///////////////////////////////////////////////////////////////////////////// // // (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. // ///////////////////////////////////////////////////////////////////////////// // // Scapegoat tree algorithms are taken from the paper titled: // "Scapegoat Trees" by Igal Galperin Ronald L. Rivest. // ///////////////////////////////////////////////////////////////////////////// #ifndef BOOST_INTRUSIVE_SGTREE_ALGORITHMS_HPP #define BOOST_INTRUSIVE_SGTREE_ALGORITHMS_HPP #include #include #include #include #include #include #include namespace boost { namespace intrusive { //! sgtree_algorithms is configured with a NodeTraits class, which encapsulates the //! information about the node to be manipulated. NodeTraits must support the //! following interface: //! //! Typedefs: //! //! node: The type of the node that forms the circular list //! //! node_ptr: A pointer to a node //! //! const_node_ptr: A pointer to a const node //! //! Static functions: //! //! static node_ptr get_parent(const_node_ptr n); //! //! static void set_parent(node_ptr n, node_ptr parent); //! //! static node_ptr get_left(const_node_ptr n); //! //! static void set_left(node_ptr n, node_ptr left); //! //! static node_ptr get_right(const_node_ptr n); //! //! static void set_right(node_ptr n, node_ptr right); template class sgtree_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; /// @cond private: typedef detail::tree_algorithms tree_algorithms; static node_ptr uncast(const const_node_ptr & ptr) { return pointer_traits::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 : tree_algorithms::insert_commit_data { std::size_t depth; }; //! Requires: header1 and header2 must be the header nodes //! of two trees. //! //! Effects: Swaps two trees. After the function header1 will contain //! links to the second tree and header2 will have links to the first tree. //! //! Complexity: Constant. //! //! Throws: Nothing. static void swap_tree(const node_ptr & header1, const node_ptr & header2) { return tree_algorithms::swap_tree(header1, header2); } //! Requires: node1 and node2 can't be header nodes //! of two trees. //! //! Effects: 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. //! //! Complexity: Logarithmic. //! //! Throws: Nothing. //! //! Note: 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); } //! Requires: node1 and node2 can't be header nodes //! of two trees with header header1 and header2. //! //! Effects: 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. //! //! Complexity: Constant. //! //! Throws: Nothing. //! //! Note: 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); } //! Requires: node_to_be_replaced must be inserted in a tree //! and new_node must not be inserted in a tree. //! //! Effects: Replaces node_to_be_replaced in its position in the //! tree with new_node. The tree does not need to be rebalanced //! //! Complexity: Logarithmic. //! //! Throws: Nothing. //! //! Note: 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); } //! Requires: node_to_be_replaced must be inserted in a tree //! with header "header" and new_node must not be inserted in a tree. //! //! Effects: Replaces node_to_be_replaced in its position in the //! tree with new_node. The tree does not need to be rebalanced //! //! Complexity: Constant. //! //! Throws: Nothing. //! //! Note: 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); } //! Requires: node is a tree node but not the header. //! //! Effects: Unlinks the node and rebalances the tree. //! //! Complexity: Average complexity is constant time. //! //! Throws: Nothing. 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); tree_algorithms::erase(x, node); } } //! Requires: header is the header of a tree. //! //! Effects: Unlinks the leftmost node from the tree, and //! updates the header link to the new leftmost node. //! //! Complexity: Average complexity is constant time. //! //! Throws: Nothing. //! //! Notes: 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); } //! Requires: node is a node of the tree or an node initialized //! by init(...). //! //! Effects: Returns true if the node is initialized by init(). //! //! Complexity: Constant time. //! //! Throws: Nothing. static bool unique(const const_node_ptr & node) { return tree_algorithms::unique(node); } //! Requires: node is a node of the tree but it's not the header. //! //! Effects: Returns the number of nodes of the subtree. //! //! Complexity: Linear time. //! //! Throws: Nothing. static std::size_t count(const const_node_ptr & node) { return