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 /////////////////////////////////////////////////////////////////////////////
 //
 // (C) Copyright Ion Gaztanaga  2006-2014.
 //
 // Distributed under the Boost Software License, Version 1.0.
 //    (See accompanying file LICENSE_1_0.txt or copy at
 //          http://www.boost.org/LICENSE_1_0.txt)
 //
 // See http://www.boost.org/libs/intrusive for documentation.
 //
 /////////////////////////////////////////////////////////////////////////////
 
 #ifndef BOOST_INTRUSIVE_TREAP_ALGORITHMS_HPP
 #define BOOST_INTRUSIVE_TREAP_ALGORITHMS_HPP
 
 #include <boost/intrusive/detail/config_begin.hpp>
 #include <boost/intrusive/intrusive_fwd.hpp>
 
 #include <cstddef>
 
 #include <boost/intrusive/detail/assert.hpp>
 #include <boost/intrusive/detail/algo_type.hpp>
 #include <boost/intrusive/bstree_algorithms.hpp>
 
 #if defined(BOOST_HAS_PRAGMA_ONCE)
 #  pragma once
 #endif
 
 namespace boost {
 namespace intrusive {
 
 #ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
 
 namespace detail
 {
 
 template<class ValueTraits, class NodePtrPrioCompare, class ExtraChecker>
 struct treap_node_extra_checker
       : public ExtraChecker
 {
    typedef ExtraChecker                            base_checker_t;
    typedef ValueTraits                             value_traits;
    typedef typename value_traits::node_traits      node_traits;
    typedef typename node_traits::const_node_ptr const_node_ptr;
 
    typedef typename base_checker_t::return_type    return_type;
 
    treap_node_extra_checker(const NodePtrPrioCompare& prio_comp, ExtraChecker extra_checker)
       : base_checker_t(extra_checker), prio_comp_(prio_comp)
    {}
 
    void operator () (const_node_ptr p,
                      const return_type& check_return_left, const return_type& check_return_right,
                      return_type& check_return)
    {
       BOOST_INTRUSIVE_INVARIANT_ASSERT(!node_traits::get_left(p) || !prio_comp_(node_traits::get_left(p), p));
       BOOST_INTRUSIVE_INVARIANT_ASSERT(!node_traits::get_right(p) || !prio_comp_(node_traits::get_right(p), p));
       base_checker_t::operator()(p, check_return_left, check_return_right, check_return);
    }
 
    const NodePtrPrioCompare prio_comp_;
 };
 
 } // namespace detail
 
 #endif   //#ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
 
 //! treap_algorithms provides basic algorithms to manipulate
 //! nodes forming a treap.
 //!
 //! (1) the header node is maintained with links not only to the root
 //! but also to the leftmost node of the tree, to enable constant time
 //! begin(), and to the rightmost node of the tree, to enable linear time
 //! performance when used with the generic set algorithms (set_union,
 //! etc.);
 //!
 //! (2) when a node being deleted has two children its successor node is
 //! relinked into its place, rather than copied, so that the only
 //! pointers invalidated are those referring to the deleted node.
 //!
 //! treap_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 treap
 //!
 //! <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 treap_algorithms
    #ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
    : public bstree_algorithms<NodeTraits>
    #endif
 {
    public:
    typedef NodeTraits                           node_traits;
    typedef typename NodeTraits::node            node;
    typedef typename NodeTraits::node_ptr       node_ptr;
    typedef typename NodeTraits::const_node_ptr const_node_ptr;
 
    /// @cond
    private:
 
    typedef bstree_algorithms<NodeTraits>  bstree_algo;
 
    class rerotate_on_destroy
    {
       rerotate_on_destroy& operator=(const rerotate_on_destroy&);
 
       public:
       rerotate_on_destroy(node_ptr header, node_ptr p, std::size_t &n)
          :  header_(header), p_(p), n_(n), remove_it_(true)
       {}
 
