<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 all_set = (1 << n) - 1;
        unordered_map<string, int> skill_to_index;
        for (int i = 0; i < n; i++){
            skill_to_index[req_skills[i]] = i;
        }

        vector<int> people_skills;
        vector<vector<int>> hash(n, vector<int>());
        for (int i = 0; i < people.size(); i++){
            auto& skills = people[i];
            int skill = 0;
            for (string s: skills){
                skill |= (1 << skill_to_index[s]);
                hash[skill_to_index[s]].push_back(i);
            }
            people_skills.push_back(skill);
        }

        unordered_set<int> team;
        unordered_map<string, int> dp;
        dfs(0, 0, hash, people_skills, team, dp);
        vector<int> res;
        for (int i = 0; i < people.size(); i++){
            if (global_team.find(i) != global_team.end()){
                res.push_back(i);
            }
        }
        return res;
    }
    unordered_set<int> global_team;
    long dfs(int i, int skills, vector<vector<int>>& hash, vector<int>& people_skills, unordered_set<int>& team, unordered_map<string, int>& dp){
        if (i == hash.size()){
            if (global_team.empty() || global_team.size() >= team.size()){
                global_team = team;
            }
            return 0;
        }

        if (!global_team.empty() && team.size() > global_team.size()){
            return INT_MAX;
        }

        string state = to_string(team.size()) + " " + to_string(skills);
        if (dp.find(state) != dp.end()){
            return dp[state];
        }

        if (skills & (1 << i)){
            return dp[state] = dfs(i + 1, skills, hash, people_skills, team, dp);
        }

        long min_team = INT_MAX;
        for (auto& p: hash[i]){
            team.insert(p);
            long tsize = 1 + dfs(i + 1, skills | people_skills[p], hash, people_skills, team, dp);
            team.erase(p);
            min_team = min(min_team, tsize);
        }
        return dp[state] = min_team;
    }
};
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