## 题目描述：

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.

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.

There are several ways to represent a graph. For example, the input prerequisites is a graph represented by a list of edges. Is this graph representation appropriate?

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.

2, [[1,0]]

2, [[1,0],[0,1]]

## Python代码：

``````class Solution:
# @param {integer} numCourses
# @param {integer[][]} prerequisites
# @return {boolean}
def canFinish(self, numCourses, prerequisites):
degrees = [0] * numCourses
childs = [[] for x in range(numCourses)]
for pair in prerequisites:
degrees[pair[0]] += 1
childs[pair[1]].append(pair[0])
courses = set(range(numCourses))
flag = True
while flag and len(courses):
flag = False
removeList = []
for x in courses:
if degrees[x] == 0:
for child in childs[x]:
degrees[child] -= 1
removeList.append(x)
flag = True
for x in removeList:
courses.remove(x)
return len(courses) == 0
``````

Pingbacks已关闭。