<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) {
        // Courses where I have a dependency, courses that have a dependency on me
        unordered_map<int, pair<unordered_set<int>, unordered_set<int>>> graph;
        for (int i = 0; i < numCourses; i++)
        {
            graph[i] = pair<unordered_set<int>, unordered_set<int>>(unordered_set<int>(), unordered_set<int>());
        }

        for (int p = 0; p < prerequisites.size(); p++)
        {
            graph[prerequisites[p][0]].first.insert(prerequisites[p][1]);
            graph[prerequisites[p][1]].second.insert(prerequisites[p][0]);
        }

        queue<int> completedCourses;
        for (auto it = graph.begin(); it != graph.end(); it++)
        {
            if (it->second.first.empty())
            {
                completedCourses.push(it->first);
            }
        }
        
        int completedCoursesCount = 0;
        while (!completedCourses.empty())
        {
            int completedCourse = completedCourses.front();
            for (auto dependantCourseIt = graph[completedCourse].second.begin(); dependantCourseIt != graph[completedCourse].second.end(); dependantCourseIt++)
            {
                graph[*dependantCourseIt].first.erase(completedCourse);
                if (graph[*dependantCourseIt].first.empty())
                {
                    completedCourses.push(*dependantCourseIt);
                }
            }
            completedCourses.pop();
            completedCoursesCount++;
        }

        return completedCoursesCount == numCourses;
    }
};
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