<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]:
        m = len(req_skills)
        n = len(people)
        skill_index = {v:i for i, v in enumerate(req_skills)}
        cand=[]
        for skills in people:
            val=0
            for skill in skills:
                val |= 1 << skill_index[skill]
            cand.append(val)
        @cache
        def fn(i, mask):
            if mask==0:
                return []
            if i==n:
                return [0]*100
            
            if not mask & cand[i]:
                return fn(i+1, mask)
            return min(fn(i+1, mask), [i] + fn(i+1, mask &~cand[i]), key = len)
        
        return fn(0, (1<< m)-1)


        # m=len(req_skills)
        # n=len(people)
        # skill_index={v:i for i,v in enumerate(req_skills)}
        # cand=[]
        # for skills in people:
        #     val=0
        #     for skill in skills:
        #         val |=1<<skill_index[skill]

        #     cand.append(val)

        # @cache
        # def fn(i,mask):
        #     if mask==0:
        #         return []

        #     if i==n:
        #         return [0]*100

        #     if not (mask & cand[i]):
        #         return fn(i+1,mask)

        #     return min(fn(i+1,mask),[i]+fn(i+1,mask &~cand[i]),key=len)

        # return fn(0,(1<<m)-1)  


            
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