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.

Follow up:

How would you handle overflow for very large input integers?

Credits:

Special thanks to  for adding this problem and creating all test cases.

 

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1 public class Solution { 2     public boolean isAdditiveNumber(String num) { 3         int len = num.length(); 4         for(int i = 1; i <= len/2; i++){ 5             for(int j = 1; Math.max(i,j) <= len-i-j;j++){ 6                 if(isValid(i,j,num)) return true; 7             } 8         } 9         return false;10     }11     12     public boolean isValid(int i,int j,String num){13         if(num.charAt(0) == '0' && i > 1) return false;14         if(num.charAt(i) == '0' && j > 1) return false;15         String sum;16         Long one = Long.parseLong(num.substring(0,i));17         Long two = Long.parseLong(num.substring(i,i+j));18         for(int s = i+j; s < num.length(); s += sum.length()){19             two = two + one;20             one = two - one;21             sum = two.toString();22             if(!num.startsWith(sum,s)) return false;23         }24         return true;25     }26 }

递归解法：

https://discuss.leetcode.com/topic/50580/java-recursive-simple-dfs-solution

https://discuss.leetcode.com/topic/29856/java-recursive-and-iterative-solutions