算法题解之图论与搜索

Additive Number

加法数

思路：一开始以为要用DP来做，但是这道题除非能保证每个相加数的划分是唯一的（事实上不是唯一的），否则只能用搜索。      

 1 public class Solution {
 2     public boolean isAdditiveNumber(String num) {
 3         for (int firstEnd = 0; firstEnd <= num.length() - 3; firstEnd++) {
 4             if (num.charAt(0) == '0' && firstEnd > 0) {
 5                 break;
 6             }
 7             for (int secondEnd = firstEnd + 1; secondEnd <= num.length() - 2; secondEnd++) {
 8                 if (num.charAt(firstEnd + 1) == '0' && secondEnd > firstEnd + 1) {
 9                     break;
10                 }
11                 long first = Long.parseLong(num.substring(0, firstEnd + 1));
12                 long second = Long.parseLong(num.substring(firstEnd + 1, secondEnd + 1));
13                 if (helper(num, secondEnd + 1, first + second, second)) {
14                     return true;
15                 }
16             }
17         }
18         return false;
19     }
20     
21     public boolean helper(String num, int start, long expect_num, long pre_num) {
22         if (start > num.length() - 1) {
23             return true;
24         }
25         if (num.charAt(start) == '0' && expect_num != 0) {
26             return false;
27         }
28         int end = start + String.valueOf(expect_num).length() - 1;
29         if (end + 1 > num.length()) {
30             return false;
31         }
32         long cur = Long.parseLong(num.substring(start, end + 1));
33         if (cur == expect_num) {
34             long next_expect = pre_num + cur;
35             return helper(num, end + 1, next_expect, cur);
36         }
37         return false;
38     }
39 }

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