<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:
    bool bt(string num, vector<int>& ans, int index) {
        if (index == num.size() && ans.size() >= 3) {
            return true;
        }

        for (int i = index; i < num.size(); i++) {
            // Skip numbers with leading zeroes
            if (num[index] == '0' && i > index) {
                break;
            }

            // Extract substring and convert to long
            string part = num.substr(index, i - index + 1);
            long number = stol(part);

            // If number exceeds INT_MAX, break
            if (number > INT_MAX) {
                break;
            }

            int size = ans.size();

            // If there are at least two numbers in the sequence and the current number
            // is greater than the sum of the last two, break
            if (size >= 2 && number > (long)ans[size - 1] + ans[size - 2]) {
                break;
            }

            // If the number forms a valid Fibonacci sequence or we have less than two numbers
            if (size < 2 || number == (long)ans[size - 1] + ans[size - 2]) {
                ans.push_back((int)number);

                // Recursively attempt to build the sequence
                if (bt(num, ans, i + 1)) {
                    return true;
                }

                // Backtrack
                ans.pop_back();
            }
        }
        return false;
    }

    vector<int> splitIntoFibonacci(string num) {
        vector<int> ans;
        bt(num, ans, 0);
        return ans;
    }
};

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