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## Class template sg_multiset

boost::intrusive::sg_multiset

## Synopsis

    template<typename T, class... Options>
    class sg_multiset {
    public:
      // types
      typedef implementation_defined::value_type             value_type;
      typedef implementation_defined::value_traits           value_traits;
      typedef implementation_defined::pointer                pointer;
      typedef implementation_defined::const_pointer          const_pointer;
      typedef implementation_defined::reference              reference;
      typedef implementation_defined::const_reference        const_reference;
      typedef implementation_defined::difference_type        difference_type;
      typedef implementation_defined::size_type              size_type;
      typedef implementation_defined::value_compare          value_compare;
      typedef implementation_defined::key_compare            key_compare;
      typedef implementation_defined::iterator               iterator;
      typedef implementation_defined::const_iterator         const_iterator;
      typedef implementation_defined::reverse_iterator       reverse_iterator;
      typedef implementation_defined::const_reverse_iterator const_reverse_iterator;
      typedef implementation_defined::insert_commit_data     insert_commit_data;
      typedef implementation_defined::node_traits            node_traits;
      typedef implementation_defined::node                   node;
      typedef implementation_defined::node_ptr               node_ptr;
      typedef implementation_defined::const_node_ptr         const_node_ptr;
      typedef implementation_defined::node_algorithms        node_algorithms;

      // construct/copy/destruct
      sg_multiset(const value_compare & = value_compare(),
                  const value_traits & = value_traits());
      template<typename Iterator>
        sg_multiset(Iterator, Iterator, const value_compare & = value_compare(),
                    const value_traits & = value_traits());
      ~sg_multiset();

      // public member functions
      iterator begin() ;
      const_iterator begin() const;
      const_iterator cbegin() const;
      iterator end() ;
      const_iterator end() const;
      const_iterator cend() const;
      reverse_iterator rbegin() ;
      const_reverse_iterator rbegin() const;
      const_reverse_iterator crbegin() const;
      reverse_iterator rend() ;
      const_reverse_iterator rend() const;
      const_reverse_iterator crend() const;
      key_compare key_comp() const;
      value_compare value_comp() const;
      bool empty() const;
      size_type size() const;
      void swap(sg_multiset &) ;
      template<typename Cloner, typename Disposer>
        void clone_from(const sg_multiset &, Cloner, Disposer) ;
      iterator insert(reference) ;
      iterator insert(const_iterator, reference) ;
      template<typename Iterator> void insert(Iterator, Iterator) ;
      iterator erase(iterator) ;
      iterator erase(iterator, iterator) ;
      size_type erase(const_reference) ;
      template<typename KeyType, typename KeyValueCompare>
        size_type erase(const KeyType &, KeyValueCompare) ;
      template<typename Disposer> iterator erase_and_dispose(iterator, Disposer) ;
      template<typename Disposer>
        iterator erase_and_dispose(iterator, iterator, Disposer) ;
      template<typename Disposer>
        size_type erase_and_dispose(const_reference, Disposer) ;
      template<typename KeyType, typename KeyValueCompare, typename Disposer>
        size_type erase_and_dispose(const KeyType &, KeyValueCompare, Disposer) ;
      void clear() ;
      template<typename Disposer> void clear_and_dispose(Disposer) ;
      size_type count(const_reference) const;
      template<typename KeyType, typename KeyValueCompare>
        size_type count(const KeyType &, KeyValueCompare) const;
      iterator lower_bound(const_reference) ;
      template<typename KeyType, typename KeyValueCompare>
        iterator lower_bound(const KeyType &, KeyValueCompare) ;
      const_iterator lower_bound(const_reference) const;
      template<typename KeyType, typename KeyValueCompare>
        const_iterator lower_bound(const KeyType &, KeyValueCompare) const;
      iterator upper_bound(const_reference) ;
      template<typename KeyType, typename KeyValueCompare>
        iterator upper_bound(const KeyType &, KeyValueCompare) ;
      const_iterator upper_bound(const_reference) const;
      template<typename KeyType, typename KeyValueCompare>
        const_iterator upper_bound(const KeyType &, KeyValueCompare) const;
      iterator find(const_reference) ;
      template<typename KeyType, typename KeyValueCompare>
        iterator find(const KeyType &, KeyValueCompare) ;
      const_iterator find(const_reference) const;
      template<typename KeyType, typename KeyValueCompare>
        const_iterator find(const KeyType &, KeyValueCompare) const;
      std::pair< iterator, iterator > equal_range(const_reference) ;
      template<typename KeyType, typename KeyValueCompare>
        std::pair< iterator, iterator >
        equal_range(const KeyType &, KeyValueCompare) ;
      std::pair< const_iterator, const_iterator >
      equal_range(const_reference) const;
      template<typename KeyType, typename KeyValueCompare>
        std::pair< const_iterator, const_iterator >
        equal_range(const KeyType &, KeyValueCompare) const;
      iterator iterator_to(reference) ;
      const_iterator iterator_to(const_reference) const;
      pointer unlink_leftmost_without_rebalance() ;
      void replace_node(iterator, reference) ;
      void rebalance() ;
      iterator rebalance_subtree(iterator) ;
      float balance_factor() const;
      void balance_factor(float) ;

