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Longest Common Substring
In computer science, a longest common substring of two or more strings is a longest string that is a substring of all of them. There may be more than one longest common substring. Applications include data deduplication and plagiarism detection. Examples The picture shows two strings where the problem has multiple solutions. Although the substring occurrences always overlap, it is impossible to obtain a longer common substring by "uniting" them. The strings "ABABC", "BABCA" and "ABCBA" have only one longest common substring, viz. "ABC" of length 3. Other common substrings are "A", "AB", "B", "BA", "BC" and "C". ABABC , , , BABCA , , , ABCBA Problem definition Given two strings, S of length m and T of length n, find a longest string which is substring of both S and T. A generalization is the ''k''-common substring problem. Given the set of strings S = \, where , S_i, =n_i and \sum n_i = N. Find for each 2 \leq k \leq K, a longest string which occurs a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including the design and implementation of hardware and software). Computer science is generally considered an area of academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing security vulnerabilities. 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 repositories ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Dynamic Programming
Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. In both contexts it refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner. While some decision problems cannot be taken apart this way, decisions that span several points in time do often break apart recursively. Likewise, in computer science, if a problem can be solved optimally by breaking it into sub-problems and then recursively finding the optimal solutions to the sub-problems, then it is said to have '' optimal substructure''. If sub-problems can be nested recursively inside larger problems, so that dynamic programming methods are applicable, then there is a relation between the value of the larger problem and the values of the sub-problems.Cormen, T. H.; Leiserson, C. E.; Riv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Problems On Strings
A problem is a difficulty which may be resolved by problem solving. Problem(s) or The Problem may also refer to: People * Problem (rapper), (born 1985) American rapper Books * ''Problems'' (Aristotle), an Aristotelian (or pseudo-Aristotelian) collection of problems in question and answer form * ''The Problem'' (play), by A. R. Gurney Film and TV * ''Problems'' (TV series), a 2012 Australian comedy television series. * '' The Problem with Jon Stewart'', an American current affairs television series. Music Albums * ''The Problem'' (album), by Mathematics * ''Problems'' (album), a 2019 album by The Get Up Kids Songs * "Problem" (Ariana Grande song), 2014 * "Problem" (Natalia Kills song), 2013 * "Problems" (song), a 1958 song by The Everly Brothers * "Fuckin' Problems", sometimes known as "Problems", a 2012 song by A$AP Rocky * "Problem", by Becky G * "Problem", by Erin Bowman * "Problem", by Šarlo Akrobata from '' Bistriji ili tuplji čovek biva kad...'' * "Problems", by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Algorithm Implementation/Strings/Longest Common Substring
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm can be expressed within a finite amount of space and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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N-gram
In the fields of computational linguistics and probability, an ''n''-gram (sometimes also called Q-gram) is a contiguous sequence of ''n'' items from a given sample of text or speech. The items can be phonemes, syllables, letters, words or base pairs according to the application. The ''n''-grams typically are collected from a text or speech corpus. When the items are words, -grams may also be called ''shingles''. Using Latin numerical prefixes, an ''n''-gram of size 1 is referred to as a "unigram"; size 2 is a " bigram" (or, less commonly, a "digram"); size 3 is a " trigram". English cardinal numbers are sometimes used, e.g., "four-gram", "five-gram", and so on. In computational biology, a polymer or oligomer of a known size is called a ''k''-mer instead of an ''n''-gram, with specific names using Greek numerical prefixes such as "monomer", "dimer", "trimer", "tetramer", "pentamer", etc., or English cardinal numbers, "one-mer", "two-mer", "three-mer", etc. App ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Longest Palindromic Substring
In computer science, the longest palindromic substring or longest symmetric factor problem is the problem of finding a maximum-length contiguous substring of a given string that is also a palindrome. For example, the longest palindromic substring of "bananas" is "anana". The longest palindromic substring is not guaranteed to be unique; for example, in the string "abracadabra", there is no palindromic substring with length greater than three, but there are two palindromic substrings with length three, namely, "aca" and "ada". In some applications it may be necessary to return all maximal palindromic substrings (that is, all substrings that are themselves palindromes and cannot be extended to larger palindromic substrings) rather than returning only one substring or returning the maximum length of a palindromic substring. invented an O(n)-time algorithm for listing all the palindromes that appear at the start of a given string of length n. However, as observed e.g., by , the same algo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Lowest Common Ancestor
