COIN-OR::LEMON - Graph Library

source: lemon/lemon/maps.h @ 768:99124ea4f048

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1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2009
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19#ifndef LEMON_MAPS_H
20#define LEMON_MAPS_H
21
22#include <iterator>
23#include <functional>
24#include <vector>
25#include <map>
26
27#include <lemon/core.h>
28
29///\file
30///\ingroup maps
31///\brief Miscellaneous property maps
32
33namespace lemon {
34
35  /// \addtogroup maps
36  /// @{
37
38  /// Base class of maps.
39
40  /// Base class of maps. It provides the necessary type definitions
41  /// required by the map %concepts.
42  template<typename K, typename V>
43  class MapBase {
44  public:
45    /// \brief The key type of the map.
46    typedef K Key;
47    /// \brief The value type of the map.
48    /// (The type of objects associated with the keys).
49    typedef V Value;
50  };
51
52
53  /// Null map. (a.k.a. DoNothingMap)
54
55  /// This map can be used if you have to provide a map only for
56  /// its type definitions, or if you have to provide a writable map,
57  /// but data written to it is not required (i.e. it will be sent to
58  /// <tt>/dev/null</tt>).
59  /// It conforms the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
60  ///
61  /// \sa ConstMap
62  template<typename K, typename V>
63  class NullMap : public MapBase<K, V> {
64  public:
65    ///\e
66    typedef K Key;
67    ///\e
68    typedef V Value;
69
70    /// Gives back a default constructed element.
71    Value operator[](const Key&) const { return Value(); }
72    /// Absorbs the value.
73    void set(const Key&, const Value&) {}
74  };
75
76  /// Returns a \c NullMap class
77
78  /// This function just returns a \c NullMap class.
79  /// \relates NullMap
80  template <typename K, typename V>
81  NullMap<K, V> nullMap() {
82    return NullMap<K, V>();
83  }
84
85
86  /// Constant map.
87
88  /// This \ref concepts::ReadMap "readable map" assigns a specified
89  /// value to each key.
90  ///
91  /// In other aspects it is equivalent to \c NullMap.
92  /// So it conforms the \ref concepts::ReadWriteMap "ReadWriteMap"
93  /// concept, but it absorbs the data written to it.
94  ///
95  /// The simplest way of using this map is through the constMap()
96  /// function.
97  ///
98  /// \sa NullMap
99  /// \sa IdentityMap
100  template<typename K, typename V>
101  class ConstMap : public MapBase<K, V> {
102  private:
103    V _value;
104  public:
105    ///\e
106    typedef K Key;
107    ///\e
108    typedef V Value;
109
110    /// Default constructor
111
112    /// Default constructor.
113    /// The value of the map will be default constructed.
114    ConstMap() {}
115
116    /// Constructor with specified initial value
117
118    /// Constructor with specified initial value.
119    /// \param v The initial value of the map.
120    ConstMap(const Value &v) : _value(v) {}
121
122    /// Gives back the specified value.
123    Value operator[](const Key&) const { return _value; }
124
125    /// Absorbs the value.
126    void set(const Key&, const Value&) {}
127
128    /// Sets the value that is assigned to each key.
129    void setAll(const Value &v) {
130      _value = v;
131    }
132
133    template<typename V1>
134    ConstMap(const ConstMap<K, V1> &, const Value &v) : _value(v) {}
135  };
136
137  /// Returns a \c ConstMap class
138
139  /// This function just returns a \c ConstMap class.
140  /// \relates ConstMap
141  template<typename K, typename V>
142  inline ConstMap<K, V> constMap(const V &v) {
143    return ConstMap<K, V>(v);
144  }
145
146  template<typename K, typename V>
147  inline ConstMap<K, V> constMap() {
148    return ConstMap<K, V>();
149  }
150
151
152  template<typename T, T v>
153  struct Const {};
154
155  /// Constant map with inlined constant value.
156
157  /// This \ref concepts::ReadMap "readable map" assigns a specified
158  /// value to each key.
159  ///
160  /// In other aspects it is equivalent to \c NullMap.
161  /// So it conforms the \ref concepts::ReadWriteMap "ReadWriteMap"
162  /// concept, but it absorbs the data written to it.
163  ///
164  /// The simplest way of using this map is through the constMap()
165  /// function.
166  ///
167  /// \sa NullMap
168  /// \sa IdentityMap
169  template<typename K, typename V, V v>
170  class ConstMap<K, Const<V, v> > : public MapBase<K, V> {
171  public:
172    ///\e
173    typedef K Key;
174    ///\e
175    typedef V Value;
176
177    /// Constructor.
178    ConstMap() {}
179
180    /// Gives back the specified value.
181    Value operator[](const Key&) const { return v; }
182
183    /// Absorbs the value.
184    void set(const Key&, const Value&) {}
185  };
186
187  /// Returns a \c ConstMap class with inlined constant value
188
189  /// This function just returns a \c ConstMap class with inlined
190  /// constant value.
191  /// \relates ConstMap
192  template<typename K, typename V, V v>
193  inline ConstMap<K, Const<V, v> > constMap() {
194    return ConstMap<K, Const<V, v> >();
195  }
196
197
198  /// Identity map.
199
200  /// This \ref concepts::ReadMap "read-only map" gives back the given
201  /// key as value without any modification.
202  ///
203  /// \sa ConstMap
204  template <typename T>
205  class IdentityMap : public MapBase<T, T> {
206  public:
207    ///\e
208    typedef T Key;
209    ///\e
210    typedef T Value;
211
212    /// Gives back the given value without any modification.
213    Value operator[](const Key &k) const {
214      return k;
215    }
216  };
217
218  /// Returns an \c IdentityMap class
219
220  /// This function just returns an \c IdentityMap class.
221  /// \relates IdentityMap
222  template<typename T>
223  inline IdentityMap<T> identityMap() {
224    return IdentityMap<T>();
225  }
226
227
228  /// \brief Map for storing values for integer keys from the range
229  /// <tt>[0..size-1]</tt>.
230  ///
231  /// This map is essentially a wrapper for \c std::vector. It assigns
232  /// values to integer keys from the range <tt>[0..size-1]</tt>.
233  /// It can be used with some data structures, for example
234  /// \c UnionFind, \c BinHeap, when the used items are small
235  /// integers. This map conforms the \ref concepts::ReferenceMap
236  /// "ReferenceMap" concept.
237  ///
238  /// The simplest way of using this map is through the rangeMap()
239  /// function.
240  template <typename V>
241  class RangeMap : public MapBase<int, V> {
242    template <typename V1>
243    friend class RangeMap;
244  private:
245
246    typedef std::vector<V> Vector;
247    Vector _vector;
248
249  public:
250
251    /// Key type
252    typedef int Key;
253    /// Value type
254    typedef V Value;
255    /// Reference type
256    typedef typename Vector::reference Reference;
257    /// Const reference type
258    typedef typename Vector::const_reference ConstReference;
259
260    typedef True ReferenceMapTag;
261
262  public:
263
264    /// Constructor with specified default value.
265    RangeMap(int size = 0, const Value &value = Value())
266      : _vector(size, value) {}
267
268    /// Constructs the map from an appropriate \c std::vector.
269    template <typename V1>
270    RangeMap(const std::vector<V1>& vector)
271      : _vector(vector.begin(), vector.end()) {}
272
273    /// Constructs the map from another \c RangeMap.
274    template <typename V1>
275    RangeMap(const RangeMap<V1> &c)
276      : _vector(c._vector.begin(), c._vector.end()) {}
277
278    /// Returns the size of the map.
279    int size() {
280      return _vector.size();
281    }
282
283    /// Resizes the map.
284
285    /// Resizes the underlying \c std::vector container, so changes the
286    /// keyset of the map.
287    /// \param size The new size of the map. The new keyset will be the
288    /// range <tt>[0..size-1]</tt>.
289    /// \param value The default value to assign to the new keys.
290    void resize(int size, const Value &value = Value()) {
291      _vector.resize(size, value);
292    }
293
294  private:
295
296    RangeMap& operator=(const RangeMap&);
297
298  public:
299
300    ///\e
301    Reference operator[](const Key &k) {
302      return _vector[k];
303    }
304
305    ///\e
306    ConstReference operator[](const Key &k) const {
307      return _vector[k];
308    }
309
310    ///\e
311    void set(const Key &k, const Value &v) {
312      _vector[k] = v;
313    }
314  };
315
316  /// Returns a \c RangeMap class
317
318  /// This function just returns a \c RangeMap class.
319  /// \relates RangeMap
320  template<typename V>
321  inline RangeMap<V> rangeMap(int size = 0, const V &value = V()) {
322    return RangeMap<V>(size, value);
323  }
324
325  /// \brief Returns a \c RangeMap class created from an appropriate
326  /// \c std::vector
327
328  /// This function just returns a \c RangeMap class created from an
329  /// appropriate \c std::vector.
330  /// \relates RangeMap
331  template<typename V>
332  inline RangeMap<V> rangeMap(const std::vector<V> &vector) {
333    return RangeMap<V>(vector);
334  }
335
336
337  /// Map type based on \c std::map
338
339  /// This map is essentially a wrapper for \c std::map with addition
340  /// that you can specify a default value for the keys that are not
341  /// stored actually. This value can be different from the default
342  /// contructed value (i.e. \c %Value()).
343  /// This type conforms the \ref concepts::ReferenceMap "ReferenceMap"
344  /// concept.
345  ///
346  /// This map is useful if a default value should be assigned to most of
347  /// the keys and different values should be assigned only to a few
348  /// keys (i.e. the map is "sparse").
349  /// The name of this type also refers to this important usage.
350  ///
351  /// Apart form that this map can be used in many other cases since it
352  /// is based on \c std::map, which is a general associative container.
353  /// However keep in mind that it is usually not as efficient as other
354  /// maps.
355  ///
356  /// The simplest way of using this map is through the sparseMap()
357  /// function.
358  template <typename K, typename V, typename Comp = std::less<K> >
359  class SparseMap : public MapBase<K, V> {
360    template <typename K1, typename V1, typename C1>
361    friend class SparseMap;
362  public:
363
364    /// Key type
365    typedef K Key;
366    /// Value type
367    typedef V Value;
368    /// Reference type
369    typedef Value& Reference;
370    /// Const reference type
371    typedef const Value& ConstReference;
372
373    typedef True ReferenceMapTag;
374
375  private:
376
377    typedef std::map<K, V, Comp> Map;
378    Map _map;
379    Value _value;
380
381  public:
382
383    /// \brief Constructor with specified default value.
384    SparseMap(const Value &value = Value()) : _value(value) {}
385    /// \brief Constructs the map from an appropriate \c std::map, and
386    /// explicitly specifies a default value.
387    template <typename V1, typename Comp1>
388    SparseMap(const std::map<Key, V1, Comp1> &map,
389              const Value &value = Value())
390      : _map(map.begin(), map.end()), _value(value) {}
391
392    /// \brief Constructs the map from another \c SparseMap.
393    template<typename V1, typename Comp1>
394    SparseMap(const SparseMap<Key, V1, Comp1> &c)
395      : _map(c._map.begin(), c._map.end()), _value(c._value) {}
396
397  private:
398
399    SparseMap& operator=(const SparseMap&);
400
401  public:
402
403    ///\e
404    Reference operator[](const Key &k) {
405      typename Map::iterator it = _map.lower_bound(k);
406      if (it != _map.end() && !_map.key_comp()(k, it->first))
407        return it->second;
408      else
409        return _map.insert(it, std::make_pair(k, _value))->second;
410    }
411
412    ///\e
413    ConstReference operator[](const Key &k) const {
414      typename Map::const_iterator it = _map.find(k);
415      if (it != _map.end())
416        return it->second;
417      else
418        return _value;
419    }
420
421    ///\e
422    void set(const Key &k, const Value &v) {
423      typename Map::iterator it = _map.lower_bound(k);
424      if (it != _map.end() && !_map.key_comp()(k, it->first))
425        it->second = v;
426      else
427        _map.insert(it, std::make_pair(k, v));
428    }
429
430    ///\e
431    void setAll(const Value &v) {
432      _value = v;
433      _map.clear();
434    }
435  };
436
437  /// Returns a \c SparseMap class
438
439  /// This function just returns a \c SparseMap class with specified
440  /// default value.
441  /// \relates SparseMap
442  template<typename K, typename V, typename Compare>
443  inline SparseMap<K, V, Compare> sparseMap(const V& value = V()) {
444    return SparseMap<K, V, Compare>(value);
445  }
446
447  template<typename K, typename V>
448  inline SparseMap<K, V, std::less<K> > sparseMap(const V& value = V()) {
449    return SparseMap<K, V, std::less<K> >(value);
450  }
451
452  /// \brief Returns a \c SparseMap class created from an appropriate
453  /// \c std::map
454
455  /// This function just returns a \c SparseMap class created from an
456  /// appropriate \c std::map.
457  /// \relates SparseMap
458  template<typename K, typename V, typename Compare>
459  inline SparseMap<K, V, Compare>
460    sparseMap(const std::map<K, V, Compare> &map, const V& value = V())
461  {
462    return SparseMap<K, V, Compare>(map, value);
463  }
464
465  /// @}
466
467  /// \addtogroup map_adaptors
468  /// @{
469
470  /// Composition of two maps
471
472  /// This \ref concepts::ReadMap "read-only map" returns the
473  /// composition of two given maps. That is to say, if \c m1 is of
474  /// type \c M1 and \c m2 is of \c M2, then for
475  /// \code
476  ///   ComposeMap<M1, M2> cm(m1,m2);
477  /// \endcode
478  /// <tt>cm[x]</tt> will be equal to <tt>m1[m2[x]]</tt>.
479  ///
480  /// The \c Key type of the map is inherited from \c M2 and the
481  /// \c Value type is from \c M1.
482  /// \c M2::Value must be convertible to \c M1::Key.
483  ///
484  /// The simplest way of using this map is through the composeMap()
485  /// function.
486  ///
487  /// \sa CombineMap
488  template <typename M1, typename M2>
489  class ComposeMap : public MapBase<typename M2::Key, typename M1::Value> {
490    const M1 &_m1;
491    const M2 &_m2;
492  public:
493    ///\e
494    typedef typename M2::Key Key;
495    ///\e
496    typedef typename M1::Value Value;
497
498    /// Constructor
499    ComposeMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
500
501    ///\e
502    typename MapTraits<M1>::ConstReturnValue
503    operator[](const Key &k) const { return _m1[_m2[k]]; }
504  };
505
506  /// Returns a \c ComposeMap class
507
508  /// This function just returns a \c ComposeMap class.
509  ///
510  /// If \c m1 and \c m2 are maps and the \c Value type of \c m2 is
511  /// convertible to the \c Key of \c m1, then <tt>composeMap(m1,m2)[x]</tt>
512  /// will be equal to <tt>m1[m2[x]]</tt>.
513  ///
514  /// \relates ComposeMap
515  template <typename M1, typename M2>
516  inline ComposeMap<M1, M2> composeMap(const M1 &m1, const M2 &m2) {
517    return ComposeMap<M1, M2>(m1, m2);
518  }
519
520
521  /// Combination of two maps using an STL (binary) functor.
522
523  /// This \ref concepts::ReadMap "read-only map" takes two maps and a
524  /// binary functor and returns the combination of the two given maps
525  /// using the functor.
