<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:
    set<pair<int,string>> m;
    int x[14][14];
    int computelps(string &word,string &state){
        string s=word;
        s.push_back('$');
        for(auto j:state) s.push_back(j);
        int n=s.size();
        vector<int> lps(n,0);
        int i=1,len=0;
        while(i<n){
            if(s[i]==s[len]){
                len++;
                lps[i]=len;
                i++;
            }else{
                if(len!=0) len=lps[len-1];
                else{
                    lps[i]=0;
                    i++;
                } 
            }
        }
        return lps[n-1];
    }
    string dp(int mask,int prev,vector<string>& words,vector<vector<string>> &ans){
        int n=words.size();
        if(mask==(1<<n)-1){
            return "";
        } 
        if(ans[prev][mask]!="") return ans[prev][mask];
         int l=INT_MAX;string z;
        for(int j=0;j<n;j++){
            if((mask&(1<<j))==0){
                int len=x[prev][j];
                string res=words[j].substr(len)+dp(mask|(1<<j),j,words,ans);
                if(res.size()<l){
                    l=res.size();
                    z=res;
                }
            }
        }
        return ans[prev][mask]=z;
    }
    string shortestSuperstring(vector<string>& words){
        int n=words.size();
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(i!=j){
                    x[j][i]=computelps(words[i],words[j]);
                }
            }
        }
        
        vector<vector<string>> ans(n+1,vector<string>((1<<n)-1,""));
        return dp(0,n,words,ans);
    }
};
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