boost/intrusive/detail/tree_algorithms.hpp
///////////////////////////////////////////////////////////////////////////// // // (C) Copyright Ion Gaztanaga 2007. // // Distributed under the Boost Software License, Version 1.0. // (See accompanying file LICENSE_1_0.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) // // See http://www.boost.org/libs/intrusive for documentation. // ///////////////////////////////////////////////////////////////////////////// #ifndef BOOST_INTRUSIVE_TREE_ALGORITHMS_HPP #define BOOST_INTRUSIVE_TREE_ALGORITHMS_HPP #include <boost/intrusive/detail/config_begin.hpp> #include <boost/intrusive/detail/assert.hpp> #include <boost/intrusive/intrusive_fwd.hpp> #include <cstddef> #include <boost/intrusive/detail/utilities.hpp> namespace boost { namespace intrusive { namespace detail { //! This is an implementation of a binary search tree. //! A node in the search tree has references to its children and its parent. This //! is to allow traversal of the whole tree from a given node making the //! implementation of iterator a pointer to a node. //! At the top of the tree a node is used specially. This node's parent pointer //! is pointing to the root of the tree. Its left pointer points to the //! leftmost node in the tree and the right pointer to the rightmost one. //! This node is used to represent the end-iterator. //! //! +---------+ //! header------------------------------>| | //! | | //! +----------(left)--------| |--------(right)---------+ //! | +---------+ | //! | | | //! | | (parent) | //! | | | //! | | | //! | +---------+ | //! root of tree ..|......................> | | | //! | | D | | //! | | | | //! | +-------+---------+-------+ | //! | | | | //! | | | | //! | | | | //! | | | | //! | | | | //! | +---------+ +---------+ | //! | | | | | | //! | | B | | F | | //! | | | | | | //! | +--+---------+--+ +--+---------+--+ | //! | | | | | | //! | | | | | | //! | | | | | | //! | +---+-----+ +-----+---+ +---+-----+ +-----+---+ | //! +-->| | | | | | | |<--+ //! | A | | C | | E | | G | //! | | | | | | | | //! +---------+ +---------+ +---------+ +---------+ //! //! tree_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 tree_algorithms { public: typedef typename NodeTraits::node node; typedef NodeTraits node_traits; typedef typename NodeTraits::node_ptr node_ptr; typedef typename NodeTraits::const_node_ptr const_node_ptr; //! This type is the information that will be filled by insert_unique_check struct insert_commit_data { insert_commit_data() : link_left(false) , node(0) {} bool link_left; node_ptr node; }; struct nop_erase_fixup { void operator()(node_ptr, node_ptr){} }; /// @cond private: template<class Disposer> struct dispose_subtree_disposer { dispose_subtree_disposer(Disposer &disp, node_ptr subtree) : disposer_(&disp), subtree_(subtree) {} void release() { disposer_ = 0; } ~dispose_subtree_disposer() { if(disposer_){ dispose_subtree(subtree_, *disposer_); } } Disposer *disposer_; node_ptr subtree_; }; static node_ptr uncast(const_node_ptr ptr) { return node_ptr(const_cast<node*>(::boost::intrusive::detail::get_pointer(ptr))); } /// @endcond public: static node_ptr begin_node(const_node_ptr header) { return node_traits::get_left(header); } static node_ptr end_node(const_node_ptr header) { return uncast(header); } //! <b>Requires</b>: node is a node of the tree or an node initialized //! by init(...) or init_node. //! //! <b>Effects</b>: Returns true if the node is initialized by init() or init_node(). //! //! <b>Complexity</b>: Constant time. //! //! <b>Throws</b>: Nothing. static bool unique(const_node_ptr node) { return NodeTraits::get_parent(node) == 0; } static node_ptr get_header(const_node_ptr node) { node_ptr h = uncast(node); if(NodeTraits::get_parent(node)){ h = NodeTraits::get_parent(node); while(!is_header(h)) h = NodeTraits::get_parent(h); } return h; } //! <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(node_ptr node1, node_ptr node2) { if(node1 == node2) return; node_ptr header1(get_header(node1)), header2(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(node_ptr node1, node_ptr header1, node_ptr node2, node_ptr header2) { if(node1 == node2) return; //node1 and node2 must not be header nodes //BOOST_INTRUSIVE_INVARIANT_ASSERT((header1 != node1 && header2 != node2)); if(header1 != header2){ //Update header1 if necessary if(node1 == NodeTraits::get_left(header1)){ NodeTraits::set_left(header1, node2); } if(node1 == NodeTraits::get_right(header1)){ NodeTraits::set_right(header1, node2); } if(node1 == NodeTraits::get_parent(header1)){ NodeTraits::set_parent(header1, node2); } //Update