COIN-OR::LEMON - Graph Library

source: lemon/lemon/maps.h @ 899:cc9e0c15d747

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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 together with some data structures, e.g.
234  /// heap types and \c UnionFind, 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).processedMap(loggerBoolMap(std::back_inserter(v))).run(s);
1793  /// \endcode
1794  /// \code
1795  ///   std::vector<Node> v(countNodes(g));
1796  ///   dfs(g).processedMap(loggerBoolMap(v.begin())).run(s);
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  /// \brief Returns an \c IdMap class.
1903  ///
1904  /// This function just returns an \c IdMap class.
1905  /// \relates IdMap
1906  template <typename K, typename GR>
1907  inline IdMap<GR, K> idMap(const GR& graph) {
1908    return IdMap<GR, K>(graph);
1909  }
1910
1911  /// \brief General cross reference graph map type.
1912
1913  /// This class provides simple invertable graph maps.
1914  /// It wraps a standard graph map (\c NodeMap, \c ArcMap or \c EdgeMap)
1915  /// and if a key is set to a new value, then stores it in the inverse map.
1916  /// The graph items can be accessed by their values either using
1917  /// \c InverseMap or \c operator()(), and the values of the map can be
1918  /// accessed with an STL compatible forward iterator (\c ValueIt).
1919  ///
1920  /// This map is intended to be used when all associated values are
1921  /// different (the map is actually invertable) or there are only a few
1922  /// items with the same value.
1923  /// Otherwise consider to use \c IterableValueMap, which is more
1924  /// suitable and more efficient for such cases. It provides iterators
1925  /// to traverse the items with the same associated value, but
1926  /// it does not have \c InverseMap.
1927  ///
1928  /// This type is not reference map, so it cannot be modified with
1929  /// the subscript operator.
1930  ///
1931  /// \tparam GR The graph type.
1932  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
1933  /// \c GR::Edge).
1934  /// \tparam V The value type of the map.
1935  ///
1936  /// \see IterableValueMap
1937  template <typename GR, typename K, typename V>
1938  class CrossRefMap
1939    : protected ItemSetTraits<GR, K>::template Map<V>::Type {
1940  private:
1941
1942    typedef typename ItemSetTraits<GR, K>::
1943      template Map<V>::Type Map;
1944
1945    typedef std::multimap<V, K> Container;
1946    Container _inv_map;
1947
1948  public:
1949
1950    /// The graph type of CrossRefMap.
1951    typedef GR Graph;
1952    typedef GR Digraph;
1953    /// The key type of CrossRefMap (\c Node, \c Arc or \c Edge).
1954    typedef K Item;
1955    /// The key type of CrossRefMap (\c Node, \c Arc or \c Edge).
1956    typedef K Key;
1957    /// The value type of CrossRefMap.
1958    typedef V Value;
1959
1960    /// \brief Constructor.
1961    ///
1962    /// Construct a new CrossRefMap for the given graph.
1963    explicit CrossRefMap(const Graph& graph) : Map(graph) {}
1964
1965    /// \brief Forward iterator for values.
1966    ///
1967    /// This iterator is an STL compatible forward
1968    /// iterator on the values of the map. The values can
1969    /// be accessed in the <tt>[beginValue, endValue)</tt> range.
1970    /// They are considered with multiplicity, so each value is
1971    /// traversed for each item it is assigned to.
1972    class ValueIt
1973      : public std::iterator<std::forward_iterator_tag, Value> {
1974      friend class CrossRefMap;
1975    private:
1976      ValueIt(typename Container::const_iterator _it)
1977        : it(_it) {}
1978    public:
1979
1980      /// Constructor
1981      ValueIt() {}
1982
1983      /// \e
1984      ValueIt& operator++() { ++it; return *this; }
1985      /// \e
1986      ValueIt operator++(int) {
1987        ValueIt tmp(*this);
1988        operator++();
1989        return tmp;
1990      }
1991
1992      /// \e
1993      const Value& operator*() const { return it->first; }
1994      /// \e
1995      const Value* operator->() const { return &(it->first); }
1996
1997      /// \e
1998      bool operator==(ValueIt jt) const { return it == jt.it; }
1999      /// \e
2000      bool operator!=(ValueIt jt) const { return it != jt.it; }
2001
2002    private:
2003      typename Container::const_iterator it;
2004    };
2005   
2006    /// Alias for \c ValueIt
2007    typedef ValueIt ValueIterator;
2008
2009    /// \brief Returns an iterator to the first value.
2010    ///
2011    /// Returns an STL compatible iterator to the
2012    /// first value of the map. The values of the
2013    /// map can be accessed in the <tt>[beginValue, endValue)</tt>
2014    /// range.
2015    ValueIt beginValue() const {
2016      return ValueIt(_inv_map.begin());
2017    }
2018
2019    /// \brief Returns an iterator after the last value.
2020    ///
2021    /// Returns an STL compatible iterator after the
2022    /// last value of the map. The values of the
2023    /// map can be accessed in the <tt>[beginValue, endValue)</tt>
2024    /// range.
2025    ValueIt endValue() const {
2026      return ValueIt(_inv_map.end());
2027    }
2028
2029    /// \brief Sets the value associated with the given key.
2030    ///
2031    /// Sets the value associated with the given key.
2032    void set(const Key& key, const Value& val) {
2033      Value oldval = Map::operator[](key);
2034      typename Container::iterator it;
2035      for (it = _inv_map.equal_range(oldval).first;
2036           it != _inv_map.equal_range(oldval).second; ++it) {
2037        if (it->second == key) {
2038          _inv_map.erase(it);
2039          break;
2040        }
2041      }
2042      _inv_map.insert(std::make_pair(val, key));
2043      Map::set(key, val);
2044    }
2045
2046    /// \brief Returns the value associated with the given key.
2047    ///
2048    /// Returns the value associated with the given key.
2049    typename MapTraits<Map>::ConstReturnValue
2050    operator[](const Key& key) const {
2051      return Map::operator[](key);
2052    }
2053
2054    /// \brief Gives back an item by its value.
2055    ///
2056    /// This function gives back an item that is assigned to
2057    /// the given value or \c INVALID if no such item exists.
2058    /// If there are more items with the same associated value,
2059    /// only one of them is returned.
2060    Key operator()(const Value& val) const {
2061      typename Container::const_iterator it = _inv_map.find(val);
2062      return it != _inv_map.end() ? it->second : INVALID;
2063    }
2064   
2065    /// \brief Returns the number of items with the given value.
2066    ///
2067    /// This function returns the number of items with the given value
2068    /// associated with it.
2069    int count(const Value &val) const {
2070      return _inv_map.count(val);
2071    }
2072
2073  protected:
2074
2075    /// \brief Erase the key from the map and the inverse map.
2076    ///
2077    /// Erase the key from the map and the inverse map. It is called by the
2078    /// \c AlterationNotifier.
2079    virtual void erase(const Key& key) {
2080      Value val = Map::operator[](key);
2081      typename Container::iterator it;
2082      for (it = _inv_map.equal_range(val).first;
2083           it != _inv_map.equal_range(val).second; ++it) {
2084        if (it->second == key) {
2085          _inv_map.erase(it);
2086          break;
2087        }
2088      }
2089      Map::erase(key);
2090    }
2091
2092    /// \brief Erase more keys from the map and the inverse map.
2093    ///
2094    /// Erase more keys from the map and the inverse map. It is called by the
2095    /// \c AlterationNotifier.
2096    virtual void erase(const std::vector<Key>& keys) {
2097      for (int i = 0; i < int(keys.size()); ++i) {
2098        Value val = Map::operator[](keys[i]);
2099        typename Container::iterator it;
2100        for (it = _inv_map.equal_range(val).first;
2101             it != _inv_map.equal_range(val).second; ++it) {
2102          if (it->second == keys[i]) {
2103            _inv_map.erase(it);
2104            break;
2105          }
2106        }
2107      }
2108      Map::erase(keys);
2109    }
2110
2111    /// \brief Clear the keys from the map and the inverse map.
2112    ///
2113    /// Clear the keys from the map and the inverse map. It is called by the
2114    /// \c AlterationNotifier.
2115    virtual void clear() {
2116      _inv_map.clear();
2117      Map::clear();
2118    }
2119
2120  public:
2121
2122    /// \brief The inverse map type of CrossRefMap.
2123    ///
2124    /// The inverse map type of CrossRefMap. The subscript operator gives
2125    /// back an item by its value.
2126    /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
2127    /// \see inverse()
2128    class InverseMap {
2129    public:
2130      /// \brief Constructor
2131      ///
2132      /// Constructor of the InverseMap.
2133      explicit InverseMap(const CrossRefMap& inverted)
2134        : _inverted(inverted) {}
2135
2136      /// The value type of the InverseMap.
2137      typedef typename CrossRefMap::Key Value;
2138      /// The key type of the InverseMap.
2139      typedef typename CrossRefMap::Value Key;
2140
2141      /// \brief Subscript operator.
2142      ///
2143      /// Subscript operator. It gives back an item
2144      /// that is assigned to the given value or \c INVALID
2145      /// if no such item exists.
