/////////////////////////////////////////////////////////////////////////////
//
// (C) Copyright Ion Gaztanaga  2006-2012.
//
// 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_TREAP_ALGORITHMS_HPP
#define BOOST_INTRUSIVE_TREAP_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/pointer_traits.hpp>
#include <boost/intrusive/detail/utilities.hpp>
#include <boost/intrusive/detail/tree_algorithms.hpp>
#include <algorithm>


namespace boost {
namespace intrusive {

//! 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 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 treap_algorithms
{
   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:

   class remove_on_destroy
   {
      remove_on_destroy(const remove_on_destroy&);
      remove_on_destroy& operator=(const remove_on_destroy&);
      public:
      remove_on_destroy(const node_ptr & header, const node_ptr & z)
         :  header_(header), z_(z), remove_it_(true)
      {}
      ~remove_on_destroy()
      {
         if(remove_it_){
            tree_algorithms::erase(header_, z_);
         }
      }

      void release()
      {  remove_it_ = false;  }

      const node_ptr header_;
      const node_ptr z_;
      bool remove_it_;
   };

   class rerotate_on_destroy
   {
      rerotate_on_destroy(const remove_on_destroy&);
      rerotate_on_destroy& operator=(const rerotate_on_destroy&);

      public:
      rerotate_on_destroy(const node_ptr & header, const 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)
   {
      for( node_ptr p_parent = NodeTraits::get_parent(p)
         ; n--
         ; p_parent = NodeTraits::get_parent(p)){
         //Check if left child
         if(p == NodeTraits::get_left(p_parent)){
            tree_algorithms::rotate_right(p_parent, header);
         }
         else{ //Right child
            tree_algorithms::rotate_left(p_parent, header);
         }
      }
   }

   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
      /// @cond
      :  public tree_algorithms::insert_commit_data
      /// @endcond
   {
      /// @cond
      std::size_t rotations;
      /// @endcond
   };

   //! <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>: If "pcomp" throws, strong guarantee
   template<class NodePtrPriorityCompare>
   static void unlink(const node_ptr & node, NodePtrPriorityCompare pcomp)
   {
      node_ptr x = NodeTraits::get_parent(node);
      if(x){
         while(!is_header(x))
            x = NodeTraits::get_parent(x);
         erase(x, node, pcomp);
      }
   }

   //! <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>: If "pcomp" throws, strong guarantee.
   template<class NodePtrPriorityCompare>
   static node_ptr erase(const node_ptr & header, const node_ptr & z, NodePtrPriorityCompare pcomp)
   {
      rebalance_for_erasure(header, z, pcomp);
      tree_algorithms::erase(header, z);
      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>: "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.
   //!   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
      (const node_ptr & h, const node_ptr & new_node, NodePtrCompare comp, NodePtrPriorityCompare pcomp)
   {
      insert_commit_data commit_data;
      tree_algorithms::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
      (const node_ptr & h, const node_ptr & new_node, NodePtrCompare comp, NodePtrPriorityCompare pcomp)
   {
      insert_commit_data commit_data;
      tree_algorithms::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
      (const node_ptr & h, const node_ptr & hint, const node_ptr & new_node, NodePtrCompare comp, NodePtrPriorityCompare pcomp)
   {
      insert_commit_data commit_data;
      tree_algorithms::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
      (const node_ptr & header, const node_ptr & pos, const node_ptr & new_node, NodePtrPriorityCompare pcomp)
   {
      insert_commit_data commit_data;
      tree_algorithms::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(const node_ptr & header, const node_ptr & new_node, NodePtrPriorityCompare pcomp)
   {
      insert_commit_data commit_data;
      tree_algorithms::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(const node_ptr & header, const node_ptr & new_node, NodePtrPriorityCompare pcomp)
   {
      insert_commit_data commit_data;
      tree_algorithms::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 KeyNodePtrPrioCompare>
   static std::pair<node_ptr, bool> insert_unique_check
      (const const_node_ptr & header,  const KeyType &key
      ,KeyNodePtrCompare comp, KeyNodePtrPrioCompare pcomp
      ,insert_commit_data &commit_data)
   {
      std::pair<node_ptr, bool> ret =
         tree_algorithms::insert_unique_check(header, key, comp, commit_data);
      if(ret.second)
         rebalance_after_insertion_check(header, commit_data.node, key, 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 KeyNodePtrPrioCompare>
   static std::pair<node_ptr, bool> insert_unique_check
      (const const_node_ptr & header, const node_ptr & hint, const KeyType &key
      ,KeyNodePtrCompare comp, KeyNodePtrPrioCompare pcomp, insert_commit_data &commit_data)
   {
      std::pair<node_ptr, bool> ret =
         tree_algorithms::insert_unique_check(header, hint, key, comp, commit_data);
      if(ret.second)
         rebalance_after_insertion_check(header, commit_data.node, key, 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
      (const node_ptr & header, const node_ptr & new_node, const insert_commit_data &commit_data)
   {
      tree_algorithms::insert_unique_commit(header, new_node, commit_data);
      rebalance_after_insertion_commit(header, new_node, commit_data.rotations);
   }

   //! <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 NodePtrPriorityCompare>
   static void rebalance_for_erasure(const node_ptr & header, const 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){
         if(!z_right || (z_left && pcomp(z_left, z_right))){
            tree_algorithms::rotate_right(z, header);
         }
         else{
            tree_algorithms::rotate_left(z, 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
      (const node_ptr & h, const 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
      tree_algorithms::insert_unique_commit(h, new_node, commit_data);
      rebalance_after_insertion_commit(h, new_node, commit_data.rotations);
   }


   template<class Key, class KeyNodePriorityCompare>
   static void rebalance_after_insertion_check
      (const const_node_ptr &header, const 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;
   }

   static void rebalance_after_insertion_commit(const node_ptr & header, const node_ptr & p, std::size_t n)
   {
      // Now execute n rotations
      for( node_ptr p_parent = NodeTraits::get_parent(p)
         ; n--
         ; p_parent = NodeTraits::get_parent(p)){
         //Check if left child
         if(p == NodeTraits::get_left(p_parent)){
            tree_algorithms::rotate_right(p_parent, header);
         }
         else{ //Right child
            tree_algorithms::rotate_left(p_parent, header);
         }
      }
   }

   template<class NodePtrPriorityCompare>
   static bool check_invariant(const 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
};

} //namespace intrusive
} //namespace boost

#include <boost/intrusive/detail/config_end.hpp>

#endif //BOOST_INTRUSIVE_TREAP_ALGORITHMS_HPP
