Add Two Huge Numbers (Strings)

/*
 * Problem : Add two big numbers given as text.
 * Input   : Two lines with digits.
 * Output  : The sum.
 * Approach: Add digit by digit with a carry.
 * Time    : O(n)
 * Space   : O(n)
 * Java    : 8 or newer.
 */
import java.util.Scanner;

public class Main {
    // This method solves the task. It receives the input and returns the answer.
    static String solve(String a, String b) {
        // Step 1: Start at the last digit of both numbers. The carry starts at 0.
        StringBuilder result = new StringBuilder();
        int i = a.length() - 1;
        int j = b.length() - 1;
        int carry = 0;

        // Step 2: Continue while there are digits left or a carry is left.
        while (i >= 0 || j >= 0 || carry > 0) {
            // Step 3: Take the digits (0 when a number is already finished) and add the carry.
            int digitA = i >= 0 ? a.charAt(i) - '0' : 0;
            int digitB = j >= 0 ? b.charAt(j) - '0' : 0;
            int total = digitA + digitB + carry;

            // Step 4: The last digit of the total goes to the result. The other part is the new carry.
            result.append(total % 10);
            carry = total / 10;
            i--;
            j--;
        }

        // Step 5: We built the result from right to left, so reverse it.
        return result.reverse().toString();
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        String a = scanner.next();
        String b = scanner.next();
        System.out.println(solve(a, b));
    }
}