<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 {
private:
    vector<vector<int>> createGraph(vector<vector<int>>& edges, vector<int>& ind, int v){
        vector<vector<int>> adjL(v);

        for(auto it:edges){
            adjL[it[1]].push_back(it[0]);
            ind[it[0]]++;
        }
        return adjL;
    }

    bool dfs(vector<vector<int>> &graph, vector<int> &vis, stack<int>& st, int node){
        vis[node] = 2;

        for(int adjN:graph[node]){
            if(!vis[adjN]){
                if(!dfs(graph, vis, st, adjN)) return false;
            } 
            else if(vis[adjN] == 2) return false;
        }

        vis[node]--;
        st.push(node);
        return true;
    }

    vector<int> courseOrderDfs(vector<vector<int>> &graph, int v){
        // Topo-Sort
        vector<int> vis(v, 0);
        stack<int> st;

        for(int i = 0; i < v; i++){
            if(!vis[i]){
                if(!dfs(graph, vis, st, i)) return {};
            }
        }

        vector<int> order;
        while(!st.empty()){
            order.push_back(st.top());
            st.pop();
        }

        return order;
    }

public:
    vector<int> findOrder(int v, vector<vector<int>>& edges) {
        vector<int> ind(v, 0);
        vector<vector<int>> graph = createGraph(edges, ind, v);
        return courseOrderDfs(graph, v);
    }
};
18500