<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:
    vector<int> smallestSufficientTeam(vector<string>& arr, vector<vector<string>>& people) {
        int n = arr.size();
        unordered_map<string, int> mp;
        for(int i = 0; i<n; i++) mp[arr[i]] = i;
        vector<int> bitArray;
        for(auto it: people){
            int num = 0;
            for(auto st: it){
                num = num|(1<<mp[st]);
            }
            bitArray.push_back(num);
        }

        // for(auto num: bitArray) cout<<num<<" ";
        // cout<<'\n';

        unordered_map<int, vector<int>> dp;
        dp[0] = {};
        int target = (1<<n)-1;

        int size = bitArray.size();
        for(int i = 0; i< size; i++){
            // cout<<"Iteration: "<<i<<'\n';
            vector<pair<int, vector<int>>> arr1;
            unordered_map<int, vector<int>> arr2;
            for(auto it: dp) {
                // cout<<it.first<<","<<it.second<<" ";
                arr1.push_back({it.first, it.second});
            }
            // cout<<'\n';
            int num = bitArray[i];
            for(auto p : arr1){
                int val = num | p.first;
                vector<int> mask = p.second;
                mask.push_back(i);
                int newCount = mask.size();
                if(dp.find(val)!=dp.end()){
                    int prevCount =dp[val].size();
                    if(newCount < prevCount) {
                        if(arr2.find(val)!=arr2.end()) {
                            int bit = arr2[val].size();
                            if(newCount < bit) arr2[val] = mask;
                        }
                        else arr2[val] = mask;
                    } 
                }
                else {
                    if(arr2.find(val)!=arr2.end()) {
                        int bit = arr2[val].size();
                        if(newCount < bit) arr2[val] = mask;
                    }
                    else arr2[val] = mask;
                }
            }
            for(auto p2: arr2) {
                // cout<<p2.first<<","<<p2.second<<" ";
                dp[p2.first] = p2.second;
            }
            // cout<<'\n';
        }

        // cout<<target<<" "<<dp[target]<<'\n';
        vector<int> ans = dp[target];
        // vector<int> res;
        // for(int i = 0; i<16; i++){
        //     if(ans&(1<<i)) res.push_back(i);
        // }
        // cout<<(17 | 6)<<" "<<(17|44|34)<<'\n';
        return ans;
    }
};
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