<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>& skills, vector<vector<string>>& people) {
        int k = 0, i, j, n = people.size(), x;
        map<string,int>mp;
        for(i=0;i<skills.size();i++) {
            k = k*2 + 1;
            mp[skills[i]] = i;
        }
        vector<vector<int>> dp = vector<vector<int>> (n+1, vector<int>(k+1, 100));
        vector<int> v, ans;
        for(i=0;i<=n;i++) {
            dp[i][k] = 0;
        }

        for(i=1;i<=n;i++){
            x = 0;
            for(j=0;j<people[i-1].size();j++) {
                x += (1<<mp[people[i-1][j]]);
            }
            v.push_back(x);
            for(j=k;j>=0;j--) {
                dp[i][j] = dp[i-1][j];
                dp[i][j] = min(dp[i][j], dp[i-1][j | x] + 1);
            }
        }

        i = n, j = 0;
        while(i>0 && j<=k) {
            if(dp[i-1][j] == dp[i][j]) {
                i--;
            } else {
                j |= v[i-1];
                ans.push_back(i-1);
                i--;
            }
        }
        reverse(ans.begin(), ans.end());
        return ans;
    }
};
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