<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[61][65536][2];
    int f(int index, int mask, int take, int numPeople, int numSkills, vector<int>& people){
        if(index==numPeople){
            int numSetBits = __builtin_popcount(mask);
            if(numSetBits==numSkills) return 0;
            return INT_MAX;
        }
        if(dp[index][mask][take]!=-1) return dp[index][mask][take];
        int newMask = mask;
        if(take){
            newMask|=people[index];
        }
        int op1 = f(index+1,newMask,1,numPeople, numSkills, people);
        int op2 = f(index+1,newMask,0,numPeople, numSkills, people);
        int ans = min(op1,op2);
        if(ans!=INT_MAX && take) ans++;
        return dp[index][mask][take] = ans;
    }
    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        int n = people.size();
        memset(dp,-1,sizeof(dp));
        map<string, int> mp;
        for(int i=0;i<req_skills.size();i++){
            mp[req_skills[i]] = i;
        }
        vector<int> peopleTransformed(people.size());
        for(int i=0; i<n; i++){
            int temp_mask = 0;
            for(auto skill: people[i]){
                temp_mask|=(1<<mp[skill]);
            }
            peopleTransformed[i] = temp_mask;
        }
        int op1 = f(0,0,1,n,req_skills.size(), peopleTransformed);
        int op2 = f(0,0,0,n,req_skills.size(), peopleTransformed);

        // calculate answer 
        vector<int> answer;
        int index= 0, j=0;
        int k = ((op1<op2) ? 1:0);
        while(index < n){
            if(k){
                answer.push_back(index);
                j|=peopleTransformed[index];
            }
            index++;
            k = dp[index][j][1] < dp[index][j][0] ? 1:0;
        }
        return answer;
    }
};
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