leetcode-problemset/leetcode-cn/originData/course-schedule-ii.json

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        "question": {
            "questionId": "210",
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            "categoryTitle": "Algorithms",
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            "title": "Course Schedule II",
            "titleSlug": "course-schedule-ii",
            "content": "<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>\n\n<ul>\n\t<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>\n</ul>\n\n<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>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> numCourses = 2, prerequisites = [[1,0]]\n<strong>Output:</strong> [0,1]\n<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].\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> numCourses = 4, prerequisites = [[1,0],[2,0],[3,1],[3,2]]\n<strong>Output:</strong> [0,2,1,3]\n<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.\nSo one correct course order is [0,1,2,3]. Another correct ordering is [0,2,1,3].\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> numCourses = 1, prerequisites = []\n<strong>Output:</strong> [0]\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= numCourses &lt;= 2000</code></li>\n\t<li><code>0 &lt;= prerequisites.length &lt;= numCourses * (numCourses - 1)</code></li>\n\t<li><code>prerequisites[i].length == 2</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; numCourses</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li>All the pairs <code>[a<sub>i</sub>, b<sub>i</sub>]</code> are <strong>distinct</strong>.</li>\n</ul>\n",
            "translatedTitle": "课程表 II",
            "translatedContent": "<p>现在你总共有 <code>numCourses</code> 门课需要选，记为&nbsp;<code>0</code>&nbsp;到&nbsp;<code>numCourses - 1</code>。给你一个数组&nbsp;<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&nbsp;<code>b<sub>i</sub></code> 。</p>\n\n<ul>\n\t<li>例如，想要学习课程 <code>0</code> ，你需要先完成课程&nbsp;<code>1</code> ，我们用一个匹配来表示：<code>[0,1]</code> 。</li>\n</ul>\n\n<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>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>numCourses = 2, prerequisites = [[1,0]]\n<strong>输出：</strong>[0,1]\n<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>\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>numCourses = 4, prerequisites = [[1,0],[2,0],[3,1],[3,2]]\n<strong>输出：</strong>[0,2,1,3]\n<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。\n因此，一个正确的课程顺序是&nbsp;<code>[0,1,2,3]</code> 。另一个正确的排序是&nbsp;<code>[0,2,1,3]</code> 。</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>numCourses = 1, prerequisites = []\n<strong>输出：</strong>[0]\n</pre>\n\n<p>&nbsp;</p>\n<strong>提示：</strong>\n\n<ul>\n\t<li><code>1 &lt;= numCourses &lt;= 2000</code></li>\n\t<li><code>0 &lt;= prerequisites.length &lt;= numCourses * (numCourses - 1)</code></li>\n\t<li><code>prerequisites[i].length == 2</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; numCourses</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li>所有<code>[a<sub>i</sub>, b<sub>i</sub>]</code> <strong>互不相同</strong></li>\n</ul>\n",
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                "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.",
                "<a href=\"https://class.coursera.org/algo-003/lecture/52\" target=\"_blank\">Topological Sort via DFS</a> - A great video tutorial (21 minutes) on Coursera explaining the basic concepts of Topological Sort.",
                "Topological sort could also be done via <a href=\"http://en.wikipedia.org/wiki/Topological_sorting#Algorithms\" target=\"_blank\">BFS</a>."
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