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Treap
In computer science, the treap and the randomized binary search tree are two closely related forms of binary search tree data structures that maintain a dynamic set of ordered keys and allow binary searches among the keys. After any sequence of insertions and deletions of keys, the shape of the tree is a random variable with the same probability distribution as a random binary tree; in particular, with high probability its height is proportional to the logarithm of the number of keys, so that each search, insertion, or deletion operation takes logarithmic time to perform. Description The treap was first described by Raimund Seidel and Cecilia R. Aragon in 1989; its name is a portmanteau word, portmanteau of Tree data structure, tree and heap (data structure), heap. It is a Cartesian tree in which each key is given a (randomly chosen) numeric priority. As with any binary search tree, the inorder traversal order of the nodes is the same as the sorted order of the keys. The stru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Tree
In computer science, a Cartesian tree is a binary tree derived from a sequence of distinct numbers. To construct the Cartesian tree, set its root to be the minimum number in the sequence, and recursively construct its left and right subtrees from the subsequences before and after this number. It is uniquely defined as a min-heap whose Tree traversal, symmetric (in-order) traversal returns the original sequence. Cartesian trees were introduced by in the context of geometric range searching data structures. They have also been used in the definition of the treap and randomized binary search tree data structures for binary search problems, in comparison sort algorithms that perform efficiently on nearly-sorted inputs, and as the basis for pattern matching algorithms. A Cartesian tree for a sequence can be constructed in linear time. Definition Cartesian trees are defined using binary trees, which are a form of rooted tree. To construct the Cartesian tree for a given sequence of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Binary Search Tree
In computer science and probability theory, a random binary tree is a binary tree selected at random from some probability distribution on binary trees. Different distributions have been used, leading to different properties for these trees. Random binary trees have been used for analyzing the average-case complexity of data structures based on binary search trees. For this application it is common to use random trees formed by inserting nodes one at a time according to a random permutation. The resulting trees are very likely to have logarithmic depth and logarithmic Strahler number. The treap and related balanced binary search trees use update operations that maintain this random structure even when the update sequence is non-random. Other distributions on random binary trees include the Uniform distribution (discrete), uniform discrete distribution in which all distinct trees are equally likely, distributions on a given number of nodes obtained by repeated splitting, binary tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finger Search
In computer science, a finger search on a data structure is an extension of any search operation that structure supports, where a reference (finger) to an element in the data structure is given along with the query. While the search time for an element is most frequently expressed as a function of the number of elements in a data structure, finger search times are a function of the distance between the element and the finger. In a set of ''n'' elements, the distance ''d''(''x'',''y'') (or simply ''d'' when unambiguous) between two elements ''x'' and ''y'' is their difference in rank. If ''x'' and ''y'' are the th and th largest elements in the structure, then the difference in rank is , , . If a normal search in some structure would normally take time, then a finger search for ''x'' with finger ''y'' should ideally take time. Remark that since ''d'' ≤ ''n'', it follows that in the worst case, finger search is only as bad as normal search. However, in practice these degenerate fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Join-based Tree Algorithms
In computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ..., join-based tree algorithms are a class of algorithms for self-balancing binary search trees. This framework aims at designing highly-parallelized algorithms for various balanced binary search trees. The algorithmic framework is based on a single operation ''join''. Under this framework, the ''join'' operation captures all balancing criteria of different balancing schemes, and all other functions ''join'' have generic implementation across different balancing schemes. The ''join-based algorithms'' can be applied to at least four balancing schemes: AVL trees, red–black trees, weight-balanced trees and treaps. The ''join''(L,k,R) operation takes as input two binary balanced trees L and R of the same balancing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Persistent Data Structure
