LCOM1920-T02G10

// -*- C++ -*-

//===----------------------------------------------------------------------===//

//

//                     The LLVM Compiler Infrastructure

//

// This file is dual licensed under the MIT and the University of Illinois Open

// Source Licenses. See LICENSE.TXT for details.

//

//===----------------------------------------------------------------------===//

#ifndef _LIBCPP___TREE

#define _LIBCPP___TREE

#include <__config>

#include <iterator>

#include <memory>

#include <stdexcept>

#include <algorithm>

#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)

#pragma GCC system_header

#endif

_LIBCPP_BEGIN_NAMESPACE_STD

template <class _Tp, class _Compare, class _Allocator> class __tree;

template <class _Tp, class _NodePtr, class _DiffType>

    class _LIBCPP_TYPE_VIS_ONLY __tree_iterator;

template <class _Tp, class _ConstNodePtr, class _DiffType>

    class _LIBCPP_TYPE_VIS_ONLY __tree_const_iterator;

/*

_NodePtr algorithms

The algorithms taking _NodePtr are red black tree algorithms.  Those

algorithms taking a parameter named __root should assume that __root

points to a proper red black tree (unless otherwise specified).

Each algorithm herein assumes that __root->__parent_ points to a non-null

structure which has a member __left_ which points back to __root.  No other

member is read or written to at __root->__parent_.

__root->__parent_ will be referred to below (in comments only) as end_node.

end_node->__left_ is an externably accessible lvalue for __root, and can be

changed by node insertion and removal (without explicit reference to end_node).

All nodes (with the exception of end_node), even the node referred to as

__root, have a non-null __parent_ field.

*/

// Returns:  true if __x is a left child of its parent, else false

// Precondition:  __x != nullptr.

template <class _NodePtr>

inline _LIBCPP_INLINE_VISIBILITY

bool

__tree_is_left_child(_NodePtr __x) _NOEXCEPT

{

    return __x == __x->__parent_->__left_;

}

// Determintes if the subtree rooted at __x is a proper red black subtree.  If

//    __x is a proper subtree, returns the black height (null counts as 1).  If

//    __x is an improper subtree, returns 0.

template <class _NodePtr>

unsigned

__tree_sub_invariant(_NodePtr __x)

{

    if (__x == nullptr)

        return 1;

    // parent consistency checked by caller

    // check __x->__left_ consistency

    if (__x->__left_ != nullptr && __x->__left_->__parent_ != __x)

        return 0;

    // check __x->__right_ consistency

    if (__x->__right_ != nullptr && __x->__right_->__parent_ != __x)

        return 0;

    // check __x->__left_ != __x->__right_ unless both are nullptr

    if (__x->__left_ == __x->__right_ && __x->__left_ != nullptr)

        return 0;

    // If this is red, neither child can be red

    if (!__x->__is_black_)

    {

        if (__x->__left_ && !__x->__left_->__is_black_)

            return 0;

        if (__x->__right_ && !__x->__right_->__is_black_)

            return 0;

    }

    unsigned __h = __tree_sub_invariant(__x->__left_);

    if (__h == 0)

        return 0;  // invalid left subtree

    if (__h != __tree_sub_invariant(__x->__right_))

        return 0;  // invalid or different height right subtree

    return __h + __x->__is_black_;  // return black height of this node

}

// Determintes if the red black tree rooted at __root is a proper red black tree.

//    __root == nullptr is a proper tree.  Returns true is __root is a proper

//    red black tree, else returns false.

template <class _NodePtr>

bool

__tree_invariant(_NodePtr __root)

{

    if (__root == nullptr)

        return true;

    // check __x->__parent_ consistency

    if (__root->__parent_ == nullptr)

        return false;

    if (!__tree_is_left_child(__root))

        return false;

    // root must be black

    if (!__root->__is_black_)

        return false;

    // do normal node checks

    return __tree_sub_invariant(__root) != 0;

}

// Returns:  pointer to the left-most node under __x.

// Precondition:  __x != nullptr.

template <class _NodePtr>

inline _LIBCPP_INLINE_VISIBILITY

_NodePtr

__tree_min(_NodePtr __x) _NOEXCEPT

{

    while (__x->__left_ != nullptr)

        __x = __x->__left_;

    return __x;

}

// Returns:  pointer to the right-most node under __x.

// Precondition:  __x != nullptr.

template <class _NodePtr>

inline _LIBCPP_INLINE_VISIBILITY

_NodePtr

__tree_max(_NodePtr __x) _NOEXCEPT

{

    while (__x->__right_ != nullptr)

        __x = __x->__right_;

    return __x;

}

// Returns:  pointer to the next in-order node after __x.

// Precondition:  __x != nullptr.

template <class _NodePtr>

_NodePtr

__tree_next(_NodePtr __x) _NOEXCEPT

{

    if (__x->__right_ != nullptr)

        return __tree_min(__x->__right_);

    while (!__tree_is_left_child(__x))

        __x = __x->__parent_;

    return __x->__parent_;

}

// Returns:  pointer to the previous in-order node before __x.

