<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;
    int VISITED_ALL;
    pair<int, string> tsp(int mask, int cur, vector< vector< pair<int, string> > > &dp, vector< vector< int > > &cost, vector<string>& s){
    if(dp[mask][cur].first!= -1) return dp[mask][cur];
    int curSize = s[cur].length();
    if(mask == VISITED_ALL) return dp[mask][cur] = {curSize, s[cur]};
    int ans = INT_MAX; 
    string res = "";
    for(int city = 0; city < n; city++){
        int c = cost[cur][city];
        if((mask&(1<<city)) == 0){
            auto [nextSize, next] = 
                        tsp(mask|(1<<city), city, dp, cost, s);
            if(curSize + nextSize - c < ans){
                res = s[cur] + next.substr(c);
                ans = curSize + nextSize - c;
            }
        }
    }
    return dp[mask][cur] = {ans, res};        
    }
    // cost to append b to string a
    int computeCost(string a, string b){
        int A = a.length(), B = b.length();
        for(int i = 0; i < A; i++){
            // cout<<a.substr(i)<<" "<<b.substr(0,A-i)<<endl;
            if((B - (A-i) >= 0) 
                    and a.substr(i) == b.substr(0,A-i)){
                return (A-i);
            }
        }
        return 0;
    }
   string shortestSuperstring(vector<string>& s) {
    s.insert(s.begin(), "");
    n = s.size();
    vector< vector< int > > cost(n, vector<int>(n, -1));
    for(int i = 0; i < n; i++){
        for(int j = 0; j < n; j++){
            cost[i][j] = computeCost(s[i], s[j]);
            // cout<< s[i] <<" " << s[j] << " " << cost[i][j] << endl;
        }
    }
    VISITED_ALL = (1<<n) - 1;
    vector< vector< pair<int, string> > > dp;
    dp.resize((1<<n), vector< pair<int, string> >(n,{-1, ""}));
    return tsp(1, 0, dp, cost, s).second;
    }
};
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