<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:
    void ans(int i, vector<int>& pskills, vector<int>& temp, vector<int>& re,
             int currentm, int req, unordered_map<string, int>& dp) {
        if (i >= pskills.size()) {
            if (currentm == pow(2, req) - 1) {
                if (re.size() == 0 || re.size() >= temp.size())
                    re = temp;
            }
            return;
        }
        if (re.size() != 0 && temp.size() >= re.size())
            return;
        // if(m[{i,currentm}]!=m.end())
        // return m[{i,currentm}];
        string key = to_string(i) + "_" + to_string(currentm);
        if (dp.find(key) != dp.end()) {
            if (dp[key] <= temp.size())
                return;
        }
        ans(i + 1, pskills, temp, re, currentm, req, dp);
        if(pskills[i]!=0){
        temp.push_back(i);
        ans(i + 1, pskills, temp, re, currentm | pskills[i], req, dp);
        temp.pop_back(); 
        dp[key] = (temp.size() != 0 ) ? temp.size() : 0;}
        
        return;
    }
    vector<int> smallestSufficientTeam(vector<string>& req_skills,
                                       vector<vector<string>>& people) {
        unordered_map<string, int> m;
        for (int i = 0; i < req_skills.size(); i++)
            m[req_skills[i]] = i;
        vector<int> pskills;
        for (int i = 0; i < people.size(); i++) {
            int temp = 0;
            for (int j = 0; j < people[i].size(); j++)
                temp = temp | (1 << m[people[i][j]]);
            pskills.push_back(temp);
        }
        vector<int> temp;
        vector<int> re;
        unordered_map<string, int> dp;
        ans(0, pskills, temp, re, 0, req_skills.size(), dp);
        return re;
    }
};
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