text: /////////////////////////////////////////////////////////////////////////////
  //
  // (C) Copyright Ion Gaztanaga 2007-2013
  //
  // 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/bstree_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 binary search tree
  //!
  //! <tt>node_ptr</tt>: A pointer to a node
  //!
  //! <tt>const_node_ptr</tt>: A pointer to a const node
  //!
  //! <b>Static functions</b>:
  //!
  //! <tt>static node_ptr get_parent(const_node_ptr n);</tt>
  //!
  //! <tt>static void set_parent(node_ptr n, node_ptr parent);</tt>
  //!
  //! <tt>static node_ptr get_left(const_node_ptr n);</tt>
  //!
  //! <tt>static void set_left(node_ptr n, node_ptr left);</tt>
  //!
  //! <tt>static node_ptr get_right(const_node_ptr n);</tt>
  //!
  //! <tt>static void set_right(node_ptr n, node_ptr right);</tt>
  template<class NodeTraits>
  class sgtree_algorithms
     #ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
     : public bstree_algorithms<NodeTraits>
     #endif
  {
     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 bstree_algorithms<NodeTraits>  bstree_algo;
  
     /// @endcond
  
     public:
     //! This type is the information that will be
     //! filled by insert_unique_check
     struct insert_commit_data
        : bstree_algo::insert_commit_data
     {
        std::size_t depth;
     };
  
     #ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
     //! @copydoc ::boost::intrusive::bstree_algorithms::get_header(const const_node_ptr&)
     static node_ptr get_header(const const_node_ptr & n);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::begin_node
     static node_ptr begin_node(const const_node_ptr & header);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::end_node
     static node_ptr end_node(const const_node_ptr & header);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::swap_tree
     static void swap_tree(const node_ptr & header1, const node_ptr & header2);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::swap_nodes(const node_ptr&,const node_ptr&)
     static void swap_nodes(const node_ptr & node1, const node_ptr & node2);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::swap_nodes(const node_ptr&,const node_ptr&,const node_ptr&,const node_ptr&)
     static void swap_nodes(const node_ptr & node1, const node_ptr & header1, const node_ptr & node2, const node_ptr & header2);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::replace_node(const node_ptr&,const node_ptr&)
     static void replace_node(const node_ptr & node_to_be_replaced, const node_ptr & new_node);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::replace_node(const node_ptr&,const node_ptr&,const node_ptr&)
     static void replace_node(const node_ptr & node_to_be_replaced, const node_ptr & header, const node_ptr & new_node);
  
     //Unlink is not possible since tree metadata is needed to update the tree
     //!static void unlink(const node_ptr & node);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::unlink_leftmost_without_rebalance
     static node_ptr unlink_leftmost_without_rebalance(const node_ptr & header);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::unique(const const_node_ptr&)
     static bool unique(const const_node_ptr & node);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::size(const const_node_ptr&)
     static std::size_t size(const const_node_ptr & header);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::next_node(const node_ptr&)
     static node_ptr next_node(const node_ptr & node);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::prev_node(const node_ptr&)
     static node_ptr prev_node(const node_ptr & node);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::init(const node_ptr&)
     static void init(const node_ptr & node);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::init_header(const node_ptr&)
     static void init_header(const node_ptr & header);
     #endif   //#ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::erase(const node_ptr&,const node_ptr&)
     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 bstree_algo::data_for_rebalance info;
        bstree_algo::erase(header, z);
        --tree_size;
        if (tree_size > 0 &&
            tree_size < alpha_by_maxsize(max_tree_size)){
           bstree_algo::rebalance(header);
           max_tree_size = tree_size;
        }
        return z;
     }
  