526  /// That is to say, if \c m1 is of type \c M1 and \c m2 is of \c M2
527  /// and \c f is of \c F, then for
528  /// \code
529  ///   CombineMap<M1,M2,F,V> cm(m1,m2,f);
530  /// \endcode
531  /// <tt>cm[x]</tt> will be equal to <tt>f(m1[x],m2[x])</tt>.
532  ///
533  /// The \c Key type of the map is inherited from \c M1 (\c M1::Key
534  /// must be convertible to \c M2::Key) and the \c Value type is \c V.
535  /// \c M2::Value and \c M1::Value must be convertible to the
536  /// corresponding input parameter of \c F and the return type of \c F
537  /// must be convertible to \c V.
538  ///
539  /// The simplest way of using this map is through the combineMap()
540  /// function.
541  ///
542  /// \sa ComposeMap
543  template<typename M1, typename M2, typename F,
544           typename V = typename F::result_type>
545  class CombineMap : public MapBase<typename M1::Key, V> {
546    const M1 &_m1;
547    const M2 &_m2;
548    F _f;
549  public:
550    ///\e
551    typedef typename M1::Key Key;
552    ///\e
553    typedef V Value;
554
555    /// Constructor
556    CombineMap(const M1 &m1, const M2 &m2, const F &f = F())
557      : _m1(m1), _m2(m2), _f(f) {}
558    ///\e
559    Value operator[](const Key &k) const { return _f(_m1[k],_m2[k]); }
560  };
561
562  /// Returns a \c CombineMap class
563
564  /// This function just returns a \c CombineMap class.
565  ///
566  /// For example, if \c m1 and \c m2 are both maps with \c double
567  /// values, then
568  /// \code
569  ///   combineMap(m1,m2,std::plus<double>())
570  /// \endcode
571  /// is equivalent to
572  /// \code
573  ///   addMap(m1,m2)
574  /// \endcode
575  ///
576  /// This function is specialized for adaptable binary function
577  /// classes and C++ functions.
578  ///
579  /// \relates CombineMap
580  template<typename M1, typename M2, typename F, typename V>
581  inline CombineMap<M1, M2, F, V>
582  combineMap(const M1 &m1, const M2 &m2, const F &f) {
583    return CombineMap<M1, M2, F, V>(m1,m2,f);
584  }
585
586  template<typename M1, typename M2, typename F>
587  inline CombineMap<M1, M2, F, typename F::result_type>
588  combineMap(const M1 &m1, const M2 &m2, const F &f) {
589    return combineMap<M1, M2, F, typename F::result_type>(m1,m2,f);
590  }
591
592  template<typename M1, typename M2, typename K1, typename K2, typename V>
593  inline CombineMap<M1, M2, V (*)(K1, K2), V>
594  combineMap(const M1 &m1, const M2 &m2, V (*f)(K1, K2)) {
595    return combineMap<M1, M2, V (*)(K1, K2), V>(m1,m2,f);
596  }
597
598
599  /// Converts an STL style (unary) functor to a map
600
601  /// This \ref concepts::ReadMap "read-only map" returns the value
602  /// of a given functor. Actually, it just wraps the functor and
603  /// provides the \c Key and \c Value typedefs.
604  ///
605  /// Template parameters \c K and \c V will become its \c Key and
606  /// \c Value. In most cases they have to be given explicitly because
607  /// a functor typically does not provide \c argument_type and
608  /// \c result_type typedefs.
609  /// Parameter \c F is the type of the used functor.
610  ///
611  /// The simplest way of using this map is through the functorToMap()
612  /// function.
613  ///
614  /// \sa MapToFunctor
615  template<typename F,
616           typename K = typename F::argument_type,
617           typename V = typename F::result_type>
618  class FunctorToMap : public MapBase<K, V> {
619    F _f;
620  public:
621    ///\e
622    typedef K Key;
623    ///\e
624    typedef V Value;
625
626    /// Constructor
627    FunctorToMap(const F &f = F()) : _f(f) {}
628    ///\e
629    Value operator[](const Key &k) const { return _f(k); }
630  };
631
632  /// Returns a \c FunctorToMap class
633
634  /// This function just returns a \c FunctorToMap class.
635  ///
636  /// This function is specialized for adaptable binary function
637  /// classes and C++ functions.
638  ///
639  /// \relates FunctorToMap
640  template<typename K, typename V, typename F>
641  inline FunctorToMap<F, K, V> functorToMap(const F &f) {
642    return FunctorToMap<F, K, V>(f);
643  }
644
645  template <typename F>
646  inline FunctorToMap<F, typename F::argument_type, typename F::result_type>
647    functorToMap(const F &f)
648  {
649    return FunctorToMap<F, typename F::argument_type,
650      typename F::result_type>(f);
651  }
652
653  template <typename K, typename V>
654  inline FunctorToMap<V (*)(K), K, V> functorToMap(V (*f)(K)) {
655    return FunctorToMap<V (*)(K), K, V>(f);
656  }
657
658
659  /// Converts a map to an STL style (unary) functor
660
661  /// This class converts a map to an STL style (unary) functor.
662  /// That is it provides an <tt>operator()</tt> to read its values.
663  ///
664  /// For the sake of convenience it also works as a usual
665  /// \ref concepts::ReadMap "readable map", i.e. <tt>operator[]</tt>
666  /// and the \c Key and \c Value typedefs also exist.
667  ///
668  /// The simplest way of using this map is through the mapToFunctor()
669  /// function.
670  ///
671  ///\sa FunctorToMap
672  template <typename M>
673  class MapToFunctor : public MapBase<typename M::Key, typename M::Value> {
674    const M &_m;
675  public:
676    ///\e
677    typedef typename M::Key Key;
678    ///\e
679    typedef typename M::Value Value;
680
681    typedef typename M::Key argument_type;
682    typedef typename M::Value result_type;
683
684    /// Constructor
685    MapToFunctor(const M &m) : _m(m) {}
686    ///\e
687    Value operator()(const Key &k) const { return _m[k]; }
688    ///\e
689    Value operator[](const Key &k) const { return _m[k]; }
690  };
691
692  /// Returns a \c MapToFunctor class
693
694  /// This function just returns a \c MapToFunctor class.
695  /// \relates MapToFunctor
696  template<typename M>
697  inline MapToFunctor<M> mapToFunctor(const M &m) {
698    return MapToFunctor<M>(m);
699  }
700
701
702  /// \brief Map adaptor to convert the \c Value type of a map to
703  /// another type using the default conversion.
704
705  /// Map adaptor to convert the \c Value type of a \ref concepts::ReadMap
706  /// "readable map" to another type using the default conversion.
707  /// The \c Key type of it is inherited from \c M and the \c Value
708  /// type is \c V.
709  /// This type conforms the \ref concepts::ReadMap "ReadMap" concept.
710  ///
711  /// The simplest way of using this map is through the convertMap()
712  /// function.
713  template <typename M, typename V>
714  class ConvertMap : public MapBase<typename M::Key, V> {
715    const M &_m;
716  public:
717    ///\e
718    typedef typename M::Key Key;
719    ///\e
720    typedef V Value;
721
722    /// Constructor
723
724    /// Constructor.
725    /// \param m The underlying map.
726    ConvertMap(const M &m) : _m(m) {}
727
728    ///\e
729    Value operator[](const Key &k) const { return _m[k]; }
730  };
731
732  /// Returns a \c ConvertMap class
733
734  /// This function just returns a \c ConvertMap class.
735  /// \relates ConvertMap
736  template<typename V, typename M>
737  inline ConvertMap<M, V> convertMap(const M &map) {
738    return ConvertMap<M, V>(map);
739  }
740
741
742  /// Applies all map setting operations to two maps
743
744  /// This map has two \ref concepts::WriteMap "writable map" parameters
745  /// and each write request will be passed to both of them.
746  /// If \c M1 is also \ref concepts::ReadMap "readable", then the read
747  /// operations will return the corresponding values of \c M1.
748  ///
749  /// The \c Key and \c Value types are inherited from \c M1.
750  /// The \c Key and \c Value of \c M2 must be convertible from those
751  /// of \c M1.
752  ///
753  /// The simplest way of using this map is through the forkMap()
754  /// function.
755  template<typename  M1, typename M2>
756  class ForkMap : public MapBase<typename M1::Key, typename M1::Value> {
757    M1 &_m1;
758    M2 &_m2;
759  public:
760    ///\e
761    typedef typename M1::Key Key;
762    ///\e
763    typedef typename M1::Value Value;
764
765    /// Constructor
766    ForkMap(M1 &m1, M2 &m2) : _m1(m1), _m2(m2) {}
767    /// Returns the value associated with the given key in the first map.
768    Value operator[](const Key &k) const { return _m1[k]; }
769    /// Sets the value associated with the given key in both maps.
770    void set(const Key &k, const Value &v) { _m1.set(k,v); _m2.set(k,v); }
771  };
772
773  /// Returns a \c ForkMap class
774
775  /// This function just returns a \c ForkMap class.
776  /// \relates ForkMap
777  template <typename M1, typename M2>
778  inline ForkMap<M1,M2> forkMap(M1 &m1, M2 &m2) {
779    return ForkMap<M1,M2>(m1,m2);
780  }
781
782
783  /// Sum of two maps
784
785  /// This \ref concepts::ReadMap "read-only map" returns the sum
786  /// of the values of the two given maps.
787  /// Its \c Key and \c Value types are inherited from \c M1.
788  /// The \c Key and \c Value of \c M2 must be convertible to those of
789  /// \c M1.
790  ///
791  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
792  /// \code
793  ///   AddMap<M1,M2> am(m1,m2);
794  /// \endcode
795  /// <tt>am[x]</tt> will be equal to <tt>m1[x]+m2[x]</tt>.
796  ///
797  /// The simplest way of using this map is through the addMap()
798  /// function.
799  ///
800  /// \sa SubMap, MulMap, DivMap
801  /// \sa ShiftMap, ShiftWriteMap
802  template<typename M1, typename M2>
803  class AddMap : public MapBase<typename M1::Key, typename M1::Value> {
804    const M1 &_m1;
805    const M2 &_m2;
806  public:
807    ///\e
808    typedef typename M1::Key Key;
809    ///\e
810    typedef typename M1::Value Value;
811
812    /// Constructor
813    AddMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
814    ///\e
815    Value operator[](const Key &k) const { return _m1[k]+_m2[k]; }
816  };
817
818  /// Returns an \c AddMap class
819
820  /// This function just returns an \c AddMap class.
821  ///
822  /// For example, if \c m1 and \c m2 are both maps with \c double
823  /// values, then <tt>addMap(m1,m2)[x]</tt> will be equal to
824  /// <tt>m1[x]+m2[x]</tt>.
825  ///
826  /// \relates AddMap
827  template<typename M1, typename M2>
828  inline AddMap<M1, M2> addMap(const M1 &m1, const M2 &m2) {
829    return AddMap<M1, M2>(m1,m2);
830  }
831
832
833  /// Difference of two maps
834
835  /// This \ref concepts::ReadMap "read-only map" returns the difference
836  /// of the values of the two given maps.
837  /// Its \c Key and \c Value types are inherited from \c M1.
838  /// The \c Key and \c Value of \c M2 must be convertible to those of
839  /// \c M1.
840  ///
841  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
842  /// \code
843  ///   SubMap<M1,M2> sm(m1,m2);
844  /// \endcode
845  /// <tt>sm[x]</tt> will be equal to <tt>m1[x]-m2[x]</tt>.
846  ///
847  /// The simplest way of using this map is through the subMap()
848  /// function.
849  ///
850  /// \sa AddMap, MulMap, DivMap
851  template<typename M1, typename M2>
852  class SubMap : public MapBase<typename M1::Key, typename M1::Value> {
853    const M1 &_m1;
854    const M2 &_m2;
855  public:
856    ///\e
857    typedef typename M1::Key Key;
858    ///\e
859    typedef typename M1::Value Value;
860
861    /// Constructor
862    SubMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
863    ///\e
864    Value operator[](const Key &k) const { return _m1[k]-_m2[k]; }
865  };
866
867  /// Returns a \c SubMap class
868
869  /// This function just returns a \c SubMap class.
870  ///
871  /// For example, if \c m1 and \c m2 are both maps with \c double
872  /// values, then <tt>subMap(m1,m2)[x]</tt> will be equal to
873  /// <tt>m1[x]-m2[x]</tt>.
874  ///
875  /// \relates SubMap
876  template<typename M1, typename M2>
877  inline SubMap<M1, M2> subMap(const M1 &m1, const M2 &m2) {
878    return SubMap<M1, M2>(m1,m2);
879  }
880
881
882  /// Product of two maps
883
884  /// This \ref concepts::ReadMap "read-only map" returns the product
885  /// of the values of the two given maps.
886  /// Its \c Key and \c Value types are inherited from \c M1.
887  /// The \c Key and \c Value of \c M2 must be convertible to those of
888  /// \c M1.
889  ///
890  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
891  /// \code
892  ///   MulMap<M1,M2> mm(m1,m2);
893  /// \endcode
894  /// <tt>mm[x]</tt> will be equal to <tt>m1[x]*m2[x]</tt>.
895  ///
896  /// The simplest way of using this map is through the mulMap()
897  /// function.
898  ///
899  /// \sa AddMap, SubMap, DivMap
900  /// \sa ScaleMap, ScaleWriteMap
901  template<typename M1, typename M2>
902  class MulMap : public MapBase<typename M1::Key, typename M1::Value> {
903    const M1 &_m1;
904    const M2 &_m2;
905  public:
906    ///\e
907    typedef typename M1::Key Key;
908    ///\e
909    typedef typename M1::Value Value;
910
911    /// Constructor
912    MulMap(const M1 &m1,const M2 &m2) : _m1(m1), _m2(m2) {}
913    ///\e
914    Value operator[](const Key &k) const { return _m1[k]*_m2[k]; }
915  };
916
917  /// Returns a \c MulMap class
918
919  /// This function just returns a \c MulMap class.
920  ///
921  /// For example, if \c m1 and \c m2 are both maps with \c double
922  /// values, then <tt>mulMap(m1,m2)[x]</tt> will be equal to
923  /// <tt>m1[x]*m2[x]</tt>.
924  ///
925  /// \relates MulMap
926  template<typename M1, typename M2>
927  inline MulMap<M1, M2> mulMap(const M1 &m1,const M2 &m2) {
928    return MulMap<M1, M2>(m1,m2);
929  }
930
931
932  /// Quotient of two maps
933
934  /// This \ref concepts::ReadMap "read-only map" returns the quotient
935  /// of the values of the two given maps.
936  /// Its \c Key and \c Value types are inherited from \c M1.
937  /// The \c Key and \c Value of \c M2 must be convertible to those of
938  /// \c M1.
939  ///
940  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
941  /// \code
942  ///   DivMap<M1,M2> dm(m1,m2);
943  /// \endcode
944  /// <tt>dm[x]</tt> will be equal to <tt>m1[x]/m2[x]</tt>.
945  ///
946  /// The simplest way of using this map is through the divMap()
947  /// function.
948  ///
949  /// \sa AddMap, SubMap, MulMap
950  template<typename M1, typename M2>
951  class DivMap : public MapBase<typename M1::Key, typename M1::Value> {
952    const M1 &_m1;
953    const M2 &_m2;
954  public:
955    ///\e
956    typedef typename M1::Key Key;
957    ///\e
958    typedef typename M1::Value Value;
959
960    /// Constructor
961    DivMap(const M1 &m1,const M2 &m2) : _m1(m1), _m2(m2) {}
962    ///\e
963    Value operator[](const Key &k) const { return _m1[k]/_m2[k]; }
964  };
965
966  /// Returns a \c DivMap class
967
968  /// This function just returns a \c DivMap class.
