# Question

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?

Example 1:

```
Input: 2, [[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.
```

Example 2:

```
Input: 2, [[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.
```

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.

# Solution

Use DFS way of topological sort.

```
from collections import defaultdict
class Solution(object):
def canFinish(self, numCourses, prerequisites):
"""
:type numCourses: int
:type prerequisites: List[List[int]]
:rtype: bool
"""
class Graph(object):
def __init__(self, vertices):
self.graph = defaultdict(list)
self.V = vertices
def addEdge(self, u, v):
self.graph[u].append(v)
def tsUtil(self, v, temporary, permanent):
if v not in temporary:
return False
temporary.remove(v)
for w in self.graph[v]:
if w in permanent:
if not self.tsUtil(w, temporary, permanent):
return False
permanent.remove(v)
return True
def isTsPossible(self):
temporary = set(range(self.V))
permanent = set(range(self.V))
while len(permanent) > 0:
if not self.tsUtil(next(iter(permanent)), temporary, permanent):
return False
return True
graph = Graph(numCourses)
for p in prerequisites:
u, v = p[1], p[0]
graph.addEdge(u, v)
return graph.isTsPossible()
```