<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 m, n;
    int target_mask;
    vector<int> result;
    vector<vector<int>> t;
    
    void solve(vector<int> &people , int idx , vector<int> &temp, int mask ) {
        
       if(idx == people.size()) {
           if(mask == target_mask) {
               if(result.size() == 0 || result.size() >= temp.size()) {
                   //vector<int> copy = temp;
                   result = temp;
               }
           }
           return;
       }
        
        if(t[idx][mask] != -1) {
            if(t[idx][mask] <= temp.size())
               return ; 
        }
        
        if(result.size() != 0 && temp.size() >= result.size()) 
            return; 
        
        solve(people , idx + 1 , temp , mask ); // no

        if( (mask | people[idx]) != mask) {
            temp.push_back(idx);
            solve(people, idx + 1, temp , mask | people[idx]);

            temp.pop_back();
            t[idx][mask] = (temp.size() != 0 ) ? temp.size() : -1;
        }

    }
    
    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        n = req_skills.size();                                                                                          
        m = people.size();
        
        unordered_map<string, int> skills; //skill -> unique number
        for (int i = 0; i < n; ++i)
            skills[req_skills[i]] = i;
        
        // represent each person by a single bitmasked number (k'th bit represents if a person has the k'th skill or not)
        vector<int> people_skill;
        for (auto &v: people) {
            int skill_bit = 0;
            for (string &skill: v)
                skill_bit |= 1 << skills[skill];
            
            people_skill.push_back(skill_bit);
        }
        
        // required set of skills mask (All set to 1s)
        target_mask = pow(2, n) - 1;

        t.resize(62, vector<int>(target_mask+1, -1));
        vector<int> temp;
        solve(people_skill, 0, temp, 0);
        return result;
    }
};
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