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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.
Various height-balanced binary search trees were introduced to confine the tree height, such as AVL trees, Treaps, and red–black trees. [5] The AVL tree was invented by Georgy Adelson-Velsky and Evgenii Landis in 1962 for the efficient organization of information. [6] [7] It was the first self-balancing binary search tree to be invented. [8]
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).
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Both AVL trees and red–black (RB) trees are self-balancing binary search trees and they are related mathematically. Indeed, every AVL tree can be colored red–black, [14] but there are RB trees which are not AVL balanced. For maintaining the AVL (or RB) tree's invariants, rotations play an important role.
AVL tree, red–black tree, and splay tree, kinds of binary search tree data structures that use rotations to maintain balance. Associativity of a binary operation means that performing a tree rotation on it does not change the final result. The Day–Stout–Warren algorithm balances an unbalanced BST.
Tree inference and visualization (hierarchical, radial and axial tree views), Horizontal gene transfer detection and HGT network visualization TidyTree [17] A client-side HTML5/SVG Phylogenetic Tree Renderer, based on D3.js: TreeVector [18] scalable, interactive, phylogenetic trees for the web, produces dynamic SVG or PNG output, implemented in ...
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