. \c M2::Key must be convertible to \c M1::Key.
  1606   ///
  1607   /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
  1608   /// \code
  1609   ///   EqualMap<M1,M2> em(m1,m2);
  1610   /// \endcode
  1611   /// <tt>em[x]</tt> will be equal to <tt>m1[x]==m2[x]</tt>.
  1612   ///
  1613   /// The simplest way of using this map is through the equalMap()
  1614   /// function.
  1615   ///
  1616   /// \sa LessMap
  1617   template<typename M1, typename M2>
  1618   class EqualMap : public MapBase<typename M1::Key, bool> {
  1619     const M1 &_m1;
  1620     const M2 &_m2;
  1621   public:
  1622     ///\e
  1623     typedef typename M1::Key Key;
  1624     ///\e
  1625     typedef bool Value;
  1626 
  1627     /// Constructor
  1628     EqualMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
  1629     ///\e
  1630     Value operator[](const Key &k) const { return _m1[k]==_m2[k]; }
  1631   };
  1632 
  1633   /// Returns an \c EqualMap class
  1634 
  1635   /// This function just returns an \c EqualMap class.
  1636   ///
  1637   /// For example, if \c m1 and \c m2 are maps with keys and values of
  1638   /// the same type, then <tt>equalMap(m1,m2)[x]</tt> will be equal to
  1639   /// <tt>m1[x]==m2[x]</tt>.
  1640   ///
  1641   /// \relates EqualMap
  1642   template<typename M1, typename M2>
  1643   inline EqualMap<M1, M2> equalMap(const M1 &m1, const M2 &m2) {
  1644     return EqualMap<M1, M2>(m1,m2);
  1645   }
  1646 
  1647 
  1648   /// Combination of two maps using the \c < operator
  1649 
  1650   /// This \ref concepts::ReadMap "read-only map" assigns \c true to
  1651   /// the keys for which the corresponding value of the first map is
  1652   /// less then the value of the second map.
  1653   /// Its \c Key type is inherited from \c M1 and its \c Value type is
  1654   /// \c bool. \c M2::Key must be convertible to \c M1::Key.
  1655   ///
  1656   /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
  1657   /// \code
  1658   ///   LessMap<M1,M2> lm(m1,m2);
  1659   /// \endcode
  1660   /// <tt>lm[x]</tt> will be equal to <tt>m1[x]<m2[x]</tt>.
  1661   ///
  1662   /// The simplest way of using this map is through the lessMap()
  1663   /// function.
  1664   ///
  1665   /// \sa EqualMap
  1666   template<typename M1, typename M2>
  1667   class LessMap : public MapBase<typename M1::Key, bool> {
  1668     const M1 &_m1;
  1669     const M2 &_m2;
  1670   public:
  1671     ///\e
  1672     typedef typename M1::Key Key;
  1673     ///\e
  1674     typedef bool Value;
  1675 
  1676     /// Constructor
  1677     LessMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
  1678     ///\e
  1679     Value operator[](const Key &k) const { return _m1[k]<_m2[k]; }
  1680   };
  1681 
  1682   /// Returns an \c LessMap class
  1683 
  1684   /// This function just returns an \c LessMap class.
  1685   ///
  1686   /// For example, if \c m1 and \c m2 are maps with keys and values of
  1687   /// the same type, then <tt>lessMap(m1,m2)[x]</tt> will be equal to
  1688   /// <tt>m1[x]<m2[x]</tt>.
  1689   ///
  1690   /// \relates LessMap
  1691   template<typename M1, typename M2>
  1692   inline LessMap<M1, M2> lessMap(const M1 &m1, const M2 &m2) {
  1693     return LessMap<M1, M2>(m1,m2);
  1694   }
  1695 
  1696   namespace _maps_bits {
  1697 
  1698     template <typename _Iterator, typename Enable = void>
  1699     struct IteratorTraits {
  1700       typedef typename std::iterator_traits<_Iterator>::value_type Value;
  1701     };
  1702 
  1703     template <typename _Iterator>
  1704     struct IteratorTraits<_Iterator,
  1705       typename exists<typename _Iterator::container_type>::type>
  1706     {
  1707       typedef typename _Iterator::container_type::value_type Value;
  1708     };
  1709 
  1710   }
  1711 
  1712   /// @}
  1713 
  1714   /// \addtogroup maps
  1715   /// @{
  1716 
  1717   /// \brief Writable bool map for logging each \c true assigned element
  1718   ///
  1719   /// A \ref concepts::WriteMap "writable" bool map for logging
  1720   /// each \c true assigned element, i.e it copies subsequently each
  1721   /// keys set to \c true to the given iterator.
  1722   /// The most important usage of it is storing certain nodes or arcs
  1723   /// that were marked \c true by an algorithm.
  1724   ///
  1725   /// There are several algorithms that provide solutions through bool
  1726   /// maps and most of them assign \c true at most once for each key.
  1727   /// In these cases it is a natural request to store each \c true
  1728   /// assigned elements (in order of the assignment), which can be
  1729   /// easily done with LoggerBoolMap.
  1730   ///
  1731   /// The simplest way of using this map is through the loggerBoolMap()
  1732   /// function.
  1733   ///
  1734   /// \tparam IT The type of the iterator.
  1735   /// \tparam KEY The key type of the map. The default value set
  1736   /// according to the iterator type should work in most cases.
  1737   ///
  1738   /// \note The container of the iterator must contain enough space
  1739   /// for the elements or the iterator should be an inserter iterator.
  1740 #ifdef DOXYGEN
  1741   template <typename IT, typename KEY>
  1742 #else
  1743   template <typename IT,
  1744             typename KEY = typename _maps_bits::IteratorTraits<IT>::Value>
  1745 #endif
  1746   class LoggerBoolMap : public MapBase<KEY, bool> {
  1747   public:
  1748 
  1749     ///\e
  1750     typedef KEY Key;
  1751     ///\e
  1752     typedef bool Value;
  1753     ///\e
  1754     typedef IT Iterator;
  1755 
  1756     /// Constructor
  1757     LoggerBoolMap(Iterator it)
  1758       : _begin(it), _end(it) {}
  1759 
  1760     /// Gives back the given iterator set for the first key
  1761     Iterator begin() const {
  1762       return _begin;
  1763     }
  1764 
  1765     /// Gives back the the 'after the last' iterator
  1766     Iterator end() const {
  1767       return _end;
  1768     }
  1769 
  1770     /// The set function of the map
  1771     void set(const Key& key, Value value) {
  1772       if (value) {
  1773         *_end++ = key;
  1774       }
  1775     }
  1776 
  1777   private:
  1778     Iterator _begin;
  1779     Iterator _end;
  1780   };
  1781 
  1782   /// Returns a \c LoggerBoolMap class
  1783 
  1784   /// This function just returns a \c LoggerBoolMap class.
  1785   ///
  1786   /// The most important usage of it is storing certain nodes or arcs
  1787   /// that were marked \c true by an algorithm.
  1788   /// For example, it makes easier to store the nodes in the processing
  1789   /// order of Dfs algorithm, as the following examples show.
  1790   /// \code
  1791   ///   std::vector<Node> v;
  1792   ///   dfs(g).processedMap(loggerBoolMap(std::back_inserter(v))).run(s);
  1793   /// \endcode
  1794   /// \code
  1795   ///   std::vector<Node> v(countNodes(g));
  1796   ///   dfs(g).processedMap(loggerBoolMap(v.begin())).run(s);
  1797   /// \endcode
  1798   ///
  1799   /// \note The container of the iterator must contain enough space
  1800   /// for the elements or the iterator should be an inserter iterator.
  1801   ///
  1802   /// \note LoggerBoolMap is just \ref concepts::WriteMap "writable", so
  1803   /// it cannot be used when a readable map is needed, for example, as
  1804   /// \c ReachedMap for \c Bfs, \c Dfs and \c Dijkstra algorithms.
  1805   ///
  1806   /// \relates LoggerBoolMap
  1807   template<typename Iterator>
  1808   inline LoggerBoolMap<Iterator> loggerBoolMap(Iterator it) {
  1809     return LoggerBoolMap<Iterator>(it);
  1810   }
  1811 
  1812   /// @}
  1813 
  1814   /// \addtogroup graph_maps
  1815   /// @{
  1816 
  1817   /// \brief Provides an immutable and unique id for each item in a graph.
  1818   ///
  1819   /// IdMap provides a unique and immutable id for each item of the
  1820   /// same type (\c Node, \c Arc or \c Edge) in a graph. This id is
  1821   ///  - \b unique: different items get different ids,
  1822   ///  - \b immutable: the id of an item does not change (even if you
  1823   ///    delete other nodes).
  1824   ///
  1825   /// Using this map you get access (i.e. can read) the inner id values of
  1826   /// the items stored in the graph, which is returned by the \c id()
  1827   /// function of the graph. This map can be inverted with its member
  1828   /// class \c InverseMap or with the \c operator()() member.
  1829   ///
  1830   /// \tparam GR The graph type.
  1831   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  1832   /// \c GR::Edge).
  1833   ///
  1834   /// \see RangeIdMap
  1835   template <typename GR, typename K>
  1836   class IdMap : public MapBase<K, int> {
  1837   public:
  1838     /// The graph type of IdMap.
  1839     typedef GR Graph;
  1840     typedef GR Digraph;
  1841     /// The key type of IdMap (\c Node, \c Arc or \c Edge).
  1842     typedef K Item;
  1843     /// The key type of IdMap (\c Node, \c Arc or \c Edge).
  1844     typedef K Key;
  1845     /// The value type of IdMap.
  1846     typedef int Value;
  1847 
  1848     /// \brief Constructor.
  1849     ///
  1850     /// Constructor of the map.
  1851     explicit IdMap(const Graph& graph) : _graph(&graph) {}
  1852 
  1853     /// \brief Gives back the \e id of the item.
  1854     ///
  1855     /// Gives back the immutable and unique \e id of the item.
  1856     int operator[](const Item& item) const { return _graph->id(item);}
  1857 
  1858     /// \brief Gives back the \e item by its id.
  1859     ///
  1860     /// Gives back the \e item by its id.
  1861     Item operator()(int id) { return _graph->fromId(id, Item()); }
  1862 
  1863   private:
  1864     const Graph* _graph;
  1865 
  1866   public:
  1867 
  1868     /// \brief The inverse map type of IdMap.
  1869     ///
  1870     /// The inverse map type of IdMap. The subscript operator gives back
  1871     /// an item by its id.
  1872     /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
  1873     /// \see inverse()
  1874     class InverseMap {
  1875     public:
  1876 
  1877       /// \brief Constructor.
  1878       ///
  1879       /// Constructor for creating an id-to-item map.
  1880       explicit InverseMap(const Graph& graph) : _graph(&graph) {}
  1881 
  1882       /// \brief Constructor.
  1883       ///
  1884       /// Constructor for creating an id-to-item map.
  1885       explicit InverseMap(const IdMap& map) : _graph(map._graph) {}
  1886 
  1887       /// \brief Gives back an item by its id.
  1888       ///
  1889       /// Gives back an item by its id.
  1890       Item operator[](int id) const { return _graph->fromId(id, Item());}
  1891 
  1892     private:
  1893       const Graph* _graph;
  1894     };
  1895 
  1896     /// \brief Gives back the inverse of the map.
