lemon/maps.h
author Balazs Dezso <deba@inf.elte.hu>
Wed, 09 Sep 2009 15:32:03 +0200
changeset 797 30cb42e3e43a
parent 684 7b1a6e963018
parent 694 71939d63ae77
child 717 684964884a2e
permissions -rw-r--r--
Port planarity related algorithms from SVN 3509 (#62)
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2009
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #ifndef LEMON_MAPS_H
    20 #define LEMON_MAPS_H
    21 
    22 #include <iterator>
    23 #include <functional>
    24 #include <vector>
    25 #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 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 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 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 with some data structures, for example
   234   /// \c UnionFind, \c BinHeap, when the used items are small
   235   /// integers. This map conforms 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 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 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,s).processedMap(loggerBoolMap(std::back_inserter(v))).run();
  1793   /// \endcode
  1794   /// \code
  1795   ///   std::vector<Node> v(countNodes(g));
  1796   ///   dfs(g,s).processedMap(loggerBoolMap(v.begin())).run();
  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 This class represents the inverse of its owner (IdMap).
  1869     ///
  1870     /// This class represents the inverse of its owner (IdMap).
  1871     /// \see inverse()
  1872     class InverseMap {
  1873     public:
  1874 
  1875       /// \brief Constructor.
  1876       ///
  1877       /// Constructor for creating an id-to-item map.
  1878       explicit InverseMap(const Graph& graph) : _graph(&graph) {}
  1879 
  1880       /// \brief Constructor.
  1881       ///
  1882       /// Constructor for creating an id-to-item map.
  1883       explicit InverseMap(const IdMap& map) : _graph(map._graph) {}
  1884 
  1885       /// \brief Gives back the given item from its id.
  1886       ///
  1887       /// Gives back the given item from its id.
  1888       Item operator[](int id) const { return _graph->fromId(id, Item());}
  1889 
  1890     private:
  1891       const Graph* _graph;
  1892     };
  1893 
  1894     /// \brief Gives back the inverse of the map.
  1895     ///
  1896     /// Gives back the inverse of the IdMap.
  1897     InverseMap inverse() const { return InverseMap(*_graph);}
  1898   };
  1899 
  1900 
  1901   /// \brief General cross reference graph map type.
  1902 
  1903   /// This class provides simple invertable graph maps.
  1904   /// It wraps a standard graph map (\c NodeMap, \c ArcMap or \c EdgeMap)
  1905   /// and if a key is set to a new value, then stores it in the inverse map.
  1906   /// The values of the map can be accessed
  1907   /// with stl compatible forward iterator.
  1908   ///
  1909   /// This type is not reference map, so it cannot be modified with
  1910   /// the subscript operator.
  1911   ///
  1912   /// \tparam GR The graph type.
  1913   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  1914   /// \c GR::Edge).
  1915   /// \tparam V The value type of the map.
  1916   ///
  1917   /// \see IterableValueMap
  1918   template <typename GR, typename K, typename V>
  1919   class CrossRefMap
  1920     : protected ItemSetTraits<GR, K>::template Map<V>::Type {
  1921   private:
  1922 
  1923     typedef typename ItemSetTraits<GR, K>::
  1924       template Map<V>::Type Map;
  1925 
  1926     typedef std::multimap<V, K> Container;
  1927     Container _inv_map;
  1928 
  1929   public:
  1930 
  1931     /// The graph type of CrossRefMap.
  1932     typedef GR Graph;
  1933     typedef GR Digraph;
  1934     /// The key type of CrossRefMap (\c Node, \c Arc or \c Edge).
  1935     typedef K Item;
  1936     /// The key type of CrossRefMap (\c Node, \c Arc or \c Edge).
  1937     typedef K Key;
  1938     /// The value type of CrossRefMap.
  1939     typedef V Value;
  1940 
  1941     /// \brief Constructor.
  1942     ///
  1943     /// Construct a new CrossRefMap for the given graph.
  1944     explicit CrossRefMap(const Graph& graph) : Map(graph) {}
  1945 
  1946     /// \brief Forward iterator for values.
  1947     ///
  1948     /// This iterator is an stl compatible forward
  1949     /// iterator on the values of the map. The values can
  1950     /// be accessed in the <tt>[beginValue, endValue)</tt> range.
  1951     /// They are considered with multiplicity, so each value is
  1952     /// traversed for each item it is assigned to.
  1953     class ValueIterator
  1954       : public std::iterator<std::forward_iterator_tag, Value> {
  1955       friend class CrossRefMap;
  1956     private:
  1957       ValueIterator(typename Container::const_iterator _it)
  1958         : it(_it) {}
  1959     public:
  1960 
  1961       ValueIterator() {}
  1962 
  1963       ValueIterator& operator++() { ++it; return *this; }
  1964       ValueIterator operator++(int) {
  1965         ValueIterator tmp(*this);
  1966         operator++();
  1967         return tmp;
  1968       }
  1969 
  1970       const Value& operator*() const { return it->first; }
  1971       const Value* operator->() const { return &(it->first); }
  1972 
  1973       bool operator==(ValueIterator jt) const { return it == jt.it; }
  1974       bool operator!=(ValueIterator jt) const { return it != jt.it; }
  1975 
  1976     private:
  1977       typename Container::const_iterator it;
  1978     };
  1979 
  1980     /// \brief Returns an iterator to the first value.
  1981     ///
  1982     /// Returns an stl compatible iterator to the
  1983     /// first value of the map. The values of the
  1984     /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  1985     /// range.
  1986     ValueIterator beginValue() const {
  1987       return ValueIterator(_inv_map.begin());
  1988     }
  1989 
  1990     /// \brief Returns an iterator after the last value.
  1991     ///
  1992     /// Returns an stl compatible iterator after the
  1993     /// last value of the map. The values of the
  1994     /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  1995     /// range.
  1996     ValueIterator endValue() const {
  1997       return ValueIterator(_inv_map.end());
  1998     }
  1999 
  2000     /// \brief Sets the value associated with the given key.
  2001     ///
  2002     /// Sets the value associated with the given key.
  2003     void set(const Key& key, const Value& val) {
  2004       Value oldval = Map::operator[](key);
  2005       typename Container::iterator it;
  2006       for (it = _inv_map.equal_range(oldval).first;
  2007            it != _inv_map.equal_range(oldval).second; ++it) {
  2008         if (it->second == key) {
  2009           _inv_map.erase(it);
  2010           break;
  2011         }
  2012       }
  2013       _inv_map.insert(std::make_pair(val, key));
  2014       Map::set(key, val);
  2015     }
  2016 
  2017     /// \brief Returns the value associated with the given key.
  2018     ///
  2019     /// Returns the value associated with the given key.
  2020     typename MapTraits<Map>::ConstReturnValue
  2021     operator[](const Key& key) const {
  2022       return Map::operator[](key);
  2023     }
  2024 
  2025     /// \brief Gives back an item by its value.
  2026     ///
  2027     /// This function gives back an item that is assigned to
  2028     /// the given value or \c INVALID if no such item exists.
  2029     /// If there are more items with the same associated value,
  2030     /// only one of them is returned.
  2031     Key operator()(const Value& val) const {
  2032       typename Container::const_iterator it = _inv_map.find(val);
  2033       return it != _inv_map.end() ? it->second : INVALID;
  2034     }
  2035 
  2036   protected:
  2037 
  2038     /// \brief Erase the key from the map and the inverse map.
  2039     ///
  2040     /// Erase the key from the map and the inverse map. It is called by the
  2041     /// \c AlterationNotifier.
  2042     virtual void erase(const Key& key) {
  2043       Value val = Map::operator[](key);
  2044       typename Container::iterator it;
  2045       for (it = _inv_map.equal_range(val).first;
  2046            it != _inv_map.equal_range(val).second; ++it) {
  2047         if (it->second == key) {
  2048           _inv_map.erase(it);
  2049           break;
  2050         }
  2051       }
  2052       Map::erase(key);
  2053     }
  2054 
  2055     /// \brief Erase more keys from the map and the inverse map.
  2056     ///
  2057     /// Erase more keys from the map and the inverse map. It is called by the
  2058     /// \c AlterationNotifier.
