92 lines
2.5 KiB
Python
92 lines
2.5 KiB
Python
"""
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An irrational decimal fraction is created by concatenating the positive integers:
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0.123456789101112131415161718192021...
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It can be seen that the 12th digit of the fractional part is 1.
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If d_n represents the nth digit of the fractional part, find the value of the following expression.
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d_1 × d_10 × d_100 × d_1000 × d_10000 × d_100000 × d_1000000
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"""
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import time
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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"{func.__name__} time: {end_time - start_time:.6f} seconds")
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return result
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return wrapper
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class ChampernownesConstant:
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def __init__(self):
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self._cache = "123456789"
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self._level = 1
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self._nth = 1
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def __iter__(self):
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if self._nth > len(self._cache):
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self._level += 1
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self._cache += "".join(str(i) for i in range(10**(self._level-1), 10**self._level))
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yield self._cache[self._nth-1]
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self._nth += 1
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def __next__(self):
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return next(self.__iter__())
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def get_nth_digit(self, nth:int) -> int :
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while True:
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if nth > len(self._cache):
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self._level += 1
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self._cache += "".join(str(i) for i in range(10**(self._level-1), 10**self._level))
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else:
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return int(self._cache[nth-1])
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@timer
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def main_longstring() -> None:
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gen = ChampernownesConstant()
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ziel = [1,10,100,1000,10000,100000,1000000]
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res = 1
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for i in ziel:
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res *= gen.get_nth_digit(i)
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print(res)
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def length_numbers(k:int) -> int :
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"""计算前k位数的总位数"""
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if k == 0:
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return 0
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return (10**k * (9*k - 1) + 1) // 9
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def get_nth_digit(nth:int) -> int :
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if nth < 0 :
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raise ValueError("nth must be non-negative")
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level = 1
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while length_numbers(level) < nth :
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level += 1
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# 计算在k位数中的偏移量
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offset = nth - length_numbers(level-1) # 在k位数中的第几个数字
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num_index = (offset - 1) // level # 第几个k位数（从0开始）
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num = 10**(level-1) + num_index # 具体的数字
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digit_index = (offset - 1) % level # 在数字中的位置
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return int(str(num)[digit_index])
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@timer
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def main_quick() -> None :
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ziel = [1,10,100,1000,10000,100000,1000000]
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res = 1
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for i in ziel:
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res *= get_nth_digit(i)
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print(res)
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if __name__ == "__main__":
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main_longstring()
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main_quick()
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