header2 if necessary if(node2 == NodeTraits::get_left(header2)){ NodeTraits::set_left(header2, node1); } if(node2 == NodeTraits::get_right(header2)){ NodeTraits::set_right(header2, node1); } if(node2 == NodeTraits::get_parent(header2)){ NodeTraits::set_parent(header2, node1); } } else{ //If both nodes are from the same tree //Update header if necessary if(node1 == NodeTraits::get_left(header1)){ NodeTraits::set_left(header1, node2); } else if(node2 == NodeTraits::get_left(header2)){ NodeTraits::set_left(header2, node1); } if(node1 == NodeTraits::get_right(header1)){ NodeTraits::set_right(header1, node2); } else if(node2 == NodeTraits::get_right(header2)){ NodeTraits::set_right(header2, node1); } if(node1 == NodeTraits::get_parent(header1)){ NodeTraits::set_parent(header1, node2); } else if(node2 == NodeTraits::get_parent(header2)){ NodeTraits::set_parent(header2, node1); } //Adjust data in nodes to be swapped //so that final link swap works as expected if(node1 == NodeTraits::get_parent(node2)){ NodeTraits::set_parent(node2, node2); if(node2 == NodeTraits::get_right(node1)){ NodeTraits::set_right(node1, node1); } else{ NodeTraits::set_left(node1, node1); } } else if(node2 == NodeTraits::get_parent(node1)){ NodeTraits::set_parent(node1, node1); if(node1 == NodeTraits::get_right(node2)){ NodeTraits::set_right(node2, node2); } else{ NodeTraits::set_left(node2, node2); } } } //Now swap all the links node_ptr temp; //swap left link temp = NodeTraits::get_left(node1); NodeTraits::set_left(node1, NodeTraits::get_left(node2)); NodeTraits::set_left(node2, temp); //swap right link temp = NodeTraits::get_right(node1); NodeTraits::set_right(node1, NodeTraits::get_right(node2)); NodeTraits::set_right(node2, temp); //swap parent link temp = NodeTraits::get_parent(node1); NodeTraits::set_parent(node1, NodeTraits::get_parent(node2)); NodeTraits::set_parent(node2, temp); //Now adjust adjacent nodes for newly inserted node 1 if((temp = NodeTraits::get_left(node1))){ NodeTraits::set_parent(temp, node1); } if((temp = NodeTraits::get_right(node1))){ NodeTraits::set_parent(temp, node1); } if((temp = NodeTraits::get_parent(node1)) && //The header has been already updated so avoid it temp != header2){ if(NodeTraits::get_left(temp) == node2){ NodeTraits::set_left(temp, node1); } if(NodeTraits::get_right(temp) == node2){ NodeTraits::set_right(temp, node1); } } //Now adjust adjacent nodes for newly inserted node 2 if((temp = NodeTraits::get_left(node2))){ NodeTraits::set_parent(temp, node2); } if((temp = NodeTraits::get_right(node2))){ NodeTraits::set_parent(temp, node2); } if((temp = NodeTraits::get_parent(node2)) && //The header has been already updated so avoid it temp != header1){ if(NodeTraits::get_left(temp) == node1){ NodeTraits::set_left(temp, node2); } if(NodeTraits::get_right(temp) == node1){ NodeTraits::set_right(temp, node2); } } } //! <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(node_ptr node_to_be_replaced, node_ptr new_node) { if(node_to_be_replaced == new_node) return; replace_node(node_to_be_replaced, 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(node_ptr node_to_be_replaced, node_ptr header, node_ptr new_node) { if(node_to_be_replaced == new_node) return; //Update header if necessary if(node_to_be_replaced == NodeTraits::get_left(header)){ NodeTraits::set_left(header, new_node); } if(node_to_be_replaced == NodeTraits::get_right(header)){ NodeTraits::set_right(header, new_node); } if(node_to_be_replaced == NodeTraits::get_parent(header)){ NodeTraits::set_parent(header, new_node); } //Now set data from the original node node_ptr temp; NodeTraits::set_left(new_node, NodeTraits::get_left(node_to_be_replaced)); NodeTraits::set_right(new_node, NodeTraits::get_right(node_to_be_replaced)); NodeTraits::set_parent(new_node, NodeTraits::get_parent(node_to_be_replaced)); //Now adjust adjacent nodes for newly inserted node if((temp = NodeTraits::get_left(new_node))){ NodeTraits::set_parent(temp, new_node); } if((temp = NodeTraits::get_right(new_node))){ NodeTraits::set_parent(temp, new_node); } if((temp = NodeTraits::get_parent(new_node)) && //The header has been already updated so avoid it temp != header){ if(NodeTraits::get_left(temp) == node_to_be_replaced){ NodeTraits::set_left(temp, new_node); } if(NodeTraits::get_right(temp) == node_to_be_replaced){ NodeTraits::set_right(temp, new_node); } } } //! <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(node_ptr p) { node_ptr p_right(NodeTraits::get_right(p)); if(p_right){ return minimum(p_right); } else { node_ptr x = NodeTraits::get_parent(p); while(p == NodeTraits::get_right(x)){ p = x; x = NodeTraits::get_parent(x); } return NodeTraits::get_right(p) != x ? x : uncast(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(node_ptr p) { if(is_header(p)){ return maximum(NodeTraits::get_parent(p)); } else if(NodeTraits::get_left(p)){ return maximum(NodeTraits::get_left(p)); } else { node_ptr x = NodeTraits::get_parent(p); while(p == NodeTraits::get_left(x)){ p = x; x = NodeTraits::get_parent(x); } return x; } } //! <b>Requires</b>: p is a node of a tree but not the header. //! //! <b>Effects</b>: Returns the minimum node of the subtree starting at p. //! //! <b>Complexity</b>: Logarithmic to the size of the subtree. //! //! <b>Throws</b>: Nothing. static node_ptr minimum (node_ptr p) { for(node_ptr p_left = NodeTraits::get_left(p) ;p_left ;p_left = NodeTraits::get_left(p)){ p = p_left; } return p; } //! <b>Requires</b>: p is a node of a tree but not the header. //! //! <b>Effects</b>: Returns the maximum node of the subtree starting at p. //! //! <b>Complexity</b>: Logarithmic to the size of the subtree. //! //! <b>Throws</b>: Nothing. static node_ptr maximum(node_ptr p) { for(node_ptr p_right = NodeTraits::get_right(p) ;p_right ;p_right = NodeTraits::get_right(p)){ p = p_right; } return 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(node_ptr node) { NodeTraits::set_parent(node, node_ptr(0)); NodeTraits::set_left(node, node_ptr(0)); NodeTraits::set_right(node, node_ptr(0)); }; //! <b>Effects</b>: Returns true if node is in the same state as if called init(node) //! //! <b>Complexity</b>: Constant. //! //! <b>Throws</b>: Nothing. static bool inited(const_node_ptr node) { return !NodeTraits::get_parent(node) && !NodeTraits::get_left(node) && !NodeTraits::get_right(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(node_ptr header) { NodeTraits::set_parent(header, node_ptr(0)); NodeTraits::set_left(header, header); NodeTraits::set_right(header, header); } //! <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()(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(node_ptr header, Disposer disposer) { node_ptr source_root = NodeTraits::get_parent(header); if(!source_root) return; dispose_subtree(source_root, disposer); init_header(header); } //! <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(node_ptr header) { node_ptr leftmost = NodeTraits::get_left(header); if (leftmost == header) return node_ptr(0); node_ptr leftmost_parent(NodeTraits::get_parent(leftmost)); node_ptr leftmost_right (NodeTraits::get_right(leftmost)); bool is_root = leftmost_parent == header; if (leftmost_right){ NodeTraits::set_parent(leftmost_right, leftmost_parent); NodeTraits::set_left(header, tree_algorithms::minimum(leftmost_right)); if (is_root) NodeTraits::set_parent(header, leftmost_right); else NodeTraits::set_left(NodeTraits::get_parent(header), leftmost_right); } else if (is_root){ NodeTraits::set_parent(header, node_ptr(0)); NodeTraits::set_left(header, header); NodeTraits::set_right(header, header); } else{ NodeTraits::set_left(leftmost_parent, node_ptr(0)); NodeTraits::set_left(header, leftmost_parent); } return leftmost; } //! <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_node_ptr subtree) { if(!subtree) return 0; std::size_t count = 0; node_ptr p = minimum(uncast(subtree)); bool continue_looping = true; while(continue_looping){ ++count; node_ptr p_right(NodeTraits::get_right(p)); if(p_right){ p = minimum(p_right); } else { for(;;){ node_ptr q; if (p == subtree){ continue_looping = false; break; } q = p; p = NodeTraits::get_parent(p); if (NodeTraits::get_left(p) == q) break; } } } return count; } //! <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 size(const_node_ptr header) { node_ptr beg(begin_node(header)); node_ptr end(end_node(header)); std::size_t i = 0; for(;beg != end; beg = next_node(beg)) ++i; return i; } //! <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(node_ptr header1, node_ptr header2) { if(header1 == header2) return; node_ptr tmp; //Parent swap tmp = NodeTraits::get_parent(header1); NodeTraits::set_parent(header1, NodeTraits::get_parent(header2)); NodeTraits::set_parent(header2, tmp); //Left swap tmp = NodeTraits::get_left(header1); NodeTraits::set_left(header1, NodeTraits::get_left(header2)); NodeTraits::set_left(header2, tmp); //Right swap tmp = NodeTraits::get_right(header1); NodeTraits::set_right(header1, NodeTraits::get_right(header2)); NodeTraits::set_right(header2, tmp); //Now test parent node_ptr h1_parent(NodeTraits::get_parent(header1)); if(h1_parent){ NodeTraits::set_parent(h1_parent, header1); } else{ NodeTraits::set_left(header1, header1); NodeTraits::set_right(header1, header1); } node_ptr