969  ///
970  /// For example, if \c m1 and \c m2 are both maps with \c double
971  /// values, then <tt>divMap(m1,m2)[x]</tt> will be equal to
972  /// <tt>m1[x]/m2[x]</tt>.
973  ///
974  /// \relates DivMap
975  template<typename M1, typename M2>
976  inline DivMap<M1, M2> divMap(const M1 &m1,const M2 &m2) {
977    return DivMap<M1, M2>(m1,m2);
978  }
979
980
981  /// Shifts a map with a constant.
982
983  /// This \ref concepts::ReadMap "read-only map" returns the sum of
984  /// the given map and a constant value (i.e. it shifts the map with
985  /// the constant). Its \c Key and \c Value are inherited from \c M.
986  ///
987  /// Actually,
988  /// \code
989  ///   ShiftMap<M> sh(m,v);
990  /// \endcode
991  /// is equivalent to
992  /// \code
993  ///   ConstMap<M::Key, M::Value> cm(v);
994  ///   AddMap<M, ConstMap<M::Key, M::Value> > sh(m,cm);
995  /// \endcode
996  ///
997  /// The simplest way of using this map is through the shiftMap()
998  /// function.
999  ///
1000  /// \sa ShiftWriteMap
1001  template<typename M, typename C = typename M::Value>
1002  class ShiftMap : public MapBase<typename M::Key, typename M::Value> {
1003    const M &_m;
1004    C _v;
1005  public:
1006    ///\e
1007    typedef typename M::Key Key;
1008    ///\e
1009    typedef typename M::Value Value;
1010
1011    /// Constructor
1012
1013    /// Constructor.
1014    /// \param m The undelying map.
1015    /// \param v The constant value.
1016    ShiftMap(const M &m, const C &v) : _m(m), _v(v) {}
1017    ///\e
1018    Value operator[](const Key &k) const { return _m[k]+_v; }
1019  };
1020
1021  /// Shifts a map with a constant (read-write version).
1022
1023  /// This \ref concepts::ReadWriteMap "read-write map" returns the sum
1024  /// of the given map and a constant value (i.e. it shifts the map with
1025  /// the constant). Its \c Key and \c Value are inherited from \c M.
1026  /// It makes also possible to write the map.
1027  ///
1028  /// The simplest way of using this map is through the shiftWriteMap()
1029  /// function.
1030  ///
1031  /// \sa ShiftMap
1032  template<typename M, typename C = typename M::Value>
1033  class ShiftWriteMap : public MapBase<typename M::Key, typename M::Value> {
1034    M &_m;
1035    C _v;
1036  public:
1037    ///\e
1038    typedef typename M::Key Key;
1039    ///\e
1040    typedef typename M::Value Value;
1041
1042    /// Constructor
1043
1044    /// Constructor.
1045    /// \param m The undelying map.
1046    /// \param v The constant value.
1047    ShiftWriteMap(M &m, const C &v) : _m(m), _v(v) {}
1048    ///\e
1049    Value operator[](const Key &k) const { return _m[k]+_v; }
1050    ///\e
1051    void set(const Key &k, const Value &v) { _m.set(k, v-_v); }
1052  };
1053
1054  /// Returns a \c ShiftMap class
1055
1056  /// This function just returns a \c ShiftMap class.
1057  ///
1058  /// For example, if \c m is a map with \c double values and \c v is
1059  /// \c double, then <tt>shiftMap(m,v)[x]</tt> will be equal to
1060  /// <tt>m[x]+v</tt>.
1061  ///
1062  /// \relates ShiftMap
1063  template<typename M, typename C>
1064  inline ShiftMap<M, C> shiftMap(const M &m, const C &v) {
1065    return ShiftMap<M, C>(m,v);
1066  }
1067
1068  /// Returns a \c ShiftWriteMap class
1069
1070  /// This function just returns a \c ShiftWriteMap class.
1071  ///
1072  /// For example, if \c m is a map with \c double values and \c v is
1073  /// \c double, then <tt>shiftWriteMap(m,v)[x]</tt> will be equal to
1074  /// <tt>m[x]+v</tt>.
1075  /// Moreover it makes also possible to write the map.
1076  ///
1077  /// \relates ShiftWriteMap
1078  template<typename M, typename C>
1079  inline ShiftWriteMap<M, C> shiftWriteMap(M &m, const C &v) {
1080    return ShiftWriteMap<M, C>(m,v);
1081  }
1082
1083
1084  /// Scales a map with a constant.
1085
1086  /// This \ref concepts::ReadMap "read-only map" returns the value of
1087  /// the given map multiplied from the left side with a constant value.
1088  /// Its \c Key and \c Value are inherited from \c M.
1089  ///
1090  /// Actually,
1091  /// \code
1092  ///   ScaleMap<M> sc(m,v);
1093  /// \endcode
1094  /// is equivalent to
1095  /// \code
1096  ///   ConstMap<M::Key, M::Value> cm(v);
1097  ///   MulMap<ConstMap<M::Key, M::Value>, M> sc(cm,m);
1098  /// \endcode
1099  ///
1100  /// The simplest way of using this map is through the scaleMap()
1101  /// function.
1102  ///
1103  /// \sa ScaleWriteMap
1104  template<typename M, typename C = typename M::Value>
1105  class ScaleMap : public MapBase<typename M::Key, typename M::Value> {
1106    const M &_m;
1107    C _v;
1108  public:
1109    ///\e
1110    typedef typename M::Key Key;
1111    ///\e
1112    typedef typename M::Value Value;
1113
1114    /// Constructor
1115
1116    /// Constructor.
1117    /// \param m The undelying map.
1118    /// \param v The constant value.
1119    ScaleMap(const M &m, const C &v) : _m(m), _v(v) {}
1120    ///\e
1121    Value operator[](const Key &k) const { return _v*_m[k]; }
1122  };
1123
1124  /// Scales a map with a constant (read-write version).
1125
1126  /// This \ref concepts::ReadWriteMap "read-write map" returns the value of
1127  /// the given map multiplied from the left side with a constant value.
1128  /// Its \c Key and \c Value are inherited from \c M.
1129  /// It can also be used as write map if the \c / operator is defined
1130  /// between \c Value and \c C and the given multiplier is not zero.
1131  ///
1132  /// The simplest way of using this map is through the scaleWriteMap()
1133  /// function.
1134  ///
1135  /// \sa ScaleMap
1136  template<typename M, typename C = typename M::Value>
1137  class ScaleWriteMap : public MapBase<typename M::Key, typename M::Value> {
1138    M &_m;
1139    C _v;
1140  public:
1141    ///\e
1142    typedef typename M::Key Key;
1143    ///\e
1144    typedef typename M::Value Value;
1145
1146    /// Constructor
1147
1148    /// Constructor.
1149    /// \param m The undelying map.
1150    /// \param v The constant value.
1151    ScaleWriteMap(M &m, const C &v) : _m(m), _v(v) {}
1152    ///\e
1153    Value operator[](const Key &k) const { return _v*_m[k]; }
1154    ///\e
1155    void set(const Key &k, const Value &v) { _m.set(k, v/_v); }
1156  };
1157
1158  /// Returns a \c ScaleMap class
1159
1160  /// This function just returns a \c ScaleMap class.
1161  ///
1162  /// For example, if \c m is a map with \c double values and \c v is
1163  /// \c double, then <tt>scaleMap(m,v)[x]</tt> will be equal to
1164  /// <tt>v*m[x]</tt>.
1165  ///
1166  /// \relates ScaleMap
1167  template<typename M, typename C>
1168  inline ScaleMap<M, C> scaleMap(const M &m, const C &v) {
1169    return ScaleMap<M, C>(m,v);
1170  }
1171
1172  /// Returns a \c ScaleWriteMap class
1173
1174  /// This function just returns a \c ScaleWriteMap class.
1175  ///
1176  /// For example, if \c m is a map with \c double values and \c v is
1177  /// \c double, then <tt>scaleWriteMap(m,v)[x]</tt> will be equal to
1178  /// <tt>v*m[x]</tt>.
1179  /// Moreover it makes also possible to write the map.
1180  ///
1181  /// \relates ScaleWriteMap
1182  template<typename M, typename C>
1183  inline ScaleWriteMap<M, C> scaleWriteMap(M &m, const C &v) {
1184    return ScaleWriteMap<M, C>(m,v);
1185  }
1186
1187
1188  /// Negative of a map
1189
1190  /// This \ref concepts::ReadMap "read-only map" returns the negative
1191  /// of the values of the given map (using the unary \c - operator).
1192  /// Its \c Key and \c Value are inherited from \c M.
1193  ///
1194  /// If M::Value is \c int, \c double etc., then
1195  /// \code
1196  ///   NegMap<M> neg(m);
1197  /// \endcode
1198  /// is equivalent to
1199  /// \code
1200  ///   ScaleMap<M> neg(m,-1);
1201  /// \endcode
1202  ///
1203  /// The simplest way of using this map is through the negMap()
1204  /// function.
1205  ///
1206  /// \sa NegWriteMap
1207  template<typename M>
1208  class NegMap : public MapBase<typename M::Key, typename M::Value> {
1209    const M& _m;
1210  public:
1211    ///\e
1212    typedef typename M::Key Key;
1213    ///\e
1214    typedef typename M::Value Value;
1215
1216    /// Constructor
1217    NegMap(const M &m) : _m(m) {}
1218    ///\e
1219    Value operator[](const Key &k) const { return -_m[k]; }
1220  };
1221
1222  /// Negative of a map (read-write version)
1223
1224  /// This \ref concepts::ReadWriteMap "read-write map" returns the
1225  /// negative of the values of the given map (using the unary \c -
1226  /// operator).
1227  /// Its \c Key and \c Value are inherited from \c M.
1228  /// It makes also possible to write the map.
1229  ///
1230  /// If M::Value is \c int, \c double etc., then
1231  /// \code
1232  ///   NegWriteMap<M> neg(m);
1233  /// \endcode
1234  /// is equivalent to
1235  /// \code
1236  ///   ScaleWriteMap<M> neg(m,-1);
1237  /// \endcode
1238  ///
1239  /// The simplest way of using this map is through the negWriteMap()
1240  /// function.
1241  ///
1242  /// \sa NegMap
1243  template<typename M>
1244  class NegWriteMap : public MapBase<typename M::Key, typename M::Value> {
1245    M &_m;
1246  public:
1247    ///\e
1248    typedef typename M::Key Key;
1249    ///\e
1250    typedef typename M::Value Value;
1251
1252    /// Constructor
1253    NegWriteMap(M &m) : _m(m) {}
1254    ///\e
1255    Value operator[](const Key &k) const { return -_m[k]; }
1256    ///\e
1257    void set(const Key &k, const Value &v) { _m.set(k, -v); }
1258  };
1259
1260  /// Returns a \c NegMap class
1261
1262  /// This function just returns a \c NegMap class.
1263  ///
1264  /// For example, if \c m is a map with \c double values, then
1265  /// <tt>negMap(m)[x]</tt> will be equal to <tt>-m[x]</tt>.
1266  ///
1267  /// \relates NegMap
1268  template <typename M>
1269  inline NegMap<M> negMap(const M &m) {
1270    return NegMap<M>(m);
1271  }
1272
1273  /// Returns a \c NegWriteMap class
1274
1275  /// This function just returns a \c NegWriteMap class.
1276  ///
1277  /// For example, if \c m is a map with \c double values, then
1278  /// <tt>negWriteMap(m)[x]</tt> will be equal to <tt>-m[x]</tt>.
1279  /// Moreover it makes also possible to write the map.
1280  ///
1281  /// \relates NegWriteMap
1282  template <typename M>
1283  inline NegWriteMap<M> negWriteMap(M &m) {
1284    return NegWriteMap<M>(m);
1285  }
1286
1287
1288  /// Absolute value of a map
1289
1290  /// This \ref concepts::ReadMap "read-only map" returns the absolute
1291  /// value of the values of the given map.
1292  /// Its \c Key and \c Value are inherited from \c M.
1293  /// \c Value must be comparable to \c 0 and the unary \c -
1294  /// operator must be defined for it, of course.
1295  ///
1296  /// The simplest way of using this map is through the absMap()
1297  /// function.
1298  template<typename M>
1299  class AbsMap : public MapBase<typename M::Key, typename M::Value> {
1300    const M &_m;
1301  public:
1302    ///\e
1303    typedef typename M::Key Key;
1304    ///\e
1305    typedef typename M::Value Value;
1306
1307    /// Constructor
1308    AbsMap(const M &m) : _m(m) {}
1309    ///\e
1310    Value operator[](const Key &k) const {
1311      Value tmp = _m[k];
1312      return tmp >= 0 ? tmp : -tmp;
1313    }
1314
1315  };
1316
1317  /// Returns an \c AbsMap class
1318
1319  /// This function just returns an \c AbsMap class.
1320  ///
1321  /// For example, if \c m is a map with \c double values, then
1322  /// <tt>absMap(m)[x]</tt> will be equal to <tt>m[x]</tt> if
1323  /// it is positive or zero and <tt>-m[x]</tt> if <tt>m[x]</tt> is
1324  /// negative.
1325  ///
1326  /// \relates AbsMap
1327  template<typename M>
1328  inline AbsMap<M> absMap(const M &m) {
1329    return AbsMap<M>(m);
1330  }
1331
1332  /// @}
1333
1334  // Logical maps and map adaptors:
1335
1336  /// \addtogroup maps
1337  /// @{
1338
1339  /// Constant \c true map.
1340
1341  /// This \ref concepts::ReadMap "read-only map" assigns \c true to
1342  /// each key.
1343  ///
1344  /// Note that
1345  /// \code
1346  ///   TrueMap<K> tm;
1347  /// \endcode
1348  /// is equivalent to
1349  /// \code
1350  ///   ConstMap<K,bool> tm(true);
1351  /// \endcode
1352  ///
1353  /// \sa FalseMap
1354  /// \sa ConstMap
1355  template <typename K>
1356  class TrueMap : public MapBase<K, bool> {
1357  public:
1358    ///\e
1359    typedef K Key;
1360    ///\e
1361    typedef bool Value;
1362
1363    /// Gives back \c true.
1364    Value operator[](const Key&) const { return true; }
1365  };
1366
1367  /// Returns a \c TrueMap class
1368
1369  /// This function just returns a \c TrueMap class.
1370  /// \relates TrueMap
1371  template<typename K>
1372  inline TrueMap<K> trueMap() {
1373    return TrueMap<K>();
1374  }
1375
1376
1377  /// Constant \c false map.
1378
1379  /// This \ref concepts::ReadMap "read-only map" assigns \c false to
1380  /// each key.
1381  ///
1382  /// Note that
1383  /// \code
1384  ///   FalseMap<K> fm;
1385  /// \endcode
1386  /// is equivalent to
1387  /// \code
1388  ///   ConstMap<K,bool> fm(false);
1389  /// \endcode
1390  ///
1391  /// \sa TrueMap
1392  /// \sa ConstMap
1393  template <typename K>
1394  class FalseMap : public MapBase<K, bool> {
1395  public:
1396    ///\e
1397    typedef K Key;
1398    ///\e
1399    typedef bool Value;
1400
1401    /// Gives back \c false.