      // public static functions
      static sg_multiset & container_from_end_iterator(iterator) ;
      static const sg_multiset & container_from_end_iterator(const_iterator) ;
      static sg_multiset & container_from_iterator(iterator) ;
      static const sg_multiset & container_from_iterator(const_iterator) ;
      static iterator s_iterator_to(reference) ;
      static const_iterator s_iterator_to(const_reference) ;
      static void init_node(reference) ;
    };

## Description

The class template sg_multiset is an intrusive container, that mimics most of the interface of std::sg_multiset as described in the C++ standard.

The template parameter `T` is the type to be managed by the container. The user can specify additional options and if no options are provided default options are used.

The container supports the following options: `base_hook<>/member_hook<>/value_traits<>`, `constant_time_size<>`, `size_type<>` and `compare<>`.

### `sg_multiset` public construct/copy/destruct

1.     sg_multiset(const value_compare & cmp = value_compare(),
                   const value_traits & v_traits = value_traits());

   Effects: Constructs an empty sg_multiset.

   Complexity: Constant.

   Throws: If value_traits::node_traits::node constructor throws (this does not happen with predefined Boost.Intrusive hooks) or the copy constructor/operator() of the value_compare object throws.

2.     template<typename Iterator>
         sg_multiset(Iterator b, Iterator e,
                     const value_compare & cmp = value_compare(),
                     const value_traits & v_traits = value_traits());

   Requires: Dereferencing iterator must yield an lvalue of type value_type. cmp must be a comparison function that induces a strict weak ordering.

   Effects: Constructs an empty sg_multiset and inserts elements from [b, e).

   Complexity: Linear in N if [b, e) is already sorted using comp and otherwise N * log N, where N is the distance between first and last

   Throws: If value_traits::node_traits::node constructor throws (this does not happen with predefined Boost.Intrusive hooks) or the copy constructor/operator() of the value_compare object throws.

3.     ~sg_multiset();

   Effects: Detaches all elements from this. The objects in the sg_multiset are not deleted (i.e. no destructors are called).

   Complexity: Linear to the number of elements on the container. if it's a safe-mode or auto-unlink value_type. Constant time otherwise.

   Throws: Nothing.

### `sg_multiset` public member functions

1.     iterator begin() ;

   Effects: Returns an iterator pointing to the beginning of the sg_multiset.

   Complexity: Constant.

   Throws: Nothing.

2.     const_iterator begin() const;

   Effects: Returns a const_iterator pointing to the beginning of the sg_multiset.

   Complexity: Constant.

   Throws: Nothing.

3.     const_iterator cbegin() const;

   Effects: Returns a const_iterator pointing to the beginning of the sg_multiset.

   Complexity: Constant.

   Throws: Nothing.

4.     iterator end() ;

   Effects: Returns an iterator pointing to the end of the sg_multiset.

   Complexity: Constant.

   Throws: Nothing.

5.     const_iterator end() const;

   Effects: Returns a const_iterator pointing to the end of the sg_multiset.

