Course Schedule II
There are a total of numCourses
courses you have to take, labeled from 0
to numCourses - 1
. You are given an array prerequisites
where prerequisites[i] = [ai, bi]
indicates that you must take course bi
first if you want to take course ai
.
- For example, the pair
[0, 1]
, indicates that to take course0
you have to first take course1
.
Return the ordering of courses you should take to finish all courses. If there are many valid answers, return any of them. If it is impossible to finish all courses, return an empty array.
Example 1:
Input: numCourses = 2, prerequisites = [[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: numCourses = 4, prerequisites = [[1,0],[2,0],[3,1],[3,2]]
Output: [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].
Example 3:
Input: numCourses = 1, prerequisites = []
Output: [0]
Constraints:
1 <= numCourses <= 2000
0 <= prerequisites.length <= numCourses * (numCourses - 1)
prerequisites[i].length == 2
0 <= ai, bi < numCourses
ai != bi
- All the pairs
[ai, bi]
are distinct.
Solution
The problems asks us to find the ordering of courses to take. We know this involves the dependency of courses, so we will find the topological ordering of these courses.
We will build a graph with directed edges from a course
's prereq
to course
itself, then find the topological sorting of the graph.
Implementation
def findOrder(numCourses: int, prerequisites: List[List[int]]) -> List[int]:
visited = [False for _ in range(numCourses)]
finished = []
graph = defaultdict(list)
for course, prereq in prerequisites:
graph[prereq].append(course)
def dfs(prereq):
for course in graph[prereq]:
if not visited[course]:
visited[course] = True
if not dfs(course): return False # unable to finish course
elif course not in finished: # cycle in graph
return False
finished.append(prereq)
return True
for i in range(numCourses): # visit all trees in graph
if not visited[i]:
visited[i] = True
if not dfs(i): return []
finished.reverse() # topological ordering = reverse finish time
return finished
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