<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) {
        const std::string_view s = num;
        if (s.size() < 3)
            return false;

        uint32_t i_num = 0;
        for (size_t i = 0; i < s.size() - 2; ++i) {
            i_num = i_num * 10 + (s[i] - '0');

            uint32_t j_num = 0;
            for (size_t j = i + 1; j < num.size() - 1; ++j) {
                j_num = j_num * 10 + (s[j] - '0');

                if (IsAdditive_r(s.substr(j + 1), i_num, j_num))
                    return true;

                if (j_num == 0)
                    break; // Ignore numbers with leading zeros.
            }

            if (i_num == 0)
                break; // Ignore numbers with leading zeros.
        }

        return false;
    }

    bool IsAdditive_r(const std::string_view s, const uint32_t prev_prev,
                      const uint32_t prev) {
        if (s.empty())
            return true;

        uint32_t num = 0;
        if (s.front() == '0') {
            if (prev_prev + prev == num && IsAdditive_r(s.substr(1), prev, num))
                return true;
        } else {
            for (size_t i = 0; i < s.size(); ++i) {
                num = num * 10 + (s[i] - '0');
                if (prev_prev + prev == num &&
                    IsAdditive_r(s.substr(i + 1), prev, num))
                    return true;
            }
        }
        return false;
    }
};
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