<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;

    string solve(int pos, int val, vector<vector<string>> &dp, vector<vector<string>> &v){

        if(val==0){
            return "";
        }
        if (dp[pos][val].size()!= 0){
            return dp[pos][val];
        }

        string ans = "";
        for (int i=0; i<n; ++i){
            int val1 = 1<<i;
            if (val & val1){
                string str = v[pos][i] + solve(i, (val^val1), dp, v);
                if(ans.size()){
                    ans = ans.size()>str.size()?str:ans;
                }
                else{
                    ans = str;
                }
            }
        }
    return dp[pos][val] = ans;
    }

    string shortestSuperstring(vector<string>& words) {
        n = words.size();
        vector<vector<string>> v(n, vector<string>(n, ""));
        for (int i=0; i<n; ++i){
            for(int j=0; j<n; ++j){
                if(i==j) continue;

                string str = words[j];
                for(int k=0; k<words[i].size(); ++k){
                    string str1, str2;
                    str1 = words[i].substr(k);

                    for(int k1=0; k1 < words[j].size()+1; ++k1){
                        str2 = words[j].substr(0,k1);
                        
                        if(str1==str2){
                            str = words[j].substr(k1);
                            goto x;
                        }
                    }
                }
                x:;
                v[i][j] = str;
            }
        }

        string ans;
        int val = 1<<n;
        val--;
        vector<vector<string>> dp(n, vector<string>(val, ""));
        
        for(int i=0; i<n; ++i){
            string str = words[i];
            str += solve(i, (val^(1<<i)), dp, v);
            if(ans.size()){
                ans = ans.size()>str.size()?str:ans;
            }
            else{
                ans = str;
            }
        }
        return ans;
    }
};
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