<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 f(vector<vector<int>> &dp, vector<vector<int>> &choice, vector<int> &skillSet,int index, int mask, int n,int m){
        // Base Case
        if(mask==(1<<m)-1) return 0;
        if(index==n) return 1e5;

        if(dp[index][mask]!=-1) return dp[index][mask];

        // solve one case
        // select that index person
        int ans1 = 1+f(dp,choice,skillSet,index+1,mask|skillSet[index],n,m);

        // don't select that person
        int ans2 = f(dp,choice,skillSet,index+1,mask,n,m);

        if(ans1<ans2){
            choice[index][mask]=1;
        }

        return dp[index][mask]= min(ans1,ans2);
    }

    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        unordered_map<string,int> mp;

        // giving linear count to every skill
        int count=0;
        // then we'll convert every skill into binary representation by using 1<<count_val
        for(auto skill:req_skills){
            mp[skill]=count;
            count++;
        }

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

        vector<int> skillSet;

        for(int i=0;i<n;i++){
            int ans=0;
            for(auto skill:people[i]){
                ans = ans|(1<<mp[skill]);
            }
            skillSet.push_back(ans);
        }

        // Now I've created the skillset vector to contain every skill in binary representation
        // to create 1111, I can do (1<<4-1)
        
        //Lets form the dp
        vector<vector<int>> dp(n+1,vector<int>((1<<m),-1));
        vector<vector<int>> choice(n+1,vector<int>((1<<m),-1));

        int numPeople = f(dp,choice,skillSet,0,0,n,m);
        
        vector<int> ans;
        int mask=0;
        for(int i=0;i<n;i++){

            if(choice[i][mask]==1){
                ans.push_back(i);
                mask = mask|skillSet[i];

                if(mask==(1<<m)-1) break;
            }
        }
        return ans;
    }
};
91995