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2104fa7aeb
* fixes #5434 * fixes broken solution * removes assert * removes assert * Apply suggestions from code review Co-authored-by: John Law <johnlaw.po@gmail.com> * Update project_euler/problem_003/sol1.py Co-authored-by: John Law <johnlaw.po@gmail.com>
105 lines
2.6 KiB
Python
105 lines
2.6 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(number: int) -> bool:
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"""Checks to see if a number is a prime in O(sqrt(n)).
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A number is prime if it has exactly two factors: 1 and itself.
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Returns boolean representing primality of given number (i.e., if the
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result is true, then the number is indeed prime else it is not).
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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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False
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>>> is_prime(1)
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False
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"""
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if 1 < number < 4:
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# 2 and 3 are primes
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return True
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elif number < 2 or number % 2 == 0 or number % 3 == 0:
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# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
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return False
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# All primes number are in format of 6k +/- 1
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for i in range(5, int(math.sqrt(number) + 1), 6):
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if number % i == 0 or number % (i + 2) == 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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