306. Additive Number

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Problem

An additive number is a string whose digits can form an 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.

Given a string containing only digits, return true if it is an additive number or false otherwise.

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: "199100199"
Output: true
Explanation: 
The additive sequence is: 1, 99, 100, 199. 
1 + 99 = 100, 99 + 100 = 199

Code

class Solution {
    public boolean isAdditiveNumber(String num) {
        if(num == null || num.length() <= 2) return false;
        
        for(int i = 1; i <= num.length() / 2; i++){
            for(int j = 1; i + j + Math.max(i, j) <= num.length(); j++){
                if(isValid(num, i, j)){
                    return true;
                }
            }
        }
        
        return false;
    }
    
    private boolean isValid(String num, int i, int j){
        if(num.charAt(0) == '0' && i > 1) return false;
        if(num.charAt(i) == '0' && j > 1) return false;
        
        Long sum = (long)0;
        Long x = Long.valueOf(num.substring(0, i));
        Long y = Long.valueOf(num.substring(i, i + j));
        
        for(int start = i + j; start < num.length(); start += String.valueOf(sum).length()){
            sum = x + y;
            x = y;
            y = sum;
            
            if(!num.startsWith(String.valueOf(sum), start)){
                return false;
            }
        }
        
        return true;
    }
}