optimizing factorial using memoization

dynamic_programming/factorial.py

@@ -4,21 +4,38 @@
 
 
 @lru_cache
-def factorial(num: int) -> int:
+def factorial(num, _memo=None):
     """
+    Returns the factorial of a non-negative integer using memoization.
+
+    >>> factorial(0)
+    1
+    >>> factorial(5)
+    120
     >>> factorial(7)
     5040
     >>> factorial(-1)
     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 _memo is None:
+        _memo = {}
+
     if num < 0:
         raise ValueError("Number should not be negative.")
 
-    return 1 if num in (0, 1) else num * factorial(num - 1)
+    if num in _memo:
+        return _memo[num]
+
+    if num in (0, 1):
+        _memo[num] = 1
+    else:
+        _memo[num] = num * factorial(num - 1, _memo)
+
+    return _memo[num]
 
 
 if __name__ == "__main__":