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The key idea is to use the bounding boxes to decide whether or not to search inside a subtree. In this way, most of the nodes in the tree are never read during a search. Like B-trees, R-trees are suitable for large data sets and databases, where nodes can be paged to memory when needed, and the whole tree cannot be kept in main memory. Even if ...
In computer science, a red–black tree is a self-balancing binary search tree data structure noted for fast storage and retrieval of ordered information. The nodes in a red-black tree hold an extra "color" bit, often drawn as red and black, which help ensure that the tree is always approximately balanced.
A left-leaning red-black tree satisfies all the properties of a red-black tree: Every node is either red or black. A NIL node is considered black. A red node does not have a red child. Every path from a given node to any of its descendant NIL nodes goes through the same number of black nodes. The root is black (by convention).
To turn a regular search tree into an order statistic tree, the nodes of the tree need to store one additional value, which is the size of the subtree rooted at that node (i.e., the number of nodes below it). All operations that modify the tree must adjust this information to preserve the invariant that size[x] = size[left[x]] + size[right[x]] + 1
To delete a node x from the treap, if x is a leaf of the tree, simply remove it. If x has a single child z, remove x from the tree and make z be the child of the parent of x (or make z the root of the tree if x had no parent).
In this way, deletion is reduced to the problem of removing a node with 0 or 1 children. Unlike a binary search tree, in a splay tree after deletion, we splay the parent of the removed node to the top of the tree. Alternatively: The node to be deleted is first splayed, i.e. brought to the root of the tree and then deleted.
Deletion from vEB trees is the trickiest of the operations. The call Delete(T, x) that deletes a value x from a vEB tree T operates as follows: If T.min = T.max = x then x is the only element stored in the tree and we set T.min = M and T.max = −1 to indicate that the tree is empty.
WAVL trees, like red–black trees, use only a constant number of tree rotations, and the constant is even better than for red–black trees. [1] [2] WAVL trees were introduced by Haeupler, Sen & Tarjan (2015). The same authors also provided a common view of AVL trees, WAVL trees, and red–black trees as all being a type of rank-balanced tree. [2]