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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 failure function for the string is computed as normal, but the string is rotated during the computation so some indices must be computed more than once as they wrap around. Once all indices of the failure function have been successfully computed without the string rotating again, the minimal lexicographical rotation is known to be found and ...
Given an input string S = ^ BANANA $ (step 1 in the table below), rotate it N times (step 2), where N = 8 is the length of the S string considering also the red ^ character representing the start of the string and the red $ character representing the 'EOF' pointer; these rotations, or circular shifts, are then sorted lexicographically (step 3).
Video: Keys pressed for calculating eight times six on a HP-32SII (employing RPN) from 1991. Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which operators follow their operands, in contrast to prefix or Polish notation (PN), in which operators precede their operands.
In mathematics, a lattice word (or lattice permutation) is a string composed of positive integers, in which every prefix contains at least as many positive integers i as integers i + 1. A reverse lattice word , or Yamanouchi word (named after Takahiko Yamanouchi ), is a string whose reversal is a lattice word.
The reverse of a string is a string with the same symbols but in reverse order. For example, if s = abc (where a, b, and c are symbols of the alphabet), then the reverse of s is cba. A string that is the reverse of itself (e.g., s = madam) is called a palindrome, which also includes the empty string and all strings of length 1.
A string-searching algorithm, sometimes called string-matching algorithm, is an algorithm that searches a body of text for portions that match by pattern. A basic example of string searching is when the pattern and the searched text are arrays of elements of an alphabet ( finite set ) Σ.
It is thus well-suited for applications in which the pattern is much shorter than the text or where it persists across multiple searches. The Boyer–Moore algorithm uses information gathered during the preprocess step to skip sections of the text, resulting in a lower constant factor than many other string search algorithms.