357. Count Numbers with Unique Digits

https://leetcode.com/problems/count-numbers-with-unique-digits/
dfs解法：

class Solution {
    int res;
    void dfs(vector& used, int left) {
        if(left == 0) {return;}
        for(int i = 0; i <= 9; i++) {
            if(used[i]) 
                continue;
            used[i] = true;
            if(!i == 0)
                res ++;
            dfs(used,left-1);
            used[i] = false;
        }
    }
public:
    int countNumbersWithUniqueDigits(int n) {
        if(n > 10) 
            n = 10;
        vector used(10,false);
        res = 0;
        dfs(used,n);
        return res+1;
    }
};    

dp解法？其实我这个应该算是找规律...：

class Solution {
public:
    int countNumbersWithUniqueDigits(int n) {
        if(n > 10) 
            n = 10;
        if(n <= 0) return 1;
        if(n == 1) return 10;
        int res = 10;
        int count = 9;
        int factor = 9;
        for(int i = 2; i <= n; i++) {
            count = count * factor;
            factor--;
            res += count;
        }
        return res;
    }
};