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## Class template sgtree

boost::intrusive::sgtree

## Synopsis

    // In header: <boost/intrusive/sgtree.hpp>

    template<typename T, class... Options>
    class sgtree {
    public:
      // types
      typedef Config::value_traits                                  value_traits;
      typedef real_value_traits::pointer                            pointer;
      typedef real_value_traits::const_pointer                      const_pointer;
      typedef std::iterator_traits< pointer >::value_type           value_type;
      typedef value_type                                            key_type;
      typedef std::iterator_traits< pointer >::reference            reference;
      typedef std::iterator_traits< const_pointer >::reference      const_reference;
      typedef std::iterator_traits< pointer >::difference_type      difference_type;
      typedef Config::size_type                                     size_type;
      typedef Config::compare                                       value_compare;
      typedef value_compare                                         key_compare;
      typedef tree_iterator< sgtree, false >                        iterator;
      typedef tree_iterator< sgtree, true >                         const_iterator;
      typedef std::reverse_iterator< iterator >                     reverse_iterator;
      typedef std::reverse_iterator< const_iterator >               const_reverse_iterator;
      typedef real_value_traits::node_traits                        node_traits;
      typedef node_traits::node                                     node;
      typedef boost::pointer_to_other< pointer, node >::type        node_ptr;
      typedef boost::pointer_to_other< node_ptr, const node >::type const_node_ptr;
      typedef sgtree_algorithms< node_traits >                      node_algorithms;
      typedef node_algorithms::insert_commit_data                   insert_commit_data;

      // construct/copy/destruct
      sgtree(const value_compare & = value_compare(),
             const value_traits & = value_traits());
      template<typename Iterator>
        sgtree(bool, Iterator, Iterator, const value_compare & = value_compare(),
               const value_traits & = value_traits());
      sgtree(BOOST_RV_REF(sgtree));
      sgtree& operator=(BOOST_RV_REF(sgtree));
      ~sgtree();

      // public member functions
      const real_value_traits & get_real_value_traits() const;
      real_value_traits & get_real_value_traits();
      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;
      value_compare value_comp() const;
      bool empty() const;
      size_type size() const;
      void swap(sgtree &);
      iterator insert_equal(reference);
      iterator insert_equal(const_iterator, reference);
      template<typename Iterator> void insert_equal(Iterator, Iterator);
      std::pair< iterator, bool > insert_unique(reference);
      iterator insert_unique(const_iterator, reference);
      template<typename Iterator> void insert_unique(Iterator, Iterator);
      template<typename KeyType, typename KeyValueCompare>
        std::pair< iterator, bool >
        insert_unique_check(const KeyType &, KeyValueCompare,
                            insert_commit_data &);
      template<typename KeyType, typename KeyValueCompare>
        std::pair< iterator, bool >
        insert_unique_check(const_iterator, const KeyType &, KeyValueCompare,
                            insert_commit_data &);
      iterator insert_unique_commit(reference, const insert_commit_data &);
      iterator insert_before(const_iterator, reference);
      void push_back(reference);
      void push_front(reference);
      iterator erase(const_iterator);
      iterator erase(const_iterator, const_iterator);
      size_type erase(const_reference);
      template<typename KeyType, typename KeyValueCompare>
        size_type erase(const KeyType &, KeyValueCompare);
      template<typename Disposer>
        iterator erase_and_dispose(const_iterator, Disposer);
      template<typename Disposer>
        iterator erase_and_dispose(const_iterator, const_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);
      const_iterator lower_bound(const_reference) const;
      template<typename KeyType, typename KeyValueCompare>
        iterator lower_bound(const KeyType &, KeyValueCompare);
      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;
      template<typename Cloner, typename Disposer>
        void clone_from(const sgtree &, Cloner, Disposer);
      pointer unlink_leftmost_without_rebalance();
      void replace_node(iterator, reference);
      iterator iterator_to(reference);
      const_iterator iterator_to(const_reference) const;
      void rebalance();
      iterator rebalance_subtree(iterator);
      float balance_factor() const;
      void balance_factor(float);

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

      // private static functions
      static sgtree & priv_container_from_end_iterator(const const_iterator &);
      static sgtree & priv_container_from_iterator(const const_iterator &);

      // public data members
      static const bool floating_point;
      static const bool constant_time_size;
      static const bool stateful_value_traits;
    };

## Description

The class template sgtree is an intrusive scapegoat tree container, that is used to construct intrusive sg_set and sg_multiset containers. The no-throw guarantee holds only, if the value_compare object doesn't throw.

