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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.
It is at least the absolute value of the difference of the sizes of the two strings. It is at most the length of the longer string. It is zero if and only if the strings are equal. If the strings have the same size, the Hamming distance is an upper bound on the Levenshtein distance. The Hamming distance is the number of positions at which the ...
In information theory, the Hamming distance between two strings or vectors of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of substitutions required to change one string into the other, or equivalently, the minimum number of errors that could have transformed one string into the other.
Given two strings a and b on an alphabet Σ (e.g. the set of ASCII characters, the set of bytes [0..255], etc.), the edit distance d(a, b) is the minimum-weight series of edit operations that transforms a into b. One of the simplest sets of edit operations is that defined by Levenshtein in 1966: [2] Insertion of a single symbol.
The most widely known string metric is a rudimentary one called the Levenshtein distance (also known as edit distance). [2] It operates between two input strings, returning a number equivalent to the number of substitutions and deletions needed in order to transform one input string into another.
The naive algorithm for finding the lexicographically minimal rotation of a string is to iterate through successive rotations while keeping track of the most lexicographically minimal rotation encountered. If the string is of length n, this algorithm runs in O(n 2) time in the worst case.
Range minimum query reduced to the lowest common ancestor problem.. Given an array A[1 … n] of n objects taken from a totally ordered set, such as integers, the range minimum query RMQ A (l,r) =arg min A[k] (with 1 ≤ l ≤ k ≤ r ≤ n) returns the position of the minimal element in the specified sub-array A[l …
The longest common substrings of a set of strings can be found by building a generalized suffix tree for the strings, and then finding the deepest internal nodes which have leaf nodes from all the strings in the subtree below it. The figure on the right is the suffix tree for the strings "ABAB", "BABA" and "ABBA", padded with unique string ...