  1897     ///
  1898     /// Gives back the inverse of the IdMap.
  1899     InverseMap inverse() const { return InverseMap(*_graph);}
  1900   };
  1901 
  1902   /// \brief Returns an \c IdMap class.
  1903   ///
  1904   /// This function just returns an \c IdMap class.
  1905   /// \relates IdMap
  1906   template <typename K, typename GR>
  1907   inline IdMap<GR, K> idMap(const GR& graph) {
  1908     return IdMap<GR, K>(graph);
  1909   }
  1910 
  1911   /// \brief General cross reference graph map type.
  1912 
  1913   /// This class provides simple invertable graph maps.
  1914   /// It wraps a standard graph map (\c NodeMap, \c ArcMap or \c EdgeMap)
  1915   /// and if a key is set to a new value, then stores it in the inverse map.
  1916   /// The graph items can be accessed by their values either using
  1917   /// \c InverseMap or \c operator()(), and the values of the map can be
  1918   /// accessed with an STL compatible forward iterator (\c ValueIt).
  1919   ///
  1920   /// This map is intended to be used when all associated values are
  1921   /// different (the map is actually invertable) or there are only a few
  1922   /// items with the same value.
  1923   /// Otherwise consider to use \c IterableValueMap, which is more
  1924   /// suitable and more efficient for such cases. It provides iterators
  1925   /// to traverse the items with the same associated value, but
  1926   /// it does not have \c InverseMap.
  1927   ///
  1928   /// This type is not reference map, so it cannot be modified with
  1929   /// the subscript operator.
  1930   ///
  1931   /// \tparam GR The graph type.
  1932   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  1933   /// \c GR::Edge).
  1934   /// \tparam V The value type of the map.
  1935   ///
  1936   /// \see IterableValueMap
  1937   template <typename GR, typename K, typename V>
  1938   class CrossRefMap
  1939     : protected ItemSetTraits<GR, K>::template Map<V>::Type {
  1940   private:
  1941 
  1942     typedef typename ItemSetTraits<GR, K>::
  1943       template Map<V>::Type Map;
  1944 
  1945     typedef std::multimap<V, K> Container;
  1946     Container _inv_map;
  1947 
  1948   public:
  1949 
  1950     /// The graph type of CrossRefMap.
  1951     typedef GR Graph;
  1952     typedef GR Digraph;
  1953     /// The key type of CrossRefMap (\c Node, \c Arc or \c Edge).
  1954     typedef K Item;
  1955     /// The key type of CrossRefMap (\c Node, \c Arc or \c Edge).
  1956     typedef K Key;
  1957     /// The value type of CrossRefMap.
  1958     typedef V Value;
  1959 
  1960     /// \brief Constructor.
  1961     ///
  1962     /// Construct a new CrossRefMap for the given graph.
  1963     explicit CrossRefMap(const Graph& graph) : Map(graph) {}
  1964 
  1965     /// \brief Forward iterator for values.
  1966     ///
  1967     /// This iterator is an STL compatible forward
  1968     /// iterator on the values of the map. The values can
  1969     /// be accessed in the <tt>[beginValue, endValue)</tt> range.
  1970     /// They are considered with multiplicity, so each value is
  1971     /// traversed for each item it is assigned to.
  1972     class ValueIt
  1973       : public std::iterator<std::forward_iterator_tag, Value> {
  1974       friend class CrossRefMap;
  1975     private:
  1976       ValueIt(typename Container::const_iterator _it)
  1977         : it(_it) {}
  1978     public:
  1979 
  1980       /// Constructor
  1981       ValueIt() {}
  1982 
  1983       /// \e
  1984       ValueIt& operator++() { ++it; return *this; }
  1985       /// \e
  1986       ValueIt operator++(int) {
  1987         ValueIt tmp(*this);
  1988         operator++();
  1989         return tmp;
  1990       }
  1991 
  1992       /// \e
  1993       const Value& operator*() const { return it->first; }
  1994       /// \e
  1995       const Value* operator->() const { return &(it->first); }
  1996 
  1997       /// \e
  1998       bool operator==(ValueIt jt) const { return it == jt.it; }
  1999       /// \e
  2000       bool operator!=(ValueIt jt) const { return it != jt.it; }
  2001 
  2002     private:
  2003       typename Container::const_iterator it;
  2004     };
  2005 
  2006     /// Alias for \c ValueIt
  2007     typedef ValueIt ValueIterator;
  2008 
  2009     /// \brief Returns an iterator to the first value.
  2010     ///
  2011     /// Returns an STL compatible iterator to the
  2012     /// first value of the map. The values of the
  2013     /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  2014     /// range.
  2015     ValueIt beginValue() const {
  2016       return ValueIt(_inv_map.begin());
  2017     }
  2018 
  2019     /// \brief Returns an iterator after the last value.
  2020     ///
  2021     /// Returns an STL compatible iterator after the
  2022     /// last value of the map. The values of the
  2023     /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  2024     /// range.
  2025     ValueIt endValue() const {
  2026       return ValueIt(_inv_map.end());
  2027     }
  2028 
  2029     /// \brief Sets the value associated with the given key.
  2030     ///
  2031     /// Sets the value associated with the given key.
  2032     void set(const Key& key, const Value& val) {
  2033       Value oldval = Map::operator[](key);
  2034       typename Container::iterator it;
  2035       for (it = _inv_map.equal_range(oldval).first;
  2036            it != _inv_map.equal_range(oldval).second; ++it) {
  2037         if (it->second == key) {
  2038           _inv_map.erase(it);
  2039           break;
  2040         }
  2041       }
  2042       _inv_map.insert(std::make_pair(val, key));
  2043       Map::set(key, val);
  2044     }
  2045 
  2046     /// \brief Returns the value associated with the given key.
  2047     ///
  2048     /// Returns the value associated with the given key.
  2049     typename MapTraits<Map>::ConstReturnValue
  2050     operator[](const Key& key) const {
  2051       return Map::operator[](key);
  2052     }
  2053 
  2054     /// \brief Gives back an item by its value.
  2055     ///
  2056     /// This function gives back an item that is assigned to
  2057     /// the given value or \c INVALID if no such item exists.
  2058     /// If there are more items with the same associated value,
  2059     /// only one of them is returned.
  2060     Key operator()(const Value& val) const {
  2061       typename Container::const_iterator it = _inv_map.find(val);
  2062       return it != _inv_map.end() ? it->second : INVALID;
  2063     }
  2064 
  2065     /// \brief Returns the number of items with the given value.
  2066     ///
  2067     /// This function returns the number of items with the given value
  2068     /// associated with it.
  2069     int count(const Value &val) const {
  2070       return _inv_map.count(val);
  2071     }
  2072 
  2073   protected:
  2074 
  2075     /// \brief Erase the key from the map and the inverse map.
  2076     ///
  2077     /// Erase the key from the map and the inverse map. It is called by the
  2078     /// \c AlterationNotifier.
  2079     virtual void erase(const Key& key) {
  2080       Value val = Map::operator[](key);
  2081       typename Container::iterator it;
  2082       for (it = _inv_map.equal_range(val).first;
  2083            it != _inv_map.equal_range(val).second; ++it) {
  2084         if (it->second == key) {
  2085           _inv_map.erase(it);
  2086           break;
  2087         }
  2088       }
  2089       Map::erase(key);
  2090     }
  2091 
  2092     /// \brief Erase more keys from the map and the inverse map.
  2093     ///
  2094     /// Erase more keys from the map and the inverse map. It is called by the
  2095     /// \c AlterationNotifier.
  2096     virtual void erase(const std::vector<Key>& keys) {
  2097       for (int i = 0; i < int(keys.size()); ++i) {
  2098         Value val = Map::operator[](keys[i]);
  2099         typename Container::iterator it;
  2100         for (it = _inv_map.equal_range(val).first;
  2101              it != _inv_map.equal_range(val).second; ++it) {
  2102           if (it->second == keys[i]) {
  2103             _inv_map.erase(it);
  2104             break;
  2105           }
  2106         }
  2107       }
  2108       Map::erase(keys);
  2109     }
  2110 
  2111     /// \brief Clear the keys from the map and the inverse map.
  2112     ///
  2113     /// Clear the keys from the map and the inverse map. It is called by the
  2114     /// \c AlterationNotifier.
  2115     virtual void clear() {
  2116       _inv_map.clear();
  2117       Map::clear();
  2118     }
  2119 
  2120   public:
  2121 
  2122     /// \brief The inverse map type of CrossRefMap.
  2123     ///
  2124     /// The inverse map type of CrossRefMap. The subscript operator gives
  2125     /// back an item by its value.
  2126     /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
  2127     /// \see inverse()
  2128     class InverseMap {
  2129     public:
  2130       /// \brief Constructor
  2131       ///
  2132       /// Constructor of the InverseMap.
  2133       explicit InverseMap(const CrossRefMap& inverted)
  2134         : _inverted(inverted) {}
  2135 
  2136       /// The value type of the InverseMap.
  2137       typedef typename CrossRefMap::Key Value;
  2138       /// The key type of the InverseMap.
  2139       typedef typename CrossRefMap::Value Key;
  2140 
  2141       /// \brief Subscript operator.
  2142       ///
  2143       /// Subscript operator. It gives back an item
  2144       /// that is assigned to the given value or \c INVALID
  2145       /// if no such item exists.
  2146       Value operator[](const Key& key) const {
  2147         return _inverted(key);
  2148       }
  2149 
  2150     private:
  2151       const CrossRefMap& _inverted;
  2152     };
  2153 
  2154     /// \brief Gives back the inverse of the map.
  2155     ///
  2156     /// Gives back the inverse of the CrossRefMap.
  2157     InverseMap inverse() const {
  2158       return InverseMap(*this);
  2159     }
  2160 
  2161   };
  2162 
  2163   /// \brief Provides continuous and unique id for the
  2164   /// items of a graph.
  2165   ///
  2166   /// RangeIdMap provides a unique and continuous
  2167   /// id for each item of a given type (\c Node, \c Arc or
  2168   /// \c Edge) in a graph. This id is
  2169   ///  - \b unique: different items get different ids,
  2170   ///  - \b continuous: the range of the ids is the set of integers
  2171   ///    between 0 and \c n-1, where \c n is the number of the items of
  2172   ///    this type (\c Node, \c Arc or \c Edge).
  2173   ///  - So, the ids can change when deleting an item of the same type.
  2174   ///
  2175   /// Thus this id is not (necessarily) the same as what can get using
  2176   /// the \c id() function of the graph or \ref IdMap.
  2177   /// This map can be inverted with its member class \c InverseMap,
  2178   /// or with the \c operator()() member.
  2179   ///
  2180   /// \tparam GR The graph type.
  2181   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  2182   /// \c GR::Edge).
  2183   ///
  2184   /// \see IdMap
  2185   template <typename GR, typename K>
  2186   class RangeIdMap
  2187     : protected ItemSetTraits<GR, K>::template Map<int>::Type {
  2188 
  2189     typedef typename ItemSetTraits<GR, K>::template Map<int>::Type Map;
  2190 
  2191   public:
  2192     /// The graph type of RangeIdMap.