  2059     virtual void erase(const std::vector<Key>& keys) {
  2060       for (int i = 0; i < int(keys.size()); ++i) {
  2061         Value val = Map::operator[](keys[i]);
  2062         typename Container::iterator it;
  2063         for (it = _inv_map.equal_range(val).first;
  2064              it != _inv_map.equal_range(val).second; ++it) {
  2065           if (it->second == keys[i]) {
  2066             _inv_map.erase(it);
  2067             break;
  2068           }
  2069         }
  2070       }
  2071       Map::erase(keys);
  2072     }
  2073 
  2074     /// \brief Clear the keys from the map and the inverse map.
  2075     ///
  2076     /// Clear the keys from the map and the inverse map. It is called by the
  2077     /// \c AlterationNotifier.
  2078     virtual void clear() {
  2079       _inv_map.clear();
  2080       Map::clear();
  2081     }
  2082 
  2083   public:
  2084 
  2085     /// \brief The inverse map type.
  2086     ///
  2087     /// The inverse of this map. The subscript operator of the map
  2088     /// gives back the item that was last assigned to the value.
  2089     class InverseMap {
  2090     public:
  2091       /// \brief Constructor
  2092       ///
  2093       /// Constructor of the InverseMap.
  2094       explicit InverseMap(const CrossRefMap& inverted)
  2095         : _inverted(inverted) {}
  2096 
  2097       /// The value type of the InverseMap.
  2098       typedef typename CrossRefMap::Key Value;
  2099       /// The key type of the InverseMap.
  2100       typedef typename CrossRefMap::Value Key;
  2101 
  2102       /// \brief Subscript operator.
  2103       ///
  2104       /// Subscript operator. It gives back an item
  2105       /// that is assigned to the given value or \c INVALID
  2106       /// if no such item exists.
  2107       Value operator[](const Key& key) const {
  2108         return _inverted(key);
  2109       }
  2110 
  2111     private:
  2112       const CrossRefMap& _inverted;
  2113     };
  2114 
  2115     /// \brief It gives back the read-only inverse map.
  2116     ///
  2117     /// It gives back the read-only inverse map.
  2118     InverseMap inverse() const {
  2119       return InverseMap(*this);
  2120     }
  2121 
  2122   };
  2123 
  2124   /// \brief Provides continuous and unique ID for the
  2125   /// items of a graph.
  2126   ///
  2127   /// RangeIdMap provides a unique and continuous
  2128   /// ID for each item of a given type (\c Node, \c Arc or
  2129   /// \c Edge) in a graph. This id is
  2130   ///  - \b unique: different items get different ids,
  2131   ///  - \b continuous: the range of the ids is the set of integers
  2132   ///    between 0 and \c n-1, where \c n is the number of the items of
  2133   ///    this type (\c Node, \c Arc or \c Edge).
  2134   ///  - So, the ids can change when deleting an item of the same type.
  2135   ///
  2136   /// Thus this id is not (necessarily) the same as what can get using
  2137   /// the \c id() function of the graph or \ref IdMap.
  2138   /// This map can be inverted with its member class \c InverseMap,
  2139   /// or with the \c operator() member.
  2140   ///
  2141   /// \tparam GR The graph type.
  2142   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  2143   /// \c GR::Edge).
  2144   ///
  2145   /// \see IdMap
  2146   template <typename GR, typename K>
  2147   class RangeIdMap
  2148     : protected ItemSetTraits<GR, K>::template Map<int>::Type {
  2149 
  2150     typedef typename ItemSetTraits<GR, K>::template Map<int>::Type Map;
  2151 
  2152   public:
  2153     /// The graph type of RangeIdMap.
  2154     typedef GR Graph;
  2155     typedef GR Digraph;
  2156     /// The key type of RangeIdMap (\c Node, \c Arc or \c Edge).
  2157     typedef K Item;
  2158     /// The key type of RangeIdMap (\c Node, \c Arc or \c Edge).
  2159     typedef K Key;
  2160     /// The value type of RangeIdMap.
  2161     typedef int Value;
  2162 
  2163     /// \brief Constructor.
  2164     ///
  2165     /// Constructor.
  2166     explicit RangeIdMap(const Graph& gr) : Map(gr) {
  2167       Item it;
  2168       const typename Map::Notifier* nf = Map::notifier();
  2169       for (nf->first(it); it != INVALID; nf->next(it)) {
  2170         Map::set(it, _inv_map.size());
  2171         _inv_map.push_back(it);
  2172       }
  2173     }
  2174 
  2175   protected:
  2176 
  2177     /// \brief Adds a new key to the map.
  2178     ///
  2179     /// Add a new key to the map. It is called by the
  2180     /// \c AlterationNotifier.
  2181     virtual void add(const Item& item) {
  2182       Map::add(item);
  2183       Map::set(item, _inv_map.size());
  2184       _inv_map.push_back(item);
  2185     }
  2186 
  2187     /// \brief Add more new keys to the map.
  2188     ///
  2189     /// Add more new keys to the map. It is called by the
  2190     /// \c AlterationNotifier.
  2191     virtual void add(const std::vector<Item>& items) {
  2192       Map::add(items);
  2193       for (int i = 0; i < int(items.size()); ++i) {
  2194         Map::set(items[i], _inv_map.size());
  2195         _inv_map.push_back(items[i]);
  2196       }
  2197     }
  2198 
  2199     /// \brief Erase the key from the map.
  2200     ///
  2201     /// Erase the key from the map. It is called by the
  2202     /// \c AlterationNotifier.
  2203     virtual void erase(const Item& item) {
  2204       Map::set(_inv_map.back(), Map::operator[](item));
  2205       _inv_map[Map::operator[](item)] = _inv_map.back();
  2206       _inv_map.pop_back();
  2207       Map::erase(item);
  2208     }
  2209 
  2210     /// \brief Erase more keys from the map.
  2211     ///
  2212     /// Erase more keys from the map. It is called by the
  2213     /// \c AlterationNotifier.
  2214     virtual void erase(const std::vector<Item>& items) {
  2215       for (int i = 0; i < int(items.size()); ++i) {
  2216         Map::set(_inv_map.back(), Map::operator[](items[i]));
  2217         _inv_map[Map::operator[](items[i])] = _inv_map.back();
  2218         _inv_map.pop_back();
  2219       }
  2220       Map::erase(items);
  2221     }
  2222 
  2223     /// \brief Build the unique map.
  2224     ///
  2225     /// Build the unique map. It is called by the
  2226     /// \c AlterationNotifier.
  2227     virtual void build() {
  2228       Map::build();
  2229       Item it;
  2230       const typename Map::Notifier* nf = Map::notifier();
  2231       for (nf->first(it); it != INVALID; nf->next(it)) {
  2232         Map::set(it, _inv_map.size());
  2233         _inv_map.push_back(it);
  2234       }
  2235     }
  2236 
  2237     /// \brief Clear the keys from the map.
  2238     ///
  2239     /// Clear the keys from the map. It is called by the
  2240     /// \c AlterationNotifier.
  2241     virtual void clear() {
  2242       _inv_map.clear();
  2243       Map::clear();
  2244     }
  2245 
  2246   public:
  2247 
  2248     /// \brief Returns the maximal value plus one.
  2249     ///
  2250     /// Returns the maximal value plus one in the map.
  2251     unsigned int size() const {
  2252       return _inv_map.size();
  2253     }
  2254 
  2255     /// \brief Swaps the position of the two items in the map.
  2256     ///
  2257     /// Swaps the position of the two items in the map.
  2258     void swap(const Item& p, const Item& q) {
  2259       int pi = Map::operator[](p);
  2260       int qi = Map::operator[](q);
  2261       Map::set(p, qi);
  2262       _inv_map[qi] = p;
  2263       Map::set(q, pi);
  2264       _inv_map[pi] = q;
  2265     }
  2266 
  2267     /// \brief Gives back the \e RangeId of the item
  2268     ///
  2269     /// Gives back the \e RangeId of the item.
  2270     int operator[](const Item& item) const {
  2271       return Map::operator[](item);
  2272     }
  2273 
  2274     /// \brief Gives back the item belonging to a \e RangeId
  2275     ///
  2276     /// Gives back the item belonging to a \e RangeId.
  2277     Item operator()(int id) const {
  2278       return _inv_map[id];
  2279     }
  2280 
  2281   private:
  2282 
  2283     typedef std::vector<Item> Container;
  2284     Container _inv_map;
  2285 
  2286   public:
  2287 
  2288     /// \brief The inverse map type of RangeIdMap.
