<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)
        
        # Calculate the overlap between words[i] and words[j]
        def overlap(a, b):
            for i in range(min(len(a), len(b)), -1, -1):
                if a.endswith(b[:i]):
                    return i
            return 0
        
        # Calculate the overlap for all pairs of words
        overlaps = [[overlap(words[i], words[j]) for j in range(n)] for i in range(n)]
        
        # DP table to store the shortest superstring for each subset of words
        dp = [["" for _ in range(n)] for _ in range(1 << n)]
        
        # Initialize the DP table for single word subsets
        for i in range(n):
            dp[1 << i][i] = words[i]
        
        # Iterate over all subsets of words
        for mask in range(1, 1 << n):
            for j in range(n):
                if mask & (1 << j):
                    for k in range(n):
                        if mask & (1 << k) and j != k:
                            prev_mask = mask ^ (1 << j)
                            candidate = dp[prev_mask][k] + words[j][overlaps[k][j]:]
                            if dp[mask][j] == "" or len(candidate) < len(dp[mask][j]):
                                dp[mask][j] = candidate
        
        # Find the shortest superstring from all possible endings
        result = min([dp[(1 << n) - 1][j] for j in range(n)], key=len)
        return result

# Example usage:
solution = Solution()
words = ["alex","loves","leetcode"]
print(solution.shortestSuperstring(words))  # Output: "alexlovesleetcode"
20600