Python/maths/sieve_of_eratosthenes.py
Joyce 03e7f37329
[mypy] math/sieve_of_eratosthenes: Add type hints (#2627)
* add type hints to math/sieve
* add doctest
* math/sieve: remove manual doctest
* add check for negative
* Update maths/sieve_of_eratosthenes.py
* Update sieve_of_eratosthenes.py

Co-authored-by: Dhruv Manilawala <dhruvmanila@gmail.com>
2020-11-23 11:07:42 +05:30

66 lines
1.6 KiB
Python

"""
Sieve of Eratosthones
The sieve of Eratosthenes is an algorithm used to find prime numbers, less than or
equal to a given value.
Illustration:
https://upload.wikimedia.org/wikipedia/commons/b/b9/Sieve_of_Eratosthenes_animation.gif
Reference: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
doctest provider: Bruno Simas Hadlich (https://github.com/brunohadlich)
Also thanks to Dmitry (https://github.com/LizardWizzard) for finding the problem
"""
import math
from typing import List
def prime_sieve(num: int) -> List[int]:
"""
Returns a list with all prime numbers up to n.
>>> prime_sieve(50)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
>>> prime_sieve(25)
[2, 3, 5, 7, 11, 13, 17, 19, 23]
>>> prime_sieve(10)
[2, 3, 5, 7]
>>> prime_sieve(9)
[2, 3, 5, 7]
>>> prime_sieve(2)
[2]
>>> prime_sieve(1)
[]
"""
if num <= 0:
raise ValueError(f"{num}: Invalid input, please enter a positive integer.")
sieve = [True] * (num + 1)
prime = []
start = 2
end = int(math.sqrt(num))
while start <= end:
# If start is a prime
if sieve[start] is True:
prime.append(start)
# Set multiples of start be False
for i in range(start * start, num + 1, start):
if sieve[i] is True:
sieve[i] = False
start += 1
for j in range(end + 1, num + 1):
if sieve[j] is True:
prime.append(j)
return prime
if __name__ == "__main__":
print(prime_sieve(int(input("Enter a positive integer: ").strip())))