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Editing: bstree_algorithms.hpp

/////////////////////////////////////////////////////////////////////////////
//
// (C) Copyright Ion Gaztanaga  2007-2014
//
// 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 const_node_ptr& p,
                     const return_type& check_return_left, const return_type& check_return_right,
                     return_type& check_return)
   {
      if (check_return_left.max_key_node_ptr)
         BOOST_INTRUSIVE_INVARIANT_ASSERT(!comp_(p, check_return_left.max_key_node_ptr));
      if (check_return_right.min_key_node_ptr)
         BOOST_INTRUSIVE_INVARIANT_ASSERT(!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:
//!
//! Typedefs:
//!
//! <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
//!
//! Static functions:
//!
//! <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, const 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:
 //! Requires: 'header' is the header node of a tree.
 //!
 //! Effects: Returns the first node of the tree, the header if the tree is empty.
 //!
 //! Complexity: Constant time.
 //!
 //! Throws: Nothing.
 BOOST_INTRUSIVE_FORCEINLINE static node_ptr begin_node(const const_node_ptr & header)
 { return node_traits::get_left(header); }

//! Requires: 'header' is the header node of a tree.
 //!
 //! Effects: Returns the header of the tree.
 //!
 //! Complexity: Constant time.
 //!
 //! Throws: Nothing.
 BOOST_INTRUSIVE_FORCEINLINE static node_ptr end_node(const const_node_ptr & header)
 { return detail::uncast(header); }

//! Requires: 'header' is the header node of a tree.
 //!
 //! Effects: Returns the root of the tree if any, header otherwise
 //!
 //! Complexity: Constant time.
 //!
 //! Throws: Nothing.
 BOOST_INTRUSIVE_FORCEINLINE static node_ptr root_node(const const_node_ptr & header)
 {
 node_ptr p = node_traits::get_parent(header);
 return p ? p : detail::uncast(header);
 }

//! Requires: 'node' is a node of the tree or a node initialized
 //! by init(...) or init_node.
 //!
 //! Effects: Returns true if the node is initialized by init() or init_node().
 //!
 //! Complexity: Constant time.
 //!
 //! Throws: Nothing.
 BOOST_INTRUSIVE_FORCEINLINE static bool unique(const const_node_ptr & node)
 { return !NodeTraits::get_parent(node); }

#if defined(BOOST_INTRUSIVE_DOXYGEN_INVOKED)
 //! Requires: 'node' is a node of the tree or a header node.
 //!
 //! Effects: Returns the header of the tree.
 //!
 //! Complexity: Logarithmic.
 //!
 //! Throws: Nothing.
 static node_ptr get_header(const const_node_ptr & node);
 #endif

//! Requires: node1 and node2 can't be header nodes
 //! of two trees.
 //!
 //! Effects: 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.
 //!
 //! Complexity: Logarithmic.
 //!
 //! Throws: Nothing.
 //!
 //! Note: 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)
 {
 if(node1 == node2)
 return;

node_ptr header1(base_type::get_header(node1)), header2(base_type::get_header(node2));
      swap_nodes(node1, header1, node2, header2);
   }

//! Requires: node1 and node2 can't be header nodes
 //! of two trees with header header1 and header2.
 //!
 //! Effects: 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.
 //!
 //! Complexity: Constant.
 //!
 //! Throws: Nothing.
 //!
 //! Note: 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)
 {
 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 adjacent 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);
      }
      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);
         }
      }
      //Now adjust adjacent 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);
      }
      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);
         }
      }
   }

//! Requires: node_to_be_replaced must be inserted in a tree
 //! and new_node must not be inserted in a tree.
 //!
 //! Effects: Replaces node_to_be_replaced in its position in the
 //! tree with new_node. The tree does not need to be rebalanced
 //!
 //! Complexity: Logarithmic.
 //!
 //! Throws: Nothing.
 //!
 //! Note: 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)
 {
 if(node_to_be_replaced == new_node)
 return;
 replace_node(node_to_be_replaced, base_type::get_header(node_to_be_replaced), new_node);
 }

//! Requires: node_to_be_replaced must be inserted in a tree
 //! with header "header" and new_node must not be inserted in a tree.
 //!
 //! Effects: Replaces node_to_be_replaced in its position in the
 //! tree with new_node. The tree does not need to be rebalanced
 //!
 //! Complexity: Constant.
 //!
 //! Throws: Nothing.
 //!
 //! Note: 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)
 {
 if(node_to_be_replaced == new_node)
 return;

//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)
 //! Requires: 'node' is a node from the tree except the header.
 //!
 //! Effects: Returns the next node of the tree.
 //!
 //! Complexity: Average constant time.
 //!
 //! Throws: Nothing.
 static node_ptr next_node(const node_ptr & node);

