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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-node) 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:2-3-4 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Hopcroft
John Edward Hopcroft (born October 7, 1939) is an American theoretical computer scientist. His textbooks on theory of computation (also known as the Cinderella book) and data structures are regarded as standards in their fields. He is a professor emeritus at Cornell University, co-director of the Center on Frontiers of Computing Studies at Peking University, and the director of the John Hopcroft Center for Computer Science at Shanghai Jiao Tong University. Early life and education Hopcroft received a Bachelor of Science with a major in electrical engineering from Seattle University in 1961. He received a Master of Science in electrical engineering in 1962 and a Doctor of Philosophy in electrical engineering in 1964, both from Stanford University. Hopcroft is the grandson of Jacob Nist, who established the Seattle-Tacoma Box Company in 1889. Career and honor He worked for three years at Princeton University and since then has been at Cornell University. In addition to his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
(a,b)-tree
In computer science, a B-tree is a self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and deletions in logarithmic time. The B-tree generalizes the binary search tree, allowing for nodes with more than two children. Unlike other self-balancing binary search trees, the B-tree is well suited for storage systems that read and write relatively large blocks of data, such as databases and file systems. History While working at Boeing Research Labs, Rudolf Bayer and Edward M. McCreight invented B-trees to efficiently manage index pages for large random-access files. The basic assumption was that indices would be so voluminous that only small chunks of the tree could fit in the main memory. Bayer and McCreight's paper ''Organization and maintenance of large ordered indices'' was first circulated in July 1970 and later published in ''Acta Informatica''. Bayer and McCreight never explained what, if anything, the ''B'' sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 their originator, Swedish computer scientist Arne Andersson. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2–3 Heap
In computer science, a 2–3 heap is a data structure that implements a priority queue. It is a variation on the heap (data structure), heap, designed by Tadao Takaoka in 1999. The structure is similar to a Fibonacci heap, and borrows ideas from the 2–3 tree. The time needed for some common heap operations are as follows. * ''Delete-min'' takes O(\log(n)) amortized time and in the worst case. * ''Decrease-key'' takes constant amortized time. * ''Insertion'' takes constant amortized time and O(\log(n)) time in the worst case. Polynomial of trees Source: A linear tree of size r is a sequential path of r nodes with the first node as a root of the tree and it is represented by a bold \mathbf (e.g. \mathbf is a linear tree of a single node). Product P = ST of two trees S and T, is a tree produced by replacing every node of S by a copy of T; for each edge of S, there is an edge in ST connecting the roots of the trees that replaced the endpoints of the edge. This definition of pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Red–black Tree
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. 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 in the tree. The insert and delete operations, along with tree rearrangement and recoloring, also execute 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 (due to memory alignment present in some programming languag ... [...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] |
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, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), 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 re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leaf Node
In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the ''root'' node, which has no parent (i.e., the root node as the top-most node in the tree hierarchy). These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes (parent and children nodes of a node under consideration, if they exist) in a single straight line (called edge or link between two adjacent nodes). Binary trees are a commonly used type, which constrain the number of children for each parent to at most two. When ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
B-tree
In computer science, a B-tree is a self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and deletions in logarithmic time. The B-tree generalizes the binary search tree, allowing for nodes with more than two children. Unlike other self-balancing binary search trees, the B-tree is well suited for storage systems that read and write relatively large blocks of data, such as databases and file systems. History While working at Boeing Research Labs, Rudolf Bayer and Edward M. McCreight invented B-trees to efficiently manage index pages for large random-access files. The basic assumption was that indices would be so voluminous that only small chunks of the tree could fit in the main memory. Bayer and McCreight's paper ''Organization and maintenance of large ordered indices'' was first circulated in July 1970 and later published in '' Acta Informatica''. Bayer and McCreight never explained what, if anything, the ''B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
