<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<vector<string>> store;

    string merge(string &a,string &b){
        int idx = 0;
        int n = a.length();
        int m = b.length();
        while(idx <= n){
            if( n-idx>=0 && n-idx<=m && a.substr(idx) == b.substr(0,n-idx)){
                // cout<<b.substr(n-idx)<<endl;
                return b.substr(n-idx);
            }
            idx++;
        }
        return b;
    }
    vector<vector<string>> dp;
    string solve(int last , int mask,int n){

        if(dp[last][mask]!="") return dp[last][mask];
        string res="";
        for(int idx = 0;idx<n;idx++){
            if(mask&(1<<idx)) continue;
            string temp = store[last][idx] + solve(idx,mask|(1<<idx),n);
            if(res==""){
                res = temp;
            }
            else if(temp.length()<=res.length()){
                res = temp;
            }
        }
        return dp[last][mask]=res;
    }

    string shortestSuperstring(vector<string>& words) {
        int n = words.size();
        store.resize(n,vector<string>(n,""));
        dp.resize(n,vector<string>((1<<n),""));
        for(int i = 0;i<n;i++){
            for(int j = 0;j<n;j++){
                if(i==j) continue;
                store[i][j] = merge(words[i],words[j]); 
            }
        }
        string res = "";
        for(int i = 0;i<n;i++){
            int mask = 0;
            string temp = words[i] + solve(i,mask|(1<<i),n);
            if(res==""){
                res = temp;
            }
            else if(temp.length()<res.length()){
                res = temp;
            }
        }
        return res;
    }
};
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