Question

Given a string S of digits, such as S = “123456579”, we can split it into a Fibonacci-like sequence [123, 456, 579].

Formally, a Fibonacci-like sequence is a list F of non-negative integers such that:

  1. 0 <= F[i] <= 2^31 - 1, (that is, each integer fits a 32-bit signed integer type);
  2. F.length >= 3;
  3. and F[i] + F[i+1] = F[i+2] for all 0 <= i < F.length - 2.

Also, note that when splitting the string into pieces, each piece must not have extra leading zeroes, except if the piece is the number 0 itself.

Return any Fibonacci-like sequence split from S, or return [] if it cannot be done.

Example 1:

Input: "123456579"
Output: [123,456,579]

Example 2:

Input: "11235813"
Output: [1,1,2,3,5,8,13]

Example 3:

Input: "112358130"
Output: []
Explanation: The task is impossible.

Example 4:

Input: "0123"
Output: []
Explanation: Leading zeroes are not allowed, so "01", "2", "3" is not valid.

Example 5:

Input: "1101111"
Output: [110, 1, 111]
Explanation: The output [11, 0, 11, 11] would also be accepted.

Note:

  • 1 <= S.length <= 200
  • S contains only digits.

Solution

  1. Use dfs to solve this question. AC 99.27% 
    class Solution {
 public List<Integer> splitIntoFibonacci(String S) {
     List<Integer> empty = new ArrayList<>();
     if(S == null || S.length() == 0) return empty;
     List<Integer> result = dfs(new ArrayList<Integer>(), S);
     return result == null ? empty : result;
 }
 private List<Integer> dfs(List<Integer> result, String s){
     int len = s.length();
     List<Integer> res = null;
     if(result.size() < 2){
         int size = result.size();
         for(int i = 0; i < (len - (result.size() == 0 ? 2: 1)); i++){
             if(i != 0 && s.charAt(0) == '0') return null;
             long val = Long.parseLong(s.substring(0, i + 1));
             if(val > Integer.MAX_VALUE) return null;
             result.add((int)val);
             res = dfs(result, s.substring(i + 1));
             if(res != null) return res;
             if(size == 0) result.clear();
             else{
                 for(int j = result.size() - 1; j >= 1; j--)
                     result.remove(j);
             }
         }
     }else{
         int pre = result.get(result.size() - 1) + result.get(result.size() - 2);
         if(!s.startsWith("" + pre)) return null;
         result.add(pre);
         if(new String("" + pre).length() == s.length()) return result;
         return dfs(result, s.substring(new String("" + pre).length()));
     }
     return null;
 }
}