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62 lines
1.6 KiB
Python
62 lines
1.6 KiB
Python
"""
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Project Euler Problem 10: https://projecteuler.net/problem=10
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Summation of primes
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The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
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Find the sum of all the primes below two million.
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References:
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- https://en.wikipedia.org/wiki/Prime_number
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- https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
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"""
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def solution(n: int = 2000000) -> int:
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"""
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Returns the sum of all the primes below n using Sieve of Eratosthenes:
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The sieve of Eratosthenes is one of the most efficient ways to find all primes
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smaller than n when n is smaller than 10 million. Only for positive numbers.
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>>> solution(1000)
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76127
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>>> solution(5000)
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1548136
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>>> solution(10000)
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5736396
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>>> solution(7)
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10
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>>> solution(7.1) # doctest: +ELLIPSIS
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Traceback (most recent call last):
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...
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TypeError: 'float' object cannot be interpreted as an integer
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>>> solution(-7) # doctest: +ELLIPSIS
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Traceback (most recent call last):
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...
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IndexError: list assignment index out of range
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>>> solution("seven") # doctest: +ELLIPSIS
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Traceback (most recent call last):
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...
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TypeError: can only concatenate str (not "int") to str
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"""
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primality_list = [0 for i in range(n + 1)]
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primality_list[0] = 1
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primality_list[1] = 1
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for i in range(2, int(n**0.5) + 1):
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if primality_list[i] == 0:
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for j in range(i * i, n + 1, i):
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primality_list[j] = 1
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sum_of_primes = 0
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for i in range(n):
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if primality_list[i] == 0:
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sum_of_primes += i
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return sum_of_primes
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if __name__ == "__main__":
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print(f"{solution() = }")
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