COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/maps.h @ 680:257e91516e09

Last change on this file since 680:257e91516e09 was 617:4137ef9aacc6, checked in by Peter Kovacs <kpeter@…>, 11 years ago

Fix and uniform the usage of Graph and Parent typedefs (#268)

  • Rename Graph typedefs to GraphType? in the implementation of graph maps and MapExtender? to prevent conflicts (especially using VS). They are not public.
  • Make Parent typedefs private in all classes.
  • Replace Digraph with Graph in some places (fix faulty renamings of the script).
  • Use Graph and Digraph typedefs (more) consequently.
File size: 77.7 KB
Line 
1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2009
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19#ifndef LEMON_MAPS_H
20#define LEMON_MAPS_H
21
22#include <iterator>
23#include <functional>
24#include <vector>
25
26#include <lemon/core.h>
27
28///\file
29///\ingroup maps
30///\brief Miscellaneous property maps
31
32#include <map>
33
34namespace lemon {
35
36  /// \addtogroup maps
37  /// @{
38
39  /// Base class of maps.
40
41  /// Base class of maps. It provides the necessary type definitions
42  /// required by the map %concepts.
43  template<typename K, typename V>
44  class MapBase {
45  public:
46    /// \brief The key type of the map.
47    typedef K Key;
48    /// \brief The value type of the map.
49    /// (The type of objects associated with the keys).
50    typedef V Value;
51  };
52
53
54  /// Null map. (a.k.a. DoNothingMap)
55
56  /// This map can be used if you have to provide a map only for
57  /// its type definitions, or if you have to provide a writable map,
58  /// but data written to it is not required (i.e. it will be sent to
59  /// <tt>/dev/null</tt>).
60  /// It conforms the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
61  ///
62  /// \sa ConstMap
63  template<typename K, typename V>
64  class NullMap : public MapBase<K, V> {
65  public:
66    ///\e
67    typedef K Key;
68    ///\e
69    typedef V Value;
70
71    /// Gives back a default constructed element.
72    Value operator[](const Key&) const { return Value(); }
73    /// Absorbs the value.
74    void set(const Key&, const Value&) {}
75  };
76
77  /// Returns a \c NullMap class
78
79  /// This function just returns a \c NullMap class.
80  /// \relates NullMap
81  template <typename K, typename V>
82  NullMap<K, V> nullMap() {
83    return NullMap<K, V>();
84  }
85
86
87  /// Constant map.
88
89  /// This \ref concepts::ReadMap "readable map" assigns a specified
90  /// value to each key.
91  ///
92  /// In other aspects it is equivalent to \c NullMap.
93  /// So it conforms the \ref concepts::ReadWriteMap "ReadWriteMap"
94  /// concept, but it absorbs the data written to it.
95  ///
96  /// The simplest way of using this map is through the constMap()
97  /// function.
98  ///
99  /// \sa NullMap
100  /// \sa IdentityMap
101  template<typename K, typename V>
102  class ConstMap : public MapBase<K, V> {
103  private:
104    V _value;
105  public:
106    ///\e
107    typedef K Key;
108    ///\e
109    typedef V Value;
110
111    /// Default constructor
112
113    /// Default constructor.
114    /// The value of the map will be default constructed.
115    ConstMap() {}
116
117    /// Constructor with specified initial value
118
119    /// Constructor with specified initial value.
120    /// \param v The initial value of the map.
121    ConstMap(const Value &v) : _value(v) {}
122
123    /// Gives back the specified value.
124    Value operator[](const Key&) const { return _value; }
125
126    /// Absorbs the value.
127    void set(const Key&, const Value&) {}
128
129    /// Sets the value that is assigned to each key.
130    void setAll(const Value &v) {
131      _value = v;
132    }
133
134    template<typename V1>
135    ConstMap(const ConstMap<K, V1> &, const Value &v) : _value(v) {}
136  };
137
138  /// Returns a \c ConstMap class
139
140  /// This function just returns a \c ConstMap class.
141  /// \relates ConstMap
142  template<typename K, typename V>
143  inline ConstMap<K, V> constMap(const V &v) {
144    return ConstMap<K, V>(v);
145  }
146
147  template<typename K, typename V>
148  inline ConstMap<K, V> constMap() {
149    return ConstMap<K, V>();
150  }
151
152
153  template<typename T, T v>
154  struct Const {};
155
156  /// Constant map with inlined constant value.
157
158  /// This \ref concepts::ReadMap "readable map" assigns a specified
159  /// value to each key.
160  ///
161  /// In other aspects it is equivalent to \c NullMap.
162  /// So it conforms the \ref concepts::ReadWriteMap "ReadWriteMap"
163  /// concept, but it absorbs the data written to it.
164  ///
165  /// The simplest way of using this map is through the constMap()
166  /// function.
167  ///
168  /// \sa NullMap
169  /// \sa IdentityMap
170  template<typename K, typename V, V v>
171  class ConstMap<K, Const<V, v> > : public MapBase<K, V> {
172  public:
173    ///\e
174    typedef K Key;
175    ///\e
176    typedef V Value;
177
178    /// Constructor.
179    ConstMap() {}
180
181    /// Gives back the specified value.
182    Value operator[](const Key&) const { return v; }
183
184    /// Absorbs the value.
185    void set(const Key&, const Value&) {}
186  };
187
188  /// Returns a \c ConstMap class with inlined constant value
189
190  /// This function just returns a \c ConstMap class with inlined
191  /// constant value.
192  /// \relates ConstMap
193  template<typename K, typename V, V v>
194  inline ConstMap<K, Const<V, v> > constMap() {
195    return ConstMap<K, Const<V, v> >();
196  }
197
198
199  /// Identity map.
200
201  /// This \ref concepts::ReadMap "read-only map" gives back the given
202  /// key as value without any modification.
203  ///
204  /// \sa ConstMap
205  template <typename T>
206  class IdentityMap : public MapBase<T, T> {
207  public:
208    ///\e
209    typedef T Key;
210    ///\e
211    typedef T Value;
212
213    /// Gives back the given value without any modification.
214    Value operator[](const Key &k) const {
215      return k;
216    }
217  };
218
219  /// Returns an \c IdentityMap class
220
221  /// This function just returns an \c IdentityMap class.
222  /// \relates IdentityMap
223  template<typename T>
224  inline IdentityMap<T> identityMap() {
225    return IdentityMap<T>();
226  }
227
228
229  /// \brief Map for storing values for integer keys from the range
230  /// <tt>[0..size-1]</tt>.
231  ///
232  /// This map is essentially a wrapper for \c std::vector. It assigns
233  /// values to integer keys from the range <tt>[0..size-1]</tt>.
234  /// It can be used with some data structures, for example
235  /// \c UnionFind, \c BinHeap, when the used items are small
236  /// integers. This map conforms the \ref concepts::ReferenceMap
237  /// "ReferenceMap" concept.
238  ///
239  /// The simplest way of using this map is through the rangeMap()
240  /// function.
241  template <typename V>
242  class RangeMap : public MapBase<int, V> {
243    template <typename V1>
244    friend class RangeMap;
245  private:
246
247    typedef std::vector<V> Vector;
248    Vector _vector;
249
250  public:
251
252    /// Key type
253    typedef int Key;
254    /// Value type
255    typedef V Value;
256    /// Reference type
257    typedef typename Vector::reference Reference;
258    /// Const reference type
259    typedef typename Vector::const_reference ConstReference;
260
261    typedef True ReferenceMapTag;
262
263  public:
264
265    /// Constructor with specified default value.
266    RangeMap(int size = 0, const Value &value = Value())
267      : _vector(size, value) {}
268
269    /// Constructs the map from an appropriate \c std::vector.
270    template <typename V1>
271    RangeMap(const std::vector<V1>& vector)
272      : _vector(vector.begin(), vector.end()) {}
273
274    /// Constructs the map from another \c RangeMap.
275    template <typename V1>
276    RangeMap(const RangeMap<V1> &c)
277      : _vector(c._vector.begin(), c._vector.end()) {}
278
279    /// Returns the size of the map.
280    int size() {
281      return _vector.size();
282    }
283
284    /// Resizes the map.
285
286    /// Resizes the underlying \c std::vector container, so changes the
287    /// keyset of the map.
288    /// \param size The new size of the map. The new keyset will be the
289    /// range <tt>[0..size-1]</tt>.
290    /// \param value The default value to assign to the new keys.
291    void resize(int size, const Value &value = Value()) {
292      _vector.resize(size, value);
293    }
294
295  private:
296
297    RangeMap& operator=(const RangeMap&);
298
299  public:
300
301    ///\e
302    Reference operator[](const Key &k) {
303      return _vector[k];
304    }
305
306    ///\e
307    ConstReference operator[](const Key &k) const {
308      return _vector[k];
309    }
310
311    ///\e
312    void set(const Key &k, const Value &v) {
313      _vector[k] = v;
314    }
315  };
316
317  /// Returns a \c RangeMap class
318
319  /// This function just returns a \c RangeMap class.
320  /// \relates RangeMap
321  template<typename V>
322  inline RangeMap<V> rangeMap(int size = 0, const V &value = V()) {
323    return RangeMap<V>(size, value);
324  }
325
326  /// \brief Returns a \c RangeMap class created from an appropriate
327  /// \c std::vector
328
329  /// This function just returns a \c RangeMap class created from an
330  /// appropriate \c std::vector.
331  /// \relates RangeMap
332  template<typename V>
333  inline RangeMap<V> rangeMap(const std::vector<V> &vector) {
334    return RangeMap<V>(vector);
335  }
336
337
338  /// Map type based on \c std::map
339
340  /// This map is essentially a wrapper for \c std::map with addition
341  /// that you can specify a default value for the keys that are not
342  /// stored actually. This value can be different from the default
343  /// contructed value (i.e. \c %Value()).
344  /// This type conforms the \ref concepts::ReferenceMap "ReferenceMap"
345  /// concept.
346  ///
347  /// This map is useful if a default value should be assigned to most of
348  /// the keys and different values should be assigned only to a few
349  /// keys (i.e. the map is "sparse").
350  /// The name of this type also refers to this important usage.
351  ///
352  /// Apart form that this map can be used in many other cases since it
353  /// is based on \c std::map, which is a general associative container.
354  /// However keep in mind that it is usually not as efficient as other
355  /// maps.
356  ///
357  /// The simplest way of using this map is through the sparseMap()
358  /// function.
359  template <typename K, typename V, typename Comp = std::less<K> >
360  class SparseMap : public MapBase<K, V> {
361    template <typename K1, typename V1, typename C1>
362    friend class SparseMap;
363  public:
364
365    /// Key type
366    typedef K Key;
367    /// Value type
368    typedef V Value;
369    /// Reference type
370    typedef Value& Reference;
371    /// Const reference type
372    typedef const Value& ConstReference;
373
374    typedef True ReferenceMapTag;
375
376  private:
377
378    typedef std::map<K, V, Comp> Map;
379    Map _map;
380    Value _value;
381
382  public:
383
384    /// \brief Constructor with specified default value.
385    SparseMap(const Value &value = Value()) : _value(value) {}
386    /// \brief Constructs the map from an appropriate \c std::map, and
387    /// explicitly specifies a default value.
388    template <typename V1, typename Comp1>
389    SparseMap(const std::map<Key, V1, Comp1> &map,
390              const Value &value = Value())
391      : _map(map.begin(), map.end()), _value(value) {}
392
393    /// \brief Constructs the map from another \c SparseMap.