//! Requires: 'node' is a node from the tree except the leftmost node.
 //!
 //! Effects: Returns the previous node of the tree.
 //!
 //! Complexity: Average constant time.
 //!
 //! Throws: Nothing.
 static node_ptr prev_node(const node_ptr & node);

//! Requires: 'node' is a node of a tree but not the header.
 //!
 //! Effects: Returns the minimum node of the subtree starting at p.
 //!
 //! Complexity: Logarithmic to the size of the subtree.
 //!
 //! Throws: Nothing.
 static node_ptr minimum(node_ptr node);

//! Requires: 'node' is a node of a tree but not the header.
 //!
 //! Effects: Returns the maximum node of the subtree starting at p.
 //!
 //! Complexity: Logarithmic to the size of the subtree.
 //!
 //! Throws: Nothing.
 static node_ptr maximum(node_ptr node);
 #endif

//! Requires: 'node' must not be part of any tree.
 //!
 //! Effects: After the function unique(node) == true.
 //!
 //! Complexity: Constant.
 //!
 //! Throws: Nothing.
 //!
 //! Nodes: If node is inserted in a tree, this function corrupts the tree.
 BOOST_INTRUSIVE_FORCEINLINE static void init(node_ptr node)
 {
 NodeTraits::set_parent(node, node_ptr());
 NodeTraits::set_left(node, node_ptr());
 NodeTraits::set_right(node, node_ptr());
 }

//! Effects: Returns true if node is in the same state as if called init(node)
 //!
 //! Complexity: Constant.
 //!
 //! Throws: Nothing.
 BOOST_INTRUSIVE_FORCEINLINE static bool inited(const const_node_ptr & node)
 {
 return !NodeTraits::get_parent(node) &&
 !NodeTraits::get_left(node) &&
 !NodeTraits::get_right(node) ;
 }

//! Requires: node must not be part of any tree.
 //!
 //! Effects: Initializes the header to represent an empty tree.
 //! unique(header) == true.
 //!
 //! Complexity: Constant.
 //!
 //! Throws: Nothing.
 //!
 //! Nodes: If node is inserted in a tree, this function corrupts the tree.
 BOOST_INTRUSIVE_FORCEINLINE static void init_header(node_ptr header)
 {
 NodeTraits::set_parent(header, node_ptr());
 NodeTraits::set_left(header, header);
 NodeTraits::set_right(header, header);
 }

//! Requires: "disposer" must be an object function
 //! taking a node_ptr parameter and shouldn't throw.
 //!
 //! Effects: Empties the target tree calling
 //! <tt>void disposer::operator()(const node_ptr &)</tt> for every node of the tree
 //! except the header.
 //!
 //! Complexity: Linear to the number of element of the source tree plus the.
 //! number of elements of tree target tree when calling this function.
 //!
 //! Throws: If cloner functor throws. If this happens target nodes are disposed.
 template<class Disposer>
 static void clear_and_dispose(const node_ptr & header, Disposer disposer)
 {
 node_ptr source_root = NodeTraits::get_parent(header);
 if(!source_root)
 return;
 dispose_subtree(source_root, disposer);
 init_header(header);
 }

//! Requires: header is the header of a tree.
 //!
 //! Effects: Unlinks the leftmost node from the tree, and
 //! updates the header link to the new leftmost node.
 //!
 //! Complexity: Average complexity is constant time.
 //!
 //! Throws: Nothing.
 //!
 //! Notes: This function breaks the tree and the tree can
 //! only be used for more unlink_leftmost_without_rebalance calls.
 //! This function is normally used to achieve a step by step
 //! controlled destruction of the tree.
 static node_ptr unlink_leftmost_without_rebalance(node_ptr header)
 {
 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;
   }

//! Requires: node is a node of the tree but it's not the header.
 //!
 //! Effects: Returns the number of nodes of the subtree.
 //!
 //! Complexity: Linear time.
 //!
 //! Throws: Nothing.
 static std::size_t size(const const_node_ptr & header)
 {
 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;
 }

//! Requires: header1 and header2 must be the header nodes
 //! of two trees.
 //!
 //! Effects: Swaps two trees. After the function header1 will contain
 //! links to the second tree and header2 will have links to the first tree.
 //!
 //! Complexity: Constant.
 //!
 //! Throws: Nothing.
 static void swap_tree(node_ptr header1, node_ptr header2)
 {
 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)
 //! Requires: p is a node of a tree.
 //!
 //! Effects: Returns true if p is the header of the tree.
 //!
 //! Complexity: Constant.
 //!
 //! Throws: Nothing.
 static bool is_header(const const_node_ptr & p);
 #endif

