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207. Course Schedule

Depth-First Search Breadth-First Search Graph Topological Sort

Problem - Course Schedule

Medium

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:

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:

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

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class Solution:
    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
        graph = [[] for _ in range(numCourses)]
        internal_degree = [0] * numCourses

        for course, preq in prerequisites:
            graph[preq].append(course)
            internal_degree[course] += 1

        query = [i for i, x in enumerate(internal_degree) if x == 0]
        for j in query:
            numCourses -= 1
            for k in graph[j]:
                internal_degree[k] -= 1
                if internal_degree[k] == 0:
                    query.append(k)

        return numCourses == 0

Submission Stats:

  • Runtime: 4 ms (67.59%)
  • Memory: 19.2 MB (61.99%)