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M-ary Tree
In graph theory, an ''m''-ary tree (for nonnegative integers ''m'') (also known as ''n''-ary, ''k''-ary, ''k''-way or generic tree) is an arborescence (or, for some authors, an ordered tree) in which each node has no more than ''m'' children. A binary tree is an important case where ''m'' = 2; similarly, a ternary tree is one where ''m'' = 3. Types of ''m''-ary trees * A full ''m''-ary tree is an ''m''-ary tree where within each level every node has 0 or ''m'' children. * A complete ''m''-ary tree (or, less commonly, 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 root node, with a tree containing only a root node having a height of 0. * The height of a tree is equal to the maximum depth ''D'' of any node in the tree. * The total n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Tree
In computer science, a binary tree is a tree data structure in which each node has at most two children, referred to as the ''left child'' and the ''right child''. That is, it is a ''k''-ary tree with . A recursive definition using set theory is that a binary tree is a triple , where ''L'' and ''R'' are binary trees or the empty set and ''S'' is a singleton (a single–element set) containing the root. From a graph theory perspective, binary trees as defined here are arborescences. A binary tree may thus be also called a bifurcating arborescence, a term which appears in some early programming books before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than 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, but as defined above, a binary tree is always rooted. In ma ... [...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. The ... [...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 ( ... [...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 Alphabetical order, alphabetically (or by Semitic root, consonantal root for Semitic languages or radical-and-stroke sorting, radical and stroke for Logogram, logographic languages), which may include information on definitions, usage, etymologies, pronunciations, Bilingual dictionary, translation, etc.Webster's New World College Dictionary, Fourth Edition, 2002 It is a Lexicography, 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 comprehensive 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 dictionarie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trie
In computer science, a trie (, ), also known as a digital tree or prefix tree, is a specialized search tree data structure used to store and retrieve strings from a dictionary or set. Unlike a binary search tree, nodes in a trie do not store their associated key. Instead, each node's ''position'' within the trie determines its associated key, with the connections between nodes defined by individual Character (computing), characters rather than the entire key. Tries are particularly effective for tasks such as autocomplete, spell checking, and IP routing, offering advantages over hash tables due to their prefix-based organization and lack of hash collisions. Every child node shares a common prefix (computer science), prefix with its parent node, and the root node represents the empty string. While basic trie implementations can be memory-intensive, various optimization techniques such as compression and bitwise representations have been developed to improve their efficiency. A n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octree
An octree is a tree data structure in which each internal node has exactly eight child node, children. Octrees are most often used to partition a three-dimensional space by recursive subdivision, recursively subdividing it into eight Octant (geometry), 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 octant (solid geometry), octants. In a point region (PR) octree (analogous to a point quadtree), the node stores an explicit Point (geometry), 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 (analogous to a region quadtree), the subdivision point is implicitly the center of the space the node represents. The root n ... [...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] |
English Alphabet
Modern English is written with a Latin-script alphabet consisting of 26 Letter (alphabet), letters, with each having both uppercase and lowercase forms. The word ''alphabet'' is a Compound (linguistics), compound of ''alpha'' and ''beta'', the names of the first two letters in the Greek alphabet. The earliest Old English writing during the 5th century used a runic alphabet known as the Anglo-Saxon futhorc, futhorc. The Old English Latin alphabet was adopted from the 7th century onward—and over the following centuries, various letters entered and fell out of use. By the 16th century, the present set of 26 letters had largely stabilised: There are 5 vowel letters and 19 consonant letters—as well as Y and W, which may function as either type. Written English has a large number of Digraph (orthography), digraphs, such as , , , , and . Diacritics are generally not used to write native English words, which is unusual among orthographies used to write the languages of Eu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
