COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/maps.h @ 722:b52189c479fb

Last change on this file since 722:b52189c479fb was 722:b52189c479fb, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Doc improvements for several graph maps (#302)

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