<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>& req_skills, vector<vector<string>>& people) {
        int numSkills = req_skills.size();
        int numPeople = people.size();
        unordered_map<string, int> skillToIndex; // map skill to its index in the bitmask

        // create a mapping from skill to its index in the bitmask
        for (int i = 0; i < numSkills; ++i) {
            skillToIndex[req_skills[i]] = i;
        }

        vector<int> peopleSkills(numPeople, 0); // bitmask representing skills of each person

        // calculate the bitmask for each person's skills
        for (int i = 0; i < numPeople; ++i) {
            for (const string& skill : people[i]) {
                peopleSkills[i] |= (1 << skillToIndex[skill]);
            }
        }

        // dp[i] stores the smallest team for the skillset represented by bitmask i
        unordered_map<int, vector<int>> dp;
        dp[0] = {}; // base case: empty skillset requires an empty team

        for (int i = 0; i < numPeople; ++i) {
            int currentSkill = peopleSkills[i];
            
            // Iterate through a copy of the keys to avoid concurrent modification
            vector<int> skillsets;
            for (auto const& [key, val] : dp) {
                skillsets.push_back(key);
            }

            for (int skillset : skillsets) {
                int combinedSkillset = skillset | currentSkill;
                if (dp.find(combinedSkillset) == dp.end() ||
                    dp[combinedSkillset].size() > dp[skillset].size() + 1) {
                    dp[combinedSkillset] = dp[skillset];
                    dp[combinedSkillset].push_back(i);
                }
            }
        }

        return dp[(1 << numSkills) - 1]; // return the smallest team for the complete skillset
    }
};
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