LeetCode-in-All

207. 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 <= 105
• 0 <= prerequisites.length <= 5000
• prerequisites[i].length == 2
• 0 <= ai, bi < numCourses
• All the pairs prerequisites[i] are unique.

Solution

class Solution:
    WHITE = 0
    GRAY = 1
    BLACK = 2

    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
        adj = [[] for _ in range(numCourses)]
        for pre in prerequisites:
            adj[pre[1]].append(pre[0])
        
        colors = [self.WHITE] * numCourses
        
        for i in range(numCourses):
            if colors[i] == self.WHITE and adj[i] and self.hasCycle(adj, i, colors):
                return False
        return True

    def hasCycle(self, adj: List[List[int]], node: int, colors: List[int]) -> bool:
        colors[node] = self.GRAY
        
        for nei in adj[node]:
            if colors[nei] == self.GRAY:
                return True
            if colors[nei] == self.WHITE and self.hasCycle(adj, nei, colors):
                return True
        
        colors[node] = self.BLACK
        return False

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