Python/maths/basic_maths.py
matkosoric 7f04e5cd34
contribution guidelines checks ()
* spelling corrections

* review

* improved documentation, removed redundant variables, added testing

* added type hint

* camel case to snake case

* spelling fix

* review

* python --> Python # it is a brand name, not a snake

* explicit cast to int

* spaces in int list

* "!= None" to "is not None"

* Update comb_sort.py

* various spelling corrections in documentation & several variables naming conventions fix

* + char in file name

* import dependency - bug fix

Co-authored-by: John Law <johnlaw.po@gmail.com>
2020-03-04 13:40:28 +01:00

81 lines
1.7 KiB
Python

"""Implementation of Basic Math in Python."""
import math
def prime_factors(n: int) -> list:
"""Find Prime Factors.
>>> prime_factors(100)
[2, 2, 5, 5]
"""
pf = []
while n % 2 == 0:
pf.append(2)
n = int(n / 2)
for i in range(3, int(math.sqrt(n)) + 1, 2):
while n % i == 0:
pf.append(i)
n = int(n / i)
if n > 2:
pf.append(n)
return pf
def number_of_divisors(n: int) -> int:
"""Calculate Number of Divisors of an Integer.
>>> number_of_divisors(100)
9
"""
div = 1
temp = 1
while n % 2 == 0:
temp += 1
n = int(n / 2)
div *= temp
for i in range(3, int(math.sqrt(n)) + 1, 2):
temp = 1
while n % i == 0:
temp += 1
n = int(n / i)
div *= temp
return div
def sum_of_divisors(n: int) -> int:
"""Calculate Sum of Divisors.
>>> sum_of_divisors(100)
217
"""
s = 1
temp = 1
while n % 2 == 0:
temp += 1
n = int(n / 2)
if temp > 1:
s *= (2 ** temp - 1) / (2 - 1)
for i in range(3, int(math.sqrt(n)) + 1, 2):
temp = 1
while n % i == 0:
temp += 1
n = int(n / i)
if temp > 1:
s *= (i ** temp - 1) / (i - 1)
return int(s)
def euler_phi(n: int) -> int:
"""Calculate Euler's Phi Function.
>>> euler_phi(100)
40
"""
s = n
for x in set(prime_factors(n)):
s *= (x - 1) / x
return int(s)
if __name__ == "__main__":
print(prime_factors(100))
print(number_of_divisors(100))
print(sum_of_divisors(100))
print(euler_phi(100))