394    template<typename V1, typename Comp1>
395    SparseMap(const SparseMap<Key, V1, Comp1> &c)
396      : _map(c._map.begin(), c._map.end()), _value(c._value) {}
397
398  private:
399
400    SparseMap& operator=(const SparseMap&);
401
402  public:
403
404    ///\e
405    Reference operator[](const Key &k) {
406      typename Map::iterator it = _map.lower_bound(k);
407      if (it != _map.end() && !_map.key_comp()(k, it->first))
408        return it->second;
409      else
410        return _map.insert(it, std::make_pair(k, _value))->second;
411    }
412
413    ///\e
414    ConstReference operator[](const Key &k) const {
415      typename Map::const_iterator it = _map.find(k);
416      if (it != _map.end())
417        return it->second;
418      else
419        return _value;
420    }
421
422    ///\e
423    void set(const Key &k, const Value &v) {
424      typename Map::iterator it = _map.lower_bound(k);
425      if (it != _map.end() && !_map.key_comp()(k, it->first))
426        it->second = v;
427      else
428        _map.insert(it, std::make_pair(k, v));
429    }
430
431    ///\e
432    void setAll(const Value &v) {
433      _value = v;
434      _map.clear();
435    }
436  };
437
438  /// Returns a \c SparseMap class
439
440  /// This function just returns a \c SparseMap class with specified
441  /// default value.
442  /// \relates SparseMap
443  template<typename K, typename V, typename Compare>
444  inline SparseMap<K, V, Compare> sparseMap(const V& value = V()) {
445    return SparseMap<K, V, Compare>(value);
446  }
447
448  template<typename K, typename V>
449  inline SparseMap<K, V, std::less<K> > sparseMap(const V& value = V()) {
450    return SparseMap<K, V, std::less<K> >(value);
451  }
452
453  /// \brief Returns a \c SparseMap class created from an appropriate
454  /// \c std::map
455
456  /// This function just returns a \c SparseMap class created from an
457  /// appropriate \c std::map.
458  /// \relates SparseMap
459  template<typename K, typename V, typename Compare>
460  inline SparseMap<K, V, Compare>
461    sparseMap(const std::map<K, V, Compare> &map, const V& value = V())
462  {
463    return SparseMap<K, V, Compare>(map, value);
464  }
465
466  /// @}
467
468  /// \addtogroup map_adaptors
469  /// @{
470
471  /// Composition of two maps
472
473  /// This \ref concepts::ReadMap "read-only map" returns the
474  /// composition of two given maps. That is to say, if \c m1 is of
475  /// type \c M1 and \c m2 is of \c M2, then for
476  /// \code
477  ///   ComposeMap<M1, M2> cm(m1,m2);
478  /// \endcode
479  /// <tt>cm[x]</tt> will be equal to <tt>m1[m2[x]]</tt>.
480  ///
481  /// The \c Key type of the map is inherited from \c M2 and the
482  /// \c Value type is from \c M1.
483  /// \c M2::Value must be convertible to \c M1::Key.
484  ///
485  /// The simplest way of using this map is through the composeMap()
486  /// function.
487  ///
488  /// \sa CombineMap
489  template <typename M1, typename M2>
490  class ComposeMap : public MapBase<typename M2::Key, typename M1::Value> {
491    const M1 &_m1;
492    const M2 &_m2;
493  public:
494    ///\e
495    typedef typename M2::Key Key;
496    ///\e
497    typedef typename M1::Value Value;
498
499    /// Constructor
500    ComposeMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
501
502    ///\e
503    typename MapTraits<M1>::ConstReturnValue
504    operator[](const Key &k) const { return _m1[_m2[k]]; }
505  };
506
507  /// Returns a \c ComposeMap class
508
509  /// This function just returns a \c ComposeMap class.
510  ///
511  /// If \c m1 and \c m2 are maps and the \c Value type of \c m2 is
512  /// convertible to the \c Key of \c m1, then <tt>composeMap(m1,m2)[x]</tt>
513  /// will be equal to <tt>m1[m2[x]]</tt>.
514  ///
515  /// \relates ComposeMap
516  template <typename M1, typename M2>
517  inline ComposeMap<M1, M2> composeMap(const M1 &m1, const M2 &m2) {
518    return ComposeMap<M1, M2>(m1, m2);
519  }
520
521
522  /// Combination of two maps using an STL (binary) functor.
523
524  /// This \ref concepts::ReadMap "read-only map" takes two maps and a
525  /// binary functor and returns the combination of the two given maps
526  /// using the functor.
527  /// That is to say, if \c m1 is of type \c M1 and \c m2 is of \c M2
528  /// and \c f is of \c F, then for
529  /// \code
530  ///   CombineMap<M1,M2,F,V> cm(m1,m2,f);
531  /// \endcode
532  /// <tt>cm[x]</tt> will be equal to <tt>f(m1[x],m2[x])</tt>.
533  ///
534  /// The \c Key type of the map is inherited from \c M1 (\c M1::Key
535  /// must be convertible to \c M2::Key) and the \c Value type is \c V.
536  /// \c M2::Value and \c M1::Value must be convertible to the
537  /// corresponding input parameter of \c F and the return type of \c F
538  /// must be convertible to \c V.
539  ///
540  /// The simplest way of using this map is through the combineMap()
541  /// function.
542  ///
543  /// \sa ComposeMap
544  template<typename M1, typename M2, typename F,
545           typename V = typename F::result_type>
546  class CombineMap : public MapBase<typename M1::Key, V> {
547    const M1 &_m1;
548    const M2 &_m2;
549    F _f;
550  public:
551    ///\e
552    typedef typename M1::Key Key;
553    ///\e
554    typedef V Value;
555
556    /// Constructor
557    CombineMap(const M1 &m1, const M2 &m2, const F &f = F())
558      : _m1(m1), _m2(m2), _f(f) {}
559    ///\e
560    Value operator[](const Key &k) const { return _f(_m1[k],_m2[k]); }
561  };
562
563  /// Returns a \c CombineMap class
564
565  /// This function just returns a \c CombineMap class.
566  ///
567  /// For example, if \c m1 and \c m2 are both maps with \c double
568  /// values, then
569  /// \code
570  ///   combineMap(m1,m2,std::plus<double>())
571  /// \endcode
572  /// is equivalent to
573  /// \code
574  ///   addMap(m1,m2)
575  /// \endcode
576  ///
577  /// This function is specialized for adaptable binary function
578  /// classes and C++ functions.
579  ///
580  /// \relates CombineMap
581  template<typename M1, typename M2, typename F, typename V>
582  inline CombineMap<M1, M2, F, V>
583  combineMap(const M1 &m1, const M2 &m2, const F &f) {
584    return CombineMap<M1, M2, F, V>(m1,m2,f);
585  }
586
587  template<typename M1, typename M2, typename F>
588  inline CombineMap<M1, M2, F, typename F::result_type>
589  combineMap(const M1 &m1, const M2 &m2, const F &f) {
590    return combineMap<M1, M2, F, typename F::result_type>(m1,m2,f);
591  }
592
593  template<typename M1, typename M2, typename K1, typename K2, typename V>
594  inline CombineMap<M1, M2, V (*)(K1, K2), V>
595  combineMap(const M1 &m1, const M2 &m2, V (*f)(K1, K2)) {
596    return combineMap<M1, M2, V (*)(K1, K2), V>(m1,m2,f);
597  }
598
599
600  /// Converts an STL style (unary) functor to a map
601
602  /// This \ref concepts::ReadMap "read-only map" returns the value
603  /// of a given functor. Actually, it just wraps the functor and
604  /// provides the \c Key and \c Value typedefs.
605  ///
606  /// Template parameters \c K and \c V will become its \c Key and
607  /// \c Value. In most cases they have to be given explicitly because
608  /// a functor typically does not provide \c argument_type and
609  /// \c result_type typedefs.
610  /// Parameter \c F is the type of the used functor.
611  ///
612  /// The simplest way of using this map is through the functorToMap()
613  /// function.
614  ///
615  /// \sa MapToFunctor
616  template<typename F,
617           typename K = typename F::argument_type,
618           typename V = typename F::result_type>
619  class FunctorToMap : public MapBase<K, V> {
620    F _f;
621  public:
622    ///\e
623    typedef K Key;
624    ///\e
625    typedef V Value;
626
627    /// Constructor
628    FunctorToMap(const F &f = F()) : _f(f) {}
629    ///\e
630    Value operator[](const Key &k) const { return _f(k); }
631  };
632
633  /// Returns a \c FunctorToMap class
634
635  /// This function just returns a \c FunctorToMap class.
636  ///
637  /// This function is specialized for adaptable binary function
638  /// classes and C++ functions.
639  ///
640  /// \relates FunctorToMap
641  template<typename K, typename V, typename F>
642  inline FunctorToMap<F, K, V> functorToMap(const F &f) {
643    return FunctorToMap<F, K, V>(f);
644  }
645
646  template <typename F>
647  inline FunctorToMap<F, typename F::argument_type, typename F::result_type>
648    functorToMap(const F &f)
649  {
650    return FunctorToMap<F, typename F::argument_type,
651      typename F::result_type>(f);
652  }
653
654  template <typename K, typename V>
655  inline FunctorToMap<V (*)(K), K, V> functorToMap(V (*f)(K)) {
656    return FunctorToMap<V (*)(K), K, V>(f);
657  }
658
659
660  /// Converts a map to an STL style (unary) functor
661
662  /// This class converts a map to an STL style (unary) functor.
663  /// That is it provides an <tt>operator()</tt> to read its values.
664  ///
665  /// For the sake of convenience it also works as a usual
666  /// \ref concepts::ReadMap "readable map", i.e. <tt>operator[]</tt>
667  /// and the \c Key and \c Value typedefs also exist.
668  ///
669  /// The simplest way of using this map is through the mapToFunctor()
670  /// function.
671  ///
672  ///\sa FunctorToMap
673  template <typename M>
674  class MapToFunctor : public MapBase<typename M::Key, typename M::Value> {
675    const M &_m;
676  public:
677    ///\e
678    typedef typename M::Key Key;
679    ///\e
680    typedef typename M::Value Value;
681
682    typedef typename M::Key argument_type;
683    typedef typename M::Value result_type;
684
685    /// Constructor
686    MapToFunctor(const M &m) : _m(m) {}
687    ///\e
688    Value operator()(const Key &k) const { return _m[k]; }
689    ///\e
690    Value operator[](const Key &k) const { return _m[k]; }
691  };
692
693  /// Returns a \c MapToFunctor class
694
695  /// This function just returns a \c MapToFunctor class.
696  /// \relates MapToFunctor
697  template<typename M>
698  inline MapToFunctor<M> mapToFunctor(const M &m) {
699    return MapToFunctor<M>(m);
700  }
701
702
703  /// \brief Map adaptor to convert the \c Value type of a map to
704  /// another type using the default conversion.
705
706  /// Map adaptor to convert the \c Value type of a \ref concepts::ReadMap
707  /// "readable map" to another type using the default conversion.
708  /// The \c Key type of it is inherited from \c M and the \c Value
709  /// type is \c V.
710  /// This type conforms the \ref concepts::ReadMap "ReadMap" concept.
711  ///
712  /// The simplest way of using this map is through the convertMap()
713  /// function.
714  template <typename M, typename V>
715  class ConvertMap : public MapBase<typename M::Key, V> {
716    const M &_m;
717  public:
718    ///\e
719    typedef typename M::Key Key;
720    ///\e
721    typedef V Value;
722
723    /// Constructor
724
725    /// Constructor.
726    /// \param m The underlying map.
727    ConvertMap(const M &m) : _m(m) {}
728
729    ///\e
730    Value operator[](const Key &k) const { return _m[k]; }
731  };
732
733  /// Returns a \c ConvertMap class
734
735  /// This function just returns a \c ConvertMap class.
736  /// \relates ConvertMap
737  template<typename V, typename M>
738  inline ConvertMap<M, V> convertMap(const M &map) {
739    return ConvertMap<M, V>(map);
740  }
741
742
743  /// Applies all map setting operations to two maps
744
745  /// This map has two \ref concepts::WriteMap "writable map" parameters
746  /// and each write request will be passed to both of them.
