357. Count Numbers with Unique Digits

https://leetcode.com/problems/count-numbers-with-unique-digits/description/

Description

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

Solution

class Solution(object):
    def countNumbersWithUniqueDigits(self, n):
        """
        :type n: int
        :rtype: int
        """
        from math import factorial
        ret = 0
        for zero_cnt in range(n+1):
            if n-zero_cnt>9:
                continue
            v = n-zero_cnt+1
            if v>n: v = 1
            for i in range(n-zero_cnt):
                v *= (9-i)
            ret += v
        return ret