Additive number is a positive integer whose digits can form additive sequence. A valid additive sequence should contain at least three numbers. Except for the first two numbers, each subsequent number in the sequence must be the sum of the preceding two.

import java.math.BigInteger;
public class Solution {
    public boolean isAdditiveNumber(String num) {
        if (num == null || num.length() < 3) return false;

        for (int i = 1; i <= num.length() / 2; i++) {
            if (num.charAt(0) == '0' && i > 1) break;
            BigInteger a = new BigInteger(num.substring(0, i));
            for (int j = 1; Math.max(i, j) <= num.length() - i - j; j++) {
                if (num.charAt(i) == '0' && j > 1) break;
                BigInteger b = new BigInteger(num.substring(i, i + j));
                if (isValid(num.substring(i + j), a, b)) {
                    return true;
                }
            }
        }
        return false;
    }

    public boolean isValid(String num, BigInteger a, BigInteger b) {
        if (num.length() == 0) return true;

        b = a.add(b);
        a = b.subtract(a);
        String c = String.valueOf(b);
        return num.startsWith(c) && isValid(num.substring(c.length()), a, b);
    }
}

class Solution(object):
    def isAdditiveNumber(self, num):
        """
        :type num: str
        :rtype: bool
        """
        if not num:
            return True
        for i in xrange(1, len(num) / 2 + 1):
            if num[0] == "0" and i > 1:
                break
            for j in xrange(1, len(num) - i):
                if num[i] == "0" and j > 1:
                    break
                if self.is_valid(int(num[:i]), int(num[i:i + j]), num[i + j:]):
                    return True
        return False

    def is_valid(self, prev_1, prev_2, num):
        if len(num) == 0:
            return True
        curr = str(prev_1 + prev_2)
        if num.startswith(curr) and self.is_valid(prev_2, int(curr), num[len(curr):]):
            return True
        else:
            return False