747  /// If \c M1 is also \ref concepts::ReadMap "readable", then the read
748  /// operations will return the corresponding values of \c M1.
749  ///
750  /// The \c Key and \c Value types are inherited from \c M1.
751  /// The \c Key and \c Value of \c M2 must be convertible from those
752  /// of \c M1.
753  ///
754  /// The simplest way of using this map is through the forkMap()
755  /// function.
756  template<typename  M1, typename M2>
757  class ForkMap : public MapBase<typename M1::Key, typename M1::Value> {
758    M1 &_m1;
759    M2 &_m2;
760  public:
761    ///\e
762    typedef typename M1::Key Key;
763    ///\e
764    typedef typename M1::Value Value;
765
766    /// Constructor
767    ForkMap(M1 &m1, M2 &m2) : _m1(m1), _m2(m2) {}
768    /// Returns the value associated with the given key in the first map.
769    Value operator[](const Key &k) const { return _m1[k]; }
770    /// Sets the value associated with the given key in both maps.
771    void set(const Key &k, const Value &v) { _m1.set(k,v); _m2.set(k,v); }
772  };
773
774  /// Returns a \c ForkMap class
775
776  /// This function just returns a \c ForkMap class.
777  /// \relates ForkMap
778  template <typename M1, typename M2>
779  inline ForkMap<M1,M2> forkMap(M1 &m1, M2 &m2) {
780    return ForkMap<M1,M2>(m1,m2);
781  }
782
783
784  /// Sum of two maps
785
786  /// This \ref concepts::ReadMap "read-only map" returns the sum
787  /// of the values of the two given maps.
788  /// Its \c Key and \c Value types are inherited from \c M1.
789  /// The \c Key and \c Value of \c M2 must be convertible to those of
790  /// \c M1.
791  ///
792  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
793  /// \code
794  ///   AddMap<M1,M2> am(m1,m2);
795  /// \endcode
796  /// <tt>am[x]</tt> will be equal to <tt>m1[x]+m2[x]</tt>.
797  ///
798  /// The simplest way of using this map is through the addMap()
799  /// function.
800  ///
801  /// \sa SubMap, MulMap, DivMap
802  /// \sa ShiftMap, ShiftWriteMap
803  template<typename M1, typename M2>
804  class AddMap : public MapBase<typename M1::Key, typename M1::Value> {
805    const M1 &_m1;
806    const M2 &_m2;
807  public:
808    ///\e
809    typedef typename M1::Key Key;
810    ///\e
811    typedef typename M1::Value Value;
812
813    /// Constructor
814    AddMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
815    ///\e
816    Value operator[](const Key &k) const { return _m1[k]+_m2[k]; }
817  };
818
819  /// Returns an \c AddMap class
820
821  /// This function just returns an \c AddMap class.
822  ///
823  /// For example, if \c m1 and \c m2 are both maps with \c double
824  /// values, then <tt>addMap(m1,m2)[x]</tt> will be equal to
825  /// <tt>m1[x]+m2[x]</tt>.
826  ///
827  /// \relates AddMap
828  template<typename M1, typename M2>
829  inline AddMap<M1, M2> addMap(const M1 &m1, const M2 &m2) {
830    return AddMap<M1, M2>(m1,m2);
831  }
832
833
834  /// Difference of two maps
835
836  /// This \ref concepts::ReadMap "read-only map" returns the difference
837  /// of the values of the two given maps.
838  /// Its \c Key and \c Value types are inherited from \c M1.
839  /// The \c Key and \c Value of \c M2 must be convertible to those of
840  /// \c M1.
841  ///
842  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
843  /// \code
844  ///   SubMap<M1,M2> sm(m1,m2);
845  /// \endcode
846  /// <tt>sm[x]</tt> will be equal to <tt>m1[x]-m2[x]</tt>.
847  ///
848  /// The simplest way of using this map is through the subMap()
849  /// function.
850  ///
851  /// \sa AddMap, MulMap, DivMap
852  template<typename M1, typename M2>
853  class SubMap : public MapBase<typename M1::Key, typename M1::Value> {
854    const M1 &_m1;
855    const M2 &_m2;
856  public:
857    ///\e
858    typedef typename M1::Key Key;
859    ///\e
860    typedef typename M1::Value Value;
861
862    /// Constructor
863    SubMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
864    ///\e
865    Value operator[](const Key &k) const { return _m1[k]-_m2[k]; }
866  };
867
868  /// Returns a \c SubMap class
869
870  /// This function just returns a \c SubMap class.
871  ///
872  /// For example, if \c m1 and \c m2 are both maps with \c double
873  /// values, then <tt>subMap(m1,m2)[x]</tt> will be equal to
874  /// <tt>m1[x]-m2[x]</tt>.
875  ///
876  /// \relates SubMap
877  template<typename M1, typename M2>
878  inline SubMap<M1, M2> subMap(const M1 &m1, const M2 &m2) {
879    return SubMap<M1, M2>(m1,m2);
880  }
881
882
883  /// Product of two maps
884
885  /// This \ref concepts::ReadMap "read-only map" returns the product
886  /// of the values of the two given maps.
887  /// Its \c Key and \c Value types are inherited from \c M1.
888  /// The \c Key and \c Value of \c M2 must be convertible to those of
889  /// \c M1.
890  ///
891  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
892  /// \code
893  ///   MulMap<M1,M2> mm(m1,m2);
894  /// \endcode
895  /// <tt>mm[x]</tt> will be equal to <tt>m1[x]*m2[x]</tt>.
896  ///
897  /// The simplest way of using this map is through the mulMap()
898  /// function.
899  ///
900  /// \sa AddMap, SubMap, DivMap
901  /// \sa ScaleMap, ScaleWriteMap
902  template<typename M1, typename M2>
903  class MulMap : public MapBase<typename M1::Key, typename M1::Value> {
904    const M1 &_m1;
905    const M2 &_m2;
906  public:
907    ///\e
908    typedef typename M1::Key Key;
909    ///\e
910    typedef typename M1::Value Value;
911
912    /// Constructor
913    MulMap(const M1 &m1,const M2 &m2) : _m1(m1), _m2(m2) {}
914    ///\e
915    Value operator[](const Key &k) const { return _m1[k]*_m2[k]; }
916  };
917
918  /// Returns a \c MulMap class
919
920  /// This function just returns a \c MulMap class.
921  ///
922  /// For example, if \c m1 and \c m2 are both maps with \c double
923  /// values, then <tt>mulMap(m1,m2)[x]</tt> will be equal to
924  /// <tt>m1[x]*m2[x]</tt>.
925  ///
926  /// \relates MulMap
927  template<typename M1, typename M2>
928  inline MulMap<M1, M2> mulMap(const M1 &m1,const M2 &m2) {
929    return MulMap<M1, M2>(m1,m2);
930  }
931
932
933  /// Quotient of two maps
934
935  /// This \ref concepts::ReadMap "read-only map" returns the quotient
936  /// of the values of the two given maps.
937  /// Its \c Key and \c Value types are inherited from \c M1.
938  /// The \c Key and \c Value of \c M2 must be convertible to those of
939  /// \c M1.
940  ///
941  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
942  /// \code
943  ///   DivMap<M1,M2> dm(m1,m2);
944  /// \endcode
945  /// <tt>dm[x]</tt> will be equal to <tt>m1[x]/m2[x]</tt>.
946  ///
947  /// The simplest way of using this map is through the divMap()
948  /// function.
949  ///
950  /// \sa AddMap, SubMap, MulMap
951  template<typename M1, typename M2>
952  class DivMap : public MapBase<typename M1::Key, typename M1::Value> {
953    const M1 &_m1;
954    const M2 &_m2;
955  public:
956    ///\e
957    typedef typename M1::Key Key;
958    ///\e
959    typedef typename M1::Value Value;
960
961    /// Constructor
962    DivMap(const M1 &m1,const M2 &m2) : _m1(m1), _m2(m2) {}
963    ///\e
964    Value operator[](const Key &k) const { return _m1[k]/_m2[k]; }
965  };
966
967  /// Returns a \c DivMap class
968
969  /// This function just returns a \c DivMap class.
970  ///
971  /// For example, if \c m1 and \c m2 are both maps with \c double
972  /// values, then <tt>divMap(m1,m2)[x]</tt> will be equal to
973  /// <tt>m1[x]/m2[x]</tt>.
974  ///
975  /// \relates DivMap
976  template<typename M1, typename M2>
977  inline DivMap<M1, M2> divMap(const M1 &m1,const M2 &m2) {
978    return DivMap<M1, M2>(m1,m2);
979  }
980
981
982  /// Shifts a map with a constant.
983
984  /// This \ref concepts::ReadMap "read-only map" returns the sum of
985  /// the given map and a constant value (i.e. it shifts the map with
986  /// the constant). Its \c Key and \c Value are inherited from \c M.
987  ///
988  /// Actually,
989  /// \code
990  ///   ShiftMap<M> sh(m,v);
991  /// \endcode
992  /// is equivalent to
993  /// \code
994  ///   ConstMap<M::Key, M::Value> cm(v);
995  ///   AddMap<M, ConstMap<M::Key, M::Value> > sh(m,cm);
996  /// \endcode
997  ///
998  /// The simplest way of using this map is through the shiftMap()
999  /// function.
1000  ///
1001  /// \sa ShiftWriteMap
1002  template<typename M, typename C = typename M::Value>
1003  class ShiftMap : public MapBase<typename M::Key, typename M::Value> {
1004    const M &_m;
1005    C _v;
1006  public:
1007    ///\e
1008    typedef typename M::Key Key;
1009    ///\e
1010    typedef typename M::Value Value;
1011
1012    /// Constructor
1013
1014    /// Constructor.
1015    /// \param m The undelying map.
1016    /// \param v The constant value.
1017    ShiftMap(const M &m, const C &v) : _m(m), _v(v) {}
1018    ///\e
1019    Value operator[](const Key &k) const { return _m[k]+_v; }
1020  };
1021
1022  /// Shifts a map with a constant (read-write version).
1023
1024  /// This \ref concepts::ReadWriteMap "read-write map" returns the sum
1025  /// of the given map and a constant value (i.e. it shifts the map with
1026  /// the constant). Its \c Key and \c Value are inherited from \c M.
1027  /// It makes also possible to write the map.
1028  ///
1029  /// The simplest way of using this map is through the shiftWriteMap()
1030  /// function.
1031  ///
1032  /// \sa ShiftMap
1033  template<typename M, typename C = typename M::Value>
1034  class ShiftWriteMap : public MapBase<typename M::Key, typename M::Value> {
1035    M &_m;
1036    C _v;
1037  public:
1038    ///\e
1039    typedef typename M::Key Key;
1040    ///\e
1041    typedef typename M::Value Value;
1042
1043    /// Constructor
1044
1045    /// Constructor.
1046    /// \param m The undelying map.
1047    /// \param v The constant value.
1048    ShiftWriteMap(M &m, const C &v) : _m(m), _v(v) {}
1049    ///\e
1050    Value operator[](const Key &k) const { return _m[k]+_v; }
1051    ///\e
1052    void set(const Key &k, const Value &v) { _m.set(k, v-_v); }
1053  };
1054
1055  /// Returns a \c ShiftMap class
1056
1057  /// This function just returns a \c ShiftMap class.
1058  ///
1059  /// For example, if \c m is a map with \c double values and \c v is
1060  /// \c double, then <tt>shiftMap(m,v)[x]</tt> will be equal to
1061  /// <tt>m[x]+v</tt>.
1062  ///
1063  /// \relates ShiftMap
1064  template<typename M, typename C>
1065  inline ShiftMap<M, C> shiftMap(const M &m, const C &v) {
1066    return ShiftMap<M, C>(m,v);
1067  }
1068
1069  /// Returns a \c ShiftWriteMap class
1070
1071  /// This function just returns a \c ShiftWriteMap class.