  2289     ///
  2290     /// The inverse map type of RangeIdMap.
  2291     class InverseMap {
  2292     public:
  2293       /// \brief Constructor
  2294       ///
  2295       /// Constructor of the InverseMap.
  2296       explicit InverseMap(const RangeIdMap& inverted)
  2297         : _inverted(inverted) {}
  2298 
  2299 
  2300       /// The value type of the InverseMap.
  2301       typedef typename RangeIdMap::Key Value;
  2302       /// The key type of the InverseMap.
  2303       typedef typename RangeIdMap::Value Key;
  2304 
  2305       /// \brief Subscript operator.
  2306       ///
  2307       /// Subscript operator. It gives back the item
  2308       /// that the descriptor currently belongs to.
  2309       Value operator[](const Key& key) const {
  2310         return _inverted(key);
  2311       }
  2312 
  2313       /// \brief Size of the map.
  2314       ///
  2315       /// Returns the size of the map.
  2316       unsigned int size() const {
  2317         return _inverted.size();
  2318       }
  2319 
  2320     private:
  2321       const RangeIdMap& _inverted;
  2322     };
  2323 
  2324     /// \brief Gives back the inverse of the map.
  2325     ///
  2326     /// Gives back the inverse of the map.
  2327     const InverseMap inverse() const {
  2328       return InverseMap(*this);
  2329     }
  2330   };
  2331 
  2332   /// \brief Dynamic iterable \c bool map.
  2333   ///
  2334   /// This class provides a special graph map type which can store a
  2335   /// \c bool value for graph items (\c Node, \c Arc or \c Edge).
  2336   /// For both \c true and \c false values it is possible to iterate on
  2337   /// the keys.
  2338   ///
  2339   /// This type is a reference map, so it can be modified with the
  2340   /// subscript operator.
  2341   ///
  2342   /// \tparam GR The graph type.
  2343   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  2344   /// \c GR::Edge).
  2345   ///
  2346   /// \see IterableIntMap, IterableValueMap
  2347   /// \see CrossRefMap
  2348   template <typename GR, typename K>
  2349   class IterableBoolMap
  2350     : protected ItemSetTraits<GR, K>::template Map<int>::Type {
  2351   private:
  2352     typedef GR Graph;
  2353 
  2354     typedef typename ItemSetTraits<GR, K>::ItemIt KeyIt;
  2355     typedef typename ItemSetTraits<GR, K>::template Map<int>::Type Parent;
  2356 
  2357     std::vector<K> _array;
  2358     int _sep;
  2359 
  2360   public:
  2361 
  2362     /// Indicates that the map is reference map.
  2363     typedef True ReferenceMapTag;
  2364 
  2365     /// The key type
  2366     typedef K Key;
  2367     /// The value type
  2368     typedef bool Value;
  2369     /// The const reference type.
  2370     typedef const Value& ConstReference;
  2371 
  2372   private:
  2373 
  2374     int position(const Key& key) const {
  2375       return Parent::operator[](key);
  2376     }
  2377 
  2378   public:
  2379 
  2380     /// \brief Reference to the value of the map.
  2381     ///
  2382     /// This class is similar to the \c bool type. It can be converted to
  2383     /// \c bool and it provides the same operators.
  2384     class Reference {
  2385       friend class IterableBoolMap;
  2386     private:
  2387       Reference(IterableBoolMap& map, const Key& key)
  2388         : _key(key), _map(map) {}
  2389     public:
  2390 
  2391       Reference& operator=(const Reference& value) {
  2392         _map.set(_key, static_cast<bool>(value));
  2393          return *this;
  2394       }
  2395 
  2396       operator bool() const {
  2397         return static_cast<const IterableBoolMap&>(_map)[_key];
  2398       }
  2399 
  2400       Reference& operator=(bool value) {
  2401         _map.set(_key, value);
  2402         return *this;
  2403       }
  2404       Reference& operator&=(bool value) {
  2405         _map.set(_key, _map[_key] & value);
  2406         return *this;
  2407       }
  2408       Reference& operator|=(bool value) {
  2409         _map.set(_key, _map[_key] | value);
  2410         return *this;
  2411       }
  2412       Reference& operator^=(bool value) {
  2413         _map.set(_key, _map[_key] ^ value);
  2414         return *this;
  2415       }
  2416     private:
  2417       Key _key;
  2418       IterableBoolMap& _map;
  2419     };
  2420 
  2421     /// \brief Constructor of the map with a default value.
  2422     ///
  2423     /// Constructor of the map with a default value.
  2424     explicit IterableBoolMap(const Graph& graph, bool def = false)
  2425       : Parent(graph) {
  2426       typename Parent::Notifier* nf = Parent::notifier();
  2427       Key it;
  2428       for (nf->first(it); it != INVALID; nf->next(it)) {
  2429         Parent::set(it, _array.size());
  2430         _array.push_back(it);
  2431       }
  2432       _sep = (def ? _array.size() : 0);
  2433     }
  2434 
  2435     /// \brief Const subscript operator of the map.
  2436     ///
  2437     /// Const subscript operator of the map.
  2438     bool operator[](const Key& key) const {
  2439       return position(key) < _sep;
  2440     }
  2441 
  2442     /// \brief Subscript operator of the map.
  2443     ///
  2444     /// Subscript operator of the map.
  2445     Reference operator[](const Key& key) {
  2446       return Reference(*this, key);
  2447     }
  2448 
  2449     /// \brief Set operation of the map.
  2450     ///
  2451     /// Set operation of the map.
  2452     void set(const Key& key, bool value) {
  2453       int pos = position(key);
  2454       if (value) {
  2455         if (pos < _sep) return;
  2456         Key tmp = _array[_sep];
  2457         _array[_sep] = key;
  2458         Parent::set(key, _sep);
  2459         _array[pos] = tmp;
  2460         Parent::set(tmp, pos);
  2461         ++_sep;
  2462       } else {
  2463         if (pos >= _sep) return;
  2464         --_sep;
  2465         Key tmp = _array[_sep];
  2466         _array[_sep] = key;
  2467         Parent::set(key, _sep);
  2468         _array[pos] = tmp;
  2469         Parent::set(tmp, pos);
  2470       }
  2471     }
  2472 
  2473     /// \brief Set all items.
  2474     ///
  2475     /// Set all items in the map.
  2476     /// \note Constant time operation.
  2477     void setAll(bool value) {
  2478       _sep = (value ? _array.size() : 0);
  2479     }
  2480 
  2481     /// \brief Returns the number of the keys mapped to \c true.
  2482     ///
  2483     /// Returns the number of the keys mapped to \c true.
  2484     int trueNum() const {
  2485       return _sep;
  2486     }
  2487 
  2488     /// \brief Returns the number of the keys mapped to \c false.
  2489     ///
  2490     /// Returns the number of the keys mapped to \c false.
  2491     int falseNum() const {
  2492       return _array.size() - _sep;
  2493     }
  2494 
  2495     /// \brief Iterator for the keys mapped to \c true.
  2496     ///
  2497     /// Iterator for the keys mapped to \c true. It works
  2498     /// like a graph item iterator, it can be converted to
  2499     /// the key type of the map, incremented with \c ++ operator, and
  2500     /// if the iterator leaves the last valid key, it will be equal to
  2501     /// \c INVALID.
  2502     class TrueIt : public Key {
  2503     public:
  2504       typedef Key Parent;
  2505 
  2506       /// \brief Creates an iterator.
  2507       ///
  2508       /// Creates an iterator. It iterates on the
  2509       /// keys mapped to \c true.
  2510       /// \param map The IterableBoolMap.
  2511       explicit TrueIt(const IterableBoolMap& map)
  2512         : Parent(map._sep > 0 ? map._array[map._sep - 1] : INVALID),
  2513           _map(&map) {}
  2514 
  2515       /// \brief Invalid constructor \& conversion.
  2516       ///
  2517       /// This constructor initializes the iterator to be invalid.
  2518       /// \sa Invalid for more details.
  2519       TrueIt(Invalid) : Parent(INVALID), _map(0) {}
  2520 
  2521       /// \brief Increment operator.
  2522       ///
  2523       /// Increment operator.
