Create reverse_factorial_recursive.py

Added reverse factorial recursive algorithm with doctests

Author: afk-Parth

maths/reverse_factorial_recursive.py

@@ -0,0 +1,21 @@
+def reverse_factorial(num: int, i: int = 1) -> int:
+    """
+    Return n if n! equals the given num, else return -1.
+
+    This function finds the integer n such that n! == num using recursion.
+    If no such n exists, returns -1.
+
+    >>> reverse_factorial(120)
+    5
+    >>> reverse_factorial(24)
+    4
+    >>> reverse_factorial(150)
+    -1
+    >>> reverse_factorial(1)
+    1
+    """
+    if num == 1:
+        return i
+    if num % i != 0:
+        return -1
+    return reverse_factorial(num // i, i + 1)