text: /////////////////////////////////////////////////////////////////////////////
  //
  // (C) Copyright Daniel K. O. 2005.
  // (C) Copyright Ion Gaztanaga 2007-2012
  //
  // 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_AVLTREE_ALGORITHMS_HPP
  #define BOOST_INTRUSIVE_AVLTREE_ALGORITHMS_HPP
  
  #include <boost/intrusive/detail/config_begin.hpp>
  
  #include <cstddef>
  #include <boost/intrusive/intrusive_fwd.hpp>
  
  #include <boost/intrusive/detail/assert.hpp>
  #include <boost/intrusive/detail/utilities.hpp>
  #include <boost/intrusive/detail/tree_algorithms.hpp>
  #include <boost/intrusive/pointer_traits.hpp>
  
  
  namespace boost {
  namespace intrusive {
  
  //! avltree_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 circular list
  //!
  //! <tt>node_ptr</tt>: A pointer to a node
  //!
  //! <tt>const_node_ptr</tt>: A pointer to a const node
  //!
  //! <tt>balance</tt>: The type of the balance factor
  //!
  //! <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>
  //!
  //! <tt>static balance get_balance(const_node_ptr n);</tt>
  //!
  //! <tt>static void set_balance(node_ptr n, balance b);</tt>
  //!
  //! <tt>static balance negative();</tt>
  //!
  //! <tt>static balance zero();</tt>
  //!
  //! <tt>static balance positive();</tt>
  template<class NodeTraits>
  class avltree_algorithms
  {
     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 typename NodeTraits::balance         balance;
  
     /// @cond
     private:
     typedef detail::tree_algorithms<NodeTraits>  tree_algorithms;
  
     template<class F>
     struct avltree_node_cloner
        :  private detail::ebo_functor_holder<F>
     {
        typedef detail::ebo_functor_holder<F>                 base_t;
  
        avltree_node_cloner(F f)
           :  base_t(f)
        {}
  
        node_ptr operator()(const node_ptr &p)
        {
           node_ptr n = base_t::get()(p);
           NodeTraits::set_balance(n, NodeTraits::get_balance(p));
           return n;
        }
     };
  
     struct avltree_erase_fixup
     {
        void operator()(const node_ptr &to_erase, const node_ptr &successor)
        {  NodeTraits::set_balance(successor, NodeTraits::get_balance(to_erase));  }
     };
  
     static node_ptr uncast(const const_node_ptr & ptr)
     {  return pointer_traits<node_ptr>::const_cast_from(ptr);  }
     /// @endcond
  
     public:
     static node_ptr begin_node(const const_node_ptr & header)
     {  return tree_algorithms::begin_node(header);   }
  
     static node_ptr end_node(const const_node_ptr & header)
     {  return tree_algorithms::end_node(header);   }
  
     //! This type is the information that will be
     //! filled by insert_unique_check
     typedef typename tree_algorithms::insert_commit_data insert_commit_data;
  
     //! <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(const node_ptr & header1, const node_ptr & header2)
     {  return tree_algorithms::swap_tree(header1, header2);  }
  
     //! <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(const node_ptr & node1, const node_ptr & node2)
     {
        if(node1 == node2)
           return;
  
        node_ptr header1(tree_algorithms::get_header(node1)), header2(tree_algorithms::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(const node_ptr & node1, const node_ptr & header1, const node_ptr & node2, const node_ptr & header2)
     {
        if(node1 == node2)   return;
  
        tree_algorithms::swap_nodes(node1, header1, node2, header2);
        //Swap balance
        balance c = NodeTraits::get_balance(node1);
        NodeTraits::set_balance(node1, NodeTraits::get_balance(node2));
        NodeTraits::set_balance(node2, c);
     }
  
