<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<<16];
    bool choice[61][1<<16];
    int solve( vector<vector<string>>& people,int i,int currbit,int reqbit){
      int n = people.size();
      if(i>=n){
        if(currbit == reqbit){
           return 0;
          }
        return 1e9;
      }
      if(dp[i][currbit] != -1 )return dp[i][currbit];
      //not take
      int nt =  solve(people,i+1,currbit,reqbit);
      //take
      int newbit = currbit;
      for(auto it:people[i]){
        int ind = skillmap[it];
        newbit |= (1<<ind);
      }
      int t = 1 + solve(people,i+1,newbit,reqbit);

      if(t<nt){
        // way to hash the sequence in recursion type
        choice[i][currbit] = 1;
      }
      return dp[i][currbit] = min(t,nt);
    }
public:
    vector<int> smallestSufficientTeam(vector<string>& req, vector<vector<string>>& people) {
        int n = req.size();
        int reqbit = 0;
        memset(dp,-1,sizeof(dp));
        memset(choice,0,sizeof(choice));
        for(int i=0;i<n;i++){
          skillmap[req[i]] = i;
          reqbit |= (1<<i);
        }
        vector<int>ans;
        // solve(people,0,0,reqbit);

        // int currbit = 0;
        // // printing the sequence
        // for(int i =0;i<people.size();i++){
        //   if(choice[i][currbit]){
        //     ans.push_back(i);
        //     for(auto it:people[i]){
        //       int ind = skillmap[it];
        //       currbit |= (1<<ind);
        //    }  
        //   }
        //   if(currbit == reqbit)break;
        // }
        // return ans;


        // bottoming up 
        unordered_map<int,vector<int>>dp; // for every skillsbit indices required to make it in array
        dp.reserve(1<<16);
        dp[0] = {};

        for(int i =0;i<people.size();i++){
          int curr = 0;
          for(auto it:people[i]){
          int ind = skillmap[it];
          curr |= (1<<ind);
        }
        for(auto &it:dp){
          int combo = it.first | curr;
          if(!dp.count(combo)|| dp[combo].size()>(it.second).size()+1){
            dp[combo] = it.second;
            dp[combo].push_back(i);
          }
        }
    }
    return dp[reqbit];
    } 
};
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