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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.
For function that manipulate strings, modern object-oriented languages, like C# and Java have immutable strings and return a copy (in newly allocated dynamic memory), while others, like C manipulate the original string unless the programmer copies data to a new string.
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.
When a string appears literally in source code, it is known as a string literal or an anonymous string. [ 1 ] In formal languages , which are used in mathematical logic and theoretical computer science , a string is a finite sequence of symbols that are chosen from a set called an alphabet .
The C and Java implementations below have a space complexity (make_delta1, makeCharTable). This is the same as the original delta1 and the BMH bad-character table . This table maps a character at position i {\displaystyle i} to shift by len ( p ) − 1 − i {\displaystyle \operatorname {len} (p)-1-i} , with the last ...
The first occurrence is obtained with = b and = na, while the second occurrence is obtained with = ban and being the empty string. A substring of a string is a prefix of a suffix of the string, and equivalently a suffix of a prefix; for example, nan is a prefix of nana , which is in turn a suffix of banana .
These positions contribute to the running time of the algorithm unnecessarily, without producing a match. Additionally, the hash function used should be a rolling hash, a hash function whose value can be quickly updated from each position of the text to the next. Recomputing the hash function from scratch at each position would be too slow.
It disregards word order (and thus most of syntax or grammar) but captures multiplicity. The bag-of-words model is commonly used in methods of document classification where, for example, the (frequency of) occurrence of each word is used as a feature for training a classifier. [1] It has also been used for computer vision. [2]