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
85 lines
2.5 KiB
Python
85 lines
2.5 KiB
Python
"""
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Take the number 192 and multiply it by each of 1, 2, and 3:
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192 * 1 = 192
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192 * 2 = 384
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192 * 3 = 576
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By concatenating each product we get the 1 to 9 pandigital, 192384576.
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We will call 192384576 the concatenated product of 192 and (1,2,3).
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The same can be achieved by starting with 9 and multiplying by 1,2,3,4, and 5,
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giving the pandigital, 918273645, which is the concatenated product of 9 and (1,2,3,4,5).
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What is the largest 1 to 9 pandigital 9-digit number that can be formed as the concatenated product
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of an integer with (1,2,...,n) where n > 1?
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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"Execution time: {end_time - start_time:.6f} seconds")
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return result
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return wrapper
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# def max_pandiMulti():
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# max_num = 0
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# key = [1,2,3,4,5]
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# res = (0, [])
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# ok = False
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# for i in range(9999, 9, -1):
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# mul_keys = [i * j for j in key]
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# for j in range(5) :
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# numx = "".join(map(str, mul_keys[:j+1]))
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# if len(numx) == 9 and set(numx) == set('123456789'):
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# max_num = max(max_num, int(numx))
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# if max_num == int(numx):
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# res = (i, key[:j+1])
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# ok = True
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# break
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# if ok:
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# break
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# return max_num, res
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def max_pandiMulti_better():
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max_num = 0
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res = (0, [])
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# 配置列表：(n, start, end)，其中 start > end，表示从大到小遍历
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configs = [
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(2, 9999, 5000), # n=2: i ∈ [5000, 9999]
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(3, 333, 100), # n=3: i ∈ [100, 333]
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(4, 33, 25), # n=4: i ∈ [25, 33]
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(5, 9, 5) # n=5: i ∈ [5, 9]
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]
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for n, start, end in configs:
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for i in range(start, end - 1, -1):
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# 生成拼接字符串
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s = ''.join(str(i * k) for k in range(1, n + 1))
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# 检查是否为1-9 pandigital
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if set(s) == set('123456789'):
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num = int(s)
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if num > max_num:
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max_num = num
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res = (i, list(range(1, n + 1)))
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break # 当前n中，i递减，第一个满足条件的即为最大，可终止内层循环
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return max_num, res
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@timer
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def main():
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maxnum, ress = max_pandiMulti_better()
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print(f"{maxnum} : {ress}")
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if __name__ == "__main__":
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main()
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