String Searching Algorithm:

String searching algorithms, sometimes called string matching algorithms, are an important class of string algorithms that try to find a place where one or several strings (also called patterns) are found within a larger string or text.
Let Σ be an alphabet (finite set). Formally, both the pattern and searched text are concatenations of elements of Σ. The Σ may be a usual human alphabet (for example, the letters A through Z in English). Other applications may use binary alphabet (Σ = {0,1}) or DNA alphabet (Σ = {A,C,G,T}) in bioinformatics.
In practice how the string is encoded can affect the feasible string search algorithms. In particular if a variable width encoding is in use then it is slow (time proportional to N) to find the Nth character. This will significantly slow down many of the more advanced search algorithms. A possible solution is to search for the sequence of code units instead, but doing so may produce false matches unless the encoding is specifically designed to avoid it.
Naïve String Search:
The simplest and least efficient way to see where one string occurs inside another is to check each place it could be, one by one, to see if it's there. So first we see if there's a copy of the needle in the first few characters 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; if not, we look starting at the third character, and so forth.

Finite State automation based search:
In this approach, we avoid backtracking by constructing a deterministic finite automaton that recognizes strings containing the desired search string. These are expensive to construct—they are usually created using the powerset construction—but very quick to use. This approach is frequently generalized in practice to search for arbitrary regular expressions.
Index methods
Faster search algorithms are based on preprocessing of 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 Θ(m) time, and all z occurrences of a pattern can be found in O(m + z) time (if the alphabet size is viewed as a constant).