# 728. Self Dividing Numbers 自除数

@TOC

## # 题目描述

A self-dividing number is a number that is divisible by every digit it contains.

For example, 128 is a self-dividing number because 128 % 1 == 0, 128 % 2 == 0, and 128 % 8 == 0.

Also, a self-dividing number is not allowed to contain the digit zero.

Given a lower and upper number bound, output a list of every possible self dividing number, including the bounds if possible.

Example 1:

``````Input:
left = 1, right = 22
Output: [1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 22]
``````

Note:

``````The boundaries of each input argument are 1 <= left <= right <= 10000.
``````

## # 解题方法

### # 循环

dividing number 判断的有点麻烦，就是遍历每位数字。

``````class Solution:
def isDividingNumber(self, num):
if '0' in str(num):
return False
return 0 == sum(num % int(i) for i in str(num))
def selfDividingNumbers(self, left, right):
"""
:type left: int
:type right: int
:rtype: List[int]
"""
answer = []
for num in range(left, right+1):
print(num)
if self.isDividingNumber(num):
answer.append(num)
return answer
``````

### # filter函数

``````class Solution(object):
def selfDividingNumbers(self, left, right):
is_self_dividing = lambda num: '0' not in str(num) and all([num % int(digit) == 0 for digit in str(num)])
return filter(is_self_dividing, range(left, right + 1))
``````

As pointed out by @ManuelP, [num % int(digit) == 0 for digit in str(num)] creates an entire list which is not necessary. By leaving out the [ and ], we can make use of generators which are lazy and allows for short-circuit evaluation, i.e. all will terminate as soon as one of the digits fail the check.

The answer below improves the run time from 128 ms to 95 ms:

``````class Solution(object):
def selfDividingNumbers(self, left, right):
is_self_dividing = lambda num: '0' not in str(num) and all(num % int(digit) == 0 for digit in str(num))
return filter(is_self_dividing, range(left, right + 1))
``````

### # 数字迭代

``````class Solution:
def selfDividingNumbers(self, left, right):
"""
:type left: int
:type right: int
:rtype: List[int]
"""
res = []
for num in range(left, right + 1):
if self.isDividing(num):
res.append(num)
return res

def isDividing(self, num):
temp = num
while temp:
div = temp % 10
if not div or num % div != 0:
return False
temp //= 10
return True
``````

## # 日期

2018 年 1 月 13 日 2018 年 11 月 5 日 —— 打了羽毛球，有点累