43. Multiply Strings

the resut of num1[i]*num2[j] is located in result[i+j+1]; if >=10, carry to result[i+j];

class Solution {
    public String multiply(String num1, String num2) {
        int[] result = new int[num1.length()+num2.length()];
        
        //multiply from end to begin
        //the resut of num1[i]*num2[j] is located in result[i+j+1]; if >=10, carry to result[i+j];
        for(int i = num1.length()-1; i>=0; i--){
            for (int j= num2.length()-1; j>=0; j--){
                int multi = (num1.charAt(i)-'0')*(num2.charAt(j)-'0') + result[i+j+1];
                result[i+j+1] = multi%10;
                result[i+j] = result[i+j] + multi/10;
            }
        }
        
        // result[0]=result[0]+carry;
        StringBuilder sb = new StringBuilder();
        for (int i= 0; i<result.length;i++){
            // remember the if condition
            if (!(result[i]==0 && sb.length() == 0)) sb.append(result[i]);
        }
        return sb.length() == 0 ? "0" : sb.toString();
    }
}