<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 find(int ind, int bit, vector<string>& s,
                vector<vector<string>>& dp) {
        int n = s.size();
        if (!dp[ind][bit].empty())
            return dp[ind][bit];
        if (bit == (1 << n) - 1)
            return dp[ind][bit] = "";
        string ans;
        for (int i = 0; i < n; i++) {
            if (!(bit & (1 << i))) {
                int nind = s[ind].size();
                int j = 0;
                for (j = 0; j < nind; j++) {
                    int size = min(nind - j, (int)s[i].size());
                    bool g = true;
                    for (int k = 0; k < size; k++) {
                        if (s[ind][j + k] != s[i][k]) {
                            g = false;
                            break;
                        }
                    }
                    if (g) {
                        break;
                    }
                }

                if (nind - j > s[i].size()) {
                    string temp = find(ind, bit | (1 << i), s, dp);
                    if (ans.empty() || temp.size() < ans.size())
                        ans = temp;
                } else {
                    string temp = s[i].substr(nind-j) + find(i, bit | (1 << i), s, dp);
                    if (ans.empty() || temp.size() < ans.size())
                        ans = temp;
                }
            }
        }
        return dp[ind][bit] = ans;
    }
    string shortestSuperstring(vector<string>& s) {
        int size = s.size();
        vector<vector<string>> dp(size, vector<string>(1 << size));
        string ans;
        for (int i = 0; i < size; i++) {
            string temp = s[i] + find(i, (1 << i), s, dp);
            if (ans.empty() || temp.size() < ans.size())
                ans = temp;
        }
        return ans;
    }
};
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