<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:
    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        int n = (req_skills).size();
        int m = (int)people.size();
        map<string, int> mapping;
        for(int i = 0 ; i < n; i++){
            mapping[req_skills[i]] = i;
        }
        vector<vector<int> > v(m);
        for(int i = 0 ; i < m; i++){
            for(string s : people[i]){
                v[i].push_back(mapping[s]);
            }
        }
        vector<vector<int> > dp((1<<n), vector<int> (m, 1e9+7));
        vector<vector<int> > ans((1<<n), vector<int> (m, -1));
        //dp[mask][i] = min cost to cover all the tasks marked by mask using first i people
        //            = min(dp[mask without ones covered by i][i-1], dp[mask][i-1])
        int first = 0;
        dp[0][0] = 0;
        for(int i = 0 ; i < m; i++){
            dp[0][i] = 0;
        }
        for(int mask = 1; mask < (1<<n); mask ++){
            for(int j = 0 ; j < m; j++){
                int new_mask = mask;
                for(int i = 0; i < (int)v[j].size(); i++){
                    new_mask = new_mask & (~(1 << (v[j][i])));
                }
                if(j == 0 && new_mask != 0){
                    continue;
                }
                if(new_mask == 0){
                    dp[mask][j] = 1;
                    ans[mask][j] = j;
                    continue;
                }
                if(dp[mask][j-1] <= dp[new_mask][j-1]+1){
                    dp[mask][j] = dp[mask][j-1];
                    ans[mask][j] = ans[mask][j-1];
                }
                else{
                    dp[mask][j] = dp[new_mask][j-1]+1;
                    ans[mask][j] = j;
                }
            }
        }
        
        vector<int> answer;
        int mask = (1<<n)-1;
        int cur = ans[mask][m-1];
        int idx = (m-1);
        cout<<dp[mask][idx]<<endl;
        while(mask != 0 && idx >= 0){
            cur = ans[mask][idx];
            if(cur != -1){
                answer.push_back(cur);
                for(int j = 0; j < (int)v[cur].size(); j++){
                    mask = mask & (~(1<<(v[cur][j])));
                }
                
            }
            idx--;
        }
        return answer;
        
        


    }
};
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