<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)
        combine_shrink = [[""] * N for _ in range(N)]

        def shrink(i, j):
            w1, w2 = words[i], words[j]

            for i in range(len(w2)-1, -1, -1):
                if w1[-i:] == w2[:i]:
                    return w2[i:]

            return w2

        for i in range(N):
            for j in range(N):
                combine_shrink[i][j] = shrink(i, j)
        
    
        dp = [[(inf, "") for _ in range(N)] for _ in range(1 << N)] # (min_length, cur)
        for i in range(N):
            dp[1 << i][i] = (len(words[i]), words[i])

        for mask in range(1, 1 << N):
            for j in range(N):
                for i in range(N):
                    if (mask >> i) & 1 == 1:
                        min_length, cur = dp[mask ^ (1 << i)][j]
                    
                        tmp = combine_shrink[j][i]

                        min_length += len(tmp)
                        cur += tmp

                        if min_length < dp[mask][i][0]:
                            dp[mask][i] = (min_length, cur)

        return min(dp[(1 << N) - 1], key=lambda x: x[0])[1]

                    
        
23600