// Precondition:  __x != nullptr.

template <class _NodePtr>

_NodePtr

__tree_prev(_NodePtr __x) _NOEXCEPT

{

    if (__x->__left_ != nullptr)

        return __tree_max(__x->__left_);

    while (__tree_is_left_child(__x))

        __x = __x->__parent_;

    return __x->__parent_;

}

// Returns:  pointer to a node which has no children

// Precondition:  __x != nullptr.

template <class _NodePtr>

_NodePtr

__tree_leaf(_NodePtr __x) _NOEXCEPT

{

    while (true)

    {

        if (__x->__left_ != nullptr)

        {

            __x = __x->__left_;

            continue;

        }

        if (__x->__right_ != nullptr)

        {

            __x = __x->__right_;

            continue;

        }

        break;

    }

    return __x;

}

// Effects:  Makes __x->__right_ the subtree root with __x as its left child

//           while preserving in-order order.

// Precondition:  __x->__right_ != nullptr

template <class _NodePtr>

void

__tree_left_rotate(_NodePtr __x) _NOEXCEPT

{

    _NodePtr __y = __x->__right_;

    __x->__right_ = __y->__left_;

    if (__x->__right_ != nullptr)

        __x->__right_->__parent_ = __x;

    __y->__parent_ = __x->__parent_;

    if (__tree_is_left_child(__x))

        __x->__parent_->__left_ = __y;

    else

        __x->__parent_->__right_ = __y;

    __y->__left_ = __x;

    __x->__parent_ = __y;

}

// Effects:  Makes __x->__left_ the subtree root with __x as its right child

//           while preserving in-order order.

// Precondition:  __x->__left_ != nullptr

template <class _NodePtr>

void

__tree_right_rotate(_NodePtr __x) _NOEXCEPT

{

    _NodePtr __y = __x->__left_;

    __x->__left_ = __y->__right_;

    if (__x->__left_ != nullptr)

        __x->__left_->__parent_ = __x;

    __y->__parent_ = __x->__parent_;

    if (__tree_is_left_child(__x))

        __x->__parent_->__left_ = __y;

    else

        __x->__parent_->__right_ = __y;

    __y->__right_ = __x;

    __x->__parent_ = __y;

}

// Effects:  Rebalances __root after attaching __x to a leaf.

// Precondition:  __root != nulptr && __x != nullptr.

//                __x has no children.

//                __x == __root or == a direct or indirect child of __root.

//                If __x were to be unlinked from __root (setting __root to

//                  nullptr if __root == __x), __tree_invariant(__root) == true.

// Postcondition: __tree_invariant(end_node->__left_) == true.  end_node->__left_

//                may be different than the value passed in as __root.

template <class _NodePtr>

void

__tree_balance_after_insert(_NodePtr __root, _NodePtr __x) _NOEXCEPT

{

    __x->__is_black_ = __x == __root;

    while (__x != __root && !__x->__parent_->__is_black_)

    {

        // __x->__parent_ != __root because __x->__parent_->__is_black == false

        if (__tree_is_left_child(__x->__parent_))

        {

            _NodePtr __y = __x->__parent_->__parent_->__right_;

            if (__y != nullptr && !__y->__is_black_)

            {

                __x = __x->__parent_;

                __x->__is_black_ = true;

                __x = __x->__parent_;

                __x->__is_black_ = __x == __root;

                __y->__is_black_ = true;

            }

            else

            {

                if (!__tree_is_left_child(__x))

                {

                    __x = __x->__parent_;

                    __tree_left_rotate(__x);

                }

                __x = __x->__parent_;

                __x->__is_black_ = true;

                __x = __x->__parent_;

                __x->__is_black_ = false;

                __tree_right_rotate(__x);

                break;

            }

        }

        else

        {

            _NodePtr __y = __x->__parent_->__parent_->__left_;

            if (__y != nullptr && !__y->__is_black_)

            {

                __x = __x->__parent_;

                __x->__is_black_ = true;

                __x = __x->__parent_;

                __x->__is_black_ = __x == __root;

                __y->__is_black_ = true;

            }

            else

            {

                if (__tree_is_left_child(__x))

                {

                    __x = __x->__parent_;

                    __tree_right_rotate(__x);

                }

                __x = __x->__parent_;

                __x->__is_black_ = true;

                __x = __x->__parent_;

                __x->__is_black_ = false;

                __tree_left_rotate(__x);

                break;

            }

        }

    }

}

// Precondition:  __root != nullptr && __z != nullptr.

//                __tree_invariant(__root) == true.

//                __z == __root or == a direct or indirect child of __root.

// Effects:  unlinks __z from the tree rooted at __root, rebalancing as needed.

// Postcondition: __tree_invariant(end_node->__left_) == true && end_node->__left_

//                nor any of its children refer to __z.  end_node->__left_

//                may be different than the value passed in as __root.

template <class _NodePtr>

void

__tree_remove(_NodePtr __root, _NodePtr __z) _NOEXCEPT

{

    // __z will be removed from the tree.  Client still needs to destruct/deallocate it

    // __y is either __z, or if __z has two children, __tree_next(__z).

    // __y will have at most one child.

    // __y will be the initial hole in the tree (make the hole at a leaf)

    _NodePtr __y = (__z->__left_ == nullptr || __z->__right_ == nullptr) ?

