<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 {
    unordered_map<string,int>skillmap;
    int minsz = 61;
    int dp[61][1<<17];
    vector<int>ans;
    void solve( vector<vector<string>>& people,int i,int currbit,int reqbit,vector<int>&curr){
      int n = people.size();
      if(i>=n){
        if(currbit == reqbit){
          if(!ans.size() || ans.size()>curr.size()){
            ans = curr;
          }
        }
        return;
      }
      if(dp[i][currbit] != -1 && dp[i][currbit]<curr.size())return;
      //not take
      solve(people,i+1,currbit,reqbit,curr);
      //take
      int newbit = currbit;
      for(auto it:people[i]){
        int ind = skillmap[it];
        newbit |= (1<<ind);
      }
      curr.push_back(i);
      solve(people,i+1,newbit,reqbit,curr);
      curr.pop_back();

      dp[i][currbit] = (curr.size()!= 0)?curr.size():-1;
      return ;
    }
public:
    vector<int> smallestSufficientTeam(vector<string>& req, vector<vector<string>>& people) {
        int n = req.size();
        ans.clear();
        int reqbit = 0;
        memset(dp,-1,sizeof(dp));
        for(int i=0;i<n;i++){
          skillmap[req[i]] = i;
          reqbit |= (1<<i);
        }
        vector<int>curr;
         solve(people,0,0,reqbit,curr);
        return ans;
    }
};
182644