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);
 }

//! Requires: "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.
 //!
 //! Effects: 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.
 //!
 //! Complexity: Logarithmic.
 //!
 //! Throws: If "comp" throws.
 template<class KeyType, class KeyNodePtrCompare>
 BOOST_INTRUSIVE_FORCEINLINE static std::pair<node_ptr, node_ptr> equal_range
 (const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp)
 {
 return bounded_range(header, key, key, comp, true, true);
 }

//! Requires: "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.
 //!
 //! Effects: 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.
 //!
 //! Complexity: Logarithmic.
 //!
 //! Throws: If "comp" throws.
 template<class KeyType, class KeyNodePtrCompare>
 static std::pair<node_ptr, node_ptr> lower_bound_range
 (const 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;
 }

//! Requires: "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".
 //!
 //!
 //! Effects: Inserts new_node in the set using the information obtained
 //! from the "commit_data" that a previous "insert_check" filled.
 //!
 //! Complexity: Constant time.
 //!
 //! Throws: Nothing.
 //!
 //! Notes: 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)
 { return insert_commit(header, new_value, commit_data); }

//! Requires: "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.
 //!
 //! Effects: 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.
 //!
 //! Returns: 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.
 //!
 //! Complexity: Average complexity is at most logarithmic.
 //!
 //! Throws: If "comp" throws.
 //!
 //! Notes: 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 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;
         x = (left_child = comp(key, x)) ?
               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);
 }

//! Requires: "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.
 //!
 //! Effects: 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).
 //!
 //! Returns: 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.
 //!
 //! Complexity: Average complexity is at most logarithmic, but it is
 //! amortized constant time if new_node should be inserted immediately before "hint".
 //!
 //! Throws: If "comp" throws.
 //!
 //! Notes: 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 const_node_ptr & header, const 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);
 }

//! Requires: "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.
 //!
 //! Effects: 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).
 //!
 //! Complexity: Logarithmic in general, but it is amortized
 //! constant time if new_node is inserted immediately before "hint".
 //!
 //! Throws: 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;
 }

//! Requires: "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.
 //!
 //! Effects: Inserts new_node into the tree before the upper bound
 //! according to "comp".
 //!
 //! Complexity: Average complexity for insert element is at
 //! most logarithmic.
 //!
 //! Throws: 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;
 }

//! Requires: "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.
 //!
 //! Effects: Inserts new_node into the tree before the lower bound
 //! according to "comp".
 //!
 //! Complexity: Average complexity for insert element is at
 //! most logarithmic.
 //!
 //! Throws: 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;
 }

//! Requires: "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.
 //!
 //! Effects: Inserts new_node into the tree before "pos".
 //!
 //! Complexity: Constant-time.
 //!
 //! Throws: Nothing.
 //!
 //! Note: 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
 )
 {
 insert_commit_data commit_data;
 insert_before_check(header, pos, commit_data, pdepth);
 insert_commit(header, new_node, commit_data);
 return new_node;
 }

//! Requires: "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.
 //!
 //! Effects: Inserts new_node into the tree before "pos".
 //!
 //! Complexity: Constant-time.
 //!
 //! Throws: Nothing.
 //!
 //! Note: 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
 )
 {
 insert_commit_data commit_data;
 push_back_check(header, commit_data, pdepth);
 insert_commit(header, new_node, commit_data);
 }

//! Requires: "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.
 //!
 //! Effects: Inserts new_node into the tree before "pos".
 //!
 //! Complexity: Constant-time.
 //!
 //! Throws: Nothing.
 //!
 //! Note: 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
 )
 {
 insert_commit_data commit_data;
 push_front_check(header, commit_data, pdepth);
 insert_commit(header, new_node, commit_data);
 }

//! Requires: 'node' can't be a header node.
 //!
 //! Effects: 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.)
 //!
 //! Complexity: Logarithmic to the number of nodes in the tree.
 //!
 //! Throws: Nothing.
 static std::size_t depth(const_node_ptr node)
 {
 std::size_t depth = 0;
 node_ptr p_parent;
 while(node != NodeTraits::get_parent(p_parent = NodeTraits::get_parent(node))){
 ++depth;
 node = p_parent;
 }
 return depth;
 }

//! Requires: "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.
 //!
 //! Effects: First empties target tree calling
 //! <tt>void disposer::operator()(const 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()(const node_ptr &)</tt> to obtain
 //! the nodes of the target tree. If "cloner" throws, the cloned target nodes
 //! are disposed using <tt>void disposer(const node_ptr &)</tt>.
 //!
 //! Complexity: Linear to the number of element of the source tree plus the
 //! number of elements of tree target tree when calling this function.
 //!
 //! Throws: If cloner functor throws. If this happens target nodes are disposed.
 template <class Cloner, class Disposer>
 static void clone
 (const 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);
   }

