<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 n;
    vector<string>w;
    map<pair<int,int>,string>mp,dp;
    string rec(int l,int mask){
        if(mask==(1<<n)-1)return "";
        if(dp.find({l,mask})!=dp.end())return dp[{l,mask}];
        int sz=1e9;
        string mini;
        for(int i=0;i<n;i++){
            if(((mask>>i)&1)==0){
                string temp=mp[{l,i}]+rec(i,(mask|(1<<i)));
                if(temp.size()<sz){
                     sz=temp.size();
                    mini=temp;
                }
            }
        }
        return dp[{l,mask}]=mini;
    }
    string shortestSuperstring(vector<string>& words) {
        w=words;
        n=w.size();
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(i!=j){
                    int k=min(w[i].size(),w[j].size());
                    for(int len=k;len>=0;len--){
                        if(w[j].substr(0,len)==w[i].substr(w[i].size()-len,len)){
                            mp[{i,j}]=w[j].substr(len,w[j].size()-len);
                            break;
                        }
                    }
                }
            }
        }
        int sz=1e9;
        string mini;
        dp.clear();
        for(int i=0;i<n;i++){
            string temp=w[i]+rec(i,(1<<i));
            if(temp.size()<sz){
                sz=temp.size();
                mini=temp;
            }
        }
        return mini;
    }
};
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