207. Course Schedule

Problem Link

Description

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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.

Solution

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Python3

class Solution:
    def canFinish(self, N: int, prerequisites: List[List[int]]) -> bool:
        graph = defaultdict(list)
        indegree = [0] * N
        count = 0
 
        for a, b in prerequisites:
            graph[b].append(a)
            indegree[a] += 1
        
        queue = deque([i for i in range(N) if indegree[i] == 0])
 
        while queue:
            node = queue.popleft()
            count += 1
 
            for adj in graph[node]:
                indegree[adj] -= 1
 
                if indegree[adj] == 0:
                    queue.append(adj)
        
        return count == N