Python/project_euler/problem_10/sol3.py

"""
https://projecteuler.net/problem=10

Problem Statement:
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

Find the sum of all the primes below two million using Sieve_of_Eratosthenes:

The sieve of Eratosthenes is one of the most efficient ways to find all primes
smaller than n when n is smaller than 10 million.  Only for positive numbers.
"""


def prime_sum(n: int) -> int:
    """ Returns the sum of all the primes below n.

    >>> prime_sum(2_000_000)
    142913828922
    >>> prime_sum(1_000)
    76127
    >>> prime_sum(5_000)
    1548136
    >>> prime_sum(10_000)
    5736396
    >>> prime_sum(7)
    10
    >>> prime_sum(7.1)  # doctest: +ELLIPSIS
    Traceback (most recent call last):
    ...
    TypeError: 'float' object cannot be interpreted as an integer
    >>> prime_sum(-7)  # doctest: +ELLIPSIS
    Traceback (most recent call last):
    ...
    IndexError: list assignment index out of range
    >>> prime_sum("seven")  # doctest: +ELLIPSIS
    Traceback (most recent call last):
    ...
    TypeError: can only concatenate str (not "int") to str
    """
    list_ = [0 for i in range(n + 1)]
    list_[0] = 1
    list_[1] = 1

    for i in range(2, int(n ** 0.5) + 1):
        if list_[i] == 0:
            for j in range(i * i, n + 1, i):
                list_[j] = 1
    s = 0
    for i in range(n):
        if list_[i] == 0:
            s += i
    return s


if __name__ == "__main__":
    # import doctest
    # doctest.testmod()
    print(prime_sum(int(input().strip())))