<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:
    def get_nonzero_bits(self, n):
        ans = []
        pos = 0
        while n > 0:
            if n & 1:
                ans.append(pos)
            n >>= 1
            pos += 1
        return ans

    def smallestSufficientTeam(self, req_skills: List[str], people: List[List[str]]) -> List[int]:
        n, m = len(people), len(req_skills)
        max_team = (1 << n) - 1
        skill_id = {req_skills[i]: i for i in range(m)}
        
        people_to_skill = [0 for _ in range(n)] # skillsMaskOfPerson
        for person_id, skills in enumerate(people):
            for skill in skills:
                people_to_skill[person_id] |= 1 << skill_id[skill]

        dp = {mask: max_team for mask in range(0, 1 << m)}
        dp[0] = 0

        for mask in range(1, 1 << m):
            for person_id in range(n):
                required = mask & ~people_to_skill[person_id]
                candidate_mask = dp[required] | (1 << person_id)
                if candidate_mask.bit_count() < dp[mask].bit_count():
                    dp[mask] = candidate_mask

        return self.get_nonzero_bits(dp[2**m - 1])

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