<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<string>graph;
vector<vector<string>> req;
vector<vector<string>>dp;
string merge(string a, string b)
{
  int len = 1;
  int id = 0;
  int n = a.size();
  int m = b.size();
  string ans = "";
  while (len <= min(n, m))
  {
    if (a.substr(n - len) == b.substr(0, len))
    {
      id = len;
    }
    len++;
  }
  ans=b.substr(id);
  return ans;
}
string rec(int mask,int lastpos){
  //prunning

  //basecase
  if(mask==((1<<graph.size())-1)){
    return "";
  }
  //cache
  if(dp[mask][lastpos]!=""){
    return dp[mask][lastpos];
  }
  //compute
  string ans="";
  int minlen=INT_MAX;
  for(int i=0;i<graph.size();i++){
    if((mask&(1<<i))==0){
      string temp=req[lastpos][i]+rec(mask|(1<<i),i);
      if(temp.size()<minlen){
        minlen=temp.size();
        ans=temp;
      }
    }
  }
  //save and return 
  return dp[mask][lastpos]=ans;
}
    string shortestSuperstring(vector<string>& words) {
        graph=words;
        int n=graph.size();
        req.resize(n, vector<string> (n, ""));
  dp.resize(1 << (n+1), 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(graph[i],graph[j]);
    }
  }
      string ans="";
        int minLen=INT_MAX;
        int mask=0;
        for(int i=0; i<n; i++)
        {
            string temp=graph[i]+rec( mask|(1<<i),i);
            if(temp.size()<minLen)
            {
                minLen=temp.size();
                ans=temp;
            }
        } 
        return ans;
        
    }
};
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