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

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

class Solution:
    def findOrder(self, numCourses: int, prerequisites: list[list[int]]) -> list[int]:
        prereq = {c: [] for c in range(numCourses)}
        for crs, pre in prerequisites:
            prereq[crs].append(pre)

        # course has 3 possible states:
        # visited -> crs has been added to output
        # visiting -> crs not added to output, but added to cycle
        # unvisited -> crs not added to output nor cycle
        output = []
        visit, cycle = set(), set()

        def dfs(crs):
            if crs in cycle:
                return False
            if crs in visit:
                return True

            cycle.add(crs)
            for pre in prereq[crs]:
                if dfs(pre) == False:
                    return False

            cycle.remove(crs)
            visit.add(crs)
            output.append(crs)
            return True

        for c in range(numCourses):
            if dfs(c) == False:
                return []

        return output