1072  ///
1073  /// For example, if \c m is a map with \c double values and \c v is
1074  /// \c double, then <tt>shiftWriteMap(m,v)[x]</tt> will be equal to
1075  /// <tt>m[x]+v</tt>.
1076  /// Moreover it makes also possible to write the map.
1077  ///
1078  /// \relates ShiftWriteMap
1079  template<typename M, typename C>
1080  inline ShiftWriteMap<M, C> shiftWriteMap(M &m, const C &v) {
1081    return ShiftWriteMap<M, C>(m,v);
1082  }
1083
1084
1085  /// Scales a map with a constant.
1086
1087  /// This \ref concepts::ReadMap "read-only map" returns the value of
1088  /// the given map multiplied from the left side with a constant value.
1089  /// Its \c Key and \c Value are inherited from \c M.
1090  ///
1091  /// Actually,
1092  /// \code
1093  ///   ScaleMap<M> sc(m,v);
1094  /// \endcode
1095  /// is equivalent to
1096  /// \code
1097  ///   ConstMap<M::Key, M::Value> cm(v);
1098  ///   MulMap<ConstMap<M::Key, M::Value>, M> sc(cm,m);
1099  /// \endcode
1100  ///
1101  /// The simplest way of using this map is through the scaleMap()
1102  /// function.
1103  ///
1104  /// \sa ScaleWriteMap
1105  template<typename M, typename C = typename M::Value>
1106  class ScaleMap : public MapBase<typename M::Key, typename M::Value> {
1107    const M &_m;
1108    C _v;
1109  public:
1110    ///\e
1111    typedef typename M::Key Key;
1112    ///\e
1113    typedef typename M::Value Value;
1114
1115    /// Constructor
1116
1117    /// Constructor.
1118    /// \param m The undelying map.
1119    /// \param v The constant value.
1120    ScaleMap(const M &m, const C &v) : _m(m), _v(v) {}
1121    ///\e
1122    Value operator[](const Key &k) const { return _v*_m[k]; }
1123  };
1124
1125  /// Scales a map with a constant (read-write version).
1126
1127  /// This \ref concepts::ReadWriteMap "read-write map" returns the value of
1128  /// the given map multiplied from the left side with a constant value.
1129  /// Its \c Key and \c Value are inherited from \c M.
1130  /// It can also be used as write map if the \c / operator is defined
1131  /// between \c Value and \c C and the given multiplier is not zero.
1132  ///
1133  /// The simplest way of using this map is through the scaleWriteMap()
1134  /// function.
1135  ///
1136  /// \sa ScaleMap
1137  template<typename M, typename C = typename M::Value>
1138  class ScaleWriteMap : public MapBase<typename M::Key, typename M::Value> {
1139    M &_m;
1140    C _v;
1141  public:
1142    ///\e
1143    typedef typename M::Key Key;
1144    ///\e
1145    typedef typename M::Value Value;
1146
1147    /// Constructor
1148
1149    /// Constructor.
1150    /// \param m The undelying map.
1151    /// \param v The constant value.
1152    ScaleWriteMap(M &m, const C &v) : _m(m), _v(v) {}
1153    ///\e
1154    Value operator[](const Key &k) const { return _v*_m[k]; }
1155    ///\e
1156    void set(const Key &k, const Value &v) { _m.set(k, v/_v); }
1157  };
1158
1159  /// Returns a \c ScaleMap class
1160
1161  /// This function just returns a \c ScaleMap class.
1162  ///
1163  /// For example, if \c m is a map with \c double values and \c v is
1164  /// \c double, then <tt>scaleMap(m,v)[x]</tt> will be equal to
1165  /// <tt>v*m[x]</tt>.
1166  ///
1167  /// \relates ScaleMap
1168  template<typename M, typename C>
1169  inline ScaleMap<M, C> scaleMap(const M &m, const C &v) {
1170    return ScaleMap<M, C>(m,v);
1171  }
1172
1173  /// Returns a \c ScaleWriteMap class
1174
1175  /// This function just returns a \c ScaleWriteMap class.
1176  ///
1177  /// For example, if \c m is a map with \c double values and \c v is
1178  /// \c double, then <tt>scaleWriteMap(m,v)[x]</tt> will be equal to
1179  /// <tt>v*m[x]</tt>.
1180  /// Moreover it makes also possible to write the map.
1181  ///
1182  /// \relates ScaleWriteMap
1183  template<typename M, typename C>
1184  inline ScaleWriteMap<M, C> scaleWriteMap(M &m, const C &v) {
1185    return ScaleWriteMap<M, C>(m,v);
1186  }
1187
1188
1189  /// Negative of a map
1190
1191  /// This \ref concepts::ReadMap "read-only map" returns the negative
1192  /// of the values of the given map (using the unary \c - operator).
1193  /// Its \c Key and \c Value are inherited from \c M.
1194  ///
1195  /// If M::Value is \c int, \c double etc., then
1196  /// \code
1197  ///   NegMap<M> neg(m);
1198  /// \endcode
1199  /// is equivalent to
1200  /// \code
1201  ///   ScaleMap<M> neg(m,-1);
1202  /// \endcode
1203  ///
1204  /// The simplest way of using this map is through the negMap()
1205  /// function.
1206  ///
1207  /// \sa NegWriteMap
1208  template<typename M>
1209  class NegMap : public MapBase<typename M::Key, typename M::Value> {
1210    const M& _m;
1211  public:
1212    ///\e
1213    typedef typename M::Key Key;
1214    ///\e
1215    typedef typename M::Value Value;
1216
1217    /// Constructor
1218    NegMap(const M &m) : _m(m) {}
1219    ///\e
1220    Value operator[](const Key &k) const { return -_m[k]; }
1221  };
1222
1223  /// Negative of a map (read-write version)
1224
1225  /// This \ref concepts::ReadWriteMap "read-write map" returns the
1226  /// negative of the values of the given map (using the unary \c -
1227  /// operator).
1228  /// Its \c Key and \c Value are inherited from \c M.
1229  /// It makes also possible to write the map.
1230  ///
1231  /// If M::Value is \c int, \c double etc., then
1232  /// \code
1233  ///   NegWriteMap<M> neg(m);
1234  /// \endcode
1235  /// is equivalent to
1236  /// \code
1237  ///   ScaleWriteMap<M> neg(m,-1);
1238  /// \endcode
1239  ///
1240  /// The simplest way of using this map is through the negWriteMap()
1241  /// function.
1242  ///
1243  /// \sa NegMap
1244  template<typename M>
1245  class NegWriteMap : public MapBase<typename M::Key, typename M::Value> {
1246    M &_m;
1247  public:
1248    ///\e
1249    typedef typename M::Key Key;
1250    ///\e
1251    typedef typename M::Value Value;
1252
1253    /// Constructor
1254    NegWriteMap(M &m) : _m(m) {}
1255    ///\e
1256    Value operator[](const Key &k) const { return -_m[k]; }
1257    ///\e
1258    void set(const Key &k, const Value &v) { _m.set(k, -v); }
1259  };
1260
1261  /// Returns a \c NegMap class
1262
1263  /// This function just returns a \c NegMap class.
1264  ///
1265  /// For example, if \c m is a map with \c double values, then
1266  /// <tt>negMap(m)[x]</tt> will be equal to <tt>-m[x]</tt>.
1267  ///
1268  /// \relates NegMap
1269  template <typename M>
1270  inline NegMap<M> negMap(const M &m) {
1271    return NegMap<M>(m);
1272  }
1273
1274  /// Returns a \c NegWriteMap class
1275
1276  /// This function just returns a \c NegWriteMap class.
1277  ///
1278  /// For example, if \c m is a map with \c double values, then
1279  /// <tt>negWriteMap(m)[x]</tt> will be equal to <tt>-m[x]</tt>.
1280  /// Moreover it makes also possible to write the map.
1281  ///
1282  /// \relates NegWriteMap
1283  template <typename M>
1284  inline NegWriteMap<M> negWriteMap(M &m) {
1285    return NegWriteMap<M>(m);
1286  }
1287
1288
1289  /// Absolute value of a map
1290
1291  /// This \ref concepts::ReadMap "read-only map" returns the absolute
1292  /// value of the values of the given map.
1293  /// Its \c Key and \c Value are inherited from \c M.
1294  /// \c Value must be comparable to \c 0 and the unary \c -
1295  /// operator must be defined for it, of course.
1296  ///
1297  /// The simplest way of using this map is through the absMap()
1298  /// function.
1299  template<typename M>
1300  class AbsMap : public MapBase<typename M::Key, typename M::Value> {
1301    const M &_m;
1302  public:
1303    ///\e
1304    typedef typename M::Key Key;
1305    ///\e
1306    typedef typename M::Value Value;
1307
1308    /// Constructor
1309    AbsMap(const M &m) : _m(m) {}
1310    ///\e
1311    Value operator[](const Key &k) const {
1312      Value tmp = _m[k];
1313      return tmp >= 0 ? tmp : -tmp;
1314    }
1315
1316  };
1317
1318  /// Returns an \c AbsMap class
1319
1320  /// This function just returns an \c AbsMap class.
1321  ///
1322  /// For example, if \c m is a map with \c double values, then
1323  /// <tt>absMap(m)[x]</tt> will be equal to <tt>m[x]</tt> if
1324  /// it is positive or zero and <tt>-m[x]</tt> if <tt>m[x]</tt> is
1325  /// negative.
1326  ///
1327  /// \relates AbsMap
1328  template<typename M>
1329  inline AbsMap<M> absMap(const M &m) {
1330    return AbsMap<M>(m);
1331  }
1332
1333  /// @}
1334
1335  // Logical maps and map adaptors:
1336
1337  /// \addtogroup maps
1338  /// @{
1339
1340  /// Constant \c true map.
1341
1342  /// This \ref concepts::ReadMap "read-only map" assigns \c true to
1343  /// each key.
1344  ///
1345  /// Note that
1346  /// \code
1347  ///   TrueMap<K> tm;
1348  /// \endcode
1349  /// is equivalent to
1350  /// \code
1351  ///   ConstMap<K,bool> tm(true);
1352  /// \endcode
1353  ///
1354  /// \sa FalseMap
1355  /// \sa ConstMap
1356  template <typename K>
1357  class TrueMap : public MapBase<K, bool> {
1358  public:
1359    ///\e
1360    typedef K Key;
1361    ///\e
1362    typedef bool Value;
1363
1364    /// Gives back \c true.
1365    Value operator[](const Key&) const { return true; }
1366  };
1367
1368  /// Returns a \c TrueMap class
1369
1370  /// This function just returns a \c TrueMap class.
1371  /// \relates TrueMap
1372  template<typename K>
1373  inline TrueMap<K> trueMap() {
1374    return TrueMap<K>();
1375  }
1376
1377
1378  /// Constant \c false map.
1379
1380  /// This \ref concepts::ReadMap "read-only map" assigns \c false to
1381  /// each key.
1382  ///
1383  /// Note that
1384  /// \code
1385  ///   FalseMap<K> fm;
1386  /// \endcode
1387  /// is equivalent to
1388  /// \code
1389  ///   ConstMap<K,bool> fm(false);
1390  /// \endcode
1391  ///
1392  /// \sa TrueMap
1393  /// \sa ConstMap
1394  template <typename K>
1395  class FalseMap : public MapBase<K, bool> {
1396  public:
1397    ///\e
1398    typedef K Key;
1399    ///\e
1400    typedef bool Value;
1401
1402    /// Gives back \c false.
1403    Value operator[](const Key&) const { return false; }
1404  };
1405
1406  /// Returns a \c FalseMap class
1407
1408  /// This function just returns a \c FalseMap class.
