Knuth–Morris–Pratt algorithm

Knuth–Morris–Pratt algorithm

Class	String search
Data structure	String
Worst-case performance	${\displaystyle \Theta (m)}$ preprocessing + ${\displaystyle \Theta (n)}$ matching
Worst-case space complexity	${\displaystyle \Theta (m)}$

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.