<p>In a project, you have a list of required skills <code>req_skills</code>, and a list of people. The <code>i<sup>th</sup></code> person <code>people[i]</code> contains a list of skills that the person has.</p>

<p>Consider a sufficient team: a set of people such that for every required skill in <code>req_skills</code>, there is at least one person in the team who has that skill. We can represent these teams by the index of each person.</p>

<ul>
	<li>For example, <code>team = [0, 1, 3]</code> represents the people with skills <code>people[0]</code>, <code>people[1]</code>, and <code>people[3]</code>.</li>
</ul>

<p>Return <em>any sufficient team of the smallest possible size, represented by the index of each person</em>. You may return the answer in <strong>any order</strong>.</p>

<p>It is <strong>guaranteed</strong> an answer exists.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> req_skills = ["java","nodejs","reactjs"], people = [["java"],["nodejs"],["nodejs","reactjs"]]
<strong>Output:</strong> [0,2]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> req_skills = ["algorithms","math","java","reactjs","csharp","aws"], people = [["algorithms","math","java"],["algorithms","math","reactjs"],["java","csharp","aws"],["reactjs","csharp"],["csharp","math"],["aws","java"]]
<strong>Output:</strong> [1,2]
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= req_skills.length &lt;= 16</code></li>
	<li><code>1 &lt;= req_skills[i].length &lt;= 16</code></li>
	<li><code>req_skills[i]</code> consists of lowercase English letters.</li>
	<li>All the strings of <code>req_skills</code> are <strong>unique</strong>.</li>
	<li><code>1 &lt;= people.length &lt;= 60</code></li>
	<li><code>0 &lt;= people[i].length &lt;= 16</code></li>
	<li><code>1 &lt;= people[i][j].length &lt;= 16</code></li>
	<li><code>people[i][j]</code> consists of lowercase English letters.</li>
	<li>All the strings of <code>people[i]</code> are <strong>unique</strong>.</li>
	<li>Every skill in <code>people[i]</code> is a skill in <code>req_skills</code>.</li>
	<li>It is guaranteed a sufficient team exists.</li>
</ul>

class Solution {
public:

    vector<int> smallestSufficientTeam(vector<string>& s, vector<vector<string>>& t) {
        
        int n=s.size();
        map<string,int>mp;
        for(int i=0;i<n;i++){
            mp[s[i]]=i;
        }
        int m=t.size();
        vector<int>g[m];

        for(int i=0;i<m;i++){
            for(auto k : t[i])g[i].push_back(mp[k]);
        }

        vector<int> dp[(1<<16)];
        set<int>q,p;
        q.insert(0);
        for(int i=0;i<m;i++){
            if(g[i].size()==0)continue;
            for(auto k : q){
                int x=k;
                int y=k;

                for(auto r : g[i]){
                    x |= (1<<r);
                }
                if(dp[x].size()==0){dp[x]=dp[y];dp[x].push_back(i);}
                else if(dp[x].size()>dp[y].size()+1){
                    dp[x]=dp[y];
                    dp[x].push_back(i);
                }
                p.insert(x);
                p.insert(y);
            }
            q.clear();
            q=p;
            p.clear();
        }
        int a=pow(2,n)-1;
        return dp[a];
    }
};
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