<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>

from itertools import permutations

class Solution:
    def shortestSuperstring(self, words: List[str]) -> str:
        n = len(words)
        # Calculate the overlap between two words
        def overlap(w1, w2):
            for i in range(len(w1)):
                if w2.startswith(w1[i:]):
                    return len(w1) - i
            return 0

        # Calculate the overlap matrix
        overlaps = [[overlap(words[i], words[j]) for j in range(n)] for i in range(n)]

        # dp[mask][i] stores the minimum length of the superstring
        # that includes words from the mask, ending with words[i]
        dp = [[float('inf')] * n for _ in range(1 << n)]
        parent = [[-1] * n for _ in range(1 << n)]

        for i in range(n):
            dp[1 << i][i] = len(words[i])

        for mask in range(1, 1 << n):
            for bit in range(n):
                if mask & (1 << bit):
                    prev_mask = mask ^ (1 << bit)
                    for j in range(n):
                        if dp[prev_mask][j] + len(words[bit]) - overlaps[j][bit] < dp[mask][bit]:
                            dp[mask][bit] = dp[prev_mask][j] + len(words[bit]) - overlaps[j][bit]
                            parent[mask][bit] = j

        # Find the superstring with the minimum length
        last_word = min(range(n), key=lambda x: dp[-1][x])
        mask = (1 << n) - 1
        superstring = words[last_word]
        while parent[mask][last_word] != -1:
            prev_word = parent[mask][last_word]
            superstring = words[prev_word][:len(words[prev_word]) - overlaps[prev_word][last_word]] + superstring
            mask ^= (1 << last_word)
            last_word = prev_word

        return superstring
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