357. Count Numbers with Unique Digits 数学 找规律

Given a non-negative integer n, count all numbers with unique digits, x, where 0 ≤ x < 10n.

Example:

Given n = 2, return 91. (The answer should be the total numbers in the range of 0 ≤ x < 100, excluding 

[11,22,33,44,55,66,77,88,99]

)

Credits:

Special thanks to @memoryless for adding this problem and creating all test cases.

class Solution {
public:
    int countNumbersWithUniqueDigits(int n) {
        if(n==0) return 1;
        if(n==1) return 10;
        int res=10;
        int temp=81;
        int i=8;
        while(n>1)
        {
            res+=temp;
            temp*=i--;
            n--;
        }
        return res;
    }
};