<p>You are given a string of digits <code>num</code>, such as <code>&quot;123456579&quot;</code>. We can split it into a Fibonacci-like sequence <code>[123, 456, 579]</code>.</p>

<p>Formally, a <strong>Fibonacci-like</strong> sequence is a list <code>f</code> of non-negative integers such that:</p>

<ul>
	<li><code>0 &lt;= f[i] &lt; 2<sup>31</sup></code>, (that is, each integer fits in a <strong>32-bit</strong> signed integer type),</li>
	<li><code>f.length &gt;= 3</code>, and</li>
	<li><code>f[i] + f[i + 1] == f[i + 2]</code> for all <code>0 &lt;= i &lt; f.length - 2</code>.</li>
</ul>

<p>Note that when splitting the string into pieces, each piece must not have extra leading zeroes, except if the piece is the number <code>0</code> itself.</p>

<p>Return any Fibonacci-like sequence split from <code>num</code>, or return <code>[]</code> if it cannot be done.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;1101111&quot;
<strong>Output:</strong> [11,0,11,11]
<strong>Explanation:</strong> The output [110, 1, 111] would also be accepted.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;112358130&quot;
<strong>Output:</strong> []
<strong>Explanation:</strong> The task is impossible.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;0123&quot;
<strong>Output:</strong> []
<strong>Explanation:</strong> Leading zeroes are not allowed, so &quot;01&quot;, &quot;2&quot;, &quot;3&quot; is not valid.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= num.length &lt;= 200</code></li>
	<li><code>num</code> contains only digits.</li>
</ul>

class Solution {
 public:
  vector<int> splitIntoFibonacci(string num) {
    vector<int> ans;
    dfs(num, 0, ans);
    return ans;
  }

 private:
  bool dfs(const string& num, int s, vector<int>& ans) {
    if (s == num.length() && ans.size() >= 3)
      return true;

    for (int i = s; i < num.length(); ++i) {
      if (num[s] == '0' && i > s)
        break;
      const long val = stol(num.substr(s, i + 1 - s));
      if (val > INT_MAX)
        break;
      if (ans.size() >= 2 &&
          val > ans[ans.size() - 2] + static_cast<long>(ans.back()))
        break;
      if (ans.size() <= 1 ||
          val == ans[ans.size() - 2] + static_cast<long>(ans.back())) {
        ans.push_back(val);
        if (dfs(num, i + 1, ans))
          return true;
        ans.pop_back();
      }
    }

    return false;
  }
};
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