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.

Given a string containing only digits `'0'-'9'`, write a function to determine if it’s an additive number.

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

Example 1:

```Input: "112358"
Output: true
Explanation: 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
```

Example 2:

```Input: "235813"
Output: true
Explanation: The digits can form an additive sequence: 2, 3, 5, 8, 13
2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13```

Java solution

```package in.questionsforinterview.problems;

import java.math.BigInteger;

public static boolean additiveNumberChecker(String num) {
if (num.length() < 3) {
return false;
}
for (int i = 0; i <= num.length()/2; i++) {
if (num.charAt(0) == '0' && i > 0) {
break;
}
BigInteger x1 = new BigInteger(num.substring(0, i + 1));
//make sure remaining size is at least size of first and second integer.
for (int j = i + 1; Math.max(i, j - (i + 1)) + 1 <= num.length() - j - 1 ; j++) {
if (num.charAt(i + 1) == '0' && j > i + 1) {
break;
}
BigInteger x2 = new BigInteger(num.substring(i + 1, j + 1));
if (isValid(num, j + 1, x1, x2)) {
return true;
}
}
}
return false;
}

private static boolean isValid(String num, int start, BigInteger x1, BigInteger x2) {
if (start == num.length()) {
return true;
}
//if num starts with x3 from offset start means x3 is found. So look for next number.
return num.startsWith(x3.toString(), start) && isValid(num, start + x3.toString().length(), x2, x3);
}

// driver method to test the program
public static void main(String...as) {

``````// 1234