                    __z : __tree_next(__z);

    // __x is __y's possibly null single child

    _NodePtr __x = __y->__left_ != nullptr ? __y->__left_ : __y->__right_;

    // __w is __x's possibly null uncle (will become __x's sibling)

    _NodePtr __w = nullptr;

    // link __x to __y's parent, and find __w

    if (__x != nullptr)

        __x->__parent_ = __y->__parent_;

    if (__tree_is_left_child(__y))

    {

        __y->__parent_->__left_ = __x;

        if (__y != __root)

            __w = __y->__parent_->__right_;

        else

            __root = __x;  // __w == nullptr

    }

    else

    {

        __y->__parent_->__right_ = __x;

        // __y can't be root if it is a right child

        __w = __y->__parent_->__left_;

    }

    bool __removed_black = __y->__is_black_;

    // If we didn't remove __z, do so now by splicing in __y for __z,

    //    but copy __z's color.  This does not impact __x or __w.

    if (__y != __z)

    {

        // __z->__left_ != nulptr but __z->__right_ might == __x == nullptr

        __y->__parent_ = __z->__parent_;

        if (__tree_is_left_child(__z))

            __y->__parent_->__left_ = __y;

        else

            __y->__parent_->__right_ = __y;

        __y->__left_ = __z->__left_;

        __y->__left_->__parent_ = __y;

        __y->__right_ = __z->__right_;

        if (__y->__right_ != nullptr)

            __y->__right_->__parent_ = __y;

        __y->__is_black_ = __z->__is_black_;

        if (__root == __z)

            __root = __y;

    }

    // There is no need to rebalance if we removed a red, or if we removed

    //     the last node.

    if (__removed_black && __root != nullptr)

    {

        // Rebalance:

        // __x has an implicit black color (transferred from the removed __y)

        //    associated with it, no matter what its color is.

        // If __x is __root (in which case it can't be null), it is supposed

        //    to be black anyway, and if it is doubly black, then the double

        //    can just be ignored.

        // If __x is red (in which case it can't be null), then it can absorb

        //    the implicit black just by setting its color to black.

        // Since __y was black and only had one child (which __x points to), __x

        //   is either red with no children, else null, otherwise __y would have

        //   different black heights under left and right pointers.

        // if (__x == __root || __x != nullptr && !__x->__is_black_)

        if (__x != nullptr)

            __x->__is_black_ = true;

        else

        {

            //  Else __x isn't root, and is "doubly black", even though it may

            //     be null.  __w can not be null here, else the parent would

            //     see a black height >= 2 on the __x side and a black height

            //     of 1 on the __w side (__w must be a non-null black or a red

            //     with a non-null black child).

            while (true)

            {

                if (!__tree_is_left_child(__w))  // if x is left child

                {

                    if (!__w->__is_black_)

                    {

                        __w->__is_black_ = true;

                        __w->__parent_->__is_black_ = false;

                        __tree_left_rotate(__w->__parent_);

                        // __x is still valid

                        // reset __root only if necessary

                        if (__root == __w->__left_)

                            __root = __w;

                        // reset sibling, and it still can't be null

                        __w = __w->__left_->__right_;

                    }

                    // __w->__is_black_ is now true, __w may have null children

                    if ((__w->__left_  == nullptr || __w->__left_->__is_black_) &&

                        (__w->__right_ == nullptr || __w->__right_->__is_black_))

                    {

                        __w->__is_black_ = false;

                        __x = __w->__parent_;

                        // __x can no longer be null

                        if (__x == __root || !__x->__is_black_)

                        {

                            __x->__is_black_ = true;

                            break;

                        }

                        // reset sibling, and it still can't be null

                        __w = __tree_is_left_child(__x) ?

                                    __x->__parent_->__right_ :

                                    __x->__parent_->__left_;

                        // continue;

                    }

                    else  // __w has a red child

                    {

                        if (__w->__right_ == nullptr || __w->__right_->__is_black_)

                        {

                            // __w left child is non-null and red

                            __w->__left_->__is_black_ = true;

                            __w->__is_black_ = false;

                            __tree_right_rotate(__w);

                            // __w is known not to be root, so root hasn't changed

                            // reset sibling, and it still can't be null

                            __w = __w->__parent_;

                        }

                        // __w has a right red child, left child may be null

                        __w->__is_black_ = __w->__parent_->__is_black_;

                        __w->__parent_->__is_black_ = true;

                        __w->__right_->__is_black_ = true;

                        __tree_left_rotate(__w->__parent_);

                        break;

                    }

                }

                else

                {

                    if (!__w->__is_black_)

                    {

                        __w->__is_black_ = true;

                        __w->__parent_->__is_black_ = false;

                        __tree_right_rotate(__w->__parent_);

                        // __x is still valid

                        // reset __root only if necessary

                        if (__root == __w->__right_)

                            __root = __w;

                        // reset sibling, and it still can't be null

                        __w = __w->__right_->__left_;

                    }

                    // __w->__is_black_ is now true, __w may have null children

                    if ((__w->__left_  == nullptr || __w->__left_->__is_black_) &&

                        (__w->__right_ == nullptr || __w->__right_->__is_black_))