h2_parent(NodeTraits::get_parent(header2)); if(h2_parent){ NodeTraits::set_parent(h2_parent, header2); } else{ NodeTraits::set_left(header2, header2); NodeTraits::set_right(header2, header2); } } static bool is_header(const_node_ptr p) { /* node_ptr p_parent = NodeTraits::get_parent(p); if(!p_parent) return true; if(!NodeTraits::get_parent(p_parent) != p) return false; if(NodeTraits::get_left(p) != 0){ if(NodeTraits::get_parent(NodeTraits::get_left(p)) != p){ is_header = true; } if(NodeTraits::get_parent(p) == NodeTraits::get_left(p)){ is_header = true; } } */ bool is_header = false; if(NodeTraits::get_parent(p) == p){ is_header = true; } else if(NodeTraits::get_parent(NodeTraits::get_parent(p)) == p){ if(NodeTraits::get_left(p) != 0){ if(NodeTraits::get_parent(NodeTraits::get_left(p)) != p){ is_header = true; } if(NodeTraits::get_parent(p) == NodeTraits::get_left(p)){ is_header = true; } } } return is_header; } //! <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_node_ptr header, const KeyType &key, KeyNodePtrCompare comp) { node_ptr end = uncast(header); node_ptr y = lower_bound(header, key, comp); return (y == end || comp(key, y)) ? end : y; } //! <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_node_ptr header, const KeyType &key, KeyNodePtrCompare comp) { node_ptr y = uncast(header); node_ptr x = NodeTraits::get_parent(header); while(x){ if(comp(x, key)){ x = NodeTraits::get_right(x); } else if(comp(key, x)){ y = x; x = NodeTraits::get_left(x); } else{ node_ptr xu(x), yu(y); y = x, x = NodeTraits::get_left(x); xu = NodeTraits::get_right(xu); while(x){ if(comp(x, key)){ x = NodeTraits::get_right(x); } else { y = x; x = NodeTraits::get_left(x); } } while(xu){ if(comp(key, xu)){ yu = xu; xu = NodeTraits::get_left(xu); } else { xu = NodeTraits::get_right(xu); } } return std::pair<node_ptr,node_ptr> (y, yu); } } return std::pair<node_ptr,node_ptr> (y, y); } //! <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_node_ptr header, const KeyType &key, KeyNodePtrCompare comp) { node_ptr y = uncast(header); node_ptr x = NodeTraits::get_parent(header); while(x){ if(comp(x, key)){ x = NodeTraits::get_right(x); } else { y = x; x = NodeTraits::get_left(x); } } return y; } //! <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_node_ptr header, const KeyType &key, KeyNodePtrCompare comp) { node_ptr y = uncast(header); node_ptr x = NodeTraits::get_parent(header); while(x){ if(comp(key, x)){ y = x; x = NodeTraits::get_left(x); } else { x = NodeTraits::get_right(x); } } return y; } //! <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_value, const insert_commit_data &commit_data) { //Check if commit_data has not been initialized by a insert_unique_check call. BOOST_INTRUSIVE_INVARIANT_ASSERT(commit_data.node != 0); link(header, new_value, commit_data.node, commit_data.link_left); } //! <b>Requires</b>: "header" must be the header node of a tree. //! KeyNodePtrCompare is a function object that induces a strict weak //! ordering compatible with the strict weak ordering used to create the //! the tree. NodePtrCompare compares KeyType with a node_ptr. //! //! <b>Effects</b>: Checks if there is an equivalent node to "key" in the //! tree according to "comp" and obtains the needed information to realize //! a constant-time node insertion if there is no equivalent node. //! //! <b>Returns</b>: If there is an equivalent value //! returns a pair containing a node_ptr to the already present node //! and false. If there is not equivalent key can be inserted returns true //! in the returned pair's boolean and fills "commit_data" that is meant to //! be used with the "insert_commit" function to achieve a constant-time //! insertion function. //! //! <b>Complexity</b>: Average complexity is at most logarithmic. //! //! <b>Throws</b>: If "comp" throws. //! //! <b>Notes</b>: This function is used to improve performance when constructing //! a node is expensive and the user does not want to have two equivalent nodes //! in the tree: if there is an equivalent value //! the constructed object must be discarded. Many times, the part of the //! node that is used to impose the order is much cheaper to construct //! than the node and this function offers the possibility to use that part //! to check if the insertion will be successful. //! //! If the check is successful, the user can construct the node and use //! "insert_commit" to insert the node in constant-time. This gives a total //! logarithmic complexity to the insertion: check(O(log(N)) + commit(O(1)). //! //! "commit_data" remains valid for a subsequent "insert_unique_commit" only //! if no more objects are inserted or erased from the set. template<class KeyType, class KeyNodePtrCompare> static std::pair<node_ptr, bool> insert_unique_check (const_node_ptr header, const KeyType &key ,KeyNodePtrCompare comp, insert_commit_data &commit_data, std::size_t *pdepth = 0) { std::size_t depth = 0; node_ptr h(uncast(header)); node_ptr y(h); node_ptr x(NodeTraits::get_parent(y)); node_ptr prev(0); //Find the upper bound, cache the previous value and if we should //store it in the left or right node bool left_child = true; while(x){ ++depth; y = x; x = (left_child = comp(key, x)) ? NodeTraits::get_left(x) : (prev = y, NodeTraits::get_right(x)); } if(pdepth) *pdepth = depth; //Since we've found the upper bound there is no other value with the same key if: // - There is no previous node // - The previous node is less than the key if(!prev || comp(prev, key)){ commit_data.link_left = left_child; commit_data.node = y; return std::pair<node_ptr, bool>(node_ptr(), true); } //If the previous value was not less than key, it means that it's equal //(because we've checked the upper bound) else{ return std::pair<node_ptr, bool>(prev, false); } } template<class KeyType, class KeyNodePtrCompare> static std::pair<node_ptr, bool> insert_unique_check (const_node_ptr header, node_ptr hint, const KeyType &key ,KeyNodePtrCompare comp, insert_commit_data &commit_data, std::size_t *pdepth = 0) { //hint must be bigger than the key if(hint == header || comp(key, hint)){ node_ptr prev = hint; //The previous value should be less than the key if(prev == NodeTraits::get_left(header) || comp((prev = prev_node(hint)), key)){ commit_data.link_left = unique(header) || !NodeTraits::get_left(hint); commit_data.node = commit_data.link_left ? hint : prev; if(pdepth){ *pdepth = commit_data.node == header ? 0 : depth(commit_data.node) + 1; } return std::pair<node_ptr, bool>(node_ptr(), true); } else{ return insert_unique_check(header, key, comp, commit_data, pdepth); } } //The hint was wrong, use hintless insert else{ return insert_unique_check(header, key, comp, commit_data, pdepth); } } //! <b>Requires</b>: "header" must be the header node of a tree. //! NodePtrCompare is a function object that induces a strict weak //! ordering compatible with the strict weak ordering used to create the //! the tree. NodePtrCompare compares two node_ptrs. "hint" is node from //! the "header"'s tree. //! //! <b>Effects</b>: Inserts new_node into the tree, using "hint" as a hint to //! where it will be inserted. If "hint" is the upper_bound //! the insertion takes constant time (two comparisons in the worst case). //! //! <b>Complexity</b>: Logarithmic in general, but it is amortized //! constant time if new_node is inserted immediately before "hint". //! //! <b>Throws</b>: If "comp" throws. template<class NodePtrCompare> static node_ptr insert_equal (node_ptr header, node_ptr hint, node_ptr new_node, NodePtrCompare comp, std::size_t *pdepth = 0) { if(hint == header || !comp(hint, new_node)){ node_ptr prev(hint); if(hint == NodeTraits::get_left(header) || !comp(new_node, (prev = prev_node(hint)))){ bool link_left = unique(header) || !NodeTraits::get_left(hint); link(header, new_node, link_left ? hint : prev, link_left); if(pdepth) *pdepth = depth(new_node) + 1; return new_node; } else{ return insert_equal_upper_bound(header, new_node, comp, pdepth); } } else{ return insert_equal_lower_bound(header, new_node, comp, pdepth); } } //! <b>Requires</b>: p can't be a header node. //! //! <b>Effects</b>: Calculates the depth of a node: the depth of a //! node is the length (number of edges) of the path from the root //! to that node. (The root node is at depth 0.) //! //! <b>Complexity</b>: Logarithmic to the number of nodes in the tree. //! //! <b>Throws</b>: Nothing. static std::size_t depth(const_node_ptr p) { std::size_t depth = 0; node_ptr p_parent; while(p != NodeTraits::get_parent(p_parent = NodeTraits::get_parent(p))){ ++depth; p = p_parent; } return depth; } template<class NodePtrCompare> static node_ptr insert_equal_upper_bound (node_ptr h, node_ptr new_node, NodePtrCompare comp, std::size_t *pdepth = 0) { std::size_t depth = 0; node_ptr y(h); node_ptr x(NodeTraits::get_parent(y)); while(x){ ++depth; y = x; x = comp(new_node, x) ? NodeTraits::get_left(x) : NodeTraits::get_right(x); } bool link_left = (y == h) || comp(new_node, y); link(h, new_node, y, link_left); if(pdepth) *pdepth = depth; return new_node; } template<class NodePtrCompare> static node_ptr insert_equal_lower_bound (node_ptr h, node_ptr new_node, NodePtrCompare comp, std::size_t *pdepth = 0) { std::size_t