55db5a1b8d
* Add new solution for the euler project problem 9 - precompute the squares. * Update sol4.py * updating DIRECTORY.md * Update sol4.py * Update sol4.py * Update sol4.py --------- Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru> Co-authored-by: MaximSmolskiy <MaximSmolskiy@users.noreply.github.com>
61 lines
1.3 KiB
Python
61 lines
1.3 KiB
Python
"""
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Project Euler Problem 9: https://projecteuler.net/problem=9
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Special Pythagorean triplet
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A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
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a^2 + b^2 = c^2.
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For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
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There exists exactly one Pythagorean triplet for which a + b + c = 1000.
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Find the product abc.
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References:
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- https://en.wikipedia.org/wiki/Pythagorean_triple
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"""
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def get_squares(n: int) -> list[int]:
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"""
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>>> get_squares(0)
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[]
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>>> get_squares(1)
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[0]
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>>> get_squares(2)
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[0, 1]
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>>> get_squares(3)
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[0, 1, 4]
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>>> get_squares(4)
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[0, 1, 4, 9]
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"""
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return [number * number for number in range(n)]
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def solution(n: int = 1000) -> int:
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"""
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Precomputing squares and checking if a^2 + b^2 is the square by set look-up.
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>>> solution(12)
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60
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>>> solution(36)
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1620
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"""
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squares = get_squares(n)
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squares_set = set(squares)
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for a in range(1, n // 3):
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for b in range(a + 1, (n - a) // 2 + 1):
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if (
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squares[a] + squares[b] in squares_set
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and squares[n - a - b] == squares[a] + squares[b]
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):
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return a * b * (n - a - b)
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return -1
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if __name__ == "__main__":
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print(f"{solution() = }")
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