tree_algorithms::count(node); } //! Requires: header is the header node of the tree. //! //! Effects: Returns the number of nodes above the header. //! //! Complexity: Linear time. //! //! Throws: Nothing. static std::size_t size(const const_node_ptr & header) { return tree_algorithms::size(header); } //! Requires: p is a node from the tree except the header. //! //! Effects: Returns the next node of the tree. //! //! Complexity: Average constant time. //! //! Throws: Nothing. static node_ptr next_node(const node_ptr & p) { return tree_algorithms::next_node(p); } //! Requires: p is a node from the tree except the leftmost node. //! //! Effects: Returns the previous node of the tree. //! //! Complexity: Average constant time. //! //! Throws: Nothing. static node_ptr prev_node(const node_ptr & p) { return tree_algorithms::prev_node(p); } //! Requires: node must not be part of any tree. //! //! Effects: After the function unique(node) == true. //! //! Complexity: Constant. //! //! Throws: Nothing. //! //! Nodes: If node is inserted in a tree, this function corrupts the tree. static void init(const node_ptr & node) { tree_algorithms::init(node); } //! Requires: node must not be part of any tree. //! //! Effects: Initializes the header to represent an empty tree. //! unique(header) == true. //! //! Complexity: Constant. //! //! Throws: Nothing. //! //! Nodes: 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); } //! Requires: header must be the header of a tree, z a node //! of that tree and z != header. //! //! Effects: Erases node "z" from the tree with header "header". //! //! Complexity: Amortized constant time. //! //! Throws: Nothing. template static node_ptr erase(const node_ptr & header, const node_ptr & z, std::size_t tree_size, std::size_t &max_tree_size, AlphaByMaxSize alpha_by_maxsize) { //typename tree_algorithms::data_for_rebalance info; tree_algorithms::erase(header, z); --tree_size; if (tree_size > 0 && tree_size < alpha_by_maxsize(max_tree_size)){ tree_algorithms::rebalance(header); max_tree_size = tree_size; } return z; } //! Requires: "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. //! //! Effects: First empties target tree calling //! void disposer::operator()(const node_ptr &) for every node of the tree //! except the header. //! //! Then, duplicates the entire tree pointed by "source_header" cloning each //! source node with node_ptr Cloner::operator()(const node_ptr &) to obtain //! the nodes of the target tree. If "cloner" throws, the cloned target nodes //! are disposed using void disposer(const node_ptr &). //! //! Complexity: Linear to the number of element of the source tree plus the. //! number of elements of tree target tree when calling this function. //! //! Throws: If cloner functor throws. If this happens target nodes are disposed. template 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); } //! Requires: "disposer" must be an object function //! taking a node_ptr parameter and shouldn't throw. //! //! Effects: Empties the target tree calling //! void disposer::operator()(const node_ptr &) for every node of the tree //! except the header. //! //! Complexity: Linear to the number of element of the source tree plus the. //! number of elements of tree target tree when calling this function. //! //! Throws: If cloner functor throws. If this happens target nodes are disposed. template static void clear_and_dispose(const node_ptr & header, Disposer disposer) { tree_algorithms::clear_and_dispose(header, disposer); } //! Requires: "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. //! //! Effects: 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. //! //! Complexity: Logarithmic. //! //! Throws: If "comp" throws. template static node_ptr lower_bound (const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp) { return tree_algorithms::lower_bound(header, key, comp); } //! Requires: "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. //! //! Effects: Returns an node_ptr to the first element that is greater //! than "key" according to "comp" or "header" if that element does not exist. //! //! Complexity: Logarithmic. //! //! Throws: If "comp" throws. template static node_ptr upper_bound (const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp) { return tree_algorithms::upper_bound(header, key, comp); } //! Requires: "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. //! //! Effects: Returns an node_ptr to the element that is equivalent to //! "key" according to "comp" or "header" if that element does not exist. //! //! Complexity: Logarithmic. //! //! Throws: If "comp" throws. template static node_ptr find (const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp) { return tree_algorithms::find(header, key, comp); } //! Requires: "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. //! //! Effects: 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. //! //! Complexity: Logarithmic. //! //! Throws: If "comp" throws. template static std::pair equal_range (const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp) { return tree_algorithms::equal_range(header, key, comp); } //! Requires: "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. //! //! Effects: Inserts new_node into the tree before the upper bound //! according to "comp". //! //! Complexity: Average complexity for insert element is at //! most logarithmic. //! //! Throws: If "comp" throws. template static node_ptr insert_equal_upper_bound (const node_ptr & h, const node_ptr & new_node, NodePtrCompare comp ,std::size_t tree_size, H_Alpha h_alpha, std::size_t &max_tree_size) { std::size_t depth; tree_algorithms::insert_equal_upper_bound(h, new_node, comp, &depth); rebalance_after_insertion(new_node, depth, tree_size+1, h_alpha, max_tree_size); return new_node; } //! Requires: "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. //! //! Effects: Inserts new_node into the tree before the lower bound //! according to "comp". //! //! Complexity: Average complexity for insert element is at //! most logarithmic. //! //! Throws: If "comp" throws. template static node_ptr insert_equal_lower_bound (const node_ptr & h, const node_ptr & new_node, NodePtrCompare comp ,std::size_t tree_size, H_Alpha h_alpha, std::size_t &max_tree_size) { std::size_t depth; tree_algorithms::insert_equal_lower_bound(h, new_node, comp, &depth); rebalance_after_insertion(new_node, depth, tree_size+1, h_alpha, max_tree_size); return new_node; } //! Requires: "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. //! //! Effects: 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). //! //! Complexity: Logarithmic in general, but it is amortized //! constant time if new_node is inserted immediately before "hint". //! //! Throws: If "comp" throws. template static node_ptr insert_equal (const node_ptr & header, const node_ptr & hint, const node_ptr & new_node, NodePtrCompare comp ,std::size_t tree_size, H_Alpha h_alpha, std::size_t &max_tree_size) { std::size_t depth; tree_algorithms::insert_equal(header, hint, new_node, comp, &depth); rebalance_after_insertion(new_node, depth, tree_size+1, h_alpha, max_tree_size); return new_node; } //! Requires: "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. //! //! Effects: 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. //! //! Returns: 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. //! //! Complexity: Average complexity is at most logarithmic. //! //! Throws: If "comp" throws. //! //! Notes: 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 static std::pair insert_unique_check (const const_node_ptr & header, const KeyType &key ,KeyNodePtrCompare comp, insert_commit_data &commit_data) { std::size_t depth; std::pair ret = tree_algorithms::insert_unique_check(header, key, comp, commit_data, &depth); commit_data.depth = depth; return ret; } //! Requires: "header" must be the header node of a tree. //! "pos" must be a valid iterator or header (end) node. //! "pos" must be an iterator 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. //! //! Effects: Inserts new_node into the tree before "pos". //! //! Complexity: Constant-time. //! //! Throws: Nothing. //! //! Note: If "pos" is not the successor of the newly inserted "new_node" //! tree invariants might be broken. template static node_ptr insert_before (const node_ptr & header, const node_ptr & pos, const node_ptr & new_node ,std::size_t tree_size, H_Alpha h_alpha, std::size_t &max_tree_size) { std::size_t depth; tree_algorithms::insert_before(header, pos, new_node, &depth); rebalance_after_insertion(new_node, depth, tree_size+1, h_alpha, max_tree_size); return new_node; } //! Requires: "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. //! //! Effects: Inserts new_node into the tree before "pos". //! //! Complexity: Constant-time. //! //! Throws: Nothing. //! //! Note: If "new_node" is less than the greatest inserted key //! tree invariants are broken. This function is slightly faster than //! using "insert_before". template static void push_back(const node_ptr & header, const node_ptr & new_node ,std::size_t tree_size, H_Alpha h_alpha, std::size_t &max_tree_size) { std::size_t