400. Nth Digit

https://leetcode.com/problems/nth-digit/description/
    int findNthDigit(int n) {
        vector<int> sd(9,0);
        int d;
        for(d=1; d<9; d++) {
            // d is the length (digits of a single number) of a number
            // sd is the total digits for length from 1 to d
            sd[d] = d*pow(10, d) - (pow(10,d)-1)/9;
            if(sd[d]>=n) break;
        }
        // the length of number prior to the current length
        int d1 = d-1;
        // total digits for length d is n - total digits for length from 1 to d-1
        n -= sd[d1];
        // the number is i-th of numbers with length d
        int i = (n-1)/d;
        // the first number of length d is
        int a = pow(10, d1);
        // what is the number
        a += i;
        // the digit is the i-th digit of the number a
        i = n - i*d;
        // return the digit
        return (a/(int)(pow(10,d-i))) % 10;
    }