<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;
vector<int> anss;
bool chc[1<<16][65];
int func(int i, int val, int need, vector<int> &per,  map<string,int> &dp){
   
    if(val==need) return 0;
     if(i>=m) return 1e8;

if(dp[to_string(i)+" "+ to_string(val)]) return dp[to_string(i)+" "+ to_string(val)];
    int newv = val|per[i];
    int take = 1+ func(i+1,newv,need,per,dp);
    int nottake = func(i+1,val,need,per,dp);
    if(take<nottake) chc[val][i]=1;

    return dp[to_string(i)+" "+ to_string(val)]= min(take,nottake);
};
    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        n= req_skills.size();
        m= people.size();
        int need= (1<<n)-1;
        map<string,int> mp;
         for(int i=0;i<n;i++){
            mp[req_skills[i]]=(1<<i);
        }
  vector<int> per;
  for(int i=0;i<m;i++){
    auto vec = people[i];
    int valu=0;
    for(auto a: vec){
         if(mp.find(a)!=mp.end()) valu = valu|mp[a];
    };
    per.push_back(valu);
  };
  
  
   map<string,int> dp;
 
   func(0,0,need,per,dp);
   int mask=0;
   for(int i=0;i<m;i++){
if(chc[mask][i]){
anss.push_back(i);
mask = mask| per[i];
}; 
   };
return anss;

    };
};
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