   Complexity: Constant.

   Throws: Nothing.

6.     const_iterator cend() const;

   Effects: Returns a const_iterator pointing to the end of the sg_multiset.

   Complexity: Constant.

   Throws: Nothing.

7.     reverse_iterator rbegin() ;

   Effects: Returns a reverse_iterator pointing to the beginning of the reversed sg_multiset.

   Complexity: Constant.

   Throws: Nothing.

8.     const_reverse_iterator rbegin() const;

   Effects: Returns a const_reverse_iterator pointing to the beginning of the reversed sg_multiset.

   Complexity: Constant.

   Throws: Nothing.

9.     const_reverse_iterator crbegin() const;

   Effects: Returns a const_reverse_iterator pointing to the beginning of the reversed sg_multiset.

   Complexity: Constant.

   Throws: Nothing.

10.     reverse_iterator rend() ;

    Effects: Returns a reverse_iterator pointing to the end of the reversed sg_multiset.

    Complexity: Constant.

    Throws: Nothing.

11.     const_reverse_iterator rend() const;

    Effects: Returns a const_reverse_iterator pointing to the end of the reversed sg_multiset.

    Complexity: Constant.

    Throws: Nothing.

12.     const_reverse_iterator crend() const;

    Effects: Returns a const_reverse_iterator pointing to the end of the reversed sg_multiset.

    Complexity: Constant.

    Throws: Nothing.

13.     key_compare key_comp() const;

    Effects: Returns the key_compare object used by the sg_multiset.

    Complexity: Constant.

    Throws: If key_compare copy-constructor throws.

14.     value_compare value_comp() const;

    Effects: Returns the value_compare object used by the sg_multiset.

    Complexity: Constant.

    Throws: If value_compare copy-constructor throws.

15.     bool empty() const;

    Effects: Returns true is the container is empty.

    Complexity: Constant.

    Throws: Nothing.

16.     size_type size() const;

    Effects: Returns the number of elements stored in the sg_multiset.

    Complexity: Linear to elements contained in *this if, constant-time size option is enabled. Constant-time otherwise.

    Throws: Nothing.

17.     void swap(sg_multiset & other) ;

    Effects: Swaps the contents of two sg_multisets.

    Complexity: Constant.

    Throws: If the swap() call for the comparison functor found using ADL throws. Strong guarantee.

18.     template<typename Cloner, typename Disposer>
          void clone_from(const sg_multiset & src, Cloner cloner, Disposer disposer) ;

    Requires: Disposer::operator()(pointer) shouldn't throw. Cloner should yield to nodes equivalent to the original nodes.

    Effects: Erases all the elements from *this calling Disposer::operator()(pointer), clones all the elements from src calling Cloner::operator()(const_reference ) and inserts them on *this. Copies the predicate from the source container.

    If cloner throws, all cloned elements are unlinked and disposed calling Disposer::operator()(pointer).

    Complexity: Linear to erased plus inserted elements.

    Throws: If cloner throws or predicate copy assignment throws. Basic guarantee.

19.     iterator insert(reference value) ;

    Requires: value must be an lvalue

    Effects: Inserts value into the sg_multiset.

    Returns: An iterator that points to the position where the new element was inserted.

    Complexity: Average complexity for insert element is at most logarithmic.

    Throws: If the internal value_compare ordering function throws. Strong guarantee.

    Note: Does not affect the validity of iterators and references. No copy-constructors are called.

20.     iterator insert(const_iterator hint, reference value) ;

    Requires: value must be an lvalue

    Effects: Inserts x into the sg_multiset, using pos as a hint to where it will be inserted.

    Returns: An iterator that points to the position where the new element was inserted.

    Complexity: Logarithmic in general, but it is amortized constant time if t is inserted immediately before hint.

    Throws: If the internal value_compare ordering function throws. Strong guarantee.

    Note: Does not affect the validity of iterators and references. No copy-constructors are called.

21.     template<typename Iterator> void insert(Iterator b, Iterator e) ;

    Requires: Dereferencing iterator must yield an lvalue of type value_type.

    Effects: Inserts a range into the sg_multiset.

