<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 {
public:
    void topSortBfs(int n, vector<int>& topoOrder,unordered_map<int , list<int> >& adjList ) {
		queue<int> q;
		unordered_map<int,int> indegree;
		
		//initialise kardi indegree sabki
		for( auto i : adjList) {
			for(auto nbr: i.second) {
				indegree[nbr]++;
			}
		}
		//push all zero indegree wali node into queue
		for(int node=0; node<n; node++) {
			if(indegree[node] == 0) {
				q.push(node);
			}
		}

		//BFS chalate hai
		while(!q.empty()) {
			int frontNode = q.front();
			q.pop();
			topoOrder.push_back(frontNode);

			for(auto nbr: adjList[frontNode]) {
				indegree[nbr]--;

				//check for zero
				if(indegree[nbr] == 0) {
					q.push(nbr);
				}
			}
		}
	}

    bool canFinish(int numCourses, vector<vector<int>>& prerequisites) {
        unordered_map<int , list<int> > adjList;
        for(auto i: prerequisites){
                 int u = i[0];
                 int v = i[1];
                 adjList[v].push_back(u);

        }

        vector<int> topoSort;
        topSortBfs(numCourses,topoSort,adjList) ; 
        if(topoSort.size() == numCourses)
            return true;
        else
            return false;
    }
};
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