       ~rerotate_on_destroy()
       {
          if(remove_it_){
             rotate_up_n(header_, p_, n_);
          }
       }
 
       void release()
       {  remove_it_ = false;  }
 
       const node_ptr header_;
       const node_ptr p_;
       std::size_t &n_;
       bool remove_it_;
    };
 
    static void rotate_up_n(const node_ptr header, const node_ptr p, std::size_t n)
    {
       node_ptr p_parent(NodeTraits::get_parent(p));
       node_ptr p_grandparent(NodeTraits::get_parent(p_parent));
       while(n--){
          if(p == NodeTraits::get_left(p_parent)){  //p is left child
             bstree_algo::rotate_right(p_parent, p, p_grandparent, header);
          }
          else{ //p is right child
             bstree_algo::rotate_left(p_parent, p, p_grandparent, header);
          }
          p_parent      = p_grandparent;
          p_grandparent = NodeTraits::get_parent(p_parent);
       }
    }
 
    /// @endcond
 
    public:
    //! This type is the information that will be
    //! filled by insert_unique_check
    struct insert_commit_data
       /// @cond
       :  public bstree_algo::insert_commit_data
       /// @endcond
    {
       /// @cond
       std::size_t rotations;
       /// @endcond
    };
 
    #ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::get_header(const_node_ptr)
    static node_ptr get_header(const_node_ptr n) BOOST_NOEXCEPT;
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::begin_node
    static node_ptr begin_node(const_node_ptr header) BOOST_NOEXCEPT;
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::end_node
    static node_ptr end_node(const_node_ptr header) BOOST_NOEXCEPT;
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::swap_tree
    static void swap_tree(node_ptr header1, node_ptr header2) BOOST_NOEXCEPT;
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::swap_nodes(node_ptr,node_ptr)
    static void swap_nodes(node_ptr node1, node_ptr node2) BOOST_NOEXCEPT;
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::swap_nodes(node_ptr,node_ptr,node_ptr,node_ptr)
    static void swap_nodes(node_ptr node1, node_ptr header1, node_ptr node2, node_ptr header2) BOOST_NOEXCEPT;
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::replace_node(node_ptr,node_ptr)
    static void replace_node(node_ptr node_to_be_replaced, node_ptr new_node) BOOST_NOEXCEPT;
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::replace_node(node_ptr,node_ptr,node_ptr)
    static void replace_node(node_ptr node_to_be_replaced, node_ptr header, node_ptr new_node) BOOST_NOEXCEPT;
    #endif   //#ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::unlink(node_ptr)
    template<class NodePtrPriorityCompare>
    static void unlink(node_ptr n, NodePtrPriorityCompare pcomp)
    {
       node_ptr x = NodeTraits::get_parent(n);
       if(x){
          while(!bstree_algo::is_header(x))
             x = NodeTraits::get_parent(x);
          erase(x, n, pcomp);
       }
    }
 
    #ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
    //! @copydoc ::boost::intrusive::bstree_algorithms::unlink_leftmost_without_rebalance
    static node_ptr unlink_leftmost_without_rebalance(node_ptr header) BOOST_NOEXCEPT;
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::unique(const_node_ptr)
    static bool unique(const_node_ptr n) BOOST_NOEXCEPT;
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::size(const_node_ptr)
    static std::size_t size(const_node_ptr header) BOOST_NOEXCEPT;
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::next_node(node_ptr)
    static node_ptr next_node(node_ptr n) BOOST_NOEXCEPT;
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::prev_node(node_ptr)
    static node_ptr prev_node(node_ptr n) BOOST_NOEXCEPT;
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::init(node_ptr)
    static void init(node_ptr n) BOOST_NOEXCEPT;
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::init_header(node_ptr)
    static void init_header(node_ptr header) BOOST_NOEXCEPT;
    #endif   //#ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::erase(node_ptr,node_ptr)
    template<class NodePtrPriorityCompare>
    static node_ptr erase(node_ptr header, node_ptr z, NodePtrPriorityCompare pcomp)
    {
       rebalance_for_erasure(header, z, pcomp);
       bstree_algo::erase(header, z);
       return z;
    }
 
