Course Schedule II
Created: March 24, 2020 by [lek-tin]
Last updated: March 24, 2020
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] .
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 (topological sort using dfs)
possible if no cycle in a directed graph
Time: O(V+E) ~ O(V^2)
Space: O(V)
class Solution:
def findOrder(self, numCourses: int, prerequisites: List[List[int]]) -> List[int]:
self.topo_order = []
self.adj = [ [] for _ in range(numCourses) ]
for p in prerequisites:
child, parent = p
self.adj[parent].append(child)
# mark starting nodes
visiting = [ False for _ in range(numCourses) ]
visited = [ False for _ in range(numCourses) ]
for i in range(numCourses):
if self.detectCycle(i, visiting, visited):
# if a cycle exists
return []
return reversed(self.topo_order)
# cycle exists: True
# otherwies: False
def detectCycle(self, parent, visiting, visited):
# cycle detected
if visiting[parent]:
return True
# node already visited -> abort
# no cycle detected -> return False
if visited[parent]:
return False
# mark node as visiting
visiting[parent] = True
# traverse all children
for child in self.adj[parent]:
if self.detectCycle(child, visiting, visited):
return True
# unset parent as a prerequiste course
visiting[parent] = False
# mark node as visited
visited[parent] = True
# add parent to our solution array
self.topo_order.append(parent)
return False