lemon/maps.h
changeset 784 1a7fe3bef514
parent 725 11404088d1a5
parent 717 684964884a2e
child 786 e20173729589
child 789 8ddb7deabab9
     1.1 --- a/lemon/maps.h	Fri Oct 16 10:21:37 2009 +0200
     1.2 +++ b/lemon/maps.h	Thu Nov 05 15:50:01 2009 +0100
     1.3 @@ -2,7 +2,7 @@
     1.4   *
     1.5   * This file is a part of LEMON, a generic C++ optimization library.
     1.6   *
     1.7 - * Copyright (C) 2003-2008
     1.8 + * Copyright (C) 2003-2009
     1.9   * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
    1.10   * (Egervary Research Group on Combinatorial Optimization, EGRES).
    1.11   *
    1.12 @@ -22,6 +22,7 @@
    1.13  #include <iterator>
    1.14  #include <functional>
    1.15  #include <vector>
    1.16 +#include <map>
    1.17  
    1.18  #include <lemon/core.h>
    1.19  
    1.20 @@ -29,8 +30,6 @@
    1.21  ///\ingroup maps
    1.22  ///\brief Miscellaneous property maps
    1.23  
    1.24 -#include <map>
    1.25 -
    1.26  namespace lemon {
    1.27  
    1.28    /// \addtogroup maps
    1.29 @@ -57,15 +56,16 @@
    1.30    /// its type definitions, or if you have to provide a writable map,
    1.31    /// but data written to it is not required (i.e. it will be sent to
    1.32    /// <tt>/dev/null</tt>).
    1.33 -  /// It conforms the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
    1.34 +  /// It conforms to the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
    1.35    ///
    1.36    /// \sa ConstMap
    1.37    template<typename K, typename V>
    1.38    class NullMap : public MapBase<K, V> {
    1.39    public:
    1.40 -    typedef MapBase<K, V> Parent;
    1.41 -    typedef typename Parent::Key Key;
    1.42 -    typedef typename Parent::Value Value;
    1.43 +    ///\e
    1.44 +    typedef K Key;
    1.45 +    ///\e
    1.46 +    typedef V Value;
    1.47  
    1.48      /// Gives back a default constructed element.
    1.49      Value operator[](const Key&) const { return Value(); }
    1.50 @@ -89,7 +89,7 @@
    1.51    /// value to each key.
    1.52    ///
    1.53    /// In other aspects it is equivalent to \c NullMap.
    1.54 -  /// So it conforms the \ref concepts::ReadWriteMap "ReadWriteMap"
    1.55 +  /// So it conforms to the \ref concepts::ReadWriteMap "ReadWriteMap"
    1.56    /// concept, but it absorbs the data written to it.
    1.57    ///
    1.58    /// The simplest way of using this map is through the constMap()
    1.59 @@ -102,9 +102,10 @@
    1.60    private:
    1.61      V _value;
    1.62    public:
    1.63 -    typedef MapBase<K, V> Parent;
    1.64 -    typedef typename Parent::Key Key;
    1.65 -    typedef typename Parent::Value Value;
    1.66 +    ///\e
    1.67 +    typedef K Key;
    1.68 +    ///\e
    1.69 +    typedef V Value;
    1.70  
    1.71      /// Default constructor
    1.72  
    1.73 @@ -157,7 +158,7 @@
    1.74    /// value to each key.
    1.75    ///
    1.76    /// In other aspects it is equivalent to \c NullMap.
    1.77 -  /// So it conforms the \ref concepts::ReadWriteMap "ReadWriteMap"
    1.78 +  /// So it conforms to the \ref concepts::ReadWriteMap "ReadWriteMap"
    1.79    /// concept, but it absorbs the data written to it.
    1.80    ///
    1.81    /// The simplest way of using this map is through the constMap()
    1.82 @@ -168,9 +169,10 @@
    1.83    template<typename K, typename V, V v>
    1.84    class ConstMap<K, Const<V, v> > : public MapBase<K, V> {
    1.85    public:
    1.86 -    typedef MapBase<K, V> Parent;
    1.87 -    typedef typename Parent::Key Key;
    1.88 -    typedef typename Parent::Value Value;
    1.89 +    ///\e
    1.90 +    typedef K Key;
    1.91 +    ///\e
    1.92 +    typedef V Value;
    1.93  
    1.94      /// Constructor.
    1.95      ConstMap() {}
    1.96 @@ -202,9 +204,10 @@
    1.97    template <typename T>
    1.98    class IdentityMap : public MapBase<T, T> {
    1.99    public:
   1.100 -    typedef MapBase<T, T> Parent;
   1.101 -    typedef typename Parent::Key Key;
   1.102 -    typedef typename Parent::Value Value;
   1.103 +    ///\e
   1.104 +    typedef T Key;
   1.105 +    ///\e
   1.106 +    typedef T Value;
   1.107  
   1.108      /// Gives back the given value without any modification.
   1.109      Value operator[](const Key &k) const {
   1.110 @@ -229,7 +232,7 @@
   1.111    /// values to integer keys from the range <tt>[0..size-1]</tt>.
   1.112    /// It can be used with some data structures, for example
   1.113    /// \c UnionFind, \c BinHeap, when the used items are small
   1.114 -  /// integers. This map conforms the \ref concepts::ReferenceMap
   1.115 +  /// integers. This map conforms to the \ref concepts::ReferenceMap
   1.116    /// "ReferenceMap" concept.
   1.117    ///
   1.118    /// The simplest way of using this map is through the rangeMap()
   1.119 @@ -245,11 +248,10 @@
   1.120  
   1.121    public:
   1.122  
   1.123 -    typedef MapBase<int, V> Parent;
   1.124      /// Key type
   1.125 -    typedef typename Parent::Key Key;
   1.126 +    typedef int Key;
   1.127      /// Value type
   1.128 -    typedef typename Parent::Value Value;
   1.129 +    typedef V Value;
   1.130      /// Reference type
   1.131      typedef typename Vector::reference Reference;
   1.132      /// Const reference type
   1.133 @@ -338,7 +340,7 @@
   1.134    /// that you can specify a default value for the keys that are not
   1.135    /// stored actually. This value can be different from the default
   1.136    /// contructed value (i.e. \c %Value()).
   1.137 -  /// This type conforms the \ref concepts::ReferenceMap "ReferenceMap"
   1.138 +  /// This type conforms to the \ref concepts::ReferenceMap "ReferenceMap"
   1.139    /// concept.
   1.140    ///
   1.141    /// This map is useful if a default value should be assigned to most of
   1.142 @@ -353,17 +355,16 @@
   1.143    ///
   1.144    /// The simplest way of using this map is through the sparseMap()
   1.145    /// function.
   1.146 -  template <typename K, typename V, typename Compare = std::less<K> >
   1.147 +  template <typename K, typename V, typename Comp = std::less<K> >
   1.148    class SparseMap : public MapBase<K, V> {
   1.149      template <typename K1, typename V1, typename C1>
   1.150      friend class SparseMap;
   1.151    public:
   1.152  
   1.153 -    typedef MapBase<K, V> Parent;
   1.154      /// Key type
   1.155 -    typedef typename Parent::Key Key;
   1.156 +    typedef K Key;
   1.157      /// Value type
   1.158 -    typedef typename Parent::Value Value;
   1.159 +    typedef V Value;
   1.160      /// Reference type
   1.161      typedef Value& Reference;
   1.162      /// Const reference type
   1.163 @@ -373,7 +374,7 @@
   1.164  
   1.165    private:
   1.166  
   1.167 -    typedef std::map<K, V, Compare> Map;
   1.168 +    typedef std::map<K, V, Comp> Map;
   1.169      Map _map;
   1.170      Value _value;
   1.171  
   1.172 @@ -489,14 +490,15 @@
   1.173      const M1 &_m1;
   1.174      const M2 &_m2;
   1.175    public:
   1.176 -    typedef MapBase<typename M2::Key, typename M1::Value> Parent;
   1.177 -    typedef typename Parent::Key Key;
   1.178 -    typedef typename Parent::Value Value;
   1.179 +    ///\e
   1.180 +    typedef typename M2::Key Key;
   1.181 +    ///\e
   1.182 +    typedef typename M1::Value Value;
   1.183  
   1.184      /// Constructor
   1.185      ComposeMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
   1.186  
   1.187 -    /// \e
   1.188 +    ///\e
   1.189      typename MapTraits<M1>::ConstReturnValue
   1.190      operator[](const Key &k) const { return _m1[_m2[k]]; }
   1.191    };
   1.192 @@ -545,14 +547,15 @@
   1.193      const M2 &_m2;
   1.194      F _f;
   1.195    public:
   1.196 -    typedef MapBase<typename M1::Key, V> Parent;
   1.197 -    typedef typename Parent::Key Key;
   1.198 -    typedef typename Parent::Value Value;
   1.199 +    ///\e
   1.200 +    typedef typename M1::Key Key;
   1.201 +    ///\e
   1.202 +    typedef V Value;
   1.203  
   1.204      /// Constructor
   1.205      CombineMap(const M1 &m1, const M2 &m2, const F &f = F())
   1.206        : _m1(m1), _m2(m2), _f(f) {}
   1.207 -    /// \e
   1.208 +    ///\e
   1.209      Value operator[](const Key &k) const { return _f(_m1[k],_m2[k]); }
   1.210    };
   1.211  
   1.212 @@ -615,13 +618,14 @@
   1.213    class FunctorToMap : public MapBase<K, V> {
   1.214      F _f;
   1.215    public:
   1.216 -    typedef MapBase<K, V> Parent;
   1.217 -    typedef typename Parent::Key Key;
   1.218 -    typedef typename Parent::Value Value;
   1.219 +    ///\e
   1.220 +    typedef K Key;
   1.221 +    ///\e
   1.222 +    typedef V Value;
   1.223  
   1.224      /// Constructor
   1.225      FunctorToMap(const F &f = F()) : _f(f) {}
   1.226 -    /// \e
   1.227 +    ///\e
   1.228      Value operator[](const Key &k) const { return _f(k); }
   1.229    };
   1.230  
   1.231 @@ -669,18 +673,19 @@
   1.232    class MapToFunctor : public MapBase<typename M::Key, typename M::Value> {
   1.233      const M &_m;
   1.234    public:
   1.235 -    typedef MapBase<typename M::Key, typename M::Value> Parent;
   1.236 -    typedef typename Parent::Key Key;
   1.237 -    typedef typename Parent::Value Value;
   1.238 -
   1.239 -    typedef typename Parent::Key argument_type;
   1.240 -    typedef typename Parent::Value result_type;
   1.241 +    ///\e
   1.242 +    typedef typename M::Key Key;
   1.243 +    ///\e
   1.244 +    typedef typename M::Value Value;
   1.245 +
   1.246 +    typedef typename M::Key argument_type;
   1.247 +    typedef typename M::Value result_type;
   1.248  
   1.249      /// Constructor
   1.250      MapToFunctor(const M &m) : _m(m) {}
   1.251 -    /// \e
   1.252 +    ///\e
   1.253      Value operator()(const Key &k) const { return _m[k]; }
   1.254 -    /// \e
   1.255 +    ///\e
   1.256      Value operator[](const Key &k) const { return _m[k]; }
   1.257    };
   1.258  
   1.259 @@ -701,7 +706,7 @@
   1.260    /// "readable map" to another type using the default conversion.
   1.261    /// The \c Key type of it is inherited from \c M and the \c Value
   1.262    /// type is \c V.
   1.263 -  /// This type conforms the \ref concepts::ReadMap "ReadMap" concept.
   1.264 +  /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
   1.265    ///
   1.266    /// The simplest way of using this map is through the convertMap()
   1.267    /// function.
   1.268 @@ -709,9 +714,10 @@
   1.269    class ConvertMap : public MapBase<typename M::Key, V> {
   1.270      const M &_m;
   1.271    public:
   1.272 -    typedef MapBase<typename M::Key, V> Parent;
   1.273 -    typedef typename Parent::Key Key;
   1.274 -    typedef typename Parent::Value Value;
   1.275 +    ///\e
   1.276 +    typedef typename M::Key Key;
   1.277 +    ///\e
   1.278 +    typedef V Value;
   1.279  
   1.280      /// Constructor
   1.281  
   1.282 @@ -719,7 +725,7 @@
   1.283      /// \param m The underlying map.
   1.284      ConvertMap(const M &m) : _m(m) {}
   1.285  
   1.286 -    /// \e
   1.287 +    ///\e
   1.288      Value operator[](const Key &k) const { return _m[k]; }
   1.289    };
   1.290  
   1.291 @@ -751,9 +757,10 @@
   1.292      M1 &_m1;
   1.293      M2 &_m2;
   1.294    public:
   1.295 -    typedef MapBase<typename M1::Key, typename M1::Value> Parent;
   1.296 -    typedef typename Parent::Key Key;
   1.297 -    typedef typename Parent::Value Value;
   1.298 +    ///\e
   1.299 +    typedef typename M1::Key Key;
   1.300 +    ///\e
   1.301 +    typedef typename M1::Value Value;
   1.302  
   1.303      /// Constructor
   1.304      ForkMap(M1 &m1, M2 &m2) : _m1(m1), _m2(m2) {}
   1.305 @@ -797,13 +804,14 @@
   1.306      const M1 &_m1;
   1.307      const M2 &_m2;
   1.308    public:
   1.309 -    typedef MapBase<typename M1::Key, typename M1::Value> Parent;
   1.310 -    typedef typename Parent::Key Key;
   1.311 -    typedef typename Parent::Value Value;
   1.312 +    ///\e
   1.313 +    typedef typename M1::Key Key;
   1.314 +    ///\e
   1.315 +    typedef typename M1::Value Value;
   1.316  
   1.317      /// Constructor
   1.318      AddMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
   1.319 -    /// \e
   1.320 +    ///\e
   1.321      Value operator[](const Key &k) const { return _m1[k]+_m2[k]; }
   1.322    };
   1.323  
   1.324 @@ -845,13 +853,14 @@
   1.325      const M1 &_m1;
   1.326      const M2 &_m2;
   1.327    public:
   1.328 -    typedef MapBase<typename M1::Key, typename M1::Value> Parent;
   1.329 -    typedef typename Parent::Key Key;
   1.330 -    typedef typename Parent::Value Value;
   1.331 +    ///\e
   1.332 +    typedef typename M1::Key Key;
   1.333 +    ///\e
   1.334 +    typedef typename M1::Value Value;
   1.335  
   1.336      /// Constructor
   1.337      SubMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
   1.338 -    /// \e
   1.339 +    ///\e
   1.340      Value operator[](const Key &k) const { return _m1[k]-_m2[k]; }
   1.341    };
   1.342  
   1.343 @@ -894,13 +903,14 @@
   1.344      const M1 &_m1;
   1.345      const M2 &_m2;
   1.346    public:
   1.347 -    typedef MapBase<typename M1::Key, typename M1::Value> Parent;
   1.348 -    typedef typename Parent::Key Key;
   1.349 -    typedef typename Parent::Value Value;
   1.350 +    ///\e
   1.351 +    typedef typename M1::Key Key;
   1.352 +    ///\e
   1.353 +    typedef typename M1::Value Value;
   1.354  
   1.355      /// Constructor
   1.356      MulMap(const M1 &m1,const M2 &m2) : _m1(m1), _m2(m2) {}
   1.357 -    /// \e
   1.358 +    ///\e
   1.359      Value operator[](const Key &k) const { return _m1[k]*_m2[k]; }
   1.360    };
   1.361  
   1.362 @@ -942,13 +952,14 @@
   1.363      const M1 &_m1;
   1.364      const M2 &_m2;
   1.365    public:
   1.366 -    typedef MapBase<typename M1::Key, typename M1::Value> Parent;
   1.367 -    typedef typename Parent::Key Key;
   1.368 -    typedef typename Parent::Value Value;
   1.369 +    ///\e
   1.370 +    typedef typename M1::Key Key;
   1.371 +    ///\e
   1.372 +    typedef typename M1::Value Value;
   1.373  
   1.374      /// Constructor
   1.375      DivMap(const M1 &m1,const M2 &m2) : _m1(m1), _m2(m2) {}
   1.376 -    /// \e
   1.377 +    ///\e
   1.378      Value operator[](const Key &k) const { return _m1[k]/_m2[k]; }
   1.379    };
   1.380  
   1.381 @@ -992,9 +1003,10 @@
   1.382      const M &_m;
   1.383      C _v;
   1.384    public:
   1.385 -    typedef MapBase<typename M::Key, typename M::Value> Parent;
   1.386 -    typedef typename Parent::Key Key;
   1.387 -    typedef typename Parent::Value Value;
   1.388 +    ///\e
   1.389 +    typedef typename M::Key Key;
   1.390 +    ///\e
   1.391 +    typedef typename M::Value Value;
   1.392  
   1.393      /// Constructor
   1.394  
   1.395 @@ -1002,7 +1014,7 @@
   1.396      /// \param m The undelying map.
