<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];
    int rec(int level,int mask,vector<vector<string>>&people,vector<string>&req_skills,map<string,int>&mp){
        
        if(level == people.size()){
            int k = req_skills.size();
            if(mask == (1<<k)-1)return 0 ;
            else return 1e9 ;
        }

        if(dp[level][mask] != -1)return dp[level][mask];

        // not taketake
        int ans = rec(level+1,mask,people,req_skills,mp);

        // not take
        int currmask = mask ;
        for(int i =0 ; i<people[level].size() ; i++){
                int skill_idx = mp[people[level][i]];
                if(currmask & (1<<skill_idx))continue ;
                currmask = currmask|(1<<skill_idx);
        }
        ans = min(ans,1+rec(level+1,currmask,people,req_skills,mp));

        return dp[level][mask] = ans ;
    }

    void generate(int level, int mask, vector<vector<string>>&people,vector<string>&req_skills,map<string,int>&mp, vector<int>&ans){
        if(level == people.size()){
            return ;
        }

        // not taketake
        int nottake = rec(level+1,mask,people,req_skills,mp);

        // not take
        int currmask = mask ;
        for(int i =0 ; i<people[level].size() ; i++){
                int skill_idx = mp[people[level][i]];
                if(currmask & (1<<skill_idx))continue ;
                currmask = currmask|(1<<skill_idx);
        }
        int take  = 1+rec(level+1,currmask,people,req_skills,mp);

        if(take <= nottake){
            ans.push_back(level);
            generate(level+1,currmask,people,req_skills,mp,ans);
        }
        else{
            generate(level+1,mask,people,req_skills,mp,ans);
        }
        
    }
    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        map<string,int>mp;
        for(int i =0 ; i< req_skills.size() ; i++){
            mp[req_skills[i]] = i ;
        }
        memset(dp,-1,sizeof(dp));
        int len = rec(0,0,people,req_skills,mp);
        // cout<<len<<endl;
        vector<int>ans ;

        generate(0,0,people,req_skills,mp,ans);

        return ans ;
    }
};
48641