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In computer science, a substring index is a data structure which gives substring search in a text or text collection in sublinear time. Once constructed from a document or set of documents, a substring index can be used to locate all occurrences of a pattern in time linear or near-linear in the pattern size, with no dependence or only logarithmic dependence on the document size.
The variable z is used to hold the length of the longest common substring found so far. The set ret is used to hold the set of strings which are of length z. The set ret can be saved efficiently by just storing the index i, which is the last character of the longest common substring (of size z) instead of S[i-z+1..i].
After computing E(i, j) for all i and j, we can easily find a solution to the original problem: it is the substring for which E(m, j) is minimal (m being the length of the pattern P.) Computing E ( m , j ) is very similar to computing the edit distance between two strings.
A string-matching algorithm wants to find the starting index m in string S[] that matches the search word W[].. The most straightforward algorithm, known as the "brute-force" or "naive" algorithm, is to look for a word match at each index m, i.e. the position in the string being searched that corresponds to the character S[m].
P denotes the string to be searched for, called the pattern. Its length is m. S[i] denotes the character at index i of string S, counting from 1. S[i..j] denotes the substring of string S starting at index i and ending at j, inclusive. A prefix of S is a substring S[1..i] for some i in range [1, l], where l is the length of S.
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.
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.
The total length of all the strings on all of the edges in the tree is (), but each edge can be stored as the position and length of a substring of S, giving a total space usage of () computer words. The worst-case space usage of a suffix tree is seen with a fibonacci word , giving the full 2 n {\displaystyle 2n} nodes.