   1.397      /// \param v The constant value.
   1.398      ShiftMap(const M &m, const C &v) : _m(m), _v(v) {}
   1.399 -    /// \e
   1.400 +    ///\e
   1.401      Value operator[](const Key &k) const { return _m[k]+_v; }
   1.402    };
   1.403  
   1.404 @@ -1022,9 +1034,10 @@
   1.405      M &_m;
   1.406      C _v;
   1.407    public:
   1.408 -    typedef MapBase<typename M::Key, typename M::Value> Parent;
   1.409 -    typedef typename Parent::Key Key;
   1.410 -    typedef typename Parent::Value Value;
   1.411 +    ///\e
   1.412 +    typedef typename M::Key Key;
   1.413 +    ///\e
   1.414 +    typedef typename M::Value Value;
   1.415  
   1.416      /// Constructor
   1.417  
   1.418 @@ -1032,9 +1045,9 @@
   1.419      /// \param m The undelying map.
   1.420      /// \param v The constant value.
   1.421      ShiftWriteMap(M &m, const C &v) : _m(m), _v(v) {}
   1.422 -    /// \e
   1.423 +    ///\e
   1.424      Value operator[](const Key &k) const { return _m[k]+_v; }
   1.425 -    /// \e
   1.426 +    ///\e
   1.427      void set(const Key &k, const Value &v) { _m.set(k, v-_v); }
   1.428    };
   1.429  
   1.430 @@ -1093,9 +1106,10 @@
   1.431      const M &_m;
   1.432      C _v;
   1.433    public:
   1.434 -    typedef MapBase<typename M::Key, typename M::Value> Parent;
   1.435 -    typedef typename Parent::Key Key;
   1.436 -    typedef typename Parent::Value Value;
   1.437 +    ///\e
   1.438 +    typedef typename M::Key Key;
   1.439 +    ///\e
   1.440 +    typedef typename M::Value Value;
   1.441  
   1.442      /// Constructor
   1.443  
   1.444 @@ -1103,7 +1117,7 @@
   1.445      /// \param m The undelying map.
   1.446      /// \param v The constant value.
   1.447      ScaleMap(const M &m, const C &v) : _m(m), _v(v) {}
   1.448 -    /// \e
   1.449 +    ///\e
   1.450      Value operator[](const Key &k) const { return _v*_m[k]; }
   1.451    };
   1.452  
   1.453 @@ -1124,9 +1138,10 @@
   1.454      M &_m;
   1.455      C _v;
   1.456    public:
   1.457 -    typedef MapBase<typename M::Key, typename M::Value> Parent;
   1.458 -    typedef typename Parent::Key Key;
   1.459 -    typedef typename Parent::Value Value;
   1.460 +    ///\e
   1.461 +    typedef typename M::Key Key;
   1.462 +    ///\e
   1.463 +    typedef typename M::Value Value;
   1.464  
   1.465      /// Constructor
   1.466  
   1.467 @@ -1134,9 +1149,9 @@
   1.468      /// \param m The undelying map.
   1.469      /// \param v The constant value.
   1.470      ScaleWriteMap(M &m, const C &v) : _m(m), _v(v) {}
   1.471 -    /// \e
   1.472 +    ///\e
   1.473      Value operator[](const Key &k) const { return _v*_m[k]; }
   1.474 -    /// \e
   1.475 +    ///\e
   1.476      void set(const Key &k, const Value &v) { _m.set(k, v/_v); }
   1.477    };
   1.478  
   1.479 @@ -1193,13 +1208,14 @@
   1.480    class NegMap : public MapBase<typename M::Key, typename M::Value> {
   1.481      const M& _m;
   1.482    public:
   1.483 -    typedef MapBase<typename M::Key, typename M::Value> Parent;
   1.484 -    typedef typename Parent::Key Key;
   1.485 -    typedef typename Parent::Value Value;
   1.486 +    ///\e
   1.487 +    typedef typename M::Key Key;
   1.488 +    ///\e
   1.489 +    typedef typename M::Value Value;
   1.490  
   1.491      /// Constructor
   1.492      NegMap(const M &m) : _m(m) {}
   1.493 -    /// \e
   1.494 +    ///\e
   1.495      Value operator[](const Key &k) const { return -_m[k]; }
   1.496    };
   1.497  
   1.498 @@ -1228,15 +1244,16 @@
   1.499    class NegWriteMap : public MapBase<typename M::Key, typename M::Value> {
   1.500      M &_m;
   1.501    public:
   1.502 -    typedef MapBase<typename M::Key, typename M::Value> Parent;
   1.503 -    typedef typename Parent::Key Key;
   1.504 -    typedef typename Parent::Value Value;
   1.505 +    ///\e
   1.506 +    typedef typename M::Key Key;
   1.507 +    ///\e
   1.508 +    typedef typename M::Value Value;
   1.509  
   1.510      /// Constructor
   1.511      NegWriteMap(M &m) : _m(m) {}
   1.512 -    /// \e
   1.513 +    ///\e
   1.514      Value operator[](const Key &k) const { return -_m[k]; }
   1.515 -    /// \e
   1.516 +    ///\e
   1.517      void set(const Key &k, const Value &v) { _m.set(k, -v); }
   1.518    };
   1.519  
   1.520 @@ -1282,13 +1299,14 @@
   1.521    class AbsMap : public MapBase<typename M::Key, typename M::Value> {
   1.522      const M &_m;
   1.523    public:
   1.524 -    typedef MapBase<typename M::Key, typename M::Value> Parent;
   1.525 -    typedef typename Parent::Key Key;
   1.526 -    typedef typename Parent::Value Value;
   1.527 +    ///\e
   1.528 +    typedef typename M::Key Key;
   1.529 +    ///\e
   1.530 +    typedef typename M::Value Value;
   1.531  
   1.532      /// Constructor
   1.533      AbsMap(const M &m) : _m(m) {}
   1.534 -    /// \e
   1.535 +    ///\e
   1.536      Value operator[](const Key &k) const {
   1.537        Value tmp = _m[k];
   1.538        return tmp >= 0 ? tmp : -tmp;
   1.539 @@ -1337,9 +1355,10 @@
   1.540    template <typename K>
   1.541    class TrueMap : public MapBase<K, bool> {
   1.542    public:
   1.543 -    typedef MapBase<K, bool> Parent;
   1.544 -    typedef typename Parent::Key Key;
   1.545 -    typedef typename Parent::Value Value;
   1.546 +    ///\e
   1.547 +    typedef K Key;
   1.548 +    ///\e
   1.549 +    typedef bool Value;
   1.550  
   1.551      /// Gives back \c true.
   1.552      Value operator[](const Key&) const { return true; }
   1.553 @@ -1374,9 +1393,10 @@
   1.554    template <typename K>
   1.555    class FalseMap : public MapBase<K, bool> {
   1.556    public:
   1.557 -    typedef MapBase<K, bool> Parent;
   1.558 -    typedef typename Parent::Key Key;
   1.559 -    typedef typename Parent::Value Value;
   1.560 +    ///\e
   1.561 +    typedef K Key;
   1.562 +    ///\e
   1.563 +    typedef bool Value;
   1.564  
   1.565      /// Gives back \c false.
   1.566      Value operator[](const Key&) const { return false; }
   1.567 @@ -1419,13 +1439,14 @@
   1.568      const M1 &_m1;
   1.569      const M2 &_m2;
   1.570    public:
   1.571 -    typedef MapBase<typename M1::Key, bool> Parent;
   1.572 -    typedef typename Parent::Key Key;
   1.573 -    typedef typename Parent::Value Value;
   1.574 +    ///\e
   1.575 +    typedef typename M1::Key Key;
   1.576 +    ///\e
   1.577 +    typedef bool Value;
   1.578  
   1.579      /// Constructor
   1.580      AndMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
   1.581 -    /// \e
   1.582 +    ///\e
   1.583      Value operator[](const Key &k) const { return _m1[k]&&_m2[k]; }
   1.584    };
   1.585  
   1.586 @@ -1467,13 +1488,14 @@
   1.587      const M1 &_m1;
   1.588      const M2 &_m2;
   1.589    public:
   1.590 -    typedef MapBase<typename M1::Key, bool> Parent;
   1.591 -    typedef typename Parent::Key Key;
   1.592 -    typedef typename Parent::Value Value;
   1.593 +    ///\e
   1.594 +    typedef typename M1::Key Key;
   1.595 +    ///\e
   1.596 +    typedef bool Value;
   1.597  
   1.598      /// Constructor
   1.599      OrMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
   1.600 -    /// \e
   1.601 +    ///\e
   1.602      Value operator[](const Key &k) const { return _m1[k]||_m2[k]; }
   1.603    };
   1.604  
   1.605 @@ -1506,13 +1528,14 @@
   1.606    class NotMap : public MapBase<typename M::Key, bool> {
   1.607      const M &_m;
   1.608    public:
   1.609 -    typedef MapBase<typename M::Key, bool> Parent;
   1.610 -    typedef typename Parent::Key Key;
   1.611 -    typedef typename Parent::Value Value;
   1.612 +    ///\e
   1.613 +    typedef typename M::Key Key;
   1.614 +    ///\e
   1.615 +    typedef bool Value;
   1.616  
   1.617      /// Constructor
   1.618      NotMap(const M &m) : _m(m) {}
   1.619 -    /// \e
   1.620 +    ///\e
   1.621      Value operator[](const Key &k) const { return !_m[k]; }
   1.622    };
   1.623  
   1.624 @@ -1532,15 +1555,16 @@
   1.625    class NotWriteMap : public MapBase<typename M::Key, bool> {
   1.626      M &_m;
   1.627    public:
   1.628 -    typedef MapBase<typename M::Key, bool> Parent;
   1.629 -    typedef typename Parent::Key Key;
   1.630 -    typedef typename Parent::Value Value;
   1.631 +    ///\e
   1.632 +    typedef typename M::Key Key;
   1.633 +    ///\e
   1.634 +    typedef bool Value;
   1.635  
   1.636      /// Constructor
   1.637      NotWriteMap(M &m) : _m(m) {}
   1.638 -    /// \e
   1.639 +    ///\e
   1.640      Value operator[](const Key &k) const { return !_m[k]; }
   1.641 -    /// \e
   1.642 +    ///\e
   1.643      void set(const Key &k, bool v) { _m.set(k, !v); }
   1.644    };
   1.645  
   1.646 @@ -1595,13 +1619,14 @@
   1.647      const M1 &_m1;
   1.648      const M2 &_m2;
   1.649    public:
   1.650 -    typedef MapBase<typename M1::Key, bool> Parent;
   1.651 -    typedef typename Parent::Key Key;
   1.652 -    typedef typename Parent::Value Value;
   1.653 +    ///\e
   1.654 +    typedef typename M1::Key Key;
   1.655 +    ///\e
   1.656 +    typedef bool Value;
   1.657  
   1.658      /// Constructor
   1.659      EqualMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
   1.660 -    /// \e
   1.661 +    ///\e
   1.662      Value operator[](const Key &k) const { return _m1[k]==_m2[k]; }
   1.663    };
   1.664  
   1.665 @@ -1643,13 +1668,14 @@
   1.666      const M1 &_m1;
   1.667      const M2 &_m2;
   1.668    public:
   1.669 -    typedef MapBase<typename M1::Key, bool> Parent;
   1.670 -    typedef typename Parent::Key Key;
   1.671 -    typedef typename Parent::Value Value;
   1.672 +    ///\e
   1.673 +    typedef typename M1::Key Key;
   1.674 +    ///\e
   1.675 +    typedef bool Value;
   1.676  
   1.677      /// Constructor
   1.678      LessMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
   1.679 -    /// \e
   1.680 +    ///\e
   1.681      Value operator[](const Key &k) const { return _m1[k]<_m2[k]; }
   1.682    };
   1.683  
   1.684 @@ -1705,24 +1731,27 @@
   1.685    /// The simplest way of using this map is through the loggerBoolMap()
   1.686    /// function.
   1.687    ///
   1.688 -  /// \tparam It The type of the iterator.
   1.689 -  /// \tparam Ke The key type of the map. The default value set
   1.690 +  /// \tparam IT The type of the iterator.
   1.691 +  /// \tparam KEY The key type of the map. The default value set
   1.692    /// according to the iterator type should work in most cases.
   1.693    ///
   1.694    /// \note The container of the iterator must contain enough space
   1.695    /// for the elements or the iterator should be an inserter iterator.
   1.696  #ifdef DOXYGEN
   1.697 -  template <typename It, typename Ke>
   1.698 +  template <typename IT, typename KEY>
   1.699  #else
   1.700 -  template <typename It,
   1.701 -            typename Ke=typename _maps_bits::IteratorTraits<It>::Value>
   1.702 +  template <typename IT,
   1.703 +            typename KEY = typename _maps_bits::IteratorTraits<IT>::Value>
   1.704  #endif
   1.705 -  class LoggerBoolMap {
   1.706 +  class LoggerBoolMap : public MapBase<KEY, bool> {
   1.707    public:
   1.708 -    typedef It Iterator;
   1.709 -
   1.710 -    typedef Ke Key;
   1.711 +
   1.712 +    ///\e
   1.713 +    typedef KEY Key;
   1.714 +    ///\e
   1.715      typedef bool Value;
   1.716 +    ///\e
   1.717 +    typedef IT Iterator;
   1.718  
   1.719      /// Constructor
   1.720      LoggerBoolMap(Iterator it)
   1.721 @@ -1760,11 +1789,11 @@
   1.722    /// order of Dfs algorithm, as the following examples show.
