<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:
        
        
        
        
        def dist(w1,w2):
            mx=0
            for i in range(min(len(w1),len(w2))):
                if w1[-1-i:]==w2[:i+1]:
                    mx=max(mx,len(w2[:i+1]))
            return w1+w2[mx:]
        @lru_cache(maxsize=None)
        def tsp(ind,vis):
            
            if ind>=len(words):
                return 0
            
            mn=999999999
            ans=words[ind]
            for i in range(len(words)):
                if not vis & (1 << i):
                    
                    temp=dist(words[ind],tsp(i,vis | (1 << i)))
                    if len(temp)<mn:
                        mn=len(temp)
                        ans=temp
                    
            return ans
        mn=999999999
        ans=""
        vis=0
        for i in range(len(words)):
            temp=dist(words[i],tsp(i,vis | (1 << i)))
            if len(temp)<mn:
                mn=len(temp)
                ans=temp
           
        return ans
80500