> For the complete documentation index, see [llms.txt](https://nataliekung.gitbook.io/ladder_code/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://nataliekung.gitbook.io/ladder_code/l4dong-tai-gui-hua/count-numbers-with-unique-digits.md).

# Count Numbers with Unique Digits

Given a**non-negative**integer n, count all numbers with unique digits, x, where 0 ≤ x < 10n.

**Example:**

```
Input: 
2
Output: 
91 

Explanation: 
The answer should be the total numbers in the range of 0 ≤ x <100, 
excluding 11,22,33,44,55,66,77,88,99
```

分析

就是从高位起loop每个位，每个往后的数，可选数字都只能少一个，排列组合思想

```
class Solution:
    def countNumbersWithUniqueDigits(self, n: int) -> int:
        if n == 0:
            return 1
        res = 10
        avail = uniq = 9
        for i in range(2,n+1):
            uniq = avail*uniq
            res+= uniq
            avail -=1
        return res
```