    Returns: An iterator that points to the position where the new element was inserted.

    Complexity: Insert range is in general O(N * log(N)), where N is the size of the range. However, it is linear in N if the range is already sorted by value_comp().

    Throws: If the internal value_compare ordering function throws. Basic guarantee.

    Note: Does not affect the validity of iterators and references. No copy-constructors are called.

22.     iterator erase(iterator i) ;

    Effects: Erases the element pointed to by pos.

    Complexity: Average complexity is constant time.

    Returns: An iterator to the element after the erased element.

    Throws: Nothing.

    Note: Invalidates the iterators (but not the references) to the erased elements. No destructors are called.

23.     iterator erase(iterator b, iterator e) ;

    Effects: Erases the range pointed to by b end e.

    Returns: An iterator to the element after the erased elements.

    Complexity: Average complexity for erase range is at most O(log(size() + N)), where N is the number of elements in the range.

    Throws: Nothing.

    Note: Invalidates the iterators (but not the references) to the erased elements. No destructors are called.

24.     size_type erase(const_reference value) ;

    Effects: Erases all the elements with the given value.

    Returns: The number of erased elements.

    Complexity: O(log(size() + this->count(value)).

    Throws: If the internal value_compare ordering function throws. Basic guarantee.

    Note: Invalidates the iterators (but not the references) to the erased elements. No destructors are called.

25.     template<typename KeyType, typename KeyValueCompare>
          size_type erase(const KeyType & key, KeyValueCompare comp) ;

    Effects: Erases all the elements that compare equal with the given key and the given comparison functor.

    Returns: The number of erased elements.

    Complexity: O(log(size() + this->count(key, comp)).

    Throws: If comp ordering function throws. Basic guarantee.

    Note: Invalidates the iterators (but not the references) to the erased elements. No destructors are called.

26.     template<typename Disposer>
          iterator erase_and_dispose(iterator i, Disposer disposer) ;

    Requires: Disposer::operator()(pointer) shouldn't throw.

    Returns: An iterator to the element after the erased element.

    Effects: Erases the element pointed to by pos. Disposer::operator()(pointer) is called for the removed element.

    Complexity: Average complexity for erase element is constant time.

    Throws: Nothing.

    Note: Invalidates the iterators to the erased elements.

27.     template<typename Disposer>
          iterator erase_and_dispose(iterator b, iterator e, Disposer disposer) ;

    Requires: Disposer::operator()(pointer) shouldn't throw.

    Returns: An iterator to the element after the erased elements.

    Effects: Erases the range pointed to by b end e. Disposer::operator()(pointer) is called for the removed elements.

    Complexity: Average complexity for erase range is at most O(log(size() + N)), where N is the number of elements in the range.

    Throws: Nothing.

    Note: Invalidates the iterators to the erased elements.

28.     template<typename Disposer>
          size_type erase_and_dispose(const_reference value, Disposer disposer) ;

    Requires: Disposer::operator()(pointer) shouldn't throw.

    Effects: Erases all the elements with the given value. Disposer::operator()(pointer) is called for the removed elements.

    Returns: The number of erased elements.

    Complexity: O(log(size() + this->count(value)).

    Throws: If the internal value_compare ordering function throws. Basic guarantee.

    Note: Invalidates the iterators (but not the references) to the erased elements. No destructors are called.

29.     template<typename KeyType, typename KeyValueCompare, typename Disposer>
          size_type erase_and_dispose(const KeyType & key, KeyValueCompare comp,
                                      Disposer disposer) ;

    Requires: Disposer::operator()(pointer) shouldn't throw.

    Effects: Erases all the elements with the given key. according to the comparison functor "comp". Disposer::operator()(pointer) is called for the removed elements.

    Returns: The number of erased elements.

    Complexity: O(log(size() + this->count(key, comp)).

    Throws: If comp ordering function throws. Basic guarantee.

    Note: Invalidates the iterators to the erased elements.

30.     void clear() ;

    Effects: Erases all the elements of the container.

    Complexity: Linear to the number of elements on the container. if it's a safe-mode or auto-unlink value_type. Constant time otherwise.