    #ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
    //! @copydoc ::boost::intrusive::bstree_algorithms::clone(const_node_ptr,node_ptr,Cloner,Disposer)
    template <class Cloner, class Disposer>
    static void clone
       (const_node_ptr source_header, node_ptr target_header, Cloner cloner, Disposer disposer);
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::clear_and_dispose(node_ptr,Disposer)
    template<class Disposer>
    static void clear_and_dispose(node_ptr header, Disposer disposer) BOOST_NOEXCEPT;
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::lower_bound(const_node_ptr,const KeyType&,KeyNodePtrCompare)
    template<class KeyType, class KeyNodePtrCompare>
    static node_ptr lower_bound
       (const_node_ptr header, const KeyType &key, KeyNodePtrCompare comp);
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::upper_bound(const_node_ptr,const KeyType&,KeyNodePtrCompare)
    template<class KeyType, class KeyNodePtrCompare>
    static node_ptr upper_bound
       (const_node_ptr header, const KeyType &key, KeyNodePtrCompare comp);
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::find(const_node_ptr, const KeyType&,KeyNodePtrCompare)
    template<class KeyType, class KeyNodePtrCompare>
    static node_ptr find
       (const_node_ptr header, const KeyType &key, KeyNodePtrCompare comp);
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::equal_range(const_node_ptr,const KeyType&,KeyNodePtrCompare)
    template<class KeyType, class KeyNodePtrCompare>
    static std::pair<node_ptr, node_ptr> equal_range
       (const_node_ptr header, const KeyType &key, KeyNodePtrCompare comp);
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::bounded_range(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_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_node_ptr,const KeyType&,KeyNodePtrCompare)
    template<class KeyType, class KeyNodePtrCompare>
    static std::size_t count(const_node_ptr header, const KeyType &key, KeyNodePtrCompare comp);
 
    #endif   //#ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
 
    //! <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.
    //!   NodePtrPriorityCompare is a priority function object that induces a strict weak
    //!   ordering compatible with the one used to create the
    //!   the tree. NodePtrPriorityCompare compares two node_ptrs.
    //!
    //! <b>Effects</b>: Inserts new_node into the tree before the upper bound
    //!   according to "comp" and rotates the tree according to "pcomp".
    //!
    //! <b>Complexity</b>: Average complexity for insert element is at
    //!   most logarithmic.
    //!
    //! <b>Throws</b>: If "comp" throw or "pcomp" throw.
    template<class NodePtrCompare, class NodePtrPriorityCompare>
    static node_ptr insert_equal_upper_bound
       (node_ptr h, node_ptr new_node, NodePtrCompare comp, NodePtrPriorityCompare pcomp)
    {
       insert_commit_data commit_data;
       bstree_algo::insert_equal_upper_bound_check(h, new_node, comp, commit_data);
       rebalance_check_and_commit(h, new_node, pcomp, commit_data);
       return new_node;
    }
 
