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Cardinal Tree
A cardinal tree (or trie) of degree ''k'', by analogy with cardinal number In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number. For dealing with the cas ...s and by opposition with ordinal trees, is a rooted tree in which each node has positions for an edge to a child. "Representing trees of higher degree" (2005) by David Benoit, Erik D. Demaine, J. Ian Munro, Rajeev Raman, Venkatesh Raman and S. Srinivasa Rao Each node has up to children and each child of a given node is labeled by a unique integer from the set {1, 2, . . . , k}. For instance, a Binary Tree, binary ... [...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] |
Cardinal Number
In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number. For dealing with the case of infinite sets, the infinite cardinal numbers have been introduced, which are often denoted with the Hebrew letter \aleph (aleph) marked with subscript indicating their rank among the infinite cardinals. Cardinality is defined in terms of bijective functions. Two sets have the same cardinality if, and only if, there is a one-to-one correspondence (bijection) between the elements of the two sets. In the case of finite sets, this agrees with the intuitive notion of number of elements. In the case of infinite sets, the behavior is more complex. A fundamental theorem due to Georg Cantor shows that it is possible for two infinite sets to have different cardinalities, and in particular the cardinality of the set of real numbers is gre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinal Tree
{{one source , date=May 2024 An ordinal tree, by analogy with an ordinal number, is a rooted tree of arbitrary degree in which the children of each node are ordered, so that one refers to the ith child in the sequence of children of a node. "Representing trees of higher degree" (2005) by David Benoit, Erik D. Demaine, J. Ian Munro, Rajeev Raman, Venkatesh Raman and S. Srinivasa Rao See also *Cardinal tree
A cardinal tree (or trie) of degree ''k'', by analogy with cardinal number
In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal num ...
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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] |
Data Types
In computer science and computer programming, a data type (or simply type) is a collection or grouping of data values, usually specified by a set of possible values, a set of allowed operations on these values, and/or a representation of these values as machine types. A data type specification in a program constrains the possible values that an expression, such as a variable or a function call, might take. On literal data, it tells the compiler or interpreter how the programmer intends to use the data. Most programming languages support basic data types of integer numbers (of varying sizes), floating-point numbers (which approximate real numbers), characters and Booleans. Concept A data type may be specified for many reasons: similarity, convenience, or to focus the attention. It is frequently a matter of good organization that aids the understanding of complex definitions. Almost all programming languages explicitly include the notion of data type, though the possible da ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trees (data Structures)
In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, e.g., including only woody plants with secondary growth, only plants that are usable as lumber, or only plants above a specified height. But wider definitions include taller palms, tree ferns, bananas, and bamboos. Trees are not a monophyletic taxonomic group but consist of a wide variety of plant species that have independently evolved a trunk and branches as a way to tower above other plants to compete for sunlight. The majority of tree species are angiosperms or hardwoods; of the rest, many are gymnosperms or softwoods. Trees tend to be long-lived, some trees reaching several thousand years old. Trees evolved around 400 million years ago, and it is estimated that there are around three trillion mature trees in the world currently. A tree typically has many secondary branches supported clear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knowledge Representation
Knowledge representation (KR) aims to model information in a structured manner to formally represent it as knowledge in knowledge-based systems whereas knowledge representation and reasoning (KRR, KR&R, or KR²) also aims to understand, reason, and interpret knowledge. KRR is widely used in the field of artificial intelligence (AI) with the goal to represent information about the world in a form that a computer system can use to solve complex tasks, such as diagnosing a medical condition or having a natural-language dialog. KR incorporates findings from psychology about how humans solve problems and represent knowledge, in order to design formalisms that make complex systems easier to design and build. KRR also incorporates findings from logic to automate various kinds of ''reasoning''. Traditional KRR focuses more on the declarative representation of knowledge. Related knowledge representation formalisms mainly include vocabularies, thesaurus, semantic networks, axiom system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
