<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)
        graph = [[0]*n for _ in range(n)] # graph as adjacency matrix 
        
        for i in range(n):
            for j in range(n): 
                if i != j: 
                    for k in range(len(words[j])): 
                        if words[i].endswith(words[j][:k]): 
                            graph[i][j] = len(words[j]) - k 
                            
        @cache
        def fn(prev, mask): 
            """Return length of shortest superstring & current choice of word."""
            if mask == 0: return 0, None
            vv, kk = inf, None
            for k in range(n): 
                if mask & 1<<k: 
                    v, _ = fn(k, mask ^ 1<<k)
                    offset = len(words[k]) if prev == -1 else graph[prev][k]
                    if v + offset < vv: vv, kk = v + offset, k
            return vv, kk
        
        ans = []
        prev = -1 
        mask = (1<<n) - 1
        while mask: 
            _, k = fn(prev, mask)
            if ans: ans.append(words[k][-graph[prev][k]:])
            else: ans.append(words[k])
            prev = k
            mask ^= 1<<k 
        return "".join(ans)
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