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Reduced Time Complexity to O(sqrt(n)) (#7429)

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* Reduced Time Complexity to O(sqrt(n))

* Added testmod

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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Pradyumn Singh Rahar 2022-10-23 17:56:40 +05:30 committed by GitHub
parent b092f9979f
commit a3383ce3fd
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1 changed files with 20 additions and 4 deletions
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24
maths/factors.py
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@ -1,3 +1,7 @@
from doctest import testmod
from math import sqrt
def factors_of_a_number(num: int) -> list:
"""
>>> factors_of_a_number(1)
@ -9,10 +13,22 @@ def factors_of_a_number(num: int) -> list:
>>> factors_of_a_number(-24)
[]
"""
return [i for i in range(1, num + 1) if num % i == 0]
facs: list[int] = []
if num < 1:
return facs
facs.append(1)
if num == 1:
return facs
facs.append(num)
for i in range(2, int(sqrt(num)) + 1):
if num % i == 0: # If i is a factor of num
facs.append(i)
d = num // i # num//i is the other factor of num
if d != i: # If d and i are distinct
facs.append(d) # we have found another factor
facs.sort()
return facs
if __name__ == "__main__":
num = int(input("Enter a number to find its factors: "))
factors = factors_of_a_number(num)
print(f"{num} has {len(factors)} factors: {', '.join(str(f) for f in factors)}")
testmod(name="factors_of_a_number", verbose=True)