<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:
        
        @cache
        def connect(j, k):
            possible_suffix = []
            word_j, word_k = words[j], words[k]

            for i in range(len(word_j)):
                if i == 0 or word_j[-i:] == word_k[:i]:
                    possible_suffix.append(word_k[i:])

            return possible_suffix[-1]

        n = len(words)
        dp = [[(float('inf'), "")] * n for _ in range(1 << n)]

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

        print(dp)   


        for mask in range(1 << n):
            used = [i for i in range(n) if mask & (1 << i)]


            for j, k in permutations(used, 2):
                new_super_str = dp[mask ^ (1 << j)][k][1] + connect(k, j)
                dp[mask][j] = min(dp[mask][j], (len(new_super_str), new_super_str))


        return min(dp[-1])[1]
        
24300