<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<vector<int>> dp;
    vector<int> find(unordered_map<string, int>& skills, vector<vector<string>>& people, int mask){
        // cout << mask << '\n';
        if (mask == 0)
            return {};
        if (dp[mask].size() != 0)
            return dp[mask];
        
        vector<int> minV(70);
        int n = people.size();
        for (int i = 0; i < people.size(); i++){
            int mask_decrease = mask;
            for (string &skill : people[i]){
                int idx = skills[skill];
                if (mask_decrease & (1 << idx))
                    mask_decrease -= (1 << idx);
            }
            if (mask_decrease == mask)
                continue;
            
            auto ret = find(skills, people, mask_decrease);
            ret.push_back(i);
            // ret.first++;
            // ret.second += (1LL << i);
            if (ret.size() <= minV.size())
                minV = ret;
        }
        dp[mask] = minV;
        return minV;
    }

    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        int n = req_skills.size();
        dp.resize((1 << n), {});
        unordered_map<string, int> skills;
        int idx = 0;
        for (string &s : req_skills){
            skills[s] = idx++;
        }
        // int candidates = 0;
        // for (int i = 0; i < people.size(); i++)
            // candidates.insert(i);
        auto ret = find(skills, people, (1 << n) - 1);
        // cout << ret.first << " " << ret.second << "\n";
        // vector<int> res;
        // for (int i = 0; i < 60; i++)
            // if (ret.second & (1LL << i))
                // res.push_back(i);
        return ret;
    }
};
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