From cc5751dfc819bd39f263f11913cecb9806e32dcd Mon Sep 17 00:00:00 2001
From: SubhranShu2332 <124662904+SubhranShu2332@users.noreply.github.com>
Date: Sun, 8 Oct 2023 13:56:06 +0530
Subject: [PATCH 1/2] In place of calculating the factorial several times we
 can run a loop k times to calculate the combination

### Describe your change:

for example:
5 C 3 = 5! / (3! * (5-3)! )
= (5 * 4 * 3 * 2 * 1)/[(3 * 2 * 1) * (2 * 1)]
=(5 * 4 * 3)/(3 * 2 * 1)
so running a loop k times will reduce the time complexity to O(k)
---
 maths/combinations.py | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/maths/combinations.py b/maths/combinations.py
index a2324012c01f..d4c03264fbea 100644
--- a/maths/combinations.py
+++ b/maths/combinations.py
@@ -1,9 +1,6 @@
 """
 https://en.wikipedia.org/wiki/Combination
 """
-from math import factorial
-
-
 def combinations(n: int, k: int) -> int:
     """
     Returns the number of different combinations of k length which can
@@ -35,8 +32,11 @@ def combinations(n: int, k: int) -> int:
     # to calculate a factorial of a negative number, which is not possible
     if n < k or k < 0:
         raise ValueError("Please enter positive integers for n and k where n >= k")
-    return factorial(n) // (factorial(k) * factorial(n - k))
-
+    res = 1
+    for i in range(k):
+        res = res * (n - i)
+        res = res // (i + 1)
+    return res
 
 if __name__ == "__main__":
     print(

From 52c9e4b96b4e4993bff3dbbfc4e63d4cfc67acab Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 8 Oct 2023 08:27:31 +0000
Subject: [PATCH 2/2] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/combinations.py | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/maths/combinations.py b/maths/combinations.py
index d4c03264fbea..f65155801b52 100644
--- a/maths/combinations.py
+++ b/maths/combinations.py
@@ -1,6 +1,8 @@
 """
 https://en.wikipedia.org/wiki/Combination
 """
+
+
 def combinations(n: int, k: int) -> int:
     """
     Returns the number of different combinations of k length which can
@@ -38,6 +40,7 @@ def combinations(n: int, k: int) -> int:
         res = res // (i + 1)
     return res
 
+
 if __name__ == "__main__":
     print(
         "The number of five-card hands possible from a standard",