   1.723    /// \code
   1.724    ///   std::vector<Node> v;
   1.725 -  ///   dfs(g,s).processedMap(loggerBoolMap(std::back_inserter(v))).run();
   1.726 +  ///   dfs(g).processedMap(loggerBoolMap(std::back_inserter(v))).run(s);
   1.727    /// \endcode
   1.728    /// \code
   1.729    ///   std::vector<Node> v(countNodes(g));
   1.730 -  ///   dfs(g,s).processedMap(loggerBoolMap(v.begin())).run();
   1.731 +  ///   dfs(g).processedMap(loggerBoolMap(v.begin())).run(s);
   1.732    /// \endcode
   1.733    ///
   1.734    /// \note The container of the iterator must contain enough space
   1.735 @@ -1785,23 +1814,36 @@
   1.736    /// \addtogroup graph_maps
   1.737    /// @{
   1.738  
   1.739 -  /// Provides an immutable and unique id for each item in the graph.
   1.740 -
   1.741 -  /// The IdMap class provides a unique and immutable id for each item of the
   1.742 -  /// same type (e.g. node) in the graph. This id is <ul><li>\b unique:
   1.743 -  /// different items (nodes) get different ids <li>\b immutable: the id of an
   1.744 -  /// item (node) does not change (even if you delete other nodes).  </ul>
   1.745 -  /// Through this map you get access (i.e. can read) the inner id values of
   1.746 -  /// the items stored in the graph. This map can be inverted with its member
   1.747 -  /// class \c InverseMap or with the \c operator() member.
   1.748 +  /// \brief Provides an immutable and unique id for each item in a graph.
   1.749    ///
   1.750 -  template <typename _Graph, typename _Item>
   1.751 -  class IdMap {
   1.752 +  /// IdMap provides a unique and immutable id for each item of the
   1.753 +  /// same type (\c Node, \c Arc or \c Edge) in a graph. This id is
   1.754 +  ///  - \b unique: different items get different ids,
   1.755 +  ///  - \b immutable: the id of an item does not change (even if you
   1.756 +  ///    delete other nodes).
   1.757 +  ///
   1.758 +  /// Using this map you get access (i.e. can read) the inner id values of
   1.759 +  /// the items stored in the graph, which is returned by the \c id()
   1.760 +  /// function of the graph. This map can be inverted with its member
   1.761 +  /// class \c InverseMap or with the \c operator()() member.
   1.762 +  ///
   1.763 +  /// \tparam GR The graph type.
   1.764 +  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
   1.765 +  /// \c GR::Edge).
   1.766 +  ///
   1.767 +  /// \see RangeIdMap
   1.768 +  template <typename GR, typename K>
   1.769 +  class IdMap : public MapBase<K, int> {
   1.770    public:
   1.771 -    typedef _Graph Graph;
   1.772 +    /// The graph type of IdMap.
   1.773 +    typedef GR Graph;
   1.774 +    typedef GR Digraph;
   1.775 +    /// The key type of IdMap (\c Node, \c Arc or \c Edge).
   1.776 +    typedef K Item;
   1.777 +    /// The key type of IdMap (\c Node, \c Arc or \c Edge).
   1.778 +    typedef K Key;
   1.779 +    /// The value type of IdMap.
   1.780      typedef int Value;
   1.781 -    typedef _Item Item;
   1.782 -    typedef _Item Key;
   1.783  
   1.784      /// \brief Constructor.
   1.785      ///
   1.786 @@ -1813,9 +1855,9 @@
   1.787      /// Gives back the immutable and unique \e id of the item.
   1.788      int operator[](const Item& item) const { return _graph->id(item);}
   1.789  
   1.790 -    /// \brief Gives back the item by its id.
   1.791 +    /// \brief Gives back the \e item by its id.
   1.792      ///
   1.793 -    /// Gives back the item by its id.
   1.794 +    /// Gives back the \e item by its id.
   1.795      Item operator()(int id) { return _graph->fromId(id, Item()); }
   1.796  
   1.797    private:
   1.798 @@ -1823,9 +1865,11 @@
   1.799  
   1.800    public:
   1.801  
   1.802 -    /// \brief The class represents the inverse of its owner (IdMap).
   1.803 +    /// \brief The inverse map type of IdMap.
   1.804      ///
   1.805 -    /// The class represents the inverse of its owner (IdMap).
   1.806 +    /// The inverse map type of IdMap. The subscript operator gives back
   1.807 +    /// an item by its id.
   1.808 +    /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
   1.809      /// \see inverse()
   1.810      class InverseMap {
   1.811      public:
   1.812 @@ -1840,10 +1884,9 @@
   1.813        /// Constructor for creating an id-to-item map.
   1.814        explicit InverseMap(const IdMap& map) : _graph(map._graph) {}
   1.815  
   1.816 -      /// \brief Gives back the given item from its id.
   1.817 +      /// \brief Gives back an item by its id.
   1.818        ///
   1.819 -      /// Gives back the given item from its id.
   1.820 -      ///
   1.821 +      /// Gives back an item by its id.
   1.822        Item operator[](int id) const { return _graph->fromId(id, Item());}
   1.823  
   1.824      private:
   1.825 @@ -1854,165 +1897,220 @@
   1.826      ///
   1.827      /// Gives back the inverse of the IdMap.
   1.828      InverseMap inverse() const { return InverseMap(*_graph);}
   1.829 -
   1.830    };
   1.831  
   1.832 -
   1.833 -  /// \brief General invertable graph-map type.
   1.834 -
   1.835 -  /// This type provides simple invertable graph-maps.
   1.836 -  /// The InvertableMap wraps an arbitrary ReadWriteMap
   1.837 -  /// and if a key is set to a new value then store it
   1.838 -  /// in the inverse map.
   1.839 +  /// \brief Returns an \c IdMap class.
   1.840    ///
   1.841 -  /// The values of the map can be accessed
   1.842 -  /// with stl compatible forward iterator.
   1.843 +  /// This function just returns an \c IdMap class.
   1.844 +  /// \relates IdMap
   1.845 +  template <typename K, typename GR>
   1.846 +  inline IdMap<GR, K> idMap(const GR& graph) {
   1.847 +    return IdMap<GR, K>(graph);
   1.848 +  }
   1.849 +
   1.850 +  /// \brief General cross reference graph map type.
   1.851 +
   1.852 +  /// This class provides simple invertable graph maps.
   1.853 +  /// It wraps a standard graph map (\c NodeMap, \c ArcMap or \c EdgeMap)
   1.854 +  /// and if a key is set to a new value, then stores it in the inverse map.
   1.855 +  /// The graph items can be accessed by their values either using
   1.856 +  /// \c InverseMap or \c operator()(), and the values of the map can be
   1.857 +  /// accessed with an STL compatible forward iterator (\c ValueIt).
   1.858 +  /// 
   1.859 +  /// This map is intended to be used when all associated values are
   1.860 +  /// different (the map is actually invertable) or there are only a few
   1.861 +  /// items with the same value.
   1.862 +  /// Otherwise consider to use \c IterableValueMap, which is more 
   1.863 +  /// suitable and more efficient for such cases. It provides iterators
   1.864 +  /// to traverse the items with the same associated value, however
   1.865 +  /// it does not have \c InverseMap.
   1.866    ///
   1.867 -  /// \tparam _Graph The graph type.
   1.868 -  /// \tparam _Item The item type of the graph.
   1.869 -  /// \tparam _Value The value type of the map.
   1.870 +  /// This type is not reference map, so it cannot be modified with
   1.871 +  /// the subscript operator.
   1.872 +  ///
   1.873 +  /// \tparam GR The graph type.
   1.874 +  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
   1.875 +  /// \c GR::Edge).
   1.876 +  /// \tparam V The value type of the map.
   1.877    ///
   1.878    /// \see IterableValueMap
   1.879 -  template <typename _Graph, typename _Item, typename _Value>
   1.880 -  class InvertableMap
   1.881 -    : protected ItemSetTraits<_Graph, _Item>::template Map<_Value>::Type {
   1.882 +  template <typename GR, typename K, typename V>
   1.883 +  class CrossRefMap
   1.884 +    : protected ItemSetTraits<GR, K>::template Map<V>::Type {
   1.885    private:
   1.886  
   1.887 -    typedef typename ItemSetTraits<_Graph, _Item>::
   1.888 -    template Map<_Value>::Type Map;
   1.889 -    typedef _Graph Graph;
   1.890 -
   1.891 -    typedef std::map<_Value, _Item> Container;
   1.892 +    typedef typename ItemSetTraits<GR, K>::
   1.893 +      template Map<V>::Type Map;
   1.894 +
   1.895 +    typedef std::multimap<V, K> Container;
   1.896      Container _inv_map;
   1.897  
   1.898    public:
   1.899  
   1.900 -    /// The key type of InvertableMap (Node, Arc, Edge).
   1.901 -    typedef typename Map::Key Key;
   1.902 -    /// The value type of the InvertableMap.
   1.903 -    typedef typename Map::Value Value;
   1.904 +    /// The graph type of CrossRefMap.
   1.905 +    typedef GR Graph;
   1.906 +    typedef GR Digraph;
   1.907 +    /// The key type of CrossRefMap (\c Node, \c Arc or \c Edge).
   1.908 +    typedef K Item;
   1.909 +    /// The key type of CrossRefMap (\c Node, \c Arc or \c Edge).
   1.910 +    typedef K Key;
   1.911 +    /// The value type of CrossRefMap.
   1.912 +    typedef V Value;
   1.913  
   1.914      /// \brief Constructor.
   1.915      ///
   1.916 -    /// Construct a new InvertableMap for the graph.
   1.917 -    ///
   1.918 -    explicit InvertableMap(const Graph& graph) : Map(graph) {}
   1.919 +    /// Construct a new CrossRefMap for the given graph.
   1.920 +    explicit CrossRefMap(const Graph& graph) : Map(graph) {}
   1.921  
   1.922      /// \brief Forward iterator for values.
   1.923      ///
   1.924 -    /// This iterator is an stl compatible forward
   1.925 +    /// This iterator is an STL compatible forward
   1.926      /// iterator on the values of the map. The values can
   1.927 -    /// be accessed in the [beginValue, endValue) range.
   1.928 -    ///
   1.929 -    class ValueIterator
   1.930 +    /// be accessed in the <tt>[beginValue, endValue)</tt> range.
   1.931 +    /// They are considered with multiplicity, so each value is
   1.932 +    /// traversed for each item it is assigned to.
   1.933 +    class ValueIt
   1.934        : public std::iterator<std::forward_iterator_tag, Value> {
   1.935 -      friend class InvertableMap;
   1.936 +      friend class CrossRefMap;
   1.937      private:
   1.938 -      ValueIterator(typename Container::const_iterator _it)
   1.939 +      ValueIt(typename Container::const_iterator _it)
   1.940          : it(_it) {}
   1.941      public:
   1.942  
   1.943 -      ValueIterator() {}
   1.944 -
   1.945 -      ValueIterator& operator++() { ++it; return *this; }
   1.946 -      ValueIterator operator++(int) {
   1.947 -        ValueIterator tmp(*this);
   1.948 +      /// Constructor
   1.949 +      ValueIt() {}
   1.950 +
   1.951 +      /// \e
   1.952 +      ValueIt& operator++() { ++it; return *this; }
   1.953 +      /// \e
   1.954 +      ValueIt operator++(int) {
   1.955 +        ValueIt tmp(*this);
   1.956          operator++();
   1.957          return tmp;
   1.958        }
   1.959  
   1.960 +      /// \e
   1.961        const Value& operator*() const { return it->first; }
   1.962 +      /// \e
   1.963        const Value* operator->() const { return &(it->first); }
   1.964  
   1.965 -      bool operator==(ValueIterator jt) const { return it == jt.it; }
   1.966 -      bool operator!=(ValueIterator jt) const { return it != jt.it; }
   1.967 +      /// \e
   1.968 +      bool operator==(ValueIt jt) const { return it == jt.it; }
   1.969 +      /// \e
   1.970 +      bool operator!=(ValueIt jt) const { return it != jt.it; }
   1.971  
   1.972      private:
   1.973        typename Container::const_iterator it;
   1.974      };
   1.975 +    
   1.976 +    /// Alias for \c ValueIt
   1.977 +    typedef ValueIt ValueIterator;
   1.978  
   1.979      /// \brief Returns an iterator to the first value.
   1.980      ///
   1.981 -    /// Returns an stl compatible iterator to the
   1.982 +    /// Returns an STL compatible iterator to the
   1.983      /// first value of the map. The values of the
   1.984 -    /// map can be accessed in the [beginValue, endValue)
   1.985 +    /// map can be accessed in the <tt>[beginValue, endValue)</tt>
   1.986      /// range.
   1.987 -    ValueIterator beginValue() const {
   1.988 -      return ValueIterator(_inv_map.begin());
   1.989 +    ValueIt beginValue() const {
   1.990 +      return ValueIt(_inv_map.begin());
   1.991      }
   1.992  
   1.993      /// \brief Returns an iterator after the last value.
   1.994      ///
   1.995 -    /// Returns an stl compatible iterator after the
   1.996 +    /// Returns an STL compatible iterator after the
   1.997      /// last value of the map. The values of the
   1.998 -    /// map can be accessed in the [beginValue, endValue)
   1.999 +    /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  1.1000      /// range.
  1.1001 -    ValueIterator endValue() const {
  1.1002 -      return ValueIterator(_inv_map.end());
  1.1003 +    ValueIt endValue() const {
  1.1004 +      return ValueIt(_inv_map.end());
  1.1005      }
  1.1006  
  1.1007 -    /// \brief The setter function of the map.
  1.1008 +    /// \brief Sets the value associated with the given key.
  1.1009      ///
  1.1010 -    /// Sets the mapped value.
  1.1011 +    /// Sets the value associated with the given key.
  1.1012      void set(const Key& key, const Value& val) {
  1.1013        Value oldval = Map::operator[](key);
  1.1014 -      typename Container::iterator it = _inv_map.find(oldval);
  1.1015 -      if (it != _inv_map.end() && it->second == key) {
  1.1016 -        _inv_map.erase(it);
  1.1017 +      typename Container::iterator it;
  1.1018 +      for (it = _inv_map.equal_range(oldval).first;
  1.1019 +           it != _inv_map.equal_range(oldval).second; ++it) {
  1.1020 +        if (it->second == key) {
  1.1021 +          _inv_map.erase(it);
  1.1022 +          break;
  1.1023 +        }
  1.1024        }
  1.1025 -      _inv_map.insert(make_pair(val, key));
  1.1026 +      _inv_map.insert(std::make_pair(val, key));
  1.1027        Map::set(key, val);
  1.1028      }
  1.1029  
  1.1030 -    /// \brief The getter function of the map.
  1.1031 +    /// \brief Returns the value associated with the given key.
  1.1032      ///
  1.1033 -    /// It gives back the value associated with the key.
  1.1034 +    /// Returns the value associated with the given key.
  1.1035      typename MapTraits<Map>::ConstReturnValue
  1.1036      operator[](const Key& key) const {
  1.1037        return Map::operator[](key);
  1.1038      }
  1.1039  
  1.1040 -    /// \brief Gives back the item by its value.
  1.1041 +    /// \brief Gives back an item by its value.
  1.1042      ///
  1.1043 -    /// Gives back the item by its value.
  1.1044 -    Key operator()(const Value& key) const {
  1.1045 -      typename Container::const_iterator it = _inv_map.find(key);
  1.1046 +    /// This function gives back an item that is assigned to
  1.1047 +    /// the given value or \c INVALID if no such item exists.
  1.1048 +    /// If there are more items with the same associated value,
  1.1049 +    /// only one of them is returned.
  1.1050 +    Key operator()(const Value& val) const {
  1.1051 +      typename Container::const_iterator it = _inv_map.find(val);
  1.1052        return it != _inv_map.end() ? it->second : INVALID;
  1.1053      }
  1.1054 +    
  1.1055 +    /// \brief Returns the number of items with the given value.
