<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)
        overlap = [[''] * n for _ in range(n)]

        def getOverlap(a, b):
            l, i = 0, 1
            while i <= min(len(a), len(b)):
                if a[len(a)-i:] == b[:i]:
                    l = i
                i += 1
            return b[l:]

        for i in range(n):
            for j in range(n):
                if i != j: overlap[i][j] = getOverlap(words[i], words[j])

        def TSP(prev, mask, dp):
            if (prev, mask) in dp: return dp[(prev, mask)]
            if mask == ((1 << n) - 1): return ''
            ans = '*' * 1000000
            for i in range(n):
                if mask & (1 << i): continue
                word = overlap[prev][i] if prev != -1 else words[i]
                ans = min(ans, word + TSP(i, mask | (1 << i), dp), key=len)
            dp[(prev, mask)] = ans
            return ans

        return TSP(-1, 0, {})
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