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Z-function and z-algorithm Z-function and z-algorithm
Z-algorithm is a **string-matching algorithm**, which is used to find a place where a string is found within a larger string. It uses the value of **z-function** for a given string. Z-algorithm is a **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 **z-function** to do so.
Let's first see what is a **z-function**. Let's first see what is a **z-function**.
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$O(N)$, as at each step of the algorithm $r$ at least increases one step, and the maximum possible value of r is $n-1$. $O(N)$, as at each step of the algorithm $r$ at least increases one step, and the maximum possible value of r is $n-1$.
## Search for a string ## Z-algorithm
Z-algorithm is used to search all occurrences of pattern-string $p$ in a string $s$ in $O(N)$. Z-algorithm is used to search all occurrences of pattern-string $p$ in a string $s$ in $O(N)$.
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} }
``` ```
Z-function can also be used to solve various string related problems. Let's see some applications.
## To find the period of a string ## To find the period of a string