mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-01 00:41:09 +00:00
98e9d6bdb6
* Fix style of the first ten solutions for Project Euler - Unify the header docstring, and add reference URLs to wikipedia or similar - Fix docstrings to be properly multilined - Add newlines where appropriate - Add doctests where they were missing - Remove doctests that test for the correct solution - fix obvious spelling or grammar mistakes in comments and exception messages - Fix line endings to be UNIX. This makes two of the files seem to have changed completely - no functional changes in any of the solutions were done (except for the spelling fixes mentioned above) * Fix docstrings and main function as per Style Guide
105 lines
2.5 KiB
Python
105 lines
2.5 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 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:
|
|
return True
|
|
elif num % 2 == 0:
|
|
return False
|
|
for i in range(3, int(math.sqrt(num)) + 1, 2):
|
|
if num % i == 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 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() = }")
|