<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:
    int len;
    vector<int>ans;
    vector<int> splitIntoFibonacci(string num) 
    {
        len=num.length();
        int idx=0;
        vector<int>v;
        fun(idx,num,v);
        return ans;
    }
    void fun(int idx,string &nums,vector<int>&v)
    {
       if(idx >= nums.length())
       {
            if(v.size() > 2)
            {
                 ans=v;
            }

            return;
       }

       long long int num=0;
       string str="";

       for(int i=idx;i<nums.length();i++)
       {
           char ch = nums[i];
           num = (num * 10LL) + ch-'0';
           str.push_back(ch);

           if(str.length() > (len/2) or (num>INT_MAX))
           {
               return;
           }
           //checking for the leading zeros
           if(str.length()>0 and str[0]=='0' and num>0)       // 005
           {
              return; 
           }

           if(v.size()<2)   //0 1
           {
               v.push_back(num);
               fun(i+1,nums,v);

               if(ans.size()!=0)
               return;

               v.pop_back();  
           }
           else if(v.size() >= 2)
           {
               long long temp_sum=0LL+v[v.size()-1]+v[v.size()-2];
               if(num < temp_sum)
               {
                   continue;
               }
               else if(num > temp_sum)
               {
                  return;
               }
               if(num == temp_sum)
               {
                   v.push_back(num);
                   fun(i+1,nums,v);

                   if(ans.size()!=0)
                   return;

                   v.pop_back();
               }
           }
       }
    }
};
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