Knuth–Morris–Pratt algorithm
string searching algorithm
In computer science, the Knuth–Morris–Pratt algorithm (or KMP algorithm) is a string-searching algorithm that searches for occurrences of a "word" W within a main "text string" S by employing the observation that when a mismatch occurs, the word itself embodies sufficient information to determine where the next match could begin, thus bypassing re-examination of previously matched characters.
The algorithm was conceived by James H. Morris and independently discovered by Donald Knuth "a few weeks later" from automata theory.
Morris and Vaughan Pratt published a technical report in 1970.
The three also published the algorithm jointly in 1977. Independently, in 1969, Matiyasevich discovered a similar algorithm, coded by a two-dimensional Turing machine, while studying a string-pattern-matching recognition problem over a binary alphabet. This was the first linear-time algorithm for string matching.
Background
A string-matching algorithm wants to find the starting index m in string s that matches the search word w.
The most straightforward algorithm, known as the "brute-force" or "naive" algorithm, is to look for a word match at each index m, i.e. the position in the string being searched that corresponds to the character s[m]. At each position m the algorithm first checks for equality of the first character in the word being searched, i.e.
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This entry incorporates text from “Knuth–Morris–Pratt algorithm” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.