<p>An <strong>additive number</strong> is a string whose digits can form an <strong>additive sequence</strong>.</p>

<p>A valid <strong>additive sequence</strong> should contain <strong>at least</strong> three numbers. Except for the first two numbers, each subsequent number in the sequence must be the sum of the preceding two.</p>

<p>Given a string containing only digits, return <code>true</code> if it is an <strong>additive number</strong> or <code>false</code> otherwise.</p>

<p><strong>Note:</strong> Numbers in the additive sequence <strong>cannot</strong> have leading zeros, so sequence <code>1, 2, 03</code> or <code>1, 02, 3</code> is invalid.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> &quot;112358&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> 
The digits can form an additive sequence: 1, 1, 2, 3, 5, 8. 
1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> &quot;199100199&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> 
The additive sequence is: 1, 99, 100, 199.&nbsp;
1 + 99 = 100, 99 + 100 = 199
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= num.length &lt;= 35</code></li>
	<li><code>num</code> consists only of digits.</li>
</ul>

<p>&nbsp;</p>
<p><strong>Follow up:</strong> How would you handle overflow for very large input integers?</p>

class Solution {
public:
    bool isAdditiveNumber(string num) {
        int n = num.size();
        // Try every pair of starting numbers num1 and num2
        for (int i = 1; i <= n / 2; ++i) {
            for (int j = 1; j <= (n - i) / 2; ++j) {
                string num1 = num.substr(0, i);
                string num2 = num.substr(i, j);
                string remaining = num.substr(i + j);
                
                if (isValidAdditiveSequence(num1, num2, remaining))
                    return true;
            }
        }
        
        return false;
    }
private:
    bool isValidAdditiveSequence(string num1, string num2, string remaining) {
        // Handle leading zeros, numbers other than "0" cannot start with '0'
        if ((num1.size() > 1 && num1[0] == '0') || (num2.size() > 1 && num2[0] == '0'))
            return false;
        
        // Calculate the sum of num1 and num2
        string sum = to_string(stoll(num1) + stoll(num2));
        
        // Check if the remaining string starts with the sum
        if (remaining.substr(0, sum.size()) != sum) 
            return false;
        
        // If we've matched the entire remaining string, it's valid
        if (remaining.size() == sum.size()) 
            return true;
        
        // Recursively check the rest of the string
        return isValidAdditiveSequence(num2, sum, remaining.substr(sum.size()));
    }       
};
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