<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:
    void backtrack(vector<int> &ret, vector<int> &cur, string num, int index){
        if(cur.size() != 0){
            return;
        }
        if(index == num.size() && ret.size() > 2){
            cur = ret;
            return;
        }
        long long target = -1;
        if(ret.size() >= 2){
            target = (long long)ret[ret.size() - 1] + ret[ret.size() - 2];
        }
        int end_index = num.size();
        if(num[index] == '0'){
            end_index = index + 1;
        }
        for(int i = index; i < end_index; i++){
            if(i - index == 10){
                break;
            }
            if(i - index == 9){
                //check to see if it over flows
                long long val = stod(num.substr(index, i - index +1));
                if(val > INT_MAX){
                    break;
                }
            }
            int new_val = stoi(num.substr(index, i - index + 1));
            if(new_val == target || target == -1){
                ret.push_back(stoi(num.substr(index, i - index + 1)));
                backtrack(ret, cur, num, i + 1);
                ret.pop_back();
            }
        }
    }
    vector<int> splitIntoFibonacci(string num) {
        vector<int> ret;
        vector<int> cur;
        backtrack(ret, cur, num, 0);
        return cur;
    }
};
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