<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 getCommon(string &a,string &b){
        int i=1;
        int ans = 0;
        int n = a.size();
        while(i<=n && i<=b.size()){
            if(a.substr(n-i,i)==b.substr(0,i)){
                ans = i;
            }
            i++;
        }
        return ans;
    }
    string merge(string &a,string &b){
        int i =1;
        int n =a.size();
        int ans = 0;
        while(i<=n && i<=b.size()){
            if(a.substr(n-i,i)==b.substr(0,i)){
                ans = i;
            }
            i++;
        }
        a+=b.substr(ans);
        return a;
    }
    vector<string> v;
    int dp[14][1<<13];
    int solve(int ind,int mask){

        if(mask==0)
            return 0;
        
        if(~dp[ind+1][mask])
            return dp[ind+1][mask];

        int ans = 1e9; 

        if(ind==-1){
            for(int i=0;i<v.size();i++){
                if(mask&(1<<i)){
                    ans = min(ans , int(v[i].size()) + solve(i,mask^(1<<i)));
                }
            }
        }
        else
            for(int i=0;i<v.size();i++){
                if(mask&(1<<i)){
                    ans = min(ans , int(v[i].size()) - getCommon(v[ind],v[i]) + solve(i,mask^(1<<i)));
                }
            }
        
        return dp[ind+1][mask] = ans;
    }
    string fa;
    void traceroute(int ind,int mask){
        if(mask == 0)
            return ;
        
        int ans = dp[ind+1][mask];

        if(ind==-1){
            for(int i=0;i<v.size();i++){
                if( mask&(1<<i) &&  ans == (int(v[i].size()) + dp[i+1][mask^(1<<i)])){
                    fa = v[i];
                    traceroute(i,mask^(1<<i));
                    return;
                }
            }
        }
        else
            for(int i=0;i<v.size();i++){
                if( mask&(1<<i) && ans== (int(v[i].size()) - getCommon(v[ind],v[i]) + solve(i,mask^(1<<i)) ) ){

                    fa = merge(fa,v[i]);
                    traceroute(i,mask^(1<<i));
                    return;
                }

            }
    }
    string shortestSuperstring(vector<string>& words) {
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
        v = words;
        int n = words.size();
        if(n==1)
            return words[0];
        memset(dp,-1,sizeof(dp));

        solve(-1,(1<<n)-1);
        traceroute(-1,(1<<n)-1);

        return fa;
    }
};
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