<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 smallestSufficientTeam(self, req_skills: List[str], people: List[List[str]]) -> List[int]:
        N, K = len(req_skills), len(people)
        people_skills = [0 for _ in range(K)]
        lookup = {}
        for i in range(N):
            lookup[req_skills[i]] = i
        for i in range(K):
            cur = 0
            for skill in people[i]:
                cur |= (1 << lookup[skill])
            people_skills[i] = cur

        smallest = K
        res = 0
        def has_hit(i, mask):
            for j in range(K):
                if (1 << j) & mask:
                    if (1 << i) & people_skills[j]:
                        return True
            return False

        def dp(i, mask): # i is current request skill, mask means how many people has been selected
            nonlocal smallest, res
            if i == N:
                if mask.bit_count() < smallest:
                    smallest = mask.bit_count()
                    res = mask
                return 0
            if mask.bit_count() >= smallest:
                return

            if has_hit(i, mask): # if current skill is already in team, go to require next skill
                dp(i+1, mask)
            else:
                for j in range(K): # choose one more people to cover current skill
                    if (1 << j) & mask:
                        continue
                    if (1 << i) & people_skills[j]:
                        dp(i+1, mask | (1 << j))

        dp(0, 0)
        
        team = []
        for i in range(K):
            if (1 << i) & res:
                team.append(i)
        return team
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