1402    Value operator[](const Key&) const { return false; }
1403  };
1404
1405  /// Returns a \c FalseMap class
1406
1407  /// This function just returns a \c FalseMap class.
1408  /// \relates FalseMap
1409  template<typename K>
1410  inline FalseMap<K> falseMap() {
1411    return FalseMap<K>();
1412  }
1413
1414  /// @}
1415
1416  /// \addtogroup map_adaptors
1417  /// @{
1418
1419  /// Logical 'and' of two maps
1420
1421  /// This \ref concepts::ReadMap "read-only map" returns the logical
1422  /// 'and' of the values of the two given maps.
1423  /// Its \c Key type is inherited from \c M1 and its \c Value type is
1424  /// \c bool. \c M2::Key must be convertible to \c M1::Key.
1425  ///
1426  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
1427  /// \code
1428  ///   AndMap<M1,M2> am(m1,m2);
1429  /// \endcode
1430  /// <tt>am[x]</tt> will be equal to <tt>m1[x]&&m2[x]</tt>.
1431  ///
1432  /// The simplest way of using this map is through the andMap()
1433  /// function.
1434  ///
1435  /// \sa OrMap
1436  /// \sa NotMap, NotWriteMap
1437  template<typename M1, typename M2>
1438  class AndMap : public MapBase<typename M1::Key, bool> {
1439    const M1 &_m1;
1440    const M2 &_m2;
1441  public:
1442    ///\e
1443    typedef typename M1::Key Key;
1444    ///\e
1445    typedef bool Value;
1446
1447    /// Constructor
1448    AndMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
1449    ///\e
1450    Value operator[](const Key &k) const { return _m1[k]&&_m2[k]; }
1451  };
1452
1453  /// Returns an \c AndMap class
1454
1455  /// This function just returns an \c AndMap class.
1456  ///
1457  /// For example, if \c m1 and \c m2 are both maps with \c bool values,
1458  /// then <tt>andMap(m1,m2)[x]</tt> will be equal to
1459  /// <tt>m1[x]&&m2[x]</tt>.
1460  ///
1461  /// \relates AndMap
1462  template<typename M1, typename M2>
1463  inline AndMap<M1, M2> andMap(const M1 &m1, const M2 &m2) {
1464    return AndMap<M1, M2>(m1,m2);
1465  }
1466
1467
1468  /// Logical 'or' of two maps
1469
1470  /// This \ref concepts::ReadMap "read-only map" returns the logical
1471  /// 'or' of the values of the two given maps.
1472  /// Its \c Key type is inherited from \c M1 and its \c Value type is
1473  /// \c bool. \c M2::Key must be convertible to \c M1::Key.
1474  ///
1475  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
1476  /// \code
1477  ///   OrMap<M1,M2> om(m1,m2);
1478  /// \endcode
1479  /// <tt>om[x]</tt> will be equal to <tt>m1[x]||m2[x]</tt>.
1480  ///
1481  /// The simplest way of using this map is through the orMap()
1482  /// function.
1483  ///
1484  /// \sa AndMap
1485  /// \sa NotMap, NotWriteMap
1486  template<typename M1, typename M2>
1487  class OrMap : public MapBase<typename M1::Key, bool> {
1488    const M1 &_m1;
1489    const M2 &_m2;
1490  public:
1491    ///\e
1492    typedef typename M1::Key Key;
1493    ///\e
1494    typedef bool Value;
1495
1496    /// Constructor
1497    OrMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
1498    ///\e
1499    Value operator[](const Key &k) const { return _m1[k]||_m2[k]; }
1500  };
1501
1502  /// Returns an \c OrMap class
1503
1504  /// This function just returns an \c OrMap class.
1505  ///
1506  /// For example, if \c m1 and \c m2 are both maps with \c bool values,
1507  /// then <tt>orMap(m1,m2)[x]</tt> will be equal to
1508  /// <tt>m1[x]||m2[x]</tt>.
1509  ///
1510  /// \relates OrMap
1511  template<typename M1, typename M2>
1512  inline OrMap<M1, M2> orMap(const M1 &m1, const M2 &m2) {
1513    return OrMap<M1, M2>(m1,m2);
1514  }
1515
1516
1517  /// Logical 'not' of a map
1518
1519  /// This \ref concepts::ReadMap "read-only map" returns the logical
1520  /// negation of the values of the given map.
1521  /// Its \c Key is inherited from \c M and its \c Value is \c bool.
1522  ///
1523  /// The simplest way of using this map is through the notMap()
1524  /// function.
1525  ///
1526  /// \sa NotWriteMap
1527  template <typename M>
1528  class NotMap : public MapBase<typename M::Key, bool> {
1529    const M &_m;
1530  public:
1531    ///\e
1532    typedef typename M::Key Key;
1533    ///\e
1534    typedef bool Value;
1535
1536    /// Constructor
1537    NotMap(const M &m) : _m(m) {}
1538    ///\e
1539    Value operator[](const Key &k) const { return !_m[k]; }
1540  };
1541
1542  /// Logical 'not' of a map (read-write version)
1543
1544  /// This \ref concepts::ReadWriteMap "read-write map" returns the
1545  /// logical negation of the values of the given map.
1546  /// Its \c Key is inherited from \c M and its \c Value is \c bool.
1547  /// It makes also possible to write the map. When a value is set,
1548  /// the opposite value is set to the original map.
1549  ///
1550  /// The simplest way of using this map is through the notWriteMap()
1551  /// function.
1552  ///
1553  /// \sa NotMap
1554  template <typename M>
1555  class NotWriteMap : public MapBase<typename M::Key, bool> {
1556    M &_m;
1557  public:
1558    ///\e
1559    typedef typename M::Key Key;
1560    ///\e
1561    typedef bool Value;
1562
1563    /// Constructor
1564    NotWriteMap(M &m) : _m(m) {}
1565    ///\e
1566    Value operator[](const Key &k) const { return !_m[k]; }
1567    ///\e
1568    void set(const Key &k, bool v) { _m.set(k, !v); }
1569  };
1570
1571  /// Returns a \c NotMap class
1572
1573  /// This function just returns a \c NotMap class.
1574  ///
1575  /// For example, if \c m is a map with \c bool values, then
1576  /// <tt>notMap(m)[x]</tt> will be equal to <tt>!m[x]</tt>.
1577  ///
1578  /// \relates NotMap
1579  template <typename M>
1580  inline NotMap<M> notMap(const M &m) {
1581    return NotMap<M>(m);
1582  }
1583
1584  /// Returns a \c NotWriteMap class
1585
1586  /// This function just returns a \c NotWriteMap class.
1587  ///
1588  /// For example, if \c m is a map with \c bool values, then
1589  /// <tt>notWriteMap(m)[x]</tt> will be equal to <tt>!m[x]</tt>.
1590  /// Moreover it makes also possible to write the map.
1591  ///
1592  /// \relates NotWriteMap
1593  template <typename M>
1594  inline NotWriteMap<M> notWriteMap(M &m) {
1595    return NotWriteMap<M>(m);
1596  }
1597
1598
1599  /// Combination of two maps using the \c == operator
1600
1601  /// This \ref concepts::ReadMap "read-only map" assigns \c true to
1602  /// the keys for which the corresponding values of the two maps are
1603  /// equal.
1604  /// Its \c Key type is inherited from \c M1 and its \c Value type is
1605  /// \c bool. \c M2::Key must be convertible to \c M1::Key.
1606  ///
1607  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
1608  /// \code
1609  ///   EqualMap<M1,M2> em(m1,m2);
1610  /// \endcode
1611  /// <tt>em[x]</tt> will be equal to <tt>m1[x]==m2[x]</tt>.
1612  ///
1613  /// The simplest way of using this map is through the equalMap()
1614  /// function.
1615  ///
1616  /// \sa LessMap
1617  template<typename M1, typename M2>
1618  class EqualMap : public MapBase<typename M1::Key, bool> {
1619    const M1 &_m1;
1620    const M2 &_m2;
1621  public:
1622    ///\e
1623    typedef typename M1::Key Key;
1624    ///\e
1625    typedef bool Value;
1626
1627    /// Constructor
1628    EqualMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
1629    ///\e
1630    Value operator[](const Key &k) const { return _m1[k]==_m2[k]; }
1631  };
1632
1633  /// Returns an \c EqualMap class
1634
1635  /// This function just returns an \c EqualMap class.
1636  ///
1637  /// For example, if \c m1 and \c m2 are maps with keys and values of
1638  /// the same type, then <tt>equalMap(m1,m2)[x]</tt> will be equal to
1639  /// <tt>m1[x]==m2[x]</tt>.
1640  ///
1641  /// \relates EqualMap
1642  template<typename M1, typename M2>
1643  inline EqualMap<M1, M2> equalMap(const M1 &m1, const M2 &m2) {
1644    return EqualMap<M1, M2>(m1,m2);
1645  }
1646
1647
1648  /// Combination of two maps using the \c < operator
1649
1650  /// This \ref concepts::ReadMap "read-only map" assigns \c true to
1651  /// the keys for which the corresponding value of the first map is
1652  /// less then the value of the second map.
1653  /// Its \c Key type is inherited from \c M1 and its \c Value type is
1654  /// \c bool. \c M2::Key must be convertible to \c M1::Key.
1655  ///
1656  /// If \c m1 is of type \c M1 and \c m2 is of \c M2, then for
1657  /// \code
1658  ///   LessMap<M1,M2> lm(m1,m2);
1659  /// \endcode
1660  /// <tt>lm[x]</tt> will be equal to <tt>m1[x]<m2[x]</tt>.
1661  ///
1662  /// The simplest way of using this map is through the lessMap()
1663  /// function.
1664  ///
1665  /// \sa EqualMap
1666  template<typename M1, typename M2>
1667  class LessMap : public MapBase<typename M1::Key, bool> {
1668    const M1 &_m1;
1669    const M2 &_m2;
1670  public:
1671    ///\e
1672    typedef typename M1::Key Key;
1673    ///\e
1674    typedef bool Value;
1675
1676    /// Constructor
1677    LessMap(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}
1678    ///\e
1679    Value operator[](const Key &k) const { return _m1[k]<_m2[k]; }
1680  };
1681
1682  /// Returns an \c LessMap class
1683
1684  /// This function just returns an \c LessMap class.
1685  ///
1686  /// For example, if \c m1 and \c m2 are maps with keys and values of
1687  /// the same type, then <tt>lessMap(m1,m2)[x]</tt> will be equal to
1688  /// <tt>m1[x]<m2[x]</tt>.
1689  ///
1690  /// \relates LessMap
1691  template<typename M1, typename M2>
1692  inline LessMap<M1, M2> lessMap(const M1 &m1, const M2 &m2) {
1693    return LessMap<M1, M2>(m1,m2);
1694  }
1695
1696  namespace _maps_bits {
1697
1698    template <typename _Iterator, typename Enable = void>
1699    struct IteratorTraits {
1700      typedef typename std::iterator_traits<_Iterator>::value_type Value;
1701    };
1702
1703    template <typename _Iterator>
1704    struct IteratorTraits<_Iterator,
1705      typename exists<typename _Iterator::container_type>::type>
1706    {
1707      typedef typename _Iterator::container_type::value_type Value;
1708    };
1709
1710  }
1711
1712  /// @}
1713
1714  /// \addtogroup maps
1715  /// @{
1716
1717  /// \brief Writable bool map for logging each \c true assigned element
1718  ///
1719  /// A \ref concepts::WriteMap "writable" bool map for logging
1720  /// each \c true assigned element, i.e it copies subsequently each
1721  /// keys set to \c true to the given iterator.
1722  /// The most important usage of it is storing certain nodes or arcs
1723  /// that were marked \c true by an algorithm.
1724  ///
1725  /// There are several algorithms that provide solutions through bool
1726  /// maps and most of them assign \c true at most once for each key.
1727  /// In these cases it is a natural request to store each \c true
1728  /// assigned elements (in order of the assignment), which can be
1729  /// easily done with LoggerBoolMap.
1730  ///
1731  /// The simplest way of using this map is through the loggerBoolMap()
1732  /// function.
1733  ///
1734  /// \tparam IT The type of the iterator.
1735  /// \tparam KEY The key type of the map. The default value set
1736  /// according to the iterator type should work in most cases.
1737  ///
1738  /// \note The container of the iterator must contain enough space
1739  /// for the elements or the iterator should be an inserter iterator.
1740#ifdef DOXYGEN
1741  template <typename IT, typename KEY>
1742#else
1743  template <typename IT,
1744            typename KEY = typename _maps_bits::IteratorTraits<IT>::Value>
1745#endif
1746  class LoggerBoolMap : public MapBase<KEY, bool> {
1747  public:
1748
1749    ///\e
1750    typedef KEY Key;
1751    ///\e
1752    typedef bool Value;
1753    ///\e
1754    typedef IT Iterator;
1755
1756    /// Constructor
1757    LoggerBoolMap(Iterator it)
1758      : _begin(it), _end(it) {}
1759
1760    /// Gives back the given iterator set for the first key
1761    Iterator begin() const {
1762      return _begin;
1763    }
1764
1765    /// Gives back the the 'after the last' iterator
1766    Iterator end() const {
1767      return _end;
1768    }
1769
1770    /// The set function of the map
1771    void set(const Key& key, Value value) {
1772      if (value) {
1773        *_end++ = key;
1774      }
1775    }
1776
1777  private:
1778    Iterator _begin;
1779    Iterator _end;
1780  };
1781
1782  /// Returns a \c LoggerBoolMap class
1783
1784  /// This function just returns a \c LoggerBoolMap class.
1785  ///
1786  /// The most important usage of it is storing certain nodes or arcs
1787  /// that were marked \c true by an algorithm.
1788  /// For example it makes easier to store the nodes in the processing
1789  /// order of Dfs algorithm, as the following examples show.
1790  /// \code
1791  ///   std::vector<Node> v;
1792  ///   dfs(g,s).processedMap(loggerBoolMap(std::back_inserter(v))).run();
1793  /// \endcode
1794  /// \code
1795  ///   std::vector<Node> v(countNodes(g));
1796  ///   dfs(g,s).processedMap(loggerBoolMap(v.begin())).run();
1797  /// \endcode
1798  ///
1799  /// \note The container of the iterator must contain enough space
1800  /// for the elements or the iterator should be an inserter iterator.
1801  ///
1802  /// \note LoggerBoolMap is just \ref concepts::WriteMap "writable", so
1803  /// it cannot be used when a readable map is needed, for example as
1804  /// \c ReachedMap for \c Bfs, \c Dfs and \c Dijkstra algorithms.
1805  ///
1806  /// \relates LoggerBoolMap
1807  template<typename Iterator>
1808  inline LoggerBoolMap<Iterator> loggerBoolMap(Iterator it) {
1809    return LoggerBoolMap<Iterator>(it);
1810  }
1811
1812  /// @}
1813
1814  /// \addtogroup graph_maps
1815  /// @{
1816
1817  /// \brief Provides an immutable and unique id for each item in a graph.
1818  ///
1819  /// IdMap provides a unique and immutable id for each item of the
1820  /// same type (\c Node, \c Arc or \c Edge) in a graph. This id is
1821  ///  - \b unique: different items get different ids,
1822  ///  - \b immutable: the id of an item does not change (even if you
1823  ///    delete other nodes).
