Additive Number

Additive number is a string 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.

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.

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

分析：

递归。先确定前两个数，第三个数的位置由前两个数决定。

 public class Solution {
     public boolean isAdditiveNumber(String num) {

         if (num.length() < ) return false;

         for (int i = ; i <= num.length() - ; i++) {
             for (int j = i + ; j <= num.length() - ; j++) {
                 if (helper(num, i, j - i)) {
                     return true;
                 }
             }
         }
         return false;
     }

     private boolean helper(String num, int num1Length, int num2Length) {
         if (num.length() <= num1Length + num2Length) return false;

         String number1 = num.substring(, num1Length);
         String number2 = num.substring(num1Length, num1Length + num2Length);

         if (number1.length() >  && number1.charAt() == '') return false;
         if (number2.length() >  && number2.charAt() == '') return false;

         for (int i = num1Length + num2Length + ; i <= num.length(); i++) {
             String number3 = num.substring(num1Length + num2Length, i);
             if (number3.length() >  && number3.charAt() == '') return false;
             if (Long.parseLong(number1) + Long.parseLong(number2) == Long.parseLong(number3)) {
                 if (i == num.length()) {
                     return true;
                 } else if (helper(num.substring(num1Length), num2Length, i - num1Length - num2Length)) {
                     return true;
                 }
             } else if (Long.parseLong(number1) + Long.parseLong(number2) < Long.parseLong(number3)) {
                 break;
             }
         }
         return false;
     }
 }