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 /////////////////////////////////////////////////////////////////////////////
 //
 // (C) Copyright Ion Gaztanaga  2007-2021
 // (C) Copyright Daniel Steck   2021
 //
 // Distributed under the Boost Software License, Version 1.0.
 //    (See accompanying file LICENSE_1_0.txt or copy at
 //          http://www.boost.org/LICENSE_1_0.txt)
 //
 // See http://www.boost.org/libs/intrusive for documentation.
 //
 /////////////////////////////////////////////////////////////////////////////
 
 #ifndef BOOST_INTRUSIVE_BSTREE_ALGORITHMS_HPP
 #define BOOST_INTRUSIVE_BSTREE_ALGORITHMS_HPP
 
 #include <cstddef>
 #include <boost/intrusive/detail/config_begin.hpp>
 #include <boost/intrusive/intrusive_fwd.hpp>
 #include <boost/intrusive/detail/bstree_algorithms_base.hpp>
 #include <boost/intrusive/detail/assert.hpp>
 #include <boost/intrusive/detail/uncast.hpp>
 #include <boost/intrusive/detail/math.hpp>
 #include <boost/intrusive/detail/algo_type.hpp>
 
 #include <boost/intrusive/detail/minimal_pair_header.hpp>
 
 #if defined(BOOST_HAS_PRAGMA_ONCE)
 #  pragma once
 #endif
 
 namespace boost {
 namespace intrusive {
 
 /// @cond
 
 //! This type is the information that will be filled by insert_unique_check
 template <class NodePtr>
 struct insert_commit_data_t
 {
    BOOST_INTRUSIVE_FORCEINLINE insert_commit_data_t()
       : link_left(false), node()
    {}
    bool     link_left;
    NodePtr  node;
 };
 
 template <class NodePtr>
 struct data_for_rebalance_t
 {
    NodePtr  x;
    NodePtr  x_parent;
    NodePtr  y;
 };
 
 namespace detail {
 
 template<class ValueTraits, class NodePtrCompare, class ExtraChecker>
 struct bstree_node_checker
    : public ExtraChecker
 {
    typedef ExtraChecker                            base_checker_t;
    typedef ValueTraits                             value_traits;
    typedef typename value_traits::node_traits      node_traits;
    typedef typename node_traits::const_node_ptr    const_node_ptr;
 
    struct return_type
       : public base_checker_t::return_type
    {
       BOOST_INTRUSIVE_FORCEINLINE return_type()
          : min_key_node_ptr(const_node_ptr()), max_key_node_ptr(const_node_ptr()), node_count(0)
       {}
 
       const_node_ptr min_key_node_ptr;
       const_node_ptr max_key_node_ptr;
       size_t   node_count;
    };
 
    BOOST_INTRUSIVE_FORCEINLINE bstree_node_checker(const NodePtrCompare& comp, ExtraChecker extra_checker)
       : base_checker_t(extra_checker), comp_(comp)
    {}
 
    void operator () (const_node_ptr p,
                      const return_type& check_return_left, const return_type& check_return_right,
                      return_type& check_return)
    {
       BOOST_INTRUSIVE_INVARIANT_ASSERT(!check_return_left.max_key_node_ptr || !comp_(p, check_return_left.max_key_node_ptr));
       BOOST_INTRUSIVE_INVARIANT_ASSERT(!check_return_right.min_key_node_ptr || !comp_(check_return_right.min_key_node_ptr, p));
       check_return.min_key_node_ptr = node_traits::get_left(p)? check_return_left.min_key_node_ptr : p;
       check_return.max_key_node_ptr = node_traits::get_right(p)? check_return_right.max_key_node_ptr : p;
       check_return.node_count = check_return_left.node_count + check_return_right.node_count + 1;
       base_checker_t::operator()(p, check_return_left, check_return_right, check_return);
    }
 
    const NodePtrCompare comp_;
 };
 
 } // namespace detail
 
 /// @endcond
 
 
 
 //!   This is an implementation of a binary search tree.
 //!   A node in the search tree has references to its children and its parent. This
 //!   is to allow traversal of the whole tree from a given node making the
 //!   implementation of iterator a pointer to a node.
 //!   At the top of the tree a node is used specially. This node's parent pointer
 //!   is pointing to the root of the tree. Its left pointer points to the
 //!   leftmost node in the tree and the right pointer to the rightmost one.
 //!   This node is used to represent the end-iterator.
 //!
 //!                                            +---------+
 //!       header------------------------------>|         |
 //!                                            |         |
 //!                   +----------(left)--------|         |--------(right)---------+
 //!                   |                        +---------+                        |
 //!                   |                             |                             |
 //!                   |                             | (parent)                    |
 //!                   |                             |                             |
 //!                   |                             |                             |
 //!                   |                        +---------+                        |
 //!    root of tree ..|......................> |         |                        |
 //!                   |                        |    D    |                        |
 //!                   |                        |         |                        |
 //!                   |                +-------+---------+-------+                |
 //!                   |                |                         |                |
 //!                   |                |                         |                |
 //!                   |                |                         |                |
 //!                   |                |                         |                |
 //!                   |                |                         |                |
 //!                   |          +---------+                 +---------+          |
 //!                   |          |         |                 |         |          |
 //!                   |          |    B    |                 |    F    |          |
 //!                   |          |         |                 |         |          |
 //!                   |       +--+---------+--+           +--+---------+--+       |
 //!                   |       |               |           |               |       |
 //!                   |       |               |           |               |       |
 //!                   |       |               |           |               |       |
 //!                   |   +---+-----+   +-----+---+   +---+-----+   +-----+---+   |
 //!                   +-->|         |   |         |   |         |   |         |<--+
 //!                       |    A    |   |    C    |   |    E    |   |    G    |
 //!                       |         |   |         |   |         |   |         |
 //!                       +---------+   +---------+   +---------+   +---------+
 //!
 //! bstree_algorithms is configured with a NodeTraits class, which encapsulates the
 //! information about the node to be manipulated. NodeTraits must support the
 //! following interface:
 //!
 //! <b>Typedefs</b>:
 //!
 //! <tt>node</tt>: The type of the node that forms the binary search tree
 //!
 //! <tt>node_ptr</tt>: A pointer to a node
 //!
 //! <tt>const_node_ptr</tt>: A pointer to a const node
 //!
 //! <b>Static functions</b>:
 //!
 //! <tt>static node_ptr get_parent(const_node_ptr n);</tt>
 //!
 //! <tt>static void set_parent(node_ptr n, node_ptr parent);</tt>
 //!
 //! <tt>static node_ptr get_left(const_node_ptr n);</tt>
 //!
 //! <tt>static void set_left(node_ptr n, node_ptr left);</tt>
 //!
 //! <tt>static node_ptr get_right(const_node_ptr n);</tt>
 //!
 //! <tt>static void set_right(node_ptr n, node_ptr right);</tt>
 template<class NodeTraits>
 class bstree_algorithms : public bstree_algorithms_base<NodeTraits>
 {
    public:
    typedef typename NodeTraits::node            node;
    typedef NodeTraits                           node_traits;
    typedef typename NodeTraits::node_ptr        node_ptr;
    typedef typename NodeTraits::const_node_ptr  const_node_ptr;
    typedef insert_commit_data_t<node_ptr>       insert_commit_data;
    typedef data_for_rebalance_t<node_ptr>       data_for_rebalance;
 
    /// @cond
    typedef bstree_algorithms<NodeTraits>        this_type;
    typedef bstree_algorithms_base<NodeTraits>   base_type;
    private:
    template<class Disposer>
    struct dispose_subtree_disposer
    {
       BOOST_INTRUSIVE_FORCEINLINE dispose_subtree_disposer(Disposer &disp, node_ptr subtree)
          : disposer_(&disp), subtree_(subtree)
       {}
 
       BOOST_INTRUSIVE_FORCEINLINE void release()
       {  disposer_ = 0;  }
 
       BOOST_INTRUSIVE_FORCEINLINE ~dispose_subtree_disposer()
       {
          if(disposer_){
             dispose_subtree(subtree_, *disposer_);
          }
       }
       Disposer *disposer_;
       const node_ptr subtree_;
    };
 
    /// @endcond
 
    public:
    //! <b>Requires</b>: 'header' is the header node of a tree.
    //!
    //! <b>Effects</b>: Returns the first node of the tree, the header if the tree is empty.
    //!
    //! <b>Complexity</b>: Constant time.
    //!
    //! <b>Throws</b>: Nothing.
    BOOST_INTRUSIVE_FORCEINLINE static node_ptr begin_node(const_node_ptr header) BOOST_NOEXCEPT
    {  return node_traits::get_left(header);   }
 
    //! <b>Requires</b>: 'header' is the header node of a tree.
    //!
    //! <b>Effects</b>: Returns the header of the tree.
    //!
    //! <b>Complexity</b>: Constant time.
    //!
    //! <b>Throws</b>: Nothing.
    BOOST_INTRUSIVE_FORCEINLINE static node_ptr end_node(const_node_ptr header) BOOST_NOEXCEPT
    {  return detail::uncast(header);   }
 
    //! <b>Requires</b>: 'header' is the header node of a tree.
    //!
    //! <b>Effects</b>: Returns the root of the tree if any, header otherwise
    //!
    //! <b>Complexity</b>: Constant time.
    //!
    //! <b>Throws</b>: Nothing.
    BOOST_INTRUSIVE_FORCEINLINE static node_ptr root_node(const_node_ptr header) BOOST_NOEXCEPT
    {
       node_ptr p = node_traits::get_parent(header);
       return p ? p : detail::uncast(header);
    }
 
    //! <b>Requires</b>: 'n' is a node of the tree or a node initialized
    //!   by init(...) or init_node.
    //!
    //! <b>Effects</b>: Returns true if the node is initialized by init() or init_node().
    //!
    //! <b>Complexity</b>: Constant time.
    //!
    //! <b>Throws</b>: Nothing.
    BOOST_INTRUSIVE_FORCEINLINE static bool unique(const_node_ptr n) BOOST_NOEXCEPT
    { return !NodeTraits::get_parent(n); }
 
