Anatree
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Anatree
An anatree is a data structure designed to solve anagrams. Solving an anagram is the problem of finding a word from a given list of letters. These problems are commonly encountered in word games like Scrabble or in newspaper crossword puzzles. The problem for the wordwheel also has the condition that the central letter appear in all the words framed with the given set. Some other conditions may be introduced regarding the frequency (number of appearances) of each of the letters in the given input string. These problems are classified as Constraint satisfaction problem in computer science literature. An anatree is represented as a directed tree (graph theory), tree which contains a set of words (W) encoded as strings in some alphabet. The internal vertices are labelled with some letter in the alphabet and the leaves contain words. The edges are labelled with non-negative integers. An anatree has the property that the sum of the edge labels from the root to the leaf is the length ...
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Anagram
An anagram is a word or phrase formed by rearranging the letters of a different word or phrase, typically using all the original letters exactly once. For example, the word ''anagram'' itself can be rearranged into ''nag a ram'', also the word ''binary'' into ''brainy'' and the word ''adobe'' into ''abode''. The original word or phrase is known as the ''subject'' of the anagram. Any word or phrase that exactly reproduces the letters in another order is an anagram. Someone who creates anagrams may be called an "anagrammatist", and the goal of a serious or skilled anagrammatist is to produce anagrams that reflect or comment on their subject. Examples Anagrams may be created as a commentary on the subject. They may be a parody, a criticism or satire. For example: * "New York Times" = " monkeys write" * "Church of Scientology" = "rich-chosen goofy cult" * "McDonald's restaurants" = " Uncle Sam's standard rot" * "coronavirus" = "carnivorous" * "She Sells Sanctuary" = "Santa; shy, l ...
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Image Of An Anatree1
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensional picture, that resembles a subject. In the context of signal processing, an image is a distributed amplitude of color(s). In optics, the term “image” may refer specifically to a 2D image. An image does not have to use the entire visual system to be a visual representation. A popular example of this is of a greyscale image, which uses the visual system's sensitivity to brightness across all wavelengths, without taking into account different colors. A black and white visual representation of something is still an image, even though it does not make full use of the visual system's capabilities. Images are typically still, but in some cases can be moving or animated. Characteristics Images may be two or three-dimensional, such as a pho ...
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Data Structure
In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data, i.e., it is an algebraic structure about data. Usage Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type. Different types of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, relational databases commonly use B-tree indexes for data retrieval, while compiler implementations usually use hash tables to look up identifiers. Data structures provide a means to manage large amounts of data efficiently for uses such as large databases and internet indexing services. Usually, ...
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Scrabble
''Scrabble'' is a word game in which two to four players score points by placing tiles, each bearing a single letter, onto a game board divided into a 15×15 grid of squares. The tiles must form words that, in crossword fashion, read left to right in rows or downward in columns and are included in a standard dictionary or lexicon. The name ''Scrabble'' is a trademark of Mattel in most of the world, except in the United States and Canada, where it is a trademark of Hasbro, under the brands of both of its subsidiaries, Milton Bradley and Parker Brothers. The game is sold in 121 countries and is available in more than 30 languages; approximately 150 million sets have been sold worldwide, and roughly one-third of American and half of British homes have a ''Scrabble'' set. There are approximately 4,000 ''Scrabble'' clubs around the world. Game details The game is played by two to four players on a square game board imprinted with a 15×15 grid of cells (individually known as " ...
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Crossword
A crossword is a word puzzle that usually takes the form of a square or a rectangular grid of white- and black-shaded squares. The goal is to fill the white squares with letters, forming words or phrases, by solving clues which lead to the answers. In languages that are written left-to-right, the answer words and phrases are placed in the grid from left to right ("across") and from top to bottom ("down"). The shaded squares are used to separate the words or phrases. Types Crossword grids such as those appearing in most North American newspapers and magazines feature solid areas of white squares. Every letter is checked (i.e. is part of both an "across" word and a "down" word) and usually each answer must contain at least three letters. In such puzzles shaded squares are typically limited to about one-sixth of the total. Crossword grids elsewhere, such as in Britain, South Africa, India and Australia, have a lattice-like structure, with a higher percentage of shaded squares ...
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Constraint Satisfaction Problem
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods. CSPs are the subject of research in both artificial intelligence and operations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families. CSPs often exhibit high complexity, requiring a combination of heuristics and combinatorial search methods to be solved in a reasonable time. Constraint programming (CP) is the field of research that specifically focuses on tackling these kinds of problems. Additionally, Boolean satisfiability problem (SAT), the satisfiability modulo theories (SMT), mixed integer programming (MIP) and answer set programming (ASP) are all fields of research focusin ...
