<p>For two strings <code>s</code> and <code>t</code>, we say &quot;<code>t</code> divides <code>s</code>&quot; if and only if <code>s = t + t + t + ... + t + t</code> (i.e., <code>t</code> is concatenated with itself one or more times).</p>

<p>Given two strings <code>str1</code> and <code>str2</code>, return <em>the largest string </em><code>x</code><em> such that </em><code>x</code><em> divides both </em><code>str1</code><em> and </em><code>str2</code>.</p>

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

<pre>
<strong>Input:</strong> str1 = &quot;ABCABC&quot;, str2 = &quot;ABC&quot;
<strong>Output:</strong> &quot;ABC&quot;
</pre>

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

<pre>
<strong>Input:</strong> str1 = &quot;ABABAB&quot;, str2 = &quot;ABAB&quot;
<strong>Output:</strong> &quot;AB&quot;
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> str1 = &quot;LEET&quot;, str2 = &quot;CODE&quot;
<strong>Output:</strong> &quot;&quot;
</pre>

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

<ul>
	<li><code>1 &lt;= str1.length, str2.length &lt;= 1000</code></li>
	<li><code>str1</code> and <code>str2</code> consist of English uppercase letters.</li>
</ul>

class Solution
{
    public:
        string gcdOfStrings(string str1, string str2)
        {
           string lStr = str1.size() > str2.size() ? str1 : str2;
           string sStr = str1.size() > str2.size() ? str2 : str1;

           for (size_t i = sStr.size(); i > 0; --i)
           {
                string candidate = sStr.substr(0, i);
                if (divides_string(candidate, sStr) && divides_string(candidate, lStr))
                {
                    return candidate;
                }
           }
           return string();
        }
    private:
        bool divides_string(string candidate, string str)
        {
            size_t c_size = candidate.size();
            size_t s_size = str.size();

            // Cannot divide ==> invalid candidate ==> don't have to check
            if (s_size % c_size != 0)
            {
                return false;
            }

            size_t i = 0;
            while ((i + 1) * c_size <= s_size)
            {
                string substr_to_compare = str.substr(i * c_size, c_size);
                if (candidate == substr_to_compare)
                {
                    i++;
                }
                else
                {
                    return false;
                }
            }
            return true;
        }
};
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