<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 {
    vector<vector<string>> required;
    string merge(string& a, string& b) // a is followed by b (ab)
    {
        int n = a.size(), m = b.size(), len = 1, index = 0;
        while (len <= min(n, m)) 
        {
            if (a.substr(n - len) == b.substr(0, len)) 
            {
                index = len;
            }
            len++;
        }
        string ans = b.substr(index);
        return ans;
    }
    string solve(vector<string>& words, int prev, int mask, int n, vector<vector<string>> &dp)  {
        if (dp[prev][mask] != "")
            return dp[prev][mask];
        string ans = "";
        int len = INT_MAX;
        for (int i = 0; i < n; i++) 
        {
            if (mask & (1 << i))
                continue;
            string temp =
                required[prev][i] + solve(words, i, mask | (1 << i), n, dp);
            if (temp.size() < len) 
            {
                len = temp.size();
                ans = temp;
            }
        }
        return dp[prev][mask] = ans;
    }

public:
    string shortestSuperstring(vector<string>& words) 
    {
        int n = words.size();
        required.resize(n, vector<string>(n, ""));
        vector<vector<string>> dp(n, vector<string>((1 << (n + 1)), ""));
        for (int i = 0; i < n; i++) 
        {
            for (int j = 0; j < n; j++) 
            {
                if (i == j)
                    continue;
                required[i][j] = merge(words[i], words[j]);
            }
        }
        string ans = "";
        int len = INT_MAX;
        int mask = 0;
        for (int i = 0; i < n; i++) 
        {
            string temp = words[i] + solve(words, i, mask | (1 << i), n, dp);
            if (temp.size() < len) 
            {
                len = temp.size();
                ans = temp;
            }
        }
        return ans;
    }
};
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