<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 n , m , target_mask ; 
    unordered_map<string,int>dp ; 
    vector<int>result ; 
    void solve(vector<int>&people_skill , int idx , vector<int>& temp , int mask){
        if(idx >=people_skill.size()){
            if(mask==target_mask){
                if(result.size() ==0 || result.size() > temp.size()){
                    result = temp  ;
                }
            }
            return ;
        }
        string key = to_string(idx) + "_" + to_string(mask);

        if(dp.find(key)!=dp.end()){
            if(dp[key] <= temp.size()){
                return ;
            }
        }


        if(result.size()!=0 and temp.size() > result.size()){
            return  ;
        }
        // skip 
        solve(people_skill,idx+1,temp,mask);

        // take ; 
        if((mask | people_skill[idx]) != mask){
            temp.push_back(idx);
            solve(people_skill,idx+1,temp,mask | people_skill[idx]);
            temp.pop_back();
            dp[key] = (temp.size()!=0) ? temp.size() : -1 ; 
        }

    }
    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        // make the skill vector 
        n = req_skills.size();
        m = people.size(); 
        unordered_map<string,int>skills ; 

        for(int i=0;i<n;i++){
            skills[req_skills[i]] = i ; 
        }
        vector<int>people_skill ; 
        for(auto v : people){
            int skill_bit = 0 ;
            for(string skill : v){
                skill_bit = skill_bit | (1<<skills[skill]);
            }
            people_skill.push_back(skill_bit);
        }

        target_mask = pow(2,n)-1 ; 
        vector<int>temp ; 
        solve(people_skill,0,temp,0) ;
        return result;
    }
};
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