From 27fce127b26b1c46121583340fd70af53bdfd08a Mon Sep 17 00:00:00 2001
From: Nadim Najjar <nadim.najjar@live.com>
Date: Tue, 15 Jul 2025 17:02:29 +0300
Subject: [PATCH 1/2] optimizing factorial using memoization

---
 dynamic_programming/factorial.py | 23 +++++++++++++++++++----
 1 file changed, 19 insertions(+), 4 deletions(-)

diff --git a/dynamic_programming/factorial.py b/dynamic_programming/factorial.py
index 1c9c927f5af3..b838f2a755a3 100644
--- a/dynamic_programming/factorial.py
+++ b/dynamic_programming/factorial.py
@@ -4,24 +4,39 @@
 
 
 @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__":
     import doctest
-
     doctest.testmod()

From e9e3cdacea4231c174f4b70f4d10a7ad5a6f7eee Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 15 Jul 2025 14:05:01 +0000
Subject: [PATCH 2/2] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 dynamic_programming/factorial.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/dynamic_programming/factorial.py b/dynamic_programming/factorial.py
index b838f2a755a3..158da7d8523f 100644
--- a/dynamic_programming/factorial.py
+++ b/dynamic_programming/factorial.py
@@ -37,6 +37,8 @@ def factorial(num, _memo=None):
 
     return _memo[num]
 
+
 if __name__ == "__main__":
     import doctest
+
     doctest.testmod()