In computing, a persistent data structure or not ephemeral data structure is a data structure that always preserves the previous version of itself when it is modified. Such data structures are effectively immutable, as their operations do not (visibly) update the structure in-place, but instead always yield a new updated structure. The term was introduced in Driscoll, Sarnak, Sleator, and Tarjan's 1986 article. A data structure is partially persistent if all versions can be accessed but only the newest version can be modified. The data structure is fully persistent if every version can be both accessed and modified. If there is also a meld or merge operation that can create a new version from two previous versions, the data structure is called confluently persistent. Structures that are not persistent are called ''ephemeral''. These types of data structures are particularly common in logical and functional programming, as languages in those paradigms discourage (or fully forbid) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree Rotation
In discrete mathematics, tree rotation is an operation on a binary tree that changes the structure without interfering with the order of the elements. A tree rotation moves one node up in the tree and one node down. It is used to change the shape of the tree, and in particular to decrease its height by moving smaller subtrees down and larger subtrees up, resulting in improved performance of many tree operations. There exists an inconsistency in different descriptions as to the definition of the direction of rotations. Some say that the direction of rotation reflects the direction that a node is moving upon rotation (a left child rotating into its parent's location is a right rotation) while others say that the direction of rotation reflects which subtree is rotating (a left subtree rotating into its parent's location is a left rotation, the opposite of the former). This article takes the approach of the directional movement of the rotating node. Illustration The right rotation ... [...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 tree, 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 Time complexity#Linear time, linear with respect to the height of the tree. Binary search trees allow Binary search algorithm, 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_(computer_scientist), David Wheeler. The performance of a binary search tree is dependent on the order of insertion of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raimund Seidel
Raimund G. Seidel is a German and Austrian theoretical computer scientist and an expert in computational geometry. Seidel was born in Graz, Austria, and studied with Hermann Maurer at the Graz University of Technology. He earned his M.Sc. in 1981 from University of British Columbia under David G. Kirkpatrick. He received his Ph.D. in 1987 from Cornell University under the supervision of John Gilbert. After teaching at the University of California, Berkeley, he moved in 1994 to Saarland University. In 1997, he and Christoph M. Hoffmann were program chairs for the Symposium on Computational Geometry. In 2014, he took over as Scientific Director of the Leibniz Center for Informatics (LZI) from Reinhard Wilhelm. Seidel invented backwards analysis of randomized algorithms and used it to analyze a simple linear programming algorithm that runs in linear time for problems of bounded dimension. With his student Cecilia R. Aragon in 1989 he devised the treap data structure, . an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Portmanteau Word
In linguistics, a blend—also known as a blend word, lexical blend, or portmanteau—is a word formed by combining the meanings, and parts of the sounds, of two or more words together.) Israeli שלט ''shalát'' 'remote control', an ellipsis – like English language, English ''remote'' (but using the noun instead) – of the (widely known) compound שלט רחוק ''shalát rakhók'' – cf. the Academy of the Hebrew Language's שלט רחק ''shalát rákhak''; and ** (ii) (Hebrew>) Israeli שטוט ''shitút'' 'wandering, vagrancy'. Israeli שלטוט ''shiltút'' was introduced by the Academy of the Hebrew Language in [...] 1996. Synchronically, it might appear to result from reduplication of the final consonant of ''shalát'' 'remote control'. * Another example of blending which has also been explained as mere reduplication is Israeli גחלילית ''gakhlilít'' 'fire-fly, glow-fly, ''Lampyris'''. This coinage by Hayyim Nahman Bialik blends (Hebrew>) Israeli גחלת ''g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Union (set Theory)
In set theory, the union (denoted by ∪) of a collection of Set (mathematics), sets is the set of all element (set theory), elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. A refers to a union of Zero, zero () sets and it is by definition equal to the empty set. For explanation of the symbols used in this article, refer to the List of mathematical symbols, table of mathematical symbols. Binary union The union of two sets ''A'' and ''B'' is the set of elements which are in ''A'', in ''B'', or in both ''A'' and ''B''. In set-builder notation, : A \cup B = \. For example, if ''A'' = and ''B'' = then ''A'' ∪ ''B'' = . A more elaborate example (involving two infinite sets) is: : ''A'' = : ''B'' = : A \cup B = \ As another example, the number 9 is ''not'' contained in the union of the set of prime numbers and the set of even numbers , because 9 is neither prime nor even. Sets cannot ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