  2524       TrueIt& operator++() {
  2525         int pos = _map->position(*this);
  2526         Parent::operator=(pos > 0 ? _map->_array[pos - 1] : INVALID);
  2527         return *this;
  2528       }
  2529 
  2530     private:
  2531       const IterableBoolMap* _map;
  2532     };
  2533 
  2534     /// \brief Iterator for the keys mapped to \c false.
  2535     ///
  2536     /// Iterator for the keys mapped to \c false. It works
  2537     /// like a graph item iterator, it can be converted to
  2538     /// the key type of the map, incremented with \c ++ operator, and
  2539     /// if the iterator leaves the last valid key, it will be equal to
  2540     /// \c INVALID.
  2541     class FalseIt : public Key {
  2542     public:
  2543       typedef Key Parent;
  2544 
  2545       /// \brief Creates an iterator.
  2546       ///
  2547       /// Creates an iterator. It iterates on the
  2548       /// keys mapped to \c false.
  2549       /// \param map The IterableBoolMap.
  2550       explicit FalseIt(const IterableBoolMap& map)
  2551         : Parent(map._sep < int(map._array.size()) ?
  2552                  map._array.back() : INVALID), _map(&map) {}
  2553 
  2554       /// \brief Invalid constructor \& conversion.
  2555       ///
  2556       /// This constructor initializes the iterator to be invalid.
  2557       /// \sa Invalid for more details.
  2558       FalseIt(Invalid) : Parent(INVALID), _map(0) {}
  2559 
  2560       /// \brief Increment operator.
  2561       ///
  2562       /// Increment operator.
  2563       FalseIt& operator++() {
  2564         int pos = _map->position(*this);
  2565         Parent::operator=(pos > _map->_sep ? _map->_array[pos - 1] : INVALID);
  2566         return *this;
  2567       }
  2568 
  2569     private:
  2570       const IterableBoolMap* _map;
  2571     };
  2572 
  2573     /// \brief Iterator for the keys mapped to a given value.
  2574     ///
  2575     /// Iterator for the keys mapped to a given value. It works
  2576     /// like a graph item iterator, it can be converted to
  2577     /// the key type of the map, incremented with \c ++ operator, and
  2578     /// if the iterator leaves the last valid key, it will be equal to
  2579     /// \c INVALID.
  2580     class ItemIt : public Key {
  2581     public:
  2582       typedef Key Parent;
  2583 
  2584       /// \brief Creates an iterator with a value.
  2585       ///
  2586       /// Creates an iterator with a value. It iterates on the
  2587       /// keys mapped to the given value.
  2588       /// \param map The IterableBoolMap.
  2589       /// \param value The value.
  2590       ItemIt(const IterableBoolMap& map, bool value)
  2591         : Parent(value ? 
  2592                  (map._sep > 0 ?
  2593                   map._array[map._sep - 1] : INVALID) :
  2594                  (map._sep < int(map._array.size()) ?
  2595                   map._array.back() : INVALID)), _map(&map) {}
  2596 
  2597       /// \brief Invalid constructor \& conversion.
  2598       ///
  2599       /// This constructor initializes the iterator to be invalid.
  2600       /// \sa Invalid for more details.
  2601       ItemIt(Invalid) : Parent(INVALID), _map(0) {}
  2602 
  2603       /// \brief Increment operator.
  2604       ///
  2605       /// Increment operator.
  2606       ItemIt& operator++() {
  2607         int pos = _map->position(*this);
  2608         int _sep = pos >= _map->_sep ? _map->_sep : 0;
  2609         Parent::operator=(pos > _sep ? _map->_array[pos - 1] : INVALID);
  2610         return *this;
  2611       }
  2612 
  2613     private:
  2614       const IterableBoolMap* _map;
  2615     };
  2616 
  2617   protected:
  2618 
  2619     virtual void add(const Key& key) {
  2620       Parent::add(key);
  2621       Parent::set(key, _array.size());
  2622       _array.push_back(key);
  2623     }
  2624 
  2625     virtual void add(const std::vector<Key>& keys) {
  2626       Parent::add(keys);
  2627       for (int i = 0; i < int(keys.size()); ++i) {
  2628         Parent::set(keys[i], _array.size());
  2629         _array.push_back(keys[i]);
  2630       }
  2631     }
  2632 
  2633     virtual void erase(const Key& key) {
  2634       int pos = position(key);
  2635       if (pos < _sep) {
  2636         --_sep;
  2637         Parent::set(_array[_sep], pos);
  2638         _array[pos] = _array[_sep];
  2639         Parent::set(_array.back(), _sep);
  2640         _array[_sep] = _array.back();
  2641         _array.pop_back();
  2642       } else {
  2643         Parent::set(_array.back(), pos);
  2644         _array[pos] = _array.back();
  2645         _array.pop_back();
  2646       }
  2647       Parent::erase(key);
  2648     }
  2649 
  2650     virtual void erase(const std::vector<Key>& keys) {
  2651       for (int i = 0; i < int(keys.size()); ++i) {
  2652         int pos = position(keys[i]);
  2653         if (pos < _sep) {
  2654           --_sep;
  2655           Parent::set(_array[_sep], pos);
  2656           _array[pos] = _array[_sep];
  2657           Parent::set(_array.back(), _sep);
  2658           _array[_sep] = _array.back();
  2659           _array.pop_back();
  2660         } else {
  2661           Parent::set(_array.back(), pos);
  2662           _array[pos] = _array.back();
  2663           _array.pop_back();
  2664         }
  2665       }
  2666       Parent::erase(keys);
  2667     }
  2668 
  2669     virtual void build() {
  2670       Parent::build();
  2671       typename Parent::Notifier* nf = Parent::notifier();
  2672       Key it;
  2673       for (nf->first(it); it != INVALID; nf->next(it)) {
  2674         Parent::set(it, _array.size());
  2675         _array.push_back(it);
  2676       }
  2677       _sep = 0;
  2678     }
  2679 
  2680     virtual void clear() {
  2681       _array.clear();
  2682       _sep = 0;
  2683       Parent::clear();
  2684     }
  2685 
  2686   };
  2687 
  2688 
  2689   namespace _maps_bits {
  2690     template <typename Item>
  2691     struct IterableIntMapNode {
  2692       IterableIntMapNode() : value(-1) {}
  2693       IterableIntMapNode(int _value) : value(_value) {}
  2694       Item prev, next;
  2695       int value;
  2696     };
  2697   }
  2698 
  2699   /// \brief Dynamic iterable integer map.
  2700   ///
  2701   /// This class provides a special graph map type which can store an
  2702   /// integer value for graph items (\c Node, \c Arc or \c Edge).
  2703   /// For each non-negative value it is possible to iterate on the keys
  2704   /// mapped to the value.
  2705   ///
  2706   /// This type is a reference map, so it can be modified with the
  2707   /// subscript operator.
  2708   ///
  2709   /// \note The size of the data structure depends on the largest
  2710   /// value in the map.
  2711   ///
  2712   /// \tparam GR The graph type.
  2713   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  2714   /// \c GR::Edge).
  2715   ///
  2716   /// \see IterableBoolMap, IterableValueMap
  2717   /// \see CrossRefMap
  2718   template <typename GR, typename K>
  2719   class IterableIntMap
  2720     : protected ItemSetTraits<GR, K>::
  2721         template Map<_maps_bits::IterableIntMapNode<K> >::Type {
  2722   public:
  2723     typedef typename ItemSetTraits<GR, K>::
  2724       template Map<_maps_bits::IterableIntMapNode<K> >::Type Parent;
  2725 
  2726     /// The key type
  2727     typedef K Key;
  2728     /// The value type
  2729     typedef int Value;
  2730     /// The graph type
  2731     typedef GR Graph;
  2732 
  2733     /// \brief Constructor of the map.
  2734     ///
  2735     /// Constructor of the map. It sets all values to -1.
  2736     explicit IterableIntMap(const Graph& graph)
  2737       : Parent(graph) {}
  2738 
  2739     /// \brief Constructor of the map with a given value.
  2740     ///
  2741     /// Constructor of the map with a given value.
