<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:
    int vis[12][1<<12];
    int par[12][1<<12];
    int n;
    int common(string a,string b){
      int i=1;int ans=0;
      while(i<=a.size()&&i<=b.size()){
          if(a.substr(a.size()-i,i)==b.substr(0,i)){
              ans=i;
          }
          i++;
      }
      return ans;
    }
    int recru(vector<string>&arr,int prev,int mask){
        if(mask==((1<<n)-1))return 0;
        if(vis[prev][mask]!=-1)return vis[prev][mask];
        int ans=INT_MAX;
        int next=-1;
        for(int i=0;i<n;i++){
            if(!(mask&(1<<i))){
                int shared=common(arr[prev],arr[i]);
                int curr=arr[i].size()-shared+recru(arr,i,(mask|(1<<i)));
                if(curr<ans){
                    ans=curr;
                    next=i;
                }
            }
        }
        par[prev][mask]=next;
        return vis[prev][mask]=ans;
    }
    string shortestSuperstring(vector<string>& arr) {
        n=arr.size();
        memset(vis,-1,sizeof(vis));
        memset(par,-1,sizeof(par));
        int min1=INT_MAX;int begin=0;
        for(int i=0;i<n;i++){
            int temp=recru(arr,i,(1<<i));
            int length1=arr[i].size()+temp;
            if(length1<min1){
                min1=length1;
                begin=i;
            }
        }
        string finalans="";
        int mask=0;string ans="";
        while(begin!=-1){
            string prev=arr[begin];
            mask|=(1<<begin);
            begin=par[begin][mask];
            string next= (begin==-1) ? "" : arr[begin];
            int shared=common(prev,next);
            ans+=prev.substr(0,prev.size()-shared);
        }
        return ans;
    }

};
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