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A basic example of string searching is when the pattern and the searched text are arrays of elements of an alphabet Σ. Σ may be a human language alphabet, for example, the letters A through Z and other applications may use a binary alphabet (Σ = {0,1}) or a DNA alphabet (Σ = {A,C,G,T}) in bioinformatics.
«FUNCTION» BYTE-LENGTH(string) number of characters and number of bytes, respectively COBOL: string length string: a decimal string giving the number of characters Tcl: ≢ string: APL: string.len() Number of bytes Rust [30] string.chars().count() Number of Unicode code points Rust [31]
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; substitution: coat → cost; These three operations may be generalized as forms of substitution by adding a NULL character (here symbolized by *) wherever a character has been ...
P denotes the string to be searched for, called the pattern. Its length is m. S[i] denotes the character at index i of string S, counting from 1. S[i..j] denotes the substring of string S starting at index i and ending at j, inclusive. A prefix of S is a substring S[1..i] for some i in range [1, l], where l is the length of S.
To find any of a large number, say k, fixed length patterns in a text, a simple variant of the Rabin–Karp algorithm uses a Bloom filter or a set data structure to check whether the hash of a given string belongs to a set of hash values of patterns we are looking for:
A match is made, not when all the atoms of the string are matched, but rather when all the pattern atoms in the regex have matched. The idea is to make a small pattern of characters stand for a large number of possible strings, rather than compiling a large list of all the literal possibilities.
For example, if the string was "ababc", the "Old" palindrome could be "bab" with the Center being the second "b" and the MirroredCenter being the first "b". Since the palindrome at the MirroredCenter is "aba" and extends beyond the boundaries of the "Old" palindrome, we know the longest palindrome at the second "b" can only extend up to the ...
This representation of an n-character string takes n + 1 space (1 for the terminator), and is thus an implicit data structure. In terminated strings, the terminating code is not an allowable character in any string. Strings with length field do not have this limitation and can also store arbitrary binary data.