<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 <code>true</code> if you can finish all courses. Otherwise, return <code>false</code>.</p>

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

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

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

<pre>
<strong>Input:</strong> numCourses = 2, prerequisites = [[1,0],[0,1]]
<strong>Output:</strong> false
<strong>Explanation:</strong> There are a total of 2 courses to take. 
To take course 1 you should have finished course 0, and to take course 0 you should also have finished course 1. So it is impossible.
</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;= 5000</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>All the pairs prerequisites[i] are <strong>unique</strong>.</li>
</ul>

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

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

        return adjL;
    }

    // bool canCompleteDfs(vector<vector<int>> &graph, vector<int> &vis, int course){
    //     vis[course] = 2;

    //     for(int adjC: graph[course]){
    //         if(!vis[adjC]){
    //             if(!canComplete(graph, vis, adjC)) return false;
    //         }else if(vis[adjC] == 2) return false;
    //     }
    //     vis[course]--;
    //     return true;
    // }

    bool canCompleteBfs(vector<vector<int>> &graph, vector<int> &ind, int v){
        // TopologicalSort
        // Kahn's Algo

        queue<int> q;
        vector<int> topo;
        for(int i = 0; i < v; i++){
            if(!ind[i]){
                q.push(i);
                topo.push_back(i);
            }
        }

        while(!q.empty()){
            int node = q.front();
            q.pop();

            for(int adjN:graph[node]){
                ind[adjN]--;
                if(!ind[adjN]){
                    q.push(adjN);
                    topo.push_back(adjN);
                }
            }
        }

        return topo.size() == v;
    }
public:
    bool canFinish(int v, vector<vector<int>>& edges) {
        vector<int> ind(v, 0);
        vector<vector<int>> graph = createGraph(v, edges, ind);

        return canCompleteBfs(graph, ind, v);
    }
};
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