<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 minChosen;
    long min;
    int end;
    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        minChosen = INT_MAX;
        min = 0;
        end = (1 << req_skills.size()) - 1;
        std::cout << "End: " << end << "\n";

        unordered_map<string, int> m;
        for(int i = 0; i < req_skills.size(); i++) {
            m[req_skills[i]] = i;
        }
        vector<vector<int>> p;
        for(vector<string>& person : people) {
            vector<int> up;
            for(string& skill : person) {
                up.push_back(m[skill]);
            }
            p.push_back(std::move(up));
        }

        vector<int> skills;
        for(string& s : req_skills) {
            skills.push_back(m[s]);
        }

        unordered_map<int, unordered_map<int, vector<int>>> memo;
        int state = 0;
        vector<int> res = func(p, 0, state, memo);
        res.pop_back();
        return res;
    }

    vector<int> func(vector<vector<int>>& p, int i, int state, unordered_map<int, unordered_map<int, vector<int>>>& memo) {
        if (i == p.size()) {
            if (state != end) {
                return {-1};
            }
            return {0};
        } else if (memo[i].find(state) != memo[i].end()) {
            return memo[i][state];
        }

        vector<int> best = {-1};
        int nuState = state;
        for(int skill : p[i]) {
            nuState |= (1 << skill);
        }
        // Pick this person if we're fulfilling a skill.
        if (nuState != state) {
            vector<int> res = func(p, i+1, nuState, memo);
            if (res[0] != -1) {
                best = {i};
                best.insert(best.end(), res.begin(), res.end());
            }
        }
        // Also try not picking this person.
        vector<int> res = func(p, i+1, state, memo);
        if (res[0] != -1) {
            if (best[0] == -1 || res.size() < best.size()) {
                best = res;
            }
        }
        memo[i][state] = best;
        return best;
    }

    int hd(long value) {
        int count = 0;
        while(value > 0) {
            if ((value & 1) > 0) {
                ++count;
            }
            value >>= 1;
        }
        return count;
    }
};
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