CGAL 5.0.2 - STL Extensions for CGAL
CGAL::Multiset< Type, Compare, Allocator > Class Template Reference

#include <CGAL/Multiset.h>

## Definition

An instance s of the parametrized data type Multiset is a multi-set of elements of type Type, represented as a red-black tree (see [[3] Chapter 13 for an excellent introduction to red-black trees). The main difference between Multiset and the STL std::multiset is that the latter uses a less-than functor with a Boolean return type, while our Multiset class is parameterized by a comparison functor Compare that returns the three-valued Comparison_result (namely it returns either SMALLER, EQUAL, or LARGER). It is thus possible to maintain the underlying red-black tree with less invocations of the comparison functor. This leads to a speedup of about 5% even if we maintain a set of integers. When each comparison of two elements of type Type is an expensive operation (for example, when they are geometric entities represented using exact arithmetic), the usage of a three-valued comparison functor can lead to considerable decrease in the running times.

Moreover, Multiset allows the insertion of an element into the set given its exact position, and not just using an insertion hint, as done by std::multiset. This can further reduce the running times, as additional comparison operations can be avoided.

In addition, the Multiset guarantees that the order of elements sent to the comparison functor is fixed. For example, if we insert a new element x into the set (or erase an element from the set), then we always invoke Compare() (x, y) (and never Compare() (y, x)), where y is an element already stored in the set. This behavior, not supported by std::multiset, is sometimes crucial for designing more efficient comparison predicates.

Multiset also allows for look-up of keys whose type may differ from Type, as long as users supply a comparison functor CompareKey, where CompareKey() (key, y) returns the three-valued Comparison_result (key is the look-up key and y is an element of type Type). Indeed, it is very convenient to look-up equivalent objects in the set given just by their key. We note however that it is also possible to use a key of type Type and to employ the default Compare functor for the look-up, as done when using the std::multiset class.

Warning
Finally, Multiset introduces the catenate() and split() functions. The first function operates on s and accepts a second set s2, such that the maximum element in s is not greater than the minimal element in s2, and concatenates s2 to s. The second function splits s into two sets, one containing all the elements that are less than a given key, and the other contains all elements greater than (or equal to) this key.
Template Parameters
 Type the type of the stored elements. Compare the comparison-functor type. This type should provide the following operator for comparing two Type elements, namely: Comparison_result operator() (const Type& t1, const Type& t2) const; The CGAL::Compare functor is used by default. In this case, Type must support an equality operator (operator==) and a less-than operator (operator<). Allocator the allocator type. CGAL_ALLOCATOR is used by default.

Assertions

The assertion and precondition flags for the Multiset class use MULTISET in their names (i.e., CGAL_MULTISET_NO_ASSERTIONS and CGAL_MULTISET_NO_PRECONDITIONS).

Implementation

Multiset uses a proprietary implementation of a red-black tree data-structure. The red-black tree invariants guarantee that the height of a tree containing $$n$$ elements is $$O(\log{n})$$ (more precisely, it is bounded by $$2 \log_{2}{n}$$). As a consequence, all methods that accept an element and need to locate it in the tree (namely insert(x), erase(x), find(x), count(x), lower_bound(x) , upper_bound(x), find_lower(x) and equal_range(x)) take $$O(\log{n})$$ time and perform $$O(\log{n})$$ comparison operations.

On the other hand, the set operations that accept a position iterator (namely insert_before(pos, x), insert_after(pos, x) and erase(pos)) are much more efficient as they can be performed at a constant amortized cost (see [4] and [6] for more details). More important, these set operations require no comparison operations. Therefore, it is highly recommended to maintain the set via iterators to the stored elements, whenever possible. The function insert(pos, x) is safer to use, but it takes amortized $$O(\min\{d,\log{n}\})$$ time, where $$d$$ is the distance between the given position and the true position of x. In addition, it always performs at least two comparison operations.

The catenate() and split() functions are also very efficient, and can be performed in $$O(\log{n})$$ time, where $$n$$ is the total number of elements in the sets, and without performing any comparison operations (see [6] for the details). Note however that the size of two sets resulting from a split operation is initially unknown, as it is impossible to compute it in less than linear time. Thus, the first invocation of size() on such a set takes linear time, and not constant time.

The design is derived from the STL multiset class-template (see, e.g, [5]), where the main differences between the two classes are highlighted in the class definition above.

