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LC210 - Course Schedule II

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Datastructure and Algorithm: DAY 51. Leetcode: 206/2710

Description

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.

Example 1:

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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:

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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:

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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

  • Prerequesite is stored in courses: [following courses]
  • The number of pre-courses required for each course is stored in pre_nums
  • Traverse pre_nums, if the number of pre-courses of the current course is 0, append the course to the queue
  • After processing all pre_nums[nxt], enqueue all courses with an in-degree of 0 (meaning subjects without pre-course requirements), and run topological sorting. If the length ans of the sorted courses is equal to numCourses, return ans, otherwise return [].
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#O(n+m) time | O(n+m) space
from collections import deque
class Solution:
    def findOrder(self, numCourses: int, prerequisites: List[List[int]]) -> List[int]:
        courses = defaultdict(list)
        pre_nums = [0] * numCourses
        queue = deque([])
        for cur, pre in prerequisites:
            courses[pre].append(cur)
            pre_nums[cur] +=1
        
        for i in range(numCourses):
            if pre_nums[i] == 0:
                queue.append(i)
        
        ans = []
        while queue:
            cur = queue.popleft()
            ans.append(cur)
            for nxt in courses[cur]:
                pre_nums[nxt] -=1
                if pre_nums[nxt] == 0:
                    queue.append(nxt)
        return ans if len(ans) == numCourses else []