    Throws: Nothing.

    Note: Invalidates the iterators (but not the references) to the erased elements. No destructors are called.

31.     template<typename Disposer> void clear_and_dispose(Disposer disposer) ;

    Requires: Disposer::operator()(pointer) shouldn't throw.

    Effects: Erases all the elements of the container.

    Complexity: Linear to the number of elements on the container. Disposer::operator()(pointer) is called for the removed elements.

    Throws: Nothing.

    Note: Invalidates the iterators (but not the references) to the erased elements. No destructors are called.

32.     size_type count(const_reference value) const;

    Effects: Returns the number of contained elements with the given key

    Complexity: Logarithmic to the number of elements contained plus lineal to number of objects with the given key.

    Throws: If the internal value_compare ordering function throws.

33.     template<typename KeyType, typename KeyValueCompare>
          size_type count(const KeyType & key, KeyValueCompare comp) const;

    Effects: Returns the number of contained elements with the same key compared with the given comparison functor.

    Complexity: Logarithmic to the number of elements contained plus lineal to number of objects with the given key.

    Throws: If comp ordering function throws.

34.     iterator lower_bound(const_reference value) ;

    Effects: Returns an iterator to the first element whose key is not less than k or end() if that element does not exist.

    Complexity: Logarithmic.

    Throws: If the internal value_compare ordering function throws.

35.     template<typename KeyType, typename KeyValueCompare>
          iterator lower_bound(const KeyType & key, KeyValueCompare comp) ;

    Requires: comp must imply the same element order as value_compare. Usually key is the part of the value_type that is used in the ordering functor.

    Effects: Returns an iterator to the first element whose key according to the comparison functor is not less than k or end() if that element does not exist.

    Complexity: Logarithmic.

    Throws: If comp ordering function throws.

    Note: This function is used when constructing a value_type is expensive and the value_type can be compared with a cheaper key type. Usually this key is part of the value_type.

36.     const_iterator lower_bound(const_reference value) const;

    Effects: Returns a const iterator to the first element whose key is not less than k or end() if that element does not exist.

    Complexity: Logarithmic.

    Throws: If the internal value_compare ordering function throws.

37.     template<typename KeyType, typename KeyValueCompare>
          const_iterator lower_bound(const KeyType & key, KeyValueCompare comp) const;

    Requires: comp must imply the same element order as value_compare. Usually key is the part of the value_type that is used in the ordering functor.

    Effects: Returns a const_iterator to the first element whose key according to the comparison functor is not less than k or end() if that element does not exist.

    Complexity: Logarithmic.

    Throws: If comp ordering function throws.

    Note: This function is used when constructing a value_type is expensive and the value_type can be compared with a cheaper key type. Usually this key is part of the value_type.

38.     iterator upper_bound(const_reference value) ;

    Effects: Returns an iterator to the first element whose key is greater than k or end() if that element does not exist.

    Complexity: Logarithmic.

    Throws: If the internal value_compare ordering function throws.

39.     template<typename KeyType, typename KeyValueCompare>
          iterator upper_bound(const KeyType & key, KeyValueCompare comp) ;

    Requires: comp must imply the same element order as value_compare. Usually key is the part of the value_type that is used in the ordering functor.

    Effects: Returns an iterator to the first element whose key according to the comparison functor is greater than key or end() if that element does not exist.

    Complexity: Logarithmic.

    Throws: If comp ordering function throws.

    Note: This function is used when constructing a value_type is expensive and the value_type can be compared with a cheaper key type. Usually this key is part of the value_type.

40.     const_iterator upper_bound(const_reference value) const;

    Effects: Returns an iterator to the first element whose key is greater than k or end() if that element does not exist.

    Complexity: Logarithmic.

    Throws: If the internal value_compare ordering function throws.

41.     template<typename KeyType, typename KeyValueCompare>
          const_iterator upper_bound(const KeyType & key, KeyValueCompare comp) const;

    Requires: comp must imply the same element order as value_compare. Usually key is the part of the value_type that is used in the ordering functor.