depth = 0; node_ptr y(h); node_ptr x(NodeTraits::get_parent(y)); while(x){ ++depth; y = x; x = !comp(x, new_node) ? NodeTraits::get_left(x) : NodeTraits::get_right(x); } bool link_left = (y == h) || !comp(y, new_node); link(h, new_node, y, link_left); if(pdepth) *pdepth = depth; return new_node; } //! <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()(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()(node_ptr)</tt> to obtain //! the nodes of the target tree. If "cloner" throws, the cloned target nodes //! are disposed using <tt>void disposer(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_node_ptr source_header, node_ptr target_header, Cloner cloner, Disposer disposer) { if(!unique(target_header)){ clear_and_dispose(target_header, disposer); } node_ptr leftmost, rightmost; node_ptr new_root = clone_subtree (source_header, target_header, cloner, disposer, leftmost, rightmost); //Now update header node NodeTraits::set_parent(target_header, new_root); NodeTraits::set_left (target_header, leftmost); NodeTraits::set_right (target_header, rightmost); } template <class Cloner, class Disposer> static node_ptr clone_subtree ( const_node_ptr source_parent, node_ptr target_parent , Cloner cloner, Disposer disposer , node_ptr &leftmost_out, node_ptr &rightmost_out ) { node_ptr target_sub_root = target_parent; node_ptr source_root = NodeTraits::get_parent(source_parent); if(!source_root){ leftmost_out = rightmost_out = source_root; } else{ //We'll calculate leftmost and rightmost nodes while iterating node_ptr current = source_root; node_ptr insertion_point = target_sub_root = cloner(current); //We'll calculate leftmost and rightmost nodes while iterating node_ptr leftmost = target_sub_root; node_ptr rightmost = target_sub_root; //First set the subroot NodeTraits::set_left(target_sub_root, node_ptr(0)); NodeTraits::set_right(target_sub_root, node_ptr(0)); NodeTraits::set_parent(target_sub_root, target_parent); dispose_subtree_disposer<Disposer> rollback(disposer, target_sub_root); while(true) { //First clone left nodes if( NodeTraits::get_left(current) && !NodeTraits::get_left(insertion_point)) { current = NodeTraits::get_left(current); node_ptr temp = insertion_point; //Clone and mark as leaf insertion_point = cloner(current); NodeTraits::set_left (insertion_point, node_ptr(0)); NodeTraits::set_right (insertion_point, node_ptr(0)); //Insert left NodeTraits::set_parent(insertion_point, temp); NodeTraits::set_left (temp, insertion_point); //Update leftmost if(rightmost == target_sub_root) leftmost = insertion_point; } //Then clone right nodes else if( NodeTraits::get_right(current) && !NodeTraits::get_right(insertion_point)){ current = NodeTraits::get_right(current); node_ptr temp = insertion_point; //Clone and mark as leaf insertion_point = cloner(current); NodeTraits::set_left (insertion_point, node_ptr(0)); NodeTraits::set_right (insertion_point, node_ptr(0)); //Insert right NodeTraits::set_parent(insertion_point, temp); NodeTraits::set_right (temp, insertion_point); //Update rightmost rightmost = insertion_point; } //If not, go up else if(current == source_root){ break; } else{ //Branch completed, go up searching more nodes to clone current = NodeTraits::get_parent(current); insertion_point = NodeTraits::get_parent(insertion_point); } } rollback.release(); leftmost_out = leftmost; rightmost_out = rightmost; } return target_sub_root; } template<class Disposer> static void dispose_subtree(node_ptr x, Disposer disposer) { node_ptr save; while (x){ save = NodeTraits::get_left(x); if (save) { // Right rotation NodeTraits::set_left(x, NodeTraits::get_right(save)); NodeTraits::set_right(save, x); } else { save = NodeTraits::get_right(x); init(x); disposer(x); } x = save; } } //! <b>Requires</b>: p is a node of a tree. //! //! <b>Effects</b>: Returns true if p is a left child. //! //! <b>Complexity</b>: Constant. //! //! <b>Throws</b>: Nothing. static bool is_left_child(node_ptr p) { return NodeTraits::get_left(NodeTraits::get_parent(p)) == p; } //! <b>Requires</b>: p is a node of a tree. //! //! <b>Effects</b>: Returns true if p is a right child. //! //! <b>Complexity</b>: Constant. //! //! <b>Throws</b>: Nothing. static bool is_right_child (node_ptr p) { return NodeTraits::get_right(NodeTraits::get_parent(p)) == p; } static void replace_own (node_ptr own, node_ptr x, node_ptr header) { if(NodeTraits::get_parent(header) == own) NodeTraits::set_parent(header, x); else if(is_left_child(own)) NodeTraits::set_left(NodeTraits::get_parent(own), x); else NodeTraits::set_right(NodeTraits::get_parent(own), x); } static void rotate_left(node_ptr