boost/intrusive/avltree_algorithms.hpp
///////////////////////////////////////////////////////////////////////////// // // (C) Copyright Daniel K. O. 2005. // (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. // ///////////////////////////////////////////////////////////////////////////// #ifndef BOOST_INTRUSIVE_AVLTREE_ALGORITHMS_HPP #define BOOST_INTRUSIVE_AVLTREE_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/utilities.hpp> #include <boost/intrusive/bstree_algorithms.hpp> #include <boost/intrusive/pointer_traits.hpp> namespace boost { namespace intrusive { /// @cond template<class NodeTraits, class F> struct avltree_node_cloner : private detail::ebo_functor_holder<F> { typedef typename NodeTraits::node_ptr node_ptr; typedef detail::ebo_functor_holder<F> base_t; avltree_node_cloner(F f) : base_t(f) {} node_ptr operator()(const node_ptr & p) { node_ptr n = base_t::get()(p); NodeTraits::set_balance(n, NodeTraits::get_balance(p)); return n; } }; /// @endcond //! avltree_algorithms is configured with a NodeTraits class, which encapsulates the //! information about the node to be manipulated. NodeTraits must support the //! following interface: //! //! <b>Typedefs</b>: //! //! <tt>node</tt>: The type of the node that forms the binary search tree //! //! <tt>node_ptr</tt>: A pointer to a node //! //! <tt>const_node_ptr</tt>: A pointer to a const node //! //! <tt>balance</tt>: The type of the balance factor //! //! <b>Static functions</b>: //! //! <tt>static node_ptr get_parent(const_node_ptr n);</tt> //! //! <tt>static void set_parent(node_ptr n, node_ptr parent);</tt> //! //! <tt>static node_ptr get_left(const_node_ptr n);</tt> //! //! <tt>static void set_left(node_ptr n, node_ptr left);</tt> //! //! <tt>static node_ptr get_right(const_node_ptr n);</tt> //! //! <tt>static void set_right(node_ptr n, node_ptr right);</tt> //! //! <tt>static balance get_balance(const_node_ptr n);</tt> //! //! <tt>static void set_balance(node_ptr n, balance b);</tt> //! //! <tt>static balance negative();</tt> //! //! <tt>static balance zero();</tt> //! //! <tt>static balance positive();</tt> template<class NodeTraits> class avltree_algorithms #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; typedef typename NodeTraits::balance balance; /// @cond private: typedef bstree_algorithms<NodeTraits> bstree_algo; /// @endcond public: //! This type is the information that will be //! filled by insert_unique_check typedef typename bstree_algo::insert_commit_data insert_commit_data; #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); #endif //#ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED //! @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) { if(node1 == node2) return; node_ptr header1(bstree_algo::get_header(node1)), header2(bstree_algo::get_header(node2)); swap_nodes(node1, header1, node2, header2); } //! @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) { if(node1 == node2) return; bstree_algo::swap_nodes(node1, header1, node2, header2); //Swap balance balance c = NodeTraits::get_balance(node1); NodeTraits::set_balance(node1, NodeTraits::get_balance(node2)); NodeTraits::set_balance(node2, c); } //! @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) { if(node_to_be_replaced == new_node) return; replace_node(node_to_be_replaced, bstree_algo::get_header(node_to_be_replaced), 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) { bstree_algo::replace_node(node_to_be_replaced, header, new_node); NodeTraits::set_balance(new_node, NodeTraits::get_balance(node_to_be_replaced)); } //! @copydoc ::boost::intrusive::bstree_algorithms::unlink(const node_ptr&) static void unlink(const node_ptr & node) { node_ptr x = NodeTraits::get_parent(node); if(x){ while(!is_header(x)) x = NodeTraits::get_parent(x); erase(x, node); } } #ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED //! @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); #endif //#ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED //! <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) { bstree_algo::init_header(header); NodeTraits::set_balance(header, NodeTraits::zero()); } //! @copydoc ::boost::intrusive::bstree_algorithms::erase(const node_ptr&,const node_ptr&) static node_ptr erase(const node_ptr & header, const node_ptr & z) { typename bstree_algo::data_for_rebalance info; bstree_algo::erase(header, z, info); if(info.y != z){ NodeTraits::set_balance(info.y, NodeTraits::get_balance(z)); } //Rebalance avltree rebalance_after_erasure(header, info.x, info.x_parent); return z; } //! @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) { avltree_node_cloner<NodeTraits, Cloner> new_cloner(cloner); bstree_algo::clone(source_header, target_header, new_cloner, disposer); } #ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED //! @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> static node_ptr insert_equal_upper_bound (const node_ptr & h, const node_ptr & new_node, NodePtrCompare comp) { bstree_algo::insert_equal_upper_bound(h, new_node, comp); rebalance_after_insertion(h, new_node); return new_node; } //! @copydoc ::boost::intrusive::bstree_algorithms::insert_equal_lower_bound(const node_ptr&,const node_ptr&,NodePtrCompare) template<class NodePtrCompare> static node_ptr insert_equal_lower_bound (const node_ptr & h, const node_ptr & new_node, NodePtrCompare comp) { bstree_algo::insert_equal_lower_bound(h, new_node, comp); rebalance_after_insertion(h, new_node); return new_node; } //! @copydoc ::boost::intrusive::bstree_algorithms::insert_equal(const node_ptr&,const node_ptr&,const node_ptr&,NodePtrCompare) template<class NodePtrCompare> static node_ptr insert_equal (const node_ptr & header, const node_ptr & hint, const node_ptr & new_node, NodePtrCompare comp) { bstree_algo::insert_equal(header, hint, new_node, comp); rebalance_after_insertion(header, new_node); return new_node; } //! @copydoc ::boost::intrusive::bstree_algorithms::insert_before(const node_ptr&,const node_ptr&,const node_ptr&) static node_ptr insert_before (const node_ptr & header, const node_ptr & pos, const node_ptr & new_node) { bstree_algo::insert_before(header, pos, new_node); rebalance_after_insertion(header, new_node); return new_node; } //! @copydoc ::boost::intrusive::bstree_algorithms::push_back(const node_ptr&,const node_ptr&) static void push_back(const node_ptr & header, const node_ptr & new_node) { bstree_algo::push_back(header, new_node); rebalance_after_insertion(header, new_node); } //! @copydoc ::boost::intrusive::bstree_algorithms::push_front(const node_ptr&,const node_ptr&) static void push_front(const node_ptr & header, const node_ptr & new_node) { bstree_algo::push_front(header, new_node); rebalance_after_insertion(header, new_node); } #ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED //! @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); //! @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); #endif //#ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED //! @copydoc ::boost::intrusive::bstree_algorithms::insert_unique_commit(const node_ptr&,const node_ptr&,const insert_commit_data &) static void insert_unique_commit (const node_ptr & header, const node_ptr & new_value, const insert_commit_data &commit_data) { bstree_algo::insert_unique_commit(header, new_value, commit_data); rebalance_after_insertion(header, new_value); } //! @copydoc ::boost::intrusive::bstree_algorithms::is_header static bool is_header(const const_node_ptr & p) { return NodeTraits::get_balance(p) == NodeTraits::zero() && bstree_algo::is_header(p); } /// @cond static bool verify(const node_ptr &header) { std::size_t height; std::size_t count; return verify_recursion(NodeTraits::get_parent(header), count, height); } private: static bool verify_recursion(node_ptr n, std::size_t &count, std::size_t &height) { if (!n){ count = 0; height = 0; return true; } std::size_t leftcount, rightcount; std::size_t leftheight, rightheight; if(!verify_recursion(NodeTraits::get_left (n), leftcount, leftheight) || !verify_recursion(NodeTraits::get_right(n), rightcount, rightheight) ){ return false; } count = 1u + leftcount + rightcount; height = 1u + (leftheight > rightheight ? leftheight : rightheight); //If