  1.1056 +    ///
  1.1057 +    /// This function returns the number of items with the given value
  1.1058 +    /// associated with it.
  1.1059 +    int count(const Value &val) const {
  1.1060 +      return _inv_map.count(val);
  1.1061 +    }
  1.1062  
  1.1063    protected:
  1.1064  
  1.1065 -    /// \brief Erase the key from the map.
  1.1066 +    /// \brief Erase the key from the map and the inverse map.
  1.1067      ///
  1.1068 -    /// Erase the key to the map. It is called by the
  1.1069 +    /// Erase the key from the map and the inverse map. It is called by the
  1.1070      /// \c AlterationNotifier.
  1.1071      virtual void erase(const Key& key) {
  1.1072        Value val = Map::operator[](key);
  1.1073 -      typename Container::iterator it = _inv_map.find(val);
  1.1074 -      if (it != _inv_map.end() && it->second == key) {
  1.1075 -        _inv_map.erase(it);
  1.1076 +      typename Container::iterator it;
  1.1077 +      for (it = _inv_map.equal_range(val).first;
  1.1078 +           it != _inv_map.equal_range(val).second; ++it) {
  1.1079 +        if (it->second == key) {
  1.1080 +          _inv_map.erase(it);
  1.1081 +          break;
  1.1082 +        }
  1.1083        }
  1.1084        Map::erase(key);
  1.1085      }
  1.1086  
  1.1087 -    /// \brief Erase more keys from the map.
  1.1088 +    /// \brief Erase more keys from the map and the inverse map.
  1.1089      ///
  1.1090 -    /// Erase more keys from the map. It is called by the
  1.1091 +    /// Erase more keys from the map and the inverse map. It is called by the
  1.1092      /// \c AlterationNotifier.
  1.1093      virtual void erase(const std::vector<Key>& keys) {
  1.1094        for (int i = 0; i < int(keys.size()); ++i) {
  1.1095          Value val = Map::operator[](keys[i]);
  1.1096 -        typename Container::iterator it = _inv_map.find(val);
  1.1097 -        if (it != _inv_map.end() && it->second == keys[i]) {
  1.1098 -          _inv_map.erase(it);
  1.1099 +        typename Container::iterator it;
  1.1100 +        for (it = _inv_map.equal_range(val).first;
  1.1101 +             it != _inv_map.equal_range(val).second; ++it) {
  1.1102 +          if (it->second == keys[i]) {
  1.1103 +            _inv_map.erase(it);
  1.1104 +            break;
  1.1105 +          }
  1.1106          }
  1.1107        }
  1.1108        Map::erase(keys);
  1.1109      }
  1.1110  
  1.1111 -    /// \brief Clear the keys from the map and inverse map.
  1.1112 +    /// \brief Clear the keys from the map and the inverse map.
  1.1113      ///
  1.1114 -    /// Clear the keys from the map and inverse map. It is called by the
  1.1115 +    /// Clear the keys from the map and the inverse map. It is called by the
  1.1116      /// \c AlterationNotifier.
  1.1117      virtual void clear() {
  1.1118        _inv_map.clear();
  1.1119 @@ -2021,79 +2119,90 @@
  1.1120  
  1.1121    public:
  1.1122  
  1.1123 -    /// \brief The inverse map type.
  1.1124 +    /// \brief The inverse map type of CrossRefMap.
  1.1125      ///
  1.1126 -    /// The inverse of this map. The subscript operator of the map
  1.1127 -    /// gives back always the item what was last assigned to the value.
  1.1128 +    /// The inverse map type of CrossRefMap. The subscript operator gives
  1.1129 +    /// back an item by its value.
  1.1130 +    /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
  1.1131 +    /// \see inverse()
  1.1132      class InverseMap {
  1.1133      public:
  1.1134 -      /// \brief Constructor of the InverseMap.
  1.1135 +      /// \brief Constructor
  1.1136        ///
  1.1137        /// Constructor of the InverseMap.
  1.1138 -      explicit InverseMap(const InvertableMap& inverted)
  1.1139 +      explicit InverseMap(const CrossRefMap& inverted)
  1.1140          : _inverted(inverted) {}
  1.1141  
  1.1142        /// The value type of the InverseMap.
  1.1143 -      typedef typename InvertableMap::Key Value;
  1.1144 +      typedef typename CrossRefMap::Key Value;
  1.1145        /// The key type of the InverseMap.
  1.1146 -      typedef typename InvertableMap::Value Key;
  1.1147 +      typedef typename CrossRefMap::Value Key;
  1.1148  
  1.1149        /// \brief Subscript operator.
  1.1150        ///
  1.1151 -      /// Subscript operator. It gives back always the item
  1.1152 -      /// what was last assigned to the value.
  1.1153 +      /// Subscript operator. It gives back an item
  1.1154 +      /// that is assigned to the given value or \c INVALID
  1.1155 +      /// if no such item exists.
  1.1156        Value operator[](const Key& key) const {
  1.1157          return _inverted(key);
  1.1158        }
  1.1159  
  1.1160      private:
  1.1161 -      const InvertableMap& _inverted;
  1.1162 +      const CrossRefMap& _inverted;
  1.1163      };
  1.1164  
  1.1165 -    /// \brief It gives back the just readable inverse map.
  1.1166 +    /// \brief Gives back the inverse of the map.
  1.1167      ///
  1.1168 -    /// It gives back the just readable inverse map.
  1.1169 +    /// Gives back the inverse of the CrossRefMap.
  1.1170      InverseMap inverse() const {
  1.1171        return InverseMap(*this);
  1.1172      }
  1.1173  
  1.1174    };
  1.1175  
  1.1176 -  /// \brief Provides a mutable, continuous and unique descriptor for each
  1.1177 -  /// item in the graph.
  1.1178 +  /// \brief Provides continuous and unique id for the
  1.1179 +  /// items of a graph.
  1.1180    ///
  1.1181 -  /// The DescriptorMap class provides a unique and continuous (but mutable)
  1.1182 -  /// descriptor (id) for each item of the same type (e.g. node) in the
  1.1183 -  /// graph. This id is <ul><li>\b unique: different items (nodes) get
  1.1184 -  /// different ids <li>\b continuous: the range of the ids is the set of
  1.1185 -  /// integers between 0 and \c n-1, where \c n is the number of the items of
  1.1186 -  /// this type (e.g. nodes) (so the id of a node can change if you delete an
  1.1187 -  /// other node, i.e. this id is mutable).  </ul> This map can be inverted
  1.1188 -  /// with its member class \c InverseMap, or with the \c operator() member.
  1.1189 +  /// RangeIdMap provides a unique and continuous
  1.1190 +  /// id for each item of a given type (\c Node, \c Arc or
  1.1191 +  /// \c Edge) in a graph. This id is
  1.1192 +  ///  - \b unique: different items get different ids,
  1.1193 +  ///  - \b continuous: the range of the ids is the set of integers
  1.1194 +  ///    between 0 and \c n-1, where \c n is the number of the items of
  1.1195 +  ///    this type (\c Node, \c Arc or \c Edge).
  1.1196 +  ///  - So, the ids can change when deleting an item of the same type.
  1.1197    ///
  1.1198 -  /// \tparam _Graph The graph class the \c DescriptorMap belongs to.
  1.1199 -  /// \tparam _Item The Item is the Key of the Map. It may be Node, Arc or
  1.1200 -  /// Edge.
  1.1201 -  template <typename _Graph, typename _Item>
  1.1202 -  class DescriptorMap
  1.1203 -    : protected ItemSetTraits<_Graph, _Item>::template Map<int>::Type {
  1.1204 -
  1.1205 -    typedef _Item Item;
  1.1206 -    typedef typename ItemSetTraits<_Graph, _Item>::template Map<int>::Type Map;
  1.1207 +  /// Thus this id is not (necessarily) the same as what can get using
  1.1208 +  /// the \c id() function of the graph or \ref IdMap.
  1.1209 +  /// This map can be inverted with its member class \c InverseMap,
  1.1210 +  /// or with the \c operator()() member.
  1.1211 +  ///
  1.1212 +  /// \tparam GR The graph type.
  1.1213 +  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  1.1214 +  /// \c GR::Edge).
  1.1215 +  ///
  1.1216 +  /// \see IdMap
  1.1217 +  template <typename GR, typename K>
  1.1218 +  class RangeIdMap
  1.1219 +    : protected ItemSetTraits<GR, K>::template Map<int>::Type {
  1.1220 +
  1.1221 +    typedef typename ItemSetTraits<GR, K>::template Map<int>::Type Map;
  1.1222  
  1.1223    public:
  1.1224 -    /// The graph class of DescriptorMap.
  1.1225 -    typedef _Graph Graph;
  1.1226 -
  1.1227 -    /// The key type of DescriptorMap (Node, Arc, Edge).
  1.1228 -    typedef typename Map::Key Key;
  1.1229 -    /// The value type of DescriptorMap.
  1.1230 -    typedef typename Map::Value Value;
  1.1231 +    /// The graph type of RangeIdMap.
  1.1232 +    typedef GR Graph;
  1.1233 +    typedef GR Digraph;
  1.1234 +    /// The key type of RangeIdMap (\c Node, \c Arc or \c Edge).
  1.1235 +    typedef K Item;
  1.1236 +    /// The key type of RangeIdMap (\c Node, \c Arc or \c Edge).
  1.1237 +    typedef K Key;
  1.1238 +    /// The value type of RangeIdMap.
  1.1239 +    typedef int Value;
  1.1240  
  1.1241      /// \brief Constructor.
  1.1242      ///
  1.1243 -    /// Constructor for descriptor map.
  1.1244 -    explicit DescriptorMap(const Graph& _graph) : Map(_graph) {
  1.1245 +    /// Constructor.
  1.1246 +    explicit RangeIdMap(const Graph& gr) : Map(gr) {
  1.1247        Item it;
  1.1248        const typename Map::Notifier* nf = Map::notifier();
  1.1249        for (nf->first(it); it != INVALID; nf->next(it)) {
  1.1250 @@ -2104,7 +2213,7 @@
  1.1251  
  1.1252    protected:
  1.1253  
  1.1254 -    /// \brief Add a new key to the map.
  1.1255 +    /// \brief Adds a new key to the map.
  1.1256      ///
  1.1257      /// Add a new key to the map. It is called by the
  1.1258      /// \c AlterationNotifier.
  1.1259 @@ -2194,16 +2303,16 @@
  1.1260        _inv_map[pi] = q;
  1.1261      }
  1.1262  
  1.1263 -    /// \brief Gives back the \e descriptor of the item.
  1.1264 +    /// \brief Gives back the \e range \e id of the item
  1.1265      ///
  1.1266 -    /// Gives back the mutable and unique \e descriptor of the map.
  1.1267 +    /// Gives back the \e range \e id of the item.
  1.1268      int operator[](const Item& item) const {
  1.1269        return Map::operator[](item);
  1.1270      }
  1.1271  
  1.1272 -    /// \brief Gives back the item by its descriptor.
  1.1273 +    /// \brief Gives back the item belonging to a \e range \e id
  1.1274      ///
  1.1275 -    /// Gives back th item by its descriptor.
  1.1276 +    /// Gives back the item belonging to the given \e range \e id.
  1.1277      Item operator()(int id) const {
  1.1278        return _inv_map[id];
  1.1279      }
  1.1280 @@ -2214,27 +2323,30 @@
  1.1281      Container _inv_map;
  1.1282  
  1.1283    public:
  1.1284 -    /// \brief The inverse map type of DescriptorMap.
  1.1285 +
  1.1286 +    /// \brief The inverse map type of RangeIdMap.
  1.1287      ///
  1.1288 -    /// The inverse map type of DescriptorMap.
  1.1289 +    /// The inverse map type of RangeIdMap. The subscript operator gives
  1.1290 +    /// back an item by its \e range \e id.
  1.1291 +    /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
  1.1292      class InverseMap {
  1.1293      public:
  1.1294 -      /// \brief Constructor of the InverseMap.
  1.1295 +      /// \brief Constructor
  1.1296        ///
  1.1297        /// Constructor of the InverseMap.
  1.1298 -      explicit InverseMap(const DescriptorMap& inverted)
  1.1299 +      explicit InverseMap(const RangeIdMap& inverted)
  1.1300          : _inverted(inverted) {}
  1.1301  
  1.1302  
  1.1303        /// The value type of the InverseMap.
  1.1304 -      typedef typename DescriptorMap::Key Value;
  1.1305 +      typedef typename RangeIdMap::Key Value;
  1.1306        /// The key type of the InverseMap.
  1.1307 -      typedef typename DescriptorMap::Value Key;
  1.1308 +      typedef typename RangeIdMap::Value Key;
  1.1309  
  1.1310        /// \brief Subscript operator.
  1.1311        ///
  1.1312        /// Subscript operator. It gives back the item
  1.1313 -      /// that the descriptor belongs to currently.
  1.1314 +      /// that the given \e range \e id currently belongs to.
  1.1315        Value operator[](const Key& key) const {
  1.1316          return _inverted(key);
  1.1317        }
  1.1318 @@ -2247,241 +2359,1134 @@
  1.1319        }
  1.1320  
  1.1321      private:
  1.1322 -      const DescriptorMap& _inverted;
  1.1323 +      const RangeIdMap& _inverted;
  1.1324      };
  1.1325  
  1.1326      /// \brief Gives back the inverse of the map.
  1.1327      ///
  1.1328 -    /// Gives back the inverse of the map.
  1.1329 +    /// Gives back the inverse of the RangeIdMap.
  1.1330      const InverseMap inverse() const {
  1.1331        return InverseMap(*this);
  1.1332      }
  1.1333    };
  1.1334  
  1.1335 -  /// \brief Returns the source of the given arc.
  1.1336 +  /// \brief Returns a \c RangeIdMap class.
  1.1337    ///
  1.1338 -  /// The SourceMap gives back the source Node of the given arc.
  1.1339 +  /// This function just returns an \c RangeIdMap class.
  1.1340 +  /// \relates RangeIdMap
  1.1341 +  template <typename K, typename GR>
  1.1342 +  inline RangeIdMap<GR, K> rangeIdMap(const GR& graph) {
  1.1343 +    return RangeIdMap<GR, K>(graph);
  1.1344 +  }
  1.1345 +  
  1.1346 +  /// \brief Dynamic iterable \c bool map.
  1.1347 +  ///
  1.1348 +  /// This class provides a special graph map type which can store a
  1.1349 +  /// \c bool value for graph items (\c Node, \c Arc or \c Edge).
  1.1350 +  /// For both \c true and \c false values it is possible to iterate on
  1.1351 +  /// the keys mapped to the value.
  1.1352 +  ///
  1.1353 +  /// This type is a reference map, so it can be modified with the
  1.1354 +  /// subscript operator.
  1.1355 +  ///
  1.1356 +  /// \tparam GR The graph type.
  1.1357 +  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  1.1358 +  /// \c GR::Edge).
  1.1359 +  ///
  1.1360 +  /// \see IterableIntMap, IterableValueMap
  1.1361 +  /// \see CrossRefMap
  1.1362 +  template <typename GR, typename K>
  1.1363 +  class IterableBoolMap
  1.1364 +    : protected ItemSetTraits<GR, K>::template Map<int>::Type {
  1.1365 +  private:
  1.1366 +    typedef GR Graph;
  1.1367 +
  1.1368 +    typedef typename ItemSetTraits<GR, K>::ItemIt KeyIt;
  1.1369 +    typedef typename ItemSetTraits<GR, K>::template Map<int>::Type Parent;
  1.1370 +
  1.1371 +    std::vector<K> _array;
  1.1372 +    int _sep;
  1.1373 +
  1.1374 +  public:
  1.1375 +
  1.1376 +    /// Indicates that the map is reference map.
