<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, A):
        @lru_cache(None)
        def connect(w1, w2):
            # Initialize an empty list to store possible suffixes of w2
            possible_suffixes = []
            
            # Iterate over all possible lengths of overlap from 0 to len(w1)
            for i in range(len(w1)):
                # Check if the last i characters of w1 match the first i characters of w2
                if w1[-i:] == w2[:i] or i == 0:
                    # If they match, or if i is 0 (no overlap), add the suffix of w2 starting from position i to the list
                    possible_suffixes.append(w2[i:])
            
            # Return the last element in the list, which corresponds to the maximum overlap case
            return possible_suffixes[-1]
                    
        N = len(A) 
        dp = [[(float("inf"), "")] * N for _ in range(1<<N)]
        for i in range(N): dp[1<<i][i] = (len(A[i]), A[i])
            
        for mask in range(1<<N):
            n_z_bits = [j for j in range(N) if mask & 1<<j]
            
            for j, k in permutations(n_z_bits, 2):
                cand = dp[mask ^ 1<<j][k][1] + connect(A[k], A[j])
                dp[mask][j] = min(dp[mask][j], (len(cand), cand))

        return min(dp[-1])[1]
22800