<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) {
        int courseCount = 0;
        queue<int> bfsQueue;
        unordered_map<int, int> preReqMap;
        unordered_map<int, vector<int>> graph;

        for(auto preReq: prerequisites) {
            int a = preReq[0];
            int b = preReq[1];

            preReqMap[a]++;
            graph[b].push_back(a);
        }
        for(int i=0; i < numCourses; ++i) {
            if(preReqMap.count(i) == 0) {
                bfsQueue.push(i);
            }
        }

        while(!bfsQueue.empty()) {
            ++courseCount;
            int top = bfsQueue.front();
            bfsQueue.pop();

            auto neighbours = graph[top];
            for(auto neighbour: neighbours) {
                --preReqMap[neighbour];

                if(preReqMap[neighbour] == 0) {
                    bfsQueue.push(neighbour);
                }
            }
        }

        return courseCount == numCourses;
    }
};
21500