  2742     explicit IterableIntMap(const Graph& graph, int value)
  2743       : Parent(graph, _maps_bits::IterableIntMapNode<K>(value)) {
  2744       if (value >= 0) {
  2745         for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
  2746           lace(it);
  2747         }
  2748       }
  2749     }
  2750 
  2751   private:
  2752 
  2753     void unlace(const Key& key) {
  2754       typename Parent::Value& node = Parent::operator[](key);
  2755       if (node.value < 0) return;
  2756       if (node.prev != INVALID) {
  2757         Parent::operator[](node.prev).next = node.next;
  2758       } else {
  2759         _first[node.value] = node.next;
  2760       }
  2761       if (node.next != INVALID) {
  2762         Parent::operator[](node.next).prev = node.prev;
  2763       }
  2764       while (!_first.empty() && _first.back() == INVALID) {
  2765         _first.pop_back();
  2766       }
  2767     }
  2768 
  2769     void lace(const Key& key) {
  2770       typename Parent::Value& node = Parent::operator[](key);
  2771       if (node.value < 0) return;
  2772       if (node.value >= int(_first.size())) {
  2773         _first.resize(node.value + 1, INVALID);
  2774       }
  2775       node.prev = INVALID;
  2776       node.next = _first[node.value];
  2777       if (node.next != INVALID) {
  2778         Parent::operator[](node.next).prev = key;
  2779       }
  2780       _first[node.value] = key;
  2781     }
  2782 
  2783   public:
  2784 
  2785     /// Indicates that the map is reference map.
  2786     typedef True ReferenceMapTag;
  2787 
  2788     /// \brief Reference to the value of the map.
  2789     ///
  2790     /// This class is similar to the \c int type. It can
  2791     /// be converted to \c int and it has the same operators.
  2792     class Reference {
  2793       friend class IterableIntMap;
  2794     private:
  2795       Reference(IterableIntMap& map, const Key& key)
  2796         : _key(key), _map(map) {}
  2797     public:
  2798 
  2799       Reference& operator=(const Reference& value) {
  2800         _map.set(_key, static_cast<const int&>(value));
  2801          return *this;
  2802       }
  2803 
  2804       operator const int&() const {
  2805         return static_cast<const IterableIntMap&>(_map)[_key];
  2806       }
  2807 
  2808       Reference& operator=(int value) {
  2809         _map.set(_key, value);
  2810         return *this;
  2811       }
  2812       Reference& operator++() {
  2813         _map.set(_key, _map[_key] + 1);
  2814         return *this;
  2815       }
  2816       int operator++(int) {
  2817         int value = _map[_key];
  2818         _map.set(_key, value + 1);
  2819         return value;
  2820       }
  2821       Reference& operator--() {
  2822         _map.set(_key, _map[_key] - 1);
  2823         return *this;
  2824       }
  2825       int operator--(int) {
  2826         int value = _map[_key];
  2827         _map.set(_key, value - 1);
  2828         return value;
  2829       }
  2830       Reference& operator+=(int value) {
  2831         _map.set(_key, _map[_key] + value);
  2832         return *this;
  2833       }
  2834       Reference& operator-=(int value) {
  2835         _map.set(_key, _map[_key] - value);
  2836         return *this;
  2837       }
  2838       Reference& operator*=(int value) {
  2839         _map.set(_key, _map[_key] * value);
  2840         return *this;
  2841       }
  2842       Reference& operator/=(int value) {
  2843         _map.set(_key, _map[_key] / value);
  2844         return *this;
  2845       }
  2846       Reference& operator%=(int value) {
  2847         _map.set(_key, _map[_key] % value);
  2848         return *this;
  2849       }
  2850       Reference& operator&=(int value) {
  2851         _map.set(_key, _map[_key] & value);
  2852         return *this;
  2853       }
  2854       Reference& operator|=(int value) {
  2855         _map.set(_key, _map[_key] | value);
  2856         return *this;
  2857       }
  2858       Reference& operator^=(int value) {
  2859         _map.set(_key, _map[_key] ^ value);
  2860         return *this;
  2861       }
  2862       Reference& operator<<=(int value) {
  2863         _map.set(_key, _map[_key] << value);
  2864         return *this;
  2865       }
  2866       Reference& operator>>=(int value) {
  2867         _map.set(_key, _map[_key] >> value);
  2868         return *this;
  2869       }
  2870 
  2871     private:
  2872       Key _key;
  2873       IterableIntMap& _map;
  2874     };
  2875 
  2876     /// The const reference type.
  2877     typedef const Value& ConstReference;
  2878 
  2879     /// \brief Gives back the maximal value plus one.
  2880     ///
  2881     /// Gives back the maximal value plus one.
  2882     int size() const {
  2883       return _first.size();
  2884     }
  2885 
  2886     /// \brief Set operation of the map.
  2887     ///
  2888     /// Set operation of the map.
  2889     void set(const Key& key, const Value& value) {
  2890       unlace(key);
  2891       Parent::operator[](key).value = value;
  2892       lace(key);
  2893     }
  2894 
  2895     /// \brief Const subscript operator of the map.
  2896     ///
  2897     /// Const subscript operator of the map.
  2898     const Value& operator[](const Key& key) const {
  2899       return Parent::operator[](key).value;
  2900     }
  2901 
  2902     /// \brief Subscript operator of the map.
  2903     ///
  2904     /// Subscript operator of the map.
  2905     Reference operator[](const Key& key) {
  2906       return Reference(*this, key);
  2907     }
  2908 
  2909     /// \brief Iterator for the keys with the same value.
  2910     ///
  2911     /// Iterator for the keys with the same value. It works
  2912     /// like a graph item iterator, it can be converted to
  2913     /// the item type of the map, incremented with \c ++ operator, and
  2914     /// if the iterator leaves the last valid item, it will be equal to
  2915     /// \c INVALID.
  2916     class ItemIt : public Key {
  2917     public:
  2918       typedef Key Parent;
  2919 
  2920       /// \brief Invalid constructor \& conversion.
  2921       ///
  2922       /// This constructor initializes the iterator to be invalid.
  2923       /// \sa Invalid for more details.
  2924       ItemIt(Invalid) : Parent(INVALID), _map(0) {}
  2925 
  2926       /// \brief Creates an iterator with a value.
  2927       ///
  2928       /// Creates an iterator with a value. It iterates on the
  2929       /// keys mapped to the given value.
  2930       /// \param map The IterableIntMap.
  2931       /// \param value The value.
  2932       ItemIt(const IterableIntMap& map, int value) : _map(&map) {
  2933         if (value < 0 || value >= int(_map->_first.size())) {
  2934           Parent::operator=(INVALID);
  2935         } else {
  2936           Parent::operator=(_map->_first[value]);
  2937         }
  2938       }
  2939 
  2940       /// \brief Increment operator.
  2941       ///
  2942       /// Increment operator.
  2943       ItemIt& operator++() {
  2944         Parent::operator=(_map->IterableIntMap::Parent::
  2945                           operator[](static_cast<Parent&>(*this)).next);
  2946         return *this;
  2947       }
  2948 
  2949     private:
  2950       const IterableIntMap* _map;
  2951     };
  2952 
  2953   protected:
  2954 
  2955     virtual void erase(const Key& key) {
  2956       unlace(key);
  2957       Parent::erase(key);
  2958     }
  2959 
  2960     virtual void erase(const std::vector<Key>& keys) {
  2961       for (int i = 0; i < int(keys.size()); ++i) {
  2962         unlace(keys[i]);
  2963       }
  2964       Parent::erase(keys);
  2965     }
  2966 
  2967     virtual void clear() {
  2968       _first.clear();
  2969       Parent::clear();
  2970     }
  2971 
  2972   private:
  2973     std::vector<Key> _first;
  2974   };
  2975 
  2976   namespace _maps_bits {
  2977     template <typename Item, typename Value>
  2978     struct IterableValueMapNode {
  2979       IterableValueMapNode(Value _value = Value()) : value(_value) {}
  2980       Item prev, next;
  2981       Value value;
  2982     };
  2983   }
  2984 
  2985   /// \brief Dynamic iterable map for comparable values.
  2986   ///
  2987   /// This class provides a special graph map type which can store an
  2988   /// comparable value for graph items (\c Node, \c Arc or \c Edge).
  2989   /// For each value it is possible to iterate on the keys mapped to
  2990   /// the value.
  2991   ///
  2992   /// The map stores for each value a linked list with
  2993   /// the items which mapped to the value, and the values are stored
  2994   /// in balanced binary tree. The values of the map can be accessed
  2995   /// with stl compatible forward iterator.