    //! <b>Requires</b>: "h" must be the header node of a tree.
    //!   NodePtrCompare is a function object that induces a strict weak
    //!   ordering compatible with the strict weak ordering used to create the
    //!   the tree. NodePtrCompare compares two node_ptrs.
    //!   NodePtrPriorityCompare is a priority function object that induces a strict weak
    //!   ordering compatible with the one used to create the
    //!   the tree. NodePtrPriorityCompare compares two node_ptrs.
    //!
    //! <b>Effects</b>: Inserts new_node into the tree before the upper bound
    //!   according to "comp" and rotates the tree according to "pcomp".
    //!
    //! <b>Complexity</b>: Average complexity for insert element is at
    //!   most logarithmic.
    //!
    //! <b>Throws</b>: If "comp" throws.
    template<class NodePtrCompare, class NodePtrPriorityCompare>
    static node_ptr insert_equal_lower_bound
       (node_ptr h, node_ptr new_node, NodePtrCompare comp, NodePtrPriorityCompare pcomp)
    {
       insert_commit_data commit_data;
       bstree_algo::insert_equal_lower_bound_check(h, new_node, comp, commit_data);
       rebalance_check_and_commit(h, new_node, pcomp, commit_data);
       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.
    //!   NodePtrPriorityCompare is a priority function object that induces a strict weak
    //!   ordering compatible with the one used to create the
    //!   the tree. NodePtrPriorityCompare compares two node_ptrs.
    //!
    //! <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).
    //!   Rotates the tree according to "pcomp".
    //!
    //! <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" throw or "pcomp" throw.
    template<class NodePtrCompare, class NodePtrPriorityCompare>
    static node_ptr insert_equal
       (node_ptr h, node_ptr hint, node_ptr new_node, NodePtrCompare comp, NodePtrPriorityCompare pcomp)
    {
       insert_commit_data commit_data;
       bstree_algo::insert_equal_check(h, hint, new_node, comp, commit_data);
       rebalance_check_and_commit(h, new_node, pcomp, commit_data);
       return new_node;
    }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   "pos" must be a valid node of the tree (including header end) node.
    //!   "pos" must be a node 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.
    //!   NodePtrPriorityCompare is a priority function object that induces a strict weak
    //!   ordering compatible with the one used to create the
    //!   the tree. NodePtrPriorityCompare compares two node_ptrs.
    //!
    //! <b>Effects</b>: Inserts new_node into the tree before "pos"
    //!   and rotates the tree according to "pcomp".
    //!
    //! <b>Complexity</b>: Constant-time.
    //!
    //! <b>Throws</b>: If "pcomp" throws, strong guarantee.
    //!
    //! <b>Note</b>: If "pos" is not the successor of the newly inserted "new_node"
    //! tree invariants might be broken.
    template<class NodePtrPriorityCompare>
    static node_ptr insert_before
       (node_ptr header, node_ptr pos, node_ptr new_node, NodePtrPriorityCompare pcomp)
    {
       insert_commit_data commit_data;
       bstree_algo::insert_before_check(header, pos, commit_data);
       rebalance_check_and_commit(header, new_node, pcomp, commit_data);
       return new_node;
    }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   "new_node" must be, according to the used ordering no less than the
    //!   greatest inserted key.
    //!   NodePtrPriorityCompare is a priority function object that induces a strict weak
    //!   ordering compatible with the one used to create the
    //!   the tree. NodePtrPriorityCompare compares two node_ptrs.
    //!
    //! <b>Effects</b>: Inserts x into the tree in the last position
    //!   and rotates the tree according to "pcomp".
    //!
    //! <b>Complexity</b>: Constant-time.
    //!
    //! <b>Throws</b>: If "pcomp" throws, strong guarantee.
    //!
    //! <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 NodePtrPriorityCompare>
    static void push_back(node_ptr header, node_ptr new_node, NodePtrPriorityCompare pcomp)
    {
       insert_commit_data commit_data;
       bstree_algo::push_back_check(header, commit_data);
       rebalance_check_and_commit(header, new_node, pcomp, commit_data);
    }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   "new_node" must be, according to the used ordering, no greater than the
    //!   lowest inserted key.
    //!   NodePtrPriorityCompare is a priority function object that induces a strict weak
    //!   ordering compatible with the one used to create the
    //!   the tree. NodePtrPriorityCompare compares two node_ptrs.
    //!
    //! <b>Effects</b>: Inserts x into the tree in the first position
    //!   and rotates the tree according to "pcomp".
    //!
    //! <b>Complexity</b>: Constant-time.
    //!
    //! <b>Throws</b>: If "pcomp" throws, strong guarantee.
    //!
    //! <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 NodePtrPriorityCompare>
    static void push_front(node_ptr header, node_ptr new_node, NodePtrPriorityCompare pcomp)
    {
       insert_commit_data commit_data;
       bstree_algo::push_front_check(header, commit_data);
       rebalance_check_and_commit(header, new_node, pcomp, commit_data);
    }
 