     //! <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
     static void replace_node(const node_ptr & node_to_be_replaced, const node_ptr & new_node)
     {
        if(node_to_be_replaced == new_node)
           return;
        replace_node(node_to_be_replaced, tree_algorithms::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(const node_ptr & node_to_be_replaced, const node_ptr & header, const node_ptr & new_node)
     {
        tree_algorithms::replace_node(node_to_be_replaced, header, new_node);
        NodeTraits::set_balance(new_node, NodeTraits::get_balance(node_to_be_replaced));
     }
  
     //! <b>Requires</b>: node 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(const node_ptr & node)
     {
        node_ptr x = NodeTraits::get_parent(node);
        if(x){
           while(!is_header(x))
              x = NodeTraits::get_parent(x);
           erase(x, node);
        }
     }
  
     //! <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(const node_ptr & header)
     {  return tree_algorithms::unlink_leftmost_without_rebalance(header);   }
  
     //! <b>Requires</b>: node is a node of the tree or an node initialized
     //!   by init(...).
     //!
     //! <b>Effects</b>: Returns true if the node is initialized by init().
     //!
     //! <b>Complexity</b>: Constant time.
     //!
     //! <b>Throws</b>: Nothing.
     static bool unique(const const_node_ptr & node)
     {  return tree_algorithms::unique(node);  }
  
     //! <b>Requires</b>: node 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 count(const const_node_ptr & node)
     {  return tree_algorithms::count(node);   }
  
     //! <b>Requires</b>: header is the header node of the tree.
     //!
     //! <b>Effects</b>: Returns the number of nodes above the header.
     //!
     //! <b>Complexity</b>: Linear time.
     //!
     //! <b>Throws</b>: Nothing.
     static std::size_t size(const const_node_ptr & header)
     {  return tree_algorithms::size(header);   }
  
     //! <b>Requires</b>: p 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(const node_ptr & p)
     {  return tree_algorithms::next_node(p); }
  
     //! <b>Requires</b>: p 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(const node_ptr & p)
     {  return tree_algorithms::prev_node(p); }
  
     //! <b>Requires</b>: node 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(const node_ptr & node)
     {  tree_algorithms::init(node);  }
  
     //! <b>Requires</b>: node 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 node is inserted in a tree, this function corrupts the tree.
     static void init_header(const node_ptr & header)
     {
        tree_algorithms::init_header(header);
        NodeTraits::set_balance(header, NodeTraits::zero());
     }
  
     //! <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.
     static node_ptr erase(const node_ptr & header, const node_ptr & z)
     {
        typename tree_algorithms::data_for_rebalance info;
        tree_algorithms::erase(header, z, avltree_erase_fixup(), info);
        node_ptr x = info.x;
        node_ptr x_parent = info.x_parent;
  
        //Rebalance avltree
        rebalance_after_erasure(header, x, x_parent);
        return z;
     }
  
     //! <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()(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>.
     //!
     //! <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 const_node_ptr & source_header, const node_ptr & target_header, Cloner cloner, Disposer disposer)
     {
        avltree_node_cloner<Cloner> new_cloner(cloner);
        tree_algorithms::clone(source_header, target_header, new_cloner, disposer);
     }
  
     //! <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()(const 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>: 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)
     {  tree_algorithms::clear_and_dispose(header, disposer); }
  
     //! <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 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>
     static node_ptr lower_bound
        (const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp)
     {  return tree_algorithms::lower_bound(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 an 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>
     static node_ptr upper_bound
        (const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp)
     {  return tree_algorithms::upper_bound(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 an node_ptr to the 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 const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp)
     {  return tree_algorithms::find(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 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 they 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> equal_range
        (const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp)
     {  return tree_algorithms::equal_range(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.
     //!   'lower_key' must not be greater than 'upper_key' according to 'comp'. If
     //!   'lower_key' == 'upper_key', ('left_closed' || 'right_closed') must be false.
     //!
     //! <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.
     template<class KeyType, class KeyNodePtrCompare>
     static std::pair<node_ptr, node_ptr> bounded_range
        (const const_node_ptr & header, const KeyType &lower_key, const KeyType &upper_key, KeyNodePtrCompare comp
        , bool left_closed, bool right_closed)
     {  return tree_algorithms::bounded_range(header, lower_key, upper_key, comp, left_closed, right_closed);  }
  
