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K-ary Tree
In graph theory, an ''m''-ary tree (also known as ''n''-ary, ''k''-ary or ''k''-way tree) is a rooted tree in which each node has no more than ''m'' children. A binary tree is the special case where ''m'' = 2, and a ternary tree is another case with ''m'' = 3 that limits its children to three. Types of ''m''-ary trees * A full ''m''-ary tree is an ''m''-ary tree where within each level every node has either 0 or ''m'' children. * A complete ''m''-ary tree is an ''m''-ary tree which is maximally space efficient. It must be completely filled on every level except for the last level. However, if the last level is not complete, then all nodes of the tree must be "as far left as possible". * A perfect ''m''-ary tree is a full ''m''-ary tree in which all leaf nodes are at the same depth. Properties of ''m''-ary trees * For an ''m''-ary tree with height ''h'', the upper bound for the maximum number of leaves is m^h. * The height ''h ''of an ''m''-ary tree does not include the roo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Tree
In computer science, a binary tree is a k-ary k = 2 tree data structure in which each node has at most two children, which are referred to as the ' and the '. A recursive definition using just set theory notions is that a (non-empty) binary tree is a tuple (''L'', ''S'', ''R''), where ''L'' and ''R'' are binary trees or the empty set and ''S'' is a singleton set containing the root. Some authors allow the binary tree to be the empty set as well. From a graph theory perspective, binary (and K-ary) trees as defined here are arborescences. A binary tree may thus be also called a bifurcating arborescence—a term which appears in some very old programming books, before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than a directed graph, in which case a binary tree is an ordered, rooted tree. Some authors use rooted binary tree instead of ''binary tree'' to emphasize the fact that the tree is rooted, bu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Left-child Right-sibling Binary Tree
Every multi-way or k-ary tree structure studied in computer science admits a representation as a binary tree, which goes by various names including child-sibling representation, left-child, right-sibling binary tree, doubly chained tree or filial-heir chain. In a binary tree that represents a multi-way tree , each node corresponds to a node in and has two pointers: one to the node's first child, and one to its next sibling in . The children of a node thus form a singly-linked list. To find a node 's 'th child, one needs to traverse this list: procedure kth-child(n, k): child ← n.child while k ≠ 0 and child ≠ nil: child ← child.next-sibling k ← k − 1 return child ''// may return nil'' The process of converting from a k-ary tree to an LC-RS binary tree is sometimes called the '' Knuth transform''. To form a binary tree from an arbitrary k-ary tree by this method, the root of the original tree is made the root of the binary tree. Then, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Branching Factor
In computing, tree data structures, and game theory, the branching factor is the number of children at each node, the outdegree. If this value is not uniform, an ''average branching factor'' can be calculated. For example, in chess, if a "node" is considered to be a legal position, the average branching factor has been said to be about 35, and a statistical analysis of over 2.5 million games revealed an average of 31. This means that, on average, a player has about 31 to 35 legal moves at their disposal at each turn. By comparison, the average branching factor for the game Go is 250. Higher branching factors make algorithms that follow every branch at every node, such as exhaustive brute force searches, computationally more expensive due to the exponentially increasing number of nodes, leading to combinatorial explosion. For example, if the branching factor is 10, then there will be 10 nodes one level down from the current position, 102 (or 100) nodes two levels down, 103 (or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dictionary
A dictionary is a listing of lexemes from the lexicon of one or more specific languages, often arranged alphabetically (or by radical and stroke for ideographic languages), which may include information on definitions, usage, etymologies, pronunciations, translation, etc.Webster's New World College Dictionary, Fourth Edition, 2002 It is a lexicographical reference that shows inter-relationships among the data. A broad distinction is made between general and specialized dictionaries. Specialized dictionaries include words in specialist fields, rather than a complete range of words in the language. Lexical items that describe concepts in specific fields are usually called terms instead of words, although there is no consensus whether lexicology and terminology are two different fields of study. In theory, general dictionaries are supposed to be semasiological, mapping word to definition, while specialized dictionaries are supposed to be onomasiological, first identifying ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trie
In computer science, a trie, also called digital tree or prefix tree, is a type of ''k''-ary search tree, a tree data structure used for locating specific keys from within a set. These keys are most often strings, with links between nodes defined not by the entire key, but by individual characters. In order to access a key (to recover its value, change it, or remove it), the trie is traversed depth-first, following the links between nodes, which represent each character in the key. Unlike a binary search tree, nodes in the trie do not store their associated key. Instead, a node's position in the trie defines the key with which it is associated. This distributes the value of each key across the data structure, and means that not every node necessarily has an associated value. All the children of a node have a common prefix of the string associated with that parent node, and the root is associated with the empty string. This task of storing data accessible by its prefix can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octree
An octree is a tree data structure in which each internal node has exactly eight children. Octrees are most often used to partition a three-dimensional space by recursively subdividing it into eight octants. Octrees are the three-dimensional analog of quadtrees. The word is derived from ''oct'' (Greek root meaning "eight") + ''tree''. Octrees are often used in 3D graphics and 3D game engines. For spatial representation Each node in an octree subdivides the space it represents into eight octants. In a point region (PR) octree, the node stores an explicit three-dimensional point, which is the "center" of the subdivision for that node; the point defines one of the corners for each of the eight children. In a matrix based (MX) octree, the subdivision point is implicitly the center of the space the node represents. The root node of a PR octree can represent infinite space; the root node of an MX octree must represent a finite bounded space so that the implicit centers are well-define ... [...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. Origin B-trees were invented by Rudolf Bayer and Edward M. McCreight while working at Boeing Research Labs, for the purpose of efficiently managing 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 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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English Alphabet
The alphabet for Modern English is a Latin-script alphabet consisting of 26 letters, each having an upper- and lower-case form. The word ''alphabet'' is a compound of the first two letters of the Greek alphabet, '' alpha'' and '' beta''. The alphabet originated around the 7th century CE to write Old English from Latin script. Since then, letters have been added or removed to give the current letters: The exact shape of printed letters varies depending on the typeface (and font), and the standard printed form may differ significantly from the shape of handwritten letters (which varies between individuals), especially cursive. English Vowels and English Consonants. The English alphabet has 6 vowels and 20 consonants. Written English has a large number of digraphs (e.g., ''would'', ''beak'', ''moat''); it stands out (almost uniquely) as a European language without diacritics in native words. The only exceptions are: * a diaeresis (e.g., "coöperation") may be us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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