<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>

#define ll long long int
class Solution {
public:
    unordered_map<string, ll> dp;
    ll f(ll i,vector<ll> &hash,ll mask,ll n){
        if(mask==(1<<n)-1) return 0;
        if(i>=hash.size()){
            return INT_MAX;
        }
        string key=to_string(i)+" "+to_string(mask);
        if(dp.count(key)) return dp[key];
        ll ans=INT_MAX;
        ll pick=f(i+1,hash,mask|hash[i],n);
        ll nonpick=f(i+1,hash,mask,n);
        if (__builtin_popcountll(pick)<__builtin_popcountll(nonpick)) ans=pick|(1LL<<i);
        else ans=nonpick;
        return dp[key]=ans;
    }
    vector<int> smallestSufficientTeam(vector<string>& req, vector<vector<string>>& peo) {
        ll n=req.size();
        ll m=peo.size();
        map<string,ll> mp;
        for(int i=0;i<n;i++){
            mp[req[i]]=(1<<i);
        }
        vector<ll> hash;
        for(int i=0;i<m;i++){
            int mask=0;
            for(auto x:peo[i]){
                mask=mask|mp[x];
            }
            hash.push_back(mask);
        }
        ll cnt=f(0,hash,0,n);
        vector<int> ans;
        int idx=0;
        while(cnt>0) {
            ll pick=cnt&1;
            if (pick==1) {
                ans.push_back(idx);
            }
            idx++;
            cnt=cnt/2;
        }
        return ans;
    }
};
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