TheAlgorithms-Python

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"""
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Project Euler Problem 6: https://projecteuler.net/problem=6
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Sum square difference
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The sum of the squares of the first ten natural numbers is,
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    1^2 + 2^2 + ... + 10^2 = 385
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The square of the sum of the first ten natural numbers is,
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    (1 + 2 + ... + 10)^2 = 55^2 = 3025
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Hence the difference between the sum of the squares of the first ten
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natural numbers and the square of the sum is 3025 - 385 = 2640.
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Find the difference between the sum of the squares of the first one
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hundred natural numbers and the square of the sum.
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"""
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def solution(n: int = 100) -> int:
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    """
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    Returns the difference between the sum of the squares of the first n
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    natural numbers and the square of the sum.
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    >>> solution(10)
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    2640
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    >>> solution(15)
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    13160
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    >>> solution(20)
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    41230
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    >>> solution(50)
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    1582700
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    """
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    sum_cubes = (n * (n + 1) // 2) ** 2
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    sum_squares = n * (n + 1) * (2 * n + 1) // 6
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    return sum_cubes - sum_squares
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if __name__ == "__main__":
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    print(f"{solution() = }")
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