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## Class template treap_set

boost::intrusive::treap_set

## Synopsis

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

    template<typename T, class... Options>
    class treap_set {
    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::priority_compare       priority_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
      treap_set(const value_compare & = value_compare(),
                const priority_compare & = priority_compare(),
                const value_traits & = value_traits());
      template<typename Iterator>
        treap_set(Iterator, Iterator, const value_compare & = value_compare(),
                  const priority_compare & = priority_compare(),
                  const value_traits & = value_traits());
      ~treap_set();

      // public member functions
      iterator begin();
      const_iterator begin() const;
      const_iterator cbegin() const;
      iterator end();
      const_iterator end() const;
      iterator top();
      const_iterator top() const;
      const_iterator ctop() 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;
      reverse_iterator rtop();
      const_reverse_iterator rtop() const;
      const_reverse_iterator crtop() const;
      key_compare key_comp() const;
      value_compare value_comp() const;
      priority_compare priority_comp() const;
      bool empty() const;
      size_type size() const;
      void swap(treap_set &);
      template<typename Cloner, typename Disposer>
        void clone_from(const treap_set &, Cloner, Disposer);
      std::pair< iterator, bool > insert(reference);
      iterator insert(const_iterator, reference);
      template<typename KeyType, typename KeyValueCompare,
               typename KeyValuePriorityCompare>
        std::pair< iterator, bool >
        insert_check(const KeyType &, KeyValueCompare, KeyValuePriorityCompare,
                     insert_commit_data &);
      template<typename KeyType, typename KeyValueCompare,
               typename KeyValuePriorityCompare>
        std::pair< iterator, bool >
        insert_check(const_iterator, const KeyType &, KeyValueCompare,
                     KeyValuePriorityCompare, insert_commit_data &);
      iterator insert_commit(reference, const insert_commit_data &);
      template<typename Iterator> void insert(Iterator, Iterator);
      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);
      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 treap_set & container_from_end_iterator(iterator);
      static const treap_set & container_from_end_iterator(const_iterator);
      static treap_set & container_from_iterator(iterator);
      static const treap_set & 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 treap_set is an intrusive container, that mimics most of the interface of std::set 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<>`, `compare<>` and `priority_compare<>`

### `treap_set` public construct/copy/destruct

1.     treap_set(const value_compare & cmp = value_compare(),
                 const priority_compare & pcmp = priority_compare(),
                 const value_traits & v_traits = value_traits());

   Effects: Constructs an empty treap_set.

   Complexity: Constant.

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

2.     template<typename Iterator>
         treap_set(Iterator b, Iterator e,
                   const value_compare & cmp = value_compare(),
                   const priority_compare & pcmp = priority_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 treap_set 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 std::distance(last, first).

   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.     ~treap_set();

   Effects: Detaches all elements from this. The objects in the treap_set 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.

### `treap_set` public member functions

1.     iterator begin();

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

   Complexity: Constant.

   Throws: Nothing.

2.     const_iterator begin() const;

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

   Complexity: Constant.

   Throws: Nothing.

3.     const_iterator cbegin() const;

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

   Complexity: Constant.

   Throws: Nothing.

4.     iterator end();

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

   Complexity: Constant.

   Throws: Nothing.

5.     const_iterator end() const;

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

   Complexity: Constant.

   Throws: Nothing.

6.     iterator top();

   Effects: Returns an iterator pointing to the highest priority object of the tree.

   Complexity: Constant.

   Throws: Nothing.

7.     const_iterator top() const;

   Effects: Returns a const_iterator pointing to the highest priority object of the tree..

   Complexity: Constant.

   Throws: Nothing.

8.     const_iterator ctop() const;

   Effects: Returns a const_iterator pointing to the highest priority object of the tree..

   Complexity: Constant.

   Throws: Nothing.

9.     const_iterator cend() const;

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

   Complexity: Constant.

   Throws: Nothing.

10.     reverse_iterator rbegin();

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

    Complexity: Constant.

    Throws: Nothing.

11.     const_reverse_iterator rbegin() const;

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

    Complexity: Constant.

    Throws: Nothing.

12.     const_reverse_iterator crbegin() const;

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

    Complexity: Constant.

    Throws: Nothing.

13.     reverse_iterator rend();

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

    Complexity: Constant.

    Throws: Nothing.

14.     const_reverse_iterator rend() const;

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

    Complexity: Constant.

    Throws: Nothing.

15.     const_reverse_iterator crend() const;

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

    Complexity: Constant.

    Throws: Nothing.

16.     reverse_iterator rtop();

    Effects: Returns a reverse_iterator pointing to the highest priority object of the reversed tree.

    Complexity: Constant.

    Throws: Nothing.

17.     const_reverse_iterator rtop() const;

    Effects: Returns a const_reverse_iterator pointing to the highest priority objec of the reversed tree.

    Complexity: Constant.

    Throws: Nothing.

18.     const_reverse_iterator crtop() const;

    Effects: Returns a const_reverse_iterator pointing to the highest priority object of the reversed tree.

    Complexity: Constant.

    Throws: Nothing.

19.     key_compare key_comp() const;

    Effects: Returns the key_compare object used by the treap_set.

    Complexity: Constant.

    Throws: If key_compare copy-constructor throws.

20.     value_compare value_comp() const;

    Effects: Returns the value_compare object used by the treap_set.

