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b96e6c7075
* Added solution for Project Euler problem 174. * Fixed import order and removed executable permission from sol1.py * Update docstrings, doctests, and annotations. Reference: #3256 * Update docstring * Update sol1.py Co-authored-by: Dhruv <dhruvmanila@gmail.com>
53 lines
1.5 KiB
Python
53 lines
1.5 KiB
Python
"""
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Project Euler Problem 174: https://projecteuler.net/problem=174
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We shall define a square lamina to be a square outline with a square "hole" so that
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the shape possesses vertical and horizontal symmetry.
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Given eight tiles it is possible to form a lamina in only one way: 3x3 square with a
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1x1 hole in the middle. However, using thirty-two tiles it is possible to form two
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distinct laminae.
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If t represents the number of tiles used, we shall say that t = 8 is type L(1) and
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t = 32 is type L(2).
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Let N(n) be the number of t ≤ 1000000 such that t is type L(n); for example,
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N(15) = 832.
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What is ∑ N(n) for 1 ≤ n ≤ 10?
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"""
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from collections import defaultdict
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from math import ceil, sqrt
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def solution(t_limit: int = 1000000, n_limit: int = 10) -> int:
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"""
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Return the sum of N(n) for 1 <= n <= n_limit.
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>>> solution(1000,5)
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249
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>>> solution(10000,10)
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2383
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"""
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count: defaultdict = defaultdict(int)
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for outer_width in range(3, (t_limit // 4) + 2):
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if outer_width * outer_width > t_limit:
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hole_width_lower_bound = max(
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ceil(sqrt(outer_width * outer_width - t_limit)), 1
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)
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else:
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hole_width_lower_bound = 1
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hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2
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for hole_width in range(hole_width_lower_bound, outer_width - 1, 2):
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count[outer_width * outer_width - hole_width * hole_width] += 1
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return sum(1 for n in count.values() if 1 <= n <= 10)
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if __name__ == "__main__":
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print(f"{solution() = }")
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