<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
class Solution {
public:
    unordered_map<string, ll> dp;
    vector<int> mask;
 ll f(int k, int idx, int currmask) {
        if (currmask == k)
            return 0;

        if(idx == mask.size())
            return INT_MAX;

        string key = to_string(idx)+" "+to_string(currmask);
        if (dp.count(key))
            return dp[key];
        ll ans = INT_MAX;
        ll pick = f(k,idx+1, currmask | mask[idx]);
        ll notPick = f(k, idx + 1, currmask);
        if (__builtin_popcountll(pick) < __builtin_popcountll(notPick)) 
         ans=pick | (1LL << idx);
         else 
         ans = notPick;

        dp[key] = ans;
        return ans;
    }
    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        unordered_map<string, int> mp;
        for (int i = 0; i < req_skills.size(); i++) {
            mp[req_skills[i]] = i;
        }
        mask.resize(people.size(), 0);
        for (int i = 0; i < people.size(); i++) {
            vector<string>& temp = people[i];
            int t = 0;
            for (string& skill : temp) {
                t |= 1 << mp[skill];
            }
            mask[i] = t;
        }

        int k = (1 << req_skills.size()) - 1;
        dp.clear();
        ll cnt = f(k,0,0);
        vector<int> ans;
        int index = 0;
        while (cnt > 0) {
            ll pick = cnt & 1;
            if (pick == 1) {
                ans.push_back(index);
            }
            index++;
            cnt >>= 1;
        }
        return ans;
    }
};
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