<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:
    // string merge(string &s1,string &s2)
    // {
    //     int i=0;
    //     int n=s1.length();
    //     int len=min(s1.length(),s2.length());
    //     int slen=0;
    //     while(i<len and s1.substr(i,len-i)!=s2.substr(0,len-i))
    //     {
    //         i++;
            
    //     }
    //     slen=len-i;
    //     string res=s2.substr(slen);
    //     return res;
    // }
    string merge(string &a, string &b) // a is followed by b (ab)
    {
        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 solve_val(vector<vector<string>> &mat,int mask,int prev,vector<string>&words,vector<vector<string>>&dp)
    {
        // if(mask==(1<<20))return "";
        if(dp[mask][prev]!="")return dp[mask][prev];
        int mlen=INT_MAX;
        string temp="";
        for(int i=0;i<words.size();i++)
        {
            if((1<<i)&mask)continue;
            string ans=mat[prev][i]+solve_val(mat,(1<<i | mask),i,words,dp);
            if(ans.length()<mlen)
            {
                temp=ans;
                mlen=ans.length();
            }
        }
        return dp[mask][prev]=temp;
    }

    string shortestSuperstring(vector<string>& words) {
        //hk
        // first we need to create the matrix which 
        // will store the precomputation part of combining two string

        int n=words.size();
        vector<vector<string>> mat(n,vector<string>(n));
        vector<vector<string>>dp((1<<(n+1)),vector<string>(n,""));
        for(int i=0;i<n;i++)
        {
            for(int j=0;j<n;j++)
            {
                if(i==j)continue;
                else
                {
                    mat[i][j]=merge(words[i],words[j]);
                }
            }
        }
        string ans="";
        int len=INT_MAX;
        int mask=0;
        for(int i=0;i<n;i++)
        {
            string temp=words[i]+solve_val(mat,(mask|(1<<i)),i,words,dp);
            if(temp.length()<len)
            {
                ans=temp;
                len=temp.length();
            }
        }
        return ans;
    }
};
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