Course schedule

class Solution:
    def __init__(self):
        self.g = collections.defaultdict(list)
        self.valid = True
        self.path = []
        self.visited = set()

    def dfs(self, start):
        if start in self.path:
            self.valid = False
            return
        if start in self.visited:
            return 
        if not self.valid:
            return
        self.visited.add(start)
        self.path.append(start)
        for node in self.g[start]:
            self.dfs(node)
        self.path.pop()

    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
        for _from, _to in prerequisites:
            self.g[_from].append(_to)
        for i in range(numCourses):
            self.dfs(i)
            if not self.valid:
                return False

        return True

Course Schedule

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] = [a_i, b_i] indicates that you must take course b_i first if you want to take course a_i.

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 <= a_i, b_i < numCourses
All the pairs prerequisites[i] are unique.