     #ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
     //! @copydoc ::boost::intrusive::bstree_algorithms::clone(const const_node_ptr&,const node_ptr&,Cloner,Disposer)
     template <class Cloner, class Disposer>
     static void clone
        (const const_node_ptr & source_header, const node_ptr & target_header, Cloner cloner, Disposer disposer);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::clear_and_dispose(const node_ptr&,Disposer)
     template<class Disposer>
     static void clear_and_dispose(const node_ptr & header, Disposer disposer);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::lower_bound(const const_node_ptr&,const KeyType&,KeyNodePtrCompare)
     template<class KeyType, class KeyNodePtrCompare>
     static node_ptr lower_bound
        (const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::upper_bound(const const_node_ptr&,const KeyType&,KeyNodePtrCompare)
     template<class KeyType, class KeyNodePtrCompare>
     static node_ptr upper_bound
        (const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::find(const const_node_ptr&, const KeyType&,KeyNodePtrCompare)
     template<class KeyType, class KeyNodePtrCompare>
     static node_ptr find
        (const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::equal_range(const const_node_ptr&,const KeyType&,KeyNodePtrCompare)
     template<class KeyType, class KeyNodePtrCompare>
     static std::pair<node_ptr, node_ptr> equal_range
        (const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::bounded_range(const const_node_ptr&,const KeyType&,const KeyType&,KeyNodePtrCompare,bool,bool)
     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);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::count(const const_node_ptr&,const KeyType&,KeyNodePtrCompare)
     template<class KeyType, class KeyNodePtrCompare>
     static std::size_t count(const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp);
     #endif   //#ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::insert_equal_upper_bound(const node_ptr&,const node_ptr&,NodePtrCompare)
     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;
        bstree_algo::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;
     }
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::insert_equal_lower_bound(const node_ptr&,const node_ptr&,NodePtrCompare)
     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;
        bstree_algo::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;
     }
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::insert_equal(const node_ptr&,const node_ptr&,const node_ptr&,NodePtrCompare)
     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;
        bstree_algo::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;
     }
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::insert_before(const node_ptr&,const node_ptr&,const node_ptr&)
     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;
        bstree_algo::insert_before(header, pos, new_node, &depth);
        rebalance_after_insertion(new_node, depth, tree_size+1, h_alpha, max_tree_size);
        return new_node;
     }
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::push_back(const node_ptr&,const node_ptr&)
     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;
        bstree_algo::push_back(header, new_node, &depth);
        rebalance_after_insertion(new_node, depth, tree_size+1, h_alpha, max_tree_size);
     }
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::push_front(const node_ptr&,const node_ptr&)
     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;
        bstree_algo::push_front(header, new_node, &depth);
        rebalance_after_insertion(new_node, depth, tree_size+1, h_alpha, max_tree_size);
     }
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::insert_unique_check(const const_node_ptr&,const KeyType&,KeyNodePtrCompare,insert_commit_data&)
     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 =
           bstree_algo::insert_unique_check(header, key, comp, commit_data, &depth);
        commit_data.depth = depth;
        return ret;
     }
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::insert_unique_check(const const_node_ptr&,const node_ptr&,const KeyType&,KeyNodePtrCompare,insert_commit_data&)
     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 =
           bstree_algo::insert_unique_check
              (header, hint, key, comp, commit_data, &depth);
        commit_data.depth = depth;
        return ret;
     }
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::insert_unique_commit(const node_ptr&,const node_ptr&,const insert_commit_data&)
     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)
     {
        bstree_algo::insert_unique_commit(header, new_value, commit_data);
        rebalance_after_insertion(new_value, commit_data.depth, tree_size+1, h_alpha, max_tree_size);
     }
  
     #ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
     //! @copydoc ::boost::intrusive::bstree_algorithms::is_header
     static bool is_header(const const_node_ptr & p);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::is_header
     static void rebalance(const node_ptr & header);
  
     //! @copydoc ::boost::intrusive::bstree_algorithms::rebalance_subtree
     static node_ptr rebalance_subtree(const node_ptr & old_root)
     #endif   //#ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
  
     /// @cond
     private:
  
     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 > 2 && //Nothing to do with only the root 
           //Check if the root node is unbalanced
           //Scapegoat paper depth counts root depth as zero and "depth" counts root as 1,
           //but since "depth" is the depth of the ancestor of x, i == depth
           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 ancestor = 1; true; ++ancestor){
              if(ancestor == depth){ //Check if whole tree must be rebuilt
                 max_tree_size = tree_size;
                 bstree_algo::rebalance_subtree(NodeTraits::get_parent(s));
                 break;
              }
              else{ //Go to the next scapegoat candidate
                 const node_ptr s_parent = NodeTraits::get_parent(s);
                 const node_ptr s_parent_left = NodeTraits::get_left(s_parent);
                 //Obtain parent's size (previous size + parent + sibling tree)
                 const node_ptr s_sibling = s_parent_left == s ? NodeTraits::get_right(s_parent) : s_parent_left;
                 size += 1 + bstree_algo::subtree_size(s_sibling);
                 s = s_parent;
                 if(ancestor > h_alpha(size)){ //is 's' scapegoat?
                    bstree_algo::rebalance_subtree(s);
                    break;
                 }
              }
           }
        }
     }
     /// @endcond
  };
  
  /// @cond
  
  template<class NodeTraits>
  struct get_algo<SgTreeAlgorithms, NodeTraits>
  {
     typedef sgtree_algorithms<NodeTraits> type;
  };
  
  /// @endcond
  
  } //namespace intrusive
  } //namespace boost
  
  #include <boost/intrusive/detail/config_end.hpp>
  
  #endif //BOOST_INTRUSIVE_SGTREE_ALGORITHMS_HPP
  