# 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.
You may assume that there are no duplicate edges in the input prerequisites.

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：

• 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).

Java