    #if defined(BOOST_INTRUSIVE_DOXYGEN_INVOKED)
    //! <b>Requires</b>: 'n' is a node of the tree or a header node.
    //!
    //! <b>Effects</b>: Returns the header of the tree.
    //!
    //! <b>Complexity</b>: Logarithmic.
    //!
    //! <b>Throws</b>: Nothing.
    static node_ptr get_header(const_node_ptr n);
    #endif
 
    //! <b>Requires</b>: node1 and node2 can't be header nodes
    //!  of two trees.
    //!
    //! <b>Effects</b>: Swaps two nodes. After the function node1 will be inserted
    //!   in the position node2 before the function. node2 will be inserted in the
    //!   position node1 had before the function.
    //!
    //! <b>Complexity</b>: Logarithmic.
    //!
    //! <b>Throws</b>: Nothing.
    //!
    //! <b>Note</b>: This function will break container ordering invariants if
    //!   node1 and node2 are not equivalent according to the ordering rules.
    //!
    //!Experimental function
    static void swap_nodes(node_ptr node1, node_ptr node2) BOOST_NOEXCEPT
    {
       if(node1 == node2)
          return;
 
       node_ptr header1(base_type::get_header(node1)), header2(base_type::get_header(node2));
       swap_nodes(node1, header1, node2, header2);
    }
 
    //! <b>Requires</b>: node1 and node2 can't be header nodes
    //!  of two trees with header header1 and header2.
    //!
    //! <b>Effects</b>: Swaps two nodes. After the function node1 will be inserted
    //!   in the position node2 before the function. node2 will be inserted in the
    //!   position node1 had before the function.
    //!
    //! <b>Complexity</b>: Constant.
    //!
    //! <b>Throws</b>: Nothing.
    //!
    //! <b>Note</b>: This function will break container ordering invariants if
    //!   node1 and node2 are not equivalent according to the ordering rules.
    //!
    //!Experimental function
    static void swap_nodes(node_ptr node1, node_ptr header1, node_ptr node2, node_ptr header2) BOOST_NOEXCEPT
    {
       if(node1 == node2)
          return;
 
       //node1 and node2 must not be header nodes
       //BOOST_INTRUSIVE_INVARIANT_ASSERT((header1 != node1 && header2 != node2));
       if(header1 != header2){
          //Update header1 if necessary
          if(node1 == NodeTraits::get_left(header1)){
             NodeTraits::set_left(header1, node2);
          }
 
          if(node1 == NodeTraits::get_right(header1)){
             NodeTraits::set_right(header1, node2);
          }
 
          if(node1 == NodeTraits::get_parent(header1)){
             NodeTraits::set_parent(header1, node2);
          }
 
          //Update header2 if necessary
          if(node2 == NodeTraits::get_left(header2)){
             NodeTraits::set_left(header2, node1);
          }
 
          if(node2 == NodeTraits::get_right(header2)){
             NodeTraits::set_right(header2, node1);
          }
 
          if(node2 == NodeTraits::get_parent(header2)){
             NodeTraits::set_parent(header2, node1);
          }
       }
       else{
          //If both nodes are from the same tree
          //Update header if necessary
          if(node1 == NodeTraits::get_left(header1)){
             NodeTraits::set_left(header1, node2);
          }
          else if(node2 == NodeTraits::get_left(header2)){
             NodeTraits::set_left(header2, node1);
          }
 
          if(node1 == NodeTraits::get_right(header1)){
             NodeTraits::set_right(header1, node2);
          }
          else if(node2 == NodeTraits::get_right(header2)){
             NodeTraits::set_right(header2, node1);
          }
 
          if(node1 == NodeTraits::get_parent(header1)){
             NodeTraits::set_parent(header1, node2);
          }
          else if(node2 == NodeTraits::get_parent(header2)){
             NodeTraits::set_parent(header2, node1);
          }
 
          //Adjust data in nodes to be swapped
          //so that final link swap works as expected
          if(node1 == NodeTraits::get_parent(node2)){
             NodeTraits::set_parent(node2, node2);
 
             if(node2 == NodeTraits::get_right(node1)){
                NodeTraits::set_right(node1, node1);
             }
             else{
                NodeTraits::set_left(node1, node1);
             }
          }
          else if(node2 == NodeTraits::get_parent(node1)){
             NodeTraits::set_parent(node1, node1);
 
             if(node1 == NodeTraits::get_right(node2)){
                NodeTraits::set_right(node2, node2);
             }
             else{
                NodeTraits::set_left(node2, node2);
             }
          }
       }
 
       //Now swap all the links
       node_ptr temp;
       //swap left link
       temp = NodeTraits::get_left(node1);
       NodeTraits::set_left(node1, NodeTraits::get_left(node2));
       NodeTraits::set_left(node2, temp);
       //swap right link
       temp = NodeTraits::get_right(node1);
       NodeTraits::set_right(node1, NodeTraits::get_right(node2));
       NodeTraits::set_right(node2, temp);
       //swap parent link
       temp = NodeTraits::get_parent(node1);
       NodeTraits::set_parent(node1, NodeTraits::get_parent(node2));
       NodeTraits::set_parent(node2, temp);
 
       //Now adjust child nodes for newly inserted node 1
       if((temp = NodeTraits::get_left(node1))){
          NodeTraits::set_parent(temp, node1);
       }
       if((temp = NodeTraits::get_right(node1))){
          NodeTraits::set_parent(temp, node1);
       }
       //Now adjust child nodes for newly inserted node 2
       if((temp = NodeTraits::get_left(node2))){
          NodeTraits::set_parent(temp, node2);
       }
       if((temp = NodeTraits::get_right(node2))){
          NodeTraits::set_parent(temp, node2);
       }
 
       //Finally adjust parent nodes
       if ((temp = NodeTraits::get_parent(node1)) == NodeTraits::get_parent(node2)) {
          // special logic for the case where the nodes are siblings
          const node_ptr left = NodeTraits::get_left(temp);
          NodeTraits::set_left(temp, NodeTraits::get_right(temp));
          NodeTraits::set_right(temp, left);
       } else {
          if ((temp = NodeTraits::get_parent(node1)) &&
             //The header has been already updated so avoid it
             temp != header2) {
             if (NodeTraits::get_left(temp) == node2) {
                NodeTraits::set_left(temp, node1);
             }
             if (NodeTraits::get_right(temp) == node2) {
                NodeTraits::set_right(temp, node1);
             }
          }
          if ((temp = NodeTraits::get_parent(node2)) &&
             //The header has been already updated so avoid it
             temp != header1) {
             if (NodeTraits::get_left(temp) == node1) {
                NodeTraits::set_left(temp, node2);
             }
             if (NodeTraits::get_right(temp) == node1) {
                NodeTraits::set_right(temp, node2);
             }
          }
       }
    }
 
    //! <b>Requires</b>: node_to_be_replaced must be inserted in a tree
    //!   and new_node must not be inserted in a tree.
    //!
    //! <b>Effects</b>: Replaces node_to_be_replaced in its position in the
    //!   tree with new_node. The tree does not need to be rebalanced
    //!
    //! <b>Complexity</b>: Logarithmic.
    //!
    //! <b>Throws</b>: Nothing.
    //!
    //! <b>Note</b>: This function will break container ordering invariants if
    //!   new_node is not equivalent to node_to_be_replaced according to the
    //!   ordering rules. This function is faster than erasing and inserting
    //!   the node, since no rebalancing and comparison is needed. Experimental function
    BOOST_INTRUSIVE_FORCEINLINE static void replace_node(node_ptr node_to_be_replaced, node_ptr new_node) BOOST_NOEXCEPT
    {
       replace_node(node_to_be_replaced, base_type::get_header(node_to_be_replaced), new_node);
    }
 
    //! <b>Requires</b>: node_to_be_replaced must be inserted in a tree
    //!   with header "header" and new_node must not be inserted in a tree.
    //!
    //! <b>Effects</b>: Replaces node_to_be_replaced in its position in the
    //!   tree with new_node. The tree does not need to be rebalanced
    //!
    //! <b>Complexity</b>: Constant.
    //!
    //! <b>Throws</b>: Nothing.
    //!
    //! <b>Note</b>: This function will break container ordering invariants if
    //!   new_node is not equivalent to node_to_be_replaced according to the
    //!   ordering rules. This function is faster than erasing and inserting
    //!   the node, since no rebalancing or comparison is needed. Experimental function
    static void replace_node(node_ptr node_to_be_replaced, node_ptr header, node_ptr new_node) BOOST_NOEXCEPT
    {
       BOOST_ASSERT(node_to_be_replaced != new_node);
 
       //Update header if necessary
       if(node_to_be_replaced == NodeTraits::get_left(header)){
          NodeTraits::set_left(header, new_node);
       }
 
       if(node_to_be_replaced == NodeTraits::get_right(header)){
          NodeTraits::set_right(header, new_node);
       }
 
       if(node_to_be_replaced == NodeTraits::get_parent(header)){
          NodeTraits::set_parent(header, new_node);
       }
 
       //Now set data from the original node
       node_ptr temp;
       NodeTraits::set_left(new_node, NodeTraits::get_left(node_to_be_replaced));
       NodeTraits::set_right(new_node, NodeTraits::get_right(node_to_be_replaced));
       NodeTraits::set_parent(new_node, NodeTraits::get_parent(node_to_be_replaced));
 
       //Now adjust adjacent nodes for newly inserted node
       if((temp = NodeTraits::get_left(new_node))){
          NodeTraits::set_parent(temp, new_node);
       }
       if((temp = NodeTraits::get_right(new_node))){
          NodeTraits::set_parent(temp, new_node);
       }
       if((temp = NodeTraits::get_parent(new_node)) &&
          //The header has been already updated so avoid it
          temp != header){
          if(NodeTraits::get_left(temp) == node_to_be_replaced){
             NodeTraits::set_left(temp, new_node);
          }
          if(NodeTraits::get_right(temp) == node_to_be_replaced){
             NodeTraits::set_right(temp, new_node);
          }
       }
    }
 
