Longest Palindromic Substring
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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 ...
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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 Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, 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 computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ...
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Substring
In formal language theory and computer science, a substring is a contiguous sequence of characters within a string. For instance, "''the best of''" is a substring of "''It was the best of times''". In contrast, "''Itwastimes''" is a subsequence of "''It was the best of times''", but not a substring. Prefixes and suffixes are special cases of substrings. A prefix of a string S is a substring of S that occurs at the beginning of S; likewise, a suffix of a string S is a substring that occurs at the end of S. The substrings of the string "''apple''" would be: "''a''", "''ap''", "''app''", "''appl''", "''apple''", "''p''", "''pp''", "''ppl''", "''pple''", "''pl''", "''ple''", "''l''", "''le''" "''e''", "" (note the empty string at the end). Substring A string u is a substring (or factor) of a string t if there exists two strings p and s such that t = pus. In particular, the empty string is a substring of every string. Example: The string u=ana is equal to substrings (and subse ...
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Palindrome
A palindrome is a word, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as the words ''madam'' or ''racecar'', the date and time ''11/11/11 11:11,'' and the sentence: "A man, a plan, a canal – Panama". The 19-letter Finnish word ''saippuakivikauppias'' (a soapstone vendor), is the longest single-word palindrome in everyday use, while the 12-letter term ''tattarrattat'' (from James Joyce in ''Ulysses'') is the longest in English. The word ''palindrome'' was introduced by English poet and writer Henry Peacham in 1638.Henry Peacham, ''The Truth of our Times Revealed out of One Mans Experience'', 1638p. 123/ref> The concept of a palindrome can be dated to the 3rd-century BCE, although no examples survive; the first physical examples can be dated to the 1st-century CE with the Latin acrostic word square, the Sator Square (contains both word and sentence palindromes), and the 4th-century Greek Byzantine sentence palindrome ''nipson ano ...
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Suffix Tree
In computer science, a suffix tree (also called PAT tree or, in an earlier form, position tree) is a compressed trie containing all the suffixes of the given text as their keys and positions in the text as their values. Suffix trees allow particularly fast implementations of many important string operations. The construction of such a tree for the string S takes time and space linear in the length of S. Once constructed, several operations can be performed quickly, for instance locating a substring in S, locating a substring if a certain number of mistakes are allowed, locating matches for a regular expression pattern etc. Suffix trees also provide one of the first linear-time solutions for the longest common substring problem. These speedups come at a cost: storing a string's suffix tree typically requires significantly more space than storing the string itself. History The concept was first introduced by . Rather than the suffix S ..n/math>, Weiner stored in his trie the ''pref ...
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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 expected ...
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Parallel Algorithm
In computer science, a parallel algorithm, as opposed to a traditional serial algorithm, is an algorithm which can do multiple operations in a given time. It has been a tradition of computer science to describe serial algorithms in abstract machine models, often the one known as random-access machine. Similarly, many computer science researchers have used a so-called parallel random-access machine (PRAM) as a parallel abstract machine (shared-memory). Many parallel algorithms are executed concurrently – though in general concurrent algorithms are a distinct concept – and thus these concepts are often conflated, with which aspect of an algorithm is parallel and which is concurrent not being clearly distinguished. Further, non-parallel, non-concurrent algorithms are often referred to as "sequential algorithms", by contrast with concurrent algorithms. Parallelizability Algorithms vary significantly in how parallelizable they are, ranging from easily parallelizable to completely ...
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Subsequence
In mathematics, a subsequence of a given sequence is a sequence that can be derived from the given sequence by deleting some or no elements without changing the order of the remaining elements. For example, the sequence \langle A,B,D \rangle is a subsequence of \langle A,B,C,D,E,F \rangle obtained after removal of elements C, E, and F. The relation of one sequence being the subsequence of another is a preorder. Subsequences can contain consecutive elements which were not consecutive in the original sequence. A subsequence which consists of a consecutive run of elements from the original sequence, such as \langle B,C,D \rangle, from \langle A,B,C,D,E,F \rangle, is a substring. The substring is a refinement of the subsequence. The list of all subsequences for the word "apple" would be "''a''", "''ap''", "''al''", "''ae''", "''app''", "''apl''", "''ape''", "''ale''", "''appl''", "''appe''", "''aple''", "''apple''", "''p''", "''pp''", "''pl''", "''pe''", "''ppl''", "''ppe''", "''ple' ...
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Theoretical Computer Science (journal)
''Theoretical Computer Science'' (TCS) is a computer science journal published by Elsevier, started in 1975 and covering theoretical computer science. The journal publishes 52 issues a year. It is abstracted and indexed by Scopus and the Science Citation Index. According to the Journal Citation Reports, its 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... is 0.827. References Computer science journals Elsevier academic journals Publications established in 1975 {{comp-sci-theory-stub ...
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Journal Of The ACM
The ''Journal of the ACM'' is a peer-reviewed scientific journal covering computer science in general, especially theoretical aspects. It is an official journal of the Association for Computing Machinery. Its current editor-in-chief is Venkatesan Guruswami. The journal was established in 1954 and "computer scientists universally hold the ''Journal of the ACM'' in high esteem". See also * ''Communications of the ACM ''Communications of the ACM'' is the monthly journal of the Association for Computing Machinery (ACM). It was established in 1958, with Saul Rosen as its first managing editor. It is sent to all ACM members. Articles are intended for readers with ...'' References External links * Publications established in 1954 Computer science journals Association for Computing Machinery academic journals Bimonthly journals English-language journals {{compu-journal-stub ...
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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 A ...
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