<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>

#include <vector>
#include <string>
#include <unordered_map>
#include <bitset>
#include <utility>

using namespace std;

class Solution {
public:
    map<pair<int, int>, pair<bool, vector<int>>> dp;

   
    int getSkillBitset(const vector<string>& req_skills, const vector<string>& current_skills) {
        int bitset = 0;
        for (const string& skill : current_skills) {
            for (int i = 0; i < req_skills.size(); ++i) {
                if (skill == req_skills[i]) {
                    bitset |= (1 << i);
                }
            }
        }
        return bitset;
    }

    pair<bool, vector<int>> helper(vector<string>& req_skills, vector<vector<string>>& people, int index, int covered) {
        if (index == people.size()) {
        
            return {covered == (1 << req_skills.size()) - 1, {}};
        }

        
        if (dp.find({index, covered}) != dp.end()) {
            return dp[{index, covered}];
        }

        auto result_without = helper(req_skills, people, index + 1, covered);

   
        int person_bitset = getSkillBitset(req_skills, people[index]);
        int new_covered = covered | person_bitset;
        auto result_with = helper(req_skills, people, index + 1, new_covered);

        if (result_with.first) {
            result_with.second.push_back(index);
        }

        if (result_without.first && result_with.first) {
            if (result_without.second.size() <= result_with.second.size()) {
                return dp[{index, covered}] = result_without;
            } else {
                return dp[{index, covered}] = result_with;
            }
        } else if (result_without.first) {
            return dp[{index, covered}] = result_without;
        } else if (result_with.first) {
            return dp[{index, covered}] = result_with;
        } else {
            return dp[{index, covered}] = {false, {}};
        }
    }

    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        return helper(req_skills, people, 0, 0).second;
    }
};


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