p, node_ptr header) { node_ptr x = NodeTraits::get_right(p); NodeTraits::set_right(p, NodeTraits::get_left(x)); if(NodeTraits::get_left(x) != 0) NodeTraits::set_parent(NodeTraits::get_left(x), p); NodeTraits::set_parent(x, NodeTraits::get_parent(p)); replace_own (p, x, header); NodeTraits::set_left(x, p); NodeTraits::set_parent(p, x); } static void rotate_right(node_ptr p, node_ptr header) { node_ptr x(NodeTraits::get_left(p)); node_ptr x_right(NodeTraits::get_right(x)); NodeTraits::set_left(p, x_right); if(x_right) NodeTraits::set_parent(x_right, p); NodeTraits::set_parent(x, NodeTraits::get_parent(p)); replace_own (p, x, header); NodeTraits::set_right(x, p); NodeTraits::set_parent(p, x); } // rotate node t with left child | complexity : constant | exception : nothrow static node_ptr rotate_left(node_ptr t) { node_ptr x = NodeTraits::get_right(t); NodeTraits::set_right(t, NodeTraits::get_left(x)); if( NodeTraits::get_right(t) != 0 ){ NodeTraits::set_parent(NodeTraits::get_right(t), t ); } NodeTraits::set_left(x, t); NodeTraits::set_parent(t, x); return x; } // rotate node t with right child | complexity : constant | exception : nothrow static node_ptr rotate_right(node_ptr t) { node_ptr x = NodeTraits::get_left(t); NodeTraits::set_left(t, NodeTraits::get_right(x)); if( NodeTraits::get_left(t) != 0 ){ NodeTraits::set_parent(NodeTraits::get_left(t), t); } NodeTraits::set_right(x, t); NodeTraits::set_parent(t, x); return x; } static void link(node_ptr header, node_ptr z, node_ptr par, bool left) { if(par == header){ NodeTraits::set_parent(header, z); NodeTraits::set_right(header, z); NodeTraits::set_left(header, z); } else if(left){ NodeTraits::set_left(par, z); if(par == NodeTraits::get_left(header)) NodeTraits::set_left(header, z); } else{ NodeTraits::set_right(par, z); if(par == NodeTraits::get_right(header)) NodeTraits::set_right(header, z); } NodeTraits::set_parent(z, par); NodeTraits::set_right(z, node_ptr(0)); NodeTraits::set_left(z, node_ptr(0)); } static void erase(node_ptr header, node_ptr z) { data_for_rebalance ignored; erase(header, z, nop_erase_fixup(), ignored); } struct data_for_rebalance { node_ptr x; node_ptr x_parent; node_ptr y; }; template<class F> static void erase(node_ptr header, node_ptr z, F z_and_successor_fixup, data_for_rebalance &info) { erase_impl(header, z, info); if(info.y != z){ z_and_successor_fixup(z, info.y); } } static void unlink(node_ptr node) { node_ptr x = NodeTraits::get_parent(node); if(x){ while(!is_header(x)) x = NodeTraits::get_parent(x); erase(x, node); } } static void tree_to_vine(node_ptr header) { subtree_to_vine(NodeTraits::get_parent(header)); } static void vine_to_tree(node_ptr header, std::size_t count) { vine_to_subtree(NodeTraits::get_parent(header), count); } static void rebalance(node_ptr header) { //Taken from: //"Tree rebalancing in optimal time and space" //Quentin F. Stout and Bette L. Warren std::size_t len; subtree_to_vine(NodeTraits::get_parent(header), &len); vine_to_subtree(NodeTraits::get_parent(header), len); } static node_ptr rebalance_subtree(node_ptr old_root) { std::size_t len; node_ptr new_root = subtree_to_vine(old_root, &len); return vine_to_subtree(new_root, len); } static node_ptr subtree_to_vine(node_ptr old_root, std::size_t *plen = 0) { std::size_t len; len = 0; if(!old_root) return node_ptr(0); //To avoid irregularities in the algorithm (old_root can be a //left or right child or even the root of the tree) just put the //root as the right child of its parent. Before doing this backup //information to restore the original relationship after //the algorithm is applied. node_ptr super_root = NodeTraits::get_parent(old_root); BOOST_INTRUSIVE_INVARIANT_ASSERT(super_root); //Get info node_ptr super_root_right_backup = NodeTraits::get_right(super_root); bool super_root_is_header = is_header(super_root); bool old_root_is_right = is_right_child(old_root); node_ptr x(old_root); node_ptr new_root(x); node_ptr save; bool moved_to_right = false; for( ; x; x = save){ save = NodeTraits::get_left(x); if(save){ // Right rotation node_ptr save_right = NodeTraits::get_right(save); node_ptr x_parent = NodeTraits::get_parent(x); NodeTraits::set_parent(save, x_parent); NodeTraits::set_right (x_parent, save); NodeTraits::set_parent(x, save); NodeTraits::set_right (save, x); NodeTraits::set_left(x, save_right); if(save_right) NodeTraits::set_parent(save_right, x); if(!moved_to_right) new_root = save; } else{ moved_to_right = true; save = NodeTraits::get_right(x); ++len; } } if(super_root_is_header){ NodeTraits::set_right(super_root, super_root_right_backup); NodeTraits::set_parent(super_root, new_root); } else