                    {

                        __w->__is_black_ = false;

                        __x = __w->__parent_;

                        // __x can no longer be null

                        if (!__x->__is_black_ || __x == __root)

                        {

                            __x->__is_black_ = true;

                            break;

                        }

                        // reset sibling, and it still can't be null

                        __w = __tree_is_left_child(__x) ?

                                    __x->__parent_->__right_ :

                                    __x->__parent_->__left_;

                        // continue;

                    }

                    else  // __w has a red child

                    {

                        if (__w->__left_ == nullptr || __w->__left_->__is_black_)

                        {

                            // __w right child is non-null and red

                            __w->__right_->__is_black_ = true;

                            __w->__is_black_ = false;

                            __tree_left_rotate(__w);

                            // __w is known not to be root, so root hasn't changed

                            // reset sibling, and it still can't be null

                            __w = __w->__parent_;

                        }

                        // __w has a left red child, right child may be null

                        __w->__is_black_ = __w->__parent_->__is_black_;

                        __w->__parent_->__is_black_ = true;

                        __w->__left_->__is_black_ = true;

                        __tree_right_rotate(__w->__parent_);

                        break;

                    }

                }

            }

        }

    }

}

template <class _Allocator> class __map_node_destructor;

template <class _Allocator>

class __tree_node_destructor

{

    typedef _Allocator                                      allocator_type;

    typedef allocator_traits<allocator_type>                __alloc_traits;

    typedef typename __alloc_traits::value_type::value_type value_type;

public:

    typedef typename __alloc_traits::pointer                pointer;

private:

    allocator_type& __na_;

    __tree_node_destructor& operator=(const __tree_node_destructor&);

public:

    bool __value_constructed;

    _LIBCPP_INLINE_VISIBILITY

    explicit __tree_node_destructor(allocator_type& __na, bool __val = false) _NOEXCEPT

        : __na_(__na),

          __value_constructed(__val)

        {}

    _LIBCPP_INLINE_VISIBILITY

    void operator()(pointer __p) _NOEXCEPT

    {

        if (__value_constructed)

            __alloc_traits::destroy(__na_, _VSTD::addressof(__p->__value_));

        if (__p)

            __alloc_traits::deallocate(__na_, __p, 1);

    }

    template <class> friend class __map_node_destructor;

};

// node

template <class _Pointer>

class __tree_end_node

{

public:

    typedef _Pointer pointer;

    pointer __left_;

    _LIBCPP_INLINE_VISIBILITY

    __tree_end_node() _NOEXCEPT : __left_() {}

};

template <class _VoidPtr>

class __tree_node_base

    : public __tree_end_node

             <

                typename pointer_traits<_VoidPtr>::template

#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES

                     rebind<__tree_node_base<_VoidPtr> >

#else

                     rebind<__tree_node_base<_VoidPtr> >::other

#endif

             >

{

    __tree_node_base(const __tree_node_base&);

    __tree_node_base& operator=(const __tree_node_base&);

public:

    typedef typename pointer_traits<_VoidPtr>::template

#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES

            rebind<__tree_node_base>

#else

            rebind<__tree_node_base>::other

#endif

                                                pointer;

    typedef typename pointer_traits<_VoidPtr>::template

#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES

            rebind<const __tree_node_base>

#else

            rebind<const __tree_node_base>::other

#endif

                                                const_pointer;

    typedef __tree_end_node<pointer> base;

    pointer __right_;

    pointer __parent_;

    bool __is_black_;

    _LIBCPP_INLINE_VISIBILITY

    __tree_node_base() _NOEXCEPT

        : __right_(), __parent_(), __is_black_(false) {}

};

template <class _Tp, class _VoidPtr>

class __tree_node

    : public __tree_node_base<_VoidPtr>

{

public:

    typedef __tree_node_base<_VoidPtr> base;

    typedef _Tp value_type;

    value_type __value_;

#if !defined(_LIBCPP_HAS_NO_RVALUE_REFERENCES) && !defined(_LIBCPP_HAS_NO_VARIADICS)

    template <class ..._Args>

        _LIBCPP_INLINE_VISIBILITY

        explicit __tree_node(_Args&& ...__args)

            : __value_(_VSTD::forward<_Args>(__args)...) {}

#else  // !defined(_LIBCPP_HAS_NO_RVALUE_REFERENCES) && !defined(_LIBCPP_HAS_NO_VARIADICS)

    _LIBCPP_INLINE_VISIBILITY

    explicit __tree_node(const value_type& __v)

            : __value_(__v) {}

#endif  // !defined(_LIBCPP_HAS_NO_RVALUE_REFERENCES) && !defined(_LIBCPP_HAS_NO_VARIADICS)

};

template <class _TreeIterator> class _LIBCPP_TYPE_VIS_ONLY __map_iterator;

template <class _TreeIterator> class _LIBCPP_TYPE_VIS_ONLY __map_const_iterator;

template <class _Tp, class _NodePtr, class _DiffType>

class _LIBCPP_TYPE_VIS_ONLY __tree_iterator

{

    typedef _NodePtr                                              __node_pointer;

    typedef typename pointer_traits<__node_pointer>::element_type __node;

