<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:
  //you need to be extra concious about the large input beacuse it is given in string format . in java we can handle //that but in c++ we need different technique to handle that....
    bool backtrack(string s,vector<int>&ans,int index,long long f1,long long f2,int size)
    {
      // base case if we reach end and our ans have more than 2 element than its true otherwise false
      if(s.size()==index)
        return size>2;
      long long int n=0;
      for(int i=index;i<s.size();i++)
      {
        n=n*10+(s[i]-'0');
        //to avoid negative overflow 
        if(n<0)
          return false;
        //to avoid positive overflow
        if(n>INT_MAX)
          break;
        //if we had not reach to 3 elements i.e ans have only two elements than we need to check if we can put this //number into our ans or not
        if(size<2||f1+f2==n)
        {
          ans.push_back(n);
          //basic backtrack step to check further cases if it is true then we would return true
          if(backtrack(s,ans,i+1,f2,n,size+1))
            return true;
          //if we are not able to find ans then we would backtrack our answer and thus we would remove this last element
          ans.pop_back();
        }if(n==0)// if n is 0 i.e at start only if n is 0 we would return false because this would voilate question rules.
          return false;
      }return false;
    }
    vector<int> splitIntoFibonacci(string S) {
        vector<int>ans;
      //here we need two to pass three different variable except string itself, ans vector, index i.e 1st numer, 2nd //number and the size of vector to avoid overflow condition because input maybe very very large...
        backtrack(S,ans,0,0,0,0);
        return ans ;
    }
};
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