Update reverse_factorial_recursive.py

Author: afk-Parth

maths/reverse_factorial_recursive.py

@@ -1,40 +1,55 @@
-def reverse_factorial(n: int, divisor: int = 1) -> int:
+def reverse_factorial_recursive(value: int, current_divisor: int = 1) -> int:
     """
-    Return x such that x! equals the given n, or -1 if no such integer exists.
+    Return x such that x! == value, otherwise return -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.
+    The function divides `value` by 1, 2, 3, ... recursively. If the repeated
+    division reduces `value` exactly to 1, the factorial root x is
+    (current_divisor - 1). If the division ever has a remainder, no integer x
+    exists and the function returns -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).
+    value : int
+        The positive integer to test (candidate factorial value).
+    current_divisor : int, optional
+        The current divisor used while reducing `value` (default is 1).
 
     Returns
     -------
     int
-        The factorial root if it exists, otherwise -1.
+        The factorial root (x) if x! == value, otherwise -1.
 
     Examples
     --------
-    >>> reverse_factorial(120)
+    >>> reverse_factorial_recursive(120)
     5
-    >>> reverse_factorial(24)
+    >>> reverse_factorial_recursive(24)
     4
-    >>> reverse_factorial(150)
+    >>> reverse_factorial_recursive(150)
     -1
-    >>> reverse_factorial(1)
+    >>> reverse_factorial_recursive(1)
     1
-    >>> reverse_factorial(720)
-    6
+    >>> reverse_factorial_recursive(2)
+    2
     """
-    if n < 1:
-        raise ValueError("Input must be a positive integer.")
-    if n == 1:
-        return divisor
-    if n % divisor != 0:
+    if not isinstance(value, int):
+        raise TypeError("value must be an integer")
+    if not isinstance(current_divisor, int):
+        raise TypeError("current_divisor must be an integer")
+
+    if value < 1:
+        raise ValueError("value must be a positive integer")
+
+    # Special-case: initial call with value == 1 should return 1 (since 1! = 1).
+    if value == 1 and current_divisor == 1:
+        return 1
+
+    # If value reduced to 1 during recursion, the factorial root is divisor - 1.
+    if value == 1:
+        return current_divisor - 1
+
+    # If not divisible by the current divisor, it's not a factorial number.
+    if value % current_divisor != 0:
         return -1
-    return reverse_factorial(n // divisor, divisor + 1)
+
+    return reverse_factorial_recursive(value // current_divisor, current_divisor + 1)