<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>

#include <bits/stdc++.h>

using namespace std;

class Solution {
public:
    vector<int> smallestSufficientTeam(vector<string> &req_skills, vector<vector<string>> &people) {
        unordered_map<string, int> map;
        auto n = req_skills.size(), m = people.size();
        for (int i = 0; i < n; i++) {
            map[req_skills[i]] = i;
        }
        vector<int> p(m);
        for (int i = 0; i < m; i++) {
            for (auto &s: people[i]) {
                p[i] |= 1 << map[s];
            }
        }
        int f[1 << n];
        memset(f, -1, sizeof f);
        f[0] = 0;
        auto dp = [&](auto &&dp, int mask) -> int {
            if (f[mask] != -1) return f[mask];
            f[mask] = 0x3f3f3f3f;
            for (int x: p) {
                if (mask & x) {
                    f[mask] = min(f[mask], dp(dp, mask ^ (mask & x)) + 1);
                }
            }
            return f[mask];
        };
        dp(dp, (1 << n) - 1);
        cout << f[(1 << n) - 1] << endl;
        vector<int> res;
        for (int mask = (1 << n) - 1; mask;) {
            for (int i = 0; i < m; i++) {
                if ((mask & p[i]) && f[mask] == f[mask ^ (mask & p[i])] + 1) {
                    mask ^= mask & p[i];
                    res.emplace_back(i);
                    break;
                }
            }
        }
        return res;
    }
};
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