<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 {
    void recur(int skillsMask,vector<int> &people_skills,int n,int m, vector<int> &result, vector<int> &temp,vector<vector<int>> &dp){
        if(skillsMask==((1<<m)-1)) {
            if(result.size()==0 || temp.size()<result.size())
                result=temp;
            return;
        }
        if(n==0) return;
        
        if(dp[skillsMask][n]<temp.size()) return;
        
        // can pick
        if((people_skills[n-1]|skillsMask)!=skillsMask){
            temp.push_back(n-1);
            recur(skillsMask|people_skills[n-1],people_skills,n-1,m,result,temp,dp);
            temp.pop_back();
        }
        
        // not pick
        recur(skillsMask,people_skills,n-1,m,result,temp,dp);
        
        dp[skillsMask][n]=temp.size();
    }
public:
    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        int i=0, m=req_skills.size(), n=people.size();
        unordered_map<string,int> hmap;
        vector<int> people_skills(n,0), result, temp;
        vector<vector<int>> dp(1<<m,vector<int>(n+1,61));
        for(string& skill:req_skills)
            hmap[skill]=i++;
        i=0;
        for(auto &skills:people){
            for(string &skill:skills){
                people_skills[i]|=(1<<hmap[skill]);
            }
            i++;
        }
        recur(0,people_skills,n,m,result,temp,dp);
        return result;
    }
};
68348