class Solution:
    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:

        from collections import defaultdict

        # make courses and add adjanceny list
        premap = defaultdict(list)
        for crs, pre in prerequisites:
            premap[crs].append(pre)

        # all courses along the current dfs path
        visit_path = set()
        def dfs(crs):

            # along a path if the course is visited again
            # this will be helpful in detecting a cycle
            if crs in visit_path:
                return False
            if premap[crs] == []:
                return True

            visit_path.add(crs)
            # loop through prereqs of this course
            for pre in premap[crs]:
                # if we find one course that can not be
                # completed then we can return false for the
                # entire function
                if not dfs(pre): return False

            visit_path.remove(crs)
            premap[crs] = []
            return True

        for crs in range(numCourses):
            if not dfs(crs): return False

        return True