#### Prefix Function

M
R
```"""
https://cp-algorithms.com/string/prefix-function.html

Prefix function Knuth-Morris-Pratt algorithm

Different algorithm than Knuth-Morris-Pratt pattern finding

E.x. Finding longest prefix which is also suffix

Time Complexity: O(n) - where n is the length of the string
"""

def prefix_function(input_string: str) -> list:
"""
For the given string this function computes value for each index(i),
which represents the longest coincidence of prefix and suffix
for given substring (input_str[0...i])

For the value of the first element the algorithm always returns 0

>>> prefix_function("aabcdaabc")
[0, 1, 0, 0, 0, 1, 2, 3, 4]
[0, 0, 0, 1, 2, 3, 4, 0]
"""

# list for the result values
prefix_result = [0] * len(input_string)

for i in range(1, len(input_string)):
# use last results for better performance - dynamic programming
j = prefix_result[i - 1]
while j > 0 and input_string[i] != input_string[j]:
j = prefix_result[j - 1]

if input_string[i] == input_string[j]:
j += 1
prefix_result[i] = j

return prefix_result

def longest_prefix(input_str: str) -> int:
"""
Prefix-function use case
Finding longest prefix which is suffix as well

>>> longest_prefix("aabcdaabc")
4
4
>>> longest_prefix("abcab")
2
"""

# just returning maximum value of the array gives us answer
return max(prefix_function(input_str))

if __name__ == "__main__":
import doctest

doctest.testmod()
```