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Tree (graph Theory)
In graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ..., a tree is an undirected graph in which any two Vertex (graph theory), vertices are connected by ''exactly one'' Path (graph theory), path, or equivalently a Connected graph, connected Cycle (graph theory), acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by ''at most one'' path, or equivalently an acyclic undirected graph, or equivalently a Disjoint union of graphs, disjoint union of trees. A polytreeSee . (or directed tree or oriented treeSee .See . or singly connected networkSee .) is a directed acyclic graph (DAG) whose underlying undirected graph is a tree. A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirecte ...
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Alphabet
An alphabet is a standardized set of basic written graphemes (called letters) that represent the phonemes of certain spoken languages. Not all writing systems represent language in this way; in a syllabary, each character represents a syllable, and logographic systems use characters to represent words, morphemes, or other semantic units. The first fully phonemic script, the Proto-Sinaitic script, later known as the Phoenician alphabet, is considered to be the first alphabet and is the ancestor of most modern alphabets, including Arabic, Cyrillic, Greek, Hebrew, Latin, and possibly Brahmic. It was created by Semitic-speaking workers and slaves in the Sinai Peninsula (as the Proto-Sinaitic script), by selecting a small number of hieroglyphs commonly seen in their Egyptian surroundings to describe the sounds, as opposed to the semantic values of the Canaanite languages. However, Peter T. Daniels distinguishes an abugida, a set of graphemes that represent consonantal base ...
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Image Of A Mixed Anatree
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensional picture, that resembles a subject. In the context of signal processing, an image is a distributed amplitude of color(s). In optics, the term “image” may refer specifically to a 2D image. An image does not have to use the entire visual system to be a visual representation. A popular example of this is of a greyscale image, which uses the visual system's sensitivity to brightness across all wavelengths, without taking into account different colors. A black and white visual representation of something is still an image, even though it does not make full use of the visual system's capabilities. Images are typically still, but in some cases can be moving or animated. Characteristics Images may be two or three-dimensional, such as a pho ...
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Hash Table
In computing, a hash table, also known as hash map, is a data structure that implements an associative array or dictionary. It is an abstract data type that maps keys to values. A hash table uses a hash function to compute an ''index'', also called a ''hash code'', into an array of ''buckets'' or ''slots'', from which the desired value can be found. During lookup, the key is hashed and the resulting hash indicates where the corresponding value is stored. Ideally, the hash function will assign each key to a unique bucket, but most hash table designs employ an imperfect hash function, which might cause hash ''collisions'' where the hash function generates the same index for more than one key. Such collisions are typically accommodated in some way. In a well-dimensioned hash table, the average time complexity for each lookup is independent of the number of elements stored in the table. Many hash table designs also allow arbitrary insertions and deletions of key–value pairs, ...
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Lexicon
A lexicon is the vocabulary of a language or branch of knowledge (such as nautical or medical). In linguistics, a lexicon is a language's inventory of lexemes. The word ''lexicon'' derives from Koine Greek language, Greek word (), neuter of () meaning 'of or for words'. Linguistic theories generally regard human languages as consisting of two parts: a lexicon, essentially a catalogue of a language's words (its wordstock); and a grammar, a system of rules which allow for the combination of those words into meaningful sentences. The lexicon is also thought to include bound morphemes, which cannot stand alone as words (such as most affixes). In some analyses, compound words and certain classes of idiomatic expressions, collocations and other phrases are also considered to be part of the lexicon. Dictionary, Dictionaries are lists of the lexicon, in alphabetical order, of a given language; usually, however, bound morphemes are not included. Size and organization Items in the le ...
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Counting Sort
In computer science, counting sort is an algorithm for sorting a collection of objects according to keys that are small positive integers; that is, it is an integer sorting algorithm. It operates by counting the number of objects that possess distinct key values, and applying prefix sum on those counts to determine the positions of each key value in the output sequence. Its running time is linear in the number of items and the difference between the maximum key value and the minimum key value, so it is only suitable for direct use in situations where the variation in keys is not significantly greater than the number of items. It is often used as a subroutine in radix sort, another sorting algorithm, which can handle larger keys more efficiently.. See also the historical notes on page 181... Counting sort is not a comparison sort; it uses key values as indexes into an array and the lower bound for comparison sorting will not apply. Bucket sort may be used in lieu of counting sort ...
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