    __node_pointer __ptr_;

    typedef pointer_traits<__node_pointer> __pointer_traits;

public:

    typedef bidirectional_iterator_tag iterator_category;

    typedef _Tp                        value_type;

    typedef _DiffType                  difference_type;

    typedef value_type&                reference;

    typedef typename pointer_traits<__node_pointer>::template

#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES

            rebind<value_type>

#else

            rebind<value_type>::other

#endif

                                       pointer;

    _LIBCPP_INLINE_VISIBILITY __tree_iterator() _NOEXCEPT

#if _LIBCPP_STD_VER > 11

    : __ptr_(nullptr)

#endif

    {}

    _LIBCPP_INLINE_VISIBILITY reference operator*() const {return __ptr_->__value_;}

    _LIBCPP_INLINE_VISIBILITY pointer operator->() const

        {return pointer_traits<pointer>::pointer_to(__ptr_->__value_);}

    _LIBCPP_INLINE_VISIBILITY

    __tree_iterator& operator++() {

      __ptr_ = static_cast<__node_pointer>(

          __tree_next(static_cast<typename __node::base::pointer>(__ptr_)));

      return *this;

    }

    _LIBCPP_INLINE_VISIBILITY

    __tree_iterator operator++(int)

        {__tree_iterator __t(*this); ++(*this); return __t;}

    _LIBCPP_INLINE_VISIBILITY

    __tree_iterator& operator--() {

      __ptr_ = static_cast<__node_pointer>(

          __tree_prev(static_cast<typename __node::base::pointer>(__ptr_)));

      return *this;

    }

    _LIBCPP_INLINE_VISIBILITY

    __tree_iterator operator--(int)

        {__tree_iterator __t(*this); --(*this); return __t;}

    friend _LIBCPP_INLINE_VISIBILITY

        bool operator==(const __tree_iterator& __x, const __tree_iterator& __y)

        {return __x.__ptr_ == __y.__ptr_;}

    friend _LIBCPP_INLINE_VISIBILITY

        bool operator!=(const __tree_iterator& __x, const __tree_iterator& __y)

        {return !(__x == __y);}

private:

    _LIBCPP_INLINE_VISIBILITY

    explicit __tree_iterator(__node_pointer __p) _NOEXCEPT : __ptr_(__p) {}

    template <class, class, class> friend class __tree;

    template <class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY __tree_const_iterator;

    template <class> friend class _LIBCPP_TYPE_VIS_ONLY __map_iterator;

    template <class, class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY map;

    template <class, class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY multimap;

    template <class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY set;

    template <class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY multiset;

};

template <class _Tp, class _ConstNodePtr, class _DiffType>

class _LIBCPP_TYPE_VIS_ONLY __tree_const_iterator

{

    typedef _ConstNodePtr                                         __node_pointer;

    typedef typename pointer_traits<__node_pointer>::element_type __node;

    __node_pointer __ptr_;

    typedef pointer_traits<__node_pointer> __pointer_traits;

public:

    typedef bidirectional_iterator_tag       iterator_category;

    typedef _Tp                              value_type;

    typedef _DiffType                        difference_type;

    typedef const value_type&                reference;

    typedef typename pointer_traits<__node_pointer>::template

#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES

            rebind<const value_type>

#else

            rebind<const value_type>::other

#endif

                                       pointer;

    _LIBCPP_INLINE_VISIBILITY __tree_const_iterator() _NOEXCEPT

#if _LIBCPP_STD_VER > 11

    : __ptr_(nullptr)

#endif

    {}

private:

    typedef typename remove_const<__node>::type  __non_const_node;

    typedef typename pointer_traits<__node_pointer>::template

#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES

            rebind<__non_const_node>

#else

            rebind<__non_const_node>::other

#endif

                                                 __non_const_node_pointer;

    typedef __tree_iterator<value_type, __non_const_node_pointer, difference_type>

                                                 __non_const_iterator;

public:

    _LIBCPP_INLINE_VISIBILITY

    __tree_const_iterator(__non_const_iterator __p) _NOEXCEPT

        : __ptr_(__p.__ptr_) {}

    _LIBCPP_INLINE_VISIBILITY reference operator*() const {return __ptr_->__value_;}

    _LIBCPP_INLINE_VISIBILITY pointer operator->() const

        {return pointer_traits<pointer>::pointer_to(__ptr_->__value_);}

    _LIBCPP_INLINE_VISIBILITY

    __tree_const_iterator& operator++() {

      typedef typename pointer_traits<__node_pointer>::template

#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES

          rebind<typename __node::base>

#else

          rebind<typename __node::base>::other

#endif

              __node_base_pointer;

      __ptr_ = static_cast<__node_pointer>(

          __tree_next(static_cast<__node_base_pointer>(__ptr_)));

      return *this;

    }

    _LIBCPP_INLINE_VISIBILITY

    __tree_const_iterator operator++(int)

        {__tree_const_iterator __t(*this); ++(*this); return __t;}

    _LIBCPP_INLINE_VISIBILITY

    __tree_const_iterator& operator--() {

      typedef typename pointer_traits<__node_pointer>::template

#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES

          rebind<typename __node::base>

#else

          rebind<typename __node::base>::other

#endif

              __node_base_pointer;

      __ptr_ = static_cast<__node_pointer>(

          __tree_prev(static_cast<__node_base_pointer>(__ptr_)));

      return *this;

