<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 {
public:
   vector<vector<string>> req;
 string merge(string &a, string &b) 
    {
        int n=a.size(), m=b.size(), len=1, idx=0;
        while(len<=min(n, m))
        {
            if(a.substr(n-len)==b.substr(0, len))
            {
                idx=len;
            }
            len++;
        }
        string res=b.substr(idx);
        return res;
    }
 string f(int bitmask,vector<string>& words,int n,int prev,vector<vector<string>>&dp){
    int ans=INT_MAX;
    if(dp[prev][bitmask]!="-1") return dp[prev][bitmask];
    string res="";
    for(int i=0;i<n;i++){
        if((bitmask>>i)&1) continue;
          string p= req[prev][i]+f((bitmask|(1<<i)),words,n,i,dp);
          if(p.length()<ans){
            ans=p.length();
            res=p;
          
          }

    }
    return dp[prev][bitmask]=res;
  }
    string shortestSuperstring(vector<string>& words) {
      int n=words.size();
      vector<vector<string>>dp(n,vector<string>((1<<n),"-1"));
       req.resize(n, vector<string> (n, ""));
       for(int i=0;i<n;i++){
        for(int j=0;j<n;j++){
            if(i==j) continue;
            req[i][j]=merge(words[i],words[j]);
        }
       }
       int ans=INT_MAX;
       string res="";
       for(int i=0;i<n;i++){
        string k=words[i]+f(0|(1<<i),words,n,i,dp);
        if(k.length()<ans){
            ans=k.length();
            res=k;
        }
       }
       return res;
    }
};
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