if(old_root_is_right){ NodeTraits::set_right(super_root, new_root); } else{ NodeTraits::set_right(super_root, super_root_right_backup); NodeTraits::set_left(super_root, new_root); } if(plen) *plen = len; return new_root; } static node_ptr vine_to_subtree(node_ptr old_root, std::size_t count) { std::size_t leaf_nodes = count + 1 - ((size_t) 1 << floor_log2 (count + 1)); std::size_t vine_nodes = count - leaf_nodes; node_ptr new_root = compress_subtree(old_root, leaf_nodes); while(vine_nodes > 1){ vine_nodes /= 2; new_root = compress_subtree(new_root, vine_nodes); } return new_root; } static node_ptr compress_subtree(node_ptr old_root, std::size_t count) { if(!old_root) return old_root; //To avoid irregularities in the algorithm (old_root can be //left or right child or even the root of the tree) just put the //root as the right child of its parent. First obtain //information to restore the original relationship after //the algorithm is applied. node_ptr super_root = NodeTraits::get_parent(old_root); BOOST_INTRUSIVE_INVARIANT_ASSERT(super_root); //Get info node_ptr super_root_right_backup = NodeTraits::get_right(super_root); bool super_root_is_header = is_header(super_root); bool old_root_is_right = is_right_child(old_root); //Put old_root as right child NodeTraits::set_right(super_root, old_root); //Start the compression algorithm node_ptr even_parent = super_root; node_ptr new_root = old_root; while(count--){ node_ptr even = NodeTraits::get_right(even_parent); node_ptr odd = NodeTraits::get_right(even); if(new_root == old_root) new_root = odd; node_ptr even_right = NodeTraits::get_left(odd); NodeTraits::set_right(even, even_right); if (even_right) NodeTraits::set_parent(even_right, even); NodeTraits::set_right(even_parent, odd); NodeTraits::set_parent(odd, even_parent); NodeTraits::set_left(odd, even); NodeTraits::set_parent(even, odd); even_parent = odd; } if(super_root_is_header){ NodeTraits::set_parent(super_root, new_root); NodeTraits::set_right(super_root, super_root_right_backup); } else if(old_root_is_right){ NodeTraits::set_right(super_root, new_root); } else{ NodeTraits::set_left(super_root, new_root); NodeTraits::set_right(super_root, super_root_right_backup); } return new_root; } //! <b>Requires</b>: "n" must be a node inserted in a tree. //! //! <b>Effects</b>: Returns a pointer to the header node of the tree. //! //! <b>Complexity</b>: Logarithmic. //! //! <b>Throws</b>: Nothing. static node_ptr get_root(node_ptr node) { BOOST_INTRUSIVE_INVARIANT_ASSERT((!inited(node))); node_ptr x = NodeTraits::get_parent(node); if(x){ while(!is_header(x)){ x = NodeTraits::get_parent(x); } return x; } else{ return node; } } private: static void erase_impl(node_ptr header, node_ptr z, data_for_rebalance &info) { node_ptr y(z); node_ptr x; node_ptr x_parent(0); node_ptr z_left(NodeTraits::get_left(z)); node_ptr z_right(NodeTraits::get_right(z)); if(!z_left){ x = z_right; // x might be null. } else if(!z_right){ // z has exactly one non-null child. y == z. x = z_left; // x is not null. } else{ // find z's successor y = tree_algorithms::minimum (z_right); x = NodeTraits::get_right(y); // x might be null. } if(y != z){ // relink y in place of z. y is z's successor NodeTraits::set_parent(NodeTraits::get_left(z), y); NodeTraits::set_left(y, NodeTraits::get_left(z)); if(y != NodeTraits::get_right(z)){ x_parent = NodeTraits::get_parent(y); if(x) NodeTraits::set_parent(x, x_parent); NodeTraits::set_left(x_parent, x); // y must be a child of left_ NodeTraits::set_right(y, NodeTraits::get_right(z)); NodeTraits::set_parent(NodeTraits::get_right(z), y); } else x_parent = y; tree_algorithms::replace_own (z, y, header); NodeTraits::set_parent(y, NodeTraits::get_parent(z)); } else { // y == z --> z has only one child, or none x_parent = NodeTraits::get_parent(z); if(x) NodeTraits::set_parent(x, x_parent); tree_algorithms::replace_own (z, x, header); if(NodeTraits::get_left(header) == z){ NodeTraits::set_left(header, NodeTraits::get_right(z) == 0 ? // z->get_left() must be null also NodeTraits::get_parent(z) : // makes leftmost == header if z == root tree_algorithms::minimum (x)); } if(NodeTraits::get_right(header) == z){ NodeTraits::set_right(header, NodeTraits::get_left(z) == 0 ? // z->get_right() must be null also NodeTraits::get_parent(z) : // makes rightmost == header if z == root tree_algorithms::maximum(x)); } } info.x = x; info.x_parent = x_parent; info.y = y; } }; } //namespace detail { } //namespace intrusive } //namespace boost #include <boost/intrusive/detail/config_end.hpp> #endif //BOOST_INTRUSIVE_TREE_ALGORITHMS_HPP