<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 {
public:
    int choices[1<<16][60];
    int dp[1<<16][60];

    int helper(vector<int> &p,int ind,int curr_mask,int reqd_mask){
        //base cases:
        if(curr_mask==reqd_mask)return 0;
        if(ind==p.size()) return 1e6;
        if(dp[curr_mask][ind]!=-1)return dp[curr_mask][ind];

        //two options for each index: take or notTake:
        int temp1=helper(p,ind+1,curr_mask,reqd_mask);
        int temp2=1+helper(p,ind+1,curr_mask | p[ind],reqd_mask);

        //if taking the current index is beneficial for us, we mark the
        //index as 1 in the choices, with the curr_mask as the mask needed;
        if(temp2<temp1) choices[curr_mask][ind]=1;

        //return the minimum no of people reqd for the job:
        return dp[curr_mask][ind]=min(temp1,temp2);
    }

    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people){
        memset(choices,0,sizeof(choices));
        memset(dp,-1,sizeof(dp));

        int n=req_skills.size();
        int m=people.size();

        //converting the skills from the reqd_skills into the 
        //no of bits 1 needs to be left-shifted in order to access it;
        unordered_map<string,int> skills;
        for(int i=0;i<n;i++)skills[req_skills[i]]=i;

        //converting the skills that the ith person has into bits;
        vector<int> p;
        for(auto v:people){
            int total_skills=0;
            for(auto str:v){
                total_skills |= (1<<skills[str]);
            }
            p.push_back(total_skills);
        }

        int reqd_mask=(1<<n)-1;
        helper(p,0,0,reqd_mask);

        //choose the beneficial indices with inital mask as 0 and 
        //push them into the out vector;
        vector<int> out;
        int mask=0;     //represents no people(thus no skills) at the beginning
        for(int i=0;i<m;i++){
            if(choices[mask][i]){
                mask |= p[i];
                out.push_back(i);
            }
        }
        return out;
    }
};
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