<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 common(string&s1,string &s2)
    {
        int n=s1.length();
        int m=s2.length();
        int l=min(n,m);
        string ans="";
        for(int i=l;i>=0;i--)
        {
            if(s1.substr(n-i)==s2.substr(0,i))
            {
                ans=s2.substr(i);
                break;
            }
        }
        if(m<=n)
        {
            for(int i=0;i<=(n-m);i++)
            {
                if(s1.substr(i,m)==s2)
                return "";
            }
        }
        return ans;
    }
    string solve(vector<string>&arr,int i, int mask, int n,vector<vector<string>>&dp,vector<vector<string>>&comm)
    {
        if(dp[i][mask]!="")
        return dp[i][mask];
        string res="";
        int l=1e9+7;
        for(int j=0;j<n;j++)
        {
            if(mask&(1<<j))
            continue;
            string temp=comm[i][j]+solve(arr,j,mask|(1<<j),n,dp,comm);
            if(temp.size()<l)
            {
                l=temp.size();
                res=temp;
            }
        }
        return dp[i][mask]=res;
    }
    string shortestSuperstring(vector<string>& words) {
        int n=words.size();
        vector<vector<string>>comm(n,vector<string>(n,""));
        vector<vector<string>>dp(n,vector<string>(1<<n,""));
        for(int i=0;i<n;i++)
        {
            for(int j=0;j<n;j++)
            {
                if(i==j)
                comm[i][j]=words[i];
                else
                comm[i][j]=common(words[i],words[j]);
            }
        }
        string ans="";
        int mask=0;
        int l=1e9+7;
        for(int i=0;i<n;i++)
        {
            string temp=words[i]+solve(words,i,mask|(1<<i),n,dp,comm);
            if(temp.size()<l)
            {
                l=temp.size();
                ans=temp;
            }
        }
        return ans;
    }
};
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