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The string spelled by the edges from the root to such a node is a longest repeated substring. The problem of finding the longest substring with at least k {\displaystyle k} occurrences can be solved by first preprocessing the tree to count the number of leaf descendants for each internal node, and then finding the deepest node with at least k ...
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.
Module:String This string handling template returns the number of times that a pattern or search-string occurs in a source string. Counts non-overlapping matches only.
The Boyer–Moore algorithm searches for occurrences of P in T by performing explicit character comparisons at different alignments. Instead of a brute-force search of all alignments (of which there are n − m + 1 {\displaystyle n-m+1} ), Boyer–Moore uses information gained by preprocessing P to skip as many alignments as possible.
A basic example of string searching is when the pattern and the searched text are arrays of elements of an alphabet Σ. Σ may be a human language alphabet, for example, the letters A through Z and other applications may use a binary alphabet (Σ = {0,1}) or a DNA alphabet (Σ = {A,C,G,T}) in bioinformatics.
If we convert strings (with only letters in the English alphabet) into character 3-grams, we get a -dimensional space (the first dimension measures the number of occurrences of "aaa", the second "aab", and so forth for all possible combinations of three letters). Using this representation, we lose information about the string.
Once the grammar has been built for a given input string, in order to achieve effective compression, this grammar has to be encoded efficiently. One of the simplest methods for encoding the grammar is the implicit encoding, which consists on invoking function encodeCFG(X), described below, sequentially on all the axiom's symbols. Intuitively ...
The occurrences of a given pattern in a given string can be found with a string searching algorithm. Finding the longest string which is equal to a substring of two or more strings is known as the longest common substring problem. In the mathematical literature, substrings are also called subwords (in America) or factors (in Europe).