    }

    _LIBCPP_INLINE_VISIBILITY

    __tree_const_iterator operator--(int)

        {__tree_const_iterator __t(*this); --(*this); return __t;}

    friend _LIBCPP_INLINE_VISIBILITY

        bool operator==(const __tree_const_iterator& __x, const __tree_const_iterator& __y)

        {return __x.__ptr_ == __y.__ptr_;}

    friend _LIBCPP_INLINE_VISIBILITY

        bool operator!=(const __tree_const_iterator& __x, const __tree_const_iterator& __y)

        {return !(__x == __y);}

private:

    _LIBCPP_INLINE_VISIBILITY

    explicit __tree_const_iterator(__node_pointer __p) _NOEXCEPT

        : __ptr_(__p) {}

    template <class, class, class> friend class __tree;

    template <class, class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY map;

    template <class, class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY multimap;

    template <class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY set;

    template <class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY multiset;

    template <class> friend class _LIBCPP_TYPE_VIS_ONLY __map_const_iterator;

};

template <class _Tp, class _Compare, class _Allocator>

class __tree

{

public:

    typedef _Tp                                      value_type;

    typedef _Compare                                 value_compare;

    typedef _Allocator                               allocator_type;

    typedef allocator_traits<allocator_type>         __alloc_traits;

    typedef typename __alloc_traits::pointer         pointer;

    typedef typename __alloc_traits::const_pointer   const_pointer;

    typedef typename __alloc_traits::size_type       size_type;

    typedef typename __alloc_traits::difference_type difference_type;

    typedef typename __alloc_traits::void_pointer  __void_pointer;

    typedef __tree_node<value_type, __void_pointer> __node;

    typedef __tree_node_base<__void_pointer>        __node_base;

    typedef typename __rebind_alloc_helper<__alloc_traits, __node>::type __node_allocator;

    typedef allocator_traits<__node_allocator>       __node_traits;

    typedef typename __node_traits::pointer          __node_pointer;

    typedef typename __node_traits::pointer          __node_const_pointer;

    typedef typename __node_base::pointer            __node_base_pointer;

    typedef typename __node_base::pointer            __node_base_const_pointer;

private:

    typedef typename __node_base::base __end_node_t;

    typedef typename pointer_traits<__node_pointer>::template

#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES

            rebind<__end_node_t>

#else

            rebind<__end_node_t>::other

#endif

                                                     __end_node_ptr;

    typedef typename pointer_traits<__node_pointer>::template

#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES

            rebind<__end_node_t>

#else

            rebind<__end_node_t>::other

#endif

                                                     __end_node_const_ptr;

    __node_pointer                                          __begin_node_;

    __compressed_pair<__end_node_t, __node_allocator>  __pair1_;

    __compressed_pair<size_type, value_compare>        __pair3_;

public:

    _LIBCPP_INLINE_VISIBILITY

    __node_pointer __end_node() _NOEXCEPT

    {

        return static_cast<__node_pointer>

               (

                   pointer_traits<__end_node_ptr>::pointer_to(__pair1_.first())

               );

    }

    _LIBCPP_INLINE_VISIBILITY

    __node_const_pointer __end_node() const _NOEXCEPT

    {

        return static_cast<__node_const_pointer>

               (

                   pointer_traits<__end_node_const_ptr>::pointer_to(const_cast<__end_node_t&>(__pair1_.first()))

               );

    }

    _LIBCPP_INLINE_VISIBILITY

          __node_allocator& __node_alloc() _NOEXCEPT {return __pair1_.second();}

private:

    _LIBCPP_INLINE_VISIBILITY

    const __node_allocator& __node_alloc() const _NOEXCEPT

        {return __pair1_.second();}

    _LIBCPP_INLINE_VISIBILITY

          __node_pointer& __begin_node() _NOEXCEPT {return __begin_node_;}

    _LIBCPP_INLINE_VISIBILITY

    const __node_pointer& __begin_node() const _NOEXCEPT {return __begin_node_;}

public:

    _LIBCPP_INLINE_VISIBILITY

    allocator_type __alloc() const _NOEXCEPT

        {return allocator_type(__node_alloc());}

private:

    _LIBCPP_INLINE_VISIBILITY

          size_type& size() _NOEXCEPT {return __pair3_.first();}

public:

    _LIBCPP_INLINE_VISIBILITY

    const size_type& size() const _NOEXCEPT {return __pair3_.first();}

    _LIBCPP_INLINE_VISIBILITY

          value_compare& value_comp() _NOEXCEPT {return __pair3_.second();}

    _LIBCPP_INLINE_VISIBILITY

    const value_compare& value_comp() const _NOEXCEPT

        {return __pair3_.second();}

public:

    _LIBCPP_INLINE_VISIBILITY

    __node_pointer __root() _NOEXCEPT

        {return static_cast<__node_pointer>      (__end_node()->__left_);}

    _LIBCPP_INLINE_VISIBILITY

    __node_const_pointer __root() const _NOEXCEPT

        {return static_cast<__node_const_pointer>(__end_node()->__left_);}

    typedef __tree_iterator<value_type, __node_pointer, difference_type>             iterator;

    typedef __tree_const_iterator<value_type, __node_pointer, difference_type> const_iterator;

    explicit __tree(const value_compare& __comp)

