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In place of calculating the factorial several times we can run a loop k times to calculate the combination (#10051)

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* 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)

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* Update maths/combinations.py

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SubhranShu2332 2023-10-09 00:47:02 +05:30 committed by GitHub
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maths/combinations.py
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@ -1,7 +1,6 @@
""" """
https://en.wikipedia.org/wiki/Combination https://en.wikipedia.org/wiki/Combination
""" """
from math import factorial
def combinations(n: int, k: int) -> int: def combinations(n: int, k: int) -> int:
@ -35,7 +34,11 @@ def combinations(n: int, k: int) -> int:
# to calculate a factorial of a negative number, which is not possible # to calculate a factorial of a negative number, which is not possible
if n < k or k < 0: if n < k or k < 0:
raise ValueError("Please enter positive integers for n and k where n >= k") 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 *= n - i
res //= i + 1
return res
if __name__ == "__main__": if __name__ == "__main__":