1824  ///
1825  /// Using this map you get access (i.e. can read) the inner id values of
1826  /// the items stored in the graph, which is returned by the \c id()
1827  /// function of the graph. This map can be inverted with its member
1828  /// class \c InverseMap or with the \c operator()() member.
1829  ///
1830  /// \tparam GR The graph type.
1831  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
1832  /// \c GR::Edge).
1833  ///
1834  /// \see RangeIdMap
1835  template <typename GR, typename K>
1836  class IdMap : public MapBase<K, int> {
1837  public:
1838    /// The graph type of IdMap.
1839    typedef GR Graph;
1840    typedef GR Digraph;
1841    /// The key type of IdMap (\c Node, \c Arc or \c Edge).
1842    typedef K Item;
1843    /// The key type of IdMap (\c Node, \c Arc or \c Edge).
1844    typedef K Key;
1845    /// The value type of IdMap.
1846    typedef int Value;
1847
1848    /// \brief Constructor.
1849    ///
1850    /// Constructor of the map.
1851    explicit IdMap(const Graph& graph) : _graph(&graph) {}
1852
1853    /// \brief Gives back the \e id of the item.
1854    ///
1855    /// Gives back the immutable and unique \e id of the item.
1856    int operator[](const Item& item) const { return _graph->id(item);}
1857
1858    /// \brief Gives back the \e item by its id.
1859    ///
1860    /// Gives back the \e item by its id.
1861    Item operator()(int id) { return _graph->fromId(id, Item()); }
1862
1863  private:
1864    const Graph* _graph;
1865
1866  public:
1867
1868    /// \brief This class represents the inverse of its owner (IdMap).
1869    ///
1870    /// This class represents the inverse of its owner (IdMap).
1871    /// \see inverse()
1872    class InverseMap {
1873    public:
1874
1875      /// \brief Constructor.
1876      ///
1877      /// Constructor for creating an id-to-item map.
1878      explicit InverseMap(const Graph& graph) : _graph(&graph) {}
1879
1880      /// \brief Constructor.
1881      ///
1882      /// Constructor for creating an id-to-item map.
1883      explicit InverseMap(const IdMap& map) : _graph(map._graph) {}
1884
1885      /// \brief Gives back the given item from its id.
1886      ///
1887      /// Gives back the given item from its id.
1888      Item operator[](int id) const { return _graph->fromId(id, Item());}
1889
1890    private:
1891      const Graph* _graph;
1892    };
1893
1894    /// \brief Gives back the inverse of the map.
1895    ///
1896    /// Gives back the inverse of the IdMap.
1897    InverseMap inverse() const { return InverseMap(*_graph);}
1898  };
1899
1900
1901  /// \brief General cross reference graph map type.
1902
1903  /// This class provides simple invertable graph maps.
1904  /// It wraps a standard graph map (\c NodeMap, \c ArcMap or \c EdgeMap)
1905  /// and if a key is set to a new value, then stores it in the inverse map.
1906  /// The values of the map can be accessed
1907  /// with stl compatible forward iterator.
1908  ///
1909  /// This type is not reference map, so it cannot be modified with
1910  /// the subscript operator.
1911  ///
1912  /// \tparam GR The graph type.
1913  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
1914  /// \c GR::Edge).
1915  /// \tparam V The value type of the map.
1916  ///
1917  /// \see IterableValueMap
1918  template <typename GR, typename K, typename V>
1919  class CrossRefMap
1920    : protected ItemSetTraits<GR, K>::template Map<V>::Type {
1921  private:
1922
1923    typedef typename ItemSetTraits<GR, K>::
1924      template Map<V>::Type Map;
1925
1926    typedef std::multimap<V, K> Container;
1927    Container _inv_map;
1928
1929  public:
1930
1931    /// The graph type of CrossRefMap.
1932    typedef GR Graph;
1933    typedef GR Digraph;
1934    /// The key type of CrossRefMap (\c Node, \c Arc or \c Edge).
1935    typedef K Item;
1936    /// The key type of CrossRefMap (\c Node, \c Arc or \c Edge).
1937    typedef K Key;
1938    /// The value type of CrossRefMap.
1939    typedef V Value;
1940
1941    /// \brief Constructor.
1942    ///
1943    /// Construct a new CrossRefMap for the given graph.
1944    explicit CrossRefMap(const Graph& graph) : Map(graph) {}
1945
1946    /// \brief Forward iterator for values.
1947    ///
1948    /// This iterator is an stl compatible forward
1949    /// iterator on the values of the map. The values can
1950    /// be accessed in the <tt>[beginValue, endValue)</tt> range.
1951    /// They are considered with multiplicity, so each value is
1952    /// traversed for each item it is assigned to.
1953    class ValueIterator
1954      : public std::iterator<std::forward_iterator_tag, Value> {
1955      friend class CrossRefMap;
1956    private:
1957      ValueIterator(typename Container::const_iterator _it)
1958        : it(_it) {}
1959    public:
1960
1961      ValueIterator() {}
1962
1963      ValueIterator& operator++() { ++it; return *this; }
1964      ValueIterator operator++(int) {
1965        ValueIterator tmp(*this);
1966        operator++();
1967        return tmp;
1968      }
1969
1970      const Value& operator*() const { return it->first; }
1971      const Value* operator->() const { return &(it->first); }
1972
1973      bool operator==(ValueIterator jt) const { return it == jt.it; }
1974      bool operator!=(ValueIterator jt) const { return it != jt.it; }
1975
1976    private:
1977      typename Container::const_iterator it;
1978    };
1979
1980    /// \brief Returns an iterator to the first value.
1981    ///
1982    /// Returns an stl compatible iterator to the
1983    /// first value of the map. The values of the
1984    /// map can be accessed in the <tt>[beginValue, endValue)</tt>
1985    /// range.
1986    ValueIterator beginValue() const {
1987      return ValueIterator(_inv_map.begin());
1988    }
1989
1990    /// \brief Returns an iterator after the last value.
1991    ///
1992    /// Returns an stl compatible iterator after the
1993    /// last value of the map. The values of the
1994    /// map can be accessed in the <tt>[beginValue, endValue)</tt>
1995    /// range.
1996    ValueIterator endValue() const {
1997      return ValueIterator(_inv_map.end());
1998    }
1999
2000    /// \brief Sets the value associated with the given key.
2001    ///
2002    /// Sets the value associated with the given key.
2003    void set(const Key& key, const Value& val) {
2004      Value oldval = Map::operator[](key);
2005      typename Container::iterator it;
2006      for (it = _inv_map.equal_range(oldval).first;
2007           it != _inv_map.equal_range(oldval).second; ++it) {
2008        if (it->second == key) {
2009          _inv_map.erase(it);
2010          break;
2011        }
2012      }
2013      _inv_map.insert(std::make_pair(val, key));
2014      Map::set(key, val);
2015    }
2016
2017    /// \brief Returns the value associated with the given key.
2018    ///
2019    /// Returns the value associated with the given key.
2020    typename MapTraits<Map>::ConstReturnValue
2021    operator[](const Key& key) const {
2022      return Map::operator[](key);
2023    }
2024
2025    /// \brief Gives back an item by its value.
2026    ///
2027    /// This function gives back an item that is assigned to
2028    /// the given value or \c INVALID if no such item exists.
2029    /// If there are more items with the same associated value,
2030    /// only one of them is returned.
2031    Key operator()(const Value& val) const {
2032      typename Container::const_iterator it = _inv_map.find(val);
2033      return it != _inv_map.end() ? it->second : INVALID;
2034    }
2035   
2036    /// \brief Returns the number of items with the given value.
2037    ///
2038    /// This function returns the number of items with the given value
2039    /// associated with it.
2040    int count(const Value &val) const {
2041      return _inv_map.count(val);
2042    }
2043
2044  protected:
2045
2046    /// \brief Erase the key from the map and the inverse map.
2047    ///
2048    /// Erase the key from the map and the inverse map. It is called by the
2049    /// \c AlterationNotifier.
2050    virtual void erase(const Key& key) {
2051      Value val = Map::operator[](key);
2052      typename Container::iterator it;
2053      for (it = _inv_map.equal_range(val).first;
2054           it != _inv_map.equal_range(val).second; ++it) {
2055        if (it->second == key) {
2056          _inv_map.erase(it);
2057          break;
2058        }
2059      }
2060      Map::erase(key);
2061    }
2062
2063    /// \brief Erase more keys from the map and the inverse map.
2064    ///
2065    /// Erase more keys from the map and the inverse map. It is called by the
2066    /// \c AlterationNotifier.
2067    virtual void erase(const std::vector<Key>& keys) {
2068      for (int i = 0; i < int(keys.size()); ++i) {
2069        Value val = Map::operator[](keys[i]);
2070        typename Container::iterator it;
2071        for (it = _inv_map.equal_range(val).first;
2072             it != _inv_map.equal_range(val).second; ++it) {
2073          if (it->second == keys[i]) {
2074            _inv_map.erase(it);
2075            break;
2076          }
2077        }
2078      }
2079      Map::erase(keys);
2080    }
2081
2082    /// \brief Clear the keys from the map and the inverse map.
2083    ///
2084    /// Clear the keys from the map and the inverse map. It is called by the
2085    /// \c AlterationNotifier.
2086    virtual void clear() {
2087      _inv_map.clear();
2088      Map::clear();
2089    }
2090
2091  public:
2092
2093    /// \brief The inverse map type.
2094    ///
2095    /// The inverse of this map. The subscript operator of the map
2096    /// gives back the item that was last assigned to the value.
2097    class InverseMap {
2098    public:
2099      /// \brief Constructor
2100      ///
2101      /// Constructor of the InverseMap.
2102      explicit InverseMap(const CrossRefMap& inverted)
2103        : _inverted(inverted) {}
2104
2105      /// The value type of the InverseMap.
2106      typedef typename CrossRefMap::Key Value;
2107      /// The key type of the InverseMap.
2108      typedef typename CrossRefMap::Value Key;
2109
2110      /// \brief Subscript operator.
2111      ///
2112      /// Subscript operator. It gives back an item
2113      /// that is assigned to the given value or \c INVALID
2114      /// if no such item exists.
2115      Value operator[](const Key& key) const {
2116        return _inverted(key);
2117      }
2118
2119    private:
2120      const CrossRefMap& _inverted;
2121    };
2122
2123    /// \brief It gives back the read-only inverse map.
2124    ///
2125    /// It gives back the read-only inverse map.
2126    InverseMap inverse() const {
2127      return InverseMap(*this);
2128    }
2129
2130  };
2131
2132  /// \brief Provides continuous and unique id for the
2133  /// items of a graph.
2134  ///
2135  /// RangeIdMap provides a unique and continuous
2136  /// id for each item of a given type (\c Node, \c Arc or
2137  /// \c Edge) in a graph. This id is
2138  ///  - \b unique: different items get different ids,
2139  ///  - \b continuous: the range of the ids is the set of integers
2140  ///    between 0 and \c n-1, where \c n is the number of the items of
2141  ///    this type (\c Node, \c Arc or \c Edge).
2142  ///  - So, the ids can change when deleting an item of the same type.
2143  ///
2144  /// Thus this id is not (necessarily) the same as what can get using
2145  /// the \c id() function of the graph or \ref IdMap.
2146  /// This map can be inverted with its member class \c InverseMap,
2147  /// or with the \c operator()() member.
2148  ///
2149  /// \tparam GR The graph type.
2150  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
2151  /// \c GR::Edge).
2152  ///
2153  /// \see IdMap
2154  template <typename GR, typename K>
2155  class RangeIdMap
2156    : protected ItemSetTraits<GR, K>::template Map<int>::Type {
2157
2158    typedef typename ItemSetTraits<GR, K>::template Map<int>::Type Map;
2159
2160  public:
2161    /// The graph type of RangeIdMap.
2162    typedef GR Graph;
2163    typedef GR Digraph;
2164    /// The key type of RangeIdMap (\c Node, \c Arc or \c Edge).
2165    typedef K Item;
2166    /// The key type of RangeIdMap (\c Node, \c Arc or \c Edge).
2167    typedef K Key;
2168    /// The value type of RangeIdMap.
2169    typedef int Value;
2170
2171    /// \brief Constructor.
2172    ///
2173    /// Constructor.
2174    explicit RangeIdMap(const Graph& gr) : Map(gr) {
2175      Item it;
2176      const typename Map::Notifier* nf = Map::notifier();
2177      for (nf->first(it); it != INVALID; nf->next(it)) {
2178        Map::set(it, _inv_map.size());
2179        _inv_map.push_back(it);
2180      }
2181    }
2182
2183  protected:
2184
2185    /// \brief Adds a new key to the map.
2186    ///
2187    /// Add a new key to the map. It is called by the
2188    /// \c AlterationNotifier.
2189    virtual void add(const Item& item) {
2190      Map::add(item);
2191      Map::set(item, _inv_map.size());
2192      _inv_map.push_back(item);
2193    }
2194
2195    /// \brief Add more new keys to the map.
2196    ///
2197    /// Add more new keys to the map. It is called by the
2198    /// \c AlterationNotifier.
2199    virtual void add(const std::vector<Item>& items) {
2200      Map::add(items);
2201      for (int i = 0; i < int(items.size()); ++i) {
2202        Map::set(items[i], _inv_map.size());
2203        _inv_map.push_back(items[i]);
2204      }
2205    }
2206
2207    /// \brief Erase the key from the map.
2208    ///
2209    /// Erase the key from the map. It is called by the
2210    /// \c AlterationNotifier.
2211    virtual void erase(const Item& item) {
2212      Map::set(_inv_map.back(), Map::operator[](item));
2213      _inv_map[Map::operator[](item)] = _inv_map.back();
2214      _inv_map.pop_back();
2215      Map::erase(item);
2216    }
2217
2218    /// \brief Erase more keys from the map.
2219    ///
2220    /// Erase more keys from the map. It is called by the
2221    /// \c AlterationNotifier.
2222    virtual void erase(const std::vector<Item>& items) {
2223      for (int i = 0; i < int(items.size()); ++i) {
2224        Map::set(_inv_map.back(), Map::operator[](items[i]));
2225        _inv_map[Map::operator[](items[i])] = _inv_map.back();
2226        _inv_map.pop_back();
2227      }
2228      Map::erase(items);
2229    }
2230
2231    /// \brief Build the unique map.
2232    ///
2233    /// Build the unique map. It is called by the
2234    /// \c AlterationNotifier.
2235    virtual void build() {
2236      Map::build();
2237      Item it;
2238      const typename Map::Notifier* nf = Map::notifier();
2239      for (nf->first(it); it != INVALID; nf->next(it)) {
2240        Map::set(it, _inv_map.size());
2241        _inv_map.push_back(it);
2242      }
2243    }
2244
2245    /// \brief Clear the keys from the map.
2246    ///
2247    /// Clear the keys from the map. It is called by the
2248    /// \c AlterationNotifier.
2249    virtual void clear() {
2250      _inv_map.clear();
2251      Map::clear();
2252    }
2253
2254  public:
2255
2256    /// \brief Returns the maximal value plus one.
2257    ///
2258    /// Returns the maximal value plus one in the map.
2259    unsigned int size() const {
2260      return _inv_map.size();
2261    }
2262
2263    /// \brief Swaps the position of the two items in the map.
2264    ///
2265    /// Swaps the position of the two items in the map.
