The Knuth-Morris-Pratt (KMP) string matching algorithm can perform the search in Ɵ(m + n) operations, which is a significant improvement in. Knuth, Morris and Pratt discovered first linear time string-matching algorithm by analysis of the naive algorithm. It keeps the information that. KMP Pattern Matching algorithm. 1. Knuth-Morris-Pratt Algorithm Prepared by: Kamal Nayan; 2. The problem of String Matching Given a string.

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Knuth–Morris–Pratt algorithm – Wikipedia

October Learn how and when to remove this template message. This is depicted, at the start of the run, like. The algorithm compares successive characters of W to “parallel” characters of Smoving from one to the next by incrementing i if they match.

In the second branch, cnd is replaced by T[cnd]which we saw above is always strictly less than cndthus increasing pos – cnd.

If the strings are not random, then checking a trial m may take many character comparisons. If yes, we advance the pattern index and the text index. For the moment, we assume the existence of a “partial match” table Tdescribed belowwhich indicates where we need to look for the start of a new match in the event that the current one ends in a mismatch.

Hirschberg’s algorithm Needleman—Wunsch algorithm Smith—Waterman algorithm. We want to be able to aglorithm up, for each position in Wthe length of the longest possible initial segment of W leading up to but not including that position, other than the full segment starting at W[0] that just failed to match; this is how far we have to backtrack in finding the next match.

Let s be the currently matched k -character prefix of the pattern. No, we now note that there is a shortcut to checking all suffixes: However “B” is not a prefix of the pattern W. The three published it jointly in The difference is that Marching makes use of previous match information that the straightforward algorithm does not.

Knuth–Morris–Pratt algorithm

If t is some proper suffix of s that is also a prefix of sthen we already have a partial match for t. The KMP algorithm has a better worst-case performance than the straightforward algorithm.


If S[] is 1 billion characters and W[] is characters, then the string search should complete after about one billion character comparisons. Journal of Soviet Zlgorithm.

The goal of the table is to allow the algorithm not to match any character of S more than once. When KMP discovers a mismatch, the table determines how much KMP will increase variable m and where it will resume testing variable i. Hence T[i] is exactly ppattern length of the longest possible proper initial segment of W which is also a segment of the substring ending at W[i – 1].

The above example contains all pattegn elements of the algorithm.

Knuth-Morris-Pratt string matching

Thus the algorithm not only omits previously matched characters of S the “AB”but also previously matched characters of W the prefix “AB”. KMP maintains its knowledge in the precomputed table and two state variables.

If we matched the prefix s of the pattern up to and including the character at index iwhat is the length of magching longest proper suffix t of s such that t is also a prefix of s? The chance that the first two letters will match is 1 in 26 2 1 in The most straightforward algorithm is to look for a character match at successive values of the omp mthe position in the string being searched, i.

However, just prior to the end of the lattern partial match, there was that substring “AB” that could be the beginning of a new match, so the algorithm must take this into consideration. If the index m reaches the end of the string then there is no match, in which case the search is said to “fail”. This page was last edited on 21 December lmp, at The principle is that of the overall search: Then it is clear the runtime is 2 n.

It can be done incrementally with an algorithm very similar to the search algorithm. Thus the location m of the beginning of the current potential match is increased.

KMP spends a little time precomputing a table on the order of the size of W[]O nand then it uses that table to do an efficient search of the string in O k. The example above mkp the general technique for assembling the table with a minimum of fuss.


If the strings are uniformly distributed random letters, then the chance that characters match is 1 in The text string can be streamed in because the KMP algorithm does not backtrack in the text.

In other words, we “pre-search” the pattern itself and compile a list of all possible maching positions that bypass a maximum of hopeless characters while not sacrificing any potential matches in doing so.

This was the first linear-time algorithm for string matching. The Wikibook Algorithm implementation has a page on the topic of: Thus the loop executes at most 2 n times, showing that the time complexity of the search algorithm is O n. Except for the fixed overhead incurred in entering and exiting the function, all the computations are performed in the while loop. Here is another way to think about the runtime: As in the first trial, the mismatch causes the matchhing to return to the beginning of W and begins searching at the mismatched character position of S: If all successive characters match in W at position mthen a match is found at that position in the search string.

The only minor complication is that the logic which is correct late in the string erroneously gives non-proper substrings at the beginning. The same logic shows that the longest substring we need consider has length 1, and as in the previous case it fails since “D” is not a prefix of W.

Computing the LSP table is independent of the text string to search. At each position m the algorithm first checks for equality of the first character in the word being searched, i.