    //! <b>Requires</b>: "header" must be the header node of a tree.
    //!   KeyNodePtrCompare is a function object that induces a strict weak
    //!   ordering compatible with the strict weak ordering used to create the
    //!   the tree. NodePtrCompare compares KeyType with a node_ptr.
    //!
    //! <b>Effects</b>: Checks if there is an equivalent node to "key" in the
    //!   tree according to "comp" and obtains the needed information to realize
    //!   a constant-time node insertion if there is no equivalent node.
    //!
    //! <b>Returns</b>: If there is an equivalent value
    //!   returns a pair containing a node_ptr to the already present node
    //!   and false. If there is not equivalent key can be inserted returns true
    //!   in the returned pair's boolean and fills "commit_data" that is meant to
    //!   be used with the "insert_commit" function to achieve a constant-time
    //!   insertion function.
    //!
    //! <b>Complexity</b>: Average complexity is at most logarithmic.
    //!
    //! <b>Throws</b>: If "comp" throws.
    //!
    //! <b>Notes</b>: This function is used to improve performance when constructing
    //!   a node is expensive and the user does not want to have two equivalent nodes
    //!   in the tree: if there is an equivalent value
    //!   the constructed object must be discarded. Many times, the part of the
    //!   node that is used to impose the order is much cheaper to construct
    //!   than the node and this function offers the possibility to use that part
    //!   to check if the insertion will be successful.
    //!
    //!   If the check is successful, the user can construct the node and use
    //!   "insert_commit" to insert the node in constant-time. This gives a total
    //!   logarithmic complexity to the insertion: check(O(log(N)) + commit(O(1)).
    //!
    //!   "commit_data" remains valid for a subsequent "insert_unique_commit" only
    //!   if no more objects are inserted or erased from the set.
    template<class KeyType, class KeyNodePtrCompare, class PrioType, class PrioNodePtrPrioCompare>
    static std::pair<node_ptr, bool> insert_unique_check
       ( const_node_ptr header
       , const KeyType &key, KeyNodePtrCompare comp
       , const PrioType &prio, PrioNodePtrPrioCompare pcomp
       , insert_commit_data &commit_data)
    {
       std::pair<node_ptr, bool> ret =
          bstree_algo::insert_unique_check(header, key, comp, commit_data);
       if(ret.second)
          rebalance_after_insertion_check(header, commit_data.node, prio, pcomp, commit_data.rotations);
       return ret;
    }
 
    //! <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, class PrioType, class PrioNodePtrPrioCompare>
    static std::pair<node_ptr, bool> insert_unique_check
       ( const_node_ptr header, node_ptr hint
       , const KeyType &key, KeyNodePtrCompare comp
       , const PrioType &prio, PrioNodePtrPrioCompare pcomp
       , insert_commit_data &commit_data)
    {
       std::pair<node_ptr, bool> ret =
          bstree_algo::insert_unique_check(header, hint, key, comp, commit_data);
       if(ret.second)
          rebalance_after_insertion_check(header, commit_data.node, prio, pcomp, commit_data.rotations);
       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.
    static void insert_unique_commit
       (node_ptr header, node_ptr new_node, const insert_commit_data &commit_data) BOOST_NOEXCEPT
    {
       bstree_algo::insert_unique_commit(header, new_node, commit_data);
       rotate_up_n(header, new_node, commit_data.rotations);
    }
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::transfer_unique
    template<class NodePtrCompare, class PrioNodePtrPrioCompare>
    static bool transfer_unique
       (node_ptr header1, NodePtrCompare comp, PrioNodePtrPrioCompare pcomp, node_ptr header2, node_ptr z)
    {
       insert_commit_data commit_data;
       bool const transferable = insert_unique_check(header1, z, comp, z, pcomp, commit_data).second;
       if(transferable){
          erase(header2, z, pcomp);
          insert_unique_commit(header1, z, commit_data);         
       }
       return transferable;
    }
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::transfer_equal
    template<class NodePtrCompare, class PrioNodePtrPrioCompare>
    static void transfer_equal
       (node_ptr header1, NodePtrCompare comp, PrioNodePtrPrioCompare pcomp, node_ptr header2, node_ptr z)
    {
       insert_commit_data commit_data;
       bstree_algo::insert_equal_upper_bound_check(header1, z, comp, commit_data);
       rebalance_after_insertion_check(header1, commit_data.node, z, pcomp, commit_data.rotations);
       rebalance_for_erasure(header2, z, pcomp);
       bstree_algo::erase(header2, z);
       bstree_algo::insert_unique_commit(header1, z, commit_data);
       rotate_up_n(header1, z, commit_data.rotations);
    }
 
