81 lines
1.8 KiB
Python
81 lines
1.8 KiB
Python
"""
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It can be seen that the number, 125874, and its double, 251748,
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contain exactly the same digits, but in a different order.
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Find the smallest positive integer, x, such that
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2x, 3x, 4x, 5x, and 6x contain the same digits.
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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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elapsed_time = end_time - start_time
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print(f"{func.__name__} time: {elapsed_time:.6f} seconds")
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return result
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return wrapper
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def has_same_digits(x, y):
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return sorted(str(x)) == sorted(str(y))
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def signature(n):
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count = [0] * 10
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while n:
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count[n % 10] += 1
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n //= 10
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return tuple(count)
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def find_smallest_permuted_multiple():
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x = 1
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while True:
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if not x % 9 == 0:
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x += 1
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continue
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for i in range(2, 7):
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if not has_same_digits(x, x * i):
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break
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else:
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return x
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x += 1
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def better_permuted_multiple():
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n = 1
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while True:
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start = 10 ** (n - 1)
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# 核心约束：x * 6 必须仍是n位数
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end = int(10**n / 6) + 1
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# 步长为9：利用模9同余原理
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for x in range((start + 8) // 9 * 9, end, 9):
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sig = signature(x)
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# 检查2x到6x是否共享相同签名
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if all(signature(k * x) == sig for k in range(2, 7)):
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return x
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n += 1
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@timer
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def main():
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result = find_smallest_permuted_multiple()
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print(f"{result}")
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@timer
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def main_better():
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result = better_permuted_multiple()
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print(f"{result}")
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if __name__ == "__main__":
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main()
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main_better()
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