2146      Value operator[](const Key& key) const {
2147        return _inverted(key);
2148      }
2149
2150    private:
2151      const CrossRefMap& _inverted;
2152    };
2153
2154    /// \brief Gives back the inverse of the map.
2155    ///
2156    /// Gives back the inverse of the CrossRefMap.
2157    InverseMap inverse() const {
2158      return InverseMap(*this);
2159    }
2160
2161  };
2162
2163  /// \brief Provides continuous and unique id for the
2164  /// items of a graph.
2165  ///
2166  /// RangeIdMap provides a unique and continuous
2167  /// id for each item of a given type (\c Node, \c Arc or
2168  /// \c Edge) in a graph. This id is
2169  ///  - \b unique: different items get different ids,
2170  ///  - \b continuous: the range of the ids is the set of integers
2171  ///    between 0 and \c n-1, where \c n is the number of the items of
2172  ///    this type (\c Node, \c Arc or \c Edge).
2173  ///  - So, the ids can change when deleting an item of the same type.
2174  ///
2175  /// Thus this id is not (necessarily) the same as what can get using
2176  /// the \c id() function of the graph or \ref IdMap.
2177  /// This map can be inverted with its member class \c InverseMap,
2178  /// or with the \c operator()() member.
2179  ///
2180  /// \tparam GR The graph type.
2181  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
2182  /// \c GR::Edge).
2183  ///
2184  /// \see IdMap
2185  template <typename GR, typename K>
2186  class RangeIdMap
2187    : protected ItemSetTraits<GR, K>::template Map<int>::Type {
2188
2189    typedef typename ItemSetTraits<GR, K>::template Map<int>::Type Map;
2190
2191  public:
2192    /// The graph type of RangeIdMap.
2193    typedef GR Graph;
2194    typedef GR Digraph;
2195    /// The key type of RangeIdMap (\c Node, \c Arc or \c Edge).
2196    typedef K Item;
2197    /// The key type of RangeIdMap (\c Node, \c Arc or \c Edge).
2198    typedef K Key;
2199    /// The value type of RangeIdMap.
2200    typedef int Value;
2201
2202    /// \brief Constructor.
2203    ///
2204    /// Constructor.
2205    explicit RangeIdMap(const Graph& gr) : Map(gr) {
2206      Item it;
2207      const typename Map::Notifier* nf = Map::notifier();
2208      for (nf->first(it); it != INVALID; nf->next(it)) {
2209        Map::set(it, _inv_map.size());
2210        _inv_map.push_back(it);
2211      }
2212    }
2213
2214  protected:
2215
2216    /// \brief Adds a new key to the map.
2217    ///
2218    /// Add a new key to the map. It is called by the
2219    /// \c AlterationNotifier.
2220    virtual void add(const Item& item) {
2221      Map::add(item);
2222      Map::set(item, _inv_map.size());
2223      _inv_map.push_back(item);
2224    }
2225
2226    /// \brief Add more new keys to the map.
2227    ///
2228    /// Add more new keys to the map. It is called by the
2229    /// \c AlterationNotifier.
2230    virtual void add(const std::vector<Item>& items) {
2231      Map::add(items);
2232      for (int i = 0; i < int(items.size()); ++i) {
2233        Map::set(items[i], _inv_map.size());
2234        _inv_map.push_back(items[i]);
2235      }
2236    }
2237
2238    /// \brief Erase the key from the map.
2239    ///
2240    /// Erase the key from the map. It is called by the
2241    /// \c AlterationNotifier.
2242    virtual void erase(const Item& item) {
2243      Map::set(_inv_map.back(), Map::operator[](item));
2244      _inv_map[Map::operator[](item)] = _inv_map.back();
2245      _inv_map.pop_back();
2246      Map::erase(item);
2247    }
2248
2249    /// \brief Erase more keys from the map.
2250    ///
2251    /// Erase more keys from the map. It is called by the
2252    /// \c AlterationNotifier.
2253    virtual void erase(const std::vector<Item>& items) {
2254      for (int i = 0; i < int(items.size()); ++i) {
2255        Map::set(_inv_map.back(), Map::operator[](items[i]));
2256        _inv_map[Map::operator[](items[i])] = _inv_map.back();
2257        _inv_map.pop_back();
2258      }
2259      Map::erase(items);
2260    }
2261
2262    /// \brief Build the unique map.
2263    ///
2264    /// Build the unique map. It is called by the
2265    /// \c AlterationNotifier.
2266    virtual void build() {
2267      Map::build();
2268      Item it;
2269      const typename Map::Notifier* nf = Map::notifier();
2270      for (nf->first(it); it != INVALID; nf->next(it)) {
2271        Map::set(it, _inv_map.size());
2272        _inv_map.push_back(it);
2273      }
2274    }
2275
2276    /// \brief Clear the keys from the map.
2277    ///
2278    /// Clear the keys from the map. It is called by the
2279    /// \c AlterationNotifier.
2280    virtual void clear() {
2281      _inv_map.clear();
2282      Map::clear();
2283    }
2284
2285  public:
2286
2287    /// \brief Returns the maximal value plus one.
2288    ///
2289    /// Returns the maximal value plus one in the map.
2290    unsigned int size() const {
2291      return _inv_map.size();
2292    }
2293
2294    /// \brief Swaps the position of the two items in the map.
2295    ///
2296    /// Swaps the position of the two items in the map.
2297    void swap(const Item& p, const Item& q) {
2298      int pi = Map::operator[](p);
2299      int qi = Map::operator[](q);
2300      Map::set(p, qi);
2301      _inv_map[qi] = p;
2302      Map::set(q, pi);
2303      _inv_map[pi] = q;
2304    }
2305
2306    /// \brief Gives back the \e range \e id of the item
2307    ///
2308    /// Gives back the \e range \e id of the item.
2309    int operator[](const Item& item) const {
2310      return Map::operator[](item);
2311    }
2312
2313    /// \brief Gives back the item belonging to a \e range \e id
2314    ///
2315    /// Gives back the item belonging to the given \e range \e id.
2316    Item operator()(int id) const {
2317      return _inv_map[id];
2318    }
2319
2320  private:
2321
2322    typedef std::vector<Item> Container;
2323    Container _inv_map;
2324
2325  public:
2326
2327    /// \brief The inverse map type of RangeIdMap.
2328    ///
2329    /// The inverse map type of RangeIdMap. The subscript operator gives
2330    /// back an item by its \e range \e id.
2331    /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
2332    class InverseMap {
2333    public:
2334      /// \brief Constructor
2335      ///
2336      /// Constructor of the InverseMap.
2337      explicit InverseMap(const RangeIdMap& inverted)
2338        : _inverted(inverted) {}
2339
2340
2341      /// The value type of the InverseMap.
2342      typedef typename RangeIdMap::Key Value;
2343      /// The key type of the InverseMap.
2344      typedef typename RangeIdMap::Value Key;
2345
2346      /// \brief Subscript operator.
2347      ///
2348      /// Subscript operator. It gives back the item
2349      /// that the given \e range \e id currently belongs to.
2350      Value operator[](const Key& key) const {
2351        return _inverted(key);
2352      }
2353
2354      /// \brief Size of the map.
2355      ///
2356      /// Returns the size of the map.
2357      unsigned int size() const {
2358        return _inverted.size();
2359      }
2360
2361    private:
2362      const RangeIdMap& _inverted;
2363    };
2364
2365    /// \brief Gives back the inverse of the map.
2366    ///
2367    /// Gives back the inverse of the RangeIdMap.
2368    const InverseMap inverse() const {
2369      return InverseMap(*this);
2370    }
2371  };
2372
2373  /// \brief Returns a \c RangeIdMap class.
2374  ///
2375  /// This function just returns an \c RangeIdMap class.
2376  /// \relates RangeIdMap
2377  template <typename K, typename GR>
2378  inline RangeIdMap<GR, K> rangeIdMap(const GR& graph) {
2379    return RangeIdMap<GR, K>(graph);
2380  }
2381 
2382  /// \brief Dynamic iterable \c bool map.
2383  ///
2384  /// This class provides a special graph map type which can store a
2385  /// \c bool value for graph items (\c Node, \c Arc or \c Edge).
2386  /// For both \c true and \c false values it is possible to iterate on
2387  /// the keys mapped to the value.
2388  ///
2389  /// This type is a reference map, so it can be modified with the
2390  /// subscript operator.
2391  ///
2392  /// \tparam GR The graph type.
2393  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
2394  /// \c GR::Edge).
2395  ///
2396  /// \see IterableIntMap, IterableValueMap
2397  /// \see CrossRefMap
2398  template <typename GR, typename K>
2399  class IterableBoolMap
2400    : protected ItemSetTraits<GR, K>::template Map<int>::Type {
2401  private:
2402    typedef GR Graph;
2403
2404    typedef typename ItemSetTraits<GR, K>::ItemIt KeyIt;
2405    typedef typename ItemSetTraits<GR, K>::template Map<int>::Type Parent;
2406
2407    std::vector<K> _array;
2408    int _sep;
2409
2410  public:
2411
2412    /// Indicates that the map is reference map.
