fixed error in factorial.py (TheAlgorithms#1888)

* Update factorial.py

* updating DIRECTORY.md

* Update dynamic_programming/factorial.py

* Update factorial.py

Co-authored-by: mateuszz0000 <[email protected]>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Christian Clauss <[email protected]>

dynamic_programming/factorial.py

@@ -1,36 +1,25 @@
 # Factorial of a number using memoization
-result = [-1] * 10
-result[0] = result[1] = 1
 
+from functools import lru_cache
 
-def factorial(num):
+
+@lru_cache
+def factorial(num: int) -> int:
     """
     >>> factorial(7)
     5040
     >>> factorial(-1)
-    'Number should not be negative.'
-    >>> [factorial(i) for i in range(5)]
-    [1, 1, 2, 6, 24]
+    Traceback (most recent call last):
+      ...
+    ValueError: Number should not be negative.
+    >>> [factorial(i) for i in range(10)]
+    [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
     """
-
     if num < 0:
-        return "Number should not be negative."
-    if result[num] != -1:
-        return result[num]
-    else:
-        result[num] = num * factorial(num - 1)
-        # uncomment the following to see how recalculations are avoided
-        # print(result)
-        return result[num]
+        raise ValueError("Number should not be negative.")
 
+    return 1 if num in (0, 1) else num * factorial(num - 1)
 
-# factorial of num
-# uncomment the following to see how recalculations are avoided
-# result=[-1]*10
-# result[0]=result[1]=1
-# print(factorial(5))
-# print(factorial(3))
-# print(factorial(7))
 
 if __name__ == "__main__":
     import doctest