357. 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

class Solution(object):
    def countNumbersWithUniqueDigits(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n == 0:
            return 1
        if n == 1:
            return 10
        dp = [0] * (n+1)
        dp[0] = 1
        dp[1] = 9
        sum = dp[0] + dp[1]
        for i in range(2, n+1):
            dp[i] = dp[i-1]*(10-i+1)
            sum += dp[i]
        return sum