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<>`, `floating_point<>`, `size_type<>` and `compare<>`.

### `sgtree` public construct/copy/destruct

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

   Effects: Constructs an empty tree.

   Complexity: Constant.

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

2.     template<typename Iterator>
         sgtree(bool unique, 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 tree 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. Basic guarantee.

3.     sgtree(BOOST_RV_REF(sgtree) x);

   Effects: to-do

4.     sgtree& operator=(BOOST_RV_REF(sgtree) x);

   Effects: to-do

5.     ~sgtree();

   Effects: Detaches all elements from this. The objects in the set are not deleted (i.e. no destructors are called), but the nodes according to the `value_traits` template parameter are reinitialized and thus can be reused.

   Complexity: Linear to elements contained in *this.

   Throws: Nothing.

### `sgtree` public member functions

1.     const real_value_traits & get_real_value_traits() const;

2.     real_value_traits & get_real_value_traits();

3.     iterator begin();

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

   Complexity: Constant.

   Throws: Nothing.

4.     const_iterator begin() const;

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

   Complexity: Constant.

   Throws: Nothing.

5.     const_iterator cbegin() const;

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

   Complexity: Constant.

   Throws: Nothing.

6.     iterator end();

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

   Complexity: Constant.

   Throws: Nothing.

7.     const_iterator end() const;

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

   Complexity: Constant.

   Throws: Nothing.

8.     const_iterator cend() const;

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

   Complexity: Constant.

   Throws: Nothing.

9.     reverse_iterator rbegin();

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

   Complexity: Constant.

   Throws: Nothing.

10.     const_reverse_iterator rbegin() const;

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

    Complexity: Constant.

    Throws: Nothing.

11.     const_reverse_iterator crbegin() const;

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

    Complexity: Constant.

    Throws: Nothing.

12.     reverse_iterator rend();

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

    Complexity: Constant.

    Throws: Nothing.

13.     const_reverse_iterator rend() const;

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

    Complexity: Constant.

    Throws: Nothing.

14.     const_reverse_iterator crend() const;

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

    Complexity: Constant.

    Throws: Nothing.

15.     value_compare value_comp() const;

    Effects: Returns the value_compare object used by the tree.

    Complexity: Constant.

    Throws: If value_compare copy-constructor throws.

16.     bool empty() const;

    Effects: Returns true if the container is empty.

    Complexity: Constant.

    Throws: Nothing.

17.     size_type size() const;

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

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

    Throws: Nothing.

18.     void swap(sgtree & other);

    Effects: Swaps the contents of two sgtrees.

    Complexity: Constant.

    Throws: If the comparison functor's swap call throws.

19.     iterator insert_equal(reference value);

    Requires: value must be an lvalue

    Effects: Inserts value into the tree before the upper bound.

    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_equal(const_iterator hint, reference value);

    Requires: value must be an lvalue, and "hint" must be a valid iterator.

    Effects: Inserts x into the tree, using "hint" as a hint to where it will be inserted. If "hint" is the upper_bound the insertion takes constant time (two comparisons in the worst case)

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

    Throws: Nothing.

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

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

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

    Effects: Inserts a each element of a range into the tree before the upper bound of the key of each element.

    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: Nothing.

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

22.     std::pair< iterator, bool > insert_unique(reference value);

    Requires: value must be an lvalue

    Effects: Inserts value into the tree if the value is not already present.

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

    Throws: Nothing.

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

23.     iterator insert_unique(const_iterator hint, reference value);

    Requires: value must be an lvalue, and "hint" must be a valid iterator

    Effects: Tries to insert x into the tree, using "hint" as a hint to where it will be inserted.

    Complexity: Logarithmic in general, but it is amortized constant time (two comparisons in the worst case) if t is inserted immediately before hint.

    Throws: Nothing.

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

24.     template<typename Iterator> void insert_unique(Iterator b, Iterator e);

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

    Effects: Tries to insert each element of a range into the tree.

    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: Nothing.

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

25.     template<typename KeyType, typename KeyValueCompare>
          std::pair< iterator, bool >
          insert_unique_check(const KeyType & key, KeyValueCompare key_value_comp,
                              insert_commit_data & commit_data);

    Requires: key_value_comp must be a comparison function that induces the same strict weak ordering as value_compare. The difference is that key_value_comp compares an arbitrary key with the contained values.

