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Prefix function and KMP-algorithm Prefix function and KMP-algorithm
KMP-algorithm is a widely used **string-matching algorithm**, which is used to find a place where a string is found within a larger string. It uses the value of **prefix function** for a given string. KMP-algorithm is a widely used **string-matching algorithm**, which is used to find a place where a string is found within a larger string. For example, `p = "ab"` and `s = "abbbabab"`, then KMP will find us `[0,4,6]` because $s$ has 3 occurrences of `"ab"`. It uses the value of **prefix function** to do so.
Let's first see what is a **prefix function**. Let's first see what is a **prefix function**.
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} }
``` ```
Prefix function can also be used to solve various string related problems. Let's see some applications.
## Find a period of a string ## Find a period of a string
Period of a string is the shortest length such that a larger string $s$ can be represented as a concatenation of one or more copies of a substring($t$). Period of a string is the shortest length such that a larger string $s$ can be represented as a concatenation of one or more copies of a substring($t$).