<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>& a, vector<vector<string>>& b) {
        map<string, int> mp;
        for (int i = 0; i < a.size(); ++i) {
            mp[a[i]] = i;
        }
        int m = a.size(), n = b.size();
        vector<int> mask(n, 0);
        for (int i = 0; i < n; ++i) {
            for (const auto& s : b[i]) {
                mask[i] |= (1 << mp[s]);
            }
        }
        vector<vector<int> > dp(n + 1, vector<int> (1 << m, 1e9));
        vector<vector<int> > prev(n + 1, vector<int> (1 << m, -1));
        dp[0][0] = 0;
        prev[0][0] = 0;
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < (1 << m); ++j) {
                if (dp[i + 1][j] > dp[i][j]) {
                    dp[i + 1][j] = dp[i][j];
                    prev[i + 1][j] = j;
                }
                int nmask = j | mask[i];
                if (dp[i + 1][nmask] > dp[i][j] + 1) {
                    dp[i + 1][nmask] = dp[i][j] + 1;
                    prev[i + 1][nmask] = j;
                }
            }
        }
        int ma = (1 << m) - 1;
        vector<int> ans;
        while (n > 0) {
            if (prev[n][ma] != ma) {
                ma = prev[n][ma];
                ans.push_back(n - 1);
            }
            --n;
        }
        reverse(ans.begin(), ans.end());
        return ans;
    }
};
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