    Effects: Returns a const_iterator to the first element whose key according to the comparison functor is greater than key or end() if that element does not exist.

    Complexity: Logarithmic.

    Throws: If comp ordering function throws.

    Note: This function is used when constructing a value_type is expensive and the value_type can be compared with a cheaper key type. Usually this key is part of the value_type.

42.     iterator find(const_reference value) ;

    Effects: Finds an iterator to the first element whose value is "value" or end() if that element does not exist.

    Complexity: Logarithmic.

    Throws: If the internal value_compare ordering function throws.

43.     template<typename KeyType, typename KeyValueCompare>
          iterator find(const KeyType & key, KeyValueCompare comp) ;

    Requires: comp must imply the same element order as value_compare. Usually key is the part of the value_type that is used in the ordering functor.

    Effects: Finds an iterator to the first element whose key is "key" according to the comparison functor or end() if that element does not exist.

    Complexity: Logarithmic.

    Throws: If comp ordering function throws.

    Note: This function is used when constructing a value_type is expensive and the value_type can be compared with a cheaper key type. Usually this key is part of the value_type.

44.     const_iterator find(const_reference value) const;

    Effects: Finds a const_iterator to the first element whose value is "value" or end() if that element does not exist.

    Complexity: Logarithmic.

    Throws: If the internal value_compare ordering function throws.

45.     template<typename KeyType, typename KeyValueCompare>
          const_iterator find(const KeyType & key, KeyValueCompare comp) const;

    Requires: comp must imply the same element order as value_compare. Usually key is the part of the value_type that is used in the ordering functor.

    Effects: Finds a const_iterator to the first element whose key is "key" according to the comparison functor or end() if that element does not exist.

    Complexity: Logarithmic.

    Throws: If comp ordering function throws.

    Note: This function is used when constructing a value_type is expensive and the value_type can be compared with a cheaper key type. Usually this key is part of the value_type.

46.     std::pair< iterator, iterator > equal_range(const_reference value) ;

    Effects: Finds a range containing all elements whose key is k or an empty range that indicates the position where those elements would be if they there is no elements with key k.

    Complexity: Logarithmic.

    Throws: If the internal value_compare ordering function throws.

47.     template<typename KeyType, typename KeyValueCompare>
          std::pair< iterator, iterator >
          equal_range(const KeyType & key, KeyValueCompare comp) ;

    Requires: comp must imply the same element order as value_compare. Usually key is the part of the value_type that is used in the ordering functor.

    Effects: Finds a range containing all elements whose key is k according to the comparison functor or an empty range that indicates the position where those elements would be if they there is no elements with key k.

    Complexity: Logarithmic.

    Throws: If comp ordering function throws.

    Note: This function is used when constructing a value_type is expensive and the value_type can be compared with a cheaper key type. Usually this key is part of the value_type.

48.     std::pair< const_iterator, const_iterator >
        equal_range(const_reference value) const;

    Effects: Finds a range containing all elements whose key is k or an empty range that indicates the position where those elements would be if they there is no elements with key k.

    Complexity: Logarithmic.

    Throws: If the internal value_compare ordering function throws.

49.     template<typename KeyType, typename KeyValueCompare>
          std::pair< const_iterator, const_iterator >
          equal_range(const KeyType & key, KeyValueCompare comp) const;

    Requires: comp must imply the same element order as value_compare. Usually key is the part of the value_type that is used in the ordering functor.

    Effects: Finds a range containing all elements whose key is k according to the comparison functor or an empty range that indicates the position where those elements would be if they there is no elements with key k.

    Complexity: Logarithmic.

    Throws: If comp ordering function throws.

    Note: This function is used when constructing a value_type is expensive and the value_type can be compared with a cheaper key type. Usually this key is part of the value_type.

50.     iterator iterator_to(reference value) ;

    Requires: value must be an lvalue and shall be in a sg_multiset of appropriate type. Otherwise the behavior is undefined.

    Effects: Returns: a valid iterator i belonging to the sg_multiset that points to the value

    Complexity: Constant.

    Throws: Nothing.

51.     const_iterator iterator_to(const_reference value) const;

    Requires: value must be an lvalue and shall be in a sg_multiset of appropriate type. Otherwise the behavior is undefined.

