357. Count Numbers with Unique Digits

 Let f(k) = count of numbers with unique digits with length equals k.
# f(1) = 10, ..., f(k) = 9 * 9 * 8 * ... (9 - k + 2)
#    [The first factor is 9 because a number cannot start with 0].
#dynamic programming
class Solution(object):
    def countNumbersWithUniqueDigits(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n==0: 
            return 1
        res,count=10,9
        for i in xrange(2,n+1):
            count*=(11-i)
            res+=count
        return res