Python/project_euler/problem_003/sol1.py

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"""
Project Euler Problem 3: https://projecteuler.net/problem=3
Largest prime factor
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143?
References:
- https://en.wikipedia.org/wiki/Prime_number#Unique_factorization
"""
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import math
def isprime(num: int) -> bool:
"""
Returns boolean representing primality of given number num.
>>> isprime(2)
True
>>> isprime(3)
True
>>> isprime(27)
False
>>> isprime(2999)
True
>>> isprime(0)
Traceback (most recent call last):
...
ValueError: Parameter num must be greater than or equal to two.
>>> isprime(1)
Traceback (most recent call last):
...
ValueError: Parameter num must be greater than or equal to two.
"""
if num <= 1:
raise ValueError("Parameter num must be greater than or equal to two.")
if num == 2:
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return True
elif num % 2 == 0:
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return False
for i in range(3, int(math.sqrt(num)) + 1, 2):
if num % i == 0:
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return False
return True
def solution(n: int = 600851475143) -> int:
"""
Returns the largest prime factor of a given number n.
>>> solution(13195)
29
>>> solution(10)
5
>>> solution(17)
17
>>> solution(3.4)
3
>>> solution(0)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater than or equal to one.
>>> solution(-17)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater than or equal to one.
>>> solution([])
Traceback (most recent call last):
...
TypeError: Parameter n must be int or castable to int.
>>> solution("asd")
Traceback (most recent call last):
...
TypeError: Parameter n must be int or castable to int.
"""
try:
n = int(n)
except (TypeError, ValueError):
raise TypeError("Parameter n must be int or castable to int.")
if n <= 0:
raise ValueError("Parameter n must be greater than or equal to one.")
max_number = 0
if isprime(n):
return n
while n % 2 == 0:
n //= 2
if isprime(n):
return n
for i in range(3, int(math.sqrt(n)) + 1, 2):
if n % i == 0:
if isprime(n / i):
max_number = n / i
break
elif isprime(i):
max_number = i
return max_number
if __name__ == "__main__":
print(f"{solution() = }")