  2996   ///
  2997   /// This type is not reference map, so it cannot be modified with
  2998   /// the subscript operator.
  2999   ///
  3000   /// \tparam GR The graph type.
  3001   /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  3002   /// \c GR::Edge).
  3003   /// \tparam V The value type of the map. It can be any comparable
  3004   /// value type.
  3005   ///
  3006   /// \see IterableBoolMap, IterableIntMap
  3007   /// \see CrossRefMap
  3008   template <typename GR, typename K, typename V>
  3009   class IterableValueMap
  3010     : protected ItemSetTraits<GR, K>::
  3011         template Map<_maps_bits::IterableValueMapNode<K, V> >::Type {
  3012   public:
  3013     typedef typename ItemSetTraits<GR, K>::
  3014       template Map<_maps_bits::IterableValueMapNode<K, V> >::Type Parent;
  3015 
  3016     /// The key type
  3017     typedef K Key;
  3018     /// The value type
  3019     typedef V Value;
  3020     /// The graph type
  3021     typedef GR Graph;
  3022 
  3023   public:
  3024 
  3025     /// \brief Constructor of the map with a given value.
  3026     ///
  3027     /// Constructor of the map with a given value.
  3028     explicit IterableValueMap(const Graph& graph,
  3029                               const Value& value = Value())
  3030       : Parent(graph, _maps_bits::IterableValueMapNode<K, V>(value)) {
  3031       for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
  3032         lace(it);
  3033       }
  3034     }
  3035 
  3036   protected:
  3037 
  3038     void unlace(const Key& key) {
  3039       typename Parent::Value& node = Parent::operator[](key);
  3040       if (node.prev != INVALID) {
  3041         Parent::operator[](node.prev).next = node.next;
  3042       } else {
  3043         if (node.next != INVALID) {
  3044           _first[node.value] = node.next;
  3045         } else {
  3046           _first.erase(node.value);
  3047         }
  3048       }
  3049       if (node.next != INVALID) {
  3050         Parent::operator[](node.next).prev = node.prev;
  3051       }
  3052     }
  3053 
  3054     void lace(const Key& key) {
  3055       typename Parent::Value& node = Parent::operator[](key);
  3056       typename std::map<Value, Key>::iterator it = _first.find(node.value);
  3057       if (it == _first.end()) {
  3058         node.prev = node.next = INVALID;
  3059         _first.insert(std::make_pair(node.value, key));
  3060       } else {
  3061         node.prev = INVALID;
  3062         node.next = it->second;
  3063         if (node.next != INVALID) {
  3064           Parent::operator[](node.next).prev = key;
  3065         }
  3066         it->second = key;
  3067       }
  3068     }
  3069 
  3070   public:
  3071 
  3072     /// \brief Forward iterator for values.
  3073     ///
  3074     /// This iterator is an stl compatible forward
  3075     /// iterator on the values of the map. The values can
  3076     /// be accessed in the <tt>[beginValue, endValue)</tt> range.
  3077     class ValueIterator
  3078       : public std::iterator<std::forward_iterator_tag, Value> {
  3079       friend class IterableValueMap;
  3080     private:
  3081       ValueIterator(typename std::map<Value, Key>::const_iterator _it)
  3082         : it(_it) {}
  3083     public:
  3084 
  3085       ValueIterator() {}
  3086 
  3087       ValueIterator& operator++() { ++it; return *this; }
  3088       ValueIterator operator++(int) {
  3089         ValueIterator tmp(*this);
  3090         operator++();
  3091         return tmp;
  3092       }
  3093 
  3094       const Value& operator*() const { return it->first; }
  3095       const Value* operator->() const { return &(it->first); }
  3096 
  3097       bool operator==(ValueIterator jt) const { return it == jt.it; }
  3098       bool operator!=(ValueIterator jt) const { return it != jt.it; }
  3099 
  3100     private:
  3101       typename std::map<Value, Key>::const_iterator it;
  3102     };
  3103 
  3104     /// \brief Returns an iterator to the first value.
  3105     ///
  3106     /// Returns an stl compatible iterator to the
  3107     /// first value of the map. The values of the
  3108     /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  3109     /// range.
  3110     ValueIterator beginValue() const {
  3111       return ValueIterator(_first.begin());
  3112     }
  3113 
  3114     /// \brief Returns an iterator after the last value.
  3115     ///
  3116     /// Returns an stl compatible iterator after the
  3117     /// last value of the map. The values of the
  3118     /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  3119     /// range.
  3120     ValueIterator endValue() const {
  3121       return ValueIterator(_first.end());
  3122     }
  3123 
  3124     /// \brief Set operation of the map.
  3125     ///
  3126     /// Set operation of the map.
  3127     void set(const Key& key, const Value& value) {
  3128       unlace(key);
  3129       Parent::operator[](key).value = value;
  3130       lace(key);
  3131     }
  3132 
  3133     /// \brief Const subscript operator of the map.
  3134     ///
  3135     /// Const subscript operator of the map.
  3136     const Value& operator[](const Key& key) const {
  3137       return Parent::operator[](key).value;
  3138     }
  3139 
  3140     /// \brief Iterator for the keys with the same value.
  3141     ///
  3142     /// Iterator for the keys with the same value. It works
  3143     /// like a graph item iterator, it can be converted to
  3144     /// the item type of the map, incremented with \c ++ operator, and
  3145     /// if the iterator leaves the last valid item, it will be equal to
  3146     /// \c INVALID.
  3147     class ItemIt : public Key {
  3148     public:
  3149       typedef Key Parent;
  3150 
  3151       /// \brief Invalid constructor \& conversion.
  3152       ///
  3153       /// This constructor initializes the iterator to be invalid.
  3154       /// \sa Invalid for more details.
  3155       ItemIt(Invalid) : Parent(INVALID), _map(0) {}
  3156 
  3157       /// \brief Creates an iterator with a value.
  3158       ///
  3159       /// Creates an iterator with a value. It iterates on the
  3160       /// keys which have the given value.
  3161       /// \param map The IterableValueMap
  3162       /// \param value The value
  3163       ItemIt(const IterableValueMap& map, const Value& value) : _map(&map) {
  3164         typename std::map<Value, Key>::const_iterator it =
  3165           map._first.find(value);
  3166         if (it == map._first.end()) {
  3167           Parent::operator=(INVALID);
  3168         } else {
  3169           Parent::operator=(it->second);
  3170         }
  3171       }
  3172 
  3173       /// \brief Increment operator.
  3174       ///
  3175       /// Increment Operator.
  3176       ItemIt& operator++() {
  3177         Parent::operator=(_map->IterableValueMap::Parent::
  3178                           operator[](static_cast<Parent&>(*this)).next);
  3179         return *this;
  3180       }
  3181 
  3182 
  3183     private:
  3184       const IterableValueMap* _map;
  3185     };
  3186 
  3187   protected:
  3188 
  3189     virtual void add(const Key& key) {
  3190       Parent::add(key);
  3191       unlace(key);
  3192     }
  3193 
  3194     virtual void add(const std::vector<Key>& keys) {
  3195       Parent::add(keys);
  3196       for (int i = 0; i < int(keys.size()); ++i) {
  3197         lace(keys[i]);
  3198       }
  3199     }
  3200 
  3201     virtual void erase(const Key& key) {
  3202       unlace(key);
  3203       Parent::erase(key);
  3204     }
  3205 
  3206     virtual void erase(const std::vector<Key>& keys) {
  3207       for (int i = 0; i < int(keys.size()); ++i) {
  3208         unlace(keys[i]);
  3209       }
  3210       Parent::erase(keys);
  3211     }
  3212 
  3213     virtual void build() {
  3214       Parent::build();
  3215       for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
  3216         lace(it);
  3217       }
  3218     }
  3219 
  3220     virtual void clear() {
  3221       _first.clear();
  3222       Parent::clear();
  3223     }
  3224 
  3225   private:
  3226     std::map<Value, Key> _first;
  3227   };
  3228 
  3229   /// \brief Map of the source nodes of arcs in a digraph.
  3230   ///
  3231   /// SourceMap provides access for the source node of each arc in a digraph,
  3232   /// which is returned by the \c source() function of the digraph.
  3233   /// \tparam GR The digraph type.
