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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.
A red–black tree plotted by Graphviz Undirected graph showing adjacency of the 48 contiguous United States A visualization of a JavaScript life cycle made by using Graphviz Graphviz (short for Graph Visualization Software ) is a package of open-source tools initiated by AT&T Labs Research for drawing graphs (as in nodes and edges , not as in ...
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).
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]
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.
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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 ...