    #if defined(BOOST_INTRUSIVE_DOXYGEN_INVOKED)
    //! <b>Requires</b>: 'n' is a node from the tree except the header.
    //!
    //! <b>Effects</b>: Returns the next node of the tree.
    //!
    //! <b>Complexity</b>: Average constant time.
    //!
    //! <b>Throws</b>: Nothing.
    static node_ptr next_node(node_ptr n) BOOST_NOEXCEPT;
 
    //! <b>Requires</b>: 'n' is a node from the tree except the leftmost node.
    //!
    //! <b>Effects</b>: Returns the previous node of the tree.
    //!
    //! <b>Complexity</b>: Average constant time.
    //!
    //! <b>Throws</b>: Nothing.
    static node_ptr prev_node(node_ptr n) BOOST_NOEXCEPT;
 
    //! <b>Requires</b>: 'n' is a node of a tree but not the header.
    //!
    //! <b>Effects</b>: Returns the minimum node of the subtree starting at p.
    //!
    //! <b>Complexity</b>: Logarithmic to the size of the subtree.
    //!
    //! <b>Throws</b>: Nothing.
    static node_ptr minimum(node_ptr n);
 
    //! <b>Requires</b>: 'n' is a node of a tree but not the header.
    //!
    //! <b>Effects</b>: Returns the maximum node of the subtree starting at p.
    //!
    //! <b>Complexity</b>: Logarithmic to the size of the subtree.
    //!
    //! <b>Throws</b>: Nothing.
    static node_ptr maximum(node_ptr n);
    #endif
 
    //! <b>Requires</b>: 'n' must not be part of any tree.
    //!
    //! <b>Effects</b>: After the function unique(node) == true.
    //!
    //! <b>Complexity</b>: Constant.
    //!
    //! <b>Throws</b>: Nothing.
    //!
    //! <b>Nodes</b>: If node is inserted in a tree, this function corrupts the tree.
    static void init(node_ptr n) BOOST_NOEXCEPT
    {
       NodeTraits::set_parent(n, node_ptr());
       NodeTraits::set_left(n, node_ptr());
       NodeTraits::set_right(n, node_ptr());
    }
 
    //! <b>Effects</b>: Returns true if node is in the same state as if called init(node)
    //!
    //! <b>Complexity</b>: Constant.
    //!
    //! <b>Throws</b>: Nothing.
    static bool inited(const_node_ptr n)
    {
       return !NodeTraits::get_parent(n) &&
              !NodeTraits::get_left(n)   &&
              !NodeTraits::get_right(n)  ;
    }
 
    //! <b>Requires</b>: header must not be part of any tree.
    //!
    //! <b>Effects</b>: Initializes the header to represent an empty tree.
    //!   unique(header) == true.
    //!
    //! <b>Complexity</b>: Constant.
    //!
    //! <b>Throws</b>: Nothing.
    //!
    //! <b>Nodes</b>: If header is inserted in a tree, this function corrupts the tree.
    static void init_header(node_ptr header) BOOST_NOEXCEPT
    {
       NodeTraits::set_parent(header, node_ptr());
       NodeTraits::set_left(header, header);
       NodeTraits::set_right(header, header);
    }
 
    //! <b>Requires</b>: "disposer" must be an object function
    //!   taking a node_ptr parameter and shouldn't throw.
    //!
    //! <b>Effects</b>: Empties the target tree calling
    //!   <tt>void disposer::operator()(node_ptr)</tt> for every node of the tree
    //!    except the header.
    //!
    //! <b>Complexity</b>: Linear to the number of element of the source tree plus the.
    //!   number of elements of tree target tree when calling this function.
    //!
    //! <b>Throws</b>: Nothing.
    template<class Disposer>
    static void clear_and_dispose(node_ptr header, Disposer disposer) BOOST_NOEXCEPT
    {
       node_ptr source_root = NodeTraits::get_parent(header);
       if(!source_root)
          return;
       dispose_subtree(source_root, disposer);
       init_header(header);
    }
 
    //! <b>Requires</b>: header is the header of a tree.
    //!
    //! <b>Effects</b>: Unlinks the leftmost node from the tree, and
    //!   updates the header link to the new leftmost node.
    //!
    //! <b>Complexity</b>: Average complexity is constant time.
    //!
    //! <b>Throws</b>: Nothing.
    //!
    //! <b>Notes</b>: 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.
    static node_ptr unlink_leftmost_without_rebalance(node_ptr header) BOOST_NOEXCEPT
    {
       node_ptr leftmost = NodeTraits::get_left(header);
       if (leftmost == header)
          return node_ptr();
       node_ptr leftmost_parent(NodeTraits::get_parent(leftmost));
       node_ptr leftmost_right (NodeTraits::get_right(leftmost));
       bool is_root = leftmost_parent == header;
 
       if (leftmost_right){
          NodeTraits::set_parent(leftmost_right, leftmost_parent);
          NodeTraits::set_left(header, base_type::minimum(leftmost_right));
 
          if (is_root)
             NodeTraits::set_parent(header, leftmost_right);
          else
             NodeTraits::set_left(NodeTraits::get_parent(header), leftmost_right);
       }
       else if (is_root){
          NodeTraits::set_parent(header, node_ptr());
          NodeTraits::set_left(header,  header);
          NodeTraits::set_right(header, header);
       }
       else{
          NodeTraits::set_left(leftmost_parent, node_ptr());
          NodeTraits::set_left(header, leftmost_parent);
       }
       return leftmost;
    }
 
    //! <b>Requires</b>: 'header' the header of the tree.
    //!
    //! <b>Effects</b>: Returns the number of nodes of the tree.
    //!
    //! <b>Complexity</b>: Linear time.
    //!
    //! <b>Throws</b>: Nothing.
    static std::size_t size(const_node_ptr header) BOOST_NOEXCEPT
    {
       node_ptr beg(begin_node(header));
       node_ptr end(end_node(header));
       std::size_t i = 0;
       for(;beg != end; beg = base_type::next_node(beg)) ++i;
       return i;
    }
 
    //! <b>Requires</b>: header1 and header2 must be the header nodes
    //!  of two trees.
    //!
    //! <b>Effects</b>: Swaps two trees. After the function header1 will contain
    //!   links to the second tree and header2 will have links to the first tree.
    //!
    //! <b>Complexity</b>: Constant.
    //!
    //! <b>Throws</b>: Nothing.
    static void swap_tree(node_ptr header1, node_ptr header2) BOOST_NOEXCEPT
    {
       if(header1 == header2)
          return;
 
       node_ptr tmp;
 
       //Parent swap
       tmp = NodeTraits::get_parent(header1);
       NodeTraits::set_parent(header1, NodeTraits::get_parent(header2));
       NodeTraits::set_parent(header2, tmp);
       //Left swap
       tmp = NodeTraits::get_left(header1);
       NodeTraits::set_left(header1, NodeTraits::get_left(header2));
       NodeTraits::set_left(header2, tmp);
       //Right swap
       tmp = NodeTraits::get_right(header1);
       NodeTraits::set_right(header1, NodeTraits::get_right(header2));
       NodeTraits::set_right(header2, tmp);
 
       //Now test parent
       node_ptr h1_parent(NodeTraits::get_parent(header1));
       if(h1_parent){
          NodeTraits::set_parent(h1_parent, header1);
       }
       else{
          NodeTraits::set_left(header1, header1);
          NodeTraits::set_right(header1, header1);
       }
 
       node_ptr h2_parent(NodeTraits::get_parent(header2));
       if(h2_parent){
          NodeTraits::set_parent(h2_parent, header2);
       }
       else{
          NodeTraits::set_left(header2, header2);
          NodeTraits::set_right(header2, header2);
       }
    }
 
    #if defined(BOOST_INTRUSIVE_DOXYGEN_INVOKED)
    //! <b>Requires</b>: p is a node of a tree.
    //!
    //! <b>Effects</b>: Returns true if p is the header of the tree.
    //!
    //! <b>Complexity</b>: Constant.
    //!
    //! <b>Throws</b>: Nothing.
    static bool is_header(const_node_ptr p) BOOST_NOEXCEPT;
    #endif
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   KeyNodePtrCompare is a function object that induces a strict weak
    //!   ordering compatible with the strict weak ordering used to create the
    //!   the tree. KeyNodePtrCompare can compare KeyType with tree's node_ptrs.
    //!
    //! <b>Effects</b>: Returns a node_ptr to the first element that is equivalent to
    //!   "key" according to "comp" or "header" if that element does not exist.
    //!
    //! <b>Complexity</b>: Logarithmic.
    //!
    //! <b>Throws</b>: If "comp" throws.
    template<class KeyType, class KeyNodePtrCompare>
    static node_ptr find
       (const_node_ptr header, const KeyType &key, KeyNodePtrCompare comp)
    {
       node_ptr end = detail::uncast(header);
       node_ptr y = lower_bound(header, key, comp);
       return (y == end || comp(key, y)) ? end : y;
    }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   KeyNodePtrCompare is a function object that induces a strict weak
    //!   ordering compatible with the strict weak ordering used to create the
    //!   the tree. KeyNodePtrCompare can compare KeyType with tree's node_ptrs.
    //!   'lower_key' must not be greater than 'upper_key' according to 'comp'. If
    //!   'lower_key' == 'upper_key', ('left_closed' || 'right_closed') must be true.
    //!
    //! <b>Effects</b>: Returns an a pair with the following criteria:
    //!
    //!   first = lower_bound(lower_key) if left_closed, upper_bound(lower_key) otherwise
    //!
    //!   second = upper_bound(upper_key) if right_closed, lower_bound(upper_key) otherwise
    //!
    //! <b>Complexity</b>: Logarithmic.
    //!
    //! <b>Throws</b>: If "comp" throws.
    //!
    //! <b>Note</b>: This function can be more efficient than calling upper_bound
    //!   and lower_bound for lower_key and upper_key.
    //!
    //! <b>Note</b>: Experimental function, the interface might change.
    template< class KeyType, class KeyNodePtrCompare>
    static std::pair<node_ptr, node_ptr> bounded_range
       ( const_node_ptr header
       , const KeyType &lower_key
       , const KeyType &upper_key
       , KeyNodePtrCompare comp
       , bool left_closed
       , bool right_closed)
    {
       node_ptr y = detail::uncast(header);
       node_ptr x = NodeTraits::get_parent(header);
 
