Update reverse_factorial_recursive.py

Author: afk-Parth

maths/reverse_factorial_recursive.py

@@ -1,10 +1,25 @@
-def reverse_factorial(num: int, i: int = 1) -> int:
+def reverse_factorial(n: int, divisor: int = 1) -> int:
     """
-    Return n if n! equals the given num, else return -1.
+    Return x such that x! equals the given n, or -1 if no such integer exists.
 
-    This function finds the integer n such that n! == num using recursion.
-    If no such n exists, returns -1.
+    This function recursively divides the number `n` by successive integers 
+    starting from 1 until it reaches 1. If the division completes exactly at 1,
+    the last divisor - 1 is the factorial root. Otherwise, return -1.
 
+    Parameters
+    ----------
+    n : int
+        The number whose factorial root is to be found.
+    divisor : int, optional
+        The current divisor used in the recursion (default is 1).
+
+    Returns
+    -------
+    int
+        The factorial root if it exists, otherwise -1.
+
+    Examples
+    --------
     >>> reverse_factorial(120)
     5
     >>> reverse_factorial(24)
@@ -13,9 +28,13 @@ def reverse_factorial(num: int, i: int = 1) -> int:
     -1
     >>> reverse_factorial(1)
     1
+    >>> reverse_factorial(720)
+    6
     """
-    if num == 1:
-        return i
-    if num % i != 0:
+    if n < 1:
+        raise ValueError("Input must be a positive integer.")
+    if n == 1:
+        return divisor
+    if n % divisor != 0:
         return -1
-    return reverse_factorial(num // i, i + 1)
+    return reverse_factorial(n // divisor, divisor + 1)