<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) {
        unordered_map<string, int> skill_to_idx;
        int skills_num = 0;
        for(string &skill: req_skills) {
            skill_to_idx[skill] = skills_num++;
        }
        vector<int> skill_sets(people.size(), 0);
        for(int i = 0; i < people.size(); i++) {
            for(string &skill: people[i]) {
                if (skill_to_idx.find(skill) != skill_to_idx.end()) {
                    skill_sets[i] |= (1 << skill_to_idx[skill]);
                }
            }
        }
        unordered_map<int, vector<int>> dp;
        dp[0] = vector<int>();
        dp[0].reserve(16);
        for(int i = 0; i < skill_sets.size(); i++) {
            int skill_set = skill_sets[i];
            unordered_map<int, vector<int>> tmp = dp;
            for(auto [current_skills, current_people]: dp) {
                int x = current_skills | skill_set;
                if (tmp.find(x) == tmp.end() || tmp[x].size() > current_people.size() + 1) {
                    current_people.push_back(i);
                    tmp[x] = current_people;
                }
            }
            dp = tmp;
        }
        return dp[(1 << skills_num)-1];
    }

};
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