2413    typedef True ReferenceMapTag;
2414
2415    /// The key type
2416    typedef K Key;
2417    /// The value type
2418    typedef bool Value;
2419    /// The const reference type.
2420    typedef const Value& ConstReference;
2421
2422  private:
2423
2424    int position(const Key& key) const {
2425      return Parent::operator[](key);
2426    }
2427
2428  public:
2429
2430    /// \brief Reference to the value of the map.
2431    ///
2432    /// This class is similar to the \c bool type. It can be converted to
2433    /// \c bool and it provides the same operators.
2434    class Reference {
2435      friend class IterableBoolMap;
2436    private:
2437      Reference(IterableBoolMap& map, const Key& key)
2438        : _key(key), _map(map) {}
2439    public:
2440
2441      Reference& operator=(const Reference& value) {
2442        _map.set(_key, static_cast<bool>(value));
2443         return *this;
2444      }
2445
2446      operator bool() const {
2447        return static_cast<const IterableBoolMap&>(_map)[_key];
2448      }
2449
2450      Reference& operator=(bool value) {
2451        _map.set(_key, value);
2452        return *this;
2453      }
2454      Reference& operator&=(bool value) {
2455        _map.set(_key, _map[_key] & value);
2456        return *this;
2457      }
2458      Reference& operator|=(bool value) {
2459        _map.set(_key, _map[_key] | value);
2460        return *this;
2461      }
2462      Reference& operator^=(bool value) {
2463        _map.set(_key, _map[_key] ^ value);
2464        return *this;
2465      }
2466    private:
2467      Key _key;
2468      IterableBoolMap& _map;
2469    };
2470
2471    /// \brief Constructor of the map with a default value.
2472    ///
2473    /// Constructor of the map with a default value.
2474    explicit IterableBoolMap(const Graph& graph, bool def = false)
2475      : Parent(graph) {
2476      typename Parent::Notifier* nf = Parent::notifier();
2477      Key it;
2478      for (nf->first(it); it != INVALID; nf->next(it)) {
2479        Parent::set(it, _array.size());
2480        _array.push_back(it);
2481      }
2482      _sep = (def ? _array.size() : 0);
2483    }
2484
2485    /// \brief Const subscript operator of the map.
2486    ///
2487    /// Const subscript operator of the map.
2488    bool operator[](const Key& key) const {
2489      return position(key) < _sep;
2490    }
2491
2492    /// \brief Subscript operator of the map.
2493    ///
2494    /// Subscript operator of the map.
2495    Reference operator[](const Key& key) {
2496      return Reference(*this, key);
2497    }
2498
2499    /// \brief Set operation of the map.
2500    ///
2501    /// Set operation of the map.
2502    void set(const Key& key, bool value) {
2503      int pos = position(key);
2504      if (value) {
2505        if (pos < _sep) return;
2506        Key tmp = _array[_sep];
2507        _array[_sep] = key;
2508        Parent::set(key, _sep);
2509        _array[pos] = tmp;
2510        Parent::set(tmp, pos);
2511        ++_sep;
2512      } else {
2513        if (pos >= _sep) return;
2514        --_sep;
2515        Key tmp = _array[_sep];
2516        _array[_sep] = key;
2517        Parent::set(key, _sep);
2518        _array[pos] = tmp;
2519        Parent::set(tmp, pos);
2520      }
2521    }
2522
2523    /// \brief Set all items.
2524    ///
2525    /// Set all items in the map.
2526    /// \note Constant time operation.
2527    void setAll(bool value) {
2528      _sep = (value ? _array.size() : 0);
2529    }
2530
2531    /// \brief Returns the number of the keys mapped to \c true.
2532    ///
2533    /// Returns the number of the keys mapped to \c true.
2534    int trueNum() const {
2535      return _sep;
2536    }
2537
2538    /// \brief Returns the number of the keys mapped to \c false.
2539    ///
2540    /// Returns the number of the keys mapped to \c false.
2541    int falseNum() const {
2542      return _array.size() - _sep;
2543    }
2544
2545    /// \brief Iterator for the keys mapped to \c true.
2546    ///
2547    /// Iterator for the keys mapped to \c true. It works
2548    /// like a graph item iterator, it can be converted to
2549    /// the key type of the map, incremented with \c ++ operator, and
2550    /// if the iterator leaves the last valid key, it will be equal to
2551    /// \c INVALID.
2552    class TrueIt : public Key {
2553    public:
2554      typedef Key Parent;
2555
2556      /// \brief Creates an iterator.
2557      ///
2558      /// Creates an iterator. It iterates on the
2559      /// keys mapped to \c true.
2560      /// \param map The IterableBoolMap.
2561      explicit TrueIt(const IterableBoolMap& map)
2562        : Parent(map._sep > 0 ? map._array[map._sep - 1] : INVALID),
2563          _map(&map) {}
2564
2565      /// \brief Invalid constructor \& conversion.
2566      ///
2567      /// This constructor initializes the iterator to be invalid.
2568      /// \sa Invalid for more details.
2569      TrueIt(Invalid) : Parent(INVALID), _map(0) {}
2570
2571      /// \brief Increment operator.
2572      ///
2573      /// Increment operator.
2574      TrueIt& operator++() {
2575        int pos = _map->position(*this);
2576        Parent::operator=(pos > 0 ? _map->_array[pos - 1] : INVALID);
2577        return *this;
2578      }
2579
2580    private:
2581      const IterableBoolMap* _map;
2582    };
2583
2584    /// \brief Iterator for the keys mapped to \c false.
2585    ///
2586    /// Iterator for the keys mapped to \c false. It works
2587    /// like a graph item iterator, it can be converted to
2588    /// the key type of the map, incremented with \c ++ operator, and
2589    /// if the iterator leaves the last valid key, it will be equal to
2590    /// \c INVALID.
2591    class FalseIt : public Key {
2592    public:
2593      typedef Key Parent;
2594
2595      /// \brief Creates an iterator.
2596      ///
2597      /// Creates an iterator. It iterates on the
2598      /// keys mapped to \c false.
2599      /// \param map The IterableBoolMap.
2600      explicit FalseIt(const IterableBoolMap& map)
2601        : Parent(map._sep < int(map._array.size()) ?
2602                 map._array.back() : INVALID), _map(&map) {}
2603
2604      /// \brief Invalid constructor \& conversion.
2605      ///
2606      /// This constructor initializes the iterator to be invalid.
2607      /// \sa Invalid for more details.
2608      FalseIt(Invalid) : Parent(INVALID), _map(0) {}
2609
2610      /// \brief Increment operator.
2611      ///
2612      /// Increment operator.
2613      FalseIt& operator++() {
2614        int pos = _map->position(*this);
2615        Parent::operator=(pos > _map->_sep ? _map->_array[pos - 1] : INVALID);
2616        return *this;
2617      }
2618
2619    private:
2620      const IterableBoolMap* _map;
2621    };
2622
2623    /// \brief Iterator for the keys mapped to a given value.
2624    ///
2625    /// Iterator for the keys mapped to a given value. It works
2626    /// like a graph item iterator, it can be converted to
2627    /// the key type of the map, incremented with \c ++ operator, and
2628    /// if the iterator leaves the last valid key, it will be equal to
2629    /// \c INVALID.
2630    class ItemIt : public Key {
2631    public:
2632      typedef Key Parent;
2633
2634      /// \brief Creates an iterator with a value.
2635      ///
2636      /// Creates an iterator with a value. It iterates on the
2637      /// keys mapped to the given value.
2638      /// \param map The IterableBoolMap.
2639      /// \param value The value.
2640      ItemIt(const IterableBoolMap& map, bool value)
2641        : Parent(value ?
2642                 (map._sep > 0 ?
2643                  map._array[map._sep - 1] : INVALID) :
2644                 (map._sep < int(map._array.size()) ?
2645                  map._array.back() : INVALID)), _map(&map) {}
2646
2647      /// \brief Invalid constructor \& conversion.
2648      ///
2649      /// This constructor initializes the iterator to be invalid.
2650      /// \sa Invalid for more details.
2651      ItemIt(Invalid) : Parent(INVALID), _map(0) {}
2652
2653      /// \brief Increment operator.
2654      ///
2655      /// Increment operator.