  3234   /// \see TargetMap
  3235   template <typename GR>
  3236   class SourceMap {
  3237   public:
  3238 
  3239     ///\e
  3240     typedef typename GR::Arc Key;
  3241     ///\e
  3242     typedef typename GR::Node Value;
  3243 
  3244     /// \brief Constructor
  3245     ///
  3246     /// Constructor.
  3247     /// \param digraph The digraph that the map belongs to.
  3248     explicit SourceMap(const GR& digraph) : _graph(digraph) {}
  3249 
  3250     /// \brief Returns the source node of the given arc.
  3251     ///
  3252     /// Returns the source node of the given arc.
  3253     Value operator[](const Key& arc) const {
  3254       return _graph.source(arc);
  3255     }
  3256 
  3257   private:
  3258     const GR& _graph;
  3259   };
  3260 
  3261   /// \brief Returns a \c SourceMap class.
  3262   ///
  3263   /// This function just returns an \c SourceMap class.
  3264   /// \relates SourceMap
  3265   template <typename GR>
  3266   inline SourceMap<GR> sourceMap(const GR& graph) {
  3267     return SourceMap<GR>(graph);
  3268   }
  3269 
  3270   /// \brief Map of the target nodes of arcs in a digraph.
  3271   ///
  3272   /// TargetMap provides access for the target node of each arc in a digraph,
  3273   /// which is returned by the \c target() function of the digraph.
  3274   /// \tparam GR The digraph type.
  3275   /// \see SourceMap
  3276   template <typename GR>
  3277   class TargetMap {
  3278   public:
  3279 
  3280     ///\e
  3281     typedef typename GR::Arc Key;
  3282     ///\e
  3283     typedef typename GR::Node Value;
  3284 
  3285     /// \brief Constructor
  3286     ///
  3287     /// Constructor.
  3288     /// \param digraph The digraph that the map belongs to.
  3289     explicit TargetMap(const GR& digraph) : _graph(digraph) {}
  3290 
  3291     /// \brief Returns the target node of the given arc.
  3292     ///
  3293     /// Returns the target node of the given arc.
  3294     Value operator[](const Key& e) const {
  3295       return _graph.target(e);
  3296     }
  3297 
  3298   private:
  3299     const GR& _graph;
  3300   };
  3301 
  3302   /// \brief Returns a \c TargetMap class.
  3303   ///
  3304   /// This function just returns a \c TargetMap class.
  3305   /// \relates TargetMap
  3306   template <typename GR>
  3307   inline TargetMap<GR> targetMap(const GR& graph) {
  3308     return TargetMap<GR>(graph);
  3309   }
  3310 
  3311   /// \brief Map of the "forward" directed arc view of edges in a graph.
  3312   ///
  3313   /// ForwardMap provides access for the "forward" directed arc view of
  3314   /// each edge in a graph, which is returned by the \c direct() function
  3315   /// of the graph with \c true parameter.
  3316   /// \tparam GR The graph type.
  3317   /// \see BackwardMap
  3318   template <typename GR>
  3319   class ForwardMap {
  3320   public:
  3321 
  3322     typedef typename GR::Arc Value;
  3323     typedef typename GR::Edge Key;
  3324 
  3325     /// \brief Constructor
  3326     ///
  3327     /// Constructor.
  3328     /// \param graph The graph that the map belongs to.
  3329     explicit ForwardMap(const GR& graph) : _graph(graph) {}
  3330 
  3331     /// \brief Returns the "forward" directed arc view of the given edge.
  3332     ///
  3333     /// Returns the "forward" directed arc view of the given edge.
  3334     Value operator[](const Key& key) const {
  3335       return _graph.direct(key, true);
  3336     }
  3337 
  3338   private:
  3339     const GR& _graph;
  3340   };
  3341 
  3342   /// \brief Returns a \c ForwardMap class.
  3343   ///
  3344   /// This function just returns an \c ForwardMap class.
  3345   /// \relates ForwardMap
  3346   template <typename GR>
  3347   inline ForwardMap<GR> forwardMap(const GR& graph) {
  3348     return ForwardMap<GR>(graph);
  3349   }
  3350 
  3351   /// \brief Map of the "backward" directed arc view of edges in a graph.
  3352   ///
  3353   /// BackwardMap provides access for the "backward" directed arc view of
  3354   /// each edge in a graph, which is returned by the \c direct() function
  3355   /// of the graph with \c false parameter.
  3356   /// \tparam GR The graph type.
  3357   /// \see ForwardMap
  3358   template <typename GR>
  3359   class BackwardMap {
  3360   public:
  3361 
  3362     typedef typename GR::Arc Value;
  3363     typedef typename GR::Edge Key;
  3364 
  3365     /// \brief Constructor
  3366     ///
  3367     /// Constructor.
  3368     /// \param graph The graph that the map belongs to.
  3369     explicit BackwardMap(const GR& graph) : _graph(graph) {}
  3370 
  3371     /// \brief Returns the "backward" directed arc view of the given edge.
  3372     ///
  3373     /// Returns the "backward" directed arc view of the given edge.
  3374     Value operator[](const Key& key) const {
  3375       return _graph.direct(key, false);
  3376     }
  3377 
  3378   private:
  3379     const GR& _graph;
  3380   };
  3381 
  3382   /// \brief Returns a \c BackwardMap class
  3383 
  3384   /// This function just returns a \c BackwardMap class.
  3385   /// \relates BackwardMap
  3386   template <typename GR>
  3387   inline BackwardMap<GR> backwardMap(const GR& graph) {
  3388     return BackwardMap<GR>(graph);
  3389   }
  3390 
  3391   /// \brief Map of the in-degrees of nodes in a digraph.
  3392   ///
  3393   /// This map returns the in-degree of a node. Once it is constructed,
  3394   /// the degrees are stored in a standard \c NodeMap, so each query is done
  3395   /// in constant time. On the other hand, the values are updated automatically
  3396   /// whenever the digraph changes.
  3397   ///
  3398   /// \warning Besides \c addNode() and \c addArc(), a digraph structure
  3399   /// may provide alternative ways to modify the digraph.
  3400   /// The correct behavior of InDegMap is not guarantied if these additional
  3401   /// features are used. For example the functions
  3402   /// \ref ListDigraph::changeSource() "changeSource()",
  3403   /// \ref ListDigraph::changeTarget() "changeTarget()" and
  3404   /// \ref ListDigraph::reverseArc() "reverseArc()"
  3405   /// of \ref ListDigraph will \e not update the degree values correctly.
  3406   ///
  3407   /// \sa OutDegMap
  3408   template <typename GR>
  3409   class InDegMap
  3410     : protected ItemSetTraits<GR, typename GR::Arc>
  3411       ::ItemNotifier::ObserverBase {
  3412 
  3413   public:
  3414 
  3415     /// The graph type of InDegMap
  3416     typedef GR Graph;
  3417     typedef GR Digraph;
  3418     /// The key type
  3419     typedef typename Digraph::Node Key;
  3420     /// The value type
  3421     typedef int Value;
  3422 
  3423     typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
  3424     ::ItemNotifier::ObserverBase Parent;
  3425 
  3426   private:
  3427 
  3428     class AutoNodeMap
  3429       : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {
  3430     public:
  3431 
  3432       typedef typename ItemSetTraits<Digraph, Key>::
  3433       template Map<int>::Type Parent;
  3434 
  3435       AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
  3436 
  3437       virtual void add(const Key& key) {
  3438         Parent::add(key);
  3439         Parent::set(key, 0);
  3440       }
  3441 
  3442       virtual void add(const std::vector<Key>& keys) {
  3443         Parent::add(keys);
  3444         for (int i = 0; i < int(keys.size()); ++i) {
  3445           Parent::set(keys[i], 0);
  3446         }
  3447       }
  3448 
  3449       virtual void build() {
  3450         Parent::build();
  3451         Key it;
  3452         typename Parent::Notifier* nf = Parent::notifier();
  3453         for (nf->first(it); it != INVALID; nf->next(it)) {
  3454           Parent::set(it, 0);
  3455         }
  3456       }
  3457     };
  3458 
  3459   public:
  3460 
  3461     /// \brief Constructor.
  3462     ///
  3463     /// Constructor for creating an in-degree map.