  2193     typedef GR Graph;
  2194     typedef GR Digraph;
  2195     /// The key type of RangeIdMap (\c Node, \c Arc or \c Edge).
  2196     typedef K Item;
  2197     /// The key type of RangeIdMap (\c Node, \c Arc or \c Edge).
  2198     typedef K Key;
  2199     /// The value type of RangeIdMap.
  2200     typedef int Value;
  2201 
  2202     /// \brief Constructor.
  2203     ///
  2204     /// Constructor.
  2205     explicit RangeIdMap(const Graph& gr) : Map(gr) {
  2206       Item it;
  2207       const typename Map::Notifier* nf = Map::notifier();
  2208       for (nf->first(it); it != INVALID; nf->next(it)) {
  2209         Map::set(it, _inv_map.size());
  2210         _inv_map.push_back(it);
  2211       }
  2212     }
  2213 
  2214   protected:
  2215 
  2216     /// \brief Adds a new key to the map.
  2217     ///
  2218     /// Add a new key to the map. It is called by the
  2219     /// \c AlterationNotifier.
  2220     virtual void add(const Item& item) {
  2221       Map::add(item);
  2222       Map::set(item, _inv_map.size());
  2223       _inv_map.push_back(item);
  2224     }
  2225 
  2226     /// \brief Add more new keys to the map.
  2227     ///
  2228     /// Add more new keys to the map. It is called by the
  2229     /// \c AlterationNotifier.
  2230     virtual void add(const std::vector<Item>& items) {
  2231       Map::add(items);
  2232       for (int i = 0; i < int(items.size()); ++i) {
  2233         Map::set(items[i], _inv_map.size());
  2234         _inv_map.push_back(items[i]);
  2235       }
  2236     }
  2237 
  2238     /// \brief Erase the key from the map.
  2239     ///
  2240     /// Erase the key from the map. It is called by the
  2241     /// \c AlterationNotifier.
  2242     virtual void erase(const Item& item) {
  2243       Map::set(_inv_map.back(), Map::operator[](item));
  2244       _inv_map[Map::operator[](item)] = _inv_map.back();
  2245       _inv_map.pop_back();
  2246       Map::erase(item);
  2247     }
  2248 
  2249     /// \brief Erase more keys from the map.
  2250     ///
  2251     /// Erase more keys from the map. It is called by the
  2252     /// \c AlterationNotifier.
  2253     virtual void erase(const std::vector<Item>& items) {
  2254       for (int i = 0; i < int(items.size()); ++i) {
  2255         Map::set(_inv_map.back(), Map::operator[](items[i]));
  2256         _inv_map[Map::operator[](items[i])] = _inv_map.back();
  2257         _inv_map.pop_back();
  2258       }
  2259       Map::erase(items);
  2260     }
  2261 
  2262     /// \brief Build the unique map.
  2263     ///
  2264     /// Build the unique map. It is called by the
  2265     /// \c AlterationNotifier.
  2266     virtual void build() {
  2267       Map::build();
  2268       Item it;
  2269       const typename Map::Notifier* nf = Map::notifier();
  2270       for (nf->first(it); it != INVALID; nf->next(it)) {
  2271         Map::set(it, _inv_map.size());
  2272         _inv_map.push_back(it);
  2273       }
  2274     }
  2275 
  2276     /// \brief Clear the keys from the map.
  2277     ///
  2278     /// Clear the keys from the map. It is called by the
  2279     /// \c AlterationNotifier.
  2280     virtual void clear() {
  2281       _inv_map.clear();
  2282       Map::clear();
  2283     }
  2284 
  2285   public:
  2286 
  2287     /// \brief Returns the maximal value plus one.
  2288     ///
  2289     /// Returns the maximal value plus one in the map.
  2290     unsigned int size() const {
  2291       return _inv_map.size();
  2292     }
  2293 
  2294     /// \brief Swaps the position of the two items in the map.
  2295     ///
  2296     /// Swaps the position of the two items in the map.
  2297     void swap(const Item& p, const Item& q) {
  2298       int pi = Map::operator[](p);
  2299       int qi = Map::operator[](q);
  2300       Map::set(p, qi);
  2301       _inv_map[qi] = p;
  2302       Map::set(q, pi);
  2303       _inv_map[pi] = q;
  2304     }
  2305 
  2306     /// \brief Gives back the \e range \e id of the item
  2307     ///
  2308     /// Gives back the \e range \e id of the item.
  2309     int operator[](const Item& item) const {
  2310       return Map::operator[](item);
  2311     }
  2312 
  2313     /// \brief Gives back the item belonging to a \e range \e id
  2314     ///
  2315     /// Gives back the item belonging to the given \e range \e id.
  2316     Item operator()(int id) const {
  2317       return _inv_map[id];
  2318     }
  2319 
  2320   private:
  2321 
  2322     typedef std::vector<Item> Container;
  2323     Container _inv_map;
  2324 
  2325   public:
  2326 
  2327     /// \brief The inverse map type of RangeIdMap.
  2328     ///
  2329     /// The inverse map type of RangeIdMap. The subscript operator gives
  2330     /// back an item by its \e range \e id.
  2331     /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
  2332     class InverseMap {
  2333     public:
  2334       /// \brief Constructor
  2335       ///
  2336       /// Constructor of the InverseMap.
  2337       explicit InverseMap(const RangeIdMap& inverted)
  2338         : _inverted(inverted) {}
  2339 
  2340 
  2341       /// The value type of the InverseMap.
  2342       typedef typename RangeIdMap::Key Value;
  2343       /// The key type of the InverseMap.
  2344       typedef typename RangeIdMap::Value Key;
  2345 
  2346       /// \brief Subscript operator.
  2347       ///
  2348       /// Subscript operator. It gives back the item
  2349       /// that the given \e range \e id currently belongs to.
  2350       Value operator[](const Key& key) const {
  2351         return _inverted(key);
  2352       }
  2353 
  2354       /// \brief Size of the map.
  2355       ///
  2356       /// Returns the size of the map.
  2357       unsigned int size() const {
  2358         return _inverted.size();
  2359       }
  2360 
  2361     private:
  2362       const RangeIdMap& _inverted;
  2363     };
  2364 
  2365     /// \brief Gives back the inverse of the map.
  2366     ///
  2367     /// Gives back the inverse of the RangeIdMap.
  2368     const InverseMap inverse() const {
  2369       return InverseMap(*this);
  2370     }
  2371   };
  2372 
  2373   /// \brief Returns a \c RangeIdMap class.
  2374   ///
  2375   /// This function just returns an \c RangeIdMap class.
  2376   /// \relates RangeIdMap
  2377   template <typename K, typename GR>
  2378   inline RangeIdMap<GR, K> rangeIdMap(const GR& graph) {
  2379     return RangeIdMap<GR, K>(graph);
  2380   }
  2381 
  2382   /// \brief Dynamic iterable \c bool map.
  2383   ///
  2384   /// This class provides a special graph map type which can store a
  2385   /// \c bool value for graph items (\c Node, \c Arc or \c Edge).
  2386   /// For both \c true and \c false values it is possible to iterate on
  2387   /// the keys mapped to the value.
  2388   ///
  2389   /// This type is a reference map, so it can be modified with the
  2390   /// subscript operator.
  2391   ///
  2392   /// \tparam GR The graph type.
  2393   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  2394   /// \c GR::Edge).
  2395   ///
  2396   /// \see IterableIntMap, IterableValueMap
  2397   /// \see CrossRefMap
  2398   template <typename GR, typename K>
  2399   class IterableBoolMap
  2400     : protected ItemSetTraits<GR, K>::template Map<int>::Type {
  2401   private:
  2402     typedef GR Graph;
  2403 
  2404     typedef typename ItemSetTraits<GR, K>::ItemIt KeyIt;
  2405     typedef typename ItemSetTraits<GR, K>::template Map<int>::Type Parent;
  2406 
  2407     std::vector<K> _array;
  2408     int _sep;
  2409 
  2410   public:
  2411 
  2412     /// Indicates that the map is reference map.
  2413     typedef True ReferenceMapTag;
  2414 
  2415     /// The key type
  2416     typedef K Key;
  2417     /// The value type
  2418     typedef bool Value;
  2419     /// The const reference type.
  2420     typedef const Value& ConstReference;
  2421 
  2422   private:
  2423 
  2424     int position(const Key& key) const {
  2425       return Parent::operator[](key);
  2426     }
  2427 
  2428   public:
  2429 
  2430     /// \brief Reference to the value of the map.
  2431     ///
  2432     /// This class is similar to the \c bool type. It can be converted to
  2433     /// \c bool and it provides the same operators.
  2434     class Reference {
  2435       friend class IterableBoolMap;
  2436     private:
  2437       Reference(IterableBoolMap& map, const Key& key)
  2438         : _key(key), _map(map) {}
  2439     public:
  2440 
  2441       Reference& operator=(const Reference& value) {
  2442         _map.set(_key, static_cast<bool>(value));
  2443          return *this;
  2444       }
  2445 
  2446       operator bool() const {
  2447         return static_cast<const IterableBoolMap&>(_map)[_key];
  2448       }
  2449 
  2450       Reference& operator=(bool value) {
  2451         _map.set(_key, value);
  2452         return *this;
  2453       }
  2454       Reference& operator&=(bool value) {
  2455         _map.set(_key, _map[_key] & value);
  2456         return *this;
  2457       }
  2458       Reference& operator|=(bool value) {
  2459         _map.set(_key, _map[_key] | value);
  2460         return *this;
  2461       }
  2462       Reference& operator^=(bool value) {
  2463         _map.set(_key, _map[_key] ^ value);
  2464         return *this;
  2465       }
  2466     private:
  2467       Key _key;
  2468       IterableBoolMap& _map;
  2469     };
  2470 
  2471     /// \brief Constructor of the map with a default value.
  2472     ///
  2473     /// Constructor of the map with a default value.
  2474     explicit IterableBoolMap(const Graph& graph, bool def = false)
  2475       : Parent(graph) {
  2476       typename Parent::Notifier* nf = Parent::notifier();
  2477       Key it;
  2478       for (nf->first(it); it != INVALID; nf->next(it)) {
  2479         Parent::set(it, _array.size());
  2480         _array.push_back(it);
  2481       }
  2482       _sep = (def ? _array.size() : 0);
  2483     }
  2484 
  2485     /// \brief Const subscript operator of the map.
  2486     ///
  2487     /// Const subscript operator of the map.
  2488     bool operator[](const Key& key) const {
  2489       return position(key) < _sep;
  2490     }
  2491 
  2492     /// \brief Subscript operator of the map.
  2493     ///
  2494     /// Subscript operator of the map.
  2495     Reference operator[](const Key& key) {
  2496       return Reference(*this, key);
  2497     }
  2498 
  2499     /// \brief Set operation of the map.
  2500     ///
  2501     /// Set operation of the map.
  2502     void set(const Key& key, bool value) {
  2503       int pos = position(key);
  2504       if (value) {
  2505         if (pos < _sep) return;
  2506         Key tmp = _array[_sep];
  2507         _array[_sep] = key;
  2508         Parent::set(key, _sep);
  2509         _array[pos] = tmp;
  2510         Parent::set(tmp, pos);
  2511         ++_sep;
  2512       } else {
  2513         if (pos >= _sep) return;
  2514         --_sep;
  2515         Key tmp = _array[_sep];
  2516         _array[_sep] = key;
  2517         Parent::set(key, _sep);
  2518         _array[pos] = tmp;
  2519         Parent::set(tmp, pos);
  2520       }
  2521     }
  2522 
  2523     /// \brief Set all items.
