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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

Constraints:

0 <= n <= 8

分析

F(0) = 1 F(1) = 10 F(2) = 10 +9(第一个数不能为0)9(可以从0~9中选出一个任意一个不与第一位相同的数)

F(3) = 10 +99 + 998 F(4) = …

F(n) = F(n-1) + 9 * 8 * …* 9-n+1;

public int countNumbersWithUniqueDigits(int n) {
           if(n == 0) return 1;        int sum = 10;        int step = 9;        int K = 9;        for( int i = 0 ; i < n-1;i ++){
               step = step *(K -i);            sum += step;        }        return sum;    }

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