<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)
        # Compute the overlap between each pair of words
        overlaps = [[0]*n for _ in range(n)]
        for i in range(n):
            for j in range(n):
                if i != j:
                    a, b = words[i], words[j]
                    max_olap = min(len(a), len(b))
                    for k in range(max_olap, 0, -1):
                        if a[-k:] == b[:k]:
                            overlaps[i][j] = k
                            break

        # dp[mask][i]: maximum total overlap with mask of words ending with word i
        dp = [[-1]*n for _ in range(1<<n)]
        parent = [[-1]*n for _ in range(1<<n)]

        # Initialize dp
        for i in range(n):
            dp[1<<i][i] = 0

        for mask in range(1<<n):
            for u in range(n):
                if dp[mask][u] == -1:
                    continue
                for v in range(n):
                    if mask & (1<<v) == 0:
                        next_mask = mask | (1<<v)
                        val = dp[mask][u] + overlaps[u][v]
                        if val > dp[next_mask][v]:
                            dp[next_mask][v] = val
                            parent[next_mask][v] = u

        # Find the maximum overlap
        max_len = -1
        last = -1
        full_mask = (1<<n)-1
        for i in range(n):
            if dp[full_mask][i] > max_len:
                max_len = dp[full_mask][i]
                last = i

        # Reconstruct the path
        seq = []
        mask = full_mask
        while last != -1:
            seq.append(last)
            temp = parent[mask][last]
            mask ^= (1<<last)
            last = temp
        seq = seq[::-1]

        # Build the shortest superstring
        ans = words[seq[0]]
        for i in range(1, len(seq)):
            olap = overlaps[seq[i-1]][seq[i]]
            ans += words[seq[i]][olap:]

        return ans

18000