  2524     ///
  2525     /// Set all items in the map.
  2526     /// \note Constant time operation.
  2527     void setAll(bool value) {
  2528       _sep = (value ? _array.size() : 0);
  2529     }
  2530 
  2531     /// \brief Returns the number of the keys mapped to \c true.
  2532     ///
  2533     /// Returns the number of the keys mapped to \c true.
  2534     int trueNum() const {
  2535       return _sep;
  2536     }
  2537 
  2538     /// \brief Returns the number of the keys mapped to \c false.
  2539     ///
  2540     /// Returns the number of the keys mapped to \c false.
  2541     int falseNum() const {
  2542       return _array.size() - _sep;
  2543     }
  2544 
  2545     /// \brief Iterator for the keys mapped to \c true.
  2546     ///
  2547     /// Iterator for the keys mapped to \c true. It works
  2548     /// like a graph item iterator, it can be converted to
  2549     /// the key type of the map, incremented with \c ++ operator, and
  2550     /// if the iterator leaves the last valid key, it will be equal to
  2551     /// \c INVALID.
  2552     class TrueIt : public Key {
  2553     public:
  2554       typedef Key Parent;
  2555 
  2556       /// \brief Creates an iterator.
  2557       ///
  2558       /// Creates an iterator. It iterates on the
  2559       /// keys mapped to \c true.
  2560       /// \param map The IterableBoolMap.
  2561       explicit TrueIt(const IterableBoolMap& map)
  2562         : Parent(map._sep > 0 ? map._array[map._sep - 1] : INVALID),
  2563           _map(&map) {}
  2564 
  2565       /// \brief Invalid constructor \& conversion.
  2566       ///
  2567       /// This constructor initializes the iterator to be invalid.
  2568       /// \sa Invalid for more details.
  2569       TrueIt(Invalid) : Parent(INVALID), _map(0) {}
  2570 
  2571       /// \brief Increment operator.
  2572       ///
  2573       /// Increment operator.
  2574       TrueIt& operator++() {
  2575         int pos = _map->position(*this);
  2576         Parent::operator=(pos > 0 ? _map->_array[pos - 1] : INVALID);
  2577         return *this;
  2578       }
  2579 
  2580     private:
  2581       const IterableBoolMap* _map;
  2582     };
  2583 
  2584     /// \brief Iterator for the keys mapped to \c false.
  2585     ///
  2586     /// Iterator for the keys mapped to \c false. It works
  2587     /// like a graph item iterator, it can be converted to
  2588     /// the key type of the map, incremented with \c ++ operator, and
  2589     /// if the iterator leaves the last valid key, it will be equal to
  2590     /// \c INVALID.
  2591     class FalseIt : public Key {
  2592     public:
  2593       typedef Key Parent;
  2594 
  2595       /// \brief Creates an iterator.
  2596       ///
  2597       /// Creates an iterator. It iterates on the
  2598       /// keys mapped to \c false.
  2599       /// \param map The IterableBoolMap.
  2600       explicit FalseIt(const IterableBoolMap& map)
  2601         : Parent(map._sep < int(map._array.size()) ?
  2602                  map._array.back() : INVALID), _map(&map) {}
  2603 
  2604       /// \brief Invalid constructor \& conversion.
  2605       ///
  2606       /// This constructor initializes the iterator to be invalid.
  2607       /// \sa Invalid for more details.
  2608       FalseIt(Invalid) : Parent(INVALID), _map(0) {}
  2609 
  2610       /// \brief Increment operator.
  2611       ///
  2612       /// Increment operator.
  2613       FalseIt& operator++() {
  2614         int pos = _map->position(*this);
  2615         Parent::operator=(pos > _map->_sep ? _map->_array[pos - 1] : INVALID);
  2616         return *this;
  2617       }
  2618 
  2619     private:
  2620       const IterableBoolMap* _map;
  2621     };
  2622 
  2623     /// \brief Iterator for the keys mapped to a given value.
  2624     ///
  2625     /// Iterator for the keys mapped to a given value. It works
  2626     /// like a graph item iterator, it can be converted to
  2627     /// the key type of the map, incremented with \c ++ operator, and
  2628     /// if the iterator leaves the last valid key, it will be equal to
  2629     /// \c INVALID.
  2630     class ItemIt : public Key {
  2631     public:
  2632       typedef Key Parent;
  2633 
  2634       /// \brief Creates an iterator with a value.
  2635       ///
  2636       /// Creates an iterator with a value. It iterates on the
  2637       /// keys mapped to the given value.
  2638       /// \param map The IterableBoolMap.
  2639       /// \param value The value.
  2640       ItemIt(const IterableBoolMap& map, bool value)
  2641         : Parent(value ?
  2642                  (map._sep > 0 ?
  2643                   map._array[map._sep - 1] : INVALID) :
  2644                  (map._sep < int(map._array.size()) ?
  2645                   map._array.back() : INVALID)), _map(&map) {}
  2646 
  2647       /// \brief Invalid constructor \& conversion.
  2648       ///
  2649       /// This constructor initializes the iterator to be invalid.
  2650       /// \sa Invalid for more details.
  2651       ItemIt(Invalid) : Parent(INVALID), _map(0) {}
  2652 
  2653       /// \brief Increment operator.
  2654       ///
  2655       /// Increment operator.
  2656       ItemIt& operator++() {
  2657         int pos = _map->position(*this);
  2658         int _sep = pos >= _map->_sep ? _map->_sep : 0;
  2659         Parent::operator=(pos > _sep ? _map->_array[pos - 1] : INVALID);
  2660         return *this;
  2661       }
  2662 
  2663     private:
  2664       const IterableBoolMap* _map;
  2665     };
  2666 
  2667   protected:
  2668 
  2669     virtual void add(const Key& key) {
  2670       Parent::add(key);
  2671       Parent::set(key, _array.size());
  2672       _array.push_back(key);
  2673     }
  2674 
  2675     virtual void add(const std::vector<Key>& keys) {
  2676       Parent::add(keys);
  2677       for (int i = 0; i < int(keys.size()); ++i) {
  2678         Parent::set(keys[i], _array.size());
  2679         _array.push_back(keys[i]);
  2680       }
  2681     }
  2682 
  2683     virtual void erase(const Key& key) {
  2684       int pos = position(key);
  2685       if (pos < _sep) {
  2686         --_sep;
  2687         Parent::set(_array[_sep], pos);
  2688         _array[pos] = _array[_sep];
  2689         Parent::set(_array.back(), _sep);
  2690         _array[_sep] = _array.back();
  2691         _array.pop_back();
  2692       } else {
  2693         Parent::set(_array.back(), pos);
  2694         _array[pos] = _array.back();
  2695         _array.pop_back();
  2696       }
  2697       Parent::erase(key);
  2698     }
  2699 
  2700     virtual void erase(const std::vector<Key>& keys) {
  2701       for (int i = 0; i < int(keys.size()); ++i) {
  2702         int pos = position(keys[i]);
  2703         if (pos < _sep) {
  2704           --_sep;
  2705           Parent::set(_array[_sep], pos);
  2706           _array[pos] = _array[_sep];
  2707           Parent::set(_array.back(), _sep);
  2708           _array[_sep] = _array.back();
  2709           _array.pop_back();
  2710         } else {
  2711           Parent::set(_array.back(), pos);
  2712           _array[pos] = _array.back();
  2713           _array.pop_back();
  2714         }
  2715       }
  2716       Parent::erase(keys);
  2717     }
  2718 
  2719     virtual void build() {
  2720       Parent::build();
  2721       typename Parent::Notifier* nf = Parent::notifier();
  2722       Key it;
  2723       for (nf->first(it); it != INVALID; nf->next(it)) {
  2724         Parent::set(it, _array.size());
  2725         _array.push_back(it);
  2726       }
  2727       _sep = 0;
  2728     }
  2729 
  2730     virtual void clear() {
  2731       _array.clear();
  2732       _sep = 0;
  2733       Parent::clear();
  2734     }
  2735 
  2736   };
  2737 
  2738 
  2739   namespace _maps_bits {
  2740     template <typename Item>
  2741     struct IterableIntMapNode {
  2742       IterableIntMapNode() : value(-1) {}
  2743       IterableIntMapNode(int _value) : value(_value) {}
  2744       Item prev, next;
  2745       int value;
  2746     };
  2747   }
  2748 
  2749   /// \brief Dynamic iterable integer map.
  2750   ///
  2751   /// This class provides a special graph map type which can store an
  2752   /// integer value for graph items (\c Node, \c Arc or \c Edge).
  2753   /// For each non-negative value it is possible to iterate on the keys
  2754   /// mapped to the value.
  2755   ///
  2756   /// This map is intended to be used with small integer values, for which
  2757   /// it is efficient, and supports iteration only for non-negative values.
  2758   /// If you need large values and/or iteration for negative integers,
  2759   /// consider to use \ref IterableValueMap instead.
  2760   ///
  2761   /// This type is a reference map, so it can be modified with the
  2762   /// subscript operator.
  2763   ///
  2764   /// \note The size of the data structure depends on the largest
  2765   /// value in the map.
  2766   ///
  2767   /// \tparam GR The graph type.
  2768   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  2769   /// \c GR::Edge).
  2770   ///
  2771   /// \see IterableBoolMap, IterableValueMap
  2772   /// \see CrossRefMap
  2773   template <typename GR, typename K>
  2774   class IterableIntMap
  2775     : protected ItemSetTraits<GR, K>::
  2776         template Map<_maps_bits::IterableIntMapNode<K> >::Type {
  2777   public:
  2778     typedef typename ItemSetTraits<GR, K>::
  2779       template Map<_maps_bits::IterableIntMapNode<K> >::Type Parent;
  2780 
  2781     /// The key type
  2782     typedef K Key;
  2783     /// The value type
  2784     typedef int Value;
  2785     /// The graph type
  2786     typedef GR Graph;
  2787 
  2788     /// \brief Constructor of the map.
  2789     ///
  2790     /// Constructor of the map. It sets all values to -1.
  2791     explicit IterableIntMap(const Graph& graph)
  2792       : Parent(graph) {}
  2793 
  2794     /// \brief Constructor of the map with a given value.
  2795     ///
  2796     /// Constructor of the map with a given value.
  2797     explicit IterableIntMap(const Graph& graph, int value)
  2798       : Parent(graph, _maps_bits::IterableIntMapNode<K>(value)) {
  2799       if (value >= 0) {
  2800         for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
  2801           lace(it);
  2802         }
  2803       }
  2804     }
  2805 
  2806   private:
  2807 
  2808     void unlace(const Key& key) {
  2809       typename Parent::Value& node = Parent::operator[](key);
  2810       if (node.value < 0) return;
  2811       if (node.prev != INVALID) {
  2812         Parent::operator[](node.prev).next = node.next;
  2813       } else {
  2814         _first[node.value] = node.next;
  2815       }
  2816       if (node.next != INVALID) {
  2817         Parent::operator[](node.next).prev = node.prev;
  2818       }
  2819       while (!_first.empty() && _first.back() == INVALID) {
  2820         _first.pop_back();
  2821       }
  2822     }
  2823 
  2824     void lace(const Key& key) {
  2825       typename Parent::Value& node = Parent::operator[](key);
  2826       if (node.value < 0) return;
  2827       if (node.value >= int(_first.size())) {
  2828         _first.resize(node.value + 1, INVALID);
  2829       }
  2830       node.prev = INVALID;
  2831       node.next = _first[node.value];
  2832       if (node.next != INVALID) {
  2833         Parent::operator[](node.next).prev = key;
  2834       }
  2835       _first[node.value] = key;
  2836     }
  2837 
  2838   public:
  2839 
  2840     /// Indicates that the map is reference map.