2656      ItemIt& operator++() {
2657        int pos = _map->position(*this);
2658        int _sep = pos >= _map->_sep ? _map->_sep : 0;
2659        Parent::operator=(pos > _sep ? _map->_array[pos - 1] : INVALID);
2660        return *this;
2661      }
2662
2663    private:
2664      const IterableBoolMap* _map;
2665    };
2666
2667  protected:
2668
2669    virtual void add(const Key& key) {
2670      Parent::add(key);
2671      Parent::set(key, _array.size());
2672      _array.push_back(key);
2673    }
2674
2675    virtual void add(const std::vector<Key>& keys) {
2676      Parent::add(keys);
2677      for (int i = 0; i < int(keys.size()); ++i) {
2678        Parent::set(keys[i], _array.size());
2679        _array.push_back(keys[i]);
2680      }
2681    }
2682
2683    virtual void erase(const Key& key) {
2684      int pos = position(key);
2685      if (pos < _sep) {
2686        --_sep;
2687        Parent::set(_array[_sep], pos);
2688        _array[pos] = _array[_sep];
2689        Parent::set(_array.back(), _sep);
2690        _array[_sep] = _array.back();
2691        _array.pop_back();
2692      } else {
2693        Parent::set(_array.back(), pos);
2694        _array[pos] = _array.back();
2695        _array.pop_back();
2696      }
2697      Parent::erase(key);
2698    }
2699
2700    virtual void erase(const std::vector<Key>& keys) {
2701      for (int i = 0; i < int(keys.size()); ++i) {
2702        int pos = position(keys[i]);
2703        if (pos < _sep) {
2704          --_sep;
2705          Parent::set(_array[_sep], pos);
2706          _array[pos] = _array[_sep];
2707          Parent::set(_array.back(), _sep);
2708          _array[_sep] = _array.back();
2709          _array.pop_back();
2710        } else {
2711          Parent::set(_array.back(), pos);
2712          _array[pos] = _array.back();
2713          _array.pop_back();
2714        }
2715      }
2716      Parent::erase(keys);
2717    }
2718
2719    virtual void build() {
2720      Parent::build();
2721      typename Parent::Notifier* nf = Parent::notifier();
2722      Key it;
2723      for (nf->first(it); it != INVALID; nf->next(it)) {
2724        Parent::set(it, _array.size());
2725        _array.push_back(it);
2726      }
2727      _sep = 0;
2728    }
2729
2730    virtual void clear() {
2731      _array.clear();
2732      _sep = 0;
2733      Parent::clear();
2734    }
2735
2736  };
2737
2738
2739  namespace _maps_bits {
2740    template <typename Item>
2741    struct IterableIntMapNode {
2742      IterableIntMapNode() : value(-1) {}
2743      IterableIntMapNode(int _value) : value(_value) {}
2744      Item prev, next;
2745      int value;
2746    };
2747  }
2748
2749  /// \brief Dynamic iterable integer map.
2750  ///
2751  /// This class provides a special graph map type which can store an
2752  /// integer value for graph items (\c Node, \c Arc or \c Edge).
2753  /// For each non-negative value it is possible to iterate on the keys
2754  /// mapped to the value.
2755  ///
2756  /// This map is intended to be used with small integer values, for which
2757  /// it is efficient, and supports iteration only for non-negative values.
2758  /// If you need large values and/or iteration for negative integers,
2759  /// consider to use \ref IterableValueMap instead.
2760  ///
2761  /// This type is a reference map, so it can be modified with the
2762  /// subscript operator.
2763  ///
2764  /// \note The size of the data structure depends on the largest
2765  /// value in the map.
2766  ///
2767  /// \tparam GR The graph type.
2768  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
2769  /// \c GR::Edge).
2770  ///
2771  /// \see IterableBoolMap, IterableValueMap
2772  /// \see CrossRefMap
2773  template <typename GR, typename K>
2774  class IterableIntMap
2775    : protected ItemSetTraits<GR, K>::
2776        template Map<_maps_bits::IterableIntMapNode<K> >::Type {
2777  public:
2778    typedef typename ItemSetTraits<GR, K>::
2779      template Map<_maps_bits::IterableIntMapNode<K> >::Type Parent;
2780
2781    /// The key type
2782    typedef K Key;
2783    /// The value type
2784    typedef int Value;
2785    /// The graph type
2786    typedef GR Graph;
2787
2788    /// \brief Constructor of the map.
2789    ///
2790    /// Constructor of the map. It sets all values to -1.
2791    explicit IterableIntMap(const Graph& graph)
2792      : Parent(graph) {}
2793
2794    /// \brief Constructor of the map with a given value.
2795    ///
2796    /// Constructor of the map with a given value.
2797    explicit IterableIntMap(const Graph& graph, int value)
2798      : Parent(graph, _maps_bits::IterableIntMapNode<K>(value)) {
2799      if (value >= 0) {
2800        for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
2801          lace(it);
2802        }
2803      }
2804    }
2805
2806  private:
2807
2808    void unlace(const Key& key) {
2809      typename Parent::Value& node = Parent::operator[](key);
2810      if (node.value < 0) return;
2811      if (node.prev != INVALID) {
2812        Parent::operator[](node.prev).next = node.next;
2813      } else {
2814        _first[node.value] = node.next;
2815      }
2816      if (node.next != INVALID) {
2817        Parent::operator[](node.next).prev = node.prev;
2818      }
2819      while (!_first.empty() && _first.back() == INVALID) {
2820        _first.pop_back();
2821      }
2822    }
2823
2824    void lace(const Key& key) {
2825      typename Parent::Value& node = Parent::operator[](key);
2826      if (node.value < 0) return;
2827      if (node.value >= int(_first.size())) {
2828        _first.resize(node.value + 1, INVALID);
2829      }
2830      node.prev = INVALID;
2831      node.next = _first[node.value];
2832      if (node.next != INVALID) {
2833        Parent::operator[](node.next).prev = key;
2834      }
2835      _first[node.value] = key;
2836    }
2837
2838  public:
2839
2840    /// Indicates that the map is reference map.
2841    typedef True ReferenceMapTag;
2842
2843    /// \brief Reference to the value of the map.
2844    ///
2845    /// This class is similar to the \c int type. It can
2846    /// be converted to \c int and it has the same operators.
2847    class Reference {
2848      friend class IterableIntMap;
2849    private:
2850      Reference(IterableIntMap& map, const Key& key)
2851        : _key(key), _map(map) {}
2852    public:
2853
2854      Reference& operator=(const Reference& value) {
2855        _map.set(_key, static_cast<const int&>(value));
2856         return *this;
2857      }
2858
2859      operator const int&() const {
2860        return static_cast<const IterableIntMap&>(_map)[_key];
2861      }
2862
2863      Reference& operator=(int value) {
2864        _map.set(_key, value);
2865        return *this;
2866      }
2867      Reference& operator++() {
2868        _map.set(_key, _map[_key] + 1);
2869        return *this;
2870      }
2871      int operator++(int) {
2872        int value = _map[_key];
2873        _map.set(_key, value + 1);
2874        return value;
2875      }
2876      Reference& operator--() {
2877        _map.set(_key, _map[_key] - 1);
2878        return *this;
2879      }
2880      int operator--(int) {
2881        int value = _map[_key];
2882        _map.set(_key, value - 1);
2883        return value;
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      Reference& operator&=(int value) {
2906        _map.set(_key, _map[_key] & value);
2907        return *this;
2908      }
2909      Reference& operator|=(int value) {
2910        _map.set(_key, _map[_key] | value);
2911        return *this;
2912      }
2913      Reference& operator^=(int value) {
2914        _map.set(_key, _map[_key] ^ value);
2915        return *this;
2916      }
2917      Reference& operator<<=(int value) {
2918        _map.set(_key, _map[_key] << value);
2919        return *this;
2920      }
2921      Reference& operator>>=(int value) {
2922        _map.set(_key, _map[_key] >> value);
2923        return *this;
2924      }
2925
2926    private:
2927      Key _key;
2928      IterableIntMap& _map;
2929    };
2930
2931    /// The const reference type.
2932    typedef const Value& ConstReference;
2933
2934    /// \brief Gives back the maximal value plus one.
2935    ///
2936    /// Gives back the maximal value plus one.
2937    int size() const {
2938      return _first.size();
2939    }
2940
2941    /// \brief Set operation of the map.
2942    ///
2943    /// Set operation of the map.
2944    void set(const Key& key, const Value& value) {
2945      unlace(key);
2946      Parent::operator[](key).value = value;
2947      lace(key);
2948    }
2949
2950    /// \brief Const subscript operator of the map.
2951    ///
2952    /// Const subscript operator of the map.
2953    const Value& operator[](const Key& key) const {
2954      return Parent::operator[](key).value;
2955    }
2956
2957    /// \brief Subscript operator of the map.
2958    ///
2959    /// Subscript operator of the map.
2960    Reference operator[](const Key& key) {
2961      return Reference(*this, key);
2962    }
2963
2964    /// \brief Iterator for the keys with the same value.
2965    ///
2966    /// Iterator for the keys with the same value. It works
2967    /// like a graph item iterator, it can be converted to
2968    /// the item type of the map, incremented with \c ++ operator, and
2969    /// if the iterator leaves the last valid item, it will be equal to
2970    /// \c INVALID.
2971    class ItemIt : public Key {
2972    public:
2973      typedef Key Parent;
2974
2975      /// \brief Invalid constructor \& conversion.
2976      ///
2977      /// This constructor initializes the iterator to be invalid.
2978      /// \sa Invalid for more details.
2979      ItemIt(Invalid) : Parent(INVALID), _map(0) {}
2980
2981      /// \brief Creates an iterator with a value.
2982      ///
2983      /// Creates an iterator with a value. It iterates on the
2984      /// keys mapped to the given value.
2985      /// \param map The IterableIntMap.
2986      /// \param value The value.
2987      ItemIt(const IterableIntMap& map, int value) : _map(&map) {
2988        if (value < 0 || value >= int(_map->_first.size())) {
2989          Parent::operator=(INVALID);
2990        } else {
2991          Parent::operator=(_map->_first[value]);
2992        }
2993      }
2994
2995      /// \brief Increment operator.
