<p>There are a total of <code>numCourses</code> courses you have to take, labeled from <code>0</code> to <code>numCourses - 1</code>. You are given an array <code>prerequisites</code> where <code>prerequisites[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that you <strong>must</strong> take course <code>b<sub>i</sub></code> first if you want to take course <code>a<sub>i</sub></code>.</p>

<ul>
	<li>For example, the pair <code>[0, 1]</code>, indicates that to take course <code>0</code> you have to first take course <code>1</code>.</li>
</ul>

<p>Return <em>the ordering of courses you should take to finish all courses</em>. If there are many valid answers, return <strong>any</strong> of them. If it is impossible to finish all courses, return <strong>an empty array</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> numCourses = 2, prerequisites = [[1,0]]
<strong>Output:</strong> [0,1]
<strong>Explanation:</strong> There are a total of 2 courses to take. To take course 1 you should have finished course 0. So the correct course order is [0,1].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> numCourses = 4, prerequisites = [[1,0],[2,0],[3,1],[3,2]]
<strong>Output:</strong> [0,2,1,3]
<strong>Explanation:</strong> There are a total of 4 courses to take. To take course 3 you should have finished both courses 1 and 2. Both courses 1 and 2 should be taken after you finished course 0.
So one correct course order is [0,1,2,3]. Another correct ordering is [0,2,1,3].
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> numCourses = 1, prerequisites = []
<strong>Output:</strong> [0]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= numCourses &lt;= 2000</code></li>
	<li><code>0 &lt;= prerequisites.length &lt;= numCourses * (numCourses - 1)</code></li>
	<li><code>prerequisites[i].length == 2</code></li>
	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; numCourses</code></li>
	<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
	<li>All the pairs <code>[a<sub>i</sub>, b<sub>i</sub>]</code> are <strong>distinct</strong>.</li>
</ul>

class Solution {
public:
    set<int> visited;
    set<int> cycle;
    map <int, vector<int>> mp;
    vector<int> output;

    bool dfs (int Course){
        if (cycle.find (Course) != cycle.end ()){
            return false;
        }
        if (visited.find (Course) != visited.end ()){
            return true;
        }

        cycle.insert (Course);
        for (int i = 0; i < mp[Course].size(); i++){
            if (!dfs (mp[Course][i])){
                return false;
            }
        }
        cycle.erase (Course);
        visited.insert (Course);
        output.push_back (Course);
        return true;
    }

    vector<int> findOrder(int numCourses, vector<vector<int>>& prerequisites) {
        for (int i = 0; i < prerequisites.size(); i++){
            mp[prerequisites[i][0]].push_back (prerequisites[i][1]);
        }

        for (auto itr = mp.begin(); itr != mp.end(); itr++){
            if (!dfs (itr->first)) return {};
        }

        for (int i=0; i<numCourses; i++){
            if (find(output.begin(), output.end(), i) == output.end()){
                output.push_back (i);
            }
        }
        return output;
    }
};
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