Smallest Sufficient Team
<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>
Bit Manipulation; Array; Dynamic Programming; Bitmask
class Solution {
public:
    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        unordered_map<string, int> d;
        int m = req_skills.size(), n = people.size();
        for (int i = 0; i < m; ++i) {
            d[req_skills[i]] = i;
        }
        int p[n];
        memset(p, 0, sizeof(p));
        for (int i = 0; i < n; ++i) {
            for (auto& s : people[i]) {
                p[i] |= 1 << d[s];
            }
        }
        int f[1 << m];
        int g[1 << m];
        int h[1 << m];
        memset(f, 63, sizeof(f));
        f[0] = 0;
        for (int i = 0; i < 1 << m; ++i) {
            if (f[i] == 0x3f3f3f3f) {
                continue;
            }
            for (int j = 0; j < n; ++j) {
                if (f[i] + 1 < f[i | p[j]]) {
                    f[i | p[j]] = f[i] + 1;
                    g[i | p[j]] = j;
                    h[i | p[j]] = i;
                }
            }
        }
        vector<int> ans;
        for (int i = (1 << m) - 1; i; i = h[i]) {
            ans.push_back(g[i]);
        }
        return ans;
    }
};