course_schedule.py

"""
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.
"""

class Solution:
    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
        prereqs = defaultdict(list)
        for c, p in prerequisites:
            prereqs[c].append(p)
        
        def cycle(course, seen):
            if course in seen:
                return True
            seen.add(course)
            for p in prereqs[course]:
                if cycle(p, seen):
                    return True
            prereqs[course] = []
            seen.remove(course)
            return False
        
        seen = set()
        for course in range(numCourses):
            if cycle(course, seen):
                return False
        return True