       while(x){
          //If x is less than lower_key the target
          //range is on the right part
          if(comp(x, lower_key)){
             //Check for invalid input range
             BOOST_INTRUSIVE_INVARIANT_ASSERT(comp(x, upper_key));
             x = NodeTraits::get_right(x);
          }
          //If the upper_key is less than x, the target
          //range is on the left part
          else if(comp(upper_key, x)){
             y = x;
             x = NodeTraits::get_left(x);
          }
          else{
             //x is inside the bounded range(lower_key <= x <= upper_key),
             //so we must split lower and upper searches
             //
             //Sanity check: if lower_key and upper_key are equal, then both left_closed and right_closed can't be false
             BOOST_INTRUSIVE_INVARIANT_ASSERT(left_closed || right_closed || comp(lower_key, x) || comp(x, upper_key));
             return std::pair<node_ptr,node_ptr>(
                left_closed
                   //If left_closed, then comp(x, lower_key) is already the lower_bound
                   //condition so we save one comparison and go to the next level
                   //following traditional lower_bound algo
                   ? lower_bound_loop(NodeTraits::get_left(x), x, lower_key, comp)
                   //If left-open, comp(x, lower_key) is not the upper_bound algo
                   //condition so we must recheck current 'x' node with upper_bound algo
                   : upper_bound_loop(x, y, lower_key, comp)
             ,
                right_closed
                   //If right_closed, then comp(upper_key, x) is already the upper_bound
                   //condition so we can save one comparison and go to the next level
                   //following lower_bound algo
                   ? upper_bound_loop(NodeTraits::get_right(x), y, upper_key, comp)
                   //If right-open, comp(upper_key, x) is not the lower_bound algo
                   //condition so we must recheck current 'x' node with lower_bound algo
                   : lower_bound_loop(x, y, upper_key, comp)
             );
          }
       }
       return std::pair<node_ptr,node_ptr> (y, y);
    }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   KeyNodePtrCompare is a function object that induces a strict weak
    //!   ordering compatible with the strict weak ordering used to create the
    //!   the tree. KeyNodePtrCompare can compare KeyType with tree's node_ptrs.
    //!
    //! <b>Effects</b>: Returns the number of elements with a key equivalent to "key"
    //!   according to "comp".
    //!
    //! <b>Complexity</b>: Logarithmic.
    //!
    //! <b>Throws</b>: If "comp" throws.
    template<class KeyType, class KeyNodePtrCompare>
    static std::size_t count
       (const_node_ptr header, const KeyType &key, KeyNodePtrCompare comp)
    {
       std::pair<node_ptr, node_ptr> ret = equal_range(header, key, comp);
       std::size_t n = 0;
       while(ret.first != ret.second){
          ++n;
          ret.first = base_type::next_node(ret.first);
       }
       return n;
    }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   KeyNodePtrCompare is a function object that induces a strict weak
    //!   ordering compatible with the strict weak ordering used to create the
    //!   the tree. KeyNodePtrCompare can compare KeyType with tree's node_ptrs.
    //!
    //! <b>Effects</b>: Returns an a pair of node_ptr delimiting a range containing
    //!   all elements that are equivalent to "key" according to "comp" or an
    //!   empty range that indicates the position where those elements would be
    //!   if there are no equivalent elements.
    //!
    //! <b>Complexity</b>: Logarithmic.
    //!
    //! <b>Throws</b>: If "comp" throws.
    template<class KeyType, class KeyNodePtrCompare>
    BOOST_INTRUSIVE_FORCEINLINE static std::pair<node_ptr, node_ptr> equal_range
       (const_node_ptr header, const KeyType &key, KeyNodePtrCompare comp)
    {
       return bounded_range(header, key, key, comp, true, true);
    }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   KeyNodePtrCompare is a function object that induces a strict weak
    //!   ordering compatible with the strict weak ordering used to create the
    //!   the tree. KeyNodePtrCompare can compare KeyType with tree's node_ptrs.
    //!
    //! <b>Effects</b>: Returns an a pair of node_ptr delimiting a range containing
    //!   the first element that is equivalent to "key" according to "comp" or an
    //!   empty range that indicates the position where that element would be
    //!   if there are no equivalent elements.
    //!
    //! <b>Complexity</b>: Logarithmic.
    //!
    //! <b>Throws</b>: If "comp" throws.
    template<class KeyType, class KeyNodePtrCompare>
    static std::pair<node_ptr, node_ptr> lower_bound_range
       (const_node_ptr header, const KeyType &key, KeyNodePtrCompare comp)
    {
       node_ptr const lb(lower_bound(header, key, comp));
       std::pair<node_ptr, node_ptr> ret_ii(lb, lb);
       if(lb != header && !comp(key, lb)){
          ret_ii.second = base_type::next_node(ret_ii.second);
       }
       return ret_ii;
    }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   KeyNodePtrCompare is a function object that induces a strict weak
    //!   ordering compatible with the strict weak ordering used to create the
    //!   the tree. KeyNodePtrCompare can compare KeyType with tree's node_ptrs.
    //!
    //! <b>Effects</b>: Returns a node_ptr to the first element that is
    //!   not less than "key" according to "comp" or "header" if that element does
    //!   not exist.
    //!
    //! <b>Complexity</b>: Logarithmic.
    //!
    //! <b>Throws</b>: If "comp" throws.
    template<class KeyType, class KeyNodePtrCompare>
    BOOST_INTRUSIVE_FORCEINLINE static node_ptr lower_bound
       (const_node_ptr header, const KeyType &key, KeyNodePtrCompare comp)
    {
       return lower_bound_loop(NodeTraits::get_parent(header), detail::uncast(header), key, comp);
    }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   KeyNodePtrCompare is a function object that induces a strict weak
    //!   ordering compatible with the strict weak ordering used to create the
    //!   the tree. KeyNodePtrCompare can compare KeyType with tree's node_ptrs.
    //!
    //! <b>Effects</b>: Returns a node_ptr to the first element that is greater
    //!   than "key" according to "comp" or "header" if that element does not exist.
    //!
    //! <b>Complexity</b>: Logarithmic.
    //!
    //! <b>Throws</b>: If "comp" throws.
    template<class KeyType, class KeyNodePtrCompare>
    BOOST_INTRUSIVE_FORCEINLINE static node_ptr upper_bound
       (const_node_ptr header, const KeyType &key, KeyNodePtrCompare comp)
    {
       return upper_bound_loop(NodeTraits::get_parent(header), detail::uncast(header), key, comp);
    }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   "commit_data" must have been obtained from a previous call to
    //!   "insert_unique_check". No objects should have been inserted or erased
    //!   from the set between the "insert_unique_check" that filled "commit_data"
    //!   and the call to "insert_commit".
    //!
    //!
    //! <b>Effects</b>: Inserts new_node in the set using the information obtained
    //!   from the "commit_data" that a previous "insert_check" filled.
    //!
    //! <b>Complexity</b>: Constant time.
    //!
    //! <b>Throws</b>: Nothing.
    //!
    //! <b>Notes</b>: This function has only sense if a "insert_unique_check" has been
    //!   previously executed to fill "commit_data". No value should be inserted or
    //!   erased between the "insert_check" and "insert_commit" calls.
    BOOST_INTRUSIVE_FORCEINLINE static void insert_unique_commit
       (node_ptr header, node_ptr new_value, const insert_commit_data &commit_data) BOOST_NOEXCEPT
    {  return insert_commit(header, new_value, commit_data); }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   KeyNodePtrCompare is a function object that induces a strict weak
    //!   ordering compatible with the strict weak ordering used to create the
    //!   the tree. NodePtrCompare compares KeyType with a node_ptr.
    //!
    //! <b>Effects</b>: Checks if there is an equivalent node to "key" in the
    //!   tree according to "comp" and obtains the needed information to realize
    //!   a constant-time node insertion if there is no equivalent node.
    //!
    //! <b>Returns</b>: If there is an equivalent value
    //!   returns a pair containing a node_ptr to the already present node
    //!   and false. If there is not equivalent key can be inserted returns true
    //!   in the returned pair's boolean and fills "commit_data" that is meant to
    //!   be used with the "insert_commit" function to achieve a constant-time
    //!   insertion function.
    //!
    //! <b>Complexity</b>: Average complexity is at most logarithmic.
    //!
    //! <b>Throws</b>: If "comp" throws.
    //!
    //! <b>Notes</b>: This function is used to improve performance when constructing
    //!   a node is expensive and the user does not want to have two equivalent nodes
    //!   in the tree: 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 node 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 node and use
    //!   "insert_commit" to insert the node 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_unique_commit" only
    //!   if no more objects are inserted or erased from the set.
    template<class KeyType, class KeyNodePtrCompare>
    static std::pair<node_ptr, bool> insert_unique_check
       (const_node_ptr header, const KeyType &key
       ,KeyNodePtrCompare comp, insert_commit_data &commit_data
          #ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
          , std::size_t *pdepth = 0
          #endif
       )
    {
       std::size_t depth = 0;
       node_ptr h(detail::uncast(header));
       node_ptr y(h);
       node_ptr x(NodeTraits::get_parent(y));
       node_ptr prev = node_ptr();
 
