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Description
tab: English
<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 <em>the ordering of courses you should take to finish all courses</em>. If there are many valid answers, return <strong>any</strong> of them. If it is impossible to finish all courses, return <strong>an empty array</strong>.</p>
<p> </p>
<p><strong class="example">Example 1:</strong></p>
<pre>
<strong>Input:</strong> numCourses = 2, prerequisites = [[1,0]]
<strong>Output:</strong> [0,1]
<strong>Explanation:</strong> There are a total of 2 courses to take. To take course 1 you should have finished course 0. So the correct course order is [0,1].
</pre>
<p><strong class="example">Example 2:</strong></p>
<pre>
<strong>Input:</strong> numCourses = 4, prerequisites = [[1,0],[2,0],[3,1],[3,2]]
<strong>Output:</strong> [0,2,1,3]
<strong>Explanation:</strong> There are a total of 4 courses to take. To take course 3 you should have finished both courses 1 and 2. Both courses 1 and 2 should be taken after you finished course 0.
So one correct course order is [0,1,2,3]. Another correct ordering is [0,2,1,3].
</pre>
<p><strong class="example">Example 3:</strong></p>
<pre>
<strong>Input:</strong> numCourses = 1, prerequisites = []
<strong>Output:</strong> [0]
</pre>
<p> </p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 <= numCourses <= 2000</code></li>
<li><code>0 <= prerequisites.length <= numCourses * (numCourses - 1)</code></li>
<li><code>prerequisites[i].length == 2</code></li>
<li><code>0 <= a<sub>i</sub>, b<sub>i</sub> < numCourses</code></li>
<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
<li>All the pairs <code>[a<sub>i</sub>, b<sub>i</sub>]</code> are <strong>distinct</strong>.</li>
</ul>
> [!tip]- Hint 1
>
> This problem is equivalent to finding the topological order in a directed graph. If a cycle exists, no topological ordering exists and therefore it will be impossible to take all courses.
> [!tip]- Hint 2
>
> <a href="https://www.youtube.com/watch?v=ozso3xxkVGU" target="_blank">Topological Sort via DFS</a> - A great video tutorial (21 minutes) on Coursera explaining the basic concepts of Topological Sort.
> [!tip]- Hint 3
>
> Topological sort could also be done via <a href="http://en.wikipedia.org/wiki/Topological_sorting#Algorithms" target="_blank">BFS</a>.
---
[submissions](https://leetcode.com/problems/course-schedule-ii/submissions/) | [solutions](https://leetcode.com/problems/course-schedule-ii/solutions/)
tab: 中文
<p>现在你总共有 <code>numCourses</code> 门课需要选，记为 <code>0</code> 到 <code>numCourses - 1</code>。给你一个数组 <code>prerequisites</code> ，其中 <code>prerequisites[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> ，表示在选修课程 <code>a<sub>i</sub></code> 前 <strong>必须</strong> 先选修 <code>b<sub>i</sub></code> 。</p>
<ul>
<li>例如，想要学习课程 <code>0</code> ，你需要先完成课程 <code>1</code> ，我们用一个匹配来表示：<code>[0,1]</code> 。</li>
</ul>
<p>返回你为了学完所有课程所安排的学习顺序。可能会有多个正确的顺序，你只要返回 <strong>任意一种</strong> 就可以了。如果不可能完成所有课程，返回 <strong>一个空数组</strong> 。</p>
<p> </p>
<p><strong>示例 1：</strong></p>
<pre>
<strong>输入：</strong>numCourses = 2, prerequisites = [[1,0]]
<strong>输出：</strong>[0,1]
<strong>解释：</strong>总共有 2 门课程。要学习课程 1，你需要先完成课程 0。因此，正确的课程顺序为 <code>[0,1] 。</code>
</pre>
<p><strong>示例 2：</strong></p>
<pre>
<strong>输入：</strong>numCourses = 4, prerequisites = [[1,0],[2,0],[3,1],[3,2]]
<strong>输出：</strong>[0,2,1,3]
<strong>解释：</strong>总共有 4 门课程。要学习课程 3，你应该先完成课程 1 和课程 2。并且课程 1 和课程 2 都应该排在课程 0 之后。
因此，一个正确的课程顺序是 <code>[0,1,2,3]</code> 。另一个正确的排序是 <code>[0,2,1,3]</code> 。</pre>
<p><strong>示例 3：</strong></p>
<pre>
<strong>输入：</strong>numCourses = 1, prerequisites = []
<strong>输出：</strong>[0]
</pre>
<p> </p>
<strong>提示：</strong>
<ul>
<li><code>1 <= numCourses <= 2000</code></li>
<li><code>0 <= prerequisites.length <= numCourses * (numCourses - 1)</code></li>
<li><code>prerequisites[i].length == 2</code></li>
<li><code>0 <= a<sub>i</sub>, b<sub>i</sub> < numCourses</code></li>
<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
<li>所有<code>[a<sub>i</sub>, b<sub>i</sub>]</code> <strong>互不相同</strong></li>
</ul>
> [!tip]- 提示 1
>
> This problem is equivalent to finding the topological order in a directed graph. If a cycle exists, no topological ordering exists and therefore it will be impossible to take all courses.
> [!tip]- 提示 2
>
> <a href="https://www.youtube.com/watch?v=ozso3xxkVGU" target="_blank">Topological Sort via DFS</a> - A great video tutorial (21 minutes) on Coursera explaining the basic concepts of Topological Sort.
> [!tip]- 提示 3
>
> Topological sort could also be done via <a href="http://en.wikipedia.org/wiki/Topological_sorting#Algorithms" target="_blank">BFS</a>.
---
[提交记录](https://leetcode.cn/problems/course-schedule-ii/submissions/) | [题解](https://leetcode.cn/problems/course-schedule-ii/solution/)
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