<p>Given a string array <code>words</code>, return <em>the maximum value of</em> <code>length(word[i]) * length(word[j])</code> <em>where the two words do not share common letters</em>. If no such two words exist, return <code>0</code>.</p>

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

<pre>
<strong>Input:</strong> words = [&quot;abcw&quot;,&quot;baz&quot;,&quot;foo&quot;,&quot;bar&quot;,&quot;xtfn&quot;,&quot;abcdef&quot;]
<strong>Output:</strong> 16
<strong>Explanation:</strong> The two words can be &quot;abcw&quot;, &quot;xtfn&quot;.
</pre>

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

<pre>
<strong>Input:</strong> words = [&quot;a&quot;,&quot;ab&quot;,&quot;abc&quot;,&quot;d&quot;,&quot;cd&quot;,&quot;bcd&quot;,&quot;abcd&quot;]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The two words can be &quot;ab&quot;, &quot;cd&quot;.
</pre>

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

<pre>
<strong>Input:</strong> words = [&quot;a&quot;,&quot;aa&quot;,&quot;aaa&quot;,&quot;aaaa&quot;]
<strong>Output:</strong> 0
<strong>Explanation:</strong> No such pair of words.
</pre>

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

<ul>
	<li><code>2 &lt;= words.length &lt;= 1000</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 1000</code></li>
	<li><code>words[i]</code> consists only of lowercase English letters.</li>
</ul>

class Solution:
    def maxProduct(self, words: List[str]) -> int:
        # brute force
        # iterate through all the 2-combinations
        # if the 2 words do not have shared letters, calculate their lengths' product
        # return the max product
        
        # improvement
        # for all the words with the same letters, keep only the longest one
        word_lengths = {}
        for word in words:
            word_set = frozenset(word)
            if word_set in word_lengths:
                word_lengths[word_set] = max(word_lengths[word_set], len(word))
            else:
                word_lengths[word_set] = len(word)
        words = [word for word in words if len(word) == word_lengths[frozenset(word)]]
        
        max_product = 0
        for i in range(len(words)):
            for j in range(i+1, len(words)):
                if not set(words[i]) & set(words[j]):
                    max_product = max(max_product, len(words[i]) * len(words[j]))
        return max_product
20000