count-numbers-with-unique-digits.py

# Time:  O(n)
# Space: O(1)

class Solution(object):
    def countNumbersWithUniqueDigits(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n == 0:
            return 1
        count, fk = 10, 9
        for k in xrange(2, n+1):
            fk *= 10 - (k-1)
            count += fk
        return count