<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:
    bool canFinish(int numCourses, vector<vector<int>>& prerequisites) {
        vector<int> in( numCourses, 0 );
        unordered_set<int> s;

        unordered_map<int, vector<int>> mp;
        for( auto i : prerequisites ){
            int u = i[0], v = i[1];
            mp[v].push_back(u);
            s.insert(u);
            s.insert(v);
            in[u]++;
        }
        
        queue<int> q;
        for( int i = 0 ; i < numCourses ; i++ ){
            if( (in[i] == 0) && s.find(i) != s.end() ){
                q.push(i);
            }
        }
        
        int ans =0;
        
        while( !q.empty() ){
            int f = q.front();
            q.pop();
            
            ans++;
            for( auto i : mp[f] ){
                in[i]--;
                
                if(in[i] == 0 ){
                    q.push(i);
                }
            }
        }
        return ( ans == s.size() );
        
    }
};

/*
2
[[1,0]]
2
[[1,0],[0,1]]
3
[[1,0],[1,2],[0,1]]
20
[[0,10],[3,18],[5,5],[6,11],[11,14],[13,1],[15,1],[17,4]]
5
[[1,4],[2,4],[3,1],[3,2]]
*/
21400