mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 09:10:16 +00:00
44254cf112
* Rename all Project Euler directories: Reason: The change was done to maintain consistency throughout the directory and to keep all directories in sorted order. Due to the above change, some config files had to be modified: 'problem_22` -> `problem_022` * Update scripts to pad zeroes in PE directories
58 lines
1.6 KiB
Python
58 lines
1.6 KiB
Python
"""
|
||
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.
|
||
"""
|
||
|
||
|
||
def solution(n: int = 2000000) -> int:
|
||
"""Returns the sum of all the primes below n using Sieve of Eratosthenes:
|
||
|
||
https://en.wikipedia.org/wiki/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.
|
||
|
||
>>> solution(2_000_000)
|
||
142913828922
|
||
>>> solution(1_000)
|
||
76127
|
||
>>> solution(5_000)
|
||
1548136
|
||
>>> solution(10_000)
|
||
5736396
|
||
>>> solution(7)
|
||
10
|
||
>>> solution(7.1) # doctest: +ELLIPSIS
|
||
Traceback (most recent call last):
|
||
...
|
||
TypeError: 'float' object cannot be interpreted as an integer
|
||
>>> solution(-7) # doctest: +ELLIPSIS
|
||
Traceback (most recent call last):
|
||
...
|
||
IndexError: list assignment index out of range
|
||
>>> solution("seven") # doctest: +ELLIPSIS
|
||
Traceback (most recent call last):
|
||
...
|
||
TypeError: can only concatenate str (not "int") to str
|
||
"""
|
||
primality_list = [0 for i in range(n + 1)]
|
||
primality_list[0] = 1
|
||
primality_list[1] = 1
|
||
|
||
for i in range(2, int(n ** 0.5) + 1):
|
||
if primality_list[i] == 0:
|
||
for j in range(i * i, n + 1, i):
|
||
primality_list[j] = 1
|
||
sum_of_primes = 0
|
||
for i in range(n):
|
||
if primality_list[i] == 0:
|
||
sum_of_primes += i
|
||
return sum_of_primes
|
||
|
||
|
||
if __name__ == "__main__":
|
||
print(solution(int(input().strip())))
|