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AA Tree
An AA tree in computer science is a form of balanced tree used for storing and retrieving ordered data efficiently. AA trees are named after Arne Andersson, the one who theorized them. AA trees are a variation of the red–black tree, a form of binary search tree which supports efficient addition and deletion of entries. Unlike red–black trees, red nodes on an AA tree can only be added as a right subchild. In other words, no red node can be a left sub-child. This results in the simulation of a 2–3 tree instead of a 2–3–4 tree, which greatly simplifies the maintenance operations. The maintenance algorithms for a red–black tree need to consider seven different shapes to properly balance the tree: An AA tree on the other hand only needs to consider two shapes due to the strict requirement that only right links can be red: Balancing rotations Whereas red–black trees require one bit of balancing metadata per node (the color), AA trees require O(log(log(N))) bits o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including the design and implementation of hardware and software). Computer science is generally considered an area of academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing security vulnerabilities. Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of repositories o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-balancing Binary Search Tree
In computer science, a self-balancing binary search tree (BST) is any node-based binary search tree that automatically keeps its height (maximal number of levels below the root) small in the face of arbitrary item insertions and deletions.Donald Knuth. ''The Art of Computer Programming'', Volume 3: ''Sorting and Searching'', Second Edition. Addison-Wesley, 1998. . Section 6.2.3: Balanced Trees, pp.458–481. These operations when designed for a self-balancing binary search tree, contain precautionary measures against boundlessly increasing tree height, so that these abstract data structures receive the attribute "self-balancing". For height-balanced binary trees, the height is defined to be logarithmic \mathcal O(\log n) in the number n of items. This is the case for many binary search trees, such as AVL trees and red–black trees. Splay trees and treaps are self-balancing but not height-balanced, as their height is not guaranteed to be logarithmic in the number of items. S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arne Andersson (computer Science)
Arne Andersson (27 October 1917 – 1 April 2009) was a Swedish middle distance runner who became famous for his rivalry with his compatriot Gunder Hägg in the 1940s. Andersson set a 1500 metres world record in Gothenburg in August 1943 with a time of 3:45.0 minutes. He was born in Trollhättan, Sweden. Andersson set three world records in the mile: the first in Stockholm in July 1942 in (4:06.2); this record was broken in the same year by Hägg (4:04.6). Andersson recaptured the world record in Gothenburg in July 1943 (4:02.6), and improved it further in Malmö in July 1944 (4:01.6). However, Hägg had the last word when he ran (4:01.4) in Malmö in 1945 (Hägg's record was not broken until Roger Bannister ran the first sub-4 mile in Oxford in 1954). Andersson won the Svenska Dagbladet Gold Medal in 1943. Andersson won seven national titles: two individual (1500 m, 1943–44) and five in relays (1940–42). In 1946 he was disqualified for violating amateur rules, togethe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business international ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Red–black Tree
In computer science, a red–black tree is a kind of self-balancing binary search tree. Each node stores an extra bit representing "color" ("red" or "black"), used to ensure that the tree remains balanced during insertions and deletions. When the tree is modified, the new tree is rearranged and "repainted" to restore the coloring properties that constrain how unbalanced the tree can become in the worst case. The properties are designed such that this rearranging and recoloring can be performed efficiently. The re-balancing is not perfect, but guarantees searching in O(\log n) time, where n is the number of entries. The insert and delete operations, along with the tree rearrangement and recoloring, are also performed in O(\log n) time. Tracking the color of each node requires only one bit of information per node because there are only two colors. The tree does not contain any other data specific to it being a red–black tree, so its memory footprint is almost identical to that o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Search Tree
In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree. The time complexity of operations on the binary search tree is directly proportional to the height of the tree. Binary search trees allow binary search for fast lookup, addition, and removal of data items. Since the nodes in a BST are laid out so that each comparison skips about half of the remaining tree, the lookup performance is proportional to that of binary logarithm. BSTs were devised in the 1960s for the problem of efficient storage of labeled data and are attributed to Conway Berners-Lee and David Wheeler. The performance of a binary search tree is dependent on the order of insertion of the nodes into the tree since arbitrary insertions may lead to degeneracy; several variations of the b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2–3 Tree
In computer science, a 2–3 tree is a tree data structure, where every node with children ( internal node) has either two children (2-node) and one data element or three children (3-nodes) and two data elements. A 2–3 tree is a B-tree of order 3. Nodes on the outside of the tree (leaf nodes) have no children and one or two data elements. 2–3 trees were invented by John Hopcroft in 1970. 2–3 trees are required to be balanced, meaning that each leaf is at the same level. It follows that each right, center, and left subtree of a node contains the same or close to the same amount of data. Definitions We say that an internal node is a 2-node if it has ''one'' data element and ''two'' children. We say that an internal node is a 3-node if it has ''two'' data elements and ''three'' children. A 4-node, with three data elements, may be temporarily created during manipulation of the tree but is never persistently stored in the tree. Image:2-3-4 tree 2-node.svg, 2 node Image:2- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2–3–4 Tree
In computer science, a 2–3–4 tree (also called a 2–4 tree) is a self-balancing data structure that can be used to implement dictionaries. The numbers mean a tree where every node with children (internal node) has either two, three, or four child nodes: * a 2-node has one data element, and if internal has two child nodes; * a 3-node has two data elements, and if internal has three child nodes; * a 4-node has three data elements, and if internal has four child nodes; Image:2-3-4-tree-2-node.svg, 2-node Image:2-3-4-tree-3-node.svg, 3-node Image:2-3-4-tree-4-node.svg, 4-node 2–3–4 trees are B-trees of order 4; like B-trees in general, they can search, insert and delete in O(log ''n'') time. One property of a 2–3–4 tree is that all external nodes are at the same depth. 2–3–4 trees are isomorphic to red–black trees, meaning that they are equivalent data structures. In other words, for every 2–3–4 tree, there exists at least one and at most one red–bla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Red Black Shape Cases
Red is the color at the long wavelength end of the visible spectrum of light, next to orange and opposite violet. It has a dominant wavelength of approximately 625–740 nanometres. It is a primary color in the RGB color model and a secondary color (made from magenta and yellow) in the CMYK color model, and is the complementary color of cyan. Reds range from the brilliant yellow-tinged scarlet and vermillion to bluish-red crimson, and vary in shade from the pale red pink to the dark red burgundy. Red pigment made from ochre was one of the first colors used in prehistoric art. The Ancient Egyptians and Mayans colored their faces red in ceremonies; Roman generals had their bodies colored red to celebrate victories. It was also an important color in China, where it was used to color early pottery and later the gates and walls of palaces. In the Renaissance, the brilliant red costumes for the nobility and wealthy were dyed with kermes and cochineal. The 19th century broug ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
