306. Additive Number

For example:
"112358" is an additive number because the digits can form an additive sequence: 1, 1, 2, 3, 5, 8.
1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8

"199100199" is also an additive number, the additive sequence is: 1, 99, 100, 199.
1 + 99 = 100, 99 + 100 = 199

Note: Numbers in the additive sequence cannot have leading zeros, so sequence 1, 2, 03 or 1, 02, 3 is invalid.

public class Solution {
    public boolean isAdditiveNumber(String num) {
        if(num == null || num.length() == 0) return false;
        int n = num.length();
        for(int i = 1; i <= n/2; i++){                            // len of x1
            for(int j = 1; Math.max(i, j) + i + j <= n; j++) {    // len of x2
                if(isValid(i, j, num)) return true;
            }
        }
        return false;
    }
    
    public boolean isValid(int i, int j, String num){
        if(i > 1 && num.charAt(0) == '0') return false;
        if(j > 1 && num.charAt(i) == '0') return false;
        String sum;
        Long x1 = Long.parseLong(num.substring(0, i));
        Long x2 = Long.parseLong(num.substring(i, i+j));
        for(int start = i + j; start < num.length(); start += sum.length()){
            x2 = x1 + x2;            // sum of x1 and x2, and became new x2
            x1 = x2 - x1;            // last x2 is new x1
            sum = x2.toString();
            if(!num.startsWith(sum, start)) return false;
        }
        return true;
    }
}