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bcfca67faa
* [mypy] fix type annotations for problem003/sol1 and problem003/sol3 * [mypy] fix type annotations for project euler problem007/sol2 * [mypy] fix type annotations for project euler problem008/sol2 * [mypy] fix type annotations for project euler problem009/sol1 * [mypy] fix type annotations for project euler problem014/sol1 * [mypy] fix type annotations for project euler problem 025/sol2 * [mypy] fix type annotations for project euler problem026/sol1.py * [mypy] fix type annotations for project euler problem037/sol1 * [mypy] fix type annotations for project euler problem044/sol1 * [mypy] fix type annotations for project euler problem046/sol1 * [mypy] fix type annotations for project euler problem051/sol1 * [mypy] fix type annotations for project euler problem074/sol2 * [mypy] fix type annotations for project euler problem080/sol1 * [mypy] fix type annotations for project euler problem099/sol1 * [mypy] fix type annotations for project euler problem101/sol1 * [mypy] fix type annotations for project euler problem188/sol1 * [mypy] fix type annotations for project euler problem191/sol1 * [mypy] fix type annotations for project euler problem207/sol1 * [mypy] fix type annotations for project euler problem551/sol1
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 isprime(num: int) -> bool:
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"""
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Returns boolean representing primality of given number num.
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>>> isprime(2)
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True
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>>> isprime(3)
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True
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>>> isprime(27)
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False
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>>> isprime(2999)
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True
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>>> isprime(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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>>> isprime(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 isprime(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 isprime(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 isprime(n // i):
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max_number = n // i
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break
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elif isprime(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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