## Types

In compliance with STL, the types value_type and key_type (both equivalent to Type), reference and const_reference (reference to a value-type), key_compare and value_compare (both equivalent to Compare), size_type and difference_type are defined as well.

typedef unspecified_type iterator

typedef unspecified_type const_iterator
bi-directional iterators for the elements stored in the set.

typedef unspecified_type reverse_iterator

typedef unspecified_type const_reverse_iterator
reverse bi-directional iterators for the elements stored in the set.

## Creation

Multiset ()
creates an an empty set s that uses a default comparison functor.

Multiset (const Compare &comp)
creates an an empty set s that uses the given comparison functor comp.

template<class InputIterator >
Multiset (InputIterator first, InputIterator last, const Compare &comp=Compare())
creates a set s containing all elements in the range [first, last), that uses the comparison functor comp.

Multiset (const Multiset< Type, Compare, Allocator > &other)
copy constructor.

const Multiset< Type, Compare, Allocator > & operator= (const Multiset< Type, Compare, Allocator > &other)
assignment operator.

void swap (Multiset< Type, Compare, Allocator > &other)
swaps the contents of s with those of the other set.

## Access Member Functions

Compare key_comp () const
the comparison functor used.

Compare value_comp () const
the comparison functor used (same as above). More...

bool empty ()
returns true if the set is empty, false otherwise.

size_t size ()
returns the number of elements stored in the set.

size_t max_size ()
returns the maximal number of elements the set can store (same as size()).

iterator begin ()
returns an iterator pointing to the first element stored in the set (a const version is also available).

iterator end ()
returns an iterator pointing beyond the last element stored in the set (a const version is also available).

reverse_iterator rbegin ()
returns a reverse iterator pointing beyond the last element stored in the set (a const version is also available).

reverse_iterator rend ()
returns a reverse iterator pointing to the first element stored in the set (a const version is also available).

## Comparison Operations

bool operator== (const Multiset< Type, Compare, Allocator > &other) const
returns true if the sequences of elements in the two sets are pairwise equal (using the comparison functor).

bool operator< (const Multiset< Type, Compare, Allocator > &other) const
returns true if the element sequence in s is lexicographically smaller than the element sequence of other.

## Insertion Methods

iterator insert (const Type &x)
inserts the element x into the set and returns an iterator pointing to the newly inserted element.

template<class InputIterator >
void insert (InputIterator first, InputIterator last)
inserts all elements in the range [first, last) into the set.

iterator insert (iterator position, const Type &x)
inserts the element x with a given iterator used as a hint for the position of the new element. More...

iterator insert_before (iterator position, const Type &x)
inserts the element x as the predecessor of the element at the given position. More...

iterator insert_after (iterator position, const Type &x)
inserts the element x as the successor of the element at the given position. More...

## Removal Methods

size_t erase (const Type &x)
erases all elements equivalent to x from the set and returns the number of erased elements.

void erase (iterator position)
erases the element pointed by position.

void clear ()
clears the set (erases all stored elements).

## Look-up Methods

All methods listed in this section can also accept a Type element as a look-up key.

In this case, it is not necessary to supply a CompareKey functor, as the Compare functor will be used by default.

template<class Key , class CompareKey >
iterator find (const Key &key, const CompareKey &comp_key)
searches for the an element equivalent to key in the set. More...

template<class Key , class CompareKey >
size_t count (const Key &key, const CompareKey &comp_key) const
returns the number of elements equivalent to key in the set.

template<class Key , class CompareKey >
iterator lower_bound (const Key &key, const CompareKey &comp_key)
returns an iterator pointing to the first element in the set that is not less than key. More...

template<class Key , class CompareKey >
iterator upper_bound (const Key &key, const CompareKey &comp_key)
returns an iterator pointing to the first element in the set that is greater than key. More...

template<class Key , class CompareKey >
std::pair< iterator, iteratorequal_range (const Key &key, const CompareKey &comp_key)
returns the range of set elements equivalent to the given key, namely (lower_bound(key), upper_bound(key)) (a const version is also available).

template<class Key , class CompareKey >
std::pair< iterator, bool > find_lower (const Key &key, const CompareKey &comp_key)
returns a pair comprised of lower_bound(key) and a Boolean flag indicating whether this iterator points to an element equivalent to the given key (a const version is also available).

