Imported Upstream version 1.49.0upstream/1.49.0

1 files changed, 782 insertions, 0 deletions

diff --git a/boost/intrusive/sgtree_algorithms.hpp b/boost/intrusive/sgtree_algorithms.hpp
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+++ b/boost/intrusive/sgtree_algorithms.hpp
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+/////////////////////////////////////////////////////////////////////////////
+//
+// (C) Copyright Ion Gaztanaga 2007.
+//
+// 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.
+//
+/////////////////////////////////////////////////////////////////////////////
+//
+// Scapegoat tree algorithms are taken from the paper titled:
+// "Scapegoat Trees" by Igal Galperin Ronald L. Rivest.
+//
+/////////////////////////////////////////////////////////////////////////////
+#ifndef BOOST_INTRUSIVE_SGTREE_ALGORITHMS_HPP
+#define BOOST_INTRUSIVE_SGTREE_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 {
+
+//! sgtree_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
+//!
+//! <b>Static functions</b>:
+//!
+//! <tt>static node_ptr get_parent(const_node_ptr n);</tt>
+//! 
+//! <tt>static void set_parent(node_ptr n, node_ptr parent);</tt>
+//!
+//! <tt>static node_ptr get_left(const_node_ptr n);</tt>
+//! 
+//! <tt>static void set_left(node_ptr n, node_ptr left);</tt>
+//!
+//! <tt>static node_ptr get_right(const_node_ptr n);</tt>
+//! 
+//! <tt>static void set_right(node_ptr n, node_ptr right);</tt>
+template<class NodeTraits>
+class sgtree_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;
+
+   /// @cond
+   private:
+
+   typedef detail::tree_algorithms<NodeTraits>  tree_algorithms;
+
+   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
+   struct insert_commit_data
+      :  tree_algorithms::insert_commit_data
+   {
+      std::size_t depth;
+   };
+
+   //! <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)
+   {  tree_algorithms::swap_nodes(node1, header1, node2, header2);  }
+
+   //! <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);  }
+
+   //! <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);
+         tree_algorithms::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);  }
+
+   //! <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.
+   template<class AlphaByMaxSize>
+   static node_ptr erase(const node_ptr & header, const node_ptr & z, std::size_t tree_size, std::size_t &max_tree_size, AlphaByMaxSize alpha_by_maxsize)
+   {
+      //typename tree_algorithms::data_for_rebalance info;
+      tree_algorithms::erase(header, z);
+      --tree_size;
+      if (tree_size > 0 && 
+          tree_size < alpha_by_maxsize(max_tree_size)){
+         tree_algorithms::rebalance(header);
+         max_tree_size = tree_size;
+      }
+      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)
+   {
+      tree_algorithms::clone(source_header, target_header, 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>: "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, class H_Alpha>
+   static node_ptr insert_equal_upper_bound
+      (const node_ptr & h, const node_ptr & new_node, NodePtrCompare comp
+      ,std::size_t tree_size, H_Alpha h_alpha, std::size_t &max_tree_size)
+   {
+      std::size_t depth;
+      tree_algorithms::insert_equal_upper_bound(h, new_node, comp, &depth);
+      rebalance_after_insertion(new_node, depth, tree_size+1, h_alpha, max_tree_size);
+      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, class H_Alpha>
+   static node_ptr insert_equal_lower_bound
+      (const node_ptr & h, const node_ptr & new_node, NodePtrCompare comp
+      ,std::size_t tree_size, H_Alpha h_alpha, std::size_t &max_tree_size)
+   {
+      std::size_t depth;
+      tree_algorithms::insert_equal_lower_bound(h, new_node, comp, &depth);
+      rebalance_after_insertion(new_node, depth, tree_size+1, h_alpha, max_tree_size);
+      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, class H_Alpha>
+   static node_ptr insert_equal
+      (const node_ptr & header, const node_ptr & hint, const node_ptr & new_node, NodePtrCompare comp
+      ,std::size_t tree_size, H_Alpha h_alpha, std::size_t &max_tree_size)
+   {
+      std::size_t depth;
+      tree_algorithms::insert_equal(header, hint, new_node, comp, &depth);
+      rebalance_after_insertion(new_node, depth, tree_size+1, h_alpha, max_tree_size);
+      return 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)
+   {
+      std::size_t depth;
+      std::pair<node_ptr, bool> ret = 
+         tree_algorithms::insert_unique_check(header, key, comp, commit_data, &depth);
+      commit_data.depth = depth;
+      return ret;
+   }
+
+
+   //! <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.