    Effects: Checks if a value can be inserted in the container, using a user provided key instead of the value itself.

    Returns: If there is an equivalent value returns a pair containing an iterator to the already present value and false. If the value can be inserted returns true in the returned pair boolean and fills "commit_data" that is meant to be used with the "insert_commit" function.

    Complexity: Average complexity is at most logarithmic.

    Throws: If the key_value_comp ordering function throws. Strong guarantee.

    Notes: This function is used to improve performance when constructing a value_type is expensive: if there is an equivalent value the constructed object must be discarded. Many times, the part of the node that is used to impose the order is much cheaper to construct than the value_type and this function offers the possibility to use that part to check if the insertion will be successful.

    If the check is successful, the user can construct the value_type and use "insert_commit" to insert the object in constant-time. This gives a total logarithmic complexity to the insertion: check(O(log(N)) + commit(O(1)).

    "commit_data" remains valid for a subsequent "insert_commit" only if no more objects are inserted or erased from the container.

26.     template<typename KeyType, typename KeyValueCompare>
          std::pair< iterator, bool >
          insert_unique_check(const_iterator hint, const KeyType & key,
                              KeyValueCompare key_value_comp,
                              insert_commit_data & commit_data);

    Requires: key_value_comp must be a comparison function that induces the same strict weak ordering as value_compare. The difference is that key_value_comp compares an arbitrary key with the contained values.

    Effects: Checks if a value can be inserted in the container, using a user provided key instead of the value itself, using "hint" as a hint to where it will be inserted.

    Returns: If there is an equivalent value returns a pair containing an iterator to the already present value and false. If the value can be inserted returns true in the returned pair boolean and fills "commit_data" that is meant to be used with the "insert_commit" function.

    Complexity: Logarithmic in general, but it's amortized constant time if t is inserted immediately before hint.

    Throws: If the key_value_comp ordering function throws. Strong guarantee.

    Notes: This function is used to improve performance when constructing a value_type is expensive: if there is an equivalent value the constructed object must be discarded. Many times, the part of the constructing that is used to impose the order is much cheaper to construct than the value_type and this function offers the possibility to use that key to check if the insertion will be successful.

    If the check is successful, the user can construct the value_type and use "insert_commit" to insert the object in constant-time. This can give a total constant-time complexity to the insertion: check(O(1)) + commit(O(1)).

    "commit_data" remains valid for a subsequent "insert_commit" only if no more objects are inserted or erased from the container.

27.     iterator insert_unique_commit(reference value,
                                      const insert_commit_data & commit_data);

    Requires: value must be an lvalue of type value_type. commit_data must have been obtained from a previous call to "insert_check". No objects should have been inserted or erased from the container between the "insert_check" that filled "commit_data" and the call to "insert_commit".

    Effects: Inserts the value in the `avl_set` using the information obtained from the "commit_data" that a previous "insert_check" filled.

    Returns: An iterator to the newly inserted object.

    Complexity: Constant time.

    Throws: Nothing.

    Notes: This function has only sense if a "insert_check" has been previously executed to fill "commit_data". No value should be inserted or erased between the "insert_check" and "insert_commit" calls.

28.     iterator insert_before(const_iterator pos, reference value);

    Requires: value must be an lvalue, "pos" must be a valid iterator (or end) and must be the succesor of value once inserted according to the predicate

    Effects: Inserts x into the tree before "pos".

    Complexity: Constant time.

    Throws: Nothing.

    Note: This function does not check preconditions so if "pos" is not the successor of "value" tree ordering invariant will be broken. This is a low-level function to be used only for performance reasons by advanced users.

29.     void push_back(reference value);

    Requires: value must be an lvalue, and it must be no less than the greatest inserted key

    Effects: Inserts x into the tree in the last position.

    Complexity: Constant time.

    Throws: Nothing.

    Note: This function does not check preconditions so if value is less than the greatest inserted key tree ordering invariant will be broken. This function is slightly more efficient than using "insert_before". This is a low-level function to be used only for performance reasons by advanced users.

30.     void push_front(reference value);

    Requires: value must be an lvalue, and it must be no greater than the minimum inserted key

    Effects: Inserts x into the tree in the first position.

