<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 solve(int index,int mask,vector<int>&skill,int &n, vector<vector<int>>&dp,vector<vector<int>>&did){
        if(mask==(1<<n)-1){
            return 0;
        }
        if(index==skill.size()){
            return 200;
        }
        if(dp[mask][index]!=-1)return dp[mask][index];
        int ans=solve(index+1,mask|skill[index],skill,n,dp,did)+1;
        int ans1=solve(index+1,mask,skill,n,dp,did);
        if(ans<ans1){
            did[mask][index]=1;
        }
        return dp[mask][index]= min(ans,ans1);
    }
    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        int n= req_skills.size();
        unordered_map<string ,int>m;
        for(int i=0;i<n;i++){
            m[req_skills[i]]=i;
        }
        vector<int>skill;
        for(int i=0;i<people.size();i++){
            int mask=0;
            for(auto& it:people[i]){
                if(m.find(it)!=m.end()){
                    mask|=(1<<m[it]);
                }
            }
            skill.push_back(mask);
        }
        vector<vector<int>>dp((1<<n),vector<int>(skill.size(),-1));
        vector<vector<int>>did((1<<n),vector<int>(skill.size(),0));
        solve(0,0,skill,n,dp,did);
        vector<int>ans;
        for(int i=0,mask=0;i<people.size();i++){
            if(did[mask][i]){
                mask|=skill[i];
                ans.push_back(i);
            }
            if(mask==(1<<n)-1){
                break;
            }
        }
        return ans;
    }
};
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