1409  /// \relates FalseMap
1410  template<typename K>
1411  inline FalseMap<K> falseMap() {
1412    return FalseMap<K>();
1413  }
1414
1415  /// @}
1416
1417  /// \addtogroup map_adaptors
1418  /// @{
1419
1420  /// Logical 'and' of two maps
1421
1422  /// This \ref concepts::ReadMap "read-only map" returns the logical
1423  /// 'and' of the values of the two given maps.
1424  /// Its \c Key type is inherited from \c M1 and its \c Value type is
1425  /// \c bool. \c M2::Key must be convertible to \c M1::Key.
1426  ///
1427  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
1428  /// \code
1429  ///   AndMap<M1,M2> am(m1,m2);
1430  /// \endcode
1431  /// <tt>am[x]</tt> will be equal to <tt>m1[x]&&m2[x]</tt>.
1432  ///
1433  /// The simplest way of using this map is through the andMap()
1434  /// function.
1435  ///
1436  /// \sa OrMap
1437  /// \sa NotMap, NotWriteMap
1438  template<typename M1, typename M2>
1439  class AndMap : public MapBase<typename M1::Key, bool> {
1440    const M1 &_m1;
1441    const M2 &_m2;
1442  public:
1443    ///\e
1444    typedef typename M1::Key Key;
1445    ///\e
1446    typedef bool Value;
1447
1448    /// Constructor
1449    AndMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
1450    ///\e
1451    Value operator[](const Key &k) const { return _m1[k]&&_m2[k]; }
1452  };
1453
1454  /// Returns an \c AndMap class
1455
1456  /// This function just returns an \c AndMap class.
1457  ///
1458  /// For example, if \c m1 and \c m2 are both maps with \c bool values,
1459  /// then <tt>andMap(m1,m2)[x]</tt> will be equal to
1460  /// <tt>m1[x]&&m2[x]</tt>.
1461  ///
1462  /// \relates AndMap
1463  template<typename M1, typename M2>
1464  inline AndMap<M1, M2> andMap(const M1 &m1, const M2 &m2) {
1465    return AndMap<M1, M2>(m1,m2);
1466  }
1467
1468
1469  /// Logical 'or' of two maps
1470
1471  /// This \ref concepts::ReadMap "read-only map" returns the logical
1472  /// 'or' of the values of the two given maps.
1473  /// Its \c Key type is inherited from \c M1 and its \c Value type is
1474  /// \c bool. \c M2::Key must be convertible to \c M1::Key.
1475  ///
1476  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
1477  /// \code
1478  ///   OrMap<M1,M2> om(m1,m2);
1479  /// \endcode
1480  /// <tt>om[x]</tt> will be equal to <tt>m1[x]||m2[x]</tt>.
1481  ///
1482  /// The simplest way of using this map is through the orMap()
1483  /// function.
1484  ///
1485  /// \sa AndMap
1486  /// \sa NotMap, NotWriteMap
1487  template<typename M1, typename M2>
1488  class OrMap : public MapBase<typename M1::Key, bool> {
1489    const M1 &_m1;
1490    const M2 &_m2;
1491  public:
1492    ///\e
1493    typedef typename M1::Key Key;
1494    ///\e
1495    typedef bool Value;
1496
1497    /// Constructor
1498    OrMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
1499    ///\e
1500    Value operator[](const Key &k) const { return _m1[k]||_m2[k]; }
1501  };
1502
1503  /// Returns an \c OrMap class
1504
1505  /// This function just returns an \c OrMap class.
1506  ///
1507  /// For example, if \c m1 and \c m2 are both maps with \c bool values,
1508  /// then <tt>orMap(m1,m2)[x]</tt> will be equal to
1509  /// <tt>m1[x]||m2[x]</tt>.
1510  ///
1511  /// \relates OrMap
1512  template<typename M1, typename M2>
1513  inline OrMap<M1, M2> orMap(const M1 &m1, const M2 &m2) {
1514    return OrMap<M1, M2>(m1,m2);
1515  }
1516
1517
1518  /// Logical 'not' of a map
1519
1520  /// This \ref concepts::ReadMap "read-only map" returns the logical
1521  /// negation of the values of the given map.
1522  /// Its \c Key is inherited from \c M and its \c Value is \c bool.
1523  ///
1524  /// The simplest way of using this map is through the notMap()
1525  /// function.
1526  ///
1527  /// \sa NotWriteMap
1528  template <typename M>
1529  class NotMap : public MapBase<typename M::Key, bool> {
1530    const M &_m;
1531  public:
1532    ///\e
1533    typedef typename M::Key Key;
1534    ///\e
1535    typedef bool Value;
1536
1537    /// Constructor
1538    NotMap(const M &m) : _m(m) {}
1539    ///\e
1540    Value operator[](const Key &k) const { return !_m[k]; }
1541  };
1542
1543  /// Logical 'not' of a map (read-write version)
1544
1545  /// This \ref concepts::ReadWriteMap "read-write map" returns the
1546  /// logical negation of the values of the given map.
1547  /// Its \c Key is inherited from \c M and its \c Value is \c bool.
1548  /// It makes also possible to write the map. When a value is set,
1549  /// the opposite value is set to the original map.
1550  ///
1551  /// The simplest way of using this map is through the notWriteMap()
1552  /// function.
1553  ///
1554  /// \sa NotMap
1555  template <typename M>
1556  class NotWriteMap : public MapBase<typename M::Key, bool> {
1557    M &_m;
1558  public:
1559    ///\e
1560    typedef typename M::Key Key;
1561    ///\e
1562    typedef bool Value;
1563
1564    /// Constructor
1565    NotWriteMap(M &m) : _m(m) {}
1566    ///\e
1567    Value operator[](const Key &k) const { return !_m[k]; }
1568    ///\e
1569    void set(const Key &k, bool v) { _m.set(k, !v); }
1570  };
1571
1572  /// Returns a \c NotMap class
1573
1574  /// This function just returns a \c NotMap class.
1575  ///
1576  /// For example, if \c m is a map with \c bool values, then
1577  /// <tt>notMap(m)[x]</tt> will be equal to <tt>!m[x]</tt>.
1578  ///
1579  /// \relates NotMap
1580  template <typename M>
1581  inline NotMap<M> notMap(const M &m) {
1582    return NotMap<M>(m);
1583  }
1584
1585  /// Returns a \c NotWriteMap class
1586
1587  /// This function just returns a \c NotWriteMap class.
1588  ///
1589  /// For example, if \c m is a map with \c bool values, then
1590  /// <tt>notWriteMap(m)[x]</tt> will be equal to <tt>!m[x]</tt>.
1591  /// Moreover it makes also possible to write the map.
1592  ///
1593  /// \relates NotWriteMap
1594  template <typename M>
1595  inline NotWriteMap<M> notWriteMap(M &m) {
1596    return NotWriteMap<M>(m);
1597  }
1598
1599
1600  /// Combination of two maps using the \c == operator
1601
1602  /// This \ref concepts::ReadMap "read-only map" assigns \c true to
1603  /// the keys for which the corresponding values of the two maps are
1604  /// equal.
1605  /// Its \c Key type is inherited from \c M1 and its \c Value type is
1606  /// \c bool. \c M2::Key must be convertible to \c M1::Key.
1607  ///
1608  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
1609  /// \code
1610  ///   EqualMap<M1,M2> em(m1,m2);
1611  /// \endcode
1612  /// <tt>em[x]</tt> will be equal to <tt>m1[x]==m2[x]</tt>.
1613  ///
1614  /// The simplest way of using this map is through the equalMap()
1615  /// function.
1616  ///
1617  /// \sa LessMap
1618  template<typename M1, typename M2>
1619  class EqualMap : public MapBase<typename M1::Key, bool> {
1620    const M1 &_m1;
1621    const M2 &_m2;
1622  public:
1623    ///\e
1624    typedef typename M1::Key Key;
1625    ///\e
1626    typedef bool Value;
1627
1628    /// Constructor
1629    EqualMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
1630    ///\e
1631    Value operator[](const Key &k) const { return _m1[k]==_m2[k]; }
1632  };
1633
1634  /// Returns an \c EqualMap class
1635
1636  /// This function just returns an \c EqualMap class.
1637  ///
1638  /// For example, if \c m1 and \c m2 are maps with keys and values of
1639  /// the same type, then <tt>equalMap(m1,m2)[x]</tt> will be equal to
1640  /// <tt>m1[x]==m2[x]</tt>.
1641  ///
1642  /// \relates EqualMap
1643  template<typename M1, typename M2>
1644  inline EqualMap<M1, M2> equalMap(const M1 &m1, const M2 &m2) {
1645    return EqualMap<M1, M2>(m1,m2);
1646  }
1647
1648
1649  /// Combination of two maps using the \c < operator
1650
1651  /// This \ref concepts::ReadMap "read-only map" assigns \c true to
1652  /// the keys for which the corresponding value of the first map is
1653  /// less then the value of the second map.
1654  /// Its \c Key type is inherited from \c M1 and its \c Value type is
1655  /// \c bool. \c M2::Key must be convertible to \c M1::Key.
1656  ///
1657  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
1658  /// \code
1659  ///   LessMap<M1,M2> lm(m1,m2);
1660  /// \endcode
1661  /// <tt>lm[x]</tt> will be equal to <tt>m1[x]<m2[x]</tt>.
1662  ///
1663  /// The simplest way of using this map is through the lessMap()
1664  /// function.
1665  ///
1666  /// \sa EqualMap
1667  template<typename M1, typename M2>
1668  class LessMap : public MapBase<typename M1::Key, bool> {
1669    const M1 &_m1;
1670    const M2 &_m2;
1671  public:
1672    ///\e
1673    typedef typename M1::Key Key;
1674    ///\e
1675    typedef bool Value;
1676
1677    /// Constructor
1678    LessMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
1679    ///\e
1680    Value operator[](const Key &k) const { return _m1[k]<_m2[k]; }
1681  };
1682
1683  /// Returns an \c LessMap class
1684
1685  /// This function just returns an \c LessMap class.
1686  ///
1687  /// For example, if \c m1 and \c m2 are maps with keys and values of
1688  /// the same type, then <tt>lessMap(m1,m2)[x]</tt> will be equal to
1689  /// <tt>m1[x]<m2[x]</tt>.
1690  ///
1691  /// \relates LessMap
1692  template<typename M1, typename M2>
1693  inline LessMap<M1, M2> lessMap(const M1 &m1, const M2 &m2) {
1694    return LessMap<M1, M2>(m1,m2);
1695  }
1696
1697  namespace _maps_bits {
1698
1699    template <typename _Iterator, typename Enable = void>
1700    struct IteratorTraits {
1701      typedef typename std::iterator_traits<_Iterator>::value_type Value;
1702    };
1703
1704    template <typename _Iterator>
1705    struct IteratorTraits<_Iterator,
1706      typename exists<typename _Iterator::container_type>::type>
1707    {
1708      typedef typename _Iterator::container_type::value_type Value;
1709    };
1710
1711  }
1712
1713  /// @}
1714
1715  /// \addtogroup maps
1716  /// @{
1717
1718  /// \brief Writable bool map for logging each \c true assigned element
1719  ///
1720  /// A \ref concepts::WriteMap "writable" bool map for logging
1721  /// each \c true assigned element, i.e it copies subsequently each
1722  /// keys set to \c true to the given iterator.
1723  /// The most important usage of it is storing certain nodes or arcs
1724  /// that were marked \c true by an algorithm.
1725  ///
1726  /// There are several algorithms that provide solutions through bool
1727  /// maps and most of them assign \c true at most once for each key.
1728  /// In these cases it is a natural request to store each \c true
1729  /// assigned elements (in order of the assignment), which can be
1730  /// easily done with LoggerBoolMap.
