<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 functools import lru_cache

class Solution:
    def shortestSuperstring(self, words):
        def compute_adj(words):
            l = len(words)
            adj = [["" for _ in range(l)] for _ in range(l)]
            for i in range(l):
                for j in range(l):
                    if i != j:
                        word1 = words[i]
                        word2 = words[j]
                        max_overlap = 0
                        for k in range(1, min(len(word1), len(word2)) + 1):
                            if word1[-k:] == word2[:k]:
                                max_overlap = k
                        adj[i][j] = word2[max_overlap:]
            return adj

        @lru_cache(None)
        def superstring(bits, cur):
            if bits == (1 << n) - 1: 
                return ""
            res = "a" * 240
            for i in range(n):
                if (bits & (1 << i)) == 0:
                    ans = adj[cur][i] + superstring(bits | (1 << i), i)
                    if len(res) > len(ans):
                        res = ans
            return res
        
        ans = "a" * 240 
        n = len(words)
        adj = compute_adj(words)
        for i in range(n):
            x = words[i] + superstring(1 << i, i)
            if len(x) < len(ans):
                ans = x
        return ans

sol = Solution()
words = ["alex","loves","leetcode"]
sol.shortestSuperstring(words)
77100