equal height, balance must be zero if(rightheight == leftheight){ if(NodeTraits::get_balance(n) != NodeTraits::zero()){ BOOST_ASSERT(0); return false; } } //If right is taller than left, then the difference must be at least 1 and the balance positive else if(rightheight > leftheight){ if(rightheight - leftheight > 1 ){ BOOST_ASSERT(0); return false; } else if(NodeTraits::get_balance(n) != NodeTraits::positive()){ BOOST_ASSERT(0); return false; } } //If left is taller than right, then the difference must be at least 1 and the balance negative else{ if(leftheight - rightheight > 1 ){ BOOST_ASSERT(0); return false; } else if(NodeTraits::get_balance(n) != NodeTraits::negative()){ BOOST_ASSERT(0); return false; } } return true; } static void rebalance_after_erasure(const node_ptr & header, node_ptr x, node_ptr x_parent) { for (node_ptr root = NodeTraits::get_parent(header); x != root; root = NodeTraits::get_parent(header)) { const balance x_parent_balance = NodeTraits::get_balance(x_parent); //Don't cache x_is_leftchild or similar because x can be null and //equal to both x_parent_left and x_parent_right const node_ptr x_parent_left (NodeTraits::get_left(x_parent)); const node_ptr x_parent_right(NodeTraits::get_right(x_parent)); if(x_parent_balance == NodeTraits::zero()){ NodeTraits::set_balance( x_parent, x == x_parent_right ? NodeTraits::negative() : NodeTraits::positive() ); break; // the height didn't change, let's stop here } else if(x_parent_balance == NodeTraits::negative()){ if (x == x_parent_left) { ////x is left child or x and sibling are null NodeTraits::set_balance(x_parent, NodeTraits::zero()); // balanced x = x_parent; } else { // x is right child (x_parent_left is the left child) BOOST_INTRUSIVE_INVARIANT_ASSERT(x_parent_left); if (NodeTraits::get_balance(x_parent_left) == NodeTraits::positive()) { // x_parent_left MUST have a right child BOOST_INTRUSIVE_INVARIANT_ASSERT(NodeTraits::get_right(x_parent_left)); x = avl_rotate_left_right(x_parent, x_parent_left, header); } else { avl_rotate_right(x_parent, x_parent_left, header); x = x_parent_left; } // if changed from negative to NodeTraits::positive(), no need to check above if (NodeTraits::get_balance(x) == NodeTraits::positive()){ break; } } } else if(x_parent_balance == NodeTraits::positive()){ if (x == x_parent_right) { //x is right child or x and sibling are null NodeTraits::set_balance(x_parent, NodeTraits::zero()); // balanced x = x_parent; } else { // x is left child (x_parent_right is the right child) const node_ptr x_parent_right(NodeTraits::get_right(x_parent)); BOOST_INTRUSIVE_INVARIANT_ASSERT(x_parent_right); if (NodeTraits::get_balance(x_parent_right) == NodeTraits::negative()) { // x_parent_right MUST have then a left child BOOST_INTRUSIVE_INVARIANT_ASSERT(NodeTraits::get_left(x_parent_right)); x = avl_rotate_right_left(x_parent, x_parent_right, header); } else { avl_rotate_left(x_parent, x_parent_right, header); x = x_parent_right; } // if changed from NodeTraits::positive() to negative, no need to check above if (NodeTraits::get_balance(x) == NodeTraits::negative()){ break; } } } else{ BOOST_INTRUSIVE_INVARIANT_ASSERT(false); // never reached } x_parent = NodeTraits::get_parent(x); } } static void rebalance_after_insertion(const node_ptr & header, node_ptr x) { NodeTraits::set_balance(x, NodeTraits::zero()); // Rebalance. for(node_ptr root = NodeTraits::get_parent(header); x != root; root = NodeTraits::get_parent(header)){ node_ptr const x_parent(NodeTraits::get_parent(x)); node_ptr const x_parent_left(NodeTraits::get_left(x_parent)); const balance x_parent_balance = NodeTraits::get_balance(x_parent); const bool x_is_leftchild(x == x_parent_left); if(x_parent_balance == NodeTraits::zero()){ // if x is left, parent will have parent->bal_factor = negative // else, parent->bal_factor = NodeTraits::positive() NodeTraits::set_balance( x_parent, x_is_leftchild ? NodeTraits::negative() : NodeTraits::positive() ); x = x_parent; } else if(x_parent_balance == NodeTraits::positive()){ // if x is a left child, parent->bal_factor = zero if (x_is_leftchild) NodeTraits::set_balance(x_parent, NodeTraits::zero()); else{ // x is a right child, needs rebalancing if (NodeTraits::get_balance(x) == NodeTraits::negative()) avl_rotate_right_left(x_parent, x, header); else avl_rotate_left(x_parent, x, header); } break; } else if(x_parent_balance == NodeTraits::negative()){ // if x is a left child, needs rebalancing if (x_is_leftchild) { if (NodeTraits::get_balance(x) == NodeTraits::positive()) avl_rotate_left_right(x_parent, x, header); else avl_rotate_right(x_parent, x, header); } else NodeTraits::set_balance(x_parent, NodeTraits::zero()); break; } else{ BOOST_INTRUSIVE_INVARIANT_ASSERT(false); // never reached } } } static void left_right_balancing(const node_ptr & a, const node_ptr & b, const node_ptr & c) { // balancing... const balance c_balance = NodeTraits::get_balance(c); const balance zero_balance = NodeTraits::zero(); const balance posi_balance = NodeTraits::positive(); const balance nega_balance = NodeTraits::negative(); NodeTraits::set_balance(c, zero_balance); if(c_balance == nega_balance){ NodeTraits::set_balance(a, posi_balance); NodeTraits::set_balance(b, zero_balance); } else if(c_balance == zero_balance){ NodeTraits::set_balance(a, zero_balance); NodeTraits::set_balance(b, zero_balance); } else if(c_balance == posi_balance){ NodeTraits::set_balance(a, zero_balance); NodeTraits::set_balance(b, nega_balance); } else{ BOOST_INTRUSIVE_INVARIANT_ASSERT(false); // never reached } } static node_ptr avl_rotate_left_right(const node_ptr a, const node_ptr a_oldleft, const node_ptr & hdr) { // [note: 'a_oldleft' is 'b'] // | | // // a(-2) c // // / \ / \ // // / \ ==> / \ // // (pos)b [g] b a // // / \ / \ / \ // // [d] c [d] e f [g] // // / \ // // e f // const node_ptr c = NodeTraits::get_right(a_oldleft); bstree_algo::rotate_left_no_parent_fix(a_oldleft, c); //No need to link c with a [NodeTraits::set_parent(c, a) + NodeTraits::set_left(a, c)] //as c is not root and another rotation is coming bstree_algo::rotate_right(a, c, NodeTraits::get_parent(a), hdr); left_right_balancing(a, a_oldleft, c); return c; } static node_ptr avl_rotate_right_left(const node_ptr a, const node_ptr a_oldright, const node_ptr & hdr) { // [note: 'a_oldright' is 'b'] // | | // // a(pos) c // // / \ / \ // // / \ / \ // // [d] b(neg) ==> a b // // / \ / \ / \ // // c [g] [d] e f [g] // // / \ // // e f // const node_ptr c (NodeTraits::get_left(a_oldright)); bstree_algo::rotate_right_no_parent_fix(a_oldright, c); //No need to link c with a [NodeTraits::set_parent(c, a) + NodeTraits::set_right(a, c)] //as c is not root and another rotation is coming. bstree_algo::rotate_left(a, c, NodeTraits::get_parent(a), hdr); left_right_balancing(a_oldright, a, c); return c; } static void avl_rotate_left(const node_ptr &x, const node_ptr &x_oldright, const node_ptr & hdr) { bstree_algo::rotate_left(x, x_oldright, NodeTraits::get_parent(x), hdr); // reset the balancing factor if (NodeTraits::get_balance(x_oldright) == NodeTraits::positive()) { NodeTraits::set_balance(x, NodeTraits::zero()); NodeTraits::set_balance(x_oldright, NodeTraits::zero()); } else { // this doesn't happen during insertions NodeTraits::set_balance(x, NodeTraits::positive()); NodeTraits::set_balance(x_oldright, NodeTraits::negative()); } } static void avl_rotate_right(const node_ptr &x, const node_ptr &x_oldleft, const node_ptr & hdr) { bstree_algo::rotate_right(x, x_oldleft, NodeTraits::get_parent(x), hdr); // reset the balancing factor if (NodeTraits::get_balance(x_oldleft) == NodeTraits::negative()) { NodeTraits::set_balance(x, NodeTraits::zero()); NodeTraits::set_balance(x_oldleft, NodeTraits::zero()); } else { // this doesn't happen during insertions NodeTraits::set_balance(x, NodeTraits::negative()); NodeTraits::set_balance(x_oldleft, NodeTraits::positive()); } } /// @endcond }; /// @cond template<class NodeTraits> struct get_algo<AvlTreeAlgorithms, NodeTraits> { typedef avltree_algorithms<NodeTraits> type; }; /// @endcond } //namespace intrusive } //namespace boost #include <boost/intrusive/detail/config_end.hpp> #endif //BOOST_INTRUSIVE_AVLTREE_ALGORITHMS_HPP