207. 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] = [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:
        courses = { i:[] for i in range(numCourses)}
        for course, prereq in prerequisites:
            courses[course].append(prereq)
        print(courses)
        
        visited = set()
        def dfs(course):
            if course in visited:
                return False
            if courses[course] == []:
                return True

            visited.add(course)
            for pre in courses[course]:
                if not dfs(pre):
                    return False
            visited.remove(course)
            courses[course] = []
            return True
        
        for course in range(numCourses):
            if not dfs(course): 
                return False
        return True