maths/basic_maths.py · 编程语言算法集/Python

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Python

maths

basic_maths.py

basic_maths.py 3.04 KB

"""Implementation of Basic Math in Python."""

import math

def prime_factors(n: int) -> list:
 """Find Prime Factors.
 >>> prime_factors(100)
 [2, 2, 5, 5]
 >>> prime_factors(0)
 Traceback (most recent call last):
 ...
 ValueError: Only positive integers have prime factors
 >>> prime_factors(-10)
 Traceback (most recent call last):
 ...
 ValueError: Only positive integers have prime factors
 """
 if n <= 0:
 raise ValueError("Only positive integers have prime factors")
 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
 >>> number_of_divisors(0)
 Traceback (most recent call last):
 ...
 ValueError: Only positive numbers are accepted
 >>> number_of_divisors(-10)
 Traceback (most recent call last):
 ...
 ValueError: Only positive numbers are accepted
 """
 if n <= 0:
 raise ValueError("Only positive numbers are accepted")
 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
 if n > 1:
 div *= 2
 return div

def sum_of_divisors(n: int) -> int:
 """Calculate Sum of Divisors.
 >>> sum_of_divisors(100)
 217
 >>> sum_of_divisors(0)
 Traceback (most recent call last):
 ...
 ValueError: Only positive numbers are accepted
 >>> sum_of_divisors(-10)
 Traceback (most recent call last):
 ...
 ValueError: Only positive numbers are accepted
 """
 if n <= 0:
 raise ValueError("Only positive numbers are accepted")
 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
 >>> euler_phi(0)
 Traceback (most recent call last):
 ...
 ValueError: Only positive numbers are accepted
 >>> euler_phi(-10)
 Traceback (most recent call last):
 ...
 ValueError: Only positive numbers are accepted
 """
 if n <= 0:
 raise ValueError("Only positive numbers are accepted")
 s = n
 for x in set(prime_factors(n)):
 s *= (x - 1) / x
 return int(s)

if __name__ == "__main__":
 import doctest

doctest.testmod()

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pre-commit-ci[bot] 提交于 2024年03月13日 14:52 +08:00 . [pre-commit.ci] pre-commit autoupdate (#11322)

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"""Implementation of Basic Math in Python."""

import math


def prime_factors(n: int) -> list:
 """Find Prime Factors.
 >>> prime_factors(100)
 [2, 2, 5, 5]
 >>> prime_factors(0)
 Traceback (most recent call last):
 ...
 ValueError: Only positive integers have prime factors
 >>> prime_factors(-10)
 Traceback (most recent call last):
 ...
 ValueError: Only positive integers have prime factors
 """
 if n <= 0:
 raise ValueError("Only positive integers have prime factors")
 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
 >>> number_of_divisors(0)
 Traceback (most recent call last):
 ...
 ValueError: Only positive numbers are accepted
 >>> number_of_divisors(-10)
 Traceback (most recent call last):
 ...
 ValueError: Only positive numbers are accepted
 """
 if n <= 0:
 raise ValueError("Only positive numbers are accepted")
 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
 if n > 1:
 div *= 2
 return div


def sum_of_divisors(n: int) -> int:
 """Calculate Sum of Divisors.
 >>> sum_of_divisors(100)
 217
 >>> sum_of_divisors(0)
 Traceback (most recent call last):
 ...
 ValueError: Only positive numbers are accepted
 >>> sum_of_divisors(-10)
 Traceback (most recent call last):
 ...
 ValueError: Only positive numbers are accepted
 """
 if n <= 0:
 raise ValueError("Only positive numbers are accepted")
 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
 >>> euler_phi(0)
 Traceback (most recent call last):
 ...
 ValueError: Only positive numbers are accepted
 >>> euler_phi(-10)
 Traceback (most recent call last):
 ...
 ValueError: Only positive numbers are accepted
 """
 if n <= 0:
 raise ValueError("Only positive numbers are accepted")
 s = n
 for x in set(prime_factors(n)):
 s *= (x - 1) / x
 return int(s)


if __name__ == "__main__":
 import doctest

 doctest.testmod()