       //Find the upper bound, cache the previous value and if we should
       //store it in the left or right node
       bool left_child = true;
       while(x){
          ++depth;
          y = x;
          left_child = comp(key, x);
          x = left_child ?
                NodeTraits::get_left(x) : (prev = y, NodeTraits::get_right(x));
       }
 
       if(pdepth)  *pdepth = depth;
 
       //Since we've found the upper bound there is no other value with the same key if:
       //    - There is no previous node
       //    - The previous node is less than the key
       const bool not_present = !prev || comp(prev, key);
       if(not_present){
          commit_data.link_left = left_child;
          commit_data.node      = y;
       }
       return std::pair<node_ptr, bool>(prev, not_present);
    }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   KeyNodePtrCompare is a function object that induces a strict weak
    //!   ordering compatible with the strict weak ordering used to create the
    //!   the tree. NodePtrCompare compares KeyType with a node_ptr.
    //!   "hint" is node from the "header"'s tree.
    //!
    //! <b>Effects</b>: Checks if there is an equivalent node to "key" in the
    //!   tree according to "comp" using "hint" as a hint to where it should be
    //!   inserted and obtains the needed information to realize
    //!   a constant-time node insertion if there is no equivalent node.
    //!   If "hint" is the upper_bound the function has constant time
    //!   complexity (two comparisons in the worst case).
    //!
    //! <b>Returns</b>: If there is an equivalent value
    //!   returns a pair containing a node_ptr to the already present node
    //!   and false. If there is not equivalent key can be inserted returns true
    //!   in the returned pair's boolean and fills "commit_data" that is meant to
    //!   be used with the "insert_commit" function to achieve a constant-time
    //!   insertion function.
    //!
    //! <b>Complexity</b>: Average complexity is at most logarithmic, but it is
    //!   amortized constant time if new_node should be inserted immediately before "hint".
    //!
    //! <b>Throws</b>: If "comp" throws.
    //!
    //! <b>Notes</b>: This function is used to improve performance when constructing
    //!   a node is expensive and the user does not want to have two equivalent nodes
    //!   in the tree: 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 node 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 node and use
    //!   "insert_commit" to insert the node 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_unique_commit" only
    //!   if no more objects are inserted or erased from the set.
    template<class KeyType, class KeyNodePtrCompare>
    static std::pair<node_ptr, bool> insert_unique_check
       (const_node_ptr header, node_ptr hint, const KeyType &key
       ,KeyNodePtrCompare comp, insert_commit_data &commit_data
          #ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
          , std::size_t *pdepth = 0
          #endif
       )
    {
       //hint must be bigger than the key
       if(hint == header || comp(key, hint)){
          node_ptr prev(hint);
          //Previous value should be less than the key
          if(hint == begin_node(header) || comp((prev = base_type::prev_node(hint)), key)){
             commit_data.link_left = unique(header) || !NodeTraits::get_left(hint);
             commit_data.node      = commit_data.link_left ? hint : prev;
             if(pdepth){
                *pdepth = commit_data.node == header ? 0 : depth(commit_data.node) + 1;
             }
             return std::pair<node_ptr, bool>(node_ptr(), true);
          }
       }
       //Hint was wrong, use hintless insertion
       return insert_unique_check(header, key, comp, commit_data, pdepth);
    }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   NodePtrCompare is a function object that induces a strict weak
    //!   ordering compatible with the strict weak ordering used to create the
    //!   the tree. NodePtrCompare compares two node_ptrs. "hint" is node from
    //!   the "header"'s tree.
    //!
    //! <b>Effects</b>: Inserts new_node 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).
    //!
    //! <b>Complexity</b>: Logarithmic in general, but it is amortized
    //!   constant time if new_node is inserted immediately before "hint".
    //!
    //! <b>Throws</b>: If "comp" throws.
    template<class NodePtrCompare>
    static node_ptr insert_equal
       (node_ptr h, node_ptr hint, node_ptr new_node, NodePtrCompare comp
          #ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
          , std::size_t *pdepth = 0
          #endif
       )
    {
       insert_commit_data commit_data;
       insert_equal_check(h, hint, new_node, comp, commit_data, pdepth);
       insert_commit(h, new_node, commit_data);
       return new_node;
    }
 
    //! <b>Requires</b>: "h" must be the header node of a tree.
    //!   NodePtrCompare is a function object that induces a strict weak
    //!   ordering compatible with the strict weak ordering used to create the
    //!   the tree. NodePtrCompare compares two node_ptrs.
    //!
    //! <b>Effects</b>: Inserts new_node into the tree before the upper bound
    //!   according to "comp".
    //!
    //! <b>Complexity</b>: Average complexity for insert element is at
    //!   most logarithmic.
    //!
    //! <b>Throws</b>: If "comp" throws.
    template<class NodePtrCompare>
    static node_ptr insert_equal_upper_bound
       (node_ptr h, node_ptr new_node, NodePtrCompare comp
          #ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
          , std::size_t *pdepth = 0
          #endif
       )
    {
       insert_commit_data commit_data;
       insert_equal_upper_bound_check(h, new_node, comp, commit_data, pdepth);
       insert_commit(h, new_node, commit_data);
       return new_node;
    }
 
    //! <b>Requires</b>: "h" must be the header node of a tree.
    //!   NodePtrCompare is a function object that induces a strict weak
    //!   ordering compatible with the strict weak ordering used to create the
    //!   the tree. NodePtrCompare compares two node_ptrs.
    //!
    //! <b>Effects</b>: Inserts new_node into the tree before the lower bound
    //!   according to "comp".
    //!
    //! <b>Complexity</b>: Average complexity for insert element is at
    //!   most logarithmic.
    //!
    //! <b>Throws</b>: If "comp" throws.
    template<class NodePtrCompare>
    static node_ptr insert_equal_lower_bound
       (node_ptr h, node_ptr new_node, NodePtrCompare comp
          #ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
          , std::size_t *pdepth = 0
          #endif
       )
    {
       insert_commit_data commit_data;
       insert_equal_lower_bound_check(h, new_node, comp, commit_data, pdepth);
       insert_commit(h, new_node, commit_data);
       return new_node;
    }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   "pos" must be a valid iterator or header (end) node.
    //!   "pos" must be an iterator pointing to the successor to "new_node"
    //!   once inserted according to the order of already inserted nodes. This function does not
    //!   check "pos" and this precondition must be guaranteed by the caller.
    //!
    //! <b>Effects</b>: Inserts new_node into the tree before "pos".
    //!
    //! <b>Complexity</b>: Constant-time.
    //!
    //! <b>Throws</b>: Nothing.
    //!
    //! <b>Note</b>: If "pos" is not the successor of the newly inserted "new_node"
    //! tree invariants might be broken.
    static node_ptr insert_before
       (node_ptr header, node_ptr pos, node_ptr new_node
          #ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
          , std::size_t *pdepth = 0
          #endif
       ) BOOST_NOEXCEPT
    {
       insert_commit_data commit_data;
       insert_before_check(header, pos, commit_data, pdepth);
       insert_commit(header, new_node, commit_data);
       return new_node;
    }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   "new_node" must be, according to the used ordering no less than the
    //!   greatest inserted key.
    //!
    //! <b>Effects</b>: Inserts new_node into the tree before "pos".
    //!
    //! <b>Complexity</b>: Constant-time.
    //!
    //! <b>Throws</b>: Nothing.
    //!
    //! <b>Note</b>: If "new_node" is less than the greatest inserted key
    //! tree invariants are broken. This function is slightly faster than
    //! using "insert_before".
    static void push_back
       (node_ptr header, node_ptr new_node
          #ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
          , std::size_t *pdepth = 0
          #endif
       ) BOOST_NOEXCEPT
    {
       insert_commit_data commit_data;
       push_back_check(header, commit_data, pdepth);
       insert_commit(header, new_node, commit_data);
    }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   "new_node" must be, according to the used ordering, no greater than the
    //!   lowest inserted key.
    //!
    //! <b>Effects</b>: Inserts new_node into the tree before "pos".
    //!
    //! <b>Complexity</b>: Constant-time.
    //!
    //! <b>Throws</b>: Nothing.
    //!
    //! <b>Note</b>: If "new_node" is greater than the lowest inserted key
    //! tree invariants are broken. This function is slightly faster than
    //! using "insert_before".
    static void push_front
       (node_ptr header, node_ptr new_node
          #ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
          , std::size_t *pdepth = 0
          #endif
       ) BOOST_NOEXCEPT
    {
       insert_commit_data commit_data;
       push_front_check(header, commit_data, pdepth);
       insert_commit(header, new_node, commit_data);
    }
 
    //! <b>Requires</b>: 'n' can't be a header node.
    //!
    //! <b>Effects</b>: Calculates the depth of a node: the depth of a
    //! node is the length (number of edges) of the path from the root
    //! to that node. (The root node is at depth 0.)
    //!
    //! <b>Complexity</b>: Logarithmic to the number of nodes in the tree.
    //!
    //! <b>Throws</b>: Nothing.
    static std::size_t depth(const_node_ptr n) BOOST_NOEXCEPT
    {
       std::size_t depth = 0;
       node_ptr p_parent;
       while(n != NodeTraits::get_parent(p_parent = NodeTraits::get_parent(n))){
          ++depth;
          n = p_parent;
       }
       return depth;
    }
 
