Given a non-negative integer num, repeatedly add all its digits until the result has only one digit. For example: Given num = 38, the process is like: 3 + 8 = 11, 1 + 1 = 2. Since 2 has only one digit, return it.

DigitRootProblem.java

//Digit root Problem

//Congruence formula
public int addDigits(int n) {
    int b = 10;

    if(n == 0) return 0;
    else if(n % (b - 1) == 0) return b-1;
    else return n % (b - 1);      

    // or directly  return 1 + (num - 1) % 9;
}

// Brute Force
public int addDigits2(int n) {
    int ans = 0;
    while(n > 9) {
        int result = 0;
        while(n > 0) {
            result += n%10;
            n/=10;
        }
        n = result;
    }               
    return n;
}