Editing String-searching algorithm (section)

== Examples of search algorithms ==
=== Naive string search ===
A simple and inefficient way to see where one string occurs inside another is to check at each index, one by one. First, we see if there is a copy of the needle starting at the first character of the haystack; if not, we look to see if there's a copy of the needle starting at the second character of the haystack, and so forth. In the normal case, we only have to look at one or two characters for each wrong position to see that it is a wrong position, so in the average case, this takes [[Big O notation|O]](''n'' + ''m'') steps, where ''n'' is the length of the haystack and ''m'' is the length of the needle; but in the worst case, searching for a string like "aaaab" in a string like "aaaaaaaaab", it takes [[Big O notation|O]](''nm'')

=== Finite-state-automaton-based search ===
[[Image:DFA search mommy.svg|200px|right]]
In this approach, backtracking is avoided by constructing a [[deterministic finite automaton]] (DFA) that recognizes a stored search string. These are expensive to construct—they are usually created using the [[powerset construction]]—but are very quick to use. For example, the [[deterministic finite automaton|DFA]] shown to the right recognizes the word "MOMMY". This approach is frequently generalized in practice to search for arbitrary [[regular expression]]s.

===Stubs===
[[Knuth–Morris–Pratt algorithm|Knuth–Morris–Pratt]] computes a [[deterministic finite automaton|DFA]] that recognizes inputs with the string to search for as a suffix, [[Boyer–Moore string-search algorithm|Boyer–Moore]] starts searching from the end of the needle, so it can usually jump ahead a whole needle-length at each step. Baeza–Yates keeps track of whether the previous ''j'' characters were a prefix of the search string, and is therefore adaptable to [[fuzzy string searching]]. The [[bitap algorithm]] is an application of Baeza–Yates' approach.

=== Index methods ===
Faster search algorithms preprocess the text. After building a [[substring index]], for example a [[suffix tree]] or [[suffix array]], the occurrences of a pattern can be found quickly. As an example, a suffix tree can be built in <math>\Theta(n)</math> time, and all <math>z</math> occurrences of a pattern can be found in <math>O(m)</math> time under the assumption that the alphabet has a constant size and all inner nodes in the suffix tree know what leaves are underneath them. The latter can be accomplished by running a [[Depth-first search|DFS algorithm]] from the root of the suffix tree.

=== Other variants ===
Some search methods, for instance [[trigram search]], are intended to find a "closeness" score between the search string and the text rather than a "match/non-match". These are sometimes called [[Approximate string matching|"fuzzy" searches]].