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1400cb86ff
* Fixes (#5434) * Update ciphers.rabin_miller.py maths.miller_rabin.py * Fixing ERROR maths/miller_rabin.py - ModuleNotFoundError and changing project_euler's isPrime to is_prime function names * Update sol1.py * fix: try to change to list * fix pre-commit * fix capital letters * Update miller_rabin.py * Update rabin_miller.py Co-authored-by: John Law <johnlaw.po@gmail.com>
105 lines
2.5 KiB
Python
105 lines
2.5 KiB
Python
"""
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Project Euler Problem 3: https://projecteuler.net/problem=3
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Largest prime factor
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The prime factors of 13195 are 5, 7, 13 and 29.
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What is the largest prime factor of the number 600851475143?
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References:
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- https://en.wikipedia.org/wiki/Prime_number#Unique_factorization
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"""
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import math
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def is_prime(num: int) -> bool:
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"""
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Returns boolean representing primality of given number num.
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>>> is_prime(2)
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True
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>>> is_prime(3)
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True
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>>> is_prime(27)
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False
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>>> is_prime(2999)
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True
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>>> is_prime(0)
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Traceback (most recent call last):
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...
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ValueError: Parameter num must be greater than or equal to two.
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>>> is_prime(1)
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Traceback (most recent call last):
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...
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ValueError: Parameter num must be greater than or equal to two.
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"""
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if num <= 1:
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raise ValueError("Parameter num must be greater than or equal to two.")
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if num == 2:
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return True
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elif num % 2 == 0:
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return False
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for i in range(3, int(math.sqrt(num)) + 1, 2):
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if num % i == 0:
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return False
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return True
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def solution(n: int = 600851475143) -> int:
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"""
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Returns the largest prime factor of a given number n.
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>>> solution(13195)
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29
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>>> solution(10)
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5
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>>> solution(17)
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17
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>>> solution(3.4)
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3
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>>> solution(0)
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Traceback (most recent call last):
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...
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ValueError: Parameter n must be greater than or equal to one.
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>>> solution(-17)
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Traceback (most recent call last):
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...
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ValueError: Parameter n must be greater than or equal to one.
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>>> solution([])
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Traceback (most recent call last):
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...
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TypeError: Parameter n must be int or castable to int.
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>>> solution("asd")
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Traceback (most recent call last):
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...
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TypeError: Parameter n must be int or castable to int.
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"""
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try:
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n = int(n)
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except (TypeError, ValueError):
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raise TypeError("Parameter n must be int or castable to int.")
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if n <= 0:
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raise ValueError("Parameter n must be greater than or equal to one.")
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max_number = 0
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if is_prime(n):
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return n
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while n % 2 == 0:
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n //= 2
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if is_prime(n):
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return n
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for i in range(3, int(math.sqrt(n)) + 1, 2):
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if n % i == 0:
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if is_prime(n // i):
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max_number = n // i
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break
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elif is_prime(i):
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max_number = i
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return max_number
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if __name__ == "__main__":
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print(f"{solution() = }")
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