<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:
    vector<vector<int>> dp,path;
    int func(int node, int mask, vector<vector<int>>& dist, int n){
        if (mask == (1 << n)-1) return 0;
        if (dp[node][mask]!=-1) return dp[node][mask];
        int minCost = 1e9;
        int indx = -1;
        for (int i=0; i<n; i++){
            if (mask & (1 << i)) continue;
            int curr = dist[node][i] + func(i,mask | (1 << i),dist,n);
            if (curr < minCost){
                minCost = curr;
                indx = i;
            }
        }
        path[node][mask] = indx;
        return dp[node][mask] = minCost;
    }
    vector<int> getLPS(string& curr){
        vector<int> lps(curr.size());
        for (int i=1,len=0; i<curr.size();){
            if (curr[i] == curr[len]){
                lps[i++] = ++len;
            }
            else if (len) len = lps[len-1];
            else lps[i++] = 0;
        }
        return lps;
    }
    string getShortestSS(int node, int mask, vector<string>& words, vector<vector<int>>& dist){
        string curr = words[node];
        int curr_mask = mask;
        int prev = node;
        node = path[node][mask];
        while (node!=-1){
            int m = words[node].size();
            curr+=words[node].substr(m-dist[prev][node]);
            curr_mask|=(1 << node);
            prev = node;
            node = path[node][curr_mask];
        }
        return curr;
    }
    string shortestSuperstring(vector<string>& words) {
        int n = words.size();
        vector<vector<int>> dist(n+5,vector<int>(n+5));
        for (int i=0; i<n; i++){
            for (int j=0; j<n; j++){
                if (i == j) continue;
                string curr = words[j] + "#" + words[i];
                vector<int> lps = getLPS(curr);
                int m = words[j].size();
                int q = curr.size();
                dist[i][j] = m-lps[q-1];
            }
        }
        string ans = "";
        int minLen = INT_MAX;
        dp = vector<vector<int>>(n+5,vector<int>(1 << n,-1));
        path = vector<vector<int>>(n+5,vector<int>(1 << n,-1));
        for (int i=0; i<n; i++){
            int currLen = words[i].size() + func(i,(1 << i),dist,n);
            if (currLen < minLen){
                minLen = currLen;
                string best = getShortestSS(i,(1 << i),words,dist);
                ans = best;
            }
        }   
        return ans;
    }
};
25600