<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 idx, int mask, vector<string>& a, vector<vector<int>>&w, vector<vector<string>>&dp){
        int n=a.size();
        if(mask==((1<<n) -1))return "";

        if(!dp[idx][mask].empty())return dp[idx][mask];

        int mini=1e9;
        string ans="";
        for(int i=0;i<n;i++){
            if((mask&(1<<i)) == 0){
                string temp=a[i].substr(w[idx][i])+solve(i, mask|(1<<i), a, w, dp);

                if(temp.length()<mini){
                    mini=temp.length();
                    ans=temp;
                }
            }
        }

        return dp[idx][mask]=ans;
    }
    string shortestSuperstring(vector<string>& a) {
        int n=a.size();
        vector<vector<int>>w(n+1, vector<int>(n+1, 0));
        vector<vector<string>>dp(n+2, vector<string>((1<<n)+5, ""));

        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                int nn=a[i].size(), mm=a[j].size();
                if(i==j){
                    w[i][j]=nn;
                    continue;
                }   
                int k=min(nn, mm);
                for(;k>=0;k--){
                    if(a[i].substr(nn-k)==a[j].substr(0, k)){
                        w[i][j]=k;
                        break;
                    }
                }
            }
        }

        int mini=1e9;
        string ans="";
        for(int i=0;i<n;i++){
            string temp=a[i]+solve(i, (1<<i), a, w, dp);

            if(temp.length()<mini){
                mini=temp.length();
                ans=temp;
            }
        }

        return ans;
    }
};
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