【Leetcode】207. Course Schedule

1 此问题等同于有向图检测环，vertex是course，edge是prerequisite，一般会使用topological sorting拓扑排序来检测。一个有向图如果有环则不存在topological order

2 常用的topological sort有两种：

Kahn's Algorithm：BFS based, start from vertices with 0 incoming edge, insert them into list S, at the same time, we remove all outgoing edges, after that find new vertices with 0 incoming edges and so on

Tarjan's Algorithm: DFS based, loop through each node of the graph in an arbitrary order, initiating a depth-first search that terminates when it hits any node that has already been visited since the beginning of the topological sort or the node has no outgoing edges

3 这道题本质是给我们一个图，看这个图是不是拓扑序列

4 在初始的图中，入度为0的点，即是课程中最基础的课程（比如数据结构，c语言基础）

红框中的很重要，可以减少很多多余的check

Time complexity: O(V+E) because we search each vertices and edges exactly once in this solution

space complexity: O(E) E是edges数

The usual algorithms for topological sorting have running time linear in the number of nodes plus the number of edges

Time complexity: O(n)

Space complexity: O(n)