306. Additive Number

2023-10-07 20:49

文章标签 number 306 additive

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原文链接：http://blog.csdn.net/sbitswc/article/details/50191729

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?

Solution:

brute force

[java]  view plain copy  
 public class Solution {  
     public boolean isAdditiveNumber(String num) {  
         int len = num.length();  
         if(len<=1) return false;  
         for(int i=1;i<=len/2;i++) {  
             for(int j=1;Math.max(i,j)<=len-i-j;j++) {  
                 if(isValid(i,j,num)) return true;  
             }  
         }  
         return false;  
     }  
     public boolean isValid(int i, int j, String num) {  
         if(num.charAt(i) == '0' && j>1) return false;  
         if(num.charAt(0) == '0' && i>1) return false;  
         Long x1 = Long.parseLong(num.substring(0,i));  
         Long x2 = Long.parseLong(num.substring(i,i+j));  
         String sum = "";  
         for(int k=i+j; k!=num.length();k+=sum.length()) {  
             x2 = x2+ x1;  
             x1 = x2 - x1;  
             sum = x2.toString();  
             if(!num.startsWith(sum, k)) return false;  
         }  
         return true;  
     }  
 }  