Implement prefix function, knuth-morris-pratt another usage (#2099)

* Implement prefix function, knuth-morris-pratt another usage

* fixup! Format Python code with psf/black push

* Fix style

* updating DIRECTORY.md

* Update prefix_function.py

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Christian Clauss <[email protected]>

Author: 3 people

DIRECTORY.md

@@ -650,6 +650,7 @@
   * [Manacher](https://github.com/TheAlgorithms/Python/blob/master/strings/manacher.py)
   * [Min Cost String Conversion](https://github.com/TheAlgorithms/Python/blob/master/strings/min_cost_string_conversion.py)
   * [Naive String Search](https://github.com/TheAlgorithms/Python/blob/master/strings/naive_string_search.py)
+  * [Prefix Function](https://github.com/TheAlgorithms/Python/blob/master/strings/prefix_function.py)
   * [Rabin Karp](https://github.com/TheAlgorithms/Python/blob/master/strings/rabin_karp.py)
   * [Remove Duplicate](https://github.com/TheAlgorithms/Python/blob/master/strings/remove_duplicate.py)
   * [Reverse Words](https://github.com/TheAlgorithms/Python/blob/master/strings/reverse_words.py)

strings/prefix_function.py

@@ -0,0 +1,65 @@
+"""
+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 sufix
+    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]
+    >>> prefix_function("asdasdad")
+    [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 sufix as well
+
+    >>> longest_prefix("aabcdaabc")
+    4
+    >>> longest_prefix("asdasdad")
+    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()