<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:
    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        unordered_map<string,int> map;
        int x=0;
        for(auto &i:people){
            for(auto &j:i){
                if(map.find(j)==map.end()){
                    map[j]=x;
                    cout<<j<<"is mapped to "<<x<<endl;
                    x++;
                }
            }
        }

        vector<int> masked(people.size());
        for(int i=0;i<people.size();i++){
            for(auto j:people[i]) masked[i]=masked[i]|(1<<map[j]);
        }
        int final=0;
        
        for(auto i:req_skills) final|=(1<<(map[i]));
        //cout<<final<<" ";
        int ans=INT_MAX;
        vector<int> dp((1<<16)+1,-1);
        dp[0]=0;
        vector<set<int>> sol(dp.size());
        for(int i=0;i<masked.size();i++){
            for(int j=0;j<dp.size();j++){
                if(dp[j]!=-1){
                    if(dp[j|masked[i]]==-1) {
                        dp[j|masked[i]]=1+dp[j];
                        sol[j|masked[i]]=sol[j];
                        sol[j|masked[i]].insert(i);
                    }
                    else {
                        dp[j|masked[i]]=min(dp[j|masked[i]],dp[j]+1);
                        if(dp[j|masked[i]] == dp[j]+1){
                            sol[j|masked[i]]=sol[j];
                            sol[j|masked[i]].insert(i);
                        }
                    }

                    if(((j|masked[i])&(final)) == final) ans=min(ans,dp[j|masked[i]]);
                }
            }
        }
        vector<int> zz;
        for(int i=0;i<dp.size();i++){
            if((i&final) == final && dp[i]==ans){
                for(auto j:sol[i]){
                    zz.push_back(j);
                }
                break;
            }
        }

        return zz;
        

    }
};
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