     //! <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
        (const node_ptr & h, const node_ptr & new_node, NodePtrCompare comp)
     {
        tree_algorithms::insert_equal_upper_bound(h, new_node, comp);
        rebalance_after_insertion(h, new_node);
        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
        (const node_ptr & h, const node_ptr & new_node, NodePtrCompare comp)
     {
        tree_algorithms::insert_equal_lower_bound(h, new_node, comp);
        rebalance_after_insertion(h, new_node);
        return new_node;
     }
  
     //! <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
        (const node_ptr & header, const node_ptr & hint, const node_ptr & new_node, NodePtrCompare comp)
     {
        tree_algorithms::insert_equal(header, hint, new_node, comp);
        rebalance_after_insertion(header, new_node);
        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
        (const node_ptr & header, const node_ptr & pos, const node_ptr & new_node)
     {
        tree_algorithms::insert_before(header, pos, new_node);
        rebalance_after_insertion(header, new_node);
        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(const node_ptr & header, const node_ptr & new_node)
     {
        tree_algorithms::push_back(header, new_node);
        rebalance_after_insertion(header, new_node);
     }
  
     //! <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(const node_ptr & header, const node_ptr & new_node)
     {
        tree_algorithms::push_front(header, new_node);
        rebalance_after_insertion(header, new_node);
     }
  
     //! <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 const_node_ptr & header,  const KeyType &key
        ,KeyNodePtrCompare comp, insert_commit_data &commit_data)
     {  return tree_algorithms::insert_unique_check(header, key, comp, 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.
     //!   "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 const_node_ptr & header, const node_ptr &hint, const KeyType &key
        ,KeyNodePtrCompare comp, insert_commit_data &commit_data)
     {  return tree_algorithms::insert_unique_check(header, hint, key, comp, commit_data);  }
  
     //! <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.
     static void insert_unique_commit
        (const node_ptr & header, const node_ptr & new_value, const insert_commit_data &commit_data)
     {
        tree_algorithms::insert_unique_commit(header, new_value, commit_data);
        rebalance_after_insertion(header, new_value);
     }
  
     //! <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_header(const node_ptr & n)
     {  return tree_algorithms::get_header(n);   }
  
     /// @cond
     private:
  
     //! <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 const_node_ptr & p)
     {  return NodeTraits::get_balance(p) == NodeTraits::zero() && tree_algorithms::is_header(p);  }
  
     static void rebalance_after_erasure(const node_ptr & header, const node_ptr & xnode, const node_ptr & xnode_parent)
     {
        node_ptr x(xnode), x_parent(xnode_parent);
        for (node_ptr root = NodeTraits::get_parent(header); x != root; root = NodeTraits::get_parent(header)) {
           const balance x_parent_balance = NodeTraits::get_balance(x_parent);
           if(x_parent_balance == NodeTraits::zero()){
              NodeTraits::set_balance(x_parent,
                 (x == NodeTraits::get_right(x_parent) ? NodeTraits::negative() : NodeTraits::positive()));
              break;       // the height didn't change, let's stop here
           }
           else if(x_parent_balance == NodeTraits::negative()){
              if (x == NodeTraits::get_left(x_parent)) {
                 NodeTraits::set_balance(x_parent, NodeTraits::zero()); // balanced
                 x = x_parent;
                 x_parent = NodeTraits::get_parent(x_parent);
              }
              else {
                 // x is right child
                 // a is left child
                 node_ptr a = NodeTraits::get_left(x_parent);
                 BOOST_INTRUSIVE_INVARIANT_ASSERT(a);
                 if (NodeTraits::get_balance(a) == NodeTraits::positive()) {
                    // a MUST have a right child
                    BOOST_INTRUSIVE_INVARIANT_ASSERT(NodeTraits::get_right(a));
                    rotate_left_right(x_parent, header);
                    x = NodeTraits::get_parent(x_parent);
                    x_parent = NodeTraits::get_parent(x);
                 }
                 else {
                    rotate_right(x_parent, header);
                    x = NodeTraits::get_parent(x_parent);
                    x_parent = NodeTraits::get_parent(x);
                 }
  