    Effects: Returns: a valid const_iterator i belonging to the sg_multiset that points to the value

    Complexity: Constant.

    Throws: Nothing.

52.     pointer unlink_leftmost_without_rebalance() ;

    Effects: Unlinks the leftmost node from the tree.

    Complexity: Average complexity is constant time.

    Throws: Nothing.

    Notes: This function breaks the tree and the tree can only be used for more unlink_leftmost_without_rebalance calls. This function is normally used to achieve a step by step controlled destruction of the tree.

53.     void replace_node(iterator replace_this, reference with_this) ;

    Requires: replace_this must be a valid iterator of *this and with_this must not be inserted in any tree.

    Effects: Replaces replace_this in its position in the tree with with_this. The tree does not need to be rebalanced.

    Complexity: Constant.

    Throws: Nothing.

    Note: This function will break container ordering invariants if with_this is not equivalent to *replace_this according to the ordering rules. This function is faster than erasing and inserting the node, since no rebalancing or comparison is needed.

54.     void rebalance() ;

    Effects: Rebalances the tree.

    Throws: Nothing.

    Complexity: Linear.

55.     iterator rebalance_subtree(iterator root) ;

    Requires: old_root is a node of a tree.

    Effects: Rebalances the subtree rooted at old_root.

    Returns: The new root of the subtree.

    Throws: Nothing.

    Complexity: Linear to the elements in the subtree.

56.     float balance_factor() const;

    Returns: The balance factor (alpha) used in this tree

    Throws: Nothing.

    Complexity: Constant.

57.     void balance_factor(float new_alpha) ;

    Requires: new_alpha must be a value between 0.5 and 1.0

    Effects: Establishes a new balance factor (alpha) and rebalances the tree if the new balance factor is stricter (less) than the old factor.

    Throws: Nothing.

    Complexity: Linear to the elements in the subtree.

### `sg_multiset` public static functions

1.     static sg_multiset & container_from_end_iterator(iterator end_iterator) ;

   Precondition: end_iterator must be a valid end iterator of sg_multiset.

   Effects: Returns a const reference to the sg_multiset associated to the end iterator

   Throws: Nothing.

   Complexity: Constant.

2.     static const sg_multiset &
       container_from_end_iterator(const_iterator end_iterator) ;

   Precondition: end_iterator must be a valid end const_iterator of sg_multiset.

   Effects: Returns a const reference to the sg_multiset associated to the end iterator

   Throws: Nothing.

   Complexity: Constant.

3.     static sg_multiset & container_from_iterator(iterator it) ;

   Precondition: it must be a valid iterator of multiset.

   Effects: Returns a const reference to the multiset associated to the iterator

   Throws: Nothing.

   Complexity: Constant.

4.     static const sg_multiset & container_from_iterator(const_iterator it) ;

   Precondition: it must be a valid const_iterator of multiset.

   Effects: Returns a const reference to the multiset associated to the iterator

   Throws: Nothing.

   Complexity: Constant.

5.     static iterator s_iterator_to(reference value) ;

   Requires: value must be an lvalue and shall be in a sg_multiset of appropriate type. Otherwise the behavior is undefined.

   Effects: Returns: a valid iterator i belonging to the sg_multiset that points to the value

   Complexity: Constant.

   Throws: Nothing.

   Note: This static function is available only if the value traits is stateless.

6.     static const_iterator s_iterator_to(const_reference value) ;

   Requires: value must be an lvalue and shall be in a sg_multiset of appropriate type. Otherwise the behavior is undefined.

   Effects: Returns: a valid const_iterator i belonging to the sg_multiset that points to the value

   Complexity: Constant.

   Throws: Nothing.

   Note: This static function is available only if the value traits is stateless.

7.     static void init_node(reference value) ;

   Requires: value shall not be in a sg_multiset/sg_multiset.

   Effects: init_node puts the hook of a value in a well-known default state.

   Throws: Nothing.

   Complexity: Constant time.

   Note: This function puts the hook in the well-known default state used by auto_unlink and safe hooks.