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project_euler/problem_044/sol1.py
49 строк
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Maxim Smolskiy
Enable ruff RUF002 rule (#11377)
22 апр 2024, 22:51
Не верифицирован
22 апр 2024, 22:51
4700297
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""" Problem 44: https://projecteuler.net/problem=44 Pentagonal numbers are generated by the formula, Pn=n(3n-1)/2. The first ten pentagonal numbers are: 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ... It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference, 70 - 22 = 48, is not pentagonal. Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference are pentagonal and D = |Pk - Pj| is minimised; what is the value of D? """ def is_pentagonal(n: int) -> bool: """ Returns True if n is pentagonal, False otherwise. >>> is_pentagonal(330) True >>> is_pentagonal(7683) False >>> is_pentagonal(2380) True """ root = (1 + 24 * n) ** 0.5 return ((1 + root) / 6) % 1 == 0 def solution(limit: int = 5000) -> int: """ Returns the minimum difference of two pentagonal numbers P1 and P2 such that P1 + P2 is pentagonal and P2 - P1 is pentagonal. >>> solution(5000) 5482660 """ pentagonal_nums = [(i * (3 * i - 1)) // 2 for i in range(1, limit)] for i, pentagonal_i in enumerate(pentagonal_nums): for j in range(i, len(pentagonal_nums)): pentagonal_j = pentagonal_nums[j] a = pentagonal_i + pentagonal_j b = pentagonal_j - pentagonal_i if is_pentagonal(a) and is_pentagonal(b): return b return -1 if __name__ == "__main__": print(f"{solution() = }")