Python实现获取第n个丑数

丑数：只包含质因子2，3和5的数称作丑数（Ugly Number），1为最小丑数

核心思想：新丑数一定是由已得丑数乘丑数因子得到的，要得到有序丑数列表，在已得丑数列表基础上依次追加未得最小丑数即可，进而可得第n个丑数

完整方法：

import numpy as np
from datetime import datetime


# 获取第n个丑数，n从1开始
# 返回：目标丑数，丑数列表
# 丑数：只包含质因子2，3和5的数称作丑数（Ugly Number），1为最小丑数
# 核心思想：新丑数一定是由已得丑数乘丑数因子得到的，要得到有序丑数列表，在已得丑数列表基础上依次追加未得最小丑数即可，进而可得第n个丑数
def getUglyNumber(n):
    if n < 1:
        return 0, []

    # 入参为序号，转为索引
    index = n - 1

    # 定义丑数列表并初始化前3个，3以后的丑数由程序有序添加
    ugly = [1, 2, 3]
    if index < 3:
        return ugly[index], ugly

    '''
    定义并初始化最小预备丑数二维数组
    数组每行分别为2、3、5对应最小预备丑数 和 计算最小预备丑数时使用的丑数列表中丑数的索引
    最小预备丑数=丑数因子*丑数列表中该丑数因子未乘的最小丑数  
    '''
    ugly_factor = [2, 3, 5]  # 丑数因子
    pro_ugly = np.array([[ugly_factor[0] * ugly[1], 1],  # 2已加入丑数列表，此处放2*2=4
                         [ugly_factor[1] * ugly[1], 1],  # 3已加入丑数列表，此处放3*2=6
                         [ugly_factor[2] * ugly[0], 0]])  # 此处放5*1=5

    # 向丑数列表中有序追加丑数，直到丑数数量达到要获取的序号（入参）
    while (True):

        # 从最小预备丑数二维数组中获取最小预备丑数、丑数列表索引和丑数因子索引
        ugly_factor_index = np.argmin(pro_ugly[:, 0])  # 丑数因子索引
        min_pro_ugly, ugly_index = pro_ugly[ugly_factor_index]  # 最小预备丑数、丑数列表索引

        # 将获取到的最小预备丑数追加到丑数列表
        # 注意，因为获取到的最小预备丑数一定大于丑数列表中的丑数，所以该追加是自然有序的
        ugly.append(min_pro_ugly)

        # 若找到第index个丑数，返回该丑数和丑数列表
        if (len(ugly) > index):
            return ugly[index], ugly

        # 更新取走的最小预备丑数
        while (True):

            # 计算新的最小预备丑数，丑数因子*丑数列表中该丑数因子未乘的最小丑数
            ugly_index += 1
            new_pro_ugly = ugly_factor[ugly_factor_index] * ugly[ugly_index]

            # 更新取走的最小预备丑数，新最小预备丑数不可以与已存在的最小预备丑数重复
            if (new_pro_ugly not in pro_ugly[:, 0]):
                pro_ugly[ugly_factor_index] = [new_pro_ugly, ugly_index]
                break

测试结果：

# 测试
begin = datetime.now()
uglyNum, ugly = getUglyNumber(1500)
end = datetime.now()
print("uglyNum", uglyNum)
print("uglyNum", ugly)
print("time consuming(microseconds)", (end - begin).microseconds)

# 输出：第1500个丑数、前1500个丑数列表、获取丑数耗时（微秒）
uglyNum 859963392
uglyNum [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 81, 90, 96, 100, 108, 120, 125, 128, 135, 144, 150, 160, 162, 180, 192, 200, 216, 225, 240, 243, 250, 256, 270, 288, 300, 320, 324, 360, 375, 384, 400, 405, 432, 450, 480, 486, 500, 512, 540, 576, 600, 625, 640, 648, 675, 720, 729, 750, 768, 800, 810, 864, 900, 960, 972, 1000, 1024, 1080, 1125, 1152, 1200, 1215, 1250, 1280, 1296, 1350, 1440, 1458, 1500, 1536, 1600, 1620, 1728, 1800, 1875, 1920, 1944, 2000, 2025, 2048, 2160, 2187, 2250, 2304, 2400, 2430, 2500, 2560, 2592, 2700, 2880, 2916, 3000, 3072, 3125, 3200, 3240, 3375, 3456, 3600, 3645, 3750, 3840, 3888, 4000, 4050, 4096, 4320, 4374, 4500, 4608, 4800, 4860, 5000, 5120, 5184, 5400, 5625, 5760, 5832, 6000, 6075, 6144, 6250, 6400, 6480, 6561, 6750, 6912, 7200, 7290, 7500, 7680, 7776, 8000, 8100, 8192, 8640, 8748, 9000, 9216, 9375, 9600, 9720, 10000, 10125, 10240, 10368, 10800, 10935, 11250, 11520, 11664, 12000, 12150, 12288, 12500, 12800, 12960, 13122, 13500, 13824, 14400, 14580, 15000, 15360, 15552, 15625, 16000, 16200, 16384, 16875, 17280, 17496, 18000, 18225, 18432, 18750, 19200, 19440, 19683, 20000, 20250, 20480, 20736, 21600, 21870, 22500, 23040, 23328, 24000, 24300, 24576, 25000, 25600, 25920, 26244, 27000, 27648, 28125, 28800, 29160, 30000, 30375, 30720, 31104, 31250, 32000, 32400, 32768, 32805, 33750, 34560, 34992, 36000, 36450, 36864, 37500, 38400, 38880, 39366, 40000, 40500, 40960, 41472, 43200, 43740, 45000, 46080, 46656, 46875, 48000, 48600, 49152, 50000, 50625, 51200, 51840, 52488, 54000, 54675, 55296, 56250, 57600, 58320, 59049, 60000, 60750, 61440, 62208, 62500, 64000, 64800, 65536, 65610, 67500, 69120, 69984, 72000, 72900, 73728, 75000, 76800, 77760, 78125, 78732, 80000, 81000, 81920, 82944, 84375, 86400, 87480, 90000, 91125, 92160, 93312, 93750, 96000, 97200, 98304, 98415, 100000, 101250, 102400, 103680, 104976, 108000, 109350, 110592, 112500, 115200, 116640, 118098, 120000, 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time consuming(microseconds) 33982

参考文章：https://blog.csdn.net/leex_brave/article/details/51766194