<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:
    pair<int, vector<int>> dfs(int i, vector<vector<string>> &people, vector<string> &req_skills, int mask, map<pair<int, int>, pair<int, vector<int>>> &dp){
        if(mask==(1<<req_skills.size())-1) return {0, {}};
        if(i==people.size()) return {INT_MAX, {}};
        if(dp.count({i, mask})) return dp[{i, mask}];
        // Do not consider current person
        auto a=dfs(i+1, people, req_skills, mask, dp);
        // Consider current person
        int covered=0;
        for(auto &curr_skill: people[i]){
            for(int j=0;j<req_skills.size();j++){
                if(curr_skill==req_skills[j] && !(mask&(1<<j))){
                    covered|=(1<<j);
                }
            }
        }
        pair<int, vector<int>> b={INT_MAX, {}};
        // atleast one some skills are covered
        if(covered>0){
            b=dfs(i+1, people, req_skills, mask|covered, dp);
            if(b.first!=INT_MAX){
                b.second.push_back(i);
                b.first+=1;
            }
        }

        if(a.first<b.first) return dp[{i, mask}]=a;
        return dp[{i, mask}]=b;
    }
    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        map<pair<int, int>, pair<int, vector<int>>> dp;
        int mask=0;
        return dfs(0, people, req_skills, mask, dp).second;
    }
};
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