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.

842. Split Array into Fibonacci Sequence
``````struct Solution;

impl Solution {
fn split_into_fibonacci(s: String) -> Vec<i32> {
let mut cur = vec![];
let mut res = vec![];
Self::dfs(0, &mut cur, &mut res, &s, s.len());
res
}
fn dfs(start: usize, cur: &mut Vec<i32>, res: &mut Vec<i32>, s: &str, end: usize) {
if start == end && cur.len() > 2 {
*res = cur.to_vec();
} else {
for i in 1..=(end - start) {
let t = &s[start..start + i];
if &s[start..start + 1] == "0" && i > 1 {
break;
}
if let Ok(x) = t.parse::<i32>() {
let n = cur.len();
if n < 2 {
cur.push(x);
Self::dfs(start + i, cur, res, s, end);
cur.pop();
} else {
if x > cur[n - 1] + cur[n - 2] {
break;
}
if x == cur[n - 1] + cur[n - 2] {
cur.push(x);
Self::dfs(start + i, cur, res, s, end);
cur.pop();
}
}
} else {
break;
}
}
}
}
}

#[test]
fn test() {
let s = "123456579".to_string();
let res = vec![123, 456, 579];
assert_eq!(Solution::split_into_fibonacci(s), res);
let s = "11235813".to_string();
let res = vec![1, 1, 2, 3, 5, 8, 13];
assert_eq!(Solution::split_into_fibonacci(s), res);
let s = "112358130".to_string();
let res: Vec<i32> = vec![];
assert_eq!(Solution::split_into_fibonacci(s), res);
let s = "0123".to_string();
let res: Vec<i32> = vec![];
assert_eq!(Solution::split_into_fibonacci(s), res);
let s = "1101111".to_string();
let res = vec![110, 1, 111];
assert_eq!(Solution::split_into_fibonacci(s), res);
}
``````