提问人：Alastair909 提问时间：4/12/2023 最后编辑：Tom KarzesAlastair909 更新时间：4/12/2023 访问量：226
如何使这个用于查找彩色数字的 Python 函数对任何数字进行操作？
How to make this Python function for finding colourful numbers operate on any number?
问：
彩色数字是指在其数字列表中不包含重复项的数字 + 其数字子集的乘积。例如，263 的乘积是 [2， 6， 3， 2x6， 6x3， 2x6x3]。这些都是不同的数字，所以 263 是五颜六色的。
我编写了一些代码来允许长度不超过 3 的整数这样做。它确实有效。它创建数字和子集的列表，然后将该列表转换为集合以删除重复项，然后将列表与集合进行比较。如果没有重复项，则长度将相同。
但是，它应该针对 int 的任何长度进行缩放。它也远非简洁。我应该如何使其具有可扩展性并使其可读性？
这是我的功能。它适用于长度不超过 3 的值。
def is_colorful(num):
str_num = str(num)
combos = []
if len(str_num) == 1:
x = int(str_num[0])
combos.append(x)
if len(str_num) == 2:
x = int(str_num[0])
y = int(str_num[1])
combos.append(x)
combos.append(y)
combos.append(x*y)
if len(str_num) == 3:
x = int(str_num[0])
y = int(str_num[1])
z = int(str_num[2])
combos.append(x)
combos.append(y)
combos.append(z)
combos.append(x*y)
combos.append(y*z)
combos.append(x*y*z)
set_combos = set(combos)
print(set_combos)
return True if len(set_combos) == len(combos) else False
答：
1赞
constantstranger
4/12/2023
#1
下面是一种扩展它的方法：
def is_colorful(num):
# disqualify as colorful if:
# - there are multiple digits and one of them is 0 or 1
# - any digit is a duplicate
n, prods = num, set()
while n:
digit = n % 10
if prods and digit in (0,1) or digit in prods:
return False
n, prods = n // 10, prods | {digit}
# disqualify as colorful if:
# - the product of the digits in any subset is a duplicate
n, prods = num, set()
while n:
digit, curProds = n % 10, set()
for prd in (p * digit for p in (f for group in (prods, [1]) for f in group)):
if prd in prods:
return False
curProds.add(prd)
n, prods = n // 10, prods | curProds
return True
top = 1
while top <= 10_000_000:
colorful = []
for i in range(top):
if is_colorful(i):
colorful.append(i)
print(f'for 0 to {top}, ',
f'the count of colorful numbers is {len(colorful)}), ',
f'percent = {100 * len(colorful) / top}%')
top *= 10
输出：
for 0 to 1, the count of colorful numbers is 1, percent = 100.0%
for 0 to 10, the count of colorful numbers is 10, percent = 100.0%
for 0 to 100, the count of colorful numbers is 74, percent = 74.0%
for 0 to 1000, the count of colorful numbers is 454, percent = 45.4%
for 0 to 10000, the count of colorful numbers is 2194, percent = 21.94%
for 0 to 100000, the count of colorful numbers is 7690, percent = 7.69%
for 0 to 1000000, the count of colorful numbers is 17530, percent = 1.753%
for 0 to 10000000, the count of colorful numbers is 23290, percent = 0.2329%
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