    Complexity: Constant.

    Throws: If value_compare copy-constructor throws.

21.     priority_compare priority_comp() const;

    Effects: Returns the priority_compare object used by the treap_set.

    Complexity: Constant.

    Throws: If priority_compare copy-constructor throws.

22.     bool empty() const;

    Effects: Returns true if the container is empty.

    Complexity: Constant.

    Throws: Nothing.

23.     size_type size() const;

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

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

    Throws: Nothing.

24.     void swap(treap_set & other);

    Effects: Swaps the contents of two sets.

    Complexity: Constant.

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

25.     template<typename Cloner, typename Disposer>
          void clone_from(const treap_set & 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.

26.     std::pair< iterator, bool > insert(reference value);

    Requires: value must be an lvalue

    Effects: Tries to inserts value into the treap_set.

    Returns: If the value is not already present inserts it and returns a pair containing the iterator to the new value and true. If there is an equivalent value returns a pair containing an iterator to the already present value and false.

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

    Throws: If the internal value_compare or priority_compare ordering function throw. Strong guarantee.

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

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

    Requires: value must be an lvalue

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

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

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

    Throws: If the internal value_compare or priority_compare ordering functions throw. Strong guarantee.

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

28.     template<typename KeyType, typename KeyValueCompare,
                 typename KeyValuePriorityCompare>
          std::pair< iterator, bool >
          insert_check(const KeyType & key, KeyValueCompare key_value_comp,
                       KeyValuePriorityCompare key_value_pcomp,
                       insert_commit_data & commit_data);

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

    Effects: Checks if a value can be inserted in the treap_set, 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 key_value_comp or key_value_pcomp ordering function throw. 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 treap_set.

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

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

    Effects: Checks if a value can be inserted in the treap_set, 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 key_value_comp or key_value_pcomp ordering function throw. 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 treap_set.

30.     iterator insert_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 treap_set between the "insert_check" that filled "commit_data" and the call to "insert_commit".

    Effects: Inserts the value in the treap_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.

31.     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 treap_set.

    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 or priority_compare ordering function throw. Basic guarantee.

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

32.     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. "value" must not be equal to any inserted key according to the predicate.

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

    Complexity: Constant time.

    Throws: If the internal priority_compare function throws. Strong guarantee.

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

33.     void push_back(reference value);

    Requires: value must be an lvalue, and it must be greater than any inserted key according to the predicate.

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

    Complexity: Constant time.

    Throws: If the internal priority_compare function throws. Strong guarantee.

    Note: This function does not check preconditions so if value is less than the greatest inserted key treap 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.

34.     void push_front(reference value);

    Requires: value must be an lvalue, and it must be less than any inserted key according to the predicate.

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

    Complexity: Constant time.

    Throws: If the internal priority_compare function throws. Strong guarantee.

    Note: This function does not check preconditions so if value is greater than the minimum inserted key treap 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.

35.     iterator erase(const_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: If the internal priority_compare function throws. Strong guarantee.

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

36.     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.

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

    Throws: If the internal priority_compare function throws. Basic guarantee.

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

37.     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 internal value_compare or priority_compare ordering functions throw. Basic guarantee.

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

38.     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 or internal priority_compare ordering functions throw. Basic guarantee.

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

39.     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.

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

    Throws: If the internal priority_compare function throws. Strong guarantee.

    Note: Invalidates the iterators to the erased elements.

40.     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.

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

    Throws: If the internal priority_compare function throws. Basic guarantee.

    Note: Invalidates the iterators to the erased elements.

41.     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.

    Throws: If the internal value_compare ordering function throws.

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

    Throws: If the internal priority_compare function throws. Strong guarantee.

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

42.     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 or internal priority_compare ordering functions throw. Basic guarantee.

    Note: Invalidates the iterators to the erased elements.

43.     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.

44.     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.

45.     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.

46.     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.

47.     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.

48.     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.

49.     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.

50.     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.

51.     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.

52.     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.

53.     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.

54.     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.

55.     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.

56.     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.

57.     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.

58.     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.

59.     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.

60.     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.

61.     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.

62.     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.

63.     iterator iterator_to(reference value);

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

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

    Complexity: Constant.

    Throws: Nothing.

64.     const_iterator iterator_to(const_reference value) const;

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

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

    Complexity: Constant.

    Throws: Nothing.

65.     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.

66.     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.

67.     void rebalance();

    Effects: Rebalances the tree.

    Throws: Nothing.

    Complexity: Linear.

68.     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.

69.     float balance_factor() const;

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

    Throws: Nothing.

    Complexity: Constant.

70.     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.

### `treap_set` public static functions

1.     static treap_set & container_from_end_iterator(iterator end_iterator);

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

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

   Throws: Nothing.

   Complexity: Constant.

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

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

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

   Throws: Nothing.

   Complexity: Constant.

3.     static treap_set & container_from_iterator(iterator it);

   Precondition: it must be a valid iterator of set.

   Effects: Returns a reference to the set associated to the iterator

   Throws: Nothing.

   Complexity: Logarithmic.

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

   Precondition: it must be a valid const_iterator of set.

   Effects: Returns a const reference to the set 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 treap_set of appropriate type. Otherwise the behavior is undefined.

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

   Effects: Returns: a valid const_iterator i belonging to the treap_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 treap_set/treap_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.