    #ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
 
    //! @copydoc ::boost::intrusive::bstree_algorithms::is_header
    static bool is_header(const_node_ptr p) BOOST_NOEXCEPT;
    #endif   //#ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
 
    /// @cond
    private:
 
    template<class NodePtrPriorityCompare>
    static void rebalance_for_erasure(node_ptr header, node_ptr z, NodePtrPriorityCompare pcomp)
    {
       std::size_t n = 0;
       rerotate_on_destroy rb(header, z, n);
 
       node_ptr z_left  = NodeTraits::get_left(z);
       node_ptr z_right = NodeTraits::get_right(z);
       while(z_left || z_right){
          const node_ptr z_parent(NodeTraits::get_parent(z));
          if(!z_right || (z_left && pcomp(z_left, z_right))){
             bstree_algo::rotate_right(z, z_left, z_parent, header);
          }
          else{
             bstree_algo::rotate_left(z, z_right, z_parent, header);
          }
          ++n;
          z_left  = NodeTraits::get_left(z);
          z_right = NodeTraits::get_right(z);
       }
       rb.release();
    }
 
    template<class NodePtrPriorityCompare>
    static void rebalance_check_and_commit
       (node_ptr h, node_ptr new_node, NodePtrPriorityCompare pcomp, insert_commit_data &commit_data)
    {
       rebalance_after_insertion_check(h, commit_data.node, new_node, pcomp, commit_data.rotations);
       //No-throw
       bstree_algo::insert_unique_commit(h, new_node, commit_data);
       rotate_up_n(h, new_node, commit_data.rotations);
    }
 
    template<class Key, class KeyNodePriorityCompare>
    static void rebalance_after_insertion_check
       (const_node_ptr header, const_node_ptr up, const Key &k
       , KeyNodePriorityCompare pcomp, std::size_t &num_rotations)
    {
       const_node_ptr upnode(up);
       //First check rotations since pcomp can throw
       num_rotations = 0;
       std::size_t n = 0;
       while(upnode != header && pcomp(k, upnode)){
          ++n;
          upnode = NodeTraits::get_parent(upnode);
       }
       num_rotations = n;
    }
 
    template<class NodePtrPriorityCompare>
    static bool check_invariant(const_node_ptr header, NodePtrPriorityCompare pcomp)
    {
       node_ptr beg = begin_node(header);
       node_ptr end = end_node(header);
 
       while(beg != end){
          node_ptr p = NodeTraits::get_parent(beg);
          if(p != header){
             if(pcomp(beg, p))
                return false;
          }
          beg = next_node(beg);
       }
       return true;
    }
 
    /// @endcond
 };
 
 /// @cond
 
 template<class NodeTraits>
 struct get_algo<TreapAlgorithms, NodeTraits>
 {
    typedef treap_algorithms<NodeTraits> type;
 };
 
 template <class ValueTraits, class NodePtrCompare, class ExtraChecker>
 struct get_node_checker<TreapAlgorithms, ValueTraits, NodePtrCompare, ExtraChecker>
 {
    typedef detail::bstree_node_checker<ValueTraits, NodePtrCompare, ExtraChecker> type;
 };
 
 /// @endcond
 
 } //namespace intrusive
 } //namespace boost
 
 #include <boost/intrusive/detail/config_end.hpp>
 
 #endif //BOOST_INTRUSIVE_TREAP_ALGORITHMS_HPP

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