2996      ///
2997      /// Increment operator.
2998      ItemIt& operator++() {
2999        Parent::operator=(_map->IterableIntMap::Parent::
3000                          operator[](static_cast<Parent&>(*this)).next);
3001        return *this;
3002      }
3003
3004    private:
3005      const IterableIntMap* _map;
3006    };
3007
3008  protected:
3009
3010    virtual void erase(const Key& key) {
3011      unlace(key);
3012      Parent::erase(key);
3013    }
3014
3015    virtual void erase(const std::vector<Key>& keys) {
3016      for (int i = 0; i < int(keys.size()); ++i) {
3017        unlace(keys[i]);
3018      }
3019      Parent::erase(keys);
3020    }
3021
3022    virtual void clear() {
3023      _first.clear();
3024      Parent::clear();
3025    }
3026
3027  private:
3028    std::vector<Key> _first;
3029  };
3030
3031  namespace _maps_bits {
3032    template <typename Item, typename Value>
3033    struct IterableValueMapNode {
3034      IterableValueMapNode(Value _value = Value()) : value(_value) {}
3035      Item prev, next;
3036      Value value;
3037    };
3038  }
3039
3040  /// \brief Dynamic iterable map for comparable values.
3041  ///
3042  /// This class provides a special graph map type which can store a
3043  /// comparable value for graph items (\c Node, \c Arc or \c Edge).
3044  /// For each value it is possible to iterate on the keys mapped to
3045  /// the value (\c ItemIt), and the values of the map can be accessed
3046  /// with an STL compatible forward iterator (\c ValueIt).
3047  /// The map stores a linked list for each value, which contains
3048  /// the items mapped to the value, and the used values are stored
3049  /// in balanced binary tree (\c std::map).
3050  ///
3051  /// \ref IterableBoolMap and \ref IterableIntMap are similar classes
3052  /// specialized for \c bool and \c int values, respectively.
3053  ///
3054  /// This type is not reference map, so it cannot be modified with
3055  /// the subscript operator.
3056  ///
3057  /// \tparam GR The graph type.
3058  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
3059  /// \c GR::Edge).
3060  /// \tparam V The value type of the map. It can be any comparable
3061  /// value type.
3062  ///
3063  /// \see IterableBoolMap, IterableIntMap
3064  /// \see CrossRefMap
3065  template <typename GR, typename K, typename V>
3066  class IterableValueMap
3067    : protected ItemSetTraits<GR, K>::
3068        template Map<_maps_bits::IterableValueMapNode<K, V> >::Type {
3069  public:
3070    typedef typename ItemSetTraits<GR, K>::
3071      template Map<_maps_bits::IterableValueMapNode<K, V> >::Type Parent;
3072
3073    /// The key type
3074    typedef K Key;
3075    /// The value type
3076    typedef V Value;
3077    /// The graph type
3078    typedef GR Graph;
3079
3080  public:
3081
3082    /// \brief Constructor of the map with a given value.
3083    ///
3084    /// Constructor of the map with a given value.
3085    explicit IterableValueMap(const Graph& graph,
3086                              const Value& value = Value())
3087      : Parent(graph, _maps_bits::IterableValueMapNode<K, V>(value)) {
3088      for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
3089        lace(it);
3090      }
3091    }
3092
3093  protected:
3094
3095    void unlace(const Key& key) {
3096      typename Parent::Value& node = Parent::operator[](key);
3097      if (node.prev != INVALID) {
3098        Parent::operator[](node.prev).next = node.next;
3099      } else {
3100        if (node.next != INVALID) {
3101          _first[node.value] = node.next;
3102        } else {
3103          _first.erase(node.value);
3104        }
3105      }
3106      if (node.next != INVALID) {
3107        Parent::operator[](node.next).prev = node.prev;
3108      }
3109    }
3110
3111    void lace(const Key& key) {
3112      typename Parent::Value& node = Parent::operator[](key);
3113      typename std::map<Value, Key>::iterator it = _first.find(node.value);
3114      if (it == _first.end()) {
3115        node.prev = node.next = INVALID;
3116        _first.insert(std::make_pair(node.value, key));
3117      } else {
3118        node.prev = INVALID;
3119        node.next = it->second;
3120        if (node.next != INVALID) {
3121          Parent::operator[](node.next).prev = key;
3122        }
3123        it->second = key;
3124      }
3125    }
3126
3127  public:
3128
3129    /// \brief Forward iterator for values.
3130    ///
3131    /// This iterator is an STL compatible forward
3132    /// iterator on the values of the map. The values can
3133    /// be accessed in the <tt>[beginValue, endValue)</tt> range.
3134    class ValueIt
3135      : public std::iterator<std::forward_iterator_tag, Value> {
3136      friend class IterableValueMap;
3137    private:
3138      ValueIt(typename std::map<Value, Key>::const_iterator _it)
3139        : it(_it) {}
3140    public:
3141
3142      /// Constructor
3143      ValueIt() {}
3144
3145      /// \e
3146      ValueIt& operator++() { ++it; return *this; }
3147      /// \e
3148      ValueIt operator++(int) {
3149        ValueIt tmp(*this);
3150        operator++();
3151        return tmp;
3152      }
3153
3154      /// \e
3155      const Value& operator*() const { return it->first; }
3156      /// \e
3157      const Value* operator->() const { return &(it->first); }
3158
3159      /// \e
3160      bool operator==(ValueIt jt) const { return it == jt.it; }
3161      /// \e
3162      bool operator!=(ValueIt jt) const { return it != jt.it; }
3163
3164    private:
3165      typename std::map<Value, Key>::const_iterator it;
3166    };
3167
3168    /// \brief Returns an iterator to the first value.
3169    ///
3170    /// Returns an STL compatible iterator to the
3171    /// first value of the map. The values of the
3172    /// map can be accessed in the <tt>[beginValue, endValue)</tt>
3173    /// range.
3174    ValueIt beginValue() const {
3175      return ValueIt(_first.begin());
3176    }
3177
3178    /// \brief Returns an iterator after the last value.
3179    ///
3180    /// Returns an STL compatible iterator after the
3181    /// last value of the map. The values of the
3182    /// map can be accessed in the <tt>[beginValue, endValue)</tt>
3183    /// range.
3184    ValueIt endValue() const {
3185      return ValueIt(_first.end());
3186    }
3187
3188    /// \brief Set operation of the map.
3189    ///
3190    /// Set operation of the map.
3191    void set(const Key& key, const Value& value) {
3192      unlace(key);
3193      Parent::operator[](key).value = value;
3194      lace(key);
3195    }
3196
3197    /// \brief Const subscript operator of the map.
3198    ///
3199    /// Const subscript operator of the map.
3200    const Value& operator[](const Key& key) const {
3201      return Parent::operator[](key).value;
3202    }
3203
3204    /// \brief Iterator for the keys with the same value.
3205    ///
3206    /// Iterator for the keys with the same value. It works
3207    /// like a graph item iterator, it can be converted to
3208    /// the item type of the map, incremented with \c ++ operator, and
3209    /// if the iterator leaves the last valid item, it will be equal to
3210    /// \c INVALID.
3211    class ItemIt : public Key {
3212    public:
3213      typedef Key Parent;
3214
3215      /// \brief Invalid constructor \& conversion.
3216      ///
3217      /// This constructor initializes the iterator to be invalid.
3218      /// \sa Invalid for more details.
3219      ItemIt(Invalid) : Parent(INVALID), _map(0) {}
3220
3221      /// \brief Creates an iterator with a value.
3222      ///
3223      /// Creates an iterator with a value. It iterates on the
3224      /// keys which have the given value.
3225      /// \param map The IterableValueMap
3226      /// \param value The value
3227      ItemIt(const IterableValueMap& map, const Value& value) : _map(&map) {
3228        typename std::map<Value, Key>::const_iterator it =
3229          map._first.find(value);
3230        if (it == map._first.end()) {
3231          Parent::operator=(INVALID);
3232        } else {
3233          Parent::operator=(it->second);
3234        }
3235      }
3236
3237      /// \brief Increment operator.
3238      ///
3239      /// Increment Operator.
3240      ItemIt& operator++() {
3241        Parent::operator=(_map->IterableValueMap::Parent::
3242                          operator[](static_cast<Parent&>(*this)).next);
3243        return *this;
3244      }
3245
3246
3247    private:
3248      const IterableValueMap* _map;
3249    };
3250
3251  protected:
3252
3253    virtual void add(const Key& key) {
3254      Parent::add(key);
3255      unlace(key);
3256    }
3257
3258    virtual void add(const std::vector<Key>& keys) {
3259      Parent::add(keys);
3260      for (int i = 0; i < int(keys.size()); ++i) {
3261        lace(keys[i]);
3262      }
3263    }
3264
3265    virtual void erase(const Key& key) {
3266      unlace(key);
3267      Parent::erase(key);
3268    }
3269
3270    virtual void erase(const std::vector<Key>& keys) {
3271      for (int i = 0; i < int(keys.size()); ++i) {
3272        unlace(keys[i]);
3273      }
3274      Parent::erase(keys);
3275    }
3276
3277    virtual void build() {
3278      Parent::build();
3279      for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
3280        lace(it);
3281      }
3282    }
3283
3284    virtual void clear() {
3285      _first.clear();
3286      Parent::clear();
3287    }
3288
3289  private:
3290    std::map<Value, Key> _first;
3291  };
3292
3293  /// \brief Map of the source nodes of arcs in a digraph.