    //! <b>Requires</b>: "cloner" must be a function
    //!   object taking a node_ptr and returning a new cloned node of it. "disposer" must
    //!   take a node_ptr and shouldn't throw.
    //!
    //! <b>Effects</b>: First empties target tree calling
    //!   <tt>void disposer::operator()(node_ptr)</tt> for every node of the tree
    //!    except the header.
    //!
    //!   Then, duplicates the entire tree pointed by "source_header" cloning each
    //!   source node with <tt>node_ptr Cloner::operator()(node_ptr)</tt> to obtain
    //!   the nodes of the target tree. If "cloner" throws, the cloned target nodes
    //!   are disposed using <tt>void disposer(node_ptr )</tt>.
    //!
    //! <b>Complexity</b>: Linear to the number of element of the source tree plus the
    //!   number of elements of tree target tree when calling this function.
    //!
    //! <b>Throws</b>: If cloner functor throws. If this happens target nodes are disposed.
    template <class Cloner, class Disposer>
    static void clone
       (const_node_ptr source_header, node_ptr target_header, Cloner cloner, Disposer disposer)
    {
       if(!unique(target_header)){
          clear_and_dispose(target_header, disposer);
       }
 
       node_ptr leftmost, rightmost;
       node_ptr new_root = clone_subtree
          (source_header, target_header, cloner, disposer, leftmost, rightmost);
 
       //Now update header node
       NodeTraits::set_parent(target_header, new_root);
       NodeTraits::set_left  (target_header, leftmost);
       NodeTraits::set_right (target_header, rightmost);
    }
 
    //! <b>Requires</b>: header must be the header of a tree, z a node
    //!    of that tree and z != header.
    //!
    //! <b>Effects</b>: Erases node "z" from the tree with header "header".
    //!
    //! <b>Complexity</b>: Amortized constant time.
    //!
    //! <b>Throws</b>: Nothing.
    BOOST_INTRUSIVE_FORCEINLINE static void erase(node_ptr header, node_ptr z) BOOST_NOEXCEPT
    {
       data_for_rebalance ignored;
       erase(header, z, ignored);
    }
 
    //! <b>Requires</b>: header1 and header2 must be the headers of trees tree1 and tree2
    //!   respectively, z a non-header node of tree1. NodePtrCompare is the comparison
    //!   function of tree1..
    //!
    //! <b>Effects</b>: Transfers node "z" from tree1 to tree2 if tree1 does not contain
    //!   a node that is equivalent to z.
    //!
    //! <b>Returns</b>: True if the node was trasferred, false otherwise.
    //!
    //! <b>Complexity</b>: Logarithmic.
    //!
    //! <b>Throws</b>: If the comparison throws.
    template<class NodePtrCompare>
    BOOST_INTRUSIVE_FORCEINLINE static bool transfer_unique
       (node_ptr header1, NodePtrCompare comp, node_ptr header2, node_ptr z)
    {
       data_for_rebalance ignored;
       return transfer_unique(header1, comp, header2, z, ignored);
    }
 
    //! <b>Requires</b>: header1 and header2 must be the headers of trees tree1 and tree2
    //!   respectively, z a non-header node of tree1. NodePtrCompare is the comparison
    //!   function of tree1..
    //!
    //! <b>Effects</b>: Transfers node "z" from tree1 to tree2.
    //!
    //! <b>Complexity</b>: Logarithmic.
    //!
    //! <b>Throws</b>: If the comparison throws.
    template<class NodePtrCompare>
    BOOST_INTRUSIVE_FORCEINLINE static void transfer_equal
       (node_ptr header1, NodePtrCompare comp, node_ptr header2, node_ptr z)
    {
       data_for_rebalance ignored;
       transfer_equal(header1, comp, header2, z, ignored);
    }
 
    //! <b>Requires</b>: 'n' is a tree node but not the header.
    //!
    //! <b>Effects</b>: Unlinks the node and rebalances the tree.
    //!
    //! <b>Complexity</b>: Average complexity is constant time.
    //!
    //! <b>Throws</b>: Nothing.
    static void unlink(node_ptr n) BOOST_NOEXCEPT
    {
       node_ptr x = NodeTraits::get_parent(n);
       if(x){
          while(!base_type::is_header(x))
             x = NodeTraits::get_parent(x);
          erase(x, n);
       }
    }
 
    //! <b>Requires</b>: header must be the header of a tree.
    //!
    //! <b>Effects</b>: Rebalances the tree.
    //!
    //! <b>Throws</b>: Nothing.
    //!
    //! <b>Complexity</b>: Linear.
    static void rebalance(node_ptr header) BOOST_NOEXCEPT
    {
       node_ptr root = NodeTraits::get_parent(header);
       if(root){
          rebalance_subtree(root);
       }
    }
 
    //! <b>Requires</b>: old_root is a node of a tree. It shall not be null.
    //!
    //! <b>Effects</b>: Rebalances the subtree rooted at old_root.
    //!
    //! <b>Returns</b>: The new root of the subtree.
    //!
    //! <b>Throws</b>: Nothing.
    //!
    //! <b>Complexity</b>: Linear.
    static node_ptr rebalance_subtree(node_ptr old_root) BOOST_NOEXCEPT
    {
       //Taken from:
       //"Tree rebalancing in optimal time and space"
       //Quentin F. Stout and Bette L. Warren
 
       //To avoid irregularities in the algorithm (old_root can be a
       //left or right child or even the root of the tree) just put the
       //root as the right child of its parent. Before doing this backup
       //information to restore the original relationship after
       //the algorithm is applied.
       node_ptr super_root = NodeTraits::get_parent(old_root);
       BOOST_INTRUSIVE_INVARIANT_ASSERT(super_root);
 
       //Get root info
       node_ptr super_root_right_backup = NodeTraits::get_right(super_root);
       bool super_root_is_header = NodeTraits::get_parent(super_root) == old_root;
       bool old_root_is_right  = is_right_child(old_root);
       NodeTraits::set_right(super_root, old_root);
 
       std::size_t size;
       subtree_to_vine(super_root, size);
       vine_to_subtree(super_root, size);
       node_ptr new_root = NodeTraits::get_right(super_root);
 
       //Recover root
       if(super_root_is_header){
          NodeTraits::set_right(super_root, super_root_right_backup);
          NodeTraits::set_parent(super_root, new_root);
       }
       else if(old_root_is_right){
          NodeTraits::set_right(super_root, new_root);
       }
       else{
          NodeTraits::set_right(super_root, super_root_right_backup);
          NodeTraits::set_left(super_root, new_root);
       }
       return new_root;
    }
 
    //! <b>Effects</b>: Asserts the integrity of the container with additional checks provided by the user.
    //!
    //! <b>Requires</b>: header must be the header of a tree.
    //!
    //! <b>Complexity</b>: Linear time.
    //!
    //! <b>Note</b>: The method might not have effect when asserts are turned off (e.g., with NDEBUG).
    //!   Experimental function, interface might change in future versions.
    template<class Checker>
    static void check(const_node_ptr header, Checker checker, typename Checker::return_type& checker_return)
    {
       const_node_ptr root_node_ptr = NodeTraits::get_parent(header);
       if (!root_node_ptr){
          // check left&right header pointers
          BOOST_INTRUSIVE_INVARIANT_ASSERT(NodeTraits::get_left(header) == header);
          BOOST_INTRUSIVE_INVARIANT_ASSERT(NodeTraits::get_right(header) == header);
       }
       else{
          // check parent pointer of root node
          BOOST_INTRUSIVE_INVARIANT_ASSERT(NodeTraits::get_parent(root_node_ptr) == header);
          // check subtree from root
          check_subtree(root_node_ptr, checker, checker_return);
          // check left&right header pointers
          const_node_ptr p = root_node_ptr;
          while (NodeTraits::get_left(p)) { p = NodeTraits::get_left(p); }
          BOOST_INTRUSIVE_INVARIANT_ASSERT(NodeTraits::get_left(header) == p);
          p = root_node_ptr;
          while (NodeTraits::get_right(p)) { p = NodeTraits::get_right(p); }
          BOOST_INTRUSIVE_INVARIANT_ASSERT(NodeTraits::get_right(header) == p);
       }
    }
 
    protected:
 
    template<class NodePtrCompare>
    static bool transfer_unique
       (node_ptr header1, NodePtrCompare comp, node_ptr header2, node_ptr z, data_for_rebalance &info)
    {
       insert_commit_data commit_data;
       bool const transferable = insert_unique_check(header1, z, comp, commit_data).second;
       if(transferable){
          erase(header2, z, info);
          insert_commit(header1, z, commit_data);
       }
       return transferable;
    }
 
    template<class NodePtrCompare>
    static void transfer_equal
       (node_ptr header1, NodePtrCompare comp, node_ptr header2, node_ptr z, data_for_rebalance &info)
    {
       insert_commit_data commit_data;
       insert_equal_upper_bound_check(header1, z, comp, commit_data);
       erase(header2, z, info);
       insert_commit(header1, z, commit_data);
    }
 
    static void erase(node_ptr header, node_ptr z, data_for_rebalance &info)
    {
       node_ptr y(z);
       node_ptr x;
       const node_ptr z_left(NodeTraits::get_left(z));
       const node_ptr z_right(NodeTraits::get_right(z));
 
       if(!z_left){
          x = z_right;    // x might be null.
       }
       else if(!z_right){ // z has exactly one non-null child. y == z.
          x = z_left;       // x is not null.
          BOOST_ASSERT(x);
       }
       else{ //make y != z
          // y = find z's successor
          y = base_type::minimum(z_right);
          x = NodeTraits::get_right(y);     // x might be null.
       }
 
       node_ptr x_parent;
       const node_ptr z_parent(NodeTraits::get_parent(z));
       const bool z_is_leftchild(NodeTraits::get_left(z_parent) == z);
 
       if(y != z){ //has two children and y is the minimum of z
          //y is z's successor and it has a null left child.
          //x is the right child of y (it can be null)
          //Relink y in place of z and link x with y's old parent
          NodeTraits::set_parent(z_left, y);
          NodeTraits::set_left(y, z_left);
          if(y != z_right){
             //Link y with the right tree of z
             NodeTraits::set_right(y, z_right);
             NodeTraits::set_parent(z_right, y);
             //Link x with y's old parent (y must be a left child)
             x_parent = NodeTraits::get_parent(y);
             BOOST_ASSERT(NodeTraits::get_left(x_parent) == y);
             if(x)
                NodeTraits::set_parent(x, x_parent);
             //Since y was the successor and not the right child of z, it must be a left child
             NodeTraits::set_left(x_parent, x);
          }
          else{ //y was the right child of y so no need to fix x's position
             x_parent = y;
          }
          NodeTraits::set_parent(y, z_parent);
          this_type::set_child(header, y, z_parent, z_is_leftchild);
       }
       else {  // z has zero or one child, x is one child (it can be null)
          //Just link x to z's parent
          x_parent = z_parent;
          if(x)
             NodeTraits::set_parent(x, z_parent);
          this_type::set_child(header, x, z_parent, z_is_leftchild);
 