+   template<class H_Alpha>
+   static node_ptr insert_before
+      (const node_ptr & header, const node_ptr & pos, const node_ptr & new_node
+      ,std::size_t tree_size, H_Alpha h_alpha, std::size_t &max_tree_size)
+   {
+      std::size_t depth;
+      tree_algorithms::insert_before(header, pos, new_node, &depth);
+      rebalance_after_insertion(new_node, depth, tree_size+1, h_alpha, max_tree_size);
+      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".
+   template<class H_Alpha>
+   static void push_back(const node_ptr & header, const node_ptr & new_node
+         ,std::size_t tree_size, H_Alpha h_alpha, std::size_t &max_tree_size)
+   {
+      std::size_t depth;
+      tree_algorithms::push_back(header, new_node, &depth);
+      rebalance_after_insertion(new_node, depth, tree_size+1, h_alpha, max_tree_size);
+   }
+
+   //! <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".
+   template<class H_Alpha>
+   static void push_front(const node_ptr & header, const node_ptr & new_node
+         ,std::size_t tree_size, H_Alpha h_alpha, std::size_t &max_tree_size)
+   {
+      std::size_t depth;
+      tree_algorithms::push_front(header, new_node, &depth);
+      rebalance_after_insertion(new_node, depth, tree_size+1, h_alpha, max_tree_size);
+   }
+
+   //! <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)
+   {
+      std::size_t depth;
+      std::pair<node_ptr, bool> ret = 
+         tree_algorithms::insert_unique_check
+            (header, hint, key, comp, commit_data, &depth);
+      commit_data.depth = depth;
+      return ret;
+   }
+
+   //! <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.
+   template<class H_Alpha>
+   static void insert_unique_commit
+      (const node_ptr & header, const node_ptr & new_value, const insert_commit_data &commit_data
+      ,std::size_t tree_size, H_Alpha h_alpha, std::size_t &max_tree_size)
+   {
+      tree_algorithms::insert_unique_commit(header, new_value, commit_data);
+      rebalance_after_insertion(new_value, commit_data.depth, tree_size+1, h_alpha, max_tree_size);
+   }
+
+   //! <b>Requires</b>: header must be the header of a tree.
+   //! 
+   //! <b>Effects</b>: Rebalances the tree.
+   //! 
+   //! <b>Throws</b>: Nothing.
+   //! 
+   //! <b>Complexity</b>: Linear.
+   static void rebalance(const node_ptr & header)
+   {  tree_algorithms::rebalance(header); }
+
+   //! <b>Requires</b>: old_root is a node of a tree.
+   //! 
+   //! <b>Effects</b>: Rebalances the subtree rooted at old_root.
+   //!
+   //! <b>Returns</b>: The new root of the subtree.
+   //!
+   //! <b>Throws</b>: Nothing.
+   //! 
+   //! <b>Complexity</b>: Linear.
+   static node_ptr rebalance_subtree(const node_ptr & old_root)
+   {  return tree_algorithms::rebalance_subtree(old_root); }
+
+   //! <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 tree_algorithms::is_header(p);  }
+
+   template<class H_Alpha>
+   static void rebalance_after_insertion
+      (const node_ptr &x, std::size_t depth
+      , std::size_t tree_size, H_Alpha h_alpha, std::size_t &max_tree_size)
+   {
+      if(tree_size > max_tree_size)
+         max_tree_size = tree_size;
+
+      if(tree_size != 1 && depth > h_alpha(tree_size)){
+         //Find the first non height-balanced node
+         //as described in the section 4.2 of the paper.
+         //This method is the alternative method described
+         //in the paper. Authors claim that this method
+         //may tend to yield more balanced trees on the average
+         //than the weight balanced method.
+         node_ptr s = x;
+         std::size_t size = 1;
+
+         for(std::size_t i = 1; true; ++i){
+            bool rebalance = false;
+            if(i == depth){
+               BOOST_INTRUSIVE_INVARIANT_ASSERT(tree_size == count(s));
+               rebalance = true;
+            }
+            else if(i > h_alpha(size)){
+               node_ptr s_parent = NodeTraits::get_parent(s);
+               node_ptr s_parent_left = NodeTraits::get_left(s_parent);
+               size += 1 + tree_algorithms::count
+                  ( s_parent_left == s ? NodeTraits::get_right(s_parent) : s_parent_left );
+               s = s_parent;
+               rebalance = true;
+            }
+            if(rebalance){
+               rebalance_subtree(s);
+               break;
+            }
+         }
+      }
+   }
+
+   /// @endcond
+};
+
+} //namespace intrusive 
+} //namespace boost 
+
+#include <boost/intrusive/detail/config_end.hpp>
+
+#endif //BOOST_INTRUSIVE_SGTREE_ALGORITHMS_HPP