Python/project_euler/problem_003/sol1.py
Nikos Giachoudis 2104fa7aeb
Unify O(sqrt(N)) is_prime functions under project_euler (#6258)
* 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>
2022-09-14 09:40:04 +01:00

105 lines
2.6 KiB
Python

"""
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
"""
import math
def is_prime(number: int) -> bool:
"""Checks to see if a number is a prime in O(sqrt(n)).
A number is prime if it has exactly two factors: 1 and itself.
Returns boolean representing primality of given number (i.e., if the
result is true, then the number is indeed prime else it is not).
>>> is_prime(2)
True
>>> is_prime(3)
True
>>> is_prime(27)
False
>>> is_prime(2999)
True
>>> is_prime(0)
False
>>> is_prime(1)
False
"""
if 1 < number < 4:
# 2 and 3 are primes
return True
elif number < 2 or number % 2 == 0 or number % 3 == 0:
# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
return False
# All primes number are in format of 6k +/- 1
for i in range(5, int(math.sqrt(number) + 1), 6):
if number % i == 0 or number % (i + 2) == 0:
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 is_prime(n):
return n
while n % 2 == 0:
n //= 2
if is_prime(n):
return n
for i in range(3, int(math.sqrt(n)) + 1, 2):
if n % i == 0:
if is_prime(n // i):
max_number = n // i
break
elif is_prime(i):
max_number = i
return max_number
if __name__ == "__main__":
print(f"{solution() = }")