  2841     typedef True ReferenceMapTag;
  2842 
  2843     /// \brief Reference to the value of the map.
  2844     ///
  2845     /// This class is similar to the \c int type. It can
  2846     /// be converted to \c int and it has the same operators.
  2847     class Reference {
  2848       friend class IterableIntMap;
  2849     private:
  2850       Reference(IterableIntMap& map, const Key& key)
  2851         : _key(key), _map(map) {}
  2852     public:
  2853 
  2854       Reference& operator=(const Reference& value) {
  2855         _map.set(_key, static_cast<const int&>(value));
  2856          return *this;
  2857       }
  2858 
  2859       operator const int&() const {
  2860         return static_cast<const IterableIntMap&>(_map)[_key];
  2861       }
  2862 
  2863       Reference& operator=(int value) {
  2864         _map.set(_key, value);
  2865         return *this;
  2866       }
  2867       Reference& operator++() {
  2868         _map.set(_key, _map[_key] + 1);
  2869         return *this;
  2870       }
  2871       int operator++(int) {
  2872         int value = _map[_key];
  2873         _map.set(_key, value + 1);
  2874         return value;
  2875       }
  2876       Reference& operator--() {
  2877         _map.set(_key, _map[_key] - 1);
  2878         return *this;
  2879       }
  2880       int operator--(int) {
  2881         int value = _map[_key];
  2882         _map.set(_key, value - 1);
  2883         return value;
  2884       }
  2885       Reference& operator+=(int value) {
  2886         _map.set(_key, _map[_key] + value);
  2887         return *this;
  2888       }
  2889       Reference& operator-=(int value) {
  2890         _map.set(_key, _map[_key] - value);
  2891         return *this;
  2892       }
  2893       Reference& operator*=(int value) {
  2894         _map.set(_key, _map[_key] * value);
  2895         return *this;
  2896       }
  2897       Reference& operator/=(int value) {
  2898         _map.set(_key, _map[_key] / value);
  2899         return *this;
  2900       }
  2901       Reference& operator%=(int value) {
  2902         _map.set(_key, _map[_key] % value);
  2903         return *this;
  2904       }
  2905       Reference& operator&=(int value) {
  2906         _map.set(_key, _map[_key] & value);
  2907         return *this;
  2908       }
  2909       Reference& operator|=(int value) {
  2910         _map.set(_key, _map[_key] | value);
  2911         return *this;
  2912       }
  2913       Reference& operator^=(int value) {
  2914         _map.set(_key, _map[_key] ^ value);
  2915         return *this;
  2916       }
  2917       Reference& operator<<=(int value) {
  2918         _map.set(_key, _map[_key] << value);
  2919         return *this;
  2920       }
  2921       Reference& operator>>=(int value) {
  2922         _map.set(_key, _map[_key] >> value);
  2923         return *this;
  2924       }
  2925 
  2926     private:
  2927       Key _key;
  2928       IterableIntMap& _map;
  2929     };
  2930 
  2931     /// The const reference type.
  2932     typedef const Value& ConstReference;
  2933 
  2934     /// \brief Gives back the maximal value plus one.
  2935     ///
  2936     /// Gives back the maximal value plus one.
  2937     int size() const {
  2938       return _first.size();
  2939     }
  2940 
  2941     /// \brief Set operation of the map.
  2942     ///
  2943     /// Set operation of the map.
  2944     void set(const Key& key, const Value& value) {
  2945       unlace(key);
  2946       Parent::operator[](key).value = value;
  2947       lace(key);
  2948     }
  2949 
  2950     /// \brief Const subscript operator of the map.
  2951     ///
  2952     /// Const subscript operator of the map.
  2953     const Value& operator[](const Key& key) const {
  2954       return Parent::operator[](key).value;
  2955     }
  2956 
  2957     /// \brief Subscript operator of the map.
  2958     ///
  2959     /// Subscript operator of the map.
  2960     Reference operator[](const Key& key) {
  2961       return Reference(*this, key);
  2962     }
  2963 
  2964     /// \brief Iterator for the keys with the same value.
  2965     ///
  2966     /// Iterator for the keys with the same value. It works
  2967     /// like a graph item iterator, it can be converted to
  2968     /// the item type of the map, incremented with \c ++ operator, and
  2969     /// if the iterator leaves the last valid item, it will be equal to
  2970     /// \c INVALID.
  2971     class ItemIt : public Key {
  2972     public:
  2973       typedef Key Parent;
  2974 
  2975       /// \brief Invalid constructor \& conversion.
  2976       ///
  2977       /// This constructor initializes the iterator to be invalid.
  2978       /// \sa Invalid for more details.
  2979       ItemIt(Invalid) : Parent(INVALID), _map(0) {}
  2980 
  2981       /// \brief Creates an iterator with a value.
  2982       ///
  2983       /// Creates an iterator with a value. It iterates on the
  2984       /// keys mapped to the given value.
  2985       /// \param map The IterableIntMap.
  2986       /// \param value The value.
  2987       ItemIt(const IterableIntMap& map, int value) : _map(&map) {
  2988         if (value < 0 || value >= int(_map->_first.size())) {
  2989           Parent::operator=(INVALID);
  2990         } else {
  2991           Parent::operator=(_map->_first[value]);
  2992         }
  2993       }
  2994 
  2995       /// \brief Increment operator.
  2996       ///
  2997       /// Increment operator.
  2998       ItemIt& operator++() {
  2999         Parent::operator=(_map->IterableIntMap::Parent::
  3000                           operator[](static_cast<Parent&>(*this)).next);
  3001         return *this;
  3002       }
  3003 
  3004     private:
  3005       const IterableIntMap* _map;
  3006     };
  3007 
  3008   protected:
  3009 
  3010     virtual void erase(const Key& key) {
  3011       unlace(key);
  3012       Parent::erase(key);
  3013     }
  3014 
  3015     virtual void erase(const std::vector<Key>& keys) {
  3016       for (int i = 0; i < int(keys.size()); ++i) {
  3017         unlace(keys[i]);
  3018       }
  3019       Parent::erase(keys);
  3020     }
  3021 
  3022     virtual void clear() {
  3023       _first.clear();
  3024       Parent::clear();
  3025     }
  3026 
  3027   private:
  3028     std::vector<Key> _first;
  3029   };
  3030 
  3031   namespace _maps_bits {
  3032     template <typename Item, typename Value>
  3033     struct IterableValueMapNode {
  3034       IterableValueMapNode(Value _value = Value()) : value(_value) {}
  3035       Item prev, next;
  3036       Value value;
  3037     };
  3038   }
  3039 
  3040   /// \brief Dynamic iterable map for comparable values.
  3041   ///
  3042   /// This class provides a special graph map type which can store a
  3043   /// comparable value for graph items (\c Node, \c Arc or \c Edge).
  3044   /// For each value it is possible to iterate on the keys mapped to
  3045   /// the value (\c ItemIt), and the values of the map can be accessed
  3046   /// with an STL compatible forward iterator (\c ValueIt).
  3047   /// The map stores a linked list for each value, which contains
  3048   /// the items mapped to the value, and the used values are stored
  3049   /// in balanced binary tree (\c std::map).
  3050   ///
  3051   /// \ref IterableBoolMap and \ref IterableIntMap are similar classes
  3052   /// specialized for \c bool and \c int values, respectively.
  3053   ///
  3054   /// This type is not reference map, so it cannot be modified with
  3055   /// the subscript operator.
  3056   ///
  3057   /// \tparam GR The graph type.
  3058   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  3059   /// \c GR::Edge).
  3060   /// \tparam V The value type of the map. It can be any comparable
  3061   /// value type.
  3062   ///
  3063   /// \see IterableBoolMap, IterableIntMap
  3064   /// \see CrossRefMap
  3065   template <typename GR, typename K, typename V>
  3066   class IterableValueMap
  3067     : protected ItemSetTraits<GR, K>::
  3068         template Map<_maps_bits::IterableValueMapNode<K, V> >::Type {
  3069   public:
  3070     typedef typename ItemSetTraits<GR, K>::
  3071       template Map<_maps_bits::IterableValueMapNode<K, V> >::Type Parent;
  3072 
  3073     /// The key type
  3074     typedef K Key;
  3075     /// The value type
  3076     typedef V Value;
  3077     /// The graph type
  3078     typedef GR Graph;
  3079 
  3080   public:
  3081 
  3082     /// \brief Constructor of the map with a given value.
  3083     ///
  3084     /// Constructor of the map with a given value.
  3085     explicit IterableValueMap(const Graph& graph,
  3086                               const Value& value = Value())
  3087       : Parent(graph, _maps_bits::IterableValueMapNode<K, V>(value)) {
  3088       for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
  3089         lace(it);
  3090       }
  3091     }
  3092 
  3093   protected:
  3094 
  3095     void unlace(const Key& key) {
  3096       typename Parent::Value& node = Parent::operator[](key);
  3097       if (node.prev != INVALID) {
  3098         Parent::operator[](node.prev).next = node.next;
  3099       } else {
  3100         if (node.next != INVALID) {
  3101           _first[node.value] = node.next;
  3102         } else {
  3103           _first.erase(node.value);
  3104         }
  3105       }
  3106       if (node.next != INVALID) {
  3107         Parent::operator[](node.next).prev = node.prev;
  3108       }
  3109     }
  3110 
  3111     void lace(const Key& key) {
  3112       typename Parent::Value& node = Parent::operator[](key);
  3113       typename std::map<Value, Key>::iterator it = _first.find(node.value);
  3114       if (it == _first.end()) {
  3115         node.prev = node.next = INVALID;
  3116         _first.insert(std::make_pair(node.value, key));
  3117       } else {
  3118         node.prev = INVALID;
  3119         node.next = it->second;
  3120         if (node.next != INVALID) {
  3121           Parent::operator[](node.next).prev = key;
  3122         }
  3123         it->second = key;
  3124       }
  3125     }
  3126 
  3127   public:
  3128 
  3129     /// \brief Forward iterator for values.
  3130     ///
  3131     /// This iterator is an STL compatible forward
  3132     /// iterator on the values of the map. The values can
  3133     /// be accessed in the <tt>[beginValue, endValue)</tt> range.