1731  ///
1732  /// The simplest way of using this map is through the loggerBoolMap()
1733  /// function.
1734  ///
1735  /// \tparam IT The type of the iterator.
1736  /// \tparam KEY The key type of the map. The default value set
1737  /// according to the iterator type should work in most cases.
1738  ///
1739  /// \note The container of the iterator must contain enough space
1740  /// for the elements or the iterator should be an inserter iterator.
1741#ifdef DOXYGEN
1742  template <typename IT, typename KEY>
1743#else
1744  template <typename IT,
1745            typename KEY = typename _maps_bits::IteratorTraits<IT>::Value>
1746#endif
1747  class LoggerBoolMap : public MapBase<KEY, bool> {
1748  public:
1749
1750    ///\e
1751    typedef KEY Key;
1752    ///\e
1753    typedef bool Value;
1754    ///\e
1755    typedef IT Iterator;
1756
1757    /// Constructor
1758    LoggerBoolMap(Iterator it)
1759      : _begin(it), _end(it) {}
1760
1761    /// Gives back the given iterator set for the first key
1762    Iterator begin() const {
1763      return _begin;
1764    }
1765
1766    /// Gives back the the 'after the last' iterator
1767    Iterator end() const {
1768      return _end;
1769    }
1770
1771    /// The set function of the map
1772    void set(const Key& key, Value value) {
1773      if (value) {
1774        *_end++ = key;
1775      }
1776    }
1777
1778  private:
1779    Iterator _begin;
1780    Iterator _end;
1781  };
1782
1783  /// Returns a \c LoggerBoolMap class
1784
1785  /// This function just returns a \c LoggerBoolMap class.
1786  ///
1787  /// The most important usage of it is storing certain nodes or arcs
1788  /// that were marked \c true by an algorithm.
1789  /// For example it makes easier to store the nodes in the processing
1790  /// order of Dfs algorithm, as the following examples show.
1791  /// \code
1792  ///   std::vector<Node> v;
1793  ///   dfs(g,s).processedMap(loggerBoolMap(std::back_inserter(v))).run();
1794  /// \endcode
1795  /// \code
1796  ///   std::vector<Node> v(countNodes(g));
1797  ///   dfs(g,s).processedMap(loggerBoolMap(v.begin())).run();
1798  /// \endcode
1799  ///
1800  /// \note The container of the iterator must contain enough space
1801  /// for the elements or the iterator should be an inserter iterator.
1802  ///
1803  /// \note LoggerBoolMap is just \ref concepts::WriteMap "writable", so
1804  /// it cannot be used when a readable map is needed, for example as
1805  /// \c ReachedMap for \c Bfs, \c Dfs and \c Dijkstra algorithms.
1806  ///
1807  /// \relates LoggerBoolMap
1808  template<typename Iterator>
1809  inline LoggerBoolMap<Iterator> loggerBoolMap(Iterator it) {
1810    return LoggerBoolMap<Iterator>(it);
1811  }
1812
1813  /// @}
1814
1815  /// \addtogroup graph_maps
1816  /// @{
1817
1818  /// \brief Provides an immutable and unique id for each item in a graph.
1819  ///
1820  /// IdMap provides a unique and immutable id for each item of the
1821  /// same type (\c Node, \c Arc or \c Edge) in a graph. This id is
1822  ///  - \b unique: different items get different ids,
1823  ///  - \b immutable: the id of an item does not change (even if you
1824  ///    delete other nodes).
1825  ///
1826  /// Using this map you get access (i.e. can read) the inner id values of
1827  /// the items stored in the graph, which is returned by the \c id()
1828  /// function of the graph. This map can be inverted with its member
1829  /// class \c InverseMap or with the \c operator() member.
1830  ///
1831  /// \tparam GR The graph type.
1832  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
1833  /// \c GR::Edge).
1834  ///
1835  /// \see RangeIdMap
1836  template <typename GR, typename K>
1837  class IdMap : public MapBase<K, int> {
1838  public:
1839    /// The graph type of IdMap.
1840    typedef GR Graph;
1841    typedef GR Digraph;
1842    /// The key type of IdMap (\c Node, \c Arc or \c Edge).
1843    typedef K Item;
1844    /// The key type of IdMap (\c Node, \c Arc or \c Edge).
1845    typedef K Key;
1846    /// The value type of IdMap.
1847    typedef int Value;
1848
1849    /// \brief Constructor.
1850    ///
1851    /// Constructor of the map.
1852    explicit IdMap(const Graph& graph) : _graph(&graph) {}
1853
1854    /// \brief Gives back the \e id of the item.
1855    ///
1856    /// Gives back the immutable and unique \e id of the item.
1857    int operator[](const Item& item) const { return _graph->id(item);}
1858
1859    /// \brief Gives back the \e item by its id.
1860    ///
1861    /// Gives back the \e item by its id.
1862    Item operator()(int id) { return _graph->fromId(id, Item()); }
1863
1864  private:
1865    const Graph* _graph;
1866
1867  public:
1868
1869    /// \brief This class represents the inverse of its owner (IdMap).
1870    ///
1871    /// This class represents the inverse of its owner (IdMap).
1872    /// \see inverse()
1873    class InverseMap {
1874    public:
1875
1876      /// \brief Constructor.
1877      ///
1878      /// Constructor for creating an id-to-item map.
1879      explicit InverseMap(const Graph& graph) : _graph(&graph) {}
1880
1881      /// \brief Constructor.
1882      ///
1883      /// Constructor for creating an id-to-item map.
1884      explicit InverseMap(const IdMap& map) : _graph(map._graph) {}
1885
1886      /// \brief Gives back the given item from its id.
1887      ///
1888      /// Gives back the given item from its id.
1889      Item operator[](int id) const { return _graph->fromId(id, Item());}
1890
1891    private:
1892      const Graph* _graph;
1893    };
1894
1895    /// \brief Gives back the inverse of the map.
1896    ///
1897    /// Gives back the inverse of the IdMap.
1898    InverseMap inverse() const { return InverseMap(*_graph);}
1899  };
1900
1901
1902  /// \brief General cross reference graph map type.
1903
1904  /// This class provides simple invertable graph maps.
1905  /// It wraps an arbitrary \ref concepts::ReadWriteMap "ReadWriteMap"
1906  /// and if a key is set to a new value then store it
1907  /// in the inverse map.
1908  ///
1909  /// The values of the map can be accessed
1910  /// with stl compatible forward iterator.
1911  ///
1912  /// \tparam GR The graph type.
1913  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
1914  /// \c GR::Edge).
1915  /// \tparam V The value type of the map.
1916  ///
1917  /// \see IterableValueMap
1918  template <typename GR, typename K, typename V>
1919  class CrossRefMap
1920    : protected ItemSetTraits<GR, K>::template Map<V>::Type {
1921  private:
1922
1923    typedef typename ItemSetTraits<GR, K>::
1924      template Map<V>::Type Map;
1925
1926    typedef std::map<V, K> Container;
1927    Container _inv_map;
1928
1929  public:
1930
1931    /// The graph type of CrossRefMap.
1932    typedef GR Graph;
1933    typedef GR Digraph;
1934    /// The key type of CrossRefMap (\c Node, \c Arc or \c Edge).
1935    typedef K Item;
1936    /// The key type of CrossRefMap (\c Node, \c Arc or \c Edge).
1937    typedef K Key;
1938    /// The value type of CrossRefMap.
1939    typedef V Value;
1940
1941    /// \brief Constructor.
1942    ///
1943    /// Construct a new CrossRefMap for the given graph.
1944    explicit CrossRefMap(const Graph& graph) : Map(graph) {}
1945
1946    /// \brief Forward iterator for values.
1947    ///
1948    /// This iterator is an stl compatible forward
1949    /// iterator on the values of the map. The values can
1950    /// be accessed in the <tt>[beginValue, endValue)</tt> range.
1951    class ValueIterator
1952      : public std::iterator<std::forward_iterator_tag, Value> {
1953      friend class CrossRefMap;
1954    private:
1955      ValueIterator(typename Container::const_iterator _it)
1956        : it(_it) {}
1957    public:
1958
1959      ValueIterator() {}
1960
1961      ValueIterator& operator++() { ++it; return *this; }
1962      ValueIterator operator++(int) {
1963        ValueIterator tmp(*this);
1964        operator++();
1965        return tmp;
1966      }
1967
1968      const Value& operator*() const { return it->first; }
1969      const Value* operator->() const { return &(it->first); }
1970
1971      bool operator==(ValueIterator jt) const { return it == jt.it; }
1972      bool operator!=(ValueIterator jt) const { return it != jt.it; }
1973
1974    private:
1975      typename Container::const_iterator it;
1976    };
1977
1978    /// \brief Returns an iterator to the first value.
1979    ///
1980    /// Returns an stl compatible iterator to the
1981    /// first value of the map. The values of the
1982    /// map can be accessed in the <tt>[beginValue, endValue)</tt>
1983    /// range.
1984    ValueIterator beginValue() const {
1985      return ValueIterator(_inv_map.begin());
1986    }
1987
1988    /// \brief Returns an iterator after the last value.
1989    ///
1990    /// Returns an stl compatible iterator after the
1991    /// last value of the map. The values of the
1992    /// map can be accessed in the <tt>[beginValue, endValue)</tt>
1993    /// range.
1994    ValueIterator endValue() const {
1995      return ValueIterator(_inv_map.end());
1996    }
1997
1998    /// \brief Sets the value associated with the given key.
1999    ///
2000    /// Sets the value associated with the given key.
2001    void set(const Key& key, const Value& val) {
2002      Value oldval = Map::operator[](key);
2003      typename Container::iterator it = _inv_map.find(oldval);
2004      if (it != _inv_map.end() && it->second == key) {
2005        _inv_map.erase(it);
2006      }
2007      _inv_map.insert(make_pair(val, key));
2008      Map::set(key, val);
2009    }
2010
2011    /// \brief Returns the value associated with the given key.
2012    ///
2013    /// Returns the value associated with the given key.
2014    typename MapTraits<Map>::ConstReturnValue
2015    operator[](const Key& key) const {
2016      return Map::operator[](key);
2017    }
2018
2019    /// \brief Gives back the item by its value.
2020    ///
2021    /// Gives back the item by its value.
2022    Key operator()(const Value& key) const {
2023      typename Container::const_iterator it = _inv_map.find(key);
2024      return it != _inv_map.end() ? it->second : INVALID;
2025    }
2026
2027  protected:
2028
2029    /// \brief Erase the key from the map and the inverse map.
2030    ///
2031    /// Erase the key from the map and the inverse map. It is called by the
2032    /// \c AlterationNotifier.
2033    virtual void erase(const Key& key) {
2034      Value val = Map::operator[](key);
2035      typename Container::iterator it = _inv_map.find(val);
2036      if (it != _inv_map.end() && it->second == key) {
2037        _inv_map.erase(it);
2038      }
2039      Map::erase(key);
2040    }
2041
2042    /// \brief Erase more keys from the map and the inverse map.
2043    ///
2044    /// Erase more keys from the map and the inverse map. It is called by the
2045    /// \c AlterationNotifier.
2046    virtual void erase(const std::vector<Key>& keys) {
2047      for (int i = 0; i < int(keys.size()); ++i) {
2048        Value val = Map::operator[](keys[i]);
2049        typename Container::iterator it = _inv_map.find(val);
2050        if (it != _inv_map.end() && it->second == keys[i]) {
2051          _inv_map.erase(it);
2052        }
2053      }
2054      Map::erase(keys);
2055    }
2056
2057    /// \brief Clear the keys from the map and the inverse map.
2058    ///
2059    /// Clear the keys from the map and the inverse map. It is called by the
2060    /// \c AlterationNotifier.
2061    virtual void clear() {
2062      _inv_map.clear();
2063      Map::clear();
2064    }
2065
2066  public:
2067
2068    /// \brief The inverse map type.
