<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>>& pre) {
        unordered_set<int> taken;
        unordered_map<int, unordered_set<int>> courseToRequirements;
        unordered_map<int, vector<int>> requirementToCourses;

        for (int i = 0; i < pre.size(); i++) {
            if (courseToRequirements.contains(pre[i][0])) {
                courseToRequirements[pre[i][0]].insert(pre[i][1]);
            } else {
                courseToRequirements[pre[i][0]] = unordered_set<int>{pre[i][1]};
            }

            if (requirementToCourses.contains(pre[i][1])) {
                requirementToCourses[pre[i][1]].push_back(pre[i][0]);
            } else {
                requirementToCourses[pre[i][1]] = vector<int>{pre[i][0]};
            }
        }

        vector<int> takenRound;
        for (int i = 0; i < numCourses; i++) {
            if (!courseToRequirements.contains(i)) {
                taken.insert(i);
                takenRound.push_back(i);
            }
        }

        while (takenRound.size() != 0) {
            unordered_set<int> checked;
            for (auto req : takenRound) {
                if (!requirementToCourses.contains(req)) { continue; }

                auto check = requirementToCourses.at(req);
                requirementToCourses.erase(req);

                // erase fulfilled requirements
                for (auto course : check) {
                    checked.insert(course);
                    if (courseToRequirements.contains(course)) {
                        courseToRequirements[course].erase(req);
                    }
                }
            }
           
            // build a list of requirements we now can fulfill
            vector<int> takenNow;
            for (auto course : checked) {
                if (courseToRequirements.contains(course)) {
                    if (courseToRequirements[course].size() == 0) {
                        taken.insert(course);
                        takenNow.push_back(course);
                    }
                }
            }

            takenRound = takenNow;
        }

        return taken.size() == numCourses;
    }
};
22900