Parallel Courses
<p>You are given an integer <code>n</code>, which indicates that there are <code>n</code> courses labeled from <code>1</code> to <code>n</code>. You are also given an array <code>relations</code> where <code>relations[i] = [prevCourse<sub>i</sub>, nextCourse<sub>i</sub>]</code>, representing a prerequisite relationship between course <code>prevCourse<sub>i</sub></code> and course <code>nextCourse<sub>i</sub></code>: course <code>prevCourse<sub>i</sub></code> has to be taken before course <code>nextCourse<sub>i</sub></code>.</p>

<p>In one semester, you can take <strong>any number</strong> of courses as long as you have taken all the prerequisites in the <strong>previous</strong> semester for the courses you are taking.</p>

<p>Return <em>the <strong>minimum</strong> number of semesters needed to take all courses</em>. If there is no way to take all the courses, return <code>-1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1100-1199/1136.Parallel%20Courses/images/course1graph.jpg" style="width: 222px; height: 222px;" />
<pre>
<strong>Input:</strong> n = 3, relations = [[1,3],[2,3]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The figure above represents the given graph.
In the first semester, you can take courses 1 and 2.
In the second semester, you can take course 3.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1100-1199/1136.Parallel%20Courses/images/course2graph.jpg" style="width: 222px; height: 222px;" />
<pre>
<strong>Input:</strong> n = 3, relations = [[1,2],[2,3],[3,1]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> No course can be studied because they are prerequisites of each other.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 5000</code></li>
	<li><code>1 &lt;= relations.length &lt;= 5000</code></li>
	<li><code>relations[i].length == 2</code></li>
	<li><code>1 &lt;= prevCourse<sub>i</sub>, nextCourse<sub>i</sub> &lt;= n</code></li>
	<li><code>prevCourse<sub>i</sub> != nextCourse<sub>i</sub></code></li>
	<li>All the pairs <code>[prevCourse<sub>i</sub>, nextCourse<sub>i</sub>]</code> are <strong>unique</strong>.</li>
</ul>
Graph; Topological Sort
class Solution {
public:
    int minimumSemesters(int n, vector<vector<int>>& relations) {
        vector<vector<int>> g(n);
        vector<int> indeg(n);
        for (auto& r : relations) {
            int prev = r[0] - 1, nxt = r[1] - 1;
            g[prev].push_back(nxt);
            ++indeg[nxt];
        }
        queue<int> q;
        for (int i = 0; i < n; ++i) {
            if (indeg[i] == 0) {
                q.push(i);
            }
        }
        int ans = 0;
        while (!q.empty()) {
            ++ans;
            for (int k = q.size(); k; --k) {
                int i = q.front();
                q.pop();
                --n;
                for (int& j : g[i]) {
                    if (--indeg[j] == 0) {
                        q.push(j);
                    }
                }
            }
        }
        return n == 0 ? ans : -1;
    }
};