Sidney Zhang
745989cb32
📝 docs(0037.TruncatablePrimes)：添加readme.md文档解释截断素数只有11个的原因 ✨ feat(euler_38.py)：新增全数字倍数问题的解决方案，包含优化算法和详细注释
93 lines
2.4 KiB
Python
93 lines
2.4 KiB
Python
"""
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The number 3797 has an interesting property.
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Being prime itself, it is possible to continuously remove digits from left to right,
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and remain prime at each stage: 3797, 797, 97, and 7.
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Similarly we can work from right to left: 3797, 379, 37, and 3.
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Find the sum of the only eleven primes that are both truncatable from left to right and right to left.
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NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
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"""
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import time
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from itertools import product
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def timer(func):
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def wrapper(*args, **kwargs):
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start_time = time.time()
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result = func(*args, **kwargs)
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end_time = time.time()
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print(f"Time taken: {end_time - start_time:.6f} seconds")
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return result
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return wrapper
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def combine_lists(a: list[int], b: list[int | None], c: list[int]) -> list[int]:
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"""将三个列表的每个元素组合成数字"""
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if b in [[],[None]] :
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return [int(f"{x}{z}") for x, z in product(a, c)]
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return [int(f"{x}{y}{z}") for x, y, z in product(a, b, c)]
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def is_prime(n: int) -> bool:
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"""判断一个数是否为素数"""
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if n < 2:
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return False
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for i in range(2, int(n**0.5) + 1):
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if n % i == 0:
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return False
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return True
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def truncate_left(n: int) -> bool:
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"""从左到右截断一个数"""
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length = len(str(n))
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while n > 0:
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if not is_prime(n):
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return False
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n %= 10 ** (length - 1)
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length -= 1
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return True
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def truncate_right(n: int) -> bool:
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"""从右到左截断一个数"""
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while n > 0:
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if not is_prime(n):
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return False
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n //= 10
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return True
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def TruncatablePrime() -> list[int]:
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begin = [2, 3, 5, 7]
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end = [3, 7]
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middle = [1, 3, 7, 9]
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res = []
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for length in range(2, 7):
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if length - 2 == 0:
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midb = []
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else:
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midb = product(middle, repeat=length - 2)
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midb = [int("".join(map(str, x))) for x in midb]
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nums = combine_lists(begin, midb, end)
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for num in nums:
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if is_prime(num):
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if truncate_left(num) and truncate_right(num):
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res.append(num)
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return res
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@timer
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def main():
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nums = TruncatablePrime()
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for num in nums:
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print(num)
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print(f"Answer: {sum(nums)}")
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if __name__ == "__main__":
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main()
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