          //Now update leftmost/rightmost in case z was one of them
          if(NodeTraits::get_left(header) == z){
             //z_left must be null because z is the leftmost
             BOOST_ASSERT(!z_left);
             NodeTraits::set_left(header, !z_right ?
                z_parent :  // makes leftmost == header if z == root
                base_type::minimum(z_right));
          }
          if(NodeTraits::get_right(header) == z){
             //z_right must be null because z is the rightmost
             BOOST_ASSERT(!z_right);
             NodeTraits::set_right(header, !z_left ?
                z_parent :  // makes rightmost == header if z == root
                base_type::maximum(z_left));
          }
       }
 
       //If z had 0/1 child, y == z and one of its children (and maybe null)
       //If z had 2 children, y is the successor of z and x is the right child of y
       info.x = x;
       info.y = y;
       //If z had 0/1 child, x_parent is the new parent of the old right child of y (z's successor)
       //If z had 2 children, x_parent is the new parent of y (z_parent)
       BOOST_ASSERT(!x || NodeTraits::get_parent(x) == x_parent);
       info.x_parent = x_parent;
    }
 
    //! <b>Requires</b>: 'subtree' is a node of the tree but it's not the header.
    //!
    //! <b>Effects</b>: Returns the number of nodes of the subtree.
    //!
    //! <b>Complexity</b>: Linear time.
    //!
    //! <b>Throws</b>: Nothing.
    static std::size_t subtree_size(const_node_ptr subtree) BOOST_NOEXCEPT
    {
       std::size_t count = 0;
       if (subtree){
          node_ptr n = detail::uncast(subtree);
          node_ptr m = NodeTraits::get_left(n);
          while(m){
             n = m;
             m = NodeTraits::get_left(n);
          }
 
          while(1){
             ++count;
             node_ptr n_right(NodeTraits::get_right(n));
             if(n_right){
                n = n_right;
                m = NodeTraits::get_left(n);
                while(m){
                   n = m;
                   m = NodeTraits::get_left(n);
                }
             }
             else {
                do{
                   if (n == subtree){
                      return count;
                   }
                   m = n;
                   n = NodeTraits::get_parent(n);
                }while(NodeTraits::get_left(n) != m);
             }
          }
       }
       return count;
    }
 
    //! <b>Requires</b>: p is a node of a tree.
    //!
    //! <b>Effects</b>: Returns true if p is a left child.
    //!
    //! <b>Complexity</b>: Constant.
    //!
    //! <b>Throws</b>: Nothing.
    BOOST_INTRUSIVE_FORCEINLINE static bool is_left_child(node_ptr p) BOOST_NOEXCEPT
    {  return NodeTraits::get_left(NodeTraits::get_parent(p)) == p;  }
 
    //! <b>Requires</b>: p is a node of a tree.
    //!
    //! <b>Effects</b>: Returns true if p is a right child.
    //!
    //! <b>Complexity</b>: Constant.
    //!
    //! <b>Throws</b>: Nothing.
    BOOST_INTRUSIVE_FORCEINLINE static bool is_right_child(node_ptr p) BOOST_NOEXCEPT
    {  return NodeTraits::get_right(NodeTraits::get_parent(p)) == p;  }
 
    static void insert_before_check
       (node_ptr header, node_ptr pos
       , insert_commit_data &commit_data
          #ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
          , std::size_t *pdepth = 0
          #endif
       )
    {
       node_ptr prev(pos);
       if(pos != NodeTraits::get_left(header))
          prev = base_type::prev_node(pos);
       bool link_left = unique(header) || !NodeTraits::get_left(pos);
       commit_data.link_left = link_left;
       commit_data.node = link_left ? pos : prev;
       if(pdepth){
          *pdepth = commit_data.node == header ? 0 : depth(commit_data.node) + 1;
       }
    }
 
    static void push_back_check
       (node_ptr header, insert_commit_data &commit_data
          #ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
          , std::size_t *pdepth = 0
          #endif
       ) BOOST_NOEXCEPT
    {
       node_ptr prev(NodeTraits::get_right(header));
       if(pdepth){
          *pdepth = prev == header ? 0 : depth(prev) + 1;
       }
       commit_data.link_left = false;
       commit_data.node = prev;
    }
 
    static void push_front_check
       (node_ptr header, insert_commit_data &commit_data
          #ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
          , std::size_t *pdepth = 0
          #endif
       ) BOOST_NOEXCEPT
    {
       node_ptr pos(NodeTraits::get_left(header));
       if(pdepth){
          *pdepth = pos == header ? 0 : depth(pos) + 1;
       }
       commit_data.link_left = true;
       commit_data.node = pos;
    }
 
    template<class NodePtrCompare>
    static void insert_equal_check
       (node_ptr header, node_ptr hint, node_ptr new_node, NodePtrCompare comp
       , insert_commit_data &commit_data
       /// @cond
       , std::size_t *pdepth = 0
       /// @endcond
       )
    {
       if(hint == header || !comp(hint, new_node)){
          node_ptr prev(hint);
          if(hint == NodeTraits::get_left(header) ||
             !comp(new_node, (prev = base_type::prev_node(hint)))){
             bool link_left = unique(header) || !NodeTraits::get_left(hint);
             commit_data.link_left = link_left;
             commit_data.node = link_left ? hint : prev;
             if(pdepth){
                *pdepth = commit_data.node == header ? 0 : depth(commit_data.node) + 1;
             }
          }
          else{
             insert_equal_upper_bound_check(header, new_node, comp, commit_data, pdepth);
          }
       }
       else{
          insert_equal_lower_bound_check(header, new_node, comp, commit_data, pdepth);
       }
    }
 
    template<class NodePtrCompare>
    static void insert_equal_upper_bound_check
       (node_ptr h, node_ptr new_node, NodePtrCompare comp, insert_commit_data & commit_data, std::size_t *pdepth = 0)
    {
       std::size_t depth = 0;
       node_ptr y(h);
       node_ptr x(NodeTraits::get_parent(y));
 
       while(x){
          ++depth;
          y = x;
          x = comp(new_node, x) ?
                NodeTraits::get_left(x) : NodeTraits::get_right(x);
       }
       if(pdepth)  *pdepth = depth;
       commit_data.link_left = (y == h) || comp(new_node, y);
       commit_data.node = y;
    }
 
    template<class NodePtrCompare>
    static void insert_equal_lower_bound_check
       (node_ptr h, node_ptr new_node, NodePtrCompare comp, insert_commit_data & commit_data, std::size_t *pdepth = 0)
    {
       std::size_t depth = 0;
       node_ptr y(h);
       node_ptr x(NodeTraits::get_parent(y));
 
       while(x){
          ++depth;
          y = x;
          x = !comp(x, new_node) ?
                NodeTraits::get_left(x) : NodeTraits::get_right(x);
       }
       if(pdepth)  *pdepth = depth;
       commit_data.link_left = (y == h) || !comp(y, new_node);
       commit_data.node = y;
    }
 
    static void insert_commit
       (node_ptr header, node_ptr new_node, const insert_commit_data &commit_data) BOOST_NOEXCEPT
    {
       //Check if commit_data has not been initialized by a insert_unique_check call.
       BOOST_INTRUSIVE_INVARIANT_ASSERT(commit_data.node != node_ptr());
       node_ptr parent_node(commit_data.node);
       if(parent_node == header){
          NodeTraits::set_parent(header, new_node);
          NodeTraits::set_right(header, new_node);
          NodeTraits::set_left(header, new_node);
       }
       else if(commit_data.link_left){
          NodeTraits::set_left(parent_node, new_node);
          if(parent_node == NodeTraits::get_left(header))
              NodeTraits::set_left(header, new_node);
       }
       else{
          NodeTraits::set_right(parent_node, new_node);
          if(parent_node == NodeTraits::get_right(header))
              NodeTraits::set_right(header, new_node);
       }
       NodeTraits::set_parent(new_node, parent_node);
       NodeTraits::set_right(new_node, node_ptr());
       NodeTraits::set_left(new_node, node_ptr());
    }
 
    //Fix header and own's parent data when replacing x with own, providing own's old data with parent
    static void set_child(node_ptr header, node_ptr new_child, node_ptr new_parent, const bool link_left) BOOST_NOEXCEPT
    {
       if(new_parent == header)
          NodeTraits::set_parent(header, new_child);
       else if(link_left)
          NodeTraits::set_left(new_parent, new_child);
       else
          NodeTraits::set_right(new_parent, new_child);
    }
 
    // rotate p to left (no header and p's parent fixup)
    static void rotate_left_no_parent_fix(node_ptr p, node_ptr p_right) BOOST_NOEXCEPT
    {
       node_ptr p_right_left(NodeTraits::get_left(p_right));
       NodeTraits::set_right(p, p_right_left);
       if(p_right_left){
          NodeTraits::set_parent(p_right_left, p);
       }
       NodeTraits::set_left(p_right, p);
       NodeTraits::set_parent(p, p_right);
    }
 
    // rotate p to left (with header and p's parent fixup)
    static void rotate_left(node_ptr p, node_ptr p_right, node_ptr p_parent, node_ptr header) BOOST_NOEXCEPT
    {
       const bool p_was_left(NodeTraits::get_left(p_parent) == p);
       rotate_left_no_parent_fix(p, p_right);
       NodeTraits::set_parent(p_right, p_parent);
       set_child(header, p_right, p_parent, p_was_left);
    }
 