## Special Operations

void replace (iterator position, const Type &x)
replaces the element stored at the given position with x. More...

void swap (iterator pos1, iterator pos2)
swaps places between the two elements given by pos1 and pos2. More...

void catenate (Self &s_prime)
concatenates all elements in s_prime into s and clears s_prime. More...

template<class Key , class CompareKey >
void split (Key key, CompareKey comp_key, Self &s_prime)
splits s such that it contains all elements that are less than the given key and such that s_prime contains all other elements. More...

void split (iterator position, Self &s_prime)
splits s such that it contains all set elements in the range [begin, position) and such that s_prime contains all elements in the range [position, end()). More...

## ◆ catenate()

template<typename Type , typename Compare , typename Allocator >
 void CGAL::Multiset< Type, Compare, Allocator >::catenate ( Self & s_prime )

concatenates all elements in s_prime into s and clears s_prime.

All iterators to s and to s_prime remain valid.

Precondition
The maximal element in s is not greater than the minimal element in s_prime.

## ◆ find()

template<typename Type , typename Compare , typename Allocator >
template<class Key , class CompareKey >
 iterator CGAL::Multiset< Type, Compare, Allocator >::find ( const Key & key, const CompareKey & comp_key )

searches for the an element equivalent to key in the set.

If the set contains objects equivalent to key, it returns an iterator pointing to the first one. Otherwise, end() is returned (a const version is also available).

## ◆ insert()

template<typename Type , typename Compare , typename Allocator >
 iterator CGAL::Multiset< Type, Compare, Allocator >::insert ( iterator position, const Type & x )

inserts the element x with a given iterator used as a hint for the position of the new element.

It Returns an iterator pointing to the newly inserted element.

## ◆ insert_after()

template<typename Type , typename Compare , typename Allocator >
 iterator CGAL::Multiset< Type, Compare, Allocator >::insert_after ( iterator position, const Type & x )

inserts the element x as the successor of the element at the given position.

Precondition
The operation does not violate the set order - that is, x is not less than the element pointed by position and not greater than its current successor.

## ◆ insert_before()

template<typename Type , typename Compare , typename Allocator >
 iterator CGAL::Multiset< Type, Compare, Allocator >::insert_before ( iterator position, const Type & x )

inserts the element x as the predecessor of the element at the given position.

Precondition
The operation does not violate the set order - that is, x is not greater than the element pointed by position and not less than its current predecessor.

## ◆ lower_bound()

template<typename Type , typename Compare , typename Allocator >
template<class Key , class CompareKey >
 iterator CGAL::Multiset< Type, Compare, Allocator >::lower_bound ( const Key & key, const CompareKey & comp_key )

returns an iterator pointing to the first element in the set that is not less than key.

If all set elements are less than key, end() is returned (a const version is also available).

## ◆ replace()

template<typename Type , typename Compare , typename Allocator >
 void CGAL::Multiset< Type, Compare, Allocator >::replace ( iterator position, const Type & x )

replaces the element stored at the given position with x.

Precondition
The operation does not violate the set order - that is, x is not less that position's predecessor and not greater than its successor.

## ◆ split() [1/2]

template<typename Type , typename Compare , typename Allocator >
template<class Key , class CompareKey >
 void CGAL::Multiset< Type, Compare, Allocator >::split ( Key key, CompareKey comp_key, Self & s_prime )

splits s such that it contains all elements that are less than the given key and such that s_prime contains all other elements.

Precondition
s_prime is initially empty.

## ◆ split() [2/2]

template<typename Type , typename Compare , typename Allocator >
 void CGAL::Multiset< Type, Compare, Allocator >::split ( iterator position, Self & s_prime )

splits s such that it contains all set elements in the range [begin, position) and such that s_prime contains all elements in the range [position, end()).

Precondition
s_prime is initially empty.

## ◆ swap()

template<typename Type , typename Compare , typename Allocator >
 void CGAL::Multiset< Type, Compare, Allocator >::swap ( iterator pos1, iterator pos2 )

swaps places between the two elements given by pos1 and pos2.

Precondition
The operation does not violate the set order - that is, pos1 and pos2 store equivalent elements.

## ◆ upper_bound()

template<typename Type , typename Compare , typename Allocator >
template<class Key , class CompareKey >
 iterator CGAL::Multiset< Type, Compare, Allocator >::upper_bound ( const Key & key, const CompareKey & comp_key )

returns an iterator pointing to the first element in the set that is greater than key.

If no set element is greater than key, end() is returned (a const version is also available).

## ◆ value_comp()

template<typename Type , typename Compare , typename Allocator >
 Compare CGAL::Multiset< Type, Compare, Allocator >::value_comp ( ) const

the comparison functor used (same as above).

Both functions have a non-const version that return a reference to the comparison functor.