  3464     explicit InDegMap(const Digraph& graph)
  3465       : _digraph(graph), _deg(graph) {
  3466       Parent::attach(_digraph.notifier(typename Digraph::Arc()));
  3467 
  3468       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3469         _deg[it] = countInArcs(_digraph, it);
  3470       }
  3471     }
  3472 
  3473     /// \brief Gives back the in-degree of a Node.
  3474     ///
  3475     /// Gives back the in-degree of a Node.
  3476     int operator[](const Key& key) const {
  3477       return _deg[key];
  3478     }
  3479 
  3480   protected:
  3481 
  3482     typedef typename Digraph::Arc Arc;
  3483 
  3484     virtual void add(const Arc& arc) {
  3485       ++_deg[_digraph.target(arc)];
  3486     }
  3487 
  3488     virtual void add(const std::vector<Arc>& arcs) {
  3489       for (int i = 0; i < int(arcs.size()); ++i) {
  3490         ++_deg[_digraph.target(arcs[i])];
  3491       }
  3492     }
  3493 
  3494     virtual void erase(const Arc& arc) {
  3495       --_deg[_digraph.target(arc)];
  3496     }
  3497 
  3498     virtual void erase(const std::vector<Arc>& arcs) {
  3499       for (int i = 0; i < int(arcs.size()); ++i) {
  3500         --_deg[_digraph.target(arcs[i])];
  3501       }
  3502     }
  3503 
  3504     virtual void build() {
  3505       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3506         _deg[it] = countInArcs(_digraph, it);
  3507       }
  3508     }
  3509 
  3510     virtual void clear() {
  3511       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3512         _deg[it] = 0;
  3513       }
  3514     }
  3515   private:
  3516 
  3517     const Digraph& _digraph;
  3518     AutoNodeMap _deg;
  3519   };
  3520 
  3521   /// \brief Map of the out-degrees of nodes in a digraph.
  3522   ///
  3523   /// This map returns the out-degree of a node. Once it is constructed,
  3524   /// the degrees are stored in a standard \c NodeMap, so each query is done
  3525   /// in constant time. On the other hand, the values are updated automatically
  3526   /// whenever the digraph changes.
  3527   ///
  3528   /// \warning Besides \c addNode() and \c addArc(), a digraph structure
  3529   /// may provide alternative ways to modify the digraph.
  3530   /// The correct behavior of OutDegMap is not guarantied if these additional
  3531   /// features are used. For example the functions
  3532   /// \ref ListDigraph::changeSource() "changeSource()",
  3533   /// \ref ListDigraph::changeTarget() "changeTarget()" and
  3534   /// \ref ListDigraph::reverseArc() "reverseArc()"
  3535   /// of \ref ListDigraph will \e not update the degree values correctly.
  3536   ///
  3537   /// \sa InDegMap
  3538   template <typename GR>
  3539   class OutDegMap
  3540     : protected ItemSetTraits<GR, typename GR::Arc>
  3541       ::ItemNotifier::ObserverBase {
  3542 
  3543   public:
  3544 
  3545     /// The graph type of OutDegMap
  3546     typedef GR Graph;
  3547     typedef GR Digraph;
  3548     /// The key type
  3549     typedef typename Digraph::Node Key;
  3550     /// The value type
  3551     typedef int Value;
  3552 
  3553     typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
  3554     ::ItemNotifier::ObserverBase Parent;
  3555 
  3556   private:
  3557 
  3558     class AutoNodeMap
  3559       : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {
  3560     public:
  3561 
  3562       typedef typename ItemSetTraits<Digraph, Key>::
  3563       template Map<int>::Type Parent;
  3564 
  3565       AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
  3566 
  3567       virtual void add(const Key& key) {
  3568         Parent::add(key);
  3569         Parent::set(key, 0);
  3570       }
  3571       virtual void add(const std::vector<Key>& keys) {
  3572         Parent::add(keys);
  3573         for (int i = 0; i < int(keys.size()); ++i) {
  3574           Parent::set(keys[i], 0);
  3575         }
  3576       }
  3577       virtual void build() {
  3578         Parent::build();
  3579         Key it;
  3580         typename Parent::Notifier* nf = Parent::notifier();
  3581         for (nf->first(it); it != INVALID; nf->next(it)) {
  3582           Parent::set(it, 0);
  3583         }
  3584       }
  3585     };
  3586 
  3587   public:
  3588 
  3589     /// \brief Constructor.
  3590     ///
  3591     /// Constructor for creating an out-degree map.
  3592     explicit OutDegMap(const Digraph& graph)
  3593       : _digraph(graph), _deg(graph) {
  3594       Parent::attach(_digraph.notifier(typename Digraph::Arc()));
  3595 
  3596       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3597         _deg[it] = countOutArcs(_digraph, it);
  3598       }
  3599     }
  3600 
  3601     /// \brief Gives back the out-degree of a Node.
  3602     ///
  3603     /// Gives back the out-degree of a Node.
  3604     int operator[](const Key& key) const {
  3605       return _deg[key];
  3606     }
  3607 
  3608   protected:
  3609 
  3610     typedef typename Digraph::Arc Arc;
  3611 
  3612     virtual void add(const Arc& arc) {
  3613       ++_deg[_digraph.source(arc)];
  3614     }
  3615 
  3616     virtual void add(const std::vector<Arc>& arcs) {
  3617       for (int i = 0; i < int(arcs.size()); ++i) {
  3618         ++_deg[_digraph.source(arcs[i])];
  3619       }
  3620     }
  3621 
  3622     virtual void erase(const Arc& arc) {
  3623       --_deg[_digraph.source(arc)];
  3624     }
  3625 
  3626     virtual void erase(const std::vector<Arc>& arcs) {
  3627       for (int i = 0; i < int(arcs.size()); ++i) {
  3628         --_deg[_digraph.source(arcs[i])];
  3629       }
  3630     }
  3631 
  3632     virtual void build() {
  3633       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3634         _deg[it] = countOutArcs(_digraph, it);
  3635       }
  3636     }
  3637 
  3638     virtual void clear() {
  3639       for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  3640         _deg[it] = 0;
  3641       }
  3642     }
  3643   private:
  3644 
  3645     const Digraph& _digraph;
  3646     AutoNodeMap _deg;
  3647   };
  3648 
  3649   /// \brief Potential difference map
  3650   ///
  3651   /// PotentialDifferenceMap returns the difference between the potentials of
  3652   /// the source and target nodes of each arc in a digraph, i.e. it returns
  3653   /// \code
  3654   ///   potential[gr.target(arc)] - potential[gr.source(arc)].
  3655   /// \endcode
  3656   /// \tparam GR The digraph type.
  3657   /// \tparam POT A node map storing the potentials.
  3658   template <typename GR, typename POT>
  3659   class PotentialDifferenceMap {
  3660   public:
  3661     /// Key type
  3662     typedef typename GR::Arc Key;
  3663     /// Value type
  3664     typedef typename POT::Value Value;
  3665 
  3666     /// \brief Constructor
  3667     ///
  3668     /// Contructor of the map.
  3669     explicit PotentialDifferenceMap(const GR& gr,
  3670                                     const POT& potential)
  3671       : _digraph(gr), _potential(potential) {}
  3672 
  3673     /// \brief Returns the potential difference for the given arc.
  3674     ///
  3675     /// Returns the potential difference for the given arc, i.e.
  3676     /// \code
  3677     ///   potential[gr.target(arc)] - potential[gr.source(arc)].
  3678     /// \endcode
  3679     Value operator[](const Key& arc) const {
  3680       return _potential[_digraph.target(arc)] -
  3681         _potential[_digraph.source(arc)];
  3682     }
  3683 
  3684   private:
  3685     const GR& _digraph;
  3686     const POT& _potential;
  3687   };
  3688 
  3689   /// \brief Returns a PotentialDifferenceMap.
  3690   ///
  3691   /// This function just returns a PotentialDifferenceMap.
  3692   /// \relates PotentialDifferenceMap
  3693   template <typename GR, typename POT>
  3694   PotentialDifferenceMap<GR, POT>
  3695   potentialDifferenceMap(const GR& gr, const POT& potential) {
  3696     return PotentialDifferenceMap<GR, POT>(gr, potential);
  3697   }
  3698 
  3699   /// @}
  3700 }
  3701 
  3702 #endif // LEMON_MAPS_H