357. Count Numbers with Unique Digits

Given an integer n, return the count of all numbers with unique digits, x, where 0 <= x < 10n.

class Solution {
    int dp[10][1<<10];
    int helper(int mask, int n) {
        if(__builtin_popcount(mask) == n) return 1;
        if(dp[n][mask] != -1) return dp[n][mask];
        int& res = dp[n][mask] = 0;
        for(int i = mask ? 0 : 1; i <= 9; i++) {
            if(mask & (1<<i)) continue;
            res += helper(mask | (1<<i), n);
        }
        return res;
    }
public:
    int countNumbersWithUniqueDigits(int n) {
        memset(dp, -1, sizeof dp);
        int res = 0;
        for(int i = 0; i <= n; i++)
            res += helper(0, i);
        return res;
    }
};