<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:
    // you can try out all the different lengths
    // then check whether the same length is repeated
    // You know that the length of GCD must be a factor of the length of str1
    // and str2, so that's a way you can speed up the process
    // O(min(s1,s2) * (s1+s2))
    // 
    int maxLengthOfPrefix(const string str1, const string str2) {
        int length = 0;
        for (; length < min(str1.size(), str2.size()); length++) {
            if (str1[length] != str2[length]) return length;
        }
        return length;
    }
    bool isValidDivisorLength(const string str, const int length) {
        if (str.size() % length != 0) return false;
        for (int i=0; i<str.size(); i++) {
            if (str[i] != str[i%length]) return false;
        }
        return true;
    }
    string gcdOfStrings(string str1, string str2) {
        int l1 = str1.size(), l2 = str2.size();
        for (int l=maxLengthOfPrefix(str1, str2); l>0; l--) {
            if (isValidDivisorLength(str1,l)
             && isValidDivisorLength(str2,l)) return str1.substr(0,l);
        }
        return "";
    }
};
22954