from collections import defaultdict

class Solution:
    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
        graph = defaultdict(list)
        
        for course, pre in prerequisites:
            graph[course].append(pre)
        
        cycles = set()
        visited = set()
        
        def dfs(course):
            if course in cycles:
                return False
            
            if course in visited:
                return True
            
            visited.add(course)
            cycles.add(course)
            
            for dep in graph[course]:
                if not dfs(dep):
                    return False
                
            cycles.remove(course)
            
            return True
        
        for course in range(numCourses):
            cycles = set()
            
            if not dfs(course):
                return False
        
        return True