<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, a: List[str], people: List[List[str]]) -> List[int]:
        req_skill = (1<<len(a))-1
        m = {value:idx for idx,value in enumerate(a)}
        people_skills = [0 for j in people]
        MAXI = (1<<len(people))-1
        for idx,j in enumerate(people):
            for i in j:
                people_skills[idx]|=(1<<m[i])
        people_len = len(people)
        people_taken=0
        dp = [-1 for _ in range(1<<len(a))]
        def solve(total_skill_remaining_to_take, idx):
            if(not total_skill_remaining_to_take):
                return 0
            if idx==people_len:
                return MAXI
            if dp[total_skill_remaining_to_take]==-1:
                
                # old = total_skill_remaining_to_take
                # new_skill_mask = ((~total_skill_remaining_to_take)^people_skills[idx])^old
                new_skill_mask = (total_skill_remaining_to_take|people_skills[idx])^people_skills[idx]
                ans1=solve(new_skill_mask,idx+1)|(1<<idx)
                ans2=solve(total_skill_remaining_to_take,idx+1)
            # print(total_skill_remaining_to_take,idx)
            # print("remain",total_skill_remaining_to_take,"ans1",ans1,ans2,"idx",idx)
                dp[total_skill_remaining_to_take] = ans1 if ans1.bit_count()<ans2.bit_count() else ans2
            return dp[total_skill_remaining_to_take]
            
            
        temp = solve(req_skill,0)
        
        print(temp)
        ans = []
        for i in range(len(people)):
            if temp&(1<<i)!=0:
                ans.append(i)
        return ans
18552