        _NOEXCEPT_(

            is_nothrow_default_constructible<__node_allocator>::value &&

            is_nothrow_copy_constructible<value_compare>::value);

    explicit __tree(const allocator_type& __a);

    __tree(const value_compare& __comp, const allocator_type& __a);

    __tree(const __tree& __t);

    __tree& operator=(const __tree& __t);

    template <class _InputIterator>

        void __assign_unique(_InputIterator __first, _InputIterator __last);

    template <class _InputIterator>

        void __assign_multi(_InputIterator __first, _InputIterator __last);

#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES

    __tree(__tree&& __t)

        _NOEXCEPT_(

            is_nothrow_move_constructible<__node_allocator>::value &&

            is_nothrow_move_constructible<value_compare>::value);

    __tree(__tree&& __t, const allocator_type& __a);

    __tree& operator=(__tree&& __t)

        _NOEXCEPT_(

            __node_traits::propagate_on_container_move_assignment::value &&

            is_nothrow_move_assignable<value_compare>::value &&

            is_nothrow_move_assignable<__node_allocator>::value);

#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES

    ~__tree();

    _LIBCPP_INLINE_VISIBILITY

          iterator begin()  _NOEXCEPT {return       iterator(__begin_node());}

    _LIBCPP_INLINE_VISIBILITY

    const_iterator begin() const _NOEXCEPT {return const_iterator(__begin_node());}

    _LIBCPP_INLINE_VISIBILITY

          iterator end() _NOEXCEPT {return       iterator(__end_node());}

    _LIBCPP_INLINE_VISIBILITY

    const_iterator end() const _NOEXCEPT {return const_iterator(__end_node());}

    _LIBCPP_INLINE_VISIBILITY

    size_type max_size() const _NOEXCEPT

        {return __node_traits::max_size(__node_alloc());}

    void clear() _NOEXCEPT;

    void swap(__tree& __t)

        _NOEXCEPT_(

            __is_nothrow_swappable<value_compare>::value

#if _LIBCPP_STD_VER <= 11

            && (!__node_traits::propagate_on_container_swap::value ||

                 __is_nothrow_swappable<__node_allocator>::value)

#endif

            );

#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES

#ifndef _LIBCPP_HAS_NO_VARIADICS

    template <class... _Args>

        pair<iterator, bool>

        __emplace_unique(_Args&&... __args);

    template <class... _Args>

        iterator

        __emplace_multi(_Args&&... __args);

    template <class... _Args>

        iterator

        __emplace_hint_unique(const_iterator __p, _Args&&... __args);

    template <class... _Args>

        iterator

        __emplace_hint_multi(const_iterator __p, _Args&&... __args);

#endif  // _LIBCPP_HAS_NO_VARIADICS

    template <class _Vp>

        pair<iterator, bool> __insert_unique(_Vp&& __v);

    template <class _Vp>

        iterator __insert_unique(const_iterator __p, _Vp&& __v);

    template <class _Vp>

        iterator __insert_multi(_Vp&& __v);

    template <class _Vp>

        iterator __insert_multi(const_iterator __p, _Vp&& __v);

#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES

    pair<iterator, bool> __insert_unique(const value_type& __v);

    iterator __insert_unique(const_iterator __p, const value_type& __v);

    iterator __insert_multi(const value_type& __v);

    iterator __insert_multi(const_iterator __p, const value_type& __v);

    pair<iterator, bool> __node_insert_unique(__node_pointer __nd);

    iterator             __node_insert_unique(const_iterator __p,

                                              __node_pointer __nd);

    iterator __node_insert_multi(__node_pointer __nd);

    iterator __node_insert_multi(const_iterator __p, __node_pointer __nd);

    iterator erase(const_iterator __p);

    iterator erase(const_iterator __f, const_iterator __l);

    template <class _Key>

        size_type __erase_unique(const _Key& __k);

    template <class _Key>

        size_type __erase_multi(const _Key& __k);

    void __insert_node_at(__node_base_pointer __parent,

                          __node_base_pointer& __child,

                          __node_base_pointer __new_node);

    template <class _Key>

        iterator find(const _Key& __v);

    template <class _Key>

        const_iterator find(const _Key& __v) const;

    template <class _Key>

        size_type __count_unique(const _Key& __k) const;

    template <class _Key>

        size_type __count_multi(const _Key& __k) const;

    template <class _Key>

        _LIBCPP_INLINE_VISIBILITY

        iterator lower_bound(const _Key& __v)

            {return __lower_bound(__v, __root(), __end_node());}

    template <class _Key>

        iterator __lower_bound(const _Key& __v,

                               __node_pointer __root,

                               __node_pointer __result);

    template <class _Key>

        _LIBCPP_INLINE_VISIBILITY

        const_iterator lower_bound(const _Key& __v) const

            {return __lower_bound(__v, __root(), __end_node());}

    template <class _Key>

        const_iterator __lower_bound(const _Key& __v,

                                     __node_const_pointer __root,

                                     __node_const_pointer __result) const;

    template <class _Key>

        _LIBCPP_INLINE_VISIBILITY

        iterator upper_bound(const _Key& __v)