  3134     class ValueIt
  3135       : public std::iterator<std::forward_iterator_tag, Value> {
  3136       friend class IterableValueMap;
  3137     private:
  3138       ValueIt(typename std::map<Value, Key>::const_iterator _it)
  3139         : it(_it) {}
  3140     public:
  3141 
  3142       /// Constructor
  3143       ValueIt() {}
  3144 
  3145       /// \e
  3146       ValueIt& operator++() { ++it; return *this; }
  3147       /// \e
  3148       ValueIt operator++(int) {
  3149         ValueIt tmp(*this);
  3150         operator++();
  3151         return tmp;
  3152       }
  3153 
  3154       /// \e
  3155       const Value& operator*() const { return it->first; }
  3156       /// \e
  3157       const Value* operator->() const { return &(it->first); }
  3158 
  3159       /// \e
  3160       bool operator==(ValueIt jt) const { return it == jt.it; }
  3161       /// \e
  3162       bool operator!=(ValueIt jt) const { return it != jt.it; }
  3163 
  3164     private:
  3165       typename std::map<Value, Key>::const_iterator it;
  3166     };
  3167 
  3168     /// \brief Returns an iterator to the first value.
  3169     ///
  3170     /// Returns an STL compatible iterator to the
  3171     /// first value of the map. The values of the
  3172     /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  3173     /// range.
  3174     ValueIt beginValue() const {
  3175       return ValueIt(_first.begin());
  3176     }
  3177 
  3178     /// \brief Returns an iterator after the last value.
  3179     ///
  3180     /// Returns an STL compatible iterator after the
  3181     /// last value of the map. The values of the
  3182     /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  3183     /// range.
  3184     ValueIt endValue() const {
  3185       return ValueIt(_first.end());
  3186     }
  3187 
  3188     /// \brief Set operation of the map.
  3189     ///
  3190     /// Set operation of the map.
  3191     void set(const Key& key, const Value& value) {
  3192       unlace(key);
  3193       Parent::operator[](key).value = value;
  3194       lace(key);
  3195     }
  3196 
  3197     /// \brief Const subscript operator of the map.
  3198     ///
  3199     /// Const subscript operator of the map.
  3200     const Value& operator[](const Key& key) const {
  3201       return Parent::operator[](key).value;
  3202     }
  3203 
  3204     /// \brief Iterator for the keys with the same value.
  3205     ///
  3206     /// Iterator for the keys with the same value. It works
  3207     /// like a graph item iterator, it can be converted to
  3208     /// the item type of the map, incremented with \c ++ operator, and
  3209     /// if the iterator leaves the last valid item, it will be equal to
  3210     /// \c INVALID.
  3211     class ItemIt : public Key {
  3212     public:
  3213       typedef Key Parent;
  3214 
  3215       /// \brief Invalid constructor \& conversion.
  3216       ///
  3217       /// This constructor initializes the iterator to be invalid.
  3218       /// \sa Invalid for more details.
  3219       ItemIt(Invalid) : Parent(INVALID), _map(0) {}
  3220 
  3221       /// \brief Creates an iterator with a value.
  3222       ///
  3223       /// Creates an iterator with a value. It iterates on the
  3224       /// keys which have the given value.
  3225       /// \param map The IterableValueMap
  3226       /// \param value The value
  3227       ItemIt(const IterableValueMap& map, const Value& value) : _map(&map) {
  3228         typename std::map<Value, Key>::const_iterator it =
  3229           map._first.find(value);
  3230         if (it == map._first.end()) {
  3231           Parent::operator=(INVALID);
  3232         } else {
  3233           Parent::operator=(it->second);
  3234         }
  3235       }
  3236 
  3237       /// \brief Increment operator.
  3238       ///
  3239       /// Increment Operator.
  3240       ItemIt& operator++() {
  3241         Parent::operator=(_map->IterableValueMap::Parent::
  3242                           operator[](static_cast<Parent&>(*this)).next);
  3243         return *this;
  3244       }
  3245 
  3246 
  3247     private:
  3248       const IterableValueMap* _map;
  3249     };
  3250 
  3251   protected:
  3252 
  3253     virtual void add(const Key& key) {
  3254       Parent::add(key);
  3255       lace(key);
  3256     }
  3257 
  3258     virtual void add(const std::vector<Key>& keys) {
  3259       Parent::add(keys);
  3260       for (int i = 0; i < int(keys.size()); ++i) {
  3261         lace(keys[i]);
  3262       }
  3263     }
  3264 
  3265     virtual void erase(const Key& key) {
  3266       unlace(key);
  3267       Parent::erase(key);
  3268     }
  3269 
  3270     virtual void erase(const std::vector<Key>& keys) {
  3271       for (int i = 0; i < int(keys.size()); ++i) {
  3272         unlace(keys[i]);
  3273       }
  3274       Parent::erase(keys);
  3275     }
  3276 
  3277     virtual void build() {
  3278       Parent::build();
  3279       for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
  3280         lace(it);
  3281       }
  3282     }
  3283 
  3284     virtual void clear() {
  3285       _first.clear();
  3286       Parent::clear();
  3287     }
  3288 
  3289   private:
  3290     std::map<Value, Key> _first;
  3291   };
  3292 
  3293   /// \brief Map of the source nodes of arcs in a digraph.
  3294   ///
  3295   /// SourceMap provides access for the source node of each arc in a digraph,
  3296   /// which is returned by the \c source() function of the digraph.
  3297   /// \tparam GR The digraph type.
  3298   /// \see TargetMap
  3299   template <typename GR>
  3300   class SourceMap {
  3301   public:
  3302 
  3303     /// The key type (the \c Arc type of the digraph).
  3304     typedef typename GR::Arc Key;
  3305     /// The value type (the \c Node type of the digraph).
  3306     typedef typename GR::Node Value;
  3307 
  3308     /// \brief Constructor
  3309     ///
  3310     /// Constructor.
  3311     /// \param digraph The digraph that the map belongs to.
  3312     explicit SourceMap(const GR& digraph) : _graph(digraph) {}
  3313 
  3314     /// \brief Returns the source node of the given arc.
  3315     ///
  3316     /// Returns the source node of the given arc.
  3317     Value operator[](const Key& arc) const {
  3318       return _graph.source(arc);
  3319     }
  3320 
  3321   private:
  3322     const GR& _graph;
  3323   };
  3324 
  3325   /// \brief Returns a \c SourceMap class.
  3326   ///
  3327   /// This function just returns an \c SourceMap class.
  3328   /// \relates SourceMap
  3329   template <typename GR>
  3330   inline SourceMap<GR> sourceMap(const GR& graph) {
  3331     return SourceMap<GR>(graph);
  3332   }
  3333 
  3334   /// \brief Map of the target nodes of arcs in a digraph.
  3335   ///
  3336   /// TargetMap provides access for the target node of each arc in a digraph,
  3337   /// which is returned by the \c target() function of the digraph.
  3338   /// \tparam GR The digraph type.
  3339   /// \see SourceMap
  3340   template <typename GR>
  3341   class TargetMap {
  3342   public:
  3343 
  3344     /// The key type (the \c Arc type of the digraph).
  3345     typedef typename GR::Arc Key;
  3346     /// The value type (the \c Node type of the digraph).
  3347     typedef typename GR::Node Value;
  3348 
  3349     /// \brief Constructor
  3350     ///
  3351     /// Constructor.
  3352     /// \param digraph The digraph that the map belongs to.
  3353     explicit TargetMap(const GR& digraph) : _graph(digraph) {}
  3354 
  3355     /// \brief Returns the target node of the given arc.
  3356     ///
  3357     /// Returns the target node of the given arc.
  3358     Value operator[](const Key& e) const {
  3359       return _graph.target(e);
  3360     }
  3361 
  3362   private:
  3363     const GR& _graph;
  3364   };
  3365 
  3366   /// \brief Returns a \c TargetMap class.
  3367   ///
  3368   /// This function just returns a \c TargetMap class.
  3369   /// \relates TargetMap
  3370   template <typename GR>
  3371   inline TargetMap<GR> targetMap(const GR& graph) {
  3372     return TargetMap<GR>(graph);
  3373   }
  3374 
  3375   /// \brief Map of the "forward" directed arc view of edges in a graph.
  3376   ///
  3377   /// ForwardMap provides access for the "forward" directed arc view of
  3378   /// each edge in a graph, which is returned by the \c direct() function
  3379   /// of the graph with \c true parameter.
  3380   /// \tparam GR The graph type.
  3381   /// \see BackwardMap
  3382   template <typename GR>
  3383   class ForwardMap {
  3384   public:
  3385 
  3386     /// The key type (the \c Edge type of the digraph).
  3387     typedef typename GR::Edge Key;
  3388     /// The value type (the \c Arc type of the digraph).
  3389     typedef typename GR::Arc Value;
  3390 
  3391     /// \brief Constructor
  3392     ///
  3393     /// Constructor.
  3394     /// \param graph The graph that the map belongs to.
  3395     explicit ForwardMap(const GR& graph) : _graph(graph) {}
  3396 
  3397     /// \brief Returns the "forward" directed arc view of the given edge.
  3398     ///
  3399     /// Returns the "forward" directed arc view of the given edge.
  3400     Value operator[](const Key& key) const {
  3401       return _graph.direct(key, true);
  3402     }
  3403 
  3404   private:
  3405     const GR& _graph;
  3406   };
  3407 
  3408   /// \brief Returns a \c ForwardMap class.
  3409   ///
  3410   /// This function just returns an \c ForwardMap class.
  3411   /// \relates ForwardMap
  3412   template <typename GR>
  3413   inline ForwardMap<GR> forwardMap(const GR& graph) {
  3414     return ForwardMap<GR>(graph);
  3415   }
  3416 
  3417   /// \brief Map of the "backward" directed arc view of edges in a graph.
  3418   ///
  3419   /// BackwardMap provides access for the "backward" directed arc view of
  3420   /// each edge in a graph, which is returned by the \c direct() function
  3421   /// of the graph with \c false parameter.
  3422   /// \tparam GR The graph type.
  3423   /// \see ForwardMap
  3424   template <typename GR>
  3425   class BackwardMap {
  3426   public:
  3427 
  3428     /// The key type (the \c Edge type of the digraph).
  3429     typedef typename GR::Edge Key;
  3430     /// The value type (the \c Arc type of the digraph).
  3431     typedef typename GR::Arc Value;
  3432 
  3433     /// \brief Constructor
  3434     ///
  3435     /// Constructor.
  3436     /// \param graph The graph that the map belongs to.
  3437     explicit BackwardMap(const GR& graph) : _graph(graph) {}
  3438 
  3439     /// \brief Returns the "backward" directed arc view of the given edge.
  3440     ///
  3441     /// Returns the "backward" directed arc view of the given edge.
  3442     Value operator[](const Key& key) const {
  3443       return _graph.direct(key, false);
  3444     }
  3445 
  3446   private:
  3447     const GR& _graph;
  3448   };
  3449 
  3450   /// \brief Returns a \c BackwardMap class
  3451 
  3452   /// This function just returns a \c BackwardMap class.
  3453   /// \relates BackwardMap
  3454   template <typename GR>
  3455   inline BackwardMap<GR> backwardMap(const GR& graph) {
  3456     return BackwardMap<GR>(graph);
  3457   }
  3458 
  3459   /// \brief Map of the in-degrees of nodes in a digraph.
  3460   ///
  3461   /// This map returns the in-degree of a node. Once it is constructed,
  3462   /// the degrees are stored in a standard \c NodeMap, so each query is done
  3463   /// in constant time. On the other hand, the values are updated automatically
  3464   /// whenever the digraph changes.