2069    ///
2070    /// The inverse of this map. The subscript operator of the map
2071    /// gives back the item that was last assigned to the value.
2072    class InverseMap {
2073    public:
2074      /// \brief Constructor
2075      ///
2076      /// Constructor of the InverseMap.
2077      explicit InverseMap(const CrossRefMap& inverted)
2078        : _inverted(inverted) {}
2079
2080      /// The value type of the InverseMap.
2081      typedef typename CrossRefMap::Key Value;
2082      /// The key type of the InverseMap.
2083      typedef typename CrossRefMap::Value Key;
2084
2085      /// \brief Subscript operator.
2086      ///
2087      /// Subscript operator. It gives back the item
2088      /// that was last assigned to the given value.
2089      Value operator[](const Key& key) const {
2090        return _inverted(key);
2091      }
2092
2093    private:
2094      const CrossRefMap& _inverted;
2095    };
2096
2097    /// \brief It gives back the read-only inverse map.
2098    ///
2099    /// It gives back the read-only inverse map.
2100    InverseMap inverse() const {
2101      return InverseMap(*this);
2102    }
2103
2104  };
2105
2106  /// \brief Provides continuous and unique ID for the
2107  /// items of a graph.
2108  ///
2109  /// RangeIdMap provides a unique and continuous
2110  /// ID for each item of a given type (\c Node, \c Arc or
2111  /// \c Edge) in a graph. This id is
2112  ///  - \b unique: different items get different ids,
2113  ///  - \b continuous: the range of the ids is the set of integers
2114  ///    between 0 and \c n-1, where \c n is the number of the items of
2115  ///    this type (\c Node, \c Arc or \c Edge).
2116  ///  - So, the ids can change when deleting an item of the same type.
2117  ///
2118  /// Thus this id is not (necessarily) the same as what can get using
2119  /// the \c id() function of the graph or \ref IdMap.
2120  /// This map can be inverted with its member class \c InverseMap,
2121  /// or with the \c operator() member.
2122  ///
2123  /// \tparam GR The graph type.
2124  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
2125  /// \c GR::Edge).
2126  ///
2127  /// \see IdMap
2128  template <typename GR, typename K>
2129  class RangeIdMap
2130    : protected ItemSetTraits<GR, K>::template Map<int>::Type {
2131
2132    typedef typename ItemSetTraits<GR, K>::template Map<int>::Type Map;
2133
2134  public:
2135    /// The graph type of RangeIdMap.
2136    typedef GR Graph;
2137    typedef GR Digraph;
2138    /// The key type of RangeIdMap (\c Node, \c Arc or \c Edge).
2139    typedef K Item;
2140    /// The key type of RangeIdMap (\c Node, \c Arc or \c Edge).
2141    typedef K Key;
2142    /// The value type of RangeIdMap.
2143    typedef int Value;
2144
2145    /// \brief Constructor.
2146    ///
2147    /// Constructor.
2148    explicit RangeIdMap(const Graph& gr) : Map(gr) {
2149      Item it;
2150      const typename Map::Notifier* nf = Map::notifier();
2151      for (nf->first(it); it != INVALID; nf->next(it)) {
2152        Map::set(it, _inv_map.size());
2153        _inv_map.push_back(it);
2154      }
2155    }
2156
2157  protected:
2158
2159    /// \brief Adds a new key to the map.
2160    ///
2161    /// Add a new key to the map. It is called by the
2162    /// \c AlterationNotifier.
2163    virtual void add(const Item& item) {
2164      Map::add(item);
2165      Map::set(item, _inv_map.size());
2166      _inv_map.push_back(item);
2167    }
2168
2169    /// \brief Add more new keys to the map.
2170    ///
2171    /// Add more new keys to the map. It is called by the
2172    /// \c AlterationNotifier.
2173    virtual void add(const std::vector<Item>& items) {
2174      Map::add(items);
2175      for (int i = 0; i < int(items.size()); ++i) {
2176        Map::set(items[i], _inv_map.size());
2177        _inv_map.push_back(items[i]);
2178      }
2179    }
2180
2181    /// \brief Erase the key from the map.
2182    ///
2183    /// Erase the key from the map. It is called by the
2184    /// \c AlterationNotifier.
2185    virtual void erase(const Item& item) {
2186      Map::set(_inv_map.back(), Map::operator[](item));
2187      _inv_map[Map::operator[](item)] = _inv_map.back();
2188      _inv_map.pop_back();
2189      Map::erase(item);
2190    }
2191
2192    /// \brief Erase more keys from the map.
2193    ///
2194    /// Erase more keys from the map. It is called by the
2195    /// \c AlterationNotifier.
2196    virtual void erase(const std::vector<Item>& items) {
2197      for (int i = 0; i < int(items.size()); ++i) {
2198        Map::set(_inv_map.back(), Map::operator[](items[i]));
2199        _inv_map[Map::operator[](items[i])] = _inv_map.back();
2200        _inv_map.pop_back();
2201      }
2202      Map::erase(items);
2203    }
2204
2205    /// \brief Build the unique map.
2206    ///
2207    /// Build the unique map. It is called by the
2208    /// \c AlterationNotifier.
2209    virtual void build() {
2210      Map::build();
2211      Item it;
2212      const typename Map::Notifier* nf = Map::notifier();
2213      for (nf->first(it); it != INVALID; nf->next(it)) {
2214        Map::set(it, _inv_map.size());
2215        _inv_map.push_back(it);
2216      }
2217    }
2218
2219    /// \brief Clear the keys from the map.
2220    ///
2221    /// Clear the keys from the map. It is called by the
2222    /// \c AlterationNotifier.
2223    virtual void clear() {
2224      _inv_map.clear();
2225      Map::clear();
2226    }
2227
2228  public:
2229
2230    /// \brief Returns the maximal value plus one.
2231    ///
2232    /// Returns the maximal value plus one in the map.
2233    unsigned int size() const {
2234      return _inv_map.size();
2235    }
2236
2237    /// \brief Swaps the position of the two items in the map.
2238    ///
2239    /// Swaps the position of the two items in the map.
2240    void swap(const Item& p, const Item& q) {
2241      int pi = Map::operator[](p);
2242      int qi = Map::operator[](q);
2243      Map::set(p, qi);
2244      _inv_map[qi] = p;
2245      Map::set(q, pi);
2246      _inv_map[pi] = q;
2247    }
2248
2249    /// \brief Gives back the \e RangeId of the item
2250    ///
2251    /// Gives back the \e RangeId of the item.
2252    int operator[](const Item& item) const {
2253      return Map::operator[](item);
2254    }
2255
2256    /// \brief Gives back the item belonging to a \e RangeId
2257    ///
2258    /// Gives back the item belonging to a \e RangeId.
2259    Item operator()(int id) const {
2260      return _inv_map[id];
2261    }
2262
2263  private:
2264
2265    typedef std::vector<Item> Container;
2266    Container _inv_map;
2267
2268  public:
2269
2270    /// \brief The inverse map type of RangeIdMap.
2271    ///
2272    /// The inverse map type of RangeIdMap.
2273    class InverseMap {
2274    public:
2275      /// \brief Constructor
2276      ///
2277      /// Constructor of the InverseMap.
2278      explicit InverseMap(const RangeIdMap& inverted)
2279        : _inverted(inverted) {}
2280
2281
2282      /// The value type of the InverseMap.
2283      typedef typename RangeIdMap::Key Value;
2284      /// The key type of the InverseMap.
2285      typedef typename RangeIdMap::Value Key;
2286
2287      /// \brief Subscript operator.
2288      ///
2289      /// Subscript operator. It gives back the item
2290      /// that the descriptor currently belongs to.
2291      Value operator[](const Key& key) const {
2292        return _inverted(key);
2293      }
2294
2295      /// \brief Size of the map.
2296      ///
2297      /// Returns the size of the map.
2298      unsigned int size() const {
2299        return _inverted.size();
2300      }
2301
2302    private:
2303      const RangeIdMap& _inverted;
2304    };
2305
2306    /// \brief Gives back the inverse of the map.
2307    ///
2308    /// Gives back the inverse of the map.
2309    const InverseMap inverse() const {
2310      return InverseMap(*this);
2311    }
2312  };
2313
2314  /// \brief Map of the source nodes of arcs in a digraph.
2315  ///
2316  /// SourceMap provides access for the source node of each arc in a digraph,
2317  /// which is returned by the \c source() function of the digraph.
2318  /// \tparam GR The digraph type.
2319  /// \see TargetMap
2320  template <typename GR>
2321  class SourceMap {
2322  public:
2323
2324    ///\e
2325    typedef typename GR::Arc Key;
2326    ///\e
2327    typedef typename GR::Node Value;
2328
2329    /// \brief Constructor
2330    ///
2331    /// Constructor.
2332    /// \param digraph The digraph that the map belongs to.
2333    explicit SourceMap(const GR& digraph) : _graph(digraph) {}
2334
2335    /// \brief Returns the source node of the given arc.
2336    ///
2337    /// Returns the source node of the given arc.
2338    Value operator[](const Key& arc) const {
2339      return _graph.source(arc);
2340    }
2341
2342  private:
2343    const GR& _graph;
2344  };
2345
2346  /// \brief Returns a \c SourceMap class.
2347  ///
2348  /// This function just returns an \c SourceMap class.
2349  /// \relates SourceMap
2350  template <typename GR>
2351  inline SourceMap<GR> sourceMap(const GR& graph) {
2352    return SourceMap<GR>(graph);
2353  }
2354
2355  /// \brief Map of the target nodes of arcs in a digraph.
2356  ///
2357  /// TargetMap provides access for the target node of each arc in a digraph,
2358  /// which is returned by the \c target() function of the digraph.
2359  /// \tparam GR The digraph type.
2360  /// \see SourceMap
2361  template <typename GR>
2362  class TargetMap {
2363  public:
2364
2365    ///\e
2366    typedef typename GR::Arc Key;
2367    ///\e
2368    typedef typename GR::Node Value;
2369
2370    /// \brief Constructor
2371    ///
2372    /// Constructor.
2373    /// \param digraph The digraph that the map belongs to.
2374    explicit TargetMap(const GR& digraph) : _graph(digraph) {}
2375
2376    /// \brief Returns the target node of the given arc.
2377    ///
2378    /// Returns the target node of the given arc.
2379    Value operator[](const Key& e) const {
2380      return _graph.target(e);
2381    }
2382
2383  private:
2384    const GR& _graph;
2385  };
2386
2387  /// \brief Returns a \c TargetMap class.
2388  ///
2389  /// This function just returns a \c TargetMap class.
2390  /// \relates TargetMap
2391  template <typename GR>
2392  inline TargetMap<GR> targetMap(const GR& graph) {
2393    return TargetMap<GR>(graph);
2394  }
2395
2396  /// \brief Map of the "forward" directed arc view of edges in a graph.
2397  ///
2398  /// ForwardMap provides access for the "forward" directed arc view of
2399  /// each edge in a graph, which is returned by the \c direct() function
2400  /// of the graph with \c true parameter.
2401  /// \tparam GR The graph type.
2402  /// \see BackwardMap
2403  template <typename GR>
2404  class ForwardMap {
2405  public:
2406
2407    typedef typename GR::Arc Value;
2408    typedef typename GR::Edge Key;
2409
2410    /// \brief Constructor
2411    ///
2412    /// Constructor.
2413    /// \param graph The graph that the map belongs to.
2414    explicit ForwardMap(const GR& graph) : _graph(graph) {}
2415
2416    /// \brief Returns the "forward" directed arc view of the given edge.
2417    ///
2418    /// Returns the "forward" directed arc view of the given edge.
2419    Value operator[](const Key& key) const {
2420      return _graph.direct(key, true);
2421    }
2422
2423  private:
2424    const GR& _graph;
2425  };
2426
2427  /// \brief Returns a \c ForwardMap class.
