Add recursive factorial implementation

DIRECTORY.md

@@ -1028,6 +1028,8 @@
   * [Activity Selection](other/activity_selection.py)
   * [Alternative List Arrange](other/alternative_list_arrange.py)
   * [Bankers Algorithm](other/bankers_algorithm.py)
+  * [Cheap Progress](other/cheap_progress.py)
+  * [Dancing Links](other/dancing_links.py)
   * [Davis Putnam Logemann Loveland](other/davis_putnam_logemann_loveland.py)
   * [Doomsday](other/doomsday.py)
   * [Fischer Yates Shuffle](other/fischer_yates_shuffle.py)
@@ -1051,6 +1053,7 @@
   * [Scoring Algorithm](other/scoring_algorithm.py)
   * [Sdes](other/sdes.py)
   * [Sliding Window Maximum](other/sliding_window_maximum.py)
+  * [Token Bucket](other/token_bucket.py)
   * [Tower Of Hanoi](other/tower_of_hanoi.py)
   * [Word Search](other/word_search.py)
 

maths/factorial.py

@@ -5,11 +5,17 @@
 
 def factorial(number: int) -> int:
     """
-    Calculate the factorial of specified number (n!).
+    Calculate the factorial of the specified number.
 
     >>> import math
     >>> all(factorial(i) == math.factorial(i) for i in range(20))
     True
+    >>> factorial(0)
+    1
+    >>> factorial(1)
+    1
+    >>> factorial(5)
+    120
     >>> factorial(0.1)
     Traceback (most recent call last):
         ...
@@ -18,12 +24,6 @@ def factorial(number: int) -> int:
     Traceback (most recent call last):
         ...
     ValueError: factorial() not defined for negative values
-    >>> factorial(1)
-    1
-    >>> factorial(6)
-    720
-    >>> factorial(0)
-    1
     """
     if number != int(number):
         raise ValueError("factorial() only accepts integral values")
@@ -35,14 +35,19 @@ def factorial(number: int) -> int:
     return value
 
 
-def factorial_recursive(n: int) -> int:
+def factorial_recursive(number: int) -> int:
     """
-    Calculate the factorial of a positive integer
-    https://en.wikipedia.org/wiki/Factorial
+    Calculate the factorial of a number using recursion.
 
     >>> import math
     >>> all(factorial_recursive(i) == math.factorial(i) for i in range(20))
     True
+    >>> factorial_recursive(0)
+    1
+    >>> factorial_recursive(1)
+    1
+    >>> factorial_recursive(5)
+    120
     >>> factorial_recursive(0.1)
     Traceback (most recent call last):
         ...
@@ -52,17 +57,16 @@ def factorial_recursive(n: int) -> int:
         ...
     ValueError: factorial_recursive() not defined for negative values
     """
-    if not isinstance(n, int):
+    if not isinstance(number, int):
         raise ValueError("factorial_recursive() only accepts integral values")
-    if n < 0:
+    if number < 0:
         raise ValueError("factorial_recursive() not defined for negative values")
-    return 1 if n in {0, 1} else n * factorial_recursive(n - 1)
+    return 1 if number in {0, 1} else number * factorial_recursive(number - 1)
 
 
 if __name__ == "__main__":
     import doctest
 
     doctest.testmod()
-
     n = int(input("Enter a positive integer: ").strip() or 0)
-    print(f"factorial{n} is {factorial(n)}")
+    print(f"{n = } {factorial(n) = } {factorial_recursive(n) = }")