<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> ans; // To store the result team
    
    // Modified function to use bitmask
    pair<int, vector<int>> f(int index, int mask, vector<int>& pl, map<pair<int, int>, pair<int, vector<int>>>& dp) {
        if (mask == 0) return {0, {}}; // All skills covered
        if (index == pl.size()) return {1e9, {}}; // No more people left to choose from
        
        if (dp.find({mask, index}) != dp.end()) return dp[{mask, index}]; // Check if result is already computed
        
        // Case 1: Don't take the current person
        pair<int, vector<int>> nottake = f(index + 1, mask, pl, dp);
        
        // Case 2: Take the current person
        int new_mask = mask & ~pl[index]; // Remove the skills that this person covers
        pair<int, vector<int>> take = f(index + 1, new_mask, pl, dp);
        take.first += 1; // Increment the number of people
        take.second.push_back(index); // Add this person to the team
        
        // Choose the better option between taking and not taking the current person
        if (take.first < nottake.first) {
            dp[{mask, index}] = take;
        } else {
            dp[{mask, index}] = nottake;
        }
        
        return dp[{mask, index}];
    }
    
    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        unordered_map<string, int> mp;
        int n = req_skills.size();
        for (int i = 0; i < n; i++) {
            mp[req_skills[i]] = i; // Map each skill to an index
        }
        
        vector<int> pl(people.size()); // Each person's skills as a bitmask
        for (int i = 0; i < people.size(); i++) {
            int skill_mask = 0;
            for (auto& j : people[i]) {
                if (mp.find(j) != mp.end()) {
                    skill_mask |= (1 << mp[j]); // Set the bit corresponding to this skill
                }
            }
            pl[i] = skill_mask;
        }
        
        map<pair<int, int>, pair<int, vector<int>>> dp; // DP table storing minimum team size and the team
        
        int full_mask = (1 << n) - 1; // All skills covered bitmask (111...1 with `n` bits)
        
        // Run the recursive function starting from the first person and the full skill set
        pair<int, vector<int>> result = f(0, full_mask, pl, dp);
        
        return result.second; // Return the team
    }
};

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