In graph theory and computer science, the lowest common ancestor (LCA) (also called least common ancestor) of two nodes and in a tree or directed acyclic graph (DAG) is the lowest (i.e. deepest) node that has both and as descendants, where we define each node to be a descendant of itself (so if has a direct connection from , is the lowest common ancestor). The LCA of and in is the shared ancestor of and that is located farthest from the root. Computation of lowest common ancestors may be useful, for instance, as part of a procedure for determining the distance between pairs of nodes in a tree: the distance from to can be computed as the distance from the root to , plus the distance from the root to , minus twice the distance from the root to their lowest common ancestor . In ontologies, the lowest common ancestor is also known as the least common ancestor. In a tree data structure where each node points to its parent, the lowest common ancestor can be easily deter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Suffix Tree ABAB BABA ABBA
In linguistics, a suffix is an affix which is placed after the stem of a word. Common examples are case endings, which indicate the grammatical case of nouns, adjectives, and verb endings, which form the conjugation of verbs. Suffixes can carry grammatical information (inflectional suffixes) or lexical information ( derivational/lexical suffixes'').'' An inflectional suffix or a grammatical suffix. Such inflection changes the grammatical properties of a word within its syntactic category. For derivational suffixes, they can be divided into two categories: class-changing derivation and class-maintaining derivation. Particularly in the study of Semitic languages, suffixes are called affirmatives, as they can alter the form of the words. In Indo-European studies, a distinction is made between suffixes and endings (see Proto-Indo-European root). Suffixes can carry grammatical information or lexical information. A word-final segment that is somewhere between a free morpheme and a boun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Word RAM
In theoretical computer science, the word RAM (word random-access machine) model is a model of computation in which a random-access machine does bitwise operations on a word of bits. Michael Fredman and Dan Willard created it in 1990 to simulate programming languages like C. Model The word RAM model is an abstract machine similar to a random-access machine, but with additional capabilities. It works with words of size up to bits, meaning it can store integers up to size 2^w. Because the model assumes that the word size matches the problem size, that is, for a problem of size , w \ge \log n, the word RAM model is a transdichotomous model. The model allows bitwise operations such as arithmetic and logical shifts to be done in constant time. The number of possible values is , where U \le 2^w. Algorithms and data structures In the word RAM model, integer sorting can be done fairly efficiently. Yijie Han and Mikkel Thorup created a randomized algorithm to sort integers in exp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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String (computer Science)
In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length changed, or it may be fixed (after creation). A string is generally considered as a data type and is often implemented as an array data structure of bytes (or words) that stores a sequence of elements, typically characters, using some character encoding. ''String'' may also denote more general arrays or other sequence (or list) data types and structures. Depending on the programming language and precise data type used, a variable declared to be a string may either cause storage in memory to be statically allocated for a predetermined maximum length or employ dynamic allocation to allow it to hold a variable number of elements. When a string appears literally in source code, it is known as a string literal or an anonymous string. In formal languages, which are used in mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Generalized Suffix Tree
In computer science, a generalized suffix tree is a suffix tree for a set of strings. Given the set of strings D=S_1,S_2,\dots,S_d of total length n, it is a Patricia tree containing all n suffixes of the strings. It is mostly used in bioinformatics. Functionality It can be built in \Theta(n) time and space, and can be used to find all z occurrences of a string P of length m in O(m + z) time, which is asymptotically optimal (assuming the size of the alphabet is constant). When constructing such a tree, each string should be padded with a unique out-of-alphabet marker symbol (or string) to ensure no suffix is a substring of another, guaranteeing each suffix is represented by a unique leaf node. Algorithms for constructing a GST include Ukkonen's algorithm (1995) and McCreight's algorithm (1976). Example A suffix tree for the strings ABAB and BABA is shown in a figure above. They are padded with the unique terminator strings $0 and $1. The numbers in the leaf nodes are str ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Big O Notation
Big ''O'' notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation. The letter O was chosen by Bachmann to stand for '' Ordnung'', meaning the order of approximation. In computer science, big O notation is used to classify algorithms according to how their run time or space requirements grow as the input size grows. In analytic number theory, big O notation is often used to express a bound on the difference between an arithmetical function and a better understood approximation; a famous example of such a difference is the remainder term in the prime number theorem. Big O notation is also used in many other fields to provide similar estimates. Big O notation characterizes functions according to their growth rates: d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |