From 79c7e38bb6fe6ffdd99ddd81d0ccc9b1957be283 Mon Sep 17 00:00:00 2001
From: SubhranShu2332 <124662904+SubhranShu2332@users.noreply.github.com>
Date: Sat, 7 Oct 2023 21:53:11 +0530
Subject: [PATCH 1/4] In place of calculating the factorial several times we
 can run a loop k times to calculate the combination

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 | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

diff --git a/maths/combinations.py b/maths/combinations.py
index a2324012c01f..4cb24c0eb418 100644
--- a/maths/combinations.py
+++ b/maths/combinations.py
@@ -1,8 +1,6 @@
 """
 https://en.wikipedia.org/wiki/Combination
 """
-from math import factorial
-
 
 def combinations(n: int, k: int) -> int:
     """
@@ -35,7 +33,12 @@ 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__":

From ec2491c8835338474acba43d7e4217ec90cc6c71 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sat, 7 Oct 2023 19:51:38 +0000
Subject: [PATCH 2/4] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/combinations.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/maths/combinations.py b/maths/combinations.py
index 4cb24c0eb418..f65155801b52 100644
--- a/maths/combinations.py
+++ b/maths/combinations.py
@@ -2,6 +2,7 @@
 https://en.wikipedia.org/wiki/Combination
 """
 
+
 def combinations(n: int, k: int) -> int:
     """
     Returns the number of different combinations of k length which can
@@ -33,12 +34,11 @@ 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")
-    res=1
+    res = 1
     for i in range(k):
         res = res * (n - i)
         res = res // (i + 1)
     return res
-            
 
 
 if __name__ == "__main__":

From a91ff20bd53e26928ae972037ce9a3c245f8e449 Mon Sep 17 00:00:00 2001
From: Tianyi Zheng <tianyizheng02@gmail.com>
Date: Sun, 8 Oct 2023 15:12:50 -0400
Subject: [PATCH 3/4] Update maths/combinations.py

---
 maths/combinations.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/maths/combinations.py b/maths/combinations.py
index f65155801b52..bf9aa6b7ef90 100644
--- a/maths/combinations.py
+++ b/maths/combinations.py
@@ -36,8 +36,8 @@ def combinations(n: int, k: int) -> int:
         raise ValueError("Please enter positive integers for n and k where n >= k")
     res = 1
     for i in range(k):
-        res = res * (n - i)
-        res = res // (i + 1)
+        res *= (n - i)
+        res //= (i + 1)
     return res
 
 

From 62ba0593297ce4755c86272f0660b9187c9e4e61 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 19:13:16 +0000
Subject: [PATCH 4/4] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/combinations.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/maths/combinations.py b/maths/combinations.py
index bf9aa6b7ef90..6e9e1a807067 100644
--- a/maths/combinations.py
+++ b/maths/combinations.py
@@ -36,8 +36,8 @@ def combinations(n: int, k: int) -> int:
         raise ValueError("Please enter positive integers for n and k where n >= k")
     res = 1
     for i in range(k):
-        res *= (n - i)
-        res //= (i + 1)
+        res *= n - i
+        res //= i + 1
     return res