    Complexity: Constant time.

    Throws: Nothing.

    Note: This function does not check preconditions so if value is greater than the minimum inserted key tree ordering invariant will be broken. This function is slightly more efficient than using "insert_before". This is a low-level function to be used only for performance reasons by advanced users.

31.     iterator erase(const_iterator i);

    Effects: Erases the element pointed to by pos.

    Complexity: Average complexity for erase element is constant time.

    Throws: Nothing.

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

32.     iterator erase(const_iterator b, const_iterator e);

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

    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.

33.     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() + N).

    Throws: Nothing.

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

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

    Effects: Erases all the elements with the given key. according to the comparison functor "comp".

    Returns: The number of erased elements.

    Complexity: O(log(size() + N).

    Throws: Nothing.

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

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

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

    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.

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

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

    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.

37.     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() + N).

    Throws: Nothing.

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

38.     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() + N).

    Throws: Nothing.

    Note: Invalidates the iterators to the erased elements.

39.     void clear();

    Effects: Erases all of the elements.

    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.

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

    Effects: Erases all of the elements calling disposer(p) for each node to be erased. Complexity: Average complexity for is at most O(log(size() + N)), where N is the number of elements in the container.

    Throws: Nothing.

    Note: Invalidates the iterators (but not the references) to the erased elements. Calls N times to disposer functor.

41.     size_type count(const_reference value) const;

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

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

    Throws: Nothing.

42.     template<typename KeyType, typename KeyValueCompare>
          size_type count(const KeyType & key, KeyValueCompare comp) 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: Nothing.

43.     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: Nothing.

44.     const_iterator lower_bound(const_reference value) const;

    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: Nothing.

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

    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: Nothing.

46.     template<typename KeyType, typename KeyValueCompare>
          const_iterator lower_bound(const KeyType & key, KeyValueCompare comp) 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: Nothing.

47.     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: Nothing.

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

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

    Complexity: Logarithmic.

    Throws: Nothing.

49.     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: Nothing.

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

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

    Complexity: Logarithmic.

    Throws: Nothing.

51.     iterator find(const_reference value);

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

    Complexity: Logarithmic.

    Throws: Nothing.

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

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

    Complexity: Logarithmic.

    Throws: Nothing.

53.     const_iterator find(const_reference value) const;

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

    Complexity: Logarithmic.

    Throws: Nothing.

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

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

    Complexity: Logarithmic.

    Throws: Nothing.

55.     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: Nothing.

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

    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: Nothing.

57.     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: Nothing.

58.     template<typename KeyType, typename KeyValueCompare>
          std::pair< const_iterator, const_iterator >
          equal_range(const KeyType & key, KeyValueCompare comp) 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: Nothing.

59.     template<typename Cloner, typename Disposer>
          void clone_from(const sgtree & 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.

60.     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.

61.     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.

62.     iterator iterator_to(reference value);

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

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

    Complexity: Constant.

    Throws: Nothing.

63.     const_iterator iterator_to(const_reference value) const;

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

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

    Complexity: Constant.

    Throws: Nothing.

64.     void rebalance();

    Effects: Rebalances the tree.

    Throws: Nothing.

    Complexity: Linear.

65.     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.

66.     float balance_factor() const;

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

    Throws: Nothing.

    Complexity: Constant.

67.     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.

### `sgtree` public static functions

1.     static sgtree & container_from_end_iterator(iterator end_iterator);

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

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

   Throws: Nothing.

   Complexity: Constant.

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

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

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

   Throws: Nothing.

   Complexity: Constant.

3.     static sgtree & container_from_iterator(iterator it);

   Precondition: it must be a valid iterator of rbtree.

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

   Throws: Nothing.

   Complexity: Logarithmic.

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

   Precondition: it must be a valid end const_iterator of rbtree.

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

   Throws: Nothing.

   Complexity: Logarithmic.

5.     static iterator s_iterator_to(reference value);

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

   Effects: Returns: a valid iterator i belonging to the set 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 set of appropriate type. Otherwise the behavior is undefined.

   Effects: Returns: a valid const_iterator i belonging to the set 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 tree.

   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.

### `sgtree` private static functions

1.     static sgtree &
       priv_container_from_end_iterator(const const_iterator & end_iterator);

2.     static sgtree & priv_container_from_iterator(const const_iterator & it);