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LC207 - Course Schedule

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Datastructure and Algorithm: DAY 51. Leetcode: 205/2710

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 true if you can finish all courses. Otherwise, return false.

Example 1:

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Input: numCourses = 2, prerequisites = [[1,0]]
Output: true
Explanation: There are a total of 2 courses to take. 
To take course 1 you should have finished course 0. So it is possible.

Example 2:

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Input: numCourses = 2, prerequisites = [[1,0],[0,1]]
Output: false
Explanation: There are a total of 2 courses to take. 
To take course 1 you should have finished course 0, and to take course 0 you should also have finished course 1. So it is impossible.

Constraints:
1 <= numCourses <= 2000
0 <= prerequisites.length <= 5000
prerequisites[i].length == 2
0 <= ai, bi < numCourses
All the pairs prerequisites[i] are unique.

Solutions

  • 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
  • When all pre_nums[nxt] are processed, enter all courses with an entry degree of 0 (meaning subjects without pre-course requirements) into the queue, and run the “topological sort” once, if all the number of prerequisite courses equals 0, stating that all courses can be completed.
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# O(m+n) time | O(m+n) space
from collections import deque

class Solution:
    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
        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)
        
        while queue:
            cur = queue.popleft()
            for nxt in courses[cur]:
                pre_nums[nxt] -= 1
                if pre_nums[nxt] == 0:
                    queue.append(nxt)
        return True if pre_nums == [0]*numCourses else False