<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:
    vector<int> findOrder(int numCourses, vector<vector<int>>& prerequisites) {
        vector<vector<int>> graph(numCourses);
        for(auto& a: prerequisites){
            graph[a[0]].push_back(a[1]);
        }
        vector<int> order;
        unordered_set<int> inOrder;
        vector<bool> traversed(numCourses, false);
        bool cycle = false;
        for(int i = 0; i < numCourses; i++){
            if(!inOrder.count(i)){
                dfs(traversed, order, inOrder, graph, i, cycle);
            }
        }
        if(cycle){
            return {};
        }
        else{
            return order;
        }
    }
    void dfs(vector<bool>& traversed, vector<int>& order, unordered_set<int>& inOrder, vector<vector<int>>& graph, int node, bool& cycle){
        if(traversed[node]){
            cycle = true;
            return;
        }
        else{
            traversed[node] = true;
        }
        for(auto& a: graph[node]){
            if(!inOrder.count(a)){
                dfs(traversed, order, inOrder, graph, a, cycle);
            }
        }
        traversed[node] = false;
        order.push_back(node);
        inOrder.insert(node);

    }
    // vector<int> findOrder(int numCourses, vector<vector<int>>& prerequisites) {
    //     vector<vector<bool>> table(numCourses, vector<bool>(numCourses, false));
    //     for(auto& a: prerequisites){
    //         table[a[0]][a[1]] = true;
    //     }
    //     unordered_set<int> myset;
    //     for(int i = 0; i < numCourses; i++) myset.insert(i);
    //     bool no_in_edge;
    //     vector<int> output;
    //     bool change;
    //     while(!myset.empty()){
    //         change = false;
    //         for(auto& a: myset){
    //             // cout << a << endl;
    //             no_in_edge = true;
    //             for(int i = 0; i < numCourses; i++){
    //                 if(table[a][i]){
    //                     no_in_edge = false;
    //                     break;
    //                 }
    //             }
    //             if(no_in_edge){
    //                 output.push_back(a);
    //                 for(int i = 0; i < numCourses; i++){
    //                     // cout << i << a << endl;
    //                     table[i][a] = false;
    //                 }
    //                 myset.erase(a);
    //                 change = true;
    //                 break;
    //             }
                
    //         }
    //         if(!change) return {};
    //     }
    //     return output;
    // }
};
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