                 // if changed from negative to NodeTraits::positive(), no need to check above
                 if (NodeTraits::get_balance(x) == NodeTraits::positive()){
                    break;
                 }
              }
           }
           else if(x_parent_balance == NodeTraits::positive()){
              if (x == NodeTraits::get_right(x_parent)) {
                 NodeTraits::set_balance(x_parent, NodeTraits::zero()); // balanced
                 x = x_parent;
                 x_parent = NodeTraits::get_parent(x_parent);
              }
              else {
                 // x is left child
                 // a is right child
                 node_ptr a = NodeTraits::get_right(x_parent);
                 BOOST_INTRUSIVE_INVARIANT_ASSERT(a);
                 if (NodeTraits::get_balance(a) == NodeTraits::negative()) {
                    // a MUST have then a left child
                    BOOST_INTRUSIVE_INVARIANT_ASSERT(NodeTraits::get_left(a));
                    rotate_right_left(x_parent, header);
  
                    x = NodeTraits::get_parent(x_parent);
                    x_parent = NodeTraits::get_parent(x);
                 }
                 else {
                    rotate_left(x_parent, header);
                    x = NodeTraits::get_parent(x_parent);
                    x_parent = NodeTraits::get_parent(x);
                 }
                 // if changed from NodeTraits::positive() to negative, no need to check above
                 if (NodeTraits::get_balance(x) == NodeTraits::negative()){
                    break;
                 }
              }
           }
           else{
              BOOST_INTRUSIVE_INVARIANT_ASSERT(false);  // never reached
           }
        }
     }
  
     static void rebalance_after_insertion(const node_ptr & header, const node_ptr & xnode)
     {
        node_ptr x(xnode);
        NodeTraits::set_balance(x, NodeTraits::zero());
        // Rebalance.
        for(node_ptr root = NodeTraits::get_parent(header); x != root; root = NodeTraits::get_parent(header)){
           const balance x_parent_balance = NodeTraits::get_balance(NodeTraits::get_parent(x));
  
           if(x_parent_balance == NodeTraits::zero()){
              // if x is left, parent will have parent->bal_factor = negative
              // else, parent->bal_factor = NodeTraits::positive()
              NodeTraits::set_balance( NodeTraits::get_parent(x)
                                      , x == NodeTraits::get_left(NodeTraits::get_parent(x))
                                         ? NodeTraits::negative() : NodeTraits::positive()  );
              x = NodeTraits::get_parent(x);
           }
           else if(x_parent_balance == NodeTraits::positive()){
              // if x is a left child, parent->bal_factor = zero
              if (x == NodeTraits::get_left(NodeTraits::get_parent(x)))
                 NodeTraits::set_balance(NodeTraits::get_parent(x), NodeTraits::zero());
              else{        // x is a right child, needs rebalancing
                 if (NodeTraits::get_balance(x) == NodeTraits::negative())
                    rotate_right_left(NodeTraits::get_parent(x), header);
                 else
                    rotate_left(NodeTraits::get_parent(x), header);
              }
              break;
           }
           else if(x_parent_balance == NodeTraits::negative()){
              // if x is a left child, needs rebalancing
              if (x == NodeTraits::get_left(NodeTraits::get_parent(x))) {
                 if (NodeTraits::get_balance(x) == NodeTraits::positive())
                    rotate_left_right(NodeTraits::get_parent(x), header);
                 else
                    rotate_right(NodeTraits::get_parent(x), header);
              }
              else
                 NodeTraits::set_balance(NodeTraits::get_parent(x), NodeTraits::zero());
              break;
           }
           else{
              BOOST_INTRUSIVE_INVARIANT_ASSERT(false);  // never reached
           }
        }
     }
  
