<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) {
        

        // make a hash_map marking the number of pre-reqs for the course
            // also make a hash_map marking the outbound edges for each course
        // create a queue with just the courses without any pre-reqs
        // while queue is not empty
            // decrement 
        
        std::vector<int> num_prereq;
        num_prereq.resize(numCourses, 0);
    
        std::unordered_map<int, std::vector<int>> outbound_courses;
        for (const auto& pre : prerequisites) {
            num_prereq[pre[0]]++;
            outbound_courses[pre[1]].push_back(pre[0]);
        }
        std::queue<int> courses_q;
        for (int course = 0; course < num_prereq.size(); course++) {
            std::cout << course << ":" << num_prereq[course] << std::endl;
            if (num_prereq[course] == 0) courses_q.push(course);
        }
        while (!courses_q.empty()) {

            int course_to_remove = courses_q.front();
            courses_q.pop();
            std::cout << course_to_remove << std::endl;
            for (auto outbound : outbound_courses[course_to_remove]) {
                num_prereq[outbound]--;
                if (num_prereq[outbound] == 0) {
                    courses_q.push(outbound);
                }
            }
        }
        for (auto course : num_prereq) {
            if (course != 0) return false;
        }
        return true;
    }
};
18600