95 lines
3.2 KiB
Python
95 lines
3.2 KiB
Python
"""
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The fraction 49/98 is a curious fraction,
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as an inexperienced mathematician in attempting to simplify it may incorrectly believe
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that 49/98 = 4/8 , which is correct, is obtained by cancelling the 9s.
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We shall consider fractions like, 30/50=3/5 , to be trivial examples.
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There are exactly four non-trivial examples of this type of fraction,
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less than one in value, and containing two digits in the numerator and denominator.
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If the product of these four fractions is given in its lowest common terms,
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find the value of the denominator.
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"""
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import time
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from functools import reduce
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from math import gcd
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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__} taken: {end_time - start_time:.6f} seconds")
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return result
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return wrapper
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@timer
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def main() -> None:
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res = list()
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for numerator in range(12, 100):
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for denominator in range(numerator * 2, 100):
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if numerator % 10 == 0 and denominator % 10 == 0:
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continue
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all_nums = set(
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[numerator // 10, numerator % 10, denominator // 10, denominator % 10]
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)
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if len(all_nums) == 3:
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a = [i for i in str(numerator) if i not in str(denominator)][0]
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b = [i for i in str(denominator) if i not in str(numerator)][0]
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if a != "0" and b != "0":
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if (int(a) / int(b)) == (numerator / denominator):
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print(f"{numerator}/{denominator}")
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res.append((numerator, denominator))
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res = reduce(lambda x, y: (x[0] * y[0], x[1] * y[1]), res)
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res = res[1] // gcd(res[0], res[1])
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print(f"Answer: {res}")
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@timer
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def main_two() -> None:
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results = []
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for numerator in range(11, 100):
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for denominator in range(numerator + 1, 100): # 分母必须大于分子
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# 检查是否构成非平凡的情况（有共同数字但不是都为0）
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num_str, den_str = str(numerator), str(denominator)
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common_digits = set(num_str) & set(den_str)
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# 排除平凡情况和没有共同数字的情况
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if len(common_digits) != 1 or "0" in common_digits:
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continue
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common_digit = list(common_digits)[0]
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# 构造约分后的分数
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simplified_num = int(num_str.replace(common_digit, "", 1))
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simplified_den = int(den_str.replace(common_digit, "", 1))
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# 避免除以0
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if simplified_den == 0:
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continue
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# 检查分数是否相等
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if numerator * simplified_den == denominator * simplified_num:
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print(f"{numerator}/{denominator} = {simplified_num}/{simplified_den}")
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results.append((numerator, denominator))
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# 计算最终结果（所有分数乘积的分母）
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product_num = reduce(lambda x, y: x * y[0], results, 1)
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product_den = reduce(lambda x, y: x * y[1], results, 1)
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# 化简分数
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common_divisor = gcd(product_num, product_den)
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final_answer = product_den // common_divisor
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print(f"Answer: {final_answer}")
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if __name__ == "__main__":
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main()
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main_two()
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