     static void left_right_balancing(const node_ptr & a, const node_ptr & b, const node_ptr & c)
     {
        // balancing...
        const balance c_balance = NodeTraits::get_balance(c);
        const balance zero_balance = NodeTraits::zero();
        NodeTraits::set_balance(c, zero_balance);
        if(c_balance == NodeTraits::negative()){
           NodeTraits::set_balance(a, NodeTraits::positive());
           NodeTraits::set_balance(b, zero_balance);
        }
        else if(c_balance == zero_balance){
           NodeTraits::set_balance(a, zero_balance);
           NodeTraits::set_balance(b, zero_balance);
        }
        else if(c_balance == NodeTraits::positive()){
           NodeTraits::set_balance(a, zero_balance);
           NodeTraits::set_balance(b, NodeTraits::negative());
        }
        else{
           BOOST_INTRUSIVE_INVARIANT_ASSERT(false); // never reached
        }
     }
  
     static void rotate_left_right(const node_ptr a, const node_ptr & hdr)
     {
        //             |                               |         //
        //             a(-2)                           c         //
        //            / \                             / \        //
        //           /   \        ==>                /   \       //
        //      (pos)b    [g]                       b     a      //
        //          / \                            / \   / \     //
        //        [d]  c                         [d]  e f  [g]   //
        //           / \                                         //
        //          e   f                                        //
        node_ptr b = NodeTraits::get_left(a), c = NodeTraits::get_right(b);
        tree_algorithms::rotate_left(b, hdr);
        tree_algorithms::rotate_right(a, hdr);
        left_right_balancing(a, b, c);
     }
  
     static void rotate_right_left(const node_ptr a, const node_ptr & hdr)
     {
        //              |                               |           //
        //              a(pos)                          c           //
        //             / \                             / \          //
        //            /   \                           /   \         //
        //          [d]   b(neg)         ==>         a     b        //
        //               / \                        / \   / \       //
        //              c  [g]                    [d] e  f  [g]     //
        //             / \                                          //
        //            e   f                                         //
        node_ptr b = NodeTraits::get_right(a), c = NodeTraits::get_left(b);
        tree_algorithms::rotate_right(b, hdr);
        tree_algorithms::rotate_left(a, hdr);
        left_right_balancing(b, a, c);
     }
  
     static void rotate_left(const node_ptr x, const node_ptr & hdr)
     {
        const node_ptr y = NodeTraits::get_right(x);
        tree_algorithms::rotate_left(x, hdr);
  
        // reset the balancing factor
        if (NodeTraits::get_balance(y) == NodeTraits::positive()) {
           NodeTraits::set_balance(x, NodeTraits::zero());
           NodeTraits::set_balance(y, NodeTraits::zero());
        }
        else {        // this doesn't happen during insertions
           NodeTraits::set_balance(x, NodeTraits::positive());
           NodeTraits::set_balance(y, NodeTraits::negative());
        }
     }
  
     static void rotate_right(const node_ptr x, const node_ptr & hdr)
     {
        const node_ptr y = NodeTraits::get_left(x);
        tree_algorithms::rotate_right(x, hdr);
  
        // reset the balancing factor
        if (NodeTraits::get_balance(y) == NodeTraits::negative()) {
           NodeTraits::set_balance(x, NodeTraits::zero());
           NodeTraits::set_balance(y, NodeTraits::zero());
        }
        else {        // this doesn't happen during insertions
           NodeTraits::set_balance(x, NodeTraits::negative());
           NodeTraits::set_balance(y, NodeTraits::positive());
        }
     }
  
     /// @endcond
  };
  
  } //namespace intrusive
  } //namespace boost
  
  #include <boost/intrusive/detail/config_end.hpp>
  
  #endif //BOOST_INTRUSIVE_AVLTREE_ALGORITHMS_HPP
  