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Presented here are two algorithms: the first, [8] simpler one, computes what is known as the optimal string alignment distance or restricted edit distance, [7] while the second one [9] computes the Damerau–Levenshtein distance with adjacent transpositions.
After computing E(i, j) for all i and j, we can easily find a solution to the original problem: it is the substring for which E(m, j) is minimal (m being the length of the pattern P.) Computing E ( m , j ) is very similar to computing the edit distance between two strings.
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.
In information theory, linguistics, and computer science, the Levenshtein distance is a string metric for measuring the difference between two sequences. The Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other.
Edit distance finds applications in computational biology and natural language processing, e.g. the correction of spelling mistakes or OCR errors, and approximate string matching, where the objective is to find matches for short strings in many longer texts, in situations where a small number of differences is to be expected.
In computer science, the longest repeated substring problem is the problem of finding the longest substring of a string that occurs at least twice. This problem can be solved in linear time and space Θ ( n ) {\displaystyle \Theta (n)} by building a suffix tree for the string (with a special end-of-string symbol like '$' appended), and finding ...
string" is a substring of "substring" In formal language theory and computer science, a substring is a contiguous sequence of characters within a string. [citation needed] 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.
Naively computing the hash value for the substring s[i+1..i+m] requires O(m) time because each character is examined. Since the hash computation is done on each loop, the algorithm with a naive hash computation requires O(mn) time, the same complexity as a straightforward string matching algorithm. For speed, the hash must be computed in ...