3294  ///
3295  /// SourceMap provides access for the source node of each arc in a digraph,
3296  /// which is returned by the \c source() function of the digraph.
3297  /// \tparam GR The digraph type.
3298  /// \see TargetMap
3299  template <typename GR>
3300  class SourceMap {
3301  public:
3302
3303    /// The key type (the \c Arc type of the digraph).
3304    typedef typename GR::Arc Key;
3305    /// The value type (the \c Node type of the digraph).
3306    typedef typename GR::Node Value;
3307
3308    /// \brief Constructor
3309    ///
3310    /// Constructor.
3311    /// \param digraph The digraph that the map belongs to.
3312    explicit SourceMap(const GR& digraph) : _graph(digraph) {}
3313
3314    /// \brief Returns the source node of the given arc.
3315    ///
3316    /// Returns the source node of the given arc.
3317    Value operator[](const Key& arc) const {
3318      return _graph.source(arc);
3319    }
3320
3321  private:
3322    const GR& _graph;
3323  };
3324
3325  /// \brief Returns a \c SourceMap class.
3326  ///
3327  /// This function just returns an \c SourceMap class.
3328  /// \relates SourceMap
3329  template <typename GR>
3330  inline SourceMap<GR> sourceMap(const GR& graph) {
3331    return SourceMap<GR>(graph);
3332  }
3333
3334  /// \brief Map of the target nodes of arcs in a digraph.
3335  ///
3336  /// TargetMap provides access for the target node of each arc in a digraph,
3337  /// which is returned by the \c target() function of the digraph.
3338  /// \tparam GR The digraph type.
3339  /// \see SourceMap
3340  template <typename GR>
3341  class TargetMap {
3342  public:
3343
3344    /// The key type (the \c Arc type of the digraph).
3345    typedef typename GR::Arc Key;
3346    /// The value type (the \c Node type of the digraph).
3347    typedef typename GR::Node Value;
3348
3349    /// \brief Constructor
3350    ///
3351    /// Constructor.
3352    /// \param digraph The digraph that the map belongs to.
3353    explicit TargetMap(const GR& digraph) : _graph(digraph) {}
3354
3355    /// \brief Returns the target node of the given arc.
3356    ///
3357    /// Returns the target node of the given arc.
3358    Value operator[](const Key& e) const {
3359      return _graph.target(e);
3360    }
3361
3362  private:
3363    const GR& _graph;
3364  };
3365
3366  /// \brief Returns a \c TargetMap class.
3367  ///
3368  /// This function just returns a \c TargetMap class.
3369  /// \relates TargetMap
3370  template <typename GR>
3371  inline TargetMap<GR> targetMap(const GR& graph) {
3372    return TargetMap<GR>(graph);
3373  }
3374
3375  /// \brief Map of the "forward" directed arc view of edges in a graph.
3376  ///
3377  /// ForwardMap provides access for the "forward" directed arc view of
3378  /// each edge in a graph, which is returned by the \c direct() function
3379  /// of the graph with \c true parameter.
3380  /// \tparam GR The graph type.
3381  /// \see BackwardMap
3382  template <typename GR>
3383  class ForwardMap {
3384  public:
3385
3386    /// The key type (the \c Edge type of the digraph).
3387    typedef typename GR::Edge Key;
3388    /// The value type (the \c Arc type of the digraph).
3389    typedef typename GR::Arc Value;
3390
3391    /// \brief Constructor
3392    ///
3393    /// Constructor.
3394    /// \param graph The graph that the map belongs to.
3395    explicit ForwardMap(const GR& graph) : _graph(graph) {}
3396
3397    /// \brief Returns the "forward" directed arc view of the given edge.
3398    ///
3399    /// Returns the "forward" directed arc view of the given edge.
3400    Value operator[](const Key& key) const {
3401      return _graph.direct(key, true);
3402    }
3403
3404  private:
3405    const GR& _graph;
3406  };
3407
3408  /// \brief Returns a \c ForwardMap class.
3409  ///
3410  /// This function just returns an \c ForwardMap class.
3411  /// \relates ForwardMap
3412  template <typename GR>
3413  inline ForwardMap<GR> forwardMap(const GR& graph) {
3414    return ForwardMap<GR>(graph);
3415  }
3416
3417  /// \brief Map of the "backward" directed arc view of edges in a graph.
3418  ///
3419  /// BackwardMap provides access for the "backward" directed arc view of
3420  /// each edge in a graph, which is returned by the \c direct() function
3421  /// of the graph with \c false parameter.
3422  /// \tparam GR The graph type.
3423  /// \see ForwardMap
3424  template <typename GR>
3425  class BackwardMap {
3426  public:
3427
3428    /// The key type (the \c Edge type of the digraph).
3429    typedef typename GR::Edge Key;
3430    /// The value type (the \c Arc type of the digraph).
3431    typedef typename GR::Arc Value;
3432
3433    /// \brief Constructor
3434    ///
3435    /// Constructor.
3436    /// \param graph The graph that the map belongs to.
3437    explicit BackwardMap(const GR& graph) : _graph(graph) {}
3438
3439    /// \brief Returns the "backward" directed arc view of the given edge.
3440    ///
3441    /// Returns the "backward" directed arc view of the given edge.
3442    Value operator[](const Key& key) const {
3443      return _graph.direct(key, false);
3444    }
3445
3446  private:
3447    const GR& _graph;
3448  };
3449
3450  /// \brief Returns a \c BackwardMap class
3451
3452  /// This function just returns a \c BackwardMap class.
3453  /// \relates BackwardMap
3454  template <typename GR>
3455  inline BackwardMap<GR> backwardMap(const GR& graph) {
3456    return BackwardMap<GR>(graph);
3457  }
3458
3459  /// \brief Map of the in-degrees of nodes in a digraph.
3460  ///
3461  /// This map returns the in-degree of a node. Once it is constructed,
3462  /// the degrees are stored in a standard \c NodeMap, so each query is done
3463  /// in constant time. On the other hand, the values are updated automatically
3464  /// whenever the digraph changes.
3465  ///
3466  /// \warning Besides \c addNode() and \c addArc(), a digraph structure
3467  /// may provide alternative ways to modify the digraph.
3468  /// The correct behavior of InDegMap is not guarantied if these additional
3469  /// features are used. For example, the functions
3470  /// \ref ListDigraph::changeSource() "changeSource()",
3471  /// \ref ListDigraph::changeTarget() "changeTarget()" and
3472  /// \ref ListDigraph::reverseArc() "reverseArc()"
3473  /// of \ref ListDigraph will \e not update the degree values correctly.
3474  ///
3475  /// \sa OutDegMap
3476  template <typename GR>
3477  class InDegMap
3478    : protected ItemSetTraits<GR, typename GR::Arc>
3479      ::ItemNotifier::ObserverBase {
3480
3481  public:
3482
3483    /// The graph type of InDegMap
3484    typedef GR Graph;
3485    typedef GR Digraph;
3486    /// The key type
3487    typedef typename Digraph::Node Key;
3488    /// The value type
3489    typedef int Value;
3490
3491    typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
3492    ::ItemNotifier::ObserverBase Parent;
3493
3494  private:
3495
3496    class AutoNodeMap
3497      : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {
3498    public:
3499
3500      typedef typename ItemSetTraits<Digraph, Key>::
3501      template Map<int>::Type Parent;
3502
3503      AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
3504
3505      virtual void add(const Key& key) {
3506        Parent::add(key);
3507        Parent::set(key, 0);
3508      }
3509
3510      virtual void add(const std::vector<Key>& keys) {
3511        Parent::add(keys);
3512        for (int i = 0; i < int(keys.size()); ++i) {
3513          Parent::set(keys[i], 0);
3514        }
3515      }
3516
3517      virtual void build() {
3518        Parent::build();
3519        Key it;
3520        typename Parent::Notifier* nf = Parent::notifier();
3521        for (nf->first(it); it != INVALID; nf->next(it)) {
3522          Parent::set(it, 0);
3523        }
3524      }
3525    };
3526
3527  public:
3528
3529    /// \brief Constructor.
3530    ///
3531    /// Constructor for creating an in-degree map.
3532    explicit InDegMap(const Digraph& graph)
3533      : _digraph(graph), _deg(graph) {
3534      Parent::attach(_digraph.notifier(typename Digraph::Arc()));
3535
3536      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
3537        _deg[it] = countInArcs(_digraph, it);
3538      }
3539    }
3540
3541    /// \brief Gives back the in-degree of a Node.
3542    ///
3543    /// Gives back the in-degree of a Node.