  1.1377 +    typedef True ReferenceMapTag;
  1.1378 +
  1.1379 +    /// The key type
  1.1380 +    typedef K Key;
  1.1381 +    /// The value type
  1.1382 +    typedef bool Value;
  1.1383 +    /// The const reference type.
  1.1384 +    typedef const Value& ConstReference;
  1.1385 +
  1.1386 +  private:
  1.1387 +
  1.1388 +    int position(const Key& key) const {
  1.1389 +      return Parent::operator[](key);
  1.1390 +    }
  1.1391 +
  1.1392 +  public:
  1.1393 +
  1.1394 +    /// \brief Reference to the value of the map.
  1.1395 +    ///
  1.1396 +    /// This class is similar to the \c bool type. It can be converted to
  1.1397 +    /// \c bool and it provides the same operators.
  1.1398 +    class Reference {
  1.1399 +      friend class IterableBoolMap;
  1.1400 +    private:
  1.1401 +      Reference(IterableBoolMap& map, const Key& key)
  1.1402 +        : _key(key), _map(map) {}
  1.1403 +    public:
  1.1404 +
  1.1405 +      Reference& operator=(const Reference& value) {
  1.1406 +        _map.set(_key, static_cast<bool>(value));
  1.1407 +         return *this;
  1.1408 +      }
  1.1409 +
  1.1410 +      operator bool() const {
  1.1411 +        return static_cast<const IterableBoolMap&>(_map)[_key];
  1.1412 +      }
  1.1413 +
  1.1414 +      Reference& operator=(bool value) {
  1.1415 +        _map.set(_key, value);
  1.1416 +        return *this;
  1.1417 +      }
  1.1418 +      Reference& operator&=(bool value) {
  1.1419 +        _map.set(_key, _map[_key] & value);
  1.1420 +        return *this;
  1.1421 +      }
  1.1422 +      Reference& operator|=(bool value) {
  1.1423 +        _map.set(_key, _map[_key] | value);
  1.1424 +        return *this;
  1.1425 +      }
  1.1426 +      Reference& operator^=(bool value) {
  1.1427 +        _map.set(_key, _map[_key] ^ value);
  1.1428 +        return *this;
  1.1429 +      }
  1.1430 +    private:
  1.1431 +      Key _key;
  1.1432 +      IterableBoolMap& _map;
  1.1433 +    };
  1.1434 +
  1.1435 +    /// \brief Constructor of the map with a default value.
  1.1436 +    ///
  1.1437 +    /// Constructor of the map with a default value.
  1.1438 +    explicit IterableBoolMap(const Graph& graph, bool def = false)
  1.1439 +      : Parent(graph) {
  1.1440 +      typename Parent::Notifier* nf = Parent::notifier();
  1.1441 +      Key it;
  1.1442 +      for (nf->first(it); it != INVALID; nf->next(it)) {
  1.1443 +        Parent::set(it, _array.size());
  1.1444 +        _array.push_back(it);
  1.1445 +      }
  1.1446 +      _sep = (def ? _array.size() : 0);
  1.1447 +    }
  1.1448 +
  1.1449 +    /// \brief Const subscript operator of the map.
  1.1450 +    ///
  1.1451 +    /// Const subscript operator of the map.
  1.1452 +    bool operator[](const Key& key) const {
  1.1453 +      return position(key) < _sep;
  1.1454 +    }
  1.1455 +
  1.1456 +    /// \brief Subscript operator of the map.
  1.1457 +    ///
  1.1458 +    /// Subscript operator of the map.
  1.1459 +    Reference operator[](const Key& key) {
  1.1460 +      return Reference(*this, key);
  1.1461 +    }
  1.1462 +
  1.1463 +    /// \brief Set operation of the map.
  1.1464 +    ///
  1.1465 +    /// Set operation of the map.
  1.1466 +    void set(const Key& key, bool value) {
  1.1467 +      int pos = position(key);
  1.1468 +      if (value) {
  1.1469 +        if (pos < _sep) return;
  1.1470 +        Key tmp = _array[_sep];
  1.1471 +        _array[_sep] = key;
  1.1472 +        Parent::set(key, _sep);
  1.1473 +        _array[pos] = tmp;
  1.1474 +        Parent::set(tmp, pos);
  1.1475 +        ++_sep;
  1.1476 +      } else {
  1.1477 +        if (pos >= _sep) return;
  1.1478 +        --_sep;
  1.1479 +        Key tmp = _array[_sep];
  1.1480 +        _array[_sep] = key;
  1.1481 +        Parent::set(key, _sep);
  1.1482 +        _array[pos] = tmp;
  1.1483 +        Parent::set(tmp, pos);
  1.1484 +      }
  1.1485 +    }
  1.1486 +
  1.1487 +    /// \brief Set all items.
  1.1488 +    ///
  1.1489 +    /// Set all items in the map.
  1.1490 +    /// \note Constant time operation.
  1.1491 +    void setAll(bool value) {
  1.1492 +      _sep = (value ? _array.size() : 0);
  1.1493 +    }
  1.1494 +
  1.1495 +    /// \brief Returns the number of the keys mapped to \c true.
  1.1496 +    ///
  1.1497 +    /// Returns the number of the keys mapped to \c true.
  1.1498 +    int trueNum() const {
  1.1499 +      return _sep;
  1.1500 +    }
  1.1501 +
  1.1502 +    /// \brief Returns the number of the keys mapped to \c false.
  1.1503 +    ///
  1.1504 +    /// Returns the number of the keys mapped to \c false.
  1.1505 +    int falseNum() const {
  1.1506 +      return _array.size() - _sep;
  1.1507 +    }
  1.1508 +
  1.1509 +    /// \brief Iterator for the keys mapped to \c true.
  1.1510 +    ///
  1.1511 +    /// Iterator for the keys mapped to \c true. It works
  1.1512 +    /// like a graph item iterator, it can be converted to
  1.1513 +    /// the key type of the map, incremented with \c ++ operator, and
  1.1514 +    /// if the iterator leaves the last valid key, it will be equal to
  1.1515 +    /// \c INVALID.
  1.1516 +    class TrueIt : public Key {
  1.1517 +    public:
  1.1518 +      typedef Key Parent;
  1.1519 +
  1.1520 +      /// \brief Creates an iterator.
  1.1521 +      ///
  1.1522 +      /// Creates an iterator. It iterates on the
  1.1523 +      /// keys mapped to \c true.
  1.1524 +      /// \param map The IterableBoolMap.
  1.1525 +      explicit TrueIt(const IterableBoolMap& map)
  1.1526 +        : Parent(map._sep > 0 ? map._array[map._sep - 1] : INVALID),
  1.1527 +          _map(&map) {}
  1.1528 +
  1.1529 +      /// \brief Invalid constructor \& conversion.
  1.1530 +      ///
  1.1531 +      /// This constructor initializes the iterator to be invalid.
  1.1532 +      /// \sa Invalid for more details.
  1.1533 +      TrueIt(Invalid) : Parent(INVALID), _map(0) {}
  1.1534 +
  1.1535 +      /// \brief Increment operator.
  1.1536 +      ///
  1.1537 +      /// Increment operator.
  1.1538 +      TrueIt& operator++() {
  1.1539 +        int pos = _map->position(*this);
  1.1540 +        Parent::operator=(pos > 0 ? _map->_array[pos - 1] : INVALID);
  1.1541 +        return *this;
  1.1542 +      }
  1.1543 +
  1.1544 +    private:
  1.1545 +      const IterableBoolMap* _map;
  1.1546 +    };
  1.1547 +
  1.1548 +    /// \brief Iterator for the keys mapped to \c false.
  1.1549 +    ///
  1.1550 +    /// Iterator for the keys mapped to \c false. It works
  1.1551 +    /// like a graph item iterator, it can be converted to
  1.1552 +    /// the key type of the map, incremented with \c ++ operator, and
  1.1553 +    /// if the iterator leaves the last valid key, it will be equal to
  1.1554 +    /// \c INVALID.
  1.1555 +    class FalseIt : public Key {
  1.1556 +    public:
  1.1557 +      typedef Key Parent;
  1.1558 +
  1.1559 +      /// \brief Creates an iterator.
  1.1560 +      ///
  1.1561 +      /// Creates an iterator. It iterates on the
  1.1562 +      /// keys mapped to \c false.
  1.1563 +      /// \param map The IterableBoolMap.
  1.1564 +      explicit FalseIt(const IterableBoolMap& map)
  1.1565 +        : Parent(map._sep < int(map._array.size()) ?
  1.1566 +                 map._array.back() : INVALID), _map(&map) {}
  1.1567 +
  1.1568 +      /// \brief Invalid constructor \& conversion.
  1.1569 +      ///
  1.1570 +      /// This constructor initializes the iterator to be invalid.
  1.1571 +      /// \sa Invalid for more details.
  1.1572 +      FalseIt(Invalid) : Parent(INVALID), _map(0) {}
  1.1573 +
  1.1574 +      /// \brief Increment operator.
  1.1575 +      ///
  1.1576 +      /// Increment operator.
  1.1577 +      FalseIt& operator++() {
  1.1578 +        int pos = _map->position(*this);
  1.1579 +        Parent::operator=(pos > _map->_sep ? _map->_array[pos - 1] : INVALID);
  1.1580 +        return *this;
  1.1581 +      }
  1.1582 +
  1.1583 +    private:
  1.1584 +      const IterableBoolMap* _map;
  1.1585 +    };
  1.1586 +
  1.1587 +    /// \brief Iterator for the keys mapped to a given value.
  1.1588 +    ///
  1.1589 +    /// Iterator for the keys mapped to a given value. It works
  1.1590 +    /// like a graph item iterator, it can be converted to
  1.1591 +    /// the key type of the map, incremented with \c ++ operator, and
  1.1592 +    /// if the iterator leaves the last valid key, it will be equal to
  1.1593 +    /// \c INVALID.
  1.1594 +    class ItemIt : public Key {
  1.1595 +    public:
  1.1596 +      typedef Key Parent;
  1.1597 +
  1.1598 +      /// \brief Creates an iterator with a value.
  1.1599 +      ///
  1.1600 +      /// Creates an iterator with a value. It iterates on the
  1.1601 +      /// keys mapped to the given value.
  1.1602 +      /// \param map The IterableBoolMap.
  1.1603 +      /// \param value The value.
  1.1604 +      ItemIt(const IterableBoolMap& map, bool value)
  1.1605 +        : Parent(value ? 
  1.1606 +                 (map._sep > 0 ?
  1.1607 +                  map._array[map._sep - 1] : INVALID) :
  1.1608 +                 (map._sep < int(map._array.size()) ?
  1.1609 +                  map._array.back() : INVALID)), _map(&map) {}
  1.1610 +
  1.1611 +      /// \brief Invalid constructor \& conversion.
  1.1612 +      ///
  1.1613 +      /// This constructor initializes the iterator to be invalid.
  1.1614 +      /// \sa Invalid for more details.
  1.1615 +      ItemIt(Invalid) : Parent(INVALID), _map(0) {}
  1.1616 +
  1.1617 +      /// \brief Increment operator.
  1.1618 +      ///
  1.1619 +      /// Increment operator.
  1.1620 +      ItemIt& operator++() {
  1.1621 +        int pos = _map->position(*this);
  1.1622 +        int _sep = pos >= _map->_sep ? _map->_sep : 0;
  1.1623 +        Parent::operator=(pos > _sep ? _map->_array[pos - 1] : INVALID);
  1.1624 +        return *this;
  1.1625 +      }
  1.1626 +
  1.1627 +    private:
  1.1628 +      const IterableBoolMap* _map;
  1.1629 +    };
  1.1630 +
  1.1631 +  protected:
  1.1632 +
  1.1633 +    virtual void add(const Key& key) {
  1.1634 +      Parent::add(key);
  1.1635 +      Parent::set(key, _array.size());
  1.1636 +      _array.push_back(key);
  1.1637 +    }
  1.1638 +
  1.1639 +    virtual void add(const std::vector<Key>& keys) {
  1.1640 +      Parent::add(keys);
  1.1641 +      for (int i = 0; i < int(keys.size()); ++i) {
  1.1642 +        Parent::set(keys[i], _array.size());
  1.1643 +        _array.push_back(keys[i]);
  1.1644 +      }
  1.1645 +    }
  1.1646 +
  1.1647 +    virtual void erase(const Key& key) {
  1.1648 +      int pos = position(key);
  1.1649 +      if (pos < _sep) {
  1.1650 +        --_sep;
  1.1651 +        Parent::set(_array[_sep], pos);
  1.1652 +        _array[pos] = _array[_sep];
  1.1653 +        Parent::set(_array.back(), _sep);
  1.1654 +        _array[_sep] = _array.back();
  1.1655 +        _array.pop_back();
  1.1656 +      } else {
  1.1657 +        Parent::set(_array.back(), pos);
  1.1658 +        _array[pos] = _array.back();
  1.1659 +        _array.pop_back();
  1.1660 +      }
  1.1661 +      Parent::erase(key);
  1.1662 +    }
  1.1663 +
  1.1664 +    virtual void erase(const std::vector<Key>& keys) {
  1.1665 +      for (int i = 0; i < int(keys.size()); ++i) {
  1.1666 +        int pos = position(keys[i]);
  1.1667 +        if (pos < _sep) {
  1.1668 +          --_sep;
  1.1669 +          Parent::set(_array[_sep], pos);
  1.1670 +          _array[pos] = _array[_sep];
  1.1671 +          Parent::set(_array.back(), _sep);
  1.1672 +          _array[_sep] = _array.back();
  1.1673 +          _array.pop_back();
  1.1674 +        } else {
  1.1675 +          Parent::set(_array.back(), pos);
  1.1676 +          _array[pos] = _array.back();
  1.1677 +          _array.pop_back();
  1.1678 +        }
  1.1679 +      }
  1.1680 +      Parent::erase(keys);
  1.1681 +    }
  1.1682 +
  1.1683 +    virtual void build() {
  1.1684 +      Parent::build();
  1.1685 +      typename Parent::Notifier* nf = Parent::notifier();
  1.1686 +      Key it;
  1.1687 +      for (nf->first(it); it != INVALID; nf->next(it)) {
  1.1688 +        Parent::set(it, _array.size());
  1.1689 +        _array.push_back(it);
  1.1690 +      }
  1.1691 +      _sep = 0;
  1.1692 +    }
  1.1693 +
  1.1694 +    virtual void clear() {
  1.1695 +      _array.clear();
  1.1696 +      _sep = 0;
  1.1697 +      Parent::clear();
  1.1698 +    }
  1.1699 +
  1.1700 +  };
  1.1701 +
  1.1702 +
  1.1703 +  namespace _maps_bits {
  1.1704 +    template <typename Item>
  1.1705 +    struct IterableIntMapNode {
  1.1706 +      IterableIntMapNode() : value(-1) {}
  1.1707 +      IterableIntMapNode(int _value) : value(_value) {}
  1.1708 +      Item prev, next;
  1.1709 +      int value;
  1.1710 +    };
  1.1711 +  }
  1.1712 +
  1.1713 +  /// \brief Dynamic iterable integer map.
