<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]:
        skillIdxMap = collections.defaultdict(int)
        for i,skill in enumerate(req_skills):
            skillIdxMap[skill] = i
        ppWithSkillIdx = []
        for skillList in people:
            temp = []
            for skill in skillList:
                temp.append(skillIdxMap[skill])
            ppWithSkillIdx.append(temp)
        n = len(req_skills)
        total = 1<<n
        dp = [[float('inf'), []] for _ in range(total)]
        dp[0][0] = 0
        for mask in range(total):
            if(dp[mask][0] == float('inf')):
                continue
            candidate = []
            for i in range(n):
                if(mask>>i&1 == 0):
                    candidate.append(n-1-i)
            if(not candidate):
                continue

            for pId, sList in enumerate(ppWithSkillIdx):
                nextMask = mask
                for s in sList:
                    if(s in candidate):
                        nextMask |= 1<<(n-1-s)
                        
                if(dp[nextMask][0]>dp[mask][0]+1):
                    dp[nextMask][0] = dp[mask][0]+1
                    dp[nextMask][1] = list(dp[mask][1])
                    dp[nextMask][1].append(pId)

        return dp[-1][1]
30032