2266    void swap(const Item& p, const Item& q) {
2267      int pi = Map::operator[](p);
2268      int qi = Map::operator[](q);
2269      Map::set(p, qi);
2270      _inv_map[qi] = p;
2271      Map::set(q, pi);
2272      _inv_map[pi] = q;
2273    }
2274
2275    /// \brief Gives back the \e RangeId of the item
2276    ///
2277    /// Gives back the \e RangeId of the item.
2278    int operator[](const Item& item) const {
2279      return Map::operator[](item);
2280    }
2281
2282    /// \brief Gives back the item belonging to a \e RangeId
2283    ///
2284    /// Gives back the item belonging to a \e RangeId.
2285    Item operator()(int id) const {
2286      return _inv_map[id];
2287    }
2288
2289  private:
2290
2291    typedef std::vector<Item> Container;
2292    Container _inv_map;
2293
2294  public:
2295
2296    /// \brief The inverse map type of RangeIdMap.
2297    ///
2298    /// The inverse map type of RangeIdMap.
2299    class InverseMap {
2300    public:
2301      /// \brief Constructor
2302      ///
2303      /// Constructor of the InverseMap.
2304      explicit InverseMap(const RangeIdMap& inverted)
2305        : _inverted(inverted) {}
2306
2307
2308      /// The value type of the InverseMap.
2309      typedef typename RangeIdMap::Key Value;
2310      /// The key type of the InverseMap.
2311      typedef typename RangeIdMap::Value Key;
2312
2313      /// \brief Subscript operator.
2314      ///
2315      /// Subscript operator. It gives back the item
2316      /// that the descriptor currently belongs to.
2317      Value operator[](const Key& key) const {
2318        return _inverted(key);
2319      }
2320
2321      /// \brief Size of the map.
2322      ///
2323      /// Returns the size of the map.
2324      unsigned int size() const {
2325        return _inverted.size();
2326      }
2327
2328    private:
2329      const RangeIdMap& _inverted;
2330    };
2331
2332    /// \brief Gives back the inverse of the map.
2333    ///
2334    /// Gives back the inverse of the map.
2335    const InverseMap inverse() const {
2336      return InverseMap(*this);
2337    }
2338  };
2339
2340  /// \brief Dynamic iterable \c bool map.
2341  ///
2342  /// This class provides a special graph map type which can store a
2343  /// \c bool value for graph items (\c Node, \c Arc or \c Edge).
2344  /// For both \c true and \c false values it is possible to iterate on
2345  /// the keys.
2346  ///
2347  /// This type is a reference map, so it can be modified with the
2348  /// subscription operator.
2349  ///
2350  /// \tparam GR The graph type.
2351  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
2352  /// \c GR::Edge).
2353  ///
2354  /// \see IterableIntMap, IterableValueMap
2355  /// \see CrossRefMap
2356  template <typename GR, typename K>
2357  class IterableBoolMap
2358    : protected ItemSetTraits<GR, K>::template Map<int>::Type {
2359  private:
2360    typedef GR Graph;
2361
2362    typedef typename ItemSetTraits<GR, K>::ItemIt KeyIt;
2363    typedef typename ItemSetTraits<GR, K>::template Map<int>::Type Parent;
2364
2365    std::vector<K> _array;
2366    int _sep;
2367
2368  public:
2369
2370    /// Indicates that the map is reference map.
2371    typedef True ReferenceMapTag;
2372
2373    /// The key type
2374    typedef K Key;
2375    /// The value type
2376    typedef bool Value;
2377    /// The const reference type.
2378    typedef const Value& ConstReference;
2379
2380  private:
2381
2382    int position(const Key& key) const {
2383      return Parent::operator[](key);
2384    }
2385
2386  public:
2387
2388    /// \brief Reference to the value of the map.
2389    ///
2390    /// This class is similar to the \c bool type. It can be converted to
2391    /// \c bool and it provides the same operators.
2392    class Reference {
2393      friend class IterableBoolMap;
2394    private:
2395      Reference(IterableBoolMap& map, const Key& key)
2396        : _key(key), _map(map) {}
2397    public:
2398
2399      Reference& operator=(const Reference& value) {
2400        _map.set(_key, static_cast<bool>(value));
2401         return *this;
2402      }
2403
2404      operator bool() const {
2405        return static_cast<const IterableBoolMap&>(_map)[_key];
2406      }
2407
2408      Reference& operator=(bool value) {
2409        _map.set(_key, value);
2410        return *this;
2411      }
2412      Reference& operator&=(bool value) {
2413        _map.set(_key, _map[_key] & value);
2414        return *this;
2415      }
2416      Reference& operator|=(bool value) {
2417        _map.set(_key, _map[_key] | value);
2418        return *this;
2419      }
2420      Reference& operator^=(bool value) {
2421        _map.set(_key, _map[_key] ^ value);
2422        return *this;
2423      }
2424    private:
2425      Key _key;
2426      IterableBoolMap& _map;
2427    };
2428
2429    /// \brief Constructor of the map with a default value.
2430    ///
2431    /// Constructor of the map with a default value.
2432    explicit IterableBoolMap(const Graph& graph, bool def = false)
2433      : Parent(graph) {
2434      typename Parent::Notifier* nf = Parent::notifier();
2435      Key it;
2436      for (nf->first(it); it != INVALID; nf->next(it)) {
2437        Parent::set(it, _array.size());
2438        _array.push_back(it);
2439      }
2440      _sep = (def ? _array.size() : 0);
2441    }
2442
2443    /// \brief Const subscript operator of the map.
2444    ///
2445    /// Const subscript operator of the map.
2446    bool operator[](const Key& key) const {
2447      return position(key) < _sep;
2448    }
2449
2450    /// \brief Subscript operator of the map.
2451    ///
2452    /// Subscript operator of the map.
2453    Reference operator[](const Key& key) {
2454      return Reference(*this, key);
2455    }
2456
2457    /// \brief Set operation of the map.
2458    ///
2459    /// Set operation of the map.
2460    void set(const Key& key, bool value) {
2461      int pos = position(key);
2462      if (value) {
2463        if (pos < _sep) return;
2464        Key tmp = _array[_sep];
2465        _array[_sep] = key;
2466        Parent::set(key, _sep);
2467        _array[pos] = tmp;
2468        Parent::set(tmp, pos);
2469        ++_sep;
2470      } else {
2471        if (pos >= _sep) return;
2472        --_sep;
2473        Key tmp = _array[_sep];
2474        _array[_sep] = key;
2475        Parent::set(key, _sep);
2476        _array[pos] = tmp;
2477        Parent::set(tmp, pos);
2478      }
2479    }
2480
2481    /// \brief Set all items.
2482    ///
2483    /// Set all items in the map.
2484    /// \note Constant time operation.
2485    void setAll(bool value) {
2486      _sep = (value ? _array.size() : 0);
2487    }
2488
2489    /// \brief Returns the number of the keys mapped to \c true.
2490    ///
2491    /// Returns the number of the keys mapped to \c true.
2492    int trueNum() const {
2493      return _sep;
2494    }
2495
2496    /// \brief Returns the number of the keys mapped to \c false.
2497    ///
2498    /// Returns the number of the keys mapped to \c false.
2499    int falseNum() const {
2500      return _array.size() - _sep;
2501    }
2502
2503    /// \brief Iterator for the keys mapped to \c true.
2504    ///
2505    /// Iterator for the keys mapped to \c true. It works
2506    /// like a graph item iterator, it can be converted to
2507    /// the key type of the map, incremented with \c ++ operator, and
2508    /// if the iterator leaves the last valid key, it will be equal to
2509    /// \c INVALID.
2510    class TrueIt : public Key {
2511    public:
2512      typedef Key Parent;
2513
2514      /// \brief Creates an iterator.
2515      ///
2516      /// Creates an iterator. It iterates on the
2517      /// keys mapped to \c true.
2518      /// \param map The IterableBoolMap.
2519      explicit TrueIt(const IterableBoolMap& map)
2520        : Parent(map._sep > 0 ? map._array[map._sep - 1] : INVALID),
2521          _map(&map) {}
2522
2523      /// \brief Invalid constructor \& conversion.
2524      ///
2525      /// This constructor initializes the iterator to be invalid.
2526      /// \sa Invalid for more details.
2527      TrueIt(Invalid) : Parent(INVALID), _map(0) {}
2528
2529      /// \brief Increment operator.
2530      ///
2531      /// Increment operator.
2532      TrueIt& operator++() {
2533        int pos = _map->position(*this);
2534        Parent::operator=(pos > 0 ? _map->_array[pos - 1] : INVALID);
2535        return *this;
2536      }
2537
2538    private:
2539      const IterableBoolMap* _map;
2540    };
2541
2542    /// \brief Iterator for the keys mapped to \c false.
2543    ///
2544    /// Iterator for the keys mapped to \c false. It works
2545    /// like a graph item iterator, it can be converted to
2546    /// the key type of the map, incremented with \c ++ operator, and
2547    /// if the iterator leaves the last valid key, it will be equal to
2548    /// \c INVALID.
2549    class FalseIt : public Key {
2550    public:
2551      typedef Key Parent;
2552
2553      /// \brief Creates an iterator.
2554      ///
2555      /// Creates an iterator. It iterates on the
2556      /// keys mapped to \c false.
2557      /// \param map The IterableBoolMap.
2558      explicit FalseIt(const IterableBoolMap& map)
2559        : Parent(map._sep < int(map._array.size()) ?
2560                 map._array.back() : INVALID), _map(&map) {}
2561
2562      /// \brief Invalid constructor \& conversion.
2563      ///
2564      /// This constructor initializes the iterator to be invalid.
2565      /// \sa Invalid for more details.
2566      FalseIt(Invalid) : Parent(INVALID), _map(0) {}
2567
2568      /// \brief Increment operator.
2569      ///
2570      /// Increment operator.
2571      FalseIt& operator++() {
2572        int pos = _map->position(*this);
2573        Parent::operator=(pos > _map->_sep ? _map->_array[pos - 1] : INVALID);
2574        return *this;
2575      }
2576
2577    private:
2578      const IterableBoolMap* _map;
2579    };
2580
2581    /// \brief Iterator for the keys mapped to a given value.
2582    ///
2583    /// Iterator for the keys mapped to a given value. It works
2584    /// like a graph item iterator, it can be converted to
2585    /// the key type of the map, incremented with \c ++ operator, and
2586    /// if the iterator leaves the last valid key, it will be equal to
2587    /// \c INVALID.
2588    class ItemIt : public Key {
2589    public:
2590      typedef Key Parent;
2591
2592      /// \brief Creates an iterator with a value.
2593      ///
2594      /// Creates an iterator with a value. It iterates on the
2595      /// keys mapped to the given value.
2596      /// \param map The IterableBoolMap.
2597      /// \param value The value.
2598      ItemIt(const IterableBoolMap& map, bool value)
2599        : Parent(value ?
2600                 (map._sep > 0 ?
2601                  map._array[map._sep - 1] : INVALID) :
2602                 (map._sep < int(map._array.size()) ?
2603                  map._array.back() : INVALID)), _map(&map) {}
2604
2605      /// \brief Invalid constructor \& conversion.
2606      ///
2607      /// This constructor initializes the iterator to be invalid.
2608      /// \sa Invalid for more details.
2609      ItemIt(Invalid) : Parent(INVALID), _map(0) {}
2610
2611      /// \brief Increment operator.
2612      ///
2613      /// Increment operator.
2614      ItemIt& operator++() {
2615        int pos = _map->position(*this);
2616        int _sep = pos >= _map->_sep ? _map->_sep : 0;
2617        Parent::operator=(pos > _sep ? _map->_array[pos - 1] : INVALID);
2618        return *this;
2619      }
2620
2621    private:
2622      const IterableBoolMap* _map;
2623    };
2624
2625  protected:
2626
2627    virtual void add(const Key& key) {
2628      Parent::add(key);
2629      Parent::set(key, _array.size());
2630      _array.push_back(key);
2631    }
2632
2633    virtual void add(const std::vector<Key>& keys) {
2634      Parent::add(keys);
2635      for (int i = 0; i < int(keys.size()); ++i) {
2636        Parent::set(keys[i], _array.size());
2637        _array.push_back(keys[i]);
2638      }
2639    }
2640
2641    virtual void erase(const Key& key) {
2642      int pos = position(key);
2643      if (pos < _sep) {
2644        --_sep;
2645        Parent::set(_array[_sep], pos);
2646        _array[pos] = _array[_sep];
2647        Parent::set(_array.back(), _sep);
2648        _array[_sep] = _array.back();
2649        _array.pop_back();
2650      } else {
2651        Parent::set(_array.back(), pos);
2652        _array[pos] = _array.back();
2653        _array.pop_back();
2654      }
2655      Parent::erase(key);
2656    }
2657
2658    virtual void erase(const std::vector<Key>& keys) {
2659      for (int i = 0; i < int(keys.size()); ++i) {
2660        int pos = position(keys[i]);
2661        if (pos < _sep) {
2662          --_sep;
2663          Parent::set(_array[_sep], pos);
2664          _array[pos] = _array[_sep];
2665          Parent::set(_array.back(), _sep);
2666          _array[_sep] = _array.back();
2667          _array.pop_back();
2668        } else {
2669          Parent::set(_array.back(), pos);
2670          _array[pos] = _array.back();
2671          _array.pop_back();
2672        }
2673      }
2674      Parent::erase(keys);
2675    }
2676
2677    virtual void build() {
2678      Parent::build();
2679      typename Parent::Notifier* nf = Parent::notifier();
2680      Key it;
2681      for (nf->first(it); it != INVALID; nf->next(it)) {
2682        Parent::set(it, _array.size());
2683        _array.push_back(it);
2684      }
2685      _sep = 0;
2686    }
2687
2688    virtual void clear() {
2689      _array.clear();
2690      _sep = 0;
2691      Parent::clear();
2692    }
2693
2694  };
2695
2696
2697  namespace _maps_bits {
2698    template <typename Item>
2699    struct IterableIntMapNode {
2700      IterableIntMapNode() : value(-1) {}
2701      IterableIntMapNode(int _value) : value(_value) {}
2702      Item prev, next;
2703      int value;
2704    };
2705  }
2706
2707  /// \brief Dynamic iterable integer map.
2708  ///
2709  /// This class provides a special graph map type which can store an
2710  /// integer value for graph items (\c Node, \c Arc or \c Edge).
2711  /// For each non-negative value it is possible to iterate on the keys
2712  /// mapped to the value.
2713  ///
2714  /// This type is a reference map, so it can be modified with the
2715  /// subscription operator.
2716  ///
2717  /// \note The size of the data structure depends on the largest
2718  /// value in the map.
2719  ///
2720  /// \tparam GR The graph type.
2721  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
2722  /// \c GR::Edge).
2723  ///
2724  /// \see IterableBoolMap, IterableValueMap
2725  /// \see CrossRefMap
2726  template <typename GR, typename K>
2727  class IterableIntMap
2728    : protected ItemSetTraits<GR, K>::
2729        template Map<_maps_bits::IterableIntMapNode<K> >::Type {
2730  public:
2731    typedef typename ItemSetTraits<GR, K>::
2732      template Map<_maps_bits::IterableIntMapNode<K> >::Type Parent;
2733
2734    /// The key type
2735    typedef K Key;
2736    /// The value type
2737    typedef int Value;
2738    /// The graph type
2739    typedef GR Graph;
2740
2741    /// \brief Constructor of the map.
