<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:
    void fullfillCourseInfo(
        const int& numCourses,
        const vector<vector<int>>& prerequisites,
        unordered_map<int, vector<int>>& course_children,
        unordered_map<int, int>& course_indegree) {

        for (int i = 0; i < numCourses; i++) {
            course_children[i] = {};
            course_indegree[i] = 0;
        }

        for (int i = 0; i < prerequisites.size(); i++) {
            course_children[prerequisites[i][0]].push_back(prerequisites[i][1]);
            course_indegree[prerequisites[i][1]]++;
        }
    }

    bool canFinish(int numCourses, vector<vector<int>>& prerequisites) {
        queue<int> traversal;

        unordered_map<int, vector<int>> course_children;
        unordered_map<int, int> course_indegree;
        fullfillCourseInfo(numCourses, prerequisites, course_children, course_indegree);

        unordered_set<int> visited;

        for (const auto& indegree : course_indegree) {
            if (indegree.second == 0) {
                traversal.push(indegree.first);
                visited.insert(indegree.first);
            }
        }

        int courses_count = 0;

        while (!traversal.empty()) {
            int front = traversal.front();
            traversal.pop();
            courses_count++;

            for (const int& child : course_children[front]) {
                if (visited.find(child) != visited.end()) continue;

                course_indegree[child]--;
                if (course_indegree[child] == 0) {
                    traversal.push(child);
                    visited.insert(child);
                }
            }
        }
        
        return courses_count == numCourses;
    }
};
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