  3465   ///
  3466   /// \warning Besides \c addNode() and \c addArc(), a digraph structure
  3467   /// may provide alternative ways to modify the digraph.
  3468   /// The correct behavior of InDegMap is not guarantied if these additional
  3469   /// features are used. For example, the functions
  3470   /// \ref ListDigraph::changeSource() "changeSource()",
  3471   /// \ref ListDigraph::changeTarget() "changeTarget()" and
  3472   /// \ref ListDigraph::reverseArc() "reverseArc()"
  3473   /// of \ref ListDigraph will \e not update the degree values correctly.
  3474   ///
  3475   /// \sa OutDegMap
  3476   template <typename GR>
  3477   class InDegMap
  3478     : protected ItemSetTraits<GR, typename GR::Arc>
  3479       ::ItemNotifier::ObserverBase {
  3480 
  3481   public:
  3482 
  3483     /// The graph type of InDegMap
  3484     typedef GR Graph;
  3485     typedef GR Digraph;
  3486     /// The key type
  3487     typedef typename Digraph::Node Key;
  3488     /// The value type
  3489     typedef int Value;
  3490 
  3491     typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
  3492     ::ItemNotifier::ObserverBase Parent;
  3493 
  3494   private:
  3495 
  3496     class AutoNodeMap
  3497       : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {
  3498     public:
  3499 
  3500       typedef typename ItemSetTraits<Digraph, Key>::
  3501       template Map<int>::Type Parent;
  3502 
  3503       AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
  3504 
  3505       virtual void add(const Key& key) {
  3506         Parent::add(key);
  3507         Parent::set(key, 0);
  3508       }
  3509 
  3510       virtual void add(const std::vector<Key>& keys) {
  3511         Parent::add(keys);
  3512         for (int i = 0; i < int(keys.size()); ++i) {
  3513           Parent::set(keys[i], 0);
  3514         }
  3515       }
  3516 
  3517       virtual void build() {
  3518         Parent::build();
  3519         Key it;
  3520         typename Parent::Notifier* nf = Parent::notifier();
  3521         for (nf->first(it); it != INVALID; nf->next(it)) {
  3522           Parent::set(it, 0);
  3523         }
  3524       }
  3525     };
  3526 
  3527   public:
  3528 
  3529     /// \brief Constructor.
  3530     ///
  3531     /// Constructor for creating an in-degree map.
  3532     explicit InDegMap(const Digraph& graph)
  3533       : _digraph(graph), _deg(graph) {
  3534       Parent::attach(_digraph.notifier(typename Digraph::Arc()));
  3535 
  3536       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3537         _deg[it] = countInArcs(_digraph, it);
  3538       }
  3539     }
  3540 
  3541     /// \brief Gives back the in-degree of a Node.
  3542     ///
  3543     /// Gives back the in-degree of a Node.
  3544     int operator[](const Key& key) const {
  3545       return _deg[key];
  3546     }
  3547 
  3548   protected:
  3549 
  3550     typedef typename Digraph::Arc Arc;
  3551 
  3552     virtual void add(const Arc& arc) {
  3553       ++_deg[_digraph.target(arc)];
  3554     }
  3555 
  3556     virtual void add(const std::vector<Arc>& arcs) {
  3557       for (int i = 0; i < int(arcs.size()); ++i) {
  3558         ++_deg[_digraph.target(arcs[i])];
  3559       }
  3560     }
  3561 
  3562     virtual void erase(const Arc& arc) {
  3563       --_deg[_digraph.target(arc)];
  3564     }
  3565 
  3566     virtual void erase(const std::vector<Arc>& arcs) {
  3567       for (int i = 0; i < int(arcs.size()); ++i) {
  3568         --_deg[_digraph.target(arcs[i])];
  3569       }
  3570     }
  3571 
  3572     virtual void build() {
  3573       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3574         _deg[it] = countInArcs(_digraph, it);
  3575       }
  3576     }
  3577 
  3578     virtual void clear() {
  3579       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3580         _deg[it] = 0;
  3581       }
  3582     }
  3583   private:
  3584 
  3585     const Digraph& _digraph;
  3586     AutoNodeMap _deg;
  3587   };
  3588 
  3589   /// \brief Map of the out-degrees of nodes in a digraph.
  3590   ///
  3591   /// This map returns the out-degree of a node. Once it is constructed,
  3592   /// the degrees are stored in a standard \c NodeMap, so each query is done
  3593   /// in constant time. On the other hand, the values are updated automatically
  3594   /// whenever the digraph changes.
  3595   ///
  3596   /// \warning Besides \c addNode() and \c addArc(), a digraph structure
  3597   /// may provide alternative ways to modify the digraph.
  3598   /// The correct behavior of OutDegMap is not guarantied if these additional
  3599   /// features are used. For example, the functions
  3600   /// \ref ListDigraph::changeSource() "changeSource()",
  3601   /// \ref ListDigraph::changeTarget() "changeTarget()" and
  3602   /// \ref ListDigraph::reverseArc() "reverseArc()"
  3603   /// of \ref ListDigraph will \e not update the degree values correctly.
  3604   ///
  3605   /// \sa InDegMap
  3606   template <typename GR>
  3607   class OutDegMap
  3608     : protected ItemSetTraits<GR, typename GR::Arc>
  3609       ::ItemNotifier::ObserverBase {
  3610 
  3611   public:
  3612 
  3613     /// The graph type of OutDegMap
  3614     typedef GR Graph;
  3615     typedef GR Digraph;
  3616     /// The key type
  3617     typedef typename Digraph::Node Key;
  3618     /// The value type
  3619     typedef int Value;
  3620 
  3621     typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
  3622     ::ItemNotifier::ObserverBase Parent;
  3623 
  3624   private:
  3625 
  3626     class AutoNodeMap
  3627       : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {
  3628     public:
  3629 
  3630       typedef typename ItemSetTraits<Digraph, Key>::
  3631       template Map<int>::Type Parent;
  3632 
  3633       AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
  3634 
  3635       virtual void add(const Key& key) {
  3636         Parent::add(key);
  3637         Parent::set(key, 0);
  3638       }
  3639       virtual void add(const std::vector<Key>& keys) {
  3640         Parent::add(keys);
  3641         for (int i = 0; i < int(keys.size()); ++i) {
  3642           Parent::set(keys[i], 0);
  3643         }
  3644       }
  3645       virtual void build() {
  3646         Parent::build();
  3647         Key it;
  3648         typename Parent::Notifier* nf = Parent::notifier();
  3649         for (nf->first(it); it != INVALID; nf->next(it)) {
  3650           Parent::set(it, 0);
  3651         }
  3652       }
  3653     };
  3654 
  3655   public:
  3656 
  3657     /// \brief Constructor.
  3658     ///
  3659     /// Constructor for creating an out-degree map.
  3660     explicit OutDegMap(const Digraph& graph)
  3661       : _digraph(graph), _deg(graph) {
  3662       Parent::attach(_digraph.notifier(typename Digraph::Arc()));
  3663 
  3664       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3665         _deg[it] = countOutArcs(_digraph, it);
  3666       }
  3667     }
  3668 
  3669     /// \brief Gives back the out-degree of a Node.
  3670     ///
  3671     /// Gives back the out-degree of a Node.
  3672     int operator[](const Key& key) const {
  3673       return _deg[key];
  3674     }
  3675 
  3676   protected:
  3677 
  3678     typedef typename Digraph::Arc Arc;
  3679 
  3680     virtual void add(const Arc& arc) {
  3681       ++_deg[_digraph.source(arc)];
  3682     }
  3683 
  3684     virtual void add(const std::vector<Arc>& arcs) {
  3685       for (int i = 0; i < int(arcs.size()); ++i) {
  3686         ++_deg[_digraph.source(arcs[i])];
  3687       }
  3688     }
  3689 
  3690     virtual void erase(const Arc& arc) {
  3691       --_deg[_digraph.source(arc)];
  3692     }
  3693 
  3694     virtual void erase(const std::vector<Arc>& arcs) {
  3695       for (int i = 0; i < int(arcs.size()); ++i) {
  3696         --_deg[_digraph.source(arcs[i])];
  3697       }
  3698     }
  3699 
  3700     virtual void build() {
  3701       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3702         _deg[it] = countOutArcs(_digraph, it);
  3703       }
  3704     }
  3705 
  3706     virtual void clear() {
  3707       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3708         _deg[it] = 0;
  3709       }
  3710     }
  3711   private:
  3712 
  3713     const Digraph& _digraph;
  3714     AutoNodeMap _deg;
  3715   };
  3716 
  3717   /// \brief Potential difference map
  3718   ///
  3719   /// PotentialDifferenceMap returns the difference between the potentials of
  3720   /// the source and target nodes of each arc in a digraph, i.e. it returns
  3721   /// \code
  3722   ///   potential[gr.target(arc)] - potential[gr.source(arc)].
  3723   /// \endcode
  3724   /// \tparam GR The digraph type.
  3725   /// \tparam POT A node map storing the potentials.
  3726   template <typename GR, typename POT>
  3727   class PotentialDifferenceMap {
  3728   public:
  3729     /// Key type
  3730     typedef typename GR::Arc Key;
  3731     /// Value type
  3732     typedef typename POT::Value Value;
  3733 
  3734     /// \brief Constructor
  3735     ///
  3736     /// Contructor of the map.
  3737     explicit PotentialDifferenceMap(const GR& gr,
  3738                                     const POT& potential)
  3739       : _digraph(gr), _potential(potential) {}
  3740 
  3741     /// \brief Returns the potential difference for the given arc.
  3742     ///
  3743     /// Returns the potential difference for the given arc, i.e.
  3744     /// \code
  3745     ///   potential[gr.target(arc)] - potential[gr.source(arc)].
  3746     /// \endcode
  3747     Value operator[](const Key& arc) const {
  3748       return _potential[_digraph.target(arc)] -
  3749         _potential[_digraph.source(arc)];
  3750     }
  3751 
  3752   private:
  3753     const GR& _digraph;
  3754     const POT& _potential;
  3755   };
  3756 
  3757   /// \brief Returns a PotentialDifferenceMap.
  3758   ///
  3759   /// This function just returns a PotentialDifferenceMap.
  3760   /// \relates PotentialDifferenceMap
  3761   template <typename GR, typename POT>
  3762   PotentialDifferenceMap<GR, POT>
  3763   potentialDifferenceMap(const GR& gr, const POT& potential) {
  3764     return PotentialDifferenceMap<GR, POT>(gr, potential);
  3765   }
  3766 
  3767 
  3768   /// \brief Copy the values of a graph map to another map.
  3769   ///
  3770   /// This function copies the values of a graph map to another graph map.
  3771   /// \c To::Key must be equal or convertible to \c From::Key and
  3772   /// \c From::Value must be equal or convertible to \c To::Value.
  3773   ///
  3774   /// For example, an edge map of \c int value type can be copied to
  3775   /// an arc map of \c double value type in an undirected graph, but
  3776   /// an arc map cannot be copied to an edge map.
  3777   /// Note that even a \ref ConstMap can be copied to a standard graph map,
  3778   /// but \ref mapFill() can also be used for this purpose.
  3779   ///
  3780   /// \param gr The graph for which the maps are defined.
