<p>Given an array of strings <code>words</code>, return <em>the smallest string that contains each string in</em> <code>words</code> <em>as a substring</em>. If there are multiple valid strings of the smallest length, return <strong>any of them</strong>.</p>

<p>You may assume that no string in <code>words</code> is a substring of another string in <code>words</code>.</p>

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

<pre>
<strong>Input:</strong> words = [&quot;alex&quot;,&quot;loves&quot;,&quot;leetcode&quot;]
<strong>Output:</strong> &quot;alexlovesleetcode&quot;
<strong>Explanation:</strong> All permutations of &quot;alex&quot;,&quot;loves&quot;,&quot;leetcode&quot; would also be accepted.
</pre>

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

<pre>
<strong>Input:</strong> words = [&quot;catg&quot;,&quot;ctaagt&quot;,&quot;gcta&quot;,&quot;ttca&quot;,&quot;atgcatc&quot;]
<strong>Output:</strong> &quot;gctaagttcatgcatc&quot;
</pre>

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

<ul>
	<li><code>1 &lt;= words.length &lt;= 12</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 20</code></li>
	<li><code>words[i]</code> consists of lowercase English letters.</li>
	<li>All the strings of <code>words</code> are <strong>unique</strong>.</li>
</ul>

class Solution:
    def shortestSuperstring(self, words: List[str]) -> str:
        n = len(words)
        dp = [[(float('inf'), '') for _ in range(n)] for _ in range(1 << (n))]
        for i in range(n):
            dp[1<<i][i] = (len(words[i]), words[i])
        def connect(w1, w2):
            return [w2[i:] for i in range(len(w2)+1) if w1[-i:] == w2[:i] or not i][-1]
        
        for i in range(1<<n):
            visited = [j for j in range(n) if i & (1<<j)]
            for last_visited, curr in permutations(visited, 2):
                cand = dp[i ^ 1<<curr][last_visited][1] + connect(words[last_visited],words[curr] )
                dp[i][curr] = min(dp[i][curr], (len(cand), cand))
        return min(dp[-1])[1]
            
                
26000