  1.1714 +  ///
  1.1715 +  /// This class provides a special graph map type which can store an
  1.1716 +  /// integer value for graph items (\c Node, \c Arc or \c Edge).
  1.1717 +  /// For each non-negative value it is possible to iterate on the keys
  1.1718 +  /// mapped to the value.
  1.1719 +  ///
  1.1720 +  /// This map is intended to be used with small integer values, for which
  1.1721 +  /// it is efficient, and supports iteration only for non-negative values.
  1.1722 +  /// If you need large values and/or iteration for negative integers,
  1.1723 +  /// consider to use \ref IterableValueMap instead.
  1.1724 +  ///
  1.1725 +  /// This type is a reference map, so it can be modified with the
  1.1726 +  /// subscript operator.
  1.1727 +  ///
  1.1728 +  /// \note The size of the data structure depends on the largest
  1.1729 +  /// value in the map.
  1.1730 +  ///
  1.1731 +  /// \tparam GR The graph type.
  1.1732 +  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  1.1733 +  /// \c GR::Edge).
  1.1734 +  ///
  1.1735 +  /// \see IterableBoolMap, IterableValueMap
  1.1736 +  /// \see CrossRefMap
  1.1737 +  template <typename GR, typename K>
  1.1738 +  class IterableIntMap
  1.1739 +    : protected ItemSetTraits<GR, K>::
  1.1740 +        template Map<_maps_bits::IterableIntMapNode<K> >::Type {
  1.1741 +  public:
  1.1742 +    typedef typename ItemSetTraits<GR, K>::
  1.1743 +      template Map<_maps_bits::IterableIntMapNode<K> >::Type Parent;
  1.1744 +
  1.1745 +    /// The key type
  1.1746 +    typedef K Key;
  1.1747 +    /// The value type
  1.1748 +    typedef int Value;
  1.1749 +    /// The graph type
  1.1750 +    typedef GR Graph;
  1.1751 +
  1.1752 +    /// \brief Constructor of the map.
  1.1753 +    ///
  1.1754 +    /// Constructor of the map. It sets all values to -1.
  1.1755 +    explicit IterableIntMap(const Graph& graph)
  1.1756 +      : Parent(graph) {}
  1.1757 +
  1.1758 +    /// \brief Constructor of the map with a given value.
  1.1759 +    ///
  1.1760 +    /// Constructor of the map with a given value.
  1.1761 +    explicit IterableIntMap(const Graph& graph, int value)
  1.1762 +      : Parent(graph, _maps_bits::IterableIntMapNode<K>(value)) {
  1.1763 +      if (value >= 0) {
  1.1764 +        for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
  1.1765 +          lace(it);
  1.1766 +        }
  1.1767 +      }
  1.1768 +    }
  1.1769 +
  1.1770 +  private:
  1.1771 +
  1.1772 +    void unlace(const Key& key) {
  1.1773 +      typename Parent::Value& node = Parent::operator[](key);
  1.1774 +      if (node.value < 0) return;
  1.1775 +      if (node.prev != INVALID) {
  1.1776 +        Parent::operator[](node.prev).next = node.next;
  1.1777 +      } else {
  1.1778 +        _first[node.value] = node.next;
  1.1779 +      }
  1.1780 +      if (node.next != INVALID) {
  1.1781 +        Parent::operator[](node.next).prev = node.prev;
  1.1782 +      }
  1.1783 +      while (!_first.empty() && _first.back() == INVALID) {
  1.1784 +        _first.pop_back();
  1.1785 +      }
  1.1786 +    }
  1.1787 +
  1.1788 +    void lace(const Key& key) {
  1.1789 +      typename Parent::Value& node = Parent::operator[](key);
  1.1790 +      if (node.value < 0) return;
  1.1791 +      if (node.value >= int(_first.size())) {
  1.1792 +        _first.resize(node.value + 1, INVALID);
  1.1793 +      }
  1.1794 +      node.prev = INVALID;
  1.1795 +      node.next = _first[node.value];
  1.1796 +      if (node.next != INVALID) {
  1.1797 +        Parent::operator[](node.next).prev = key;
  1.1798 +      }
  1.1799 +      _first[node.value] = key;
  1.1800 +    }
  1.1801 +
  1.1802 +  public:
  1.1803 +
  1.1804 +    /// Indicates that the map is reference map.
  1.1805 +    typedef True ReferenceMapTag;
  1.1806 +
  1.1807 +    /// \brief Reference to the value of the map.
  1.1808 +    ///
  1.1809 +    /// This class is similar to the \c int type. It can
  1.1810 +    /// be converted to \c int and it has the same operators.
  1.1811 +    class Reference {
  1.1812 +      friend class IterableIntMap;
  1.1813 +    private:
  1.1814 +      Reference(IterableIntMap& map, const Key& key)
  1.1815 +        : _key(key), _map(map) {}
  1.1816 +    public:
  1.1817 +
  1.1818 +      Reference& operator=(const Reference& value) {
  1.1819 +        _map.set(_key, static_cast<const int&>(value));
  1.1820 +         return *this;
  1.1821 +      }
  1.1822 +
  1.1823 +      operator const int&() const {
  1.1824 +        return static_cast<const IterableIntMap&>(_map)[_key];
  1.1825 +      }
  1.1826 +
  1.1827 +      Reference& operator=(int value) {
  1.1828 +        _map.set(_key, value);
  1.1829 +        return *this;
  1.1830 +      }
  1.1831 +      Reference& operator++() {
  1.1832 +        _map.set(_key, _map[_key] + 1);
  1.1833 +        return *this;
  1.1834 +      }
  1.1835 +      int operator++(int) {
  1.1836 +        int value = _map[_key];
  1.1837 +        _map.set(_key, value + 1);
  1.1838 +        return value;
  1.1839 +      }
  1.1840 +      Reference& operator--() {
  1.1841 +        _map.set(_key, _map[_key] - 1);
  1.1842 +        return *this;
  1.1843 +      }
  1.1844 +      int operator--(int) {
  1.1845 +        int value = _map[_key];
  1.1846 +        _map.set(_key, value - 1);
  1.1847 +        return value;
  1.1848 +      }
  1.1849 +      Reference& operator+=(int value) {
  1.1850 +        _map.set(_key, _map[_key] + value);
  1.1851 +        return *this;
  1.1852 +      }
  1.1853 +      Reference& operator-=(int value) {
  1.1854 +        _map.set(_key, _map[_key] - value);
  1.1855 +        return *this;
  1.1856 +      }
  1.1857 +      Reference& operator*=(int value) {
  1.1858 +        _map.set(_key, _map[_key] * value);
  1.1859 +        return *this;
  1.1860 +      }
  1.1861 +      Reference& operator/=(int value) {
  1.1862 +        _map.set(_key, _map[_key] / value);
  1.1863 +        return *this;
  1.1864 +      }
  1.1865 +      Reference& operator%=(int value) {
  1.1866 +        _map.set(_key, _map[_key] % value);
  1.1867 +        return *this;
  1.1868 +      }
  1.1869 +      Reference& operator&=(int value) {
  1.1870 +        _map.set(_key, _map[_key] & value);
  1.1871 +        return *this;
  1.1872 +      }
  1.1873 +      Reference& operator|=(int value) {
  1.1874 +        _map.set(_key, _map[_key] | value);
  1.1875 +        return *this;
  1.1876 +      }
  1.1877 +      Reference& operator^=(int value) {
  1.1878 +        _map.set(_key, _map[_key] ^ value);
  1.1879 +        return *this;
  1.1880 +      }
  1.1881 +      Reference& operator<<=(int value) {
  1.1882 +        _map.set(_key, _map[_key] << value);
  1.1883 +        return *this;
  1.1884 +      }
  1.1885 +      Reference& operator>>=(int value) {
  1.1886 +        _map.set(_key, _map[_key] >> value);
  1.1887 +        return *this;
  1.1888 +      }
  1.1889 +
  1.1890 +    private:
  1.1891 +      Key _key;
  1.1892 +      IterableIntMap& _map;
  1.1893 +    };
  1.1894 +
  1.1895 +    /// The const reference type.
  1.1896 +    typedef const Value& ConstReference;
  1.1897 +
  1.1898 +    /// \brief Gives back the maximal value plus one.
  1.1899 +    ///
  1.1900 +    /// Gives back the maximal value plus one.
  1.1901 +    int size() const {
  1.1902 +      return _first.size();
  1.1903 +    }
  1.1904 +
  1.1905 +    /// \brief Set operation of the map.
  1.1906 +    ///
  1.1907 +    /// Set operation of the map.
  1.1908 +    void set(const Key& key, const Value& value) {
  1.1909 +      unlace(key);
  1.1910 +      Parent::operator[](key).value = value;
  1.1911 +      lace(key);
  1.1912 +    }
  1.1913 +
  1.1914 +    /// \brief Const subscript operator of the map.
  1.1915 +    ///
  1.1916 +    /// Const subscript operator of the map.
  1.1917 +    const Value& operator[](const Key& key) const {
  1.1918 +      return Parent::operator[](key).value;
  1.1919 +    }
  1.1920 +
  1.1921 +    /// \brief Subscript operator of the map.
  1.1922 +    ///
  1.1923 +    /// Subscript operator of the map.
  1.1924 +    Reference operator[](const Key& key) {
  1.1925 +      return Reference(*this, key);
  1.1926 +    }
  1.1927 +
  1.1928 +    /// \brief Iterator for the keys with the same value.
  1.1929 +    ///
  1.1930 +    /// Iterator for the keys with the same value. It works
  1.1931 +    /// like a graph item iterator, it can be converted to
  1.1932 +    /// the item type of the map, incremented with \c ++ operator, and
  1.1933 +    /// if the iterator leaves the last valid item, it will be equal to
  1.1934 +    /// \c INVALID.
  1.1935 +    class ItemIt : public Key {
  1.1936 +    public:
  1.1937 +      typedef Key Parent;
  1.1938 +
  1.1939 +      /// \brief Invalid constructor \& conversion.
  1.1940 +      ///
  1.1941 +      /// This constructor initializes the iterator to be invalid.
  1.1942 +      /// \sa Invalid for more details.
  1.1943 +      ItemIt(Invalid) : Parent(INVALID), _map(0) {}
  1.1944 +
  1.1945 +      /// \brief Creates an iterator with a value.
  1.1946 +      ///
  1.1947 +      /// Creates an iterator with a value. It iterates on the
  1.1948 +      /// keys mapped to the given value.
  1.1949 +      /// \param map The IterableIntMap.
  1.1950 +      /// \param value The value.
  1.1951 +      ItemIt(const IterableIntMap& map, int value) : _map(&map) {
  1.1952 +        if (value < 0 || value >= int(_map->_first.size())) {
  1.1953 +          Parent::operator=(INVALID);
  1.1954 +        } else {
  1.1955 +          Parent::operator=(_map->_first[value]);
  1.1956 +        }
  1.1957 +      }
  1.1958 +
  1.1959 +      /// \brief Increment operator.
  1.1960 +      ///
  1.1961 +      /// Increment operator.
  1.1962 +      ItemIt& operator++() {
  1.1963 +        Parent::operator=(_map->IterableIntMap::Parent::
  1.1964 +                          operator[](static_cast<Parent&>(*this)).next);
  1.1965 +        return *this;
  1.1966 +      }
  1.1967 +
  1.1968 +    private:
  1.1969 +      const IterableIntMap* _map;
  1.1970 +    };
  1.1971 +
  1.1972 +  protected:
  1.1973 +
  1.1974 +    virtual void erase(const Key& key) {
  1.1975 +      unlace(key);
  1.1976 +      Parent::erase(key);
  1.1977 +    }
  1.1978 +
  1.1979 +    virtual void erase(const std::vector<Key>& keys) {
  1.1980 +      for (int i = 0; i < int(keys.size()); ++i) {
  1.1981 +        unlace(keys[i]);
  1.1982 +      }
  1.1983 +      Parent::erase(keys);
  1.1984 +    }
  1.1985 +
  1.1986 +    virtual void clear() {
  1.1987 +      _first.clear();
  1.1988 +      Parent::clear();
  1.1989 +    }
  1.1990 +
  1.1991 +  private:
  1.1992 +    std::vector<Key> _first;
  1.1993 +  };
  1.1994 +
  1.1995 +  namespace _maps_bits {
  1.1996 +    template <typename Item, typename Value>
  1.1997 +    struct IterableValueMapNode {
  1.1998 +      IterableValueMapNode(Value _value = Value()) : value(_value) {}
  1.1999 +      Item prev, next;
  1.2000 +      Value value;
  1.2001 +    };
  1.2002 +  }
  1.2003 +
  1.2004 +  /// \brief Dynamic iterable map for comparable values.
  1.2005 +  ///
  1.2006 +  /// This class provides a special graph map type which can store a
  1.2007 +  /// comparable value for graph items (\c Node, \c Arc or \c Edge).
  1.2008 +  /// For each value it is possible to iterate on the keys mapped to
  1.2009 +  /// the value (\c ItemIt), and the values of the map can be accessed
  1.2010 +  /// with an STL compatible forward iterator (\c ValueIt).
  1.2011 +  /// The map stores a linked list for each value, which contains
  1.2012 +  /// the items mapped to the value, and the used values are stored
  1.2013 +  /// in balanced binary tree (\c std::map).
  1.2014 +  ///
  1.2015 +  /// \ref IterableBoolMap and \ref IterableIntMap are similar classes
  1.2016 +  /// specialized for \c bool and \c int values, respectively.
  1.2017 +  ///
  1.2018 +  /// This type is not reference map, so it cannot be modified with
  1.2019 +  /// the subscript operator.
  1.2020 +  ///
  1.2021 +  /// \tparam GR The graph type.
  1.2022 +  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  1.2023 +  /// \c GR::Edge).
  1.2024 +  /// \tparam V The value type of the map. It can be any comparable
  1.2025 +  /// value type.
  1.2026 +  ///
  1.2027 +  /// \see IterableBoolMap, IterableIntMap
  1.2028 +  /// \see CrossRefMap
  1.2029 +  template <typename GR, typename K, typename V>
  1.2030 +  class IterableValueMap
  1.2031 +    : protected ItemSetTraits<GR, K>::
  1.2032 +        template Map<_maps_bits::IterableValueMapNode<K, V> >::Type {
  1.2033 +  public:
  1.2034 +    typedef typename ItemSetTraits<GR, K>::
  1.2035 +      template Map<_maps_bits::IterableValueMapNode<K, V> >::Type Parent;
  1.2036 +
  1.2037 +    /// The key type
  1.2038 +    typedef K Key;
  1.2039 +    /// The value type
  1.2040 +    typedef V Value;
  1.2041 +    /// The graph type
  1.2042 +    typedef GR Graph;
  1.2043 +
  1.2044 +  public:
  1.2045 +
  1.2046 +    /// \brief Constructor of the map with a given value.
  1.2047 +    ///
  1.2048 +    /// Constructor of the map with a given value.
