Add Z-function algorithm implementation

strings/z_function.py

@@ -0,0 +1,61 @@
+"""
+https://cp-algorithms.com/string/z-function.html
+
+For given string this algorithm computes value for each index,
+which represents the maximal length substring starting from the index
+and is same as the prefix of the same size
+
+e.x.  for string 'abab' for second index value would be 2
+
+The main adventage of the algorithm is that it's linear, using dynamic programming
+
+Time Complexity: O(n)  - where n is the length of the string
+
+
+For the value of the first element the algorithm always returns 0
+
+"""
+
+
+def z_function(input_str: str) -> list:
+    """
+    Will convert the entire string to uppercase letters
+
+    >>> z_function("abracadabra")
+    [0, 0, 0, 1, 0, 1, 0, 4, 0, 0, 1]
+    >>> z_function("aaaa")
+    [0, 3, 2, 1]
+    >>> z_function("zxxzxxz")
+    [0, 0, 0, 4, 0, 0, 1]
+
+    """
+
+    z_result = [0] * len(input_str)
+
+    # initialize interval's left pointer and right pointer
+    left_pointer, right_pointer = 0, 0
+
+    for i in range(1, len(input_str)):
+        # case when current index is inside the interval
+        if i <= right_pointer:
+            min_edge = min(right_pointer - i + 1, z_result[i - left_pointer])
+            z_result[i] = min_edge
+
+        while go_next(i, z_result, input_str):
+            z_result[i] += 1
+
+        # if new index's result gives us more right interval, we've to update left_pointer and right_pointer
+        if i + z_result[i] - 1 > right_pointer:
+            left_pointer, right_pointer = i, i + z_result[i] - 1
+
+    return z_result
+
+
+# helping function which checks if following elements are equal or not
+def go_next(i, z_result, s):
+    return i + z_result[i] < len(s) and s[z_result[i]] == s[i + z_result[i]]
+
+
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()