mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 09:10:16 +00:00
dc4f603dad
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
59 lines
1.5 KiB
Python
59 lines
1.5 KiB
Python
"""
|
|
Project Euler Problem 187: https://projecteuler.net/problem=187
|
|
|
|
A composite is a number containing at least two prime factors.
|
|
For example, 15 = 3 x 5; 9 = 3 x 3; 12 = 2 x 2 x 3.
|
|
|
|
There are ten composites below thirty containing precisely two,
|
|
not necessarily distinct, prime factors: 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.
|
|
|
|
How many composite integers, n < 10^8, have precisely two,
|
|
not necessarily distinct, prime factors?
|
|
"""
|
|
|
|
from math import isqrt
|
|
|
|
|
|
def calculate_prime_numbers(max_number: int) -> list[int]:
|
|
"""
|
|
Returns prime numbers below max_number
|
|
|
|
>>> calculate_prime_numbers(10)
|
|
[2, 3, 5, 7]
|
|
"""
|
|
|
|
is_prime = [True] * max_number
|
|
for i in range(2, isqrt(max_number - 1) + 1):
|
|
if is_prime[i]:
|
|
for j in range(i**2, max_number, i):
|
|
is_prime[j] = False
|
|
|
|
return [i for i in range(2, max_number) if is_prime[i]]
|
|
|
|
|
|
def solution(max_number: int = 10**8) -> int:
|
|
"""
|
|
Returns the number of composite integers below max_number have precisely two,
|
|
not necessarily distinct, prime factors
|
|
|
|
>>> solution(30)
|
|
10
|
|
"""
|
|
|
|
prime_numbers = calculate_prime_numbers(max_number // 2)
|
|
|
|
semiprimes_count = 0
|
|
left = 0
|
|
right = len(prime_numbers) - 1
|
|
while left <= right:
|
|
while prime_numbers[left] * prime_numbers[right] >= max_number:
|
|
right -= 1
|
|
semiprimes_count += right - left + 1
|
|
left += 1
|
|
|
|
return semiprimes_count
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(f"{solution() = }")
|