<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:
//req_skill-> rs and people ->p
    int n,m;
    int tm;
    vector<int>result;

    unordered_map<string,int>dp;

    void solve(vector<int>&ps , int idx,vector<int>&temp,int mask){
        if(idx == ps.size()){
            if(mask == tm){
                if(result.size() ==0 || result.size() >= temp.size()){
                    result =temp;
                }
            }
            return;
        }
        string key = to_string(idx) + "_" + to_string(mask);
            if(dp.find(key)!= dp.end()){
                if(dp[key] <= temp.size())
                return;
            } 

        if(result.size()!=0 && temp.size() >= result.size()){
            return;
        }
        //skip
        solve(ps,idx+1,temp,mask);

        //take
        if((mask | ps[idx])!= mask )
        {temp.push_back(idx);
        solve(ps,idx+1,temp,(mask | ps[idx]));

        temp.pop_back();

        dp[key] = (temp.size() !=0) ? temp.size() :-1;
    }

    }

    vector<int> smallestSufficientTeam(vector<string>& rs, vector<vector<string>>& p) {
        n = rs.size();
        m =p.size();

        unordered_map<string,int>skills;

        for(int i=0;i<n;i++){
            string sn=rs[i];
            skills[sn] = i;
        }

        vector<int>ps;
        for(auto v : p){
            int sb=0;
            for(string skill:v){
                sb = sb | (1<<skills[skill]);
            }
            ps.push_back(sb);
        }
        tm = pow(2,n) -1;
        vector<int>temp;
        solve(ps,0,temp,0);
        return result;
    }
};
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