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Commit c585cb1

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mindauglMaximSmolskiypre-commit-ci[bot]
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Solution for the Euler Project problem 136 (#12658)
* Add initial version of file for the Euler project problem 136 solution. * Add documentation and tests for the Euler project problem 136 solution. * Update sol1.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update sol1.py * Update sol1.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update sol1.py * Update sol1.py * Update sol1.py * Update sol1.py * Update sol1.py * Update sol1.py --------- Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
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‎project_euler/problem_136/__init__.py

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‎project_euler/problem_136/sol1.py

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"""
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Project Euler Problem 136: https://projecteuler.net/problem=136
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Singleton Difference
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The positive integers, x, y, and z, are consecutive terms of an arithmetic progression.
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Given that n is a positive integer, the equation, x^2 - y^2 - z^2 = n,
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has exactly one solution when n = 20:
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13^2 - 10^2 - 7^2 = 20.
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In fact there are twenty-five values of n below one hundred for which
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the equation has a unique solution.
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How many values of n less than fifty million have exactly one solution?
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By change of variables
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x = y + delta
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z = y - delta
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The expression can be rewritten:
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x^2 - y^2 - z^2 = y * (4 * delta - y) = n
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The algorithm loops over delta and y, which is restricted in upper and lower limits,
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to count how many solutions each n has.
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In the end it is counted how many n's have one solution.
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"""
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def solution(n_limit: int = 50 * 10**6) -> int:
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"""
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Define n count list and loop over delta, y to get the counts, then check
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which n has count == 1.
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>>> solution(3)
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0
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>>> solution(10)
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3
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>>> solution(100)
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25
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>>> solution(110)
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27
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"""
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n_sol = [0] * n_limit
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for delta in range(1, (n_limit + 1) // 4 + 1):
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for y in range(4 * delta - 1, delta, -1):
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n = y * (4 * delta - y)
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if n >= n_limit:
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break
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n_sol[n] += 1
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ans = 0
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for i in range(n_limit):
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if n_sol[i] == 1:
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ans += 1
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return ans
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if __name__ == "__main__":
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print(f"{solution() = }")

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