<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> nums;
	// Backtrack from 0th char
        backtrack(0 , num, nums) ;
        return  nums ;
    }
    
    int backtrack(int i , string &s , vector<int>&st ){
        int n = s.size() ;
        if(i==n && st.size()>=3){
            return true ;
        }
        
        int maxsplit =10 ;
        if(s[i]=='0'){
            maxsplit=1 ;
        }
        for(int j=1 ;j<=maxsplit && j+i<=s.size() ; j++){
            long long num =stoll( s.substr(i , j)) ;
            if(num>INT_MAX){
                return false ;
            }
            
            long long sz= st.size() ;
            
        if(sz >= 2 &&  (long long)st[sz-1]+(long long)st[sz-2]< num){
                return false;}
            if(sz<=1 || (long long)st[sz-1]+(long long)st[sz-2]==num){
                st.push_back(num);
                if(backtrack(j+i , s,st))
                    return true;
                st.pop_back();           
            
        }
       
    }
        return false;
    }
};
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