2742    ///
2743    /// Constructor of the map. It sets all values to -1.
2744    explicit IterableIntMap(const Graph& graph)
2745      : Parent(graph) {}
2746
2747    /// \brief Constructor of the map with a given value.
2748    ///
2749    /// Constructor of the map with a given value.
2750    explicit IterableIntMap(const Graph& graph, int value)
2751      : Parent(graph, _maps_bits::IterableIntMapNode<K>(value)) {
2752      if (value >= 0) {
2753        for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
2754          lace(it);
2755        }
2756      }
2757    }
2758
2759  private:
2760
2761    void unlace(const Key& key) {
2762      typename Parent::Value& node = Parent::operator[](key);
2763      if (node.value < 0) return;
2764      if (node.prev != INVALID) {
2765        Parent::operator[](node.prev).next = node.next;
2766      } else {
2767        _first[node.value] = node.next;
2768      }
2769      if (node.next != INVALID) {
2770        Parent::operator[](node.next).prev = node.prev;
2771      }
2772      while (!_first.empty() && _first.back() == INVALID) {
2773        _first.pop_back();
2774      }
2775    }
2776
2777    void lace(const Key& key) {
2778      typename Parent::Value& node = Parent::operator[](key);
2779      if (node.value < 0) return;
2780      if (node.value >= int(_first.size())) {
2781        _first.resize(node.value + 1, INVALID);
2782      }
2783      node.prev = INVALID;
2784      node.next = _first[node.value];
2785      if (node.next != INVALID) {
2786        Parent::operator[](node.next).prev = key;
2787      }
2788      _first[node.value] = key;
2789    }
2790
2791  public:
2792
2793    /// Indicates that the map is reference map.
2794    typedef True ReferenceMapTag;
2795
2796    /// \brief Reference to the value of the map.
2797    ///
2798    /// This class is similar to the \c int type. It can
2799    /// be converted to \c int and it has the same operators.
2800    class Reference {
2801      friend class IterableIntMap;
2802    private:
2803      Reference(IterableIntMap& map, const Key& key)
2804        : _key(key), _map(map) {}
2805    public:
2806
2807      Reference& operator=(const Reference& value) {
2808        _map.set(_key, static_cast<const int&>(value));
2809         return *this;
2810      }
2811
2812      operator const int&() const {
2813        return static_cast<const IterableIntMap&>(_map)[_key];
2814      }
2815
2816      Reference& operator=(int value) {
2817        _map.set(_key, value);
2818        return *this;
2819      }
2820      Reference& operator++() {
2821        _map.set(_key, _map[_key] + 1);
2822        return *this;
2823      }
2824      int operator++(int) {
2825        int value = _map[_key];
2826        _map.set(_key, value + 1);
2827        return value;
2828      }
2829      Reference& operator--() {
2830        _map.set(_key, _map[_key] - 1);
2831        return *this;
2832      }
2833      int operator--(int) {
2834        int value = _map[_key];
2835        _map.set(_key, value - 1);
2836        return value;
2837      }
2838      Reference& operator+=(int value) {
2839        _map.set(_key, _map[_key] + value);
2840        return *this;
2841      }
2842      Reference& operator-=(int value) {
2843        _map.set(_key, _map[_key] - value);
2844        return *this;
2845      }
2846      Reference& operator*=(int value) {
2847        _map.set(_key, _map[_key] * value);
2848        return *this;
2849      }
2850      Reference& operator/=(int value) {
2851        _map.set(_key, _map[_key] / value);
2852        return *this;
2853      }
2854      Reference& operator%=(int value) {
2855        _map.set(_key, _map[_key] % value);
2856        return *this;
2857      }
2858      Reference& operator&=(int value) {
2859        _map.set(_key, _map[_key] & value);
2860        return *this;
2861      }
2862      Reference& operator|=(int value) {
2863        _map.set(_key, _map[_key] | value);
2864        return *this;
2865      }
2866      Reference& operator^=(int value) {
2867        _map.set(_key, _map[_key] ^ value);
2868        return *this;
2869      }
2870      Reference& operator<<=(int value) {
2871        _map.set(_key, _map[_key] << value);
2872        return *this;
2873      }
2874      Reference& operator>>=(int value) {
2875        _map.set(_key, _map[_key] >> value);
2876        return *this;
2877      }
2878
2879    private:
2880      Key _key;
2881      IterableIntMap& _map;
2882    };
2883
2884    /// The const reference type.
2885    typedef const Value& ConstReference;
2886
2887    /// \brief Gives back the maximal value plus one.
2888    ///
2889    /// Gives back the maximal value plus one.
2890    int size() const {
2891      return _first.size();
2892    }
2893
2894    /// \brief Set operation of the map.
2895    ///
2896    /// Set operation of the map.
2897    void set(const Key& key, const Value& value) {
2898      unlace(key);
2899      Parent::operator[](key).value = value;
2900      lace(key);
2901    }
2902
2903    /// \brief Const subscript operator of the map.
2904    ///
2905    /// Const subscript operator of the map.
2906    const Value& operator[](const Key& key) const {
2907      return Parent::operator[](key).value;
2908    }
2909
2910    /// \brief Subscript operator of the map.
2911    ///
2912    /// Subscript operator of the map.
2913    Reference operator[](const Key& key) {
2914      return Reference(*this, key);
2915    }
2916
2917    /// \brief Iterator for the keys with the same value.
2918    ///
2919    /// Iterator for the keys with the same value. It works
2920    /// like a graph item iterator, it can be converted to
2921    /// the item type of the map, incremented with \c ++ operator, and
2922    /// if the iterator leaves the last valid item, it will be equal to
2923    /// \c INVALID.
2924    class ItemIt : public Key {
2925    public:
2926      typedef Key Parent;
2927
2928      /// \brief Invalid constructor \& conversion.
2929      ///
2930      /// This constructor initializes the iterator to be invalid.
2931      /// \sa Invalid for more details.
2932      ItemIt(Invalid) : Parent(INVALID), _map(0) {}
2933
2934      /// \brief Creates an iterator with a value.
2935      ///
2936      /// Creates an iterator with a value. It iterates on the
2937      /// keys mapped to the given value.
2938      /// \param map The IterableIntMap.
2939      /// \param value The value.
2940      ItemIt(const IterableIntMap& map, int value) : _map(&map) {
2941        if (value < 0 || value >= int(_map->_first.size())) {
2942          Parent::operator=(INVALID);
2943        } else {
2944          Parent::operator=(_map->_first[value]);
2945        }
2946      }
2947
2948      /// \brief Increment operator.
2949      ///
2950      /// Increment operator.
2951      ItemIt& operator++() {
2952        Parent::operator=(_map->IterableIntMap::Parent::
2953                          operator[](static_cast<Parent&>(*this)).next);
2954        return *this;
2955      }
2956
2957    private:
2958      const IterableIntMap* _map;
2959    };
2960
2961  protected:
2962
2963    virtual void erase(const Key& key) {
2964      unlace(key);
2965      Parent::erase(key);
2966    }
2967
2968    virtual void erase(const std::vector<Key>& keys) {
2969      for (int i = 0; i < int(keys.size()); ++i) {
2970        unlace(keys[i]);
2971      }
2972      Parent::erase(keys);
2973    }
2974
2975    virtual void clear() {
2976      _first.clear();
2977      Parent::clear();
2978    }
2979
2980  private:
2981    std::vector<Key> _first;
2982  };
2983
2984  namespace _maps_bits {
2985    template <typename Item, typename Value>
2986    struct IterableValueMapNode {
2987      IterableValueMapNode(Value _value = Value()) : value(_value) {}
2988      Item prev, next;
2989      Value value;
2990    };
2991  }
2992
2993  /// \brief Dynamic iterable map for comparable values.
2994  ///
2995  /// This class provides a special graph map type which can store an
2996  /// comparable value for graph items (\c Node, \c Arc or \c Edge).
2997  /// For each value it is possible to iterate on the keys mapped to
2998  /// the value.
2999  ///
3000  /// The map stores for each value a linked list with
3001  /// the items which mapped to the value, and the values are stored
3002  /// in balanced binary tree. The values of the map can be accessed
3003  /// with stl compatible forward iterator.
3004  ///
3005  /// This type is not reference map, so it cannot be modified with
3006  /// the subscription operator.
3007  ///
3008  /// \tparam GR The graph type.
3009  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
3010  /// \c GR::Edge).
3011  /// \tparam V The value type of the map. It can be any comparable
3012  /// value type.
3013  ///
3014  /// \see IterableBoolMap, IterableIntMap
3015  /// \see CrossRefMap
3016  template <typename GR, typename K, typename V>
3017  class IterableValueMap
3018    : protected ItemSetTraits<GR, K>::
3019        template Map<_maps_bits::IterableValueMapNode<K, V> >::Type {
3020  public:
3021    typedef typename ItemSetTraits<GR, K>::
3022      template Map<_maps_bits::IterableValueMapNode<K, V> >::Type Parent;
3023
3024    /// The key type
3025    typedef K Key;
3026    /// The value type
3027    typedef V Value;
3028    /// The graph type
3029    typedef GR Graph;
3030
3031  public:
3032
3033    /// \brief Constructor of the map with a given value.
3034    ///
3035    /// Constructor of the map with a given value.
3036    explicit IterableValueMap(const Graph& graph,
3037                              const Value& value = Value())
3038      : Parent(graph, _maps_bits::IterableValueMapNode<K, V>(value)) {
3039      for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
3040        lace(it);
3041      }
3042    }
3043
3044  protected:
3045
3046    void unlace(const Key& key) {
3047      typename Parent::Value& node = Parent::operator[](key);
3048      if (node.prev != INVALID) {
3049        Parent::operator[](node.prev).next = node.next;
3050      } else {
3051        if (node.next != INVALID) {
3052          _first[node.value] = node.next;
3053        } else {
3054          _first.erase(node.value);
3055        }
3056      }
3057      if (node.next != INVALID) {
3058        Parent::operator[](node.next).prev = node.prev;
3059      }
3060    }
3061
3062    void lace(const Key& key) {
3063      typename Parent::Value& node = Parent::operator[](key);
3064      typename std::map<Value, Key>::iterator it = _first.find(node.value);
3065      if (it == _first.end()) {
3066        node.prev = node.next = INVALID;
3067        _first.insert(std::make_pair(node.value, key));
3068      } else {
3069        node.prev = INVALID;
3070        node.next = it->second;
3071        if (node.next != INVALID) {
3072          Parent::operator[](node.next).prev = key;
3073        }
3074        it->second = key;
3075      }
3076    }
3077
3078  public:
3079
3080    /// \brief Forward iterator for values.
3081    ///
3082    /// This iterator is an stl compatible forward
3083    /// iterator on the values of the map. The values can
3084    /// be accessed in the <tt>[beginValue, endValue)</tt> range.
3085    class ValueIterator
3086      : public std::iterator<std::forward_iterator_tag, Value> {
3087      friend class IterableValueMap;
3088    private:
3089      ValueIterator(typename std::map<Value, Key>::const_iterator _it)
3090        : it(_it) {}
3091    public:
3092
3093      ValueIterator() {}
3094
3095      ValueIterator& operator++() { ++it; return *this; }
3096      ValueIterator operator++(int) {
3097        ValueIterator tmp(*this);
3098        operator++();
3099        return tmp;
3100      }
3101
3102      const Value& operator*() const { return it->first; }
3103      const Value* operator->() const { return &(it->first); }
3104
3105      bool operator==(ValueIterator jt) const { return it == jt.it; }
3106      bool operator!=(ValueIterator jt) const { return it != jt.it; }
3107
3108    private:
3109      typename std::map<Value, Key>::const_iterator it;
3110    };
3111
3112    /// \brief Returns an iterator to the first value.
3113    ///
3114    /// Returns an stl compatible iterator to the
3115    /// first value of the map. The values of the
3116    /// map can be accessed in the <tt>[beginValue, endValue)</tt>
3117    /// range.
3118    ValueIterator beginValue() const {
3119      return ValueIterator(_first.begin());
3120    }
3121
3122    /// \brief Returns an iterator after the last value.
3123    ///
3124    /// Returns an stl compatible iterator after the
3125    /// last value of the map. The values of the
3126    /// map can be accessed in the <tt>[beginValue, endValue)</tt>
3127    /// range.
3128    ValueIterator endValue() const {
3129      return ValueIterator(_first.end());
3130    }
3131
3132    /// \brief Set operation of the map.
3133    ///
3134    /// Set operation of the map.
3135    void set(const Key& key, const Value& value) {
3136      unlace(key);
3137      Parent::operator[](key).value = value;
3138      lace(key);
3139    }
3140
3141    /// \brief Const subscript operator of the map.
3142    ///
3143    /// Const subscript operator of the map.
3144    const Value& operator[](const Key& key) const {
3145      return Parent::operator[](key).value;
3146    }
3147
3148    /// \brief Iterator for the keys with the same value.
3149    ///
3150    /// Iterator for the keys with the same value. It works
3151    /// like a graph item iterator, it can be converted to
3152    /// the item type of the map, incremented with \c ++ operator, and
3153    /// if the iterator leaves the last valid item, it will be equal to
3154    /// \c INVALID.
3155    class ItemIt : public Key {
3156    public:
3157      typedef Key Parent;
3158
3159      /// \brief Invalid constructor \& conversion.
3160      ///
3161      /// This constructor initializes the iterator to be invalid.
3162      /// \sa Invalid for more details.
3163      ItemIt(Invalid) : Parent(INVALID), _map(0) {}
3164
3165      /// \brief Creates an iterator with a value.
3166      ///
3167      /// Creates an iterator with a value. It iterates on the
3168      /// keys which have the given value.
3169      /// \param map The IterableValueMap
3170      /// \param value The value
3171      ItemIt(const IterableValueMap& map, const Value& value) : _map(&map) {
3172        typename std::map<Value, Key>::const_iterator it =
3173          map._first.find(value);
3174        if (it == map._first.end()) {
3175          Parent::operator=(INVALID);
3176        } else {
3177          Parent::operator=(it->second);
3178        }
3179      }
3180
3181      /// \brief Increment operator.
3182      ///
3183      /// Increment Operator.
3184      ItemIt& operator++() {
3185        Parent::operator=(_map->IterableValueMap::Parent::
3186                          operator[](static_cast<Parent&>(*this)).next);
3187        return *this;
3188      }
3189
3190
3191    private:
3192      const IterableValueMap* _map;
3193    };
3194
3195  protected:
3196
3197    virtual void add(const Key& key) {
3198      Parent::add(key);
3199      unlace(key);
3200    }
3201
3202    virtual void add(const std::vector<Key>& keys) {
3203      Parent::add(keys);
3204      for (int i = 0; i < int(keys.size()); ++i) {
3205        lace(keys[i]);
3206      }
3207    }
3208
3209    virtual void erase(const Key& key) {
3210      unlace(key);
3211      Parent::erase(key);
3212    }
3213
3214    virtual void erase(const std::vector<Key>& keys) {
3215      for (int i = 0; i < int(keys.size()); ++i) {
3216        unlace(keys[i]);
3217      }
3218      Parent::erase(keys);
3219    }
3220
3221    virtual void build() {
3222      Parent::build();
3223      for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
3224        lace(it);
3225      }
3226    }
3227
3228    virtual void clear() {
3229      _first.clear();
3230      Parent::clear();
3231    }
3232
3233  private:
3234    std::map<Value, Key> _first;
3235  };
3236
3237  /// \brief Map of the source nodes of arcs in a digraph.
