mirror of
https://github.com/TheAlgorithms/Python.git
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53ff735701
* Factors of a number * Update factors.py * Fix mypy issue in basic_maths.py * Fix mypy error in perceptron.py * def primes(max: int) -> List[int]: * Update binomial_heap.py * Add a space * Remove a space * Add a space
81 lines
1.7 KiB
Python
81 lines
1.7 KiB
Python
"""Implementation of Basic Math in Python."""
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import math
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def prime_factors(n: int) -> list:
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"""Find Prime Factors.
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>>> prime_factors(100)
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[2, 2, 5, 5]
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"""
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pf = []
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while n % 2 == 0:
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pf.append(2)
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n = int(n / 2)
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for i in range(3, int(math.sqrt(n)) + 1, 2):
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while n % i == 0:
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pf.append(i)
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n = int(n / i)
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if n > 2:
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pf.append(n)
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return pf
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def number_of_divisors(n: int) -> int:
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"""Calculate Number of Divisors of an Integer.
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>>> number_of_divisors(100)
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9
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"""
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div = 1
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temp = 1
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while n % 2 == 0:
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temp += 1
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n = int(n / 2)
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div *= temp
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for i in range(3, int(math.sqrt(n)) + 1, 2):
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temp = 1
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while n % i == 0:
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temp += 1
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n = int(n / i)
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div *= temp
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return div
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def sum_of_divisors(n: int) -> int:
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"""Calculate Sum of Divisors.
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>>> sum_of_divisors(100)
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217
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"""
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s = 1
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temp = 1
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while n % 2 == 0:
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temp += 1
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n = int(n / 2)
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if temp > 1:
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s *= (2 ** temp - 1) / (2 - 1)
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for i in range(3, int(math.sqrt(n)) + 1, 2):
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temp = 1
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while n % i == 0:
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temp += 1
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n = int(n / i)
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if temp > 1:
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s *= (i ** temp - 1) / (i - 1)
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return int(s)
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def euler_phi(n: int) -> int:
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"""Calculte Euler's Phi Function.
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>>> euler_phi(100)
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40
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"""
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s = n
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for x in set(prime_factors(n)):
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s *= (x - 1) / x
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return int(s)
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if __name__ == "__main__":
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print(prime_factors(100))
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print(number_of_divisors(100))
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print(sum_of_divisors(100))
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print(euler_phi(100))
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