207. Course Schedule 找环
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.思路：找是否存在环，已经访问完的标记为1，正在访问的标记为2，如果遇到正在访问的就是遇到环
class Solution(object):
def canFinish(self, numCourses, prerequisites):
"""
:type numCourses: int
:type prerequisites: List[List[int]]
:rtype: bool
"""
mark = collections.defaultdict(int)
prere = collections.defaultdict(list)
for c, p in prerequisites:
prere[c].append(p)
def dfs(course):
if mark[course] == 1: # visited
return True
if mark[course] == 2: # visiting
return False
# unvisited
mark[course] = 2 # mark as visiting
preCourses = prere[course]
if preCourses == []:
mark[course] = 1
return True
else:
for preCourse in preCourses:
re = dfs(preCourse)
if not re:
return False
mark[course] = 1 # mark as visited
return True
for course, pre in prerequisites:
re = dfs(course)
if not re:
return False
return True210. Course Schedule II 拓扑排序
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, return the ordering of courses you should take to finish all courses.
There may be multiple correct orders, you just need to return one of them. If it is impossible to finish all courses, return an empty array.
Example 1:
Input: 2, [[1,0]] Output:[0,1]Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0. So the correct course order is[0,1] .
Example 2:
Input: 4, [[1,0],[2,0],[3,1],[3,2]] Output:[0,1,2,3] or [0,2,1,3]Explanation: There are a total of 4 courses to take. To take course 3 you should have finished both courses 1 and 2. Both courses 1 and 2 should be taken after you finished course 0. So one correct course order is[0,1,2,3]. Another correct ordering is[0,2,1,3] .
class Solution(object):
def findOrder(self, numCourses, prerequisites):
"""
:type numCourses: int
:type prerequisites: List[List[int]]
:rtype: List[int]
"""
self.graph = collections.defaultdict(list)
self.res = []
for c, p in prerequisites:
self.graph[c].append(p)
self.visited = [0 for x in xrange(numCourses)]
for node in xrange(numCourses):
if not self.DFS(node):
return []
return self.res
def DFS(self, node):
if self.visited[node] == -1: # visiting
return False
if self.visited[node] == 1: # visited and add to res
return True
self.visited[node] = -1 # mark as visiting
for x in self.graph[node]:
if not self.DFS(x):
return False
self.visited[node] = 1
self.res.append(node)
return True