3238  ///
3239  /// SourceMap provides access for the source node of each arc in a digraph,
3240  /// which is returned by the \c source() function of the digraph.
3241  /// \tparam GR The digraph type.
3242  /// \see TargetMap
3243  template <typename GR>
3244  class SourceMap {
3245  public:
3246
3247    ///\e
3248    typedef typename GR::Arc Key;
3249    ///\e
3250    typedef typename GR::Node Value;
3251
3252    /// \brief Constructor
3253    ///
3254    /// Constructor.
3255    /// \param digraph The digraph that the map belongs to.
3256    explicit SourceMap(const GR& digraph) : _graph(digraph) {}
3257
3258    /// \brief Returns the source node of the given arc.
3259    ///
3260    /// Returns the source node of the given arc.
3261    Value operator[](const Key& arc) const {
3262      return _graph.source(arc);
3263    }
3264
3265  private:
3266    const GR& _graph;
3267  };
3268
3269  /// \brief Returns a \c SourceMap class.
3270  ///
3271  /// This function just returns an \c SourceMap class.
3272  /// \relates SourceMap
3273  template <typename GR>
3274  inline SourceMap<GR> sourceMap(const GR& graph) {
3275    return SourceMap<GR>(graph);
3276  }
3277
3278  /// \brief Map of the target nodes of arcs in a digraph.
3279  ///
3280  /// TargetMap provides access for the target node of each arc in a digraph,
3281  /// which is returned by the \c target() function of the digraph.
3282  /// \tparam GR The digraph type.
3283  /// \see SourceMap
3284  template <typename GR>
3285  class TargetMap {
3286  public:
3287
3288    ///\e
3289    typedef typename GR::Arc Key;
3290    ///\e
3291    typedef typename GR::Node Value;
3292
3293    /// \brief Constructor
3294    ///
3295    /// Constructor.
3296    /// \param digraph The digraph that the map belongs to.
3297    explicit TargetMap(const GR& digraph) : _graph(digraph) {}
3298
3299    /// \brief Returns the target node of the given arc.
3300    ///
3301    /// Returns the target node of the given arc.
3302    Value operator[](const Key& e) const {
3303      return _graph.target(e);
3304    }
3305
3306  private:
3307    const GR& _graph;
3308  };
3309
3310  /// \brief Returns a \c TargetMap class.
3311  ///
3312  /// This function just returns a \c TargetMap class.
3313  /// \relates TargetMap
3314  template <typename GR>
3315  inline TargetMap<GR> targetMap(const GR& graph) {
3316    return TargetMap<GR>(graph);
3317  }
3318
3319  /// \brief Map of the "forward" directed arc view of edges in a graph.
3320  ///
3321  /// ForwardMap provides access for the "forward" directed arc view of
3322  /// each edge in a graph, which is returned by the \c direct() function
3323  /// of the graph with \c true parameter.
3324  /// \tparam GR The graph type.
3325  /// \see BackwardMap
3326  template <typename GR>
3327  class ForwardMap {
3328  public:
3329
3330    typedef typename GR::Arc Value;
3331    typedef typename GR::Edge Key;
3332
3333    /// \brief Constructor
3334    ///
3335    /// Constructor.
3336    /// \param graph The graph that the map belongs to.
3337    explicit ForwardMap(const GR& graph) : _graph(graph) {}
3338
3339    /// \brief Returns the "forward" directed arc view of the given edge.
3340    ///
3341    /// Returns the "forward" directed arc view of the given edge.
3342    Value operator[](const Key& key) const {
3343      return _graph.direct(key, true);
3344    }
3345
3346  private:
3347    const GR& _graph;
3348  };
3349
3350  /// \brief Returns a \c ForwardMap class.
3351  ///
3352  /// This function just returns an \c ForwardMap class.
3353  /// \relates ForwardMap
3354  template <typename GR>
3355  inline ForwardMap<GR> forwardMap(const GR& graph) {
3356    return ForwardMap<GR>(graph);
3357  }
3358
3359  /// \brief Map of the "backward" directed arc view of edges in a graph.
3360  ///
3361  /// BackwardMap provides access for the "backward" directed arc view of
3362  /// each edge in a graph, which is returned by the \c direct() function
3363  /// of the graph with \c false parameter.
3364  /// \tparam GR The graph type.
3365  /// \see ForwardMap
3366  template <typename GR>
3367  class BackwardMap {
3368  public:
3369
3370    typedef typename GR::Arc Value;
3371    typedef typename GR::Edge Key;
3372
3373    /// \brief Constructor
3374    ///
3375    /// Constructor.
3376    /// \param graph The graph that the map belongs to.
3377    explicit BackwardMap(const GR& graph) : _graph(graph) {}
3378
3379    /// \brief Returns the "backward" directed arc view of the given edge.
3380    ///
3381    /// Returns the "backward" directed arc view of the given edge.
3382    Value operator[](const Key& key) const {
3383      return _graph.direct(key, false);
3384    }
3385
3386  private:
3387    const GR& _graph;
3388  };
3389
3390  /// \brief Returns a \c BackwardMap class
3391
3392  /// This function just returns a \c BackwardMap class.
3393  /// \relates BackwardMap
3394  template <typename GR>
3395  inline BackwardMap<GR> backwardMap(const GR& graph) {
3396    return BackwardMap<GR>(graph);
3397  }
3398
3399  /// \brief Map of the in-degrees of nodes in a digraph.
3400  ///
3401  /// This map returns the in-degree of a node. Once it is constructed,
3402  /// the degrees are stored in a standard \c NodeMap, so each query is done
3403  /// in constant time. On the other hand, the values are updated automatically
3404  /// whenever the digraph changes.
3405  ///
3406  /// \warning Besides \c addNode() and \c addArc(), a digraph structure
3407  /// may provide alternative ways to modify the digraph.
3408  /// The correct behavior of InDegMap is not guarantied if these additional
3409  /// features are used. For example the functions
3410  /// \ref ListDigraph::changeSource() "changeSource()",
3411  /// \ref ListDigraph::changeTarget() "changeTarget()" and
3412  /// \ref ListDigraph::reverseArc() "reverseArc()"
3413  /// of \ref ListDigraph will \e not update the degree values correctly.
3414  ///
3415  /// \sa OutDegMap
3416  template <typename GR>
3417  class InDegMap
3418    : protected ItemSetTraits<GR, typename GR::Arc>
3419      ::ItemNotifier::ObserverBase {
3420
3421  public:
3422
3423    /// The graph type of InDegMap
3424    typedef GR Graph;
3425    typedef GR Digraph;
3426    /// The key type
3427    typedef typename Digraph::Node Key;
3428    /// The value type
3429    typedef int Value;
3430
3431    typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
3432    ::ItemNotifier::ObserverBase Parent;
3433
3434  private:
3435
3436    class AutoNodeMap
3437      : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {
3438    public:
3439
3440      typedef typename ItemSetTraits<Digraph, Key>::
3441      template Map<int>::Type Parent;
3442
3443      AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
3444
3445      virtual void add(const Key& key) {
3446        Parent::add(key);
3447        Parent::set(key, 0);
3448      }
3449
3450      virtual void add(const std::vector<Key>& keys) {
3451        Parent::add(keys);
3452        for (int i = 0; i < int(keys.size()); ++i) {
3453          Parent::set(keys[i], 0);
3454        }
3455      }
3456
3457      virtual void build() {
3458        Parent::build();
3459        Key it;
3460        typename Parent::Notifier* nf = Parent::notifier();
3461        for (nf->first(it); it != INVALID; nf->next(it)) {
3462          Parent::set(it, 0);
3463        }
3464      }
3465    };
3466
3467  public:
3468
3469    /// \brief Constructor.
3470    ///
3471    /// Constructor for creating an in-degree map.
3472    explicit InDegMap(const Digraph& graph)
3473      : _digraph(graph), _deg(graph) {
3474      Parent::attach(_digraph.notifier(typename Digraph::Arc()));
3475
3476      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
3477        _deg[it] = countInArcs(_digraph, it);
3478      }
3479    }
3480
3481    /// \brief Gives back the in-degree of a Node.
3482    ///
3483    /// Gives back the in-degree of a Node.
3484    int operator[](const Key& key) const {
3485      return _deg[key];
3486    }
3487
3488  protected:
3489
3490    typedef typename Digraph::Arc Arc;
3491
3492    virtual void add(const Arc& arc) {
3493      ++_deg[_digraph.target(arc)];
3494    }
3495
3496    virtual void add(const std::vector<Arc>& arcs) {
3497      for (int i = 0; i < int(arcs.size()); ++i) {
3498        ++_deg[_digraph.target(arcs[i])];
3499      }
3500    }
3501
3502    virtual void erase(const Arc& arc) {
3503      --_deg[_digraph.target(arc)];
3504    }
3505
3506    virtual void erase(const std::vector<Arc>& arcs) {
3507      for (int i = 0; i < int(arcs.size()); ++i) {
3508        --_deg[_digraph.target(arcs[i])];
3509      }
3510    }
3511
3512    virtual void build() {
3513      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
3514        _deg[it] = countInArcs(_digraph, it);
3515      }
3516    }
3517
3518    virtual void clear() {
3519      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
3520        _deg[it] = 0;
3521      }
3522    }
3523  private:
3524
3525    const Digraph& _digraph;
3526    AutoNodeMap _deg;
3527  };
3528
3529  /// \brief Map of the out-degrees of nodes in a digraph.
3530  ///
3531  /// This map returns the out-degree of a node. Once it is constructed,
3532  /// the degrees are stored in a standard \c NodeMap, so each query is done
3533  /// in constant time. On the other hand, the values are updated automatically
3534  /// whenever the digraph changes.
3535  ///
3536  /// \warning Besides \c addNode() and \c addArc(), a digraph structure
3537  /// may provide alternative ways to modify the digraph.
3538  /// The correct behavior of OutDegMap is not guarantied if these additional
3539  /// features are used. For example the functions
3540  /// \ref ListDigraph::changeSource() "changeSource()",
3541  /// \ref ListDigraph::changeTarget() "changeTarget()" and
3542  /// \ref ListDigraph::reverseArc() "reverseArc()"
3543  /// of \ref ListDigraph will \e not update the degree values correctly.
3544  ///
3545  /// \sa InDegMap
3546  template <typename GR>
3547  class OutDegMap
3548    : protected ItemSetTraits<GR, typename GR::Arc>
3549      ::ItemNotifier::ObserverBase {
3550
3551  public:
3552
3553    /// The graph type of OutDegMap
3554    typedef GR Graph;
3555    typedef GR Digraph;
3556    /// The key type
3557    typedef typename Digraph::Node Key;
3558    /// The value type
3559    typedef int Value;
3560
3561    typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
3562    ::ItemNotifier::ObserverBase Parent;
3563
3564  private:
3565
3566    class AutoNodeMap
3567      : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {
3568    public:
3569
3570      typedef typename ItemSetTraits<Digraph, Key>::
3571      template Map<int>::Type Parent;
3572
3573      AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
3574
3575      virtual void add(const Key& key) {
3576        Parent::add(key);
3577        Parent::set(key, 0);
3578      }
3579      virtual void add(const std::vector<Key>& keys) {
3580        Parent::add(keys);
3581        for (int i = 0; i < int(keys.size()); ++i) {
3582          Parent::set(keys[i], 0);
3583        }
3584      }
3585      virtual void build() {
3586        Parent::build();
3587        Key it;
3588        typename Parent::Notifier* nf = Parent::notifier();
3589        for (nf->first(it); it != INVALID; nf->next(it)) {
3590          Parent::set(it, 0);
3591        }
3592      }
3593    };
3594
3595  public:
3596
3597    /// \brief Constructor.
3598    ///
3599    /// Constructor for creating an out-degree map.
3600    explicit OutDegMap(const Digraph& graph)
3601      : _digraph(graph), _deg(graph) {
3602      Parent::attach(_digraph.notifier(typename Digraph::Arc()));
3603
3604      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
3605        _deg[it] = countOutArcs(_digraph, it);
3606      }
3607    }
3608
3609    /// \brief Gives back the out-degree of a Node.
3610    ///
3611    /// Gives back the out-degree of a Node.
3612    int operator[](const Key& key) const {
3613      return _deg[key];
3614    }
3615
3616  protected:
3617
3618    typedef typename Digraph::Arc Arc;
3619
3620    virtual void add(const Arc& arc) {
3621      ++_deg[_digraph.source(arc)];
3622    }
3623
3624    virtual void add(const std::vector<Arc>& arcs) {
3625      for (int i = 0; i < int(arcs.size()); ++i) {
3626        ++_deg[_digraph.source(arcs[i])];
3627      }
3628    }
3629
3630    virtual void erase(const Arc& arc) {
3631      --_deg[_digraph.source(arc)];
3632    }
3633
3634    virtual void erase(const std::vector<Arc>& arcs) {
3635      for (int i = 0; i < int(arcs.size()); ++i) {
3636        --_deg[_digraph.source(arcs[i])];
3637      }
3638    }
3639
3640    virtual void build() {
3641      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
3642        _deg[it] = countOutArcs(_digraph, it);
3643      }
3644    }
3645
3646    virtual void clear() {
3647      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
3648        _deg[it] = 0;
3649      }
3650    }
3651  private:
3652
3653    const Digraph& _digraph;
3654    AutoNodeMap _deg;
3655  };
3656
3657  /// \brief Potential difference map
3658  ///
3659  /// PotentialDifferenceMap returns the difference between the potentials of
3660  /// the source and target nodes of each arc in a digraph, i.e. it returns
3661  /// \code
3662  ///   potential[gr.target(arc)] - potential[gr.source(arc)].
3663  /// \endcode
3664  /// \tparam GR The digraph type.
3665  /// \tparam POT A node map storing the potentials.
3666  template <typename GR, typename POT>
3667  class PotentialDifferenceMap {
3668  public:
3669    /// Key type
3670    typedef typename GR::Arc Key;
3671    /// Value type
3672    typedef typename POT::Value Value;
3673
3674    /// \brief Constructor
3675    ///
3676    /// Contructor of the map.
3677    explicit PotentialDifferenceMap(const GR& gr,
3678                                    const POT& potential)
3679      : _digraph(gr), _potential(potential) {}
3680
3681    /// \brief Returns the potential difference for the given arc.
3682    ///
3683    /// Returns the potential difference for the given arc, i.e.
3684    /// \code
3685    ///   potential[gr.target(arc)] - potential[gr.source(arc)].
3686    /// \endcode
3687    Value operator[](const Key& arc) const {
3688      return _potential[_digraph.target(arc)] -
3689        _potential[_digraph.source(arc)];
3690    }
3691
3692  private:
3693    const GR& _digraph;
3694    const POT& _potential;
3695  };
3696
3697  /// \brief Returns a PotentialDifferenceMap.
3698  ///
3699  /// This function just returns a PotentialDifferenceMap.
3700  /// \relates PotentialDifferenceMap
3701  template <typename GR, typename POT>
3702  PotentialDifferenceMap<GR, POT>
3703  potentialDifferenceMap(const GR& gr, const POT& potential) {
3704    return PotentialDifferenceMap<GR, POT>(gr, potential);
3705  }
3706
3707  /// @}
3708}
3709
3710#endif // LEMON_MAPS_H
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