3544    int operator[](const Key& key) const {
3545      return _deg[key];
3546    }
3547
3548  protected:
3549
3550    typedef typename Digraph::Arc Arc;
3551
3552    virtual void add(const Arc& arc) {
3553      ++_deg[_digraph.target(arc)];
3554    }
3555
3556    virtual void add(const std::vector<Arc>& arcs) {
3557      for (int i = 0; i < int(arcs.size()); ++i) {
3558        ++_deg[_digraph.target(arcs[i])];
3559      }
3560    }
3561
3562    virtual void erase(const Arc& arc) {
3563      --_deg[_digraph.target(arc)];
3564    }
3565
3566    virtual void erase(const std::vector<Arc>& arcs) {
3567      for (int i = 0; i < int(arcs.size()); ++i) {
3568        --_deg[_digraph.target(arcs[i])];
3569      }
3570    }
3571
3572    virtual void build() {
3573      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
3574        _deg[it] = countInArcs(_digraph, it);
3575      }
3576    }
3577
3578    virtual void clear() {
3579      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
3580        _deg[it] = 0;
3581      }
3582    }
3583  private:
3584
3585    const Digraph& _digraph;
3586    AutoNodeMap _deg;
3587  };
3588
3589  /// \brief Map of the out-degrees of nodes in a digraph.
3590  ///
3591  /// This map returns the out-degree of a node. Once it is constructed,
3592  /// the degrees are stored in a standard \c NodeMap, so each query is done
3593  /// in constant time. On the other hand, the values are updated automatically
3594  /// whenever the digraph changes.
3595  ///
3596  /// \warning Besides \c addNode() and \c addArc(), a digraph structure
3597  /// may provide alternative ways to modify the digraph.
3598  /// The correct behavior of OutDegMap is not guarantied if these additional
3599  /// features are used. For example, the functions
3600  /// \ref ListDigraph::changeSource() "changeSource()",
3601  /// \ref ListDigraph::changeTarget() "changeTarget()" and
3602  /// \ref ListDigraph::reverseArc() "reverseArc()"
3603  /// of \ref ListDigraph will \e not update the degree values correctly.
3604  ///
3605  /// \sa InDegMap
3606  template <typename GR>
3607  class OutDegMap
3608    : protected ItemSetTraits<GR, typename GR::Arc>
3609      ::ItemNotifier::ObserverBase {
3610
3611  public:
3612
3613    /// The graph type of OutDegMap
3614    typedef GR Graph;
3615    typedef GR Digraph;
3616    /// The key type
3617    typedef typename Digraph::Node Key;
3618    /// The value type
3619    typedef int Value;
3620
3621    typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
3622    ::ItemNotifier::ObserverBase Parent;
3623
3624  private:
3625
3626    class AutoNodeMap
3627      : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {
3628    public:
3629
3630      typedef typename ItemSetTraits<Digraph, Key>::
3631      template Map<int>::Type Parent;
3632
3633      AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
3634
3635      virtual void add(const Key& key) {
3636        Parent::add(key);
3637        Parent::set(key, 0);
3638      }
3639      virtual void add(const std::vector<Key>& keys) {
3640        Parent::add(keys);
3641        for (int i = 0; i < int(keys.size()); ++i) {
3642          Parent::set(keys[i], 0);
3643        }
3644      }
3645      virtual void build() {
3646        Parent::build();
3647        Key it;
3648        typename Parent::Notifier* nf = Parent::notifier();
3649        for (nf->first(it); it != INVALID; nf->next(it)) {
3650          Parent::set(it, 0);
3651        }
3652      }
3653    };
3654
3655  public:
3656
3657    /// \brief Constructor.
3658    ///
3659    /// Constructor for creating an out-degree map.
3660    explicit OutDegMap(const Digraph& graph)
3661      : _digraph(graph), _deg(graph) {
3662      Parent::attach(_digraph.notifier(typename Digraph::Arc()));
3663
3664      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
3665        _deg[it] = countOutArcs(_digraph, it);
3666      }
3667    }
3668
3669    /// \brief Gives back the out-degree of a Node.
3670    ///
3671    /// Gives back the out-degree of a Node.
3672    int operator[](const Key& key) const {
3673      return _deg[key];
3674    }
3675
3676  protected:
3677
3678    typedef typename Digraph::Arc Arc;
3679
3680    virtual void add(const Arc& arc) {
3681      ++_deg[_digraph.source(arc)];
3682    }
3683
3684    virtual void add(const std::vector<Arc>& arcs) {
3685      for (int i = 0; i < int(arcs.size()); ++i) {
3686        ++_deg[_digraph.source(arcs[i])];
3687      }
3688    }
3689
3690    virtual void erase(const Arc& arc) {
3691      --_deg[_digraph.source(arc)];
3692    }
3693
3694    virtual void erase(const std::vector<Arc>& arcs) {
3695      for (int i = 0; i < int(arcs.size()); ++i) {
3696        --_deg[_digraph.source(arcs[i])];
3697      }
3698    }
3699
3700    virtual void build() {
3701      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
3702        _deg[it] = countOutArcs(_digraph, it);
3703      }
3704    }
3705
3706    virtual void clear() {
3707      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
3708        _deg[it] = 0;
3709      }
3710    }
3711  private:
3712
3713    const Digraph& _digraph;
3714    AutoNodeMap _deg;
3715  };
3716
3717  /// \brief Potential difference map
3718  ///
3719  /// PotentialDifferenceMap returns the difference between the potentials of
3720  /// the source and target nodes of each arc in a digraph, i.e. it returns
3721  /// \code
3722  ///   potential[gr.target(arc)] - potential[gr.source(arc)].
3723  /// \endcode
3724  /// \tparam GR The digraph type.
3725  /// \tparam POT A node map storing the potentials.
3726  template <typename GR, typename POT>
3727  class PotentialDifferenceMap {
3728  public:
3729    /// Key type
3730    typedef typename GR::Arc Key;
3731    /// Value type
3732    typedef typename POT::Value Value;
3733
3734    /// \brief Constructor
3735    ///
3736    /// Contructor of the map.
3737    explicit PotentialDifferenceMap(const GR& gr,
3738                                    const POT& potential)
3739      : _digraph(gr), _potential(potential) {}
3740
3741    /// \brief Returns the potential difference for the given arc.
3742    ///
3743    /// Returns the potential difference for the given arc, i.e.
3744    /// \code
3745    ///   potential[gr.target(arc)] - potential[gr.source(arc)].
3746    /// \endcode
3747    Value operator[](const Key& arc) const {
3748      return _potential[_digraph.target(arc)] -
3749        _potential[_digraph.source(arc)];
3750    }
3751
3752  private:
3753    const GR& _digraph;
3754    const POT& _potential;
3755  };
3756
3757  /// \brief Returns a PotentialDifferenceMap.
3758  ///
3759  /// This function just returns a PotentialDifferenceMap.
3760  /// \relates PotentialDifferenceMap
3761  template <typename GR, typename POT>
3762  PotentialDifferenceMap<GR, POT>
3763  potentialDifferenceMap(const GR& gr, const POT& potential) {
3764    return PotentialDifferenceMap<GR, POT>(gr, potential);
3765  }
3766
3767
3768  /// \brief Copy the values of a graph map to another map.
3769  ///
3770  /// This function copies the values of a graph map to another graph map.
3771  /// \c To::Key must be equal or convertible to \c From::Key and
3772  /// \c From::Value must be equal or convertible to \c To::Value.
3773  ///
3774  /// For example, an edge map of \c int value type can be copied to
3775  /// an arc map of \c double value type in an undirected graph, but
3776  /// an arc map cannot be copied to an edge map.
3777  /// Note that even a \ref ConstMap can be copied to a standard graph map,
3778  /// but \ref mapFill() can also be used for this purpose.
3779  ///
3780  /// \param gr The graph for which the maps are defined.
3781  /// \param from The map from which the values have to be copied.
3782  /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
3783  /// \param to The map to which the values have to be copied.
3784  /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
3785  template <typename GR, typename From, typename To>
3786  void mapCopy(const GR& gr, const From& from, To& to) {
3787    typedef typename To::Key Item;
3788    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
3789   
3790    for (ItemIt it(gr); it != INVALID; ++it) {
3791      to.set(it, from[it]);
3792    }
3793  }
3794
3795  /// \brief Compare two graph maps.
3796  ///
3797  /// This function compares the values of two graph maps. It returns
3798  /// \c true if the maps assign the same value for all items in the graph.
3799  /// The \c Key type of the maps (\c Node, \c Arc or \c Edge) must be equal
3800  /// and their \c Value types must be comparable using \c %operator==().
3801  ///
3802  /// \param gr The graph for which the maps are defined.
3803  /// \param map1 The first map.
3804  /// \param map2 The second map.
3805  template <typename GR, typename Map1, typename Map2>
3806  bool mapCompare(const GR& gr, const Map1& map1, const Map2& map2) {
3807    typedef typename Map2::Key Item;
3808    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
3809   
3810    for (ItemIt it(gr); it != INVALID; ++it) {
3811      if (!(map1[it] == map2[it])) return false;
3812    }
3813    return true;
3814  }
3815
3816  /// \brief Return an item having minimum value of a graph map.
3817  ///
3818  /// This function returns an item (\c Node, \c Arc or \c Edge) having
3819  /// minimum value of the given graph map.