    // rotate p to right (no header and p's parent fixup)
    static void rotate_right_no_parent_fix(node_ptr p, node_ptr p_left) BOOST_NOEXCEPT
    {
       node_ptr p_left_right(NodeTraits::get_right(p_left));
       NodeTraits::set_left(p, p_left_right);
       if(p_left_right){
          NodeTraits::set_parent(p_left_right, p);
       }
       NodeTraits::set_right(p_left, p);
       NodeTraits::set_parent(p, p_left);
    }
 
    // rotate p to right (with header and p's parent fixup)
    static void rotate_right(node_ptr p, node_ptr p_left, node_ptr p_parent, node_ptr header) BOOST_NOEXCEPT
    {
       const bool p_was_left(NodeTraits::get_left(p_parent) == p);
       rotate_right_no_parent_fix(p, p_left);
       NodeTraits::set_parent(p_left, p_parent);
       set_child(header, p_left, p_parent, p_was_left);
    }
 
    private:
 
    static void subtree_to_vine(node_ptr vine_tail, std::size_t &size) BOOST_NOEXCEPT
    {
       //Inspired by LibAVL:
       //It uses a clever optimization for trees with parent pointers.
       //No parent pointer is updated when transforming a tree to a vine as
       //most of them will be overriten during compression rotations.
       //A final pass must be made after the rebalancing to updated those
       //pointers not updated by tree_to_vine + compression calls
       std::size_t len = 0;
       node_ptr remainder = NodeTraits::get_right(vine_tail);
       while(remainder){
          node_ptr tempptr = NodeTraits::get_left(remainder);
          if(!tempptr){   //move vine-tail down one
             vine_tail = remainder;
             remainder = NodeTraits::get_right(remainder);
             ++len;
          }
          else{ //rotate
             NodeTraits::set_left(remainder, NodeTraits::get_right(tempptr));
             NodeTraits::set_right(tempptr, remainder);
             remainder = tempptr;
             NodeTraits::set_right(vine_tail, tempptr);
          }
       }
       size = len;
    }
 
    static void compress_subtree(node_ptr scanner, std::size_t count) BOOST_NOEXCEPT
    {
       while(count--){   //compress "count" spine nodes in the tree with pseudo-root scanner
          node_ptr child = NodeTraits::get_right(scanner);
          node_ptr child_right = NodeTraits::get_right(child);
          NodeTraits::set_right(scanner, child_right);
          //Avoid setting the parent of child_right
          scanner = child_right;
          node_ptr scanner_left = NodeTraits::get_left(scanner);
          NodeTraits::set_right(child, scanner_left);
          if(scanner_left)
             NodeTraits::set_parent(scanner_left, child);
          NodeTraits::set_left(scanner, child);
          NodeTraits::set_parent(child, scanner);
       }
    }
 
    static void vine_to_subtree(node_ptr super_root, std::size_t count) BOOST_NOEXCEPT
    {
       const std::size_t one_szt = 1u;
       std::size_t leaf_nodes = count + one_szt - std::size_t(one_szt << detail::floor_log2(count + one_szt));
       compress_subtree(super_root, leaf_nodes);  //create deepest leaves
       std::size_t vine_nodes = count - leaf_nodes;
       while(vine_nodes > 1){
          vine_nodes /= 2;
          compress_subtree(super_root, vine_nodes);
       }
 
       //Update parents of nodes still in the in the original vine line
       //as those have not been updated by subtree_to_vine or compress_subtree
       for ( node_ptr q = super_root, p = NodeTraits::get_right(super_root)
           ; p
           ; q = p, p = NodeTraits::get_right(p)){
          NodeTraits::set_parent(p, q);
       }
    }
 
    //! <b>Requires</b>: "n" must be a node inserted in a tree.
    //!
    //! <b>Effects</b>: Returns a pointer to the header node of the tree.
    //!
    //! <b>Complexity</b>: Logarithmic.
    //!
    //! <b>Throws</b>: Nothing.
    static node_ptr get_root(node_ptr n) BOOST_NOEXCEPT
    {
       BOOST_INTRUSIVE_INVARIANT_ASSERT((!inited(n)));
       node_ptr x = NodeTraits::get_parent(n);
       if(x){
          while(!base_type::is_header(x)){
             x = NodeTraits::get_parent(x);
          }
          return x;
       }
       else{
          return n;
       }
    }
 
    template <class Cloner, class Disposer>
    static node_ptr clone_subtree
       (const_node_ptr source_parent, node_ptr target_parent
       , Cloner cloner, Disposer disposer
       , node_ptr &leftmost_out, node_ptr &rightmost_out
       )
    {
       node_ptr target_sub_root = target_parent;
       node_ptr source_root = NodeTraits::get_parent(source_parent);
       if(!source_root){
          leftmost_out = rightmost_out = source_root;
       }
       else{
          //We'll calculate leftmost and rightmost nodes while iterating
          node_ptr current = source_root;
          node_ptr insertion_point = target_sub_root = cloner(current);
 
          //We'll calculate leftmost and rightmost nodes while iterating
          node_ptr leftmost  = target_sub_root;
          node_ptr rightmost = target_sub_root;
 
          //First set the subroot
          NodeTraits::set_left(target_sub_root, node_ptr());
          NodeTraits::set_right(target_sub_root, node_ptr());
          NodeTraits::set_parent(target_sub_root, target_parent);
 
          dispose_subtree_disposer<Disposer> rollback(disposer, target_sub_root);
          while(true) {
             //First clone left nodes
             if( NodeTraits::get_left(current) &&
                !NodeTraits::get_left(insertion_point)) {
                current = NodeTraits::get_left(current);
                node_ptr temp = insertion_point;
                //Clone and mark as leaf
                insertion_point = cloner(current);
                NodeTraits::set_left  (insertion_point, node_ptr());
                NodeTraits::set_right (insertion_point, node_ptr());
                //Insert left
                NodeTraits::set_parent(insertion_point, temp);
                NodeTraits::set_left  (temp, insertion_point);
                //Update leftmost
                if(rightmost == target_sub_root)
                   leftmost = insertion_point;
             }
             //Then clone right nodes
             else if( NodeTraits::get_right(current) &&
                      !NodeTraits::get_right(insertion_point)){
                current = NodeTraits::get_right(current);
                node_ptr temp = insertion_point;
                //Clone and mark as leaf
                insertion_point = cloner(current);
                NodeTraits::set_left  (insertion_point, node_ptr());
                NodeTraits::set_right (insertion_point, node_ptr());
                //Insert right
                NodeTraits::set_parent(insertion_point, temp);
                NodeTraits::set_right (temp, insertion_point);
                //Update rightmost
                rightmost = insertion_point;
             }
             //If not, go up
             else if(current == source_root){
                break;
             }
             else{
                //Branch completed, go up searching more nodes to clone
                current = NodeTraits::get_parent(current);
                insertion_point = NodeTraits::get_parent(insertion_point);
             }
          }
          rollback.release();
          leftmost_out   = leftmost;
          rightmost_out  = rightmost;
       }
       return target_sub_root;
    }
 
    template<class Disposer>
    static void dispose_subtree(node_ptr x, Disposer disposer) BOOST_NOEXCEPT
    {
       while (x){
          node_ptr save(NodeTraits::get_left(x));
          if (save) {
             // Right rotation
             NodeTraits::set_left(x, NodeTraits::get_right(save));
             NodeTraits::set_right(save, x);
          }
          else {
             save = NodeTraits::get_right(x);
             init(x);
             disposer(x);
          }
          x = save;
       }
    }
 
    template<class KeyType, class KeyNodePtrCompare>
    static node_ptr lower_bound_loop
       (node_ptr x, node_ptr y, const KeyType &key, KeyNodePtrCompare comp)
    {
       while(x){
          if(comp(x, key)){
             x = NodeTraits::get_right(x);
          }
          else{
             y = x;
             x = NodeTraits::get_left(x);
          }
       }
       return y;
    }
 
    template<class KeyType, class KeyNodePtrCompare>
    static node_ptr upper_bound_loop
       (node_ptr x, node_ptr y, const KeyType &key, KeyNodePtrCompare comp)
    {
       while(x){
          if(comp(key, x)){
             y = x;
             x = NodeTraits::get_left(x);
          }
          else{
             x = NodeTraits::get_right(x);
          }
       }
       return y;
    }
 
    template<class Checker>
    static void check_subtree(const_node_ptr n, Checker checker, typename Checker::return_type& check_return)
    {
       const_node_ptr left = NodeTraits::get_left(n);
       const_node_ptr right = NodeTraits::get_right(n);
       typename Checker::return_type check_return_left;
       typename Checker::return_type check_return_right;
       if (left)
       {
          BOOST_INTRUSIVE_INVARIANT_ASSERT(NodeTraits::get_parent(left) == n);
          check_subtree(left, checker, check_return_left);
       }
       if (right)
       {
          BOOST_INTRUSIVE_INVARIANT_ASSERT(NodeTraits::get_parent(right) == n);
          check_subtree(right, checker, check_return_right);
       }
       checker(n, check_return_left, check_return_right, check_return);
    }
 };
 
 /// @cond
 
 template<class NodeTraits>
 struct get_algo<BsTreeAlgorithms, NodeTraits>
 {
    typedef bstree_algorithms<NodeTraits> type;
 };
 
 template <class ValueTraits, class NodePtrCompare, class ExtraChecker>
 struct get_node_checker<BsTreeAlgorithms, ValueTraits, NodePtrCompare, ExtraChecker>
 {
    typedef detail::bstree_node_checker<ValueTraits, NodePtrCompare, ExtraChecker> type;
 };
 
 /// @endcond
 
 }  //namespace intrusive
 }  //namespace boost
 
 #include <boost/intrusive/detail/config_end.hpp>
 
 #endif //BOOST_INTRUSIVE_BSTREE_ALGORITHMS_HPP

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