            {return __upper_bound(__v, __root(), __end_node());}

    template <class _Key>

        iterator __upper_bound(const _Key& __v,

                               __node_pointer __root,

                               __node_pointer __result);

    template <class _Key>

        _LIBCPP_INLINE_VISIBILITY

        const_iterator upper_bound(const _Key& __v) const

            {return __upper_bound(__v, __root(), __end_node());}

    template <class _Key>

        const_iterator __upper_bound(const _Key& __v,

                                     __node_const_pointer __root,

                                     __node_const_pointer __result) const;

    template <class _Key>

        pair<iterator, iterator>

        __equal_range_unique(const _Key& __k);

    template <class _Key>

        pair<const_iterator, const_iterator>

        __equal_range_unique(const _Key& __k) const;

    template <class _Key>

        pair<iterator, iterator>

        __equal_range_multi(const _Key& __k);

    template <class _Key>

        pair<const_iterator, const_iterator>

        __equal_range_multi(const _Key& __k) const;

    typedef __tree_node_destructor<__node_allocator> _Dp;

    typedef unique_ptr<__node, _Dp> __node_holder;

    __node_holder remove(const_iterator __p) _NOEXCEPT;

private:

    typename __node_base::pointer&

        __find_leaf_low(typename __node_base::pointer& __parent, const value_type& __v);

    typename __node_base::pointer&

        __find_leaf_high(typename __node_base::pointer& __parent, const value_type& __v);

    typename __node_base::pointer&

        __find_leaf(const_iterator __hint,

                    typename __node_base::pointer& __parent, const value_type& __v);

    template <class _Key>

        typename __node_base::pointer&

        __find_equal(typename __node_base::pointer& __parent, const _Key& __v);

    template <class _Key>

        typename __node_base::pointer&

        __find_equal(const_iterator __hint, typename __node_base::pointer& __parent,

                     const _Key& __v);

#if !defined(_LIBCPP_HAS_NO_RVALUE_REFERENCES) && !defined(_LIBCPP_HAS_NO_VARIADICS)

    template <class ..._Args>

        __node_holder __construct_node(_Args&& ...__args);

#else  // !defined(_LIBCPP_HAS_NO_RVALUE_REFERENCES) && !defined(_LIBCPP_HAS_NO_VARIADICS)

        __node_holder __construct_node(const value_type& __v);

#endif

    void destroy(__node_pointer __nd) _NOEXCEPT;

    _LIBCPP_INLINE_VISIBILITY

    void __copy_assign_alloc(const __tree& __t)

        {__copy_assign_alloc(__t, integral_constant<bool,

             __node_traits::propagate_on_container_copy_assignment::value>());}

    _LIBCPP_INLINE_VISIBILITY

    void __copy_assign_alloc(const __tree& __t, true_type)

        {__node_alloc() = __t.__node_alloc();}

    _LIBCPP_INLINE_VISIBILITY

    void __copy_assign_alloc(const __tree& __t, false_type) {}

    void __move_assign(__tree& __t, false_type);

    void __move_assign(__tree& __t, true_type)

        _NOEXCEPT_(is_nothrow_move_assignable<value_compare>::value &&

                   is_nothrow_move_assignable<__node_allocator>::value);

    _LIBCPP_INLINE_VISIBILITY

    void __move_assign_alloc(__tree& __t)

        _NOEXCEPT_(

            !__node_traits::propagate_on_container_move_assignment::value ||

            is_nothrow_move_assignable<__node_allocator>::value)

        {__move_assign_alloc(__t, integral_constant<bool,

             __node_traits::propagate_on_container_move_assignment::value>());}

    _LIBCPP_INLINE_VISIBILITY

    void __move_assign_alloc(__tree& __t, true_type)

        _NOEXCEPT_(is_nothrow_move_assignable<__node_allocator>::value)

        {__node_alloc() = _VSTD::move(__t.__node_alloc());}

    _LIBCPP_INLINE_VISIBILITY

    void __move_assign_alloc(__tree& __t, false_type) _NOEXCEPT {}

    __node_pointer __detach();

    static __node_pointer __detach(__node_pointer);

    template <class, class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY map;

    template <class, class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY multimap;

};

template <class _Tp, class _Compare, class _Allocator>

__tree<_Tp, _Compare, _Allocator>::__tree(const value_compare& __comp)

        _NOEXCEPT_(

            is_nothrow_default_constructible<__node_allocator>::value &&

            is_nothrow_copy_constructible<value_compare>::value)

    : __pair3_(0, __comp)

{

    __begin_node() = __end_node();

}

template <class _Tp, class _Compare, class _Allocator>

__tree<_Tp, _Compare, _Allocator>::__tree(const allocator_type& __a)

    : __begin_node_(__node_pointer()),

      __pair1_(__node_allocator(__a)),

      __pair3_(0)

{

    __begin_node() = __end_node();

}

template <class _Tp, class _Compare, class _Allocator>

__tree<_Tp, _Compare, _Allocator>::__tree(const value_compare& __comp,

                                           const allocator_type& __a)

    : __begin_node_(__node_pointer()),