210. 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 course 0 you have to first take course 1.

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.

class Solution:
    def findOrder(self, numCourses: int, prerequisites: List[List[int]]) -> List[int]:
        g = collections.defaultdict(list)
        for pre, post in prerequisites:
            g[pre].append(post)
        
        indegrees = {}
        for node in range(numCourses):
            indegrees[node] = 0
        for node in g:
            for neighbor in g[node]:
                indegrees[neighbor] += 1
        
        q = collections.deque()
        for node in range(numCourses):
            if indegrees[node] == 0:
                q.append(node)
 
        topsort = []
        while q:
            curnode = q.popleft()
            topsort.append(curnode)
            for neighbor in g[curnode]:
                indegrees[neighbor] -= 1
                if indegrees[neighbor] == 0:
                    q.append(neighbor)
        return topsort[::-1] if len(topsort) == numCourses else []

• we create a graph using an adjacency-list and perform topological-sort on it to get the valid ordering of courses.
  • we do this by finding all the nodes with an indegree of zero, and then performing bfs, updating our indegrees everytime we’re finished with a node, and adding new nodes that now have an indegree of zero.

Related.

• 207-course-schedule.

Categories:: graph, adjacency-list, topological-sort, bfs