  3781   /// \param from The map from which the values have to be copied.
  3782   /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
  3783   /// \param to The map to which the values have to be copied.
  3784   /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
  3785   template <typename GR, typename From, typename To>
  3786   void mapCopy(const GR& gr, const From& from, To& to) {
  3787     typedef typename To::Key Item;
  3788     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  3789 
  3790     for (ItemIt it(gr); it != INVALID; ++it) {
  3791       to.set(it, from[it]);
  3792     }
  3793   }
  3794 
  3795   /// \brief Compare two graph maps.
  3796   ///
  3797   /// This function compares the values of two graph maps. It returns
  3798   /// \c true if the maps assign the same value for all items in the graph.
  3799   /// The \c Key type of the maps (\c Node, \c Arc or \c Edge) must be equal
  3800   /// and their \c Value types must be comparable using \c %operator==().
  3801   ///
  3802   /// \param gr The graph for which the maps are defined.
  3803   /// \param map1 The first map.
  3804   /// \param map2 The second map.
  3805   template <typename GR, typename Map1, typename Map2>
  3806   bool mapCompare(const GR& gr, const Map1& map1, const Map2& map2) {
  3807     typedef typename Map2::Key Item;
  3808     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  3809 
  3810     for (ItemIt it(gr); it != INVALID; ++it) {
  3811       if (!(map1[it] == map2[it])) return false;
  3812     }
  3813     return true;
  3814   }
  3815 
  3816   /// \brief Return an item having minimum value of a graph map.
  3817   ///
  3818   /// This function returns an item (\c Node, \c Arc or \c Edge) having
  3819   /// minimum value of the given graph map.
  3820   /// If the item set is empty, it returns \c INVALID.
  3821   ///
  3822   /// \param gr The graph for which the map is defined.
  3823   /// \param map The graph map.
  3824   template <typename GR, typename Map>
  3825   typename Map::Key mapMin(const GR& gr, const Map& map) {
  3826     return mapMin(gr, map, std::less<typename Map::Value>());
  3827   }
  3828 
  3829   /// \brief Return an item having minimum value of a graph map.
  3830   ///
  3831   /// This function returns an item (\c Node, \c Arc or \c Edge) having
  3832   /// minimum value of the given graph map.
  3833   /// If the item set is empty, it returns \c INVALID.
  3834   ///
  3835   /// \param gr The graph for which the map is defined.
  3836   /// \param map The graph map.
  3837   /// \param comp Comparison function object.
  3838   template <typename GR, typename Map, typename Comp>
  3839   typename Map::Key mapMin(const GR& gr, const Map& map, const Comp& comp) {
  3840     typedef typename Map::Key Item;
  3841     typedef typename Map::Value Value;
  3842     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  3843 
  3844     ItemIt min_item(gr);
  3845     if (min_item == INVALID) return INVALID;
  3846     Value min = map[min_item];
  3847     for (ItemIt it(gr); it != INVALID; ++it) {
  3848       if (comp(map[it], min)) {
  3849         min = map[it];
  3850         min_item = it;
  3851       }
  3852     }
  3853     return min_item;
  3854   }
  3855 
  3856   /// \brief Return an item having maximum value of a graph map.
  3857   ///
  3858   /// This function returns an item (\c Node, \c Arc or \c Edge) having
  3859   /// maximum value of the given graph map.
  3860   /// If the item set is empty, it returns \c INVALID.
  3861   ///
  3862   /// \param gr The graph for which the map is defined.
  3863   /// \param map The graph map.
  3864   template <typename GR, typename Map>
  3865   typename Map::Key mapMax(const GR& gr, const Map& map) {
  3866     return mapMax(gr, map, std::less<typename Map::Value>());
  3867   }
  3868 
  3869   /// \brief Return an item having maximum value of a graph map.
  3870   ///
  3871   /// This function returns an item (\c Node, \c Arc or \c Edge) having
  3872   /// maximum value of the given graph map.
  3873   /// If the item set is empty, it returns \c INVALID.
  3874   ///
  3875   /// \param gr The graph for which the map is defined.
  3876   /// \param map The graph map.
  3877   /// \param comp Comparison function object.
  3878   template <typename GR, typename Map, typename Comp>
  3879   typename Map::Key mapMax(const GR& gr, const Map& map, const Comp& comp) {
  3880     typedef typename Map::Key Item;
  3881     typedef typename Map::Value Value;
  3882     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  3883 
  3884     ItemIt max_item(gr);
  3885     if (max_item == INVALID) return INVALID;
  3886     Value max = map[max_item];
  3887     for (ItemIt it(gr); it != INVALID; ++it) {
  3888       if (comp(max, map[it])) {
  3889         max = map[it];
  3890         max_item = it;
  3891       }
  3892     }
  3893     return max_item;
  3894   }
  3895 
  3896   /// \brief Return the minimum value of a graph map.
  3897   ///
  3898   /// This function returns the minimum value of the given graph map.
  3899   /// The corresponding item set of the graph must not be empty.
  3900   ///
  3901   /// \param gr The graph for which the map is defined.
  3902   /// \param map The graph map.
  3903   template <typename GR, typename Map>
  3904   typename Map::Value mapMinValue(const GR& gr, const Map& map) {
  3905     return map[mapMin(gr, map, std::less<typename Map::Value>())];
  3906   }
  3907 
  3908   /// \brief Return the minimum value of a graph map.
  3909   ///
  3910   /// This function returns the minimum value of the given graph map.
  3911   /// The corresponding item set of the graph must not be empty.
  3912   ///
  3913   /// \param gr The graph for which the map is defined.
  3914   /// \param map The graph map.
  3915   /// \param comp Comparison function object.
  3916   template <typename GR, typename Map, typename Comp>
  3917   typename Map::Value
  3918   mapMinValue(const GR& gr, const Map& map, const Comp& comp) {
  3919     return map[mapMin(gr, map, comp)];
  3920   }
  3921 
  3922   /// \brief Return the maximum value of a graph map.
  3923   ///
  3924   /// This function returns the maximum value of the given graph map.
  3925   /// The corresponding item set of the graph must not be empty.
  3926   ///
  3927   /// \param gr The graph for which the map is defined.
  3928   /// \param map The graph map.
  3929   template <typename GR, typename Map>
  3930   typename Map::Value mapMaxValue(const GR& gr, const Map& map) {
  3931     return map[mapMax(gr, map, std::less<typename Map::Value>())];
  3932   }
  3933 
  3934   /// \brief Return the maximum value of a graph map.
  3935   ///
  3936   /// This function returns the maximum value of the given graph map.
  3937   /// The corresponding item set of the graph must not be empty.
  3938   ///
  3939   /// \param gr The graph for which the map is defined.
  3940   /// \param map The graph map.
  3941   /// \param comp Comparison function object.
  3942   template <typename GR, typename Map, typename Comp>
  3943   typename Map::Value
  3944   mapMaxValue(const GR& gr, const Map& map, const Comp& comp) {
  3945     return map[mapMax(gr, map, comp)];
  3946   }
  3947 
  3948   /// \brief Return an item having a specified value in a graph map.
  3949   ///
  3950   /// This function returns an item (\c Node, \c Arc or \c Edge) having
  3951   /// the specified assigned value in the given graph map.
  3952   /// If no such item exists, it returns \c INVALID.
  3953   ///
  3954   /// \param gr The graph for which the map is defined.
  3955   /// \param map The graph map.
  3956   /// \param val The value that have to be found.
  3957   template <typename GR, typename Map>
  3958   typename Map::Key
  3959   mapFind(const GR& gr, const Map& map, const typename Map::Value& val) {
  3960     typedef typename Map::Key Item;
  3961     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  3962 
  3963     for (ItemIt it(gr); it != INVALID; ++it) {
  3964       if (map[it] == val) return it;
  3965     }
  3966     return INVALID;
  3967   }
  3968 
  3969   /// \brief Return an item having value for which a certain predicate is
  3970   /// true in a graph map.
  3971   ///
  3972   /// This function returns an item (\c Node, \c Arc or \c Edge) having
  3973   /// such assigned value for which the specified predicate is true
  3974   /// in the given graph map.
  3975   /// If no such item exists, it returns \c INVALID.
  3976   ///
  3977   /// \param gr The graph for which the map is defined.
  3978   /// \param map The graph map.
  3979   /// \param pred The predicate function object.
  3980   template <typename GR, typename Map, typename Pred>
  3981   typename Map::Key
  3982   mapFindIf(const GR& gr, const Map& map, const Pred& pred) {
  3983     typedef typename Map::Key Item;
  3984     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  3985 
  3986     for (ItemIt it(gr); it != INVALID; ++it) {
  3987       if (pred(map[it])) return it;
  3988     }
  3989     return INVALID;
  3990   }
  3991 
  3992   /// \brief Return the number of items having a specified value in a
  3993   /// graph map.
  3994   ///
  3995   /// This function returns the number of items (\c Node, \c Arc or \c Edge)
  3996   /// having the specified assigned value in the given graph map.
  3997   ///
  3998   /// \param gr The graph for which the map is defined.
  3999   /// \param map The graph map.
  4000   /// \param val The value that have to be counted.
  4001   template <typename GR, typename Map>
  4002   int mapCount(const GR& gr, const Map& map, const typename Map::Value& val) {
  4003     typedef typename Map::Key Item;
  4004     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  4005 
  4006     int cnt = 0;
  4007     for (ItemIt it(gr); it != INVALID; ++it) {
  4008       if (map[it] == val) ++cnt;
  4009     }
  4010     return cnt;
  4011   }
  4012 
  4013   /// \brief Return the number of items having values for which a certain
  4014   /// predicate is true in a graph map.
  4015   ///
  4016   /// This function returns the number of items (\c Node, \c Arc or \c Edge)
  4017   /// having such assigned values for which the specified predicate is true
  4018   /// in the given graph map.
  4019   ///
  4020   /// \param gr The graph for which the map is defined.
  4021   /// \param map The graph map.
  4022   /// \param pred The predicate function object.
  4023   template <typename GR, typename Map, typename Pred>
  4024   int mapCountIf(const GR& gr, const Map& map, const Pred& pred) {
  4025     typedef typename Map::Key Item;
  4026     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  4027 
  4028     int cnt = 0;
  4029     for (ItemIt it(gr); it != INVALID; ++it) {
  4030       if (pred(map[it])) ++cnt;
  4031     }
  4032     return cnt;
  4033   }
  4034 
  4035   /// \brief Fill a graph map with a certain value.
  4036   ///
  4037   /// This function sets the specified value for all items (\c Node,
  4038   /// \c Arc or \c Edge) in the given graph map.
  4039   ///
  4040   /// \param gr The graph for which the map is defined.
  4041   /// \param map The graph map. It must conform to the
  4042   /// \ref concepts::WriteMap "WriteMap" concept.
  4043   /// \param val The value.
  4044   template <typename GR, typename Map>
  4045   void mapFill(const GR& gr, Map& map, const typename Map::Value& val) {
  4046     typedef typename Map::Key Item;
  4047     typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  4048 
  4049     for (ItemIt it(gr); it != INVALID; ++it) {
  4050       map.set(it, val);
  4051     }
  4052   }
  4053 
  4054   /// @}
  4055 }
  4056 
  4057 #endif // LEMON_MAPS_H