<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)
        w = [[0]*n for _ in range(n)]
        for i in range(n):
            for j in range(n):
                s1,s2 = words[i],words[j]
                for k in range(len(s1)):
                    if s2.startswith(s1[k:]):
                        w[i][j] = len(s1)-k
                        break
        dp = [[0]*(n+1) for _ in range(1<<n)]
        for mask in range(1<<n):
            for j in range(n):
                if mask>>j & 1: continue
                for i in range(n):
                    if mask>>i & 1:
                        dp[mask|1<<j][j] = max(dp[mask|1<<j][j],dp[mask][i]+w[i][j])
        def recover(mask,i):
            for j in range(n):
                # print(j,w[j][i],dp[mask-(1<<i)][j])
                if mask>>j &1 and j!=i and dp[mask][i]==w[j][i]+dp[mask-(1<<i)][j]:
                    res.append(j)
                    recover(mask-(1<<i),j)
                    break
        for i in range(n):
            if dp[(1<<n)-1][i]==max(dp[(1<<n)-1]):
                break
        res = [i]
        recover((1<<n)-1,i)
        res.reverse()
        ans = words[res[0]]
        for i in range(len(res)-1):
            y = res[i+1]
            x = res[i]
            l = w[x][y]
            ans+=words[y][l:]
        return ans


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