# Question

Formatted question description: https://leetcode.ca/all/207.html

```
207 Course Schedule
There are a total of n courses you have to take, labeled from 0 to n - 1.
Some courses may have prerequisites, for example to take course 0 you have to first take course 1,
which is expressed as a pair: [0,1]
Given the total number of courses and a list of prerequisite pairs, is it possible for you to finish all courses?
For example:
2, [[1,0]]
There are a total of 2 courses to take. To take course 1 you should have finished course 0.
So it is possible.
2, [[1,0],[0,1]]
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.
Note:
The input prerequisites is a graph represented by a list of edges, not adjacency matrices.
Read more about how a graph is represented.
You may assume that there are no duplicate edges in the input prerequisites.
click to show more hints.
Hints:
This problem is equivalent to finding if a cycle exists in a directed graph.
If a cycle exists, no topological ordering exists and therefore it will be impossible to take all courses.
Topological Sort via DFS
A great video tutorial (21 minutes) on Coursera explaining the basic concepts of Topological Sort.
Topological sort could also be done via BFS.
@tag-graph
```

# Algorithm

### Kahn’s Algorithms：

https://en.wikipedia.org/wiki/Topological_sorting#Kahn’s_algorithm

BFS based，

- start from with vertices with 0 incoming edge，insert them into list S，at the same time we remove all their outgoing edges，
- after that find new vertices with 0 incoming edges and go on.

### Tarjan’s Algorithms：

https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_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 (i.e. a leaf node).

# Code

Java