<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>

from collections import defaultdict

class Solution:
    def smallestSufficientTeam(self, req_skills: List[str], people: List[List[str]]) -> List[int]:
        skillBit = {}
        for i in range(len(req_skills)):
            skillBit[req_skills[i]] = 1 << i
        
        # print(skillBit)
        peopleSkillBits = [0] * len(people)
        for i in range(len(people)):
            for skill in people[i]:
                peopleSkillBits[i] |= skillBit[skill]
        
        # print(peopleSkillBits)
        
        dp = [[[]] * (2 ** len(req_skills)) for i in range(len(people))]
        # print(dp)

        for i in range(len(people)):
            skillI = peopleSkillBits[i]
            dp[i][skillI] = [i]
            for j in range(2 ** len(req_skills)):
                if len(dp[i-1][j]) > 0:
                    if len(dp[i][j]) == 0:
                        dp[i][j] =  dp[i - 1][j]
                    elif len(dp[i-1][j]) < len(dp[i][j]):
                        dp[i][j] =  dp[i - 1][j]


                    # if len(dp[i-1][j | skillI]) == 0:
                    if len(dp[i][j | skillI]) == 0:
                        dp[i][j | skillI] = dp[i-1][j] + [i]
                    elif len(dp[i-1][j]) + 1 < len(dp[i][j | skillI]):
                        dp[i][j | skillI] = dp[i-1][j] + [i]
                    #     continue

                    # if len(dp[i-1][j | skillI]) > 0 and len(dp[i-1][j | skillI]) < len(dp[i-1][j]) + 1:
                    #     dp[i][j | skillI] =  dp[i - 1][j | skillI]
                    #     continue                    
                    
                    # if len(dp[i-1][j | skillI]) > 0 and len(dp[i-1][j | skillI]) > len(dp[i-1][j]) + 1:
                    #     dp[i][j | skillI] = dp[i-1][j] + [i]
                    #     continue

        # print(dp)

        return dp[-1][-1]
38642