  1.2049 +    explicit IterableValueMap(const Graph& graph,
  1.2050 +                              const Value& value = Value())
  1.2051 +      : Parent(graph, _maps_bits::IterableValueMapNode<K, V>(value)) {
  1.2052 +      for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
  1.2053 +        lace(it);
  1.2054 +      }
  1.2055 +    }
  1.2056 +
  1.2057 +  protected:
  1.2058 +
  1.2059 +    void unlace(const Key& key) {
  1.2060 +      typename Parent::Value& node = Parent::operator[](key);
  1.2061 +      if (node.prev != INVALID) {
  1.2062 +        Parent::operator[](node.prev).next = node.next;
  1.2063 +      } else {
  1.2064 +        if (node.next != INVALID) {
  1.2065 +          _first[node.value] = node.next;
  1.2066 +        } else {
  1.2067 +          _first.erase(node.value);
  1.2068 +        }
  1.2069 +      }
  1.2070 +      if (node.next != INVALID) {
  1.2071 +        Parent::operator[](node.next).prev = node.prev;
  1.2072 +      }
  1.2073 +    }
  1.2074 +
  1.2075 +    void lace(const Key& key) {
  1.2076 +      typename Parent::Value& node = Parent::operator[](key);
  1.2077 +      typename std::map<Value, Key>::iterator it = _first.find(node.value);
  1.2078 +      if (it == _first.end()) {
  1.2079 +        node.prev = node.next = INVALID;
  1.2080 +        _first.insert(std::make_pair(node.value, key));
  1.2081 +      } else {
  1.2082 +        node.prev = INVALID;
  1.2083 +        node.next = it->second;
  1.2084 +        if (node.next != INVALID) {
  1.2085 +          Parent::operator[](node.next).prev = key;
  1.2086 +        }
  1.2087 +        it->second = key;
  1.2088 +      }
  1.2089 +    }
  1.2090 +
  1.2091 +  public:
  1.2092 +
  1.2093 +    /// \brief Forward iterator for values.
  1.2094 +    ///
  1.2095 +    /// This iterator is an STL compatible forward
  1.2096 +    /// iterator on the values of the map. The values can
  1.2097 +    /// be accessed in the <tt>[beginValue, endValue)</tt> range.
  1.2098 +    class ValueIt
  1.2099 +      : public std::iterator<std::forward_iterator_tag, Value> {
  1.2100 +      friend class IterableValueMap;
  1.2101 +    private:
  1.2102 +      ValueIt(typename std::map<Value, Key>::const_iterator _it)
  1.2103 +        : it(_it) {}
  1.2104 +    public:
  1.2105 +
  1.2106 +      /// Constructor
  1.2107 +      ValueIt() {}
  1.2108 +
  1.2109 +      /// \e
  1.2110 +      ValueIt& operator++() { ++it; return *this; }
  1.2111 +      /// \e
  1.2112 +      ValueIt operator++(int) {
  1.2113 +        ValueIt tmp(*this);
  1.2114 +        operator++();
  1.2115 +        return tmp;
  1.2116 +      }
  1.2117 +
  1.2118 +      /// \e
  1.2119 +      const Value& operator*() const { return it->first; }
  1.2120 +      /// \e
  1.2121 +      const Value* operator->() const { return &(it->first); }
  1.2122 +
  1.2123 +      /// \e
  1.2124 +      bool operator==(ValueIt jt) const { return it == jt.it; }
  1.2125 +      /// \e
  1.2126 +      bool operator!=(ValueIt jt) const { return it != jt.it; }
  1.2127 +
  1.2128 +    private:
  1.2129 +      typename std::map<Value, Key>::const_iterator it;
  1.2130 +    };
  1.2131 +
  1.2132 +    /// \brief Returns an iterator to the first value.
  1.2133 +    ///
  1.2134 +    /// Returns an STL compatible iterator to the
  1.2135 +    /// first value of the map. The values of the
  1.2136 +    /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  1.2137 +    /// range.
  1.2138 +    ValueIt beginValue() const {
  1.2139 +      return ValueIt(_first.begin());
  1.2140 +    }
  1.2141 +
  1.2142 +    /// \brief Returns an iterator after the last value.
  1.2143 +    ///
  1.2144 +    /// Returns an STL compatible iterator after the
  1.2145 +    /// last value of the map. The values of the
  1.2146 +    /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  1.2147 +    /// range.
  1.2148 +    ValueIt endValue() const {
  1.2149 +      return ValueIt(_first.end());
  1.2150 +    }
  1.2151 +
  1.2152 +    /// \brief Set operation of the map.
  1.2153 +    ///
  1.2154 +    /// Set operation of the map.
  1.2155 +    void set(const Key& key, const Value& value) {
  1.2156 +      unlace(key);
  1.2157 +      Parent::operator[](key).value = value;
  1.2158 +      lace(key);
  1.2159 +    }
  1.2160 +
  1.2161 +    /// \brief Const subscript operator of the map.
  1.2162 +    ///
  1.2163 +    /// Const subscript operator of the map.
  1.2164 +    const Value& operator[](const Key& key) const {
  1.2165 +      return Parent::operator[](key).value;
  1.2166 +    }
  1.2167 +
  1.2168 +    /// \brief Iterator for the keys with the same value.
  1.2169 +    ///
  1.2170 +    /// Iterator for the keys with the same value. It works
  1.2171 +    /// like a graph item iterator, it can be converted to
  1.2172 +    /// the item type of the map, incremented with \c ++ operator, and
  1.2173 +    /// if the iterator leaves the last valid item, it will be equal to
  1.2174 +    /// \c INVALID.
  1.2175 +    class ItemIt : public Key {
  1.2176 +    public:
  1.2177 +      typedef Key Parent;
  1.2178 +
  1.2179 +      /// \brief Invalid constructor \& conversion.
  1.2180 +      ///
  1.2181 +      /// This constructor initializes the iterator to be invalid.
  1.2182 +      /// \sa Invalid for more details.
  1.2183 +      ItemIt(Invalid) : Parent(INVALID), _map(0) {}
  1.2184 +
  1.2185 +      /// \brief Creates an iterator with a value.
  1.2186 +      ///
  1.2187 +      /// Creates an iterator with a value. It iterates on the
  1.2188 +      /// keys which have the given value.
  1.2189 +      /// \param map The IterableValueMap
  1.2190 +      /// \param value The value
  1.2191 +      ItemIt(const IterableValueMap& map, const Value& value) : _map(&map) {
  1.2192 +        typename std::map<Value, Key>::const_iterator it =
  1.2193 +          map._first.find(value);
  1.2194 +        if (it == map._first.end()) {
  1.2195 +          Parent::operator=(INVALID);
  1.2196 +        } else {
  1.2197 +          Parent::operator=(it->second);
  1.2198 +        }
  1.2199 +      }
  1.2200 +
  1.2201 +      /// \brief Increment operator.
  1.2202 +      ///
  1.2203 +      /// Increment Operator.
  1.2204 +      ItemIt& operator++() {
  1.2205 +        Parent::operator=(_map->IterableValueMap::Parent::
  1.2206 +                          operator[](static_cast<Parent&>(*this)).next);
  1.2207 +        return *this;
  1.2208 +      }
  1.2209 +
  1.2210 +
  1.2211 +    private:
  1.2212 +      const IterableValueMap* _map;
  1.2213 +    };
  1.2214 +
  1.2215 +  protected:
  1.2216 +
  1.2217 +    virtual void add(const Key& key) {
  1.2218 +      Parent::add(key);
  1.2219 +      unlace(key);
  1.2220 +    }
  1.2221 +
  1.2222 +    virtual void add(const std::vector<Key>& keys) {
  1.2223 +      Parent::add(keys);
  1.2224 +      for (int i = 0; i < int(keys.size()); ++i) {
  1.2225 +        lace(keys[i]);
  1.2226 +      }
  1.2227 +    }
  1.2228 +
  1.2229 +    virtual void erase(const Key& key) {
  1.2230 +      unlace(key);
  1.2231 +      Parent::erase(key);
  1.2232 +    }
  1.2233 +
  1.2234 +    virtual void erase(const std::vector<Key>& keys) {
  1.2235 +      for (int i = 0; i < int(keys.size()); ++i) {
  1.2236 +        unlace(keys[i]);
  1.2237 +      }
  1.2238 +      Parent::erase(keys);
  1.2239 +    }
  1.2240 +
  1.2241 +    virtual void build() {
  1.2242 +      Parent::build();
  1.2243 +      for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
  1.2244 +        lace(it);
  1.2245 +      }
  1.2246 +    }
  1.2247 +
  1.2248 +    virtual void clear() {
  1.2249 +      _first.clear();
  1.2250 +      Parent::clear();
  1.2251 +    }
  1.2252 +
  1.2253 +  private:
  1.2254 +    std::map<Value, Key> _first;
  1.2255 +  };
  1.2256 +
  1.2257 +  /// \brief Map of the source nodes of arcs in a digraph.
  1.2258 +  ///
  1.2259 +  /// SourceMap provides access for the source node of each arc in a digraph,
  1.2260 +  /// which is returned by the \c source() function of the digraph.
  1.2261 +  /// \tparam GR The digraph type.
  1.2262    /// \see TargetMap
  1.2263 -  template <typename Digraph>
  1.2264 +  template <typename GR>
  1.2265    class SourceMap {
  1.2266    public:
  1.2267  
  1.2268 -    typedef typename Digraph::Node Value;
  1.2269 -    typedef typename Digraph::Arc Key;
  1.2270 +    /// The key type (the \c Arc type of the digraph).
  1.2271 +    typedef typename GR::Arc Key;
  1.2272 +    /// The value type (the \c Node type of the digraph).
  1.2273 +    typedef typename GR::Node Value;
  1.2274  
  1.2275      /// \brief Constructor
  1.2276      ///
  1.2277 -    /// Constructor
  1.2278 +    /// Constructor.
  1.2279      /// \param digraph The digraph that the map belongs to.
  1.2280 -    explicit SourceMap(const Digraph& digraph) : _digraph(digraph) {}
  1.2281 -
  1.2282 -    /// \brief The subscript operator.
  1.2283 +    explicit SourceMap(const GR& digraph) : _graph(digraph) {}
  1.2284 +
  1.2285 +    /// \brief Returns the source node of the given arc.
  1.2286      ///
  1.2287 -    /// The subscript operator.
  1.2288 -    /// \param arc The arc
  1.2289 -    /// \return The source of the arc
  1.2290 +    /// Returns the source node of the given arc.
  1.2291      Value operator[](const Key& arc) const {
  1.2292 -      return _digraph.source(arc);
  1.2293 +      return _graph.source(arc);
  1.2294      }
  1.2295  
  1.2296    private:
  1.2297 -    const Digraph& _digraph;
  1.2298 +    const GR& _graph;
  1.2299    };
  1.2300  
  1.2301    /// \brief Returns a \c SourceMap class.
  1.2302    ///
  1.2303    /// This function just returns an \c SourceMap class.
  1.2304    /// \relates SourceMap
  1.2305 -  template <typename Digraph>
  1.2306 -  inline SourceMap<Digraph> sourceMap(const Digraph& digraph) {
  1.2307 -    return SourceMap<Digraph>(digraph);
  1.2308 +  template <typename GR>
  1.2309 +  inline SourceMap<GR> sourceMap(const GR& graph) {
  1.2310 +    return SourceMap<GR>(graph);
  1.2311    }
  1.2312  
  1.2313 -  /// \brief Returns the target of the given arc.
  1.2314 +  /// \brief Map of the target nodes of arcs in a digraph.
  1.2315    ///
  1.2316 -  /// The TargetMap gives back the target Node of the given arc.
  1.2317 +  /// TargetMap provides access for the target node of each arc in a digraph,
  1.2318 +  /// which is returned by the \c target() function of the digraph.
  1.2319 +  /// \tparam GR The digraph type.
  1.2320    /// \see SourceMap
  1.2321 -  template <typename Digraph>
  1.2322 +  template <typename GR>
  1.2323    class TargetMap {
  1.2324    public:
  1.2325  
  1.2326 -    typedef typename Digraph::Node Value;
  1.2327 -    typedef typename Digraph::Arc Key;
  1.2328 +    /// The key type (the \c Arc type of the digraph).
  1.2329 +    typedef typename GR::Arc Key;
  1.2330 +    /// The value type (the \c Node type of the digraph).
  1.2331 +    typedef typename GR::Node Value;
  1.2332  
  1.2333      /// \brief Constructor
  1.2334      ///
  1.2335 -    /// Constructor
  1.2336 +    /// Constructor.
  1.2337      /// \param digraph The digraph that the map belongs to.
  1.2338 -    explicit TargetMap(const Digraph& digraph) : _digraph(digraph) {}
  1.2339 -
  1.2340 -    /// \brief The subscript operator.
  1.2341 +    explicit TargetMap(const GR& digraph) : _graph(digraph) {}
  1.2342 +
  1.2343 +    /// \brief Returns the target node of the given arc.
  1.2344      ///
  1.2345 -    /// The subscript operator.
  1.2346 -    /// \param e The arc
  1.2347 -    /// \return The target of the arc
  1.2348 +    /// Returns the target node of the given arc.
  1.2349      Value operator[](const Key& e) const {
  1.2350 -      return _digraph.target(e);
  1.2351 +      return _graph.target(e);
  1.2352      }
  1.2353  
  1.2354    private:
  1.2355 -    const Digraph& _digraph;
  1.2356 +    const GR& _graph;
  1.2357    };
  1.2358  
  1.2359    /// \brief Returns a \c TargetMap class.
  1.2360    ///
  1.2361    /// This function just returns a \c TargetMap class.
  1.2362    /// \relates TargetMap
  1.2363 -  template <typename Digraph>
  1.2364 -  inline TargetMap<Digraph> targetMap(const Digraph& digraph) {
  1.2365 -    return TargetMap<Digraph>(digraph);
  1.2366 +  template <typename GR>
  1.2367 +  inline TargetMap<GR> targetMap(const GR& graph) {
  1.2368 +    return TargetMap<GR>(graph);
  1.2369    }
  1.2370  
  1.2371 -  /// \brief Returns the "forward" directed arc view of an edge.
  1.2372 +  /// \brief Map of the "forward" directed arc view of edges in a graph.
  1.2373    ///
  1.2374 -  /// Returns the "forward" directed arc view of an edge.
  1.2375 +  /// ForwardMap provides access for the "forward" directed arc view of
  1.2376 +  /// each edge in a graph, which is returned by the \c direct() function
  1.2377 +  /// of the graph with \c true parameter.
  1.2378 +  /// \tparam GR The graph type.
  1.2379    /// \see BackwardMap
  1.2380 -  template <typename Graph>
  1.2381 +  template <typename GR>
  1.2382    class ForwardMap {
  1.2383    public:
  1.2384  
  1.2385 -    typedef typename Graph::Arc Value;
  1.2386 -    typedef typename Graph::Edge Key;
  1.2387 +    /// The key type (the \c Edge type of the digraph).
  1.2388 +    typedef typename GR::Edge Key;
  1.2389 +    /// The value type (the \c Arc type of the digraph).
  1.2390 +    typedef typename GR::Arc Value;
  1.2391  
  1.2392      /// \brief Constructor
  1.2393      ///
  1.2394 -    /// Constructor
  1.2395 +    /// Constructor.
  1.2396      /// \param graph The graph that the map belongs to.
  1.2397 -    explicit ForwardMap(const Graph& graph) : _graph(graph) {}
  1.2398 -
  1.2399 -    /// \brief The subscript operator.
  1.2400 +    explicit ForwardMap(const GR& graph) : _graph(graph) {}
  1.2401 +
  1.2402 +    /// \brief Returns the "forward" directed arc view of the given edge.
  1.2403      ///
  1.2404 -    /// The subscript operator.
  1.2405 -    /// \param key An edge
  1.2406 -    /// \return The "forward" directed arc view of edge
  1.2407 +    /// Returns the "forward" directed arc view of the given edge.
