<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 n,m;
    int target_mask;
    vector<int> result;

    unordered_map<string, int> dp;

    void solve(vector<int>& people_skill, int index, vector<int>& temp, int mask) {

            if(index == people_skill.size()) {
                if(mask == target_mask) {
                    if(result.size() == 0 || result.size() >= temp.size()) {
                        result = temp;
                    } 
                }
                return;
            }

            string key = to_string(index) + "_" + to_string(mask);

            if(dp.find(key) != dp.end()) {
                if(dp[key] <= temp.size()) {
                    return;
                }
            }

            if(result.size() != 0 && temp.size() >= result.size()) {
                return;
            }

            solve(people_skill, index+1, temp, mask);

            if(mask | people_skill[index] != mask) {
                temp.push_back(index);

                solve(people_skill, index+1, temp, (mask | people_skill[index]));

                temp.pop_back();

                dp[key] = (temp.size() != 0) ? temp.size() : -1;
            }
    
    }

    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        n = req_skills.size();
        m = people.size();

        unordered_map<string, int> skills;

        for(int i=0; i<n; i++) {
            string skill_name = req_skills[i];
            skills[skill_name] = i;
        }

        vector<int> people_skill;

        for(auto &v : people) {
            
            int skill_bit = 0;
            for(string &skill:v) {
                skill_bit = skill_bit | (1 << skills[skill]);
            }

            people_skill.push_back(skill_bit);
        }

        target_mask = pow(2,n)-1;

        vector<int> temp;
        solve(people_skill, 0, temp, 0);

        return result;
    }
};
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