<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 solve(int last,int mask,int n,int need,map<int,map<int,int>>&mp,vector<string>&words,vector<vector<string>>&dp){
        if(mask==need){
            return "";
        }
        if(dp[last+1][mask]!="")
            return dp[last+1][mask];
        string curr="";
        for(int i=0;i<n;i++){
            if((mask>>i)&1)
                continue;
            string temp=words[i].substr(mp[last][i]);
            int temp_mask=(mask|(1<<i));
            temp+=solve(i,temp_mask,n,need,mp,words,dp);
            if(curr==""||temp.length()<curr.length()){
                curr=temp;
            }
        }
        return dp[last+1][mask]=curr;
    }
    string shortestSuperstring(vector<string>& words) {
        map<int,map<int,int>> mp;
        int n=words.size();
        for(int i=0;i<n;i++){
            mp[-1][i]=0;
            for(int j=0;j<n;j++){
                int m=words[i].length();
                int m2=words[j].length();
                mp[i][j]=0;
                for(int l=1;l<min(m,m2);l++){
                    string temp=words[i].substr(m-l);
                    string temp2=words[j].substr(0,l);
                    if(temp==temp2){
                        mp[i][j]=l;
                    }
                }
            }
        }
        int mask=0;
        int need=(1<<n)-1;
        int last=-1;
        vector<vector<string>> dp(n+1,vector<string>(need,""));
        return solve(last,mask,n,need,mp,words,dp);

    }
};
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