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A string is a substring (or factor) [1] of a string if there exists two strings and such that =.In particular, the empty string is a substring of every string. Example: The string = ana is equal to substrings (and subsequences) of = banana at two different offsets:
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 ...
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.
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 difference between the two algorithms consists in that the optimal string alignment algorithm computes the number of edit operations needed to make the strings equal under the condition that no substring is edited more than once, whereas the second one presents no such restriction. Take for example the edit distance between CA and ABC.
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.
The closeness of a match is measured in terms of the number of primitive operations necessary to convert the string into an exact match. This number is called the edit distance between the string and the pattern. The usual primitive operations are: [1] insertion: cot → coat; deletion: coat → cot
Various algorithms exist that solve problems beside the computation of distance between a pair of strings, to solve related types of problems. Hirschberg's algorithm computes the optimal alignment of two strings, where optimality is defined as minimizing edit distance. Approximate string matching can be formulated in terms of edit distance.