<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:
    int dp[62][1<<17];

    void f(int idx,int mask,int t,int m,vector<int>&a,vector<int>&v,vector<int>&ans){
        if(idx==m){
            if(mask==t){
               
                if(ans.size()==0 or ans.size()>=v.size())ans=v;
            }
            return;
        }
        if(dp[idx][mask]!=-1){
            if(dp[idx][mask]<=v.size())return;
        }
        if(ans.size()!=0 and v.size()>=ans.size())return;

        f(idx+1,mask,t,m,a,v,ans);
        if((mask|a[idx])!=mask){
            v.push_back(idx);
            f(idx+1,mask|a[idx],t,m,a,v,ans);
            v.pop_back();
            dp[idx][mask]=(v.size()!=0)?v.size():-1;
        }
    }
    vector<int> smallestSufficientTeam(vector<string>& r, vector<vector<string>>& p) {
        
        unordered_map<string,int>mp;
        int n=r.size();
        for(int i=0;i<n;i++){
            mp[r[i]]=i;
        }
        int m=p.size();
        vector<int>a;
        for(int i=0;i<m;i++){
            auto v=p[i];
            int mask=0;
            int sz=v.size();
            for(int j=0;j<sz;j++){
                mask|=(1<<mp[v[j]]);
            }
            a.push_back(mask);
        }
        // for(auto x:a)cout<<x<<" ";
        // cout<<endl;
        int t=(1<<n)-1;

        memset(dp,-1,sizeof(dp));
        vector<int>ans;
        vector<int>v;
        f(0,0,t,m,a,v,ans);

        return ans;

    }
};
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