3820  /// If the item set is empty, it returns \c INVALID.
3821  ///
3822  /// \param gr The graph for which the map is defined.
3823  /// \param map The graph map.
3824  template <typename GR, typename Map>
3825  typename Map::Key mapMin(const GR& gr, const Map& map) {
3826    return mapMin(gr, map, std::less<typename Map::Value>());
3827  }
3828
3829  /// \brief Return an item having minimum value of a graph map.
3830  ///
3831  /// This function returns an item (\c Node, \c Arc or \c Edge) having
3832  /// minimum value of the given graph map.
3833  /// If the item set is empty, it returns \c INVALID.
3834  ///
3835  /// \param gr The graph for which the map is defined.
3836  /// \param map The graph map.
3837  /// \param comp Comparison function object.
3838  template <typename GR, typename Map, typename Comp>
3839  typename Map::Key mapMin(const GR& gr, const Map& map, const Comp& comp) {
3840    typedef typename Map::Key Item;
3841    typedef typename Map::Value Value;
3842    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
3843
3844    ItemIt min_item(gr);
3845    if (min_item == INVALID) return INVALID;
3846    Value min = map[min_item];
3847    for (ItemIt it(gr); it != INVALID; ++it) {
3848      if (comp(map[it], min)) {
3849        min = map[it];
3850        min_item = it;
3851      }
3852    }
3853    return min_item;
3854  }
3855
3856  /// \brief Return an item having maximum value of a graph map.
3857  ///
3858  /// This function returns an item (\c Node, \c Arc or \c Edge) having
3859  /// maximum value of the given graph map.
3860  /// If the item set is empty, it returns \c INVALID.
3861  ///
3862  /// \param gr The graph for which the map is defined.
3863  /// \param map The graph map.
3864  template <typename GR, typename Map>
3865  typename Map::Key mapMax(const GR& gr, const Map& map) {
3866    return mapMax(gr, map, std::less<typename Map::Value>());
3867  }
3868
3869  /// \brief Return an item having maximum value of a graph map.
3870  ///
3871  /// This function returns an item (\c Node, \c Arc or \c Edge) having
3872  /// maximum value of the given graph map.
3873  /// If the item set is empty, it returns \c INVALID.
3874  ///
3875  /// \param gr The graph for which the map is defined.
3876  /// \param map The graph map.
3877  /// \param comp Comparison function object.
3878  template <typename GR, typename Map, typename Comp>
3879  typename Map::Key mapMax(const GR& gr, const Map& map, const Comp& comp) {
3880    typedef typename Map::Key Item;
3881    typedef typename Map::Value Value;
3882    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
3883
3884    ItemIt max_item(gr);
3885    if (max_item == INVALID) return INVALID;
3886    Value max = map[max_item];
3887    for (ItemIt it(gr); it != INVALID; ++it) {
3888      if (comp(max, map[it])) {
3889        max = map[it];
3890        max_item = it;
3891      }
3892    }
3893    return max_item;
3894  }
3895
3896  /// \brief Return the minimum value of a graph map.
3897  ///
3898  /// This function returns the minimum value of the given graph map.
3899  /// The corresponding item set of the graph must not be empty.
3900  ///
3901  /// \param gr The graph for which the map is defined.
3902  /// \param map The graph map.
3903  template <typename GR, typename Map>
3904  typename Map::Value mapMinValue(const GR& gr, const Map& map) {
3905    return map[mapMin(gr, map, std::less<typename Map::Value>())];
3906  }
3907
3908  /// \brief Return the minimum value of a graph map.
3909  ///
3910  /// This function returns the minimum value of the given graph map.
3911  /// The corresponding item set of the graph must not be empty.
3912  ///
3913  /// \param gr The graph for which the map is defined.
3914  /// \param map The graph map.
3915  /// \param comp Comparison function object.
3916  template <typename GR, typename Map, typename Comp>
3917  typename Map::Value
3918  mapMinValue(const GR& gr, const Map& map, const Comp& comp) {
3919    return map[mapMin(gr, map, comp)];
3920  }
3921
3922  /// \brief Return the maximum value of a graph map.
3923  ///
3924  /// This function returns the maximum value of the given graph map.
3925  /// The corresponding item set of the graph must not be empty.
3926  ///
3927  /// \param gr The graph for which the map is defined.
3928  /// \param map The graph map.
3929  template <typename GR, typename Map>
3930  typename Map::Value mapMaxValue(const GR& gr, const Map& map) {
3931    return map[mapMax(gr, map, std::less<typename Map::Value>())];
3932  }
3933
3934  /// \brief Return the maximum value of a graph map.
3935  ///
3936  /// This function returns the maximum value of the given graph map.
3937  /// The corresponding item set of the graph must not be empty.
3938  ///
3939  /// \param gr The graph for which the map is defined.
3940  /// \param map The graph map.
3941  /// \param comp Comparison function object.
3942  template <typename GR, typename Map, typename Comp>
3943  typename Map::Value
3944  mapMaxValue(const GR& gr, const Map& map, const Comp& comp) {
3945    return map[mapMax(gr, map, comp)];
3946  }
3947
3948  /// \brief Return an item having a specified value in a graph map.
3949  ///
3950  /// This function returns an item (\c Node, \c Arc or \c Edge) having
3951  /// the specified assigned value in the given graph map.
3952  /// If no such item exists, it returns \c INVALID.
3953  ///
3954  /// \param gr The graph for which the map is defined.
3955  /// \param map The graph map.
3956  /// \param val The value that have to be found.
3957  template <typename GR, typename Map>
3958  typename Map::Key
3959  mapFind(const GR& gr, const Map& map, const typename Map::Value& val) {
3960    typedef typename Map::Key Item;
3961    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
3962
3963    for (ItemIt it(gr); it != INVALID; ++it) {
3964      if (map[it] == val) return it;
3965    }
3966    return INVALID;
3967  }
3968
3969  /// \brief Return an item having value for which a certain predicate is
3970  /// true in a graph map.
3971  ///
3972  /// This function returns an item (\c Node, \c Arc or \c Edge) having
3973  /// such assigned value for which the specified predicate is true
3974  /// in the given graph map.
3975  /// If no such item exists, it returns \c INVALID.
3976  ///
3977  /// \param gr The graph for which the map is defined.
3978  /// \param map The graph map.
3979  /// \param pred The predicate function object.
3980  template <typename GR, typename Map, typename Pred>
3981  typename Map::Key
3982  mapFindIf(const GR& gr, const Map& map, const Pred& pred) {
3983    typedef typename Map::Key Item;
3984    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
3985
3986    for (ItemIt it(gr); it != INVALID; ++it) {
3987      if (pred(map[it])) return it;
3988    }
3989    return INVALID;
3990  }
3991
3992  /// \brief Return the number of items having a specified value in a
3993  /// graph map.
3994  ///
3995  /// This function returns the number of items (\c Node, \c Arc or \c Edge)
3996  /// having the specified assigned value in the given graph map.
3997  ///
3998  /// \param gr The graph for which the map is defined.
3999  /// \param map The graph map.
4000  /// \param val The value that have to be counted.
4001  template <typename GR, typename Map>
4002  int mapCount(const GR& gr, const Map& map, const typename Map::Value& val) {
4003    typedef typename Map::Key Item;
4004    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
4005
4006    int cnt = 0;
4007    for (ItemIt it(gr); it != INVALID; ++it) {
4008      if (map[it] == val) ++cnt;
4009    }
4010    return cnt;
4011  }
4012
4013  /// \brief Return the number of items having values for which a certain
4014  /// predicate is true in a graph map.
4015  ///
4016  /// This function returns the number of items (\c Node, \c Arc or \c Edge)
4017  /// having such assigned values for which the specified predicate is true
4018  /// in the given graph map.
4019  ///
4020  /// \param gr The graph for which the map is defined.
4021  /// \param map The graph map.
4022  /// \param pred The predicate function object.
4023  template <typename GR, typename Map, typename Pred>
4024  int mapCountIf(const GR& gr, const Map& map, const Pred& pred) {
4025    typedef typename Map::Key Item;
4026    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
4027
4028    int cnt = 0;
4029    for (ItemIt it(gr); it != INVALID; ++it) {
4030      if (pred(map[it])) ++cnt;
4031    }
4032    return cnt;
4033  }
4034
4035  /// \brief Fill a graph map with a certain value.
4036  ///
4037  /// This function sets the specified value for all items (\c Node,
4038  /// \c Arc or \c Edge) in the given graph map.
4039  ///
4040  /// \param gr The graph for which the map is defined.
4041  /// \param map The graph map. It must conform to the
4042  /// \ref concepts::WriteMap "WriteMap" concept.
4043  /// \param val The value.
4044  template <typename GR, typename Map>
4045  void mapFill(const GR& gr, Map& map, const typename Map::Value& val) {
4046    typedef typename Map::Key Item;
4047    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
4048
4049    for (ItemIt it(gr); it != INVALID; ++it) {
4050      map.set(it, val);
4051    }
4052  }
4053
4054  /// @}
4055}
4056
4057#endif // LEMON_MAPS_H
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