# 842. Split Array into Fibonacci Sequence

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:

• `0 <= F[i] <= 2^31 - 1`, (that is, each integer fits a 32-bit signed integer type);
• `F.length >= 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: []
``````

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. `1 <= S.length <= 200`
2. `S` contains only digits.

``````class Solution {
public:
vector<int> splitIntoFibonacci(string S) {
vector<int> res, out;
helper(S, 0, out, res);
return res;
}
void helper(string& S, int start, vector<int>& out, vector<int>& res) {
if (!res.empty()) return;
if (start >= S.size() && out.size() >= 3) {
res = out; return;
}
for (int i = start; i < S.size(); ++i) {
string cur = S.substr(start, i - start + 1);
if ((cur.size() > 1 && cur[0] == '0') || cur.size() > 10) break;
long num = stol(cur), len = out.size();
if (num > INT_MAX) break;
if (out.size() >= 2 && num != (long)out[len - 1] + out[len - 2]) continue;
out.push_back(num);
helper(S, i + 1, out, res);
out.pop_back();
}
}
};
``````

Fibonacci Number

https://leetcode.com/problems/split-array-into-fibonacci-sequence/

https://leetcode.com/problems/split-array-into-fibonacci-sequence/discuss/133936/short-and-fast-backtracking-solution

LeetCode All in One 题目讲解汇总(持续更新中…)

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