//! Requires: header must be the header of a tree, z a node
 //! of that tree and z != header.
 //!
 //! Effects: Erases node "z" from the tree with header "header".
 //!
 //! Complexity: Amortized constant time.
 //!
 //! Throws: Nothing.
 BOOST_INTRUSIVE_FORCEINLINE static void erase(node_ptr header, node_ptr z)
 {
 data_for_rebalance ignored;
 erase(header, z, ignored);
 }

//! Requires: 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..
 //!
 //! Effects: Transfers node "z" from tree1 to tree2 if tree1 does not contain
 //! a node that is equivalent to z.
 //!
 //! Returns: True if the node was trasferred, false otherwise.
 //!
 //! Complexity: Logarithmic.
 //!
 //! Throws: 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);
 }

//! Requires: 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..
 //!
 //! Effects: Transfers node "z" from tree1 to tree2.
 //!
 //! Complexity: Logarithmic.
 //!
 //! Throws: 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);
 }

//! Requires: node is a tree node but not the header.
 //!
 //! Effects: Unlinks the node and rebalances the tree.
 //!
 //! Complexity: Average complexity is constant time.
 //!
 //! Throws: Nothing.
 static void unlink(node_ptr node)
 {
 node_ptr x = NodeTraits::get_parent(node);
 if(x){
 while(!base_type::is_header(x))
 x = NodeTraits::get_parent(x);
 erase(x, node);
 }
 }

//! Requires: header must be the header of a tree.
 //!
 //! Effects: Rebalances the tree.
 //!
 //! Throws: Nothing.
 //!
 //! Complexity: Linear.
 static void rebalance(node_ptr header)
 {
 node_ptr root = NodeTraits::get_parent(header);
 if(root){
 rebalance_subtree(root);
 }
 }

//! Requires: old_root is a node of a tree. It shall not be null.
 //!
 //! Effects: Rebalances the subtree rooted at old_root.
 //!
 //! Returns: The new root of the subtree.
 //!
 //! Throws: Nothing.
 //!
 //! Complexity: Linear.
 static node_ptr rebalance_subtree(node_ptr old_root)
 {
 //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;
   }

//! Effects: Asserts the integrity of the container with additional checks provided by the user.
 //!
 //! Requires: header must be the header of a tree.
 //!
 //! Complexity: Linear time.
 //!
 //! Note: 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 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;
   }

//! Requires: node is a node of the tree but it's not the header.
 //!
 //! Effects: Returns the number of nodes of the subtree.
 //!
 //! Complexity: Linear time.
 //!
 //! Throws: Nothing.
 static std::size_t subtree_size(const const_node_ptr & subtree)
 {
 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;
   }

//! Requires: p is a node of a tree.
 //!
 //! Effects: Returns true if p is a left child.
 //!
 //! Complexity: Constant.
 //!
 //! Throws: Nothing.
 BOOST_INTRUSIVE_FORCEINLINE static bool is_left_child(const node_ptr & p)
 { return NodeTraits::get_left(NodeTraits::get_parent(p)) == p; }

//! Requires: p is a node of a tree.
 //!
 //! Effects: Returns true if p is a right child.
 //!
 //! Complexity: Constant.
 //!
 //! Throws: Nothing.
 BOOST_INTRUSIVE_FORCEINLINE static bool is_right_child(const node_ptr & p)
 { 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
      )
   {
      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
      )
   {
      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)
   {
      //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)
   {
      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)
   {
      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)
   {
      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)
   {
      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)
   {
      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)
   {
      //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)
   {
      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)
 {
 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);
      }
   }

//! Requires: "n" must be a node inserted in a tree.
 //!
 //! Effects: Returns a pointer to the header node of the tree.
 //!
 //! Complexity: Logarithmic.
 //!
 //! Throws: Nothing.
 static node_ptr get_root(const node_ptr & node)
 {
 BOOST_INTRUSIVE_INVARIANT_ASSERT((!inited(node)));
 node_ptr x = NodeTraits::get_parent(node);
 if(x){
 while(!base_type::is_header(x)){
 x = NodeTraits::get_parent(x);
 }
 return x;
 }
 else{
 return node;
 }
 }

template <class Cloner, class Disposer>
 static node_ptr clone_subtree
 (const 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)
 {
 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 const_node_ptr& node, Checker checker, typename Checker::return_type& check_return)
 {
 const_node_ptr left = NodeTraits::get_left(node);
 const_node_ptr right = NodeTraits::get_right(node);
 typename Checker::return_type check_return_left;
 typename Checker::return_type check_return_right;
 if (left)
 {
 BOOST_INTRUSIVE_INVARIANT_ASSERT(NodeTraits::get_parent(left) == node);
 check_subtree(left, checker, check_return_left);
 }
 if (right)
 {
 BOOST_INTRUSIVE_INVARIANT_ASSERT(NodeTraits::get_parent(right) == node);
 check_subtree(right, checker, check_return_right);
 }
 checker(node, 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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