2428  ///
2429  /// This function just returns an \c ForwardMap class.
2430  /// \relates ForwardMap
2431  template <typename GR>
2432  inline ForwardMap<GR> forwardMap(const GR& graph) {
2433    return ForwardMap<GR>(graph);
2434  }
2435
2436  /// \brief Map of the "backward" directed arc view of edges in a graph.
2437  ///
2438  /// BackwardMap provides access for the "backward" directed arc view of
2439  /// each edge in a graph, which is returned by the \c direct() function
2440  /// of the graph with \c false parameter.
2441  /// \tparam GR The graph type.
2442  /// \see ForwardMap
2443  template <typename GR>
2444  class BackwardMap {
2445  public:
2446
2447    typedef typename GR::Arc Value;
2448    typedef typename GR::Edge Key;
2449
2450    /// \brief Constructor
2451    ///
2452    /// Constructor.
2453    /// \param graph The graph that the map belongs to.
2454    explicit BackwardMap(const GR& graph) : _graph(graph) {}
2455
2456    /// \brief Returns the "backward" directed arc view of the given edge.
2457    ///
2458    /// Returns the "backward" directed arc view of the given edge.
2459    Value operator[](const Key& key) const {
2460      return _graph.direct(key, false);
2461    }
2462
2463  private:
2464    const GR& _graph;
2465  };
2466
2467  /// \brief Returns a \c BackwardMap class
2468
2469  /// This function just returns a \c BackwardMap class.
2470  /// \relates BackwardMap
2471  template <typename GR>
2472  inline BackwardMap<GR> backwardMap(const GR& graph) {
2473    return BackwardMap<GR>(graph);
2474  }
2475
2476  /// \brief Map of the in-degrees of nodes in a digraph.
2477  ///
2478  /// This map returns the in-degree of a node. Once it is constructed,
2479  /// the degrees are stored in a standard \c NodeMap, so each query is done
2480  /// in constant time. On the other hand, the values are updated automatically
2481  /// whenever the digraph changes.
2482  ///
2483  /// \warning Besides \c addNode() and \c addArc(), a digraph structure
2484  /// may provide alternative ways to modify the digraph.
2485  /// The correct behavior of InDegMap is not guarantied if these additional
2486  /// features are used. For example the functions
2487  /// \ref ListDigraph::changeSource() "changeSource()",
2488  /// \ref ListDigraph::changeTarget() "changeTarget()" and
2489  /// \ref ListDigraph::reverseArc() "reverseArc()"
2490  /// of \ref ListDigraph will \e not update the degree values correctly.
2491  ///
2492  /// \sa OutDegMap
2493  template <typename GR>
2494  class InDegMap
2495    : protected ItemSetTraits<GR, typename GR::Arc>
2496      ::ItemNotifier::ObserverBase {
2497
2498  public:
2499   
2500    /// The graph type of InDegMap
2501    typedef GR Graph;
2502    typedef GR Digraph;
2503    /// The key type
2504    typedef typename Digraph::Node Key;
2505    /// The value type
2506    typedef int Value;
2507
2508    typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
2509    ::ItemNotifier::ObserverBase Parent;
2510
2511  private:
2512
2513    class AutoNodeMap
2514      : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {
2515    public:
2516
2517      typedef typename ItemSetTraits<Digraph, Key>::
2518      template Map<int>::Type Parent;
2519
2520      AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
2521
2522      virtual void add(const Key& key) {
2523        Parent::add(key);
2524        Parent::set(key, 0);
2525      }
2526
2527      virtual void add(const std::vector<Key>& keys) {
2528        Parent::add(keys);
2529        for (int i = 0; i < int(keys.size()); ++i) {
2530          Parent::set(keys[i], 0);
2531        }
2532      }
2533
2534      virtual void build() {
2535        Parent::build();
2536        Key it;
2537        typename Parent::Notifier* nf = Parent::notifier();
2538        for (nf->first(it); it != INVALID; nf->next(it)) {
2539          Parent::set(it, 0);
2540        }
2541      }
2542    };
2543
2544  public:
2545
2546    /// \brief Constructor.
2547    ///
2548    /// Constructor for creating an in-degree map.
2549    explicit InDegMap(const Digraph& graph)
2550      : _digraph(graph), _deg(graph) {
2551      Parent::attach(_digraph.notifier(typename Digraph::Arc()));
2552
2553      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
2554        _deg[it] = countInArcs(_digraph, it);
2555      }
2556    }
2557
2558    /// \brief Gives back the in-degree of a Node.
2559    ///
2560    /// Gives back the in-degree of a Node.
2561    int operator[](const Key& key) const {
2562      return _deg[key];
2563    }
2564
2565  protected:
2566
2567    typedef typename Digraph::Arc Arc;
2568
2569    virtual void add(const Arc& arc) {
2570      ++_deg[_digraph.target(arc)];
2571    }
2572
2573    virtual void add(const std::vector<Arc>& arcs) {
2574      for (int i = 0; i < int(arcs.size()); ++i) {
2575        ++_deg[_digraph.target(arcs[i])];
2576      }
2577    }
2578
2579    virtual void erase(const Arc& arc) {
2580      --_deg[_digraph.target(arc)];
2581    }
2582
2583    virtual void erase(const std::vector<Arc>& arcs) {
2584      for (int i = 0; i < int(arcs.size()); ++i) {
2585        --_deg[_digraph.target(arcs[i])];
2586      }
2587    }
2588
2589    virtual void build() {
2590      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
2591        _deg[it] = countInArcs(_digraph, it);
2592      }
2593    }
2594
2595    virtual void clear() {
2596      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
2597        _deg[it] = 0;
2598      }
2599    }
2600  private:
2601
2602    const Digraph& _digraph;
2603    AutoNodeMap _deg;
2604  };
2605
2606  /// \brief Map of the out-degrees of nodes in a digraph.
2607  ///
2608  /// This map returns the out-degree of a node. Once it is constructed,
2609  /// the degrees are stored in a standard \c NodeMap, so each query is done
2610  /// in constant time. On the other hand, the values are updated automatically
2611  /// whenever the digraph changes.
2612  ///
2613  /// \warning Besides \c addNode() and \c addArc(), a digraph structure
2614  /// may provide alternative ways to modify the digraph.
2615  /// The correct behavior of OutDegMap is not guarantied if these additional
2616  /// features are used. For example the functions
2617  /// \ref ListDigraph::changeSource() "changeSource()",
2618  /// \ref ListDigraph::changeTarget() "changeTarget()" and
2619  /// \ref ListDigraph::reverseArc() "reverseArc()"
2620  /// of \ref ListDigraph will \e not update the degree values correctly.
2621  ///
2622  /// \sa InDegMap
2623  template <typename GR>
2624  class OutDegMap
2625    : protected ItemSetTraits<GR, typename GR::Arc>
2626      ::ItemNotifier::ObserverBase {
2627
2628  public:
2629
2630    /// The graph type of OutDegMap
2631    typedef GR Graph;
2632    typedef GR Digraph;
2633    /// The key type
2634    typedef typename Digraph::Node Key;
2635    /// The value type
2636    typedef int Value;
2637
2638    typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
2639    ::ItemNotifier::ObserverBase Parent;
2640
2641  private:
2642
2643    class AutoNodeMap
2644      : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {
2645    public:
2646
2647      typedef typename ItemSetTraits<Digraph, Key>::
2648      template Map<int>::Type Parent;
2649
2650      AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
2651
2652      virtual void add(const Key& key) {
2653        Parent::add(key);
2654        Parent::set(key, 0);
2655      }
2656      virtual void add(const std::vector<Key>& keys) {
2657        Parent::add(keys);
2658        for (int i = 0; i < int(keys.size()); ++i) {
2659          Parent::set(keys[i], 0);
2660        }
2661      }
2662      virtual void build() {
2663        Parent::build();
2664        Key it;
2665        typename Parent::Notifier* nf = Parent::notifier();
2666        for (nf->first(it); it != INVALID; nf->next(it)) {
2667          Parent::set(it, 0);
2668        }
2669      }
2670    };
2671
2672  public:
2673
2674    /// \brief Constructor.
2675    ///
2676    /// Constructor for creating an out-degree map.
2677    explicit OutDegMap(const Digraph& graph)
2678      : _digraph(graph), _deg(graph) {
2679      Parent::attach(_digraph.notifier(typename Digraph::Arc()));
2680
2681      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
2682        _deg[it] = countOutArcs(_digraph, it);
2683      }
2684    }
2685
2686    /// \brief Gives back the out-degree of a Node.
2687    ///
2688    /// Gives back the out-degree of a Node.
2689    int operator[](const Key& key) const {
2690      return _deg[key];
2691    }
2692
2693  protected:
2694
2695    typedef typename Digraph::Arc Arc;
2696
2697    virtual void add(const Arc& arc) {
2698      ++_deg[_digraph.source(arc)];
2699    }
2700
2701    virtual void add(const std::vector<Arc>& arcs) {
2702      for (int i = 0; i < int(arcs.size()); ++i) {
2703        ++_deg[_digraph.source(arcs[i])];
2704      }
2705    }
2706
2707    virtual void erase(const Arc& arc) {
2708      --_deg[_digraph.source(arc)];
2709    }
2710
2711    virtual void erase(const std::vector<Arc>& arcs) {
2712      for (int i = 0; i < int(arcs.size()); ++i) {
2713        --_deg[_digraph.source(arcs[i])];
2714      }
2715    }
2716
2717    virtual void build() {
2718      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
2719        _deg[it] = countOutArcs(_digraph, it);
2720      }
2721    }
2722
2723    virtual void clear() {
2724      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
2725        _deg[it] = 0;
2726      }
2727    }
2728  private:
2729
2730    const Digraph& _digraph;
2731    AutoNodeMap _deg;
2732  };
2733
2734  /// \brief Potential difference map
2735  ///
2736  /// PotentialDifferenceMap returns the difference between the potentials of
2737  /// the source and target nodes of each arc in a digraph, i.e. it returns
2738  /// \code
2739  ///   potential[gr.target(arc)] - potential[gr.source(arc)].
2740  /// \endcode
2741  /// \tparam GR The digraph type.
2742  /// \tparam POT A node map storing the potentials.
2743  template <typename GR, typename POT>
2744  class PotentialDifferenceMap {
2745  public:
2746    /// Key type
2747    typedef typename GR::Arc Key;
2748    /// Value type
2749    typedef typename POT::Value Value;
2750
2751    /// \brief Constructor
2752    ///
2753    /// Contructor of the map.
2754    explicit PotentialDifferenceMap(const GR& gr,
2755                                    const POT& potential)
2756      : _digraph(gr), _potential(potential) {}
2757
2758    /// \brief Returns the potential difference for the given arc.
2759    ///
2760    /// Returns the potential difference for the given arc, i.e.
2761    /// \code
2762    ///   potential[gr.target(arc)] - potential[gr.source(arc)].
2763    /// \endcode
2764    Value operator[](const Key& arc) const {
2765      return _potential[_digraph.target(arc)] -
2766        _potential[_digraph.source(arc)];
2767    }
2768
2769  private:
2770    const GR& _digraph;
2771    const POT& _potential;
2772  };
2773
2774  /// \brief Returns a PotentialDifferenceMap.
2775  ///
2776  /// This function just returns a PotentialDifferenceMap.
2777  /// \relates PotentialDifferenceMap
2778  template <typename GR, typename POT>
2779  PotentialDifferenceMap<GR, POT>
2780  potentialDifferenceMap(const GR& gr, const POT& potential) {
2781    return PotentialDifferenceMap<GR, POT>(gr, potential);
2782  }
2783
2784  /// @}
2785}
2786
2787#endif // LEMON_MAPS_H
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