depth; tree_algorithms::push_back(header, new_node, &depth); rebalance_after_insertion(new_node, depth, tree_size+1, h_alpha, max_tree_size); } //! Requires: "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. //! //! Effects: Inserts new_node into the tree before "pos". //! //! Complexity: Constant-time. //! //! Throws: Nothing. //! //! Note: If "new_node" is greater than the lowest inserted key //! tree invariants are broken. This function is slightly faster than //! using "insert_before". template static void push_front(const node_ptr & header, const node_ptr & new_node ,std::size_t tree_size, H_Alpha h_alpha, std::size_t &max_tree_size) { std::size_t depth; tree_algorithms::push_front(header, new_node, &depth); rebalance_after_insertion(new_node, depth, tree_size+1, h_alpha, max_tree_size); } //! Requires: "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. //! //! Effects: 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). //! //! Returns: 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. //! //! Complexity: Average complexity is at most logarithmic, but it is //! amortized constant time if new_node should be inserted immediately before "hint". //! //! Throws: If "comp" throws. //! //! Notes: 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 static std::pair insert_unique_check (const const_node_ptr & header, const node_ptr &hint, const KeyType &key ,KeyNodePtrCompare comp, insert_commit_data &commit_data) { std::size_t depth; std::pair ret = tree_algorithms::insert_unique_check (header, hint, key, comp, commit_data, &depth); commit_data.depth = depth; return ret; } //! Requires: "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". //! //! //! Effects: Inserts new_node in the set using the information obtained //! from the "commit_data" that a previous "insert_check" filled. //! //! Complexity: Constant time. //! //! Throws: Nothing. //! //! Notes: 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. template static void insert_unique_commit (const node_ptr & header, const node_ptr & new_value, const insert_commit_data &commit_data ,std::size_t tree_size, H_Alpha h_alpha, std::size_t &max_tree_size) { tree_algorithms::insert_unique_commit(header, new_value, commit_data); rebalance_after_insertion(new_value, commit_data.depth, tree_size+1, h_alpha, max_tree_size); } //! Requires: header must be the header of a tree. //! //! Effects: Rebalances the tree. //! //! Throws: Nothing. //! //! Complexity: Linear. static void rebalance(const node_ptr & header) { tree_algorithms::rebalance(header); } //! Requires: old_root is a node of a tree. //! //! Effects: Rebalances the subtree rooted at old_root. //! //! Returns: The new root of the subtree. //! //! Throws: Nothing. //! //! Complexity: Linear. static node_ptr rebalance_subtree(const node_ptr & old_root) { return tree_algorithms::rebalance_subtree(old_root); } //! Requires: "n" must be a node inserted in a tree. //! //! Effects: Returns a pointer to the header node of the tree. //! //! Complexity: Logarithmic. //! //! Throws: Nothing. static node_ptr get_header(const node_ptr & n) { return tree_algorithms::get_header(n); } /// @cond private: //! Requires: p is a node of a tree. //! //! Effects: Returns true if p is the header of the tree. //! //! Complexity: Constant. //! //! Throws: Nothing. static bool is_header(const const_node_ptr & p) { return tree_algorithms::is_header(p); } template static void rebalance_after_insertion (const node_ptr &x, std::size_t depth , std::size_t tree_size, H_Alpha h_alpha, std::size_t &max_tree_size) { if(tree_size > max_tree_size) max_tree_size = tree_size; if(tree_size != 1 && depth > h_alpha(tree_size)){ //Find the first non height-balanced node //as described in the section 4.2 of the paper. //This method is the alternative method described //in the paper. Authors claim that this method //may tend to yield more balanced trees on the average //than the weight balanced method. node_ptr s = x; std::size_t size = 1; for(std::size_t i = 1; true; ++i){ bool rebalance = false; if(i == depth){ BOOST_INTRUSIVE_INVARIANT_ASSERT(tree_size == count(s)); rebalance = true; } else if(i > h_alpha(size)){ node_ptr s_parent = NodeTraits::get_parent(s); node_ptr s_parent_left = NodeTraits::get_left(s_parent); size += 1 + tree_algorithms::count ( s_parent_left == s ? NodeTraits::get_right(s_parent) : s_parent_left ); s = s_parent; rebalance = true; } if(rebalance){ rebalance_subtree(s); break; } } } } /// @endcond }; } //namespace intrusive } //namespace boost #include #endif //BOOST_INTRUSIVE_SGTREE_ALGORITHMS_HPP