Multiply Large Numbers (Strings)

/*
 * Problem : Process two words.
 * Input   : Two words separated by a space.
 * Output  : The product.
 * Approach: Two digit words.
 * Time    : O(m * n)
 * Space   : O(m + 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: A number with m digits times a number with n digits has at most m + n digits.
        int[] product = new int[a.length() + b.length()];
        // Step 2: Multiply each digit pair. Put the result at i + j + 1 and carry to i + j.
        for (int i = a.length() - 1; i >= 0; i--) {
            for (int j = b.length() - 1; j >= 0; j--) {
                int sum = (a.charAt(i) - '0') * (b.charAt(j) - '0') + product[i + j + 1];
                product[i + j + 1] = sum % 10;
                product[i + j] += sum / 10;
            }
        }
        // Step 3: Skip leading zeros, then write the digits.
        StringBuilder result = new StringBuilder();
        for (int digit : product) {
            if (result.length() > 0 || digit != 0) {
                result.append(digit);
            }
        }
        return result.length() == 0 ? "0" : result.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));
    }
}