<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>

bool topo(vector<vector<int>>graph){
    int n=graph.size();
    vector<int>r(n,0);
    vector<int>ans;
    for(auto it:graph){
        for(auto x:it){
            r[x]++;
        }
    }
    queue<int>q;
    for(int i=0;i<n;i++){
        if(r[i]==0){
            q.push(i);
        }
    }
    while(!q.empty()){
        int p=q.size();
        for(int i=0;i<p;i++){
            int node=q.front();
            ans.push_back(node);
            q.pop();
            for(auto it:graph[node]){
                r[it]--;
                if(r[it]==0){q.push(it);}
            }
        }
    }
    int m=ans.size();
    if(m==n){
        return true;
    }
    return false;
}
class Solution {
public:
    bool canFinish(int n, vector<vector<int>>& p) {
        vector<vector<int>>g(n);
        int z=p.size();
        for(int i=0;i<z;i++){
            g[p[i][0]].push_back(p[i][1]);
        }
        return topo(g);
        
    }
};
20200