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Algorithms

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] = [ai, bi]</code> indicates that you must take course <code>bi</code> first if you want to take course <code>ai</code>.

<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>

Return <code>true</code> if you can finish all courses. Otherwise, return <code>false</code>.

&nbsp;
Example 1:

<pre>
Input: numCourses = 2, prerequisites = [[1,0]]
Output: true
Explanation: There are a total of 2 courses to take. 
To take course 1 you should have finished course 0. So it is possible.
</pre>

Example 2:

<pre>
Input: numCourses = 2, prerequisites = [[1,0],[0,1]]
Output: false
Explanation: 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>

&nbsp;
Constraints:

<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;= ai, bi &lt; numCourses</code></li>
	<li>All the pairs prerequisites[i] are unique.</li>
</ul>

canFinish

Course Schedule

Course Schedule II

course-schedule-ii

课程表 II

Graph Valid Tree

graph-valid-tree

以图判树

Minimum Height Trees

minimum-height-trees

最小高度树

Course Schedule III

course-schedule-iii

课程表 III

Build a Matrix With Conditions

build-a-matrix-with-conditions

给定条件下构造矩阵

Depth-First Search

Breadth-First Search

Graph

Topological Sort

有向无环图

你这个学期必须选修 <code>numCourses</code> 门课程，记为&nbsp;<code>0</code>&nbsp;到&nbsp;<code>numCourses - 1</code> 。

在选修某些课程之前需要一些先修课程。 先修课程按数组&nbsp;<code>prerequisites</code> 给出，其中&nbsp;<code>prerequisites[i] = [ai, bi]</code> ，表示如果要学习课程&nbsp;<code>ai</code> 则 必须 先学习课程&nbsp; <code>bi</code> 。

<ul>
	<li>例如，先修课程对&nbsp;<code>[0, 1]</code> 表示：想要学习课程 <code>0</code> ，你需要先完成课程 <code>1</code> 。</li>
</ul>

请你判断是否可能完成所有课程的学习？如果可以，返回 <code>true</code> ；否则，返回 <code>false</code> 。

&nbsp;

示例 1：

<pre>
输入：numCourses = 2, prerequisites = [[1,0]]
输出：true
解释：总共有 2 门课程。学习课程 1 之前，你需要完成课程 0 。这是可能的。</pre>

示例 2：

<pre>
输入：numCourses = 2, prerequisites = [[1,0],[0,1]]
输出：false
解释：总共有 2 门课程。学习课程 1 之前，你需要先完成​课程 0 ；并且学习课程 0 之前，你还应先完成课程 1 。这是不可能的。</pre>

&nbsp;

提示：

<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;= ai, bi &lt; numCourses</code></li>
	<li><code>prerequisites[i]</code> 中的所有课程对 互不相同</li>
</ul>