<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) {
        int n = num.size();       
        vector<int> ans = topDown(num, -1, -1, 0);
        reverse(ans.begin(), ans.end());
        return ans;
    }
    vector<int> topDown(string num, long long f1, long long f2, int step)
    {
/*        
        cout << string(step*2,' ')
             << "Remain text = "  << num 
             <<", f1 = " << f1
             <<", f2 = " << f2 << endl;
*/             
        int n = num.size();
        long long sum = f1 + f2 ;
        
        for(int i = 1; i <= min(10, n); i++)
        {
            string str = num.substr(0, i);
            if( str.size() > 1 && str.front() == '0' ) return {};
            long long curNum = stoll(str);
            if ( curNum > INT_MAX ) return {};
/*            
            cout << string(step*2,' ')
                 << "cur = " << curNum << endl;     
*/
            if( ( sum == curNum ) || ( f1 == -1 ) || ( f2 == -1 ) )
            {
                if( f1 >= 0 && f2 >= 0 && i == n )
                {
                    return { (int)curNum };
                }
/*
                cout << num.substr(i) << endl;
*/
                auto curAns = topDown( num.substr(i), f2 , curNum, step+1);
                
                if( curAns.size() > 0 ) 
                {
                    curAns.push_back( (int)curNum );
                    return curAns;
                }
            }
        }
        return {};
    }
};
12000