  1.2408      Value operator[](const Key& key) const {
  1.2409        return _graph.direct(key, true);
  1.2410      }
  1.2411  
  1.2412    private:
  1.2413 -    const Graph& _graph;
  1.2414 +    const GR& _graph;
  1.2415    };
  1.2416  
  1.2417    /// \brief Returns a \c ForwardMap class.
  1.2418    ///
  1.2419    /// This function just returns an \c ForwardMap class.
  1.2420    /// \relates ForwardMap
  1.2421 -  template <typename Graph>
  1.2422 -  inline ForwardMap<Graph> forwardMap(const Graph& graph) {
  1.2423 -    return ForwardMap<Graph>(graph);
  1.2424 +  template <typename GR>
  1.2425 +  inline ForwardMap<GR> forwardMap(const GR& graph) {
  1.2426 +    return ForwardMap<GR>(graph);
  1.2427    }
  1.2428  
  1.2429 -  /// \brief Returns the "backward" directed arc view of an edge.
  1.2430 +  /// \brief Map of the "backward" directed arc view of edges in a graph.
  1.2431    ///
  1.2432 -  /// Returns the "backward" directed arc view of an edge.
  1.2433 +  /// BackwardMap provides access for the "backward" directed arc view of
  1.2434 +  /// each edge in a graph, which is returned by the \c direct() function
  1.2435 +  /// of the graph with \c false parameter.
  1.2436 +  /// \tparam GR The graph type.
  1.2437    /// \see ForwardMap
  1.2438 -  template <typename Graph>
  1.2439 +  template <typename GR>
  1.2440    class BackwardMap {
  1.2441    public:
  1.2442  
  1.2443 -    typedef typename Graph::Arc Value;
  1.2444 -    typedef typename Graph::Edge Key;
  1.2445 +    /// The key type (the \c Edge type of the digraph).
  1.2446 +    typedef typename GR::Edge Key;
  1.2447 +    /// The value type (the \c Arc type of the digraph).
  1.2448 +    typedef typename GR::Arc Value;
  1.2449  
  1.2450      /// \brief Constructor
  1.2451      ///
  1.2452 -    /// Constructor
  1.2453 +    /// Constructor.
  1.2454      /// \param graph The graph that the map belongs to.
  1.2455 -    explicit BackwardMap(const Graph& graph) : _graph(graph) {}
  1.2456 -
  1.2457 -    /// \brief The subscript operator.
  1.2458 +    explicit BackwardMap(const GR& graph) : _graph(graph) {}
  1.2459 +
  1.2460 +    /// \brief Returns the "backward" directed arc view of the given edge.
  1.2461      ///
  1.2462 -    /// The subscript operator.
  1.2463 -    /// \param key An edge
  1.2464 -    /// \return The "backward" directed arc view of edge
  1.2465 +    /// Returns the "backward" directed arc view of the given edge.
  1.2466      Value operator[](const Key& key) const {
  1.2467        return _graph.direct(key, false);
  1.2468      }
  1.2469  
  1.2470    private:
  1.2471 -    const Graph& _graph;
  1.2472 +    const GR& _graph;
  1.2473    };
  1.2474  
  1.2475    /// \brief Returns a \c BackwardMap class
  1.2476  
  1.2477    /// This function just returns a \c BackwardMap class.
  1.2478    /// \relates BackwardMap
  1.2479 -  template <typename Graph>
  1.2480 -  inline BackwardMap<Graph> backwardMap(const Graph& graph) {
  1.2481 -    return BackwardMap<Graph>(graph);
  1.2482 +  template <typename GR>
  1.2483 +  inline BackwardMap<GR> backwardMap(const GR& graph) {
  1.2484 +    return BackwardMap<GR>(graph);
  1.2485    }
  1.2486  
  1.2487 -  /// \brief Potential difference map
  1.2488 -  ///
  1.2489 -  /// If there is an potential map on the nodes then we
  1.2490 -  /// can get an arc map as we get the substraction of the
  1.2491 -  /// values of the target and source.
  1.2492 -  template <typename Digraph, typename NodeMap>
  1.2493 -  class PotentialDifferenceMap {
  1.2494 -  public:
  1.2495 -    typedef typename Digraph::Arc Key;
  1.2496 -    typedef typename NodeMap::Value Value;
  1.2497 -
  1.2498 -    /// \brief Constructor
  1.2499 -    ///
  1.2500 -    /// Contructor of the map
  1.2501 -    explicit PotentialDifferenceMap(const Digraph& digraph,
  1.2502 -                                    const NodeMap& potential)
  1.2503 -      : _digraph(digraph), _potential(potential) {}
  1.2504 -
  1.2505 -    /// \brief Const subscription operator
  1.2506 -    ///
  1.2507 -    /// Const subscription operator
  1.2508 -    Value operator[](const Key& arc) const {
  1.2509 -      return _potential[_digraph.target(arc)] -
  1.2510 -        _potential[_digraph.source(arc)];
  1.2511 -    }
  1.2512 -
  1.2513 -  private:
  1.2514 -    const Digraph& _digraph;
  1.2515 -    const NodeMap& _potential;
  1.2516 -  };
  1.2517 -
  1.2518 -  /// \brief Returns a PotentialDifferenceMap.
  1.2519 -  ///
  1.2520 -  /// This function just returns a PotentialDifferenceMap.
  1.2521 -  /// \relates PotentialDifferenceMap
  1.2522 -  template <typename Digraph, typename NodeMap>
  1.2523 -  PotentialDifferenceMap<Digraph, NodeMap>
  1.2524 -  potentialDifferenceMap(const Digraph& digraph, const NodeMap& potential) {
  1.2525 -    return PotentialDifferenceMap<Digraph, NodeMap>(digraph, potential);
  1.2526 -  }
  1.2527 -
  1.2528 -  /// \brief Map of the node in-degrees.
  1.2529 +  /// \brief Map of the in-degrees of nodes in a digraph.
  1.2530    ///
  1.2531    /// This map returns the in-degree of a node. Once it is constructed,
  1.2532 -  /// the degrees are stored in a standard NodeMap, so each query is done
  1.2533 +  /// the degrees are stored in a standard \c NodeMap, so each query is done
  1.2534    /// in constant time. On the other hand, the values are updated automatically
  1.2535    /// whenever the digraph changes.
  1.2536    ///
  1.2537 -  /// \warning Besides addNode() and addArc(), a digraph structure may provide
  1.2538 -  /// alternative ways to modify the digraph. The correct behavior of InDegMap
  1.2539 -  /// is not guarantied if these additional features are used. For example
  1.2540 -  /// the functions \ref ListDigraph::changeSource() "changeSource()",
  1.2541 +  /// \warning Besides \c addNode() and \c addArc(), a digraph structure
  1.2542 +  /// may provide alternative ways to modify the digraph.
  1.2543 +  /// The correct behavior of InDegMap is not guarantied if these additional
  1.2544 +  /// features are used. For example the functions
  1.2545 +  /// \ref ListDigraph::changeSource() "changeSource()",
  1.2546    /// \ref ListDigraph::changeTarget() "changeTarget()" and
  1.2547    /// \ref ListDigraph::reverseArc() "reverseArc()"
  1.2548    /// of \ref ListDigraph will \e not update the degree values correctly.
  1.2549    ///
  1.2550    /// \sa OutDegMap
  1.2551 -
  1.2552 -  template <typename _Digraph>
  1.2553 +  template <typename GR>
  1.2554    class InDegMap
  1.2555 -    : protected ItemSetTraits<_Digraph, typename _Digraph::Arc>
  1.2556 +    : protected ItemSetTraits<GR, typename GR::Arc>
  1.2557        ::ItemNotifier::ObserverBase {
  1.2558  
  1.2559    public:
  1.2560  
  1.2561 -    typedef _Digraph Digraph;
  1.2562 +    /// The graph type of InDegMap
  1.2563 +    typedef GR Graph;
  1.2564 +    typedef GR Digraph;
  1.2565 +    /// The key type
  1.2566 +    typedef typename Digraph::Node Key;
  1.2567 +    /// The value type
  1.2568      typedef int Value;
  1.2569 -    typedef typename Digraph::Node Key;
  1.2570  
  1.2571      typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
  1.2572      ::ItemNotifier::ObserverBase Parent;
  1.2573 @@ -2523,9 +3528,9 @@
  1.2574  
  1.2575      /// \brief Constructor.
  1.2576      ///
  1.2577 -    /// Constructor for creating in-degree map.
  1.2578 -    explicit InDegMap(const Digraph& digraph)
  1.2579 -      : _digraph(digraph), _deg(digraph) {
  1.2580 +    /// Constructor for creating an in-degree map.
  1.2581 +    explicit InDegMap(const Digraph& graph)
  1.2582 +      : _digraph(graph), _deg(graph) {
  1.2583        Parent::attach(_digraph.notifier(typename Digraph::Arc()));
  1.2584  
  1.2585        for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  1.2586 @@ -2533,6 +3538,8 @@
  1.2587        }
  1.2588      }
  1.2589  
  1.2590 +    /// \brief Gives back the in-degree of a Node.
  1.2591 +    ///
  1.2592      /// Gives back the in-degree of a Node.
  1.2593      int operator[](const Key& key) const {
  1.2594        return _deg[key];
  1.2595 @@ -2579,33 +3586,37 @@
  1.2596      AutoNodeMap _deg;
  1.2597    };
  1.2598  
  1.2599 -  /// \brief Map of the node out-degrees.
  1.2600 +  /// \brief Map of the out-degrees of nodes in a digraph.
  1.2601    ///
  1.2602    /// This map returns the out-degree of a node. Once it is constructed,
  1.2603 -  /// the degrees are stored in a standard NodeMap, so each query is done
  1.2604 +  /// the degrees are stored in a standard \c NodeMap, so each query is done
  1.2605    /// in constant time. On the other hand, the values are updated automatically
  1.2606    /// whenever the digraph changes.
  1.2607    ///
  1.2608 -  /// \warning Besides addNode() and addArc(), a digraph structure may provide
  1.2609 -  /// alternative ways to modify the digraph. The correct behavior of OutDegMap
  1.2610 -  /// is not guarantied if these additional features are used. For example
  1.2611 -  /// the functions \ref ListDigraph::changeSource() "changeSource()",
  1.2612 +  /// \warning Besides \c addNode() and \c addArc(), a digraph structure
  1.2613 +  /// may provide alternative ways to modify the digraph.
  1.2614 +  /// The correct behavior of OutDegMap is not guarantied if these additional
  1.2615 +  /// features are used. For example the functions
  1.2616 +  /// \ref ListDigraph::changeSource() "changeSource()",
  1.2617    /// \ref ListDigraph::changeTarget() "changeTarget()" and
  1.2618    /// \ref ListDigraph::reverseArc() "reverseArc()"
  1.2619    /// of \ref ListDigraph will \e not update the degree values correctly.
  1.2620    ///
  1.2621    /// \sa InDegMap
  1.2622 -
  1.2623 -  template <typename _Digraph>
  1.2624 +  template <typename GR>
  1.2625    class OutDegMap
  1.2626 -    : protected ItemSetTraits<_Digraph, typename _Digraph::Arc>
  1.2627 +    : protected ItemSetTraits<GR, typename GR::Arc>
  1.2628        ::ItemNotifier::ObserverBase {
  1.2629  
  1.2630    public:
  1.2631  
  1.2632 -    typedef _Digraph Digraph;
  1.2633 +    /// The graph type of OutDegMap
  1.2634 +    typedef GR Graph;
  1.2635 +    typedef GR Digraph;
  1.2636 +    /// The key type
  1.2637 +    typedef typename Digraph::Node Key;
  1.2638 +    /// The value type
  1.2639      typedef int Value;
  1.2640 -    typedef typename Digraph::Node Key;
  1.2641  
  1.2642      typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
  1.2643      ::ItemNotifier::ObserverBase Parent;
  1.2644 @@ -2645,9 +3656,9 @@
  1.2645  
  1.2646      /// \brief Constructor.
  1.2647      ///
  1.2648 -    /// Constructor for creating out-degree map.
  1.2649 -    explicit OutDegMap(const Digraph& digraph)
  1.2650 -      : _digraph(digraph), _deg(digraph) {
  1.2651 +    /// Constructor for creating an out-degree map.
  1.2652 +    explicit OutDegMap(const Digraph& graph)
  1.2653 +      : _digraph(graph), _deg(graph) {
  1.2654        Parent::attach(_digraph.notifier(typename Digraph::Arc()));
  1.2655  
  1.2656        for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
  1.2657 @@ -2655,6 +3666,8 @@
  1.2658        }
  1.2659      }
  1.2660  
  1.2661 +    /// \brief Gives back the out-degree of a Node.
  1.2662 +    ///
  1.2663      /// Gives back the out-degree of a Node.
  1.2664      int operator[](const Key& key) const {
  1.2665        return _deg[key];
  1.2666 @@ -2701,6 +3714,56 @@
  1.2667      AutoNodeMap _deg;
  1.2668    };
  1.2669  
  1.2670 +  /// \brief Potential difference map
  1.2671 +  ///
  1.2672 +  /// PotentialDifferenceMap returns the difference between the potentials of
  1.2673 +  /// the source and target nodes of each arc in a digraph, i.e. it returns
  1.2674 +  /// \code
  1.2675 +  ///   potential[gr.target(arc)] - potential[gr.source(arc)].
  1.2676 +  /// \endcode
  1.2677 +  /// \tparam GR The digraph type.
  1.2678 +  /// \tparam POT A node map storing the potentials.
  1.2679 +  template <typename GR, typename POT>
  1.2680 +  class PotentialDifferenceMap {
  1.2681 +  public:
  1.2682 +    /// Key type
  1.2683 +    typedef typename GR::Arc Key;
  1.2684 +    /// Value type
  1.2685 +    typedef typename POT::Value Value;
  1.2686 +
  1.2687 +    /// \brief Constructor
  1.2688 +    ///
  1.2689 +    /// Contructor of the map.
  1.2690 +    explicit PotentialDifferenceMap(const GR& gr,
  1.2691 +                                    const POT& potential)
  1.2692 +      : _digraph(gr), _potential(potential) {}
  1.2693 +
  1.2694 +    /// \brief Returns the potential difference for the given arc.
  1.2695 +    ///
  1.2696 +    /// Returns the potential difference for the given arc, i.e.
  1.2697 +    /// \code
  1.2698 +    ///   potential[gr.target(arc)] - potential[gr.source(arc)].
  1.2699 +    /// \endcode
  1.2700 +    Value operator[](const Key& arc) const {
  1.2701 +      return _potential[_digraph.target(arc)] -
  1.2702 +        _potential[_digraph.source(arc)];
  1.2703 +    }
  1.2704 +
  1.2705 +  private:
  1.2706 +    const GR& _digraph;
  1.2707 +    const POT& _potential;
  1.2708 +  };
  1.2709 +
  1.2710 +  /// \brief Returns a PotentialDifferenceMap.
  1.2711 +  ///
  1.2712 +  /// This function just returns a PotentialDifferenceMap.
  1.2713 +  /// \relates PotentialDifferenceMap
  1.2714 +  template <typename GR, typename POT>
  1.2715 +  PotentialDifferenceMap<GR, POT>
  1.2716 +  potentialDifferenceMap(const GR& gr, const POT& potential) {
  1.2717 +    return PotentialDifferenceMap<GR, POT>(gr, potential);
  1.2718 +  }
  1.2719 +
  1.2720    /// @}
  1.2721  }
  1.2722