#cp-medium

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.

Solution (BFS)

Just check for cyclicity in the dg and return false is cyclic else true.

Special Note

Wrong Solution

I used CC detection for Undir Graphs which breaks for DGs.

Why the “parent” check is wrong

In an undirected graph, the standard BFS/DFS cycle check is: “if I see a visited neighbor that isn’t my immediate parent, it’s a cycle.” That works there because every edge is traversed from both directions, so any revisit that isn’t the edge you just came from must be a genuine back edge.

In a directed graph, this breaks down completely. A node can be reached from multiple different parents perfectly legitimately (a “diamond” shape or a “cross edge”) — that’s not a cycle, it’s just a DAG with converging paths. Your check flags this as a cycle anyway.

class Solution:
    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
        
        cc = 0
        visited = [0]*numCourses
        adj = [[] for _ in range(numCourses)]
        # print(adj)
        for course in prerequisites:
            # print(course)
            # a,b then b->a
            adj[course[1]].append(course[0])
        print(adj)
        
        for start in range(numCourses):
            if not visited[start]:
                # cc+=1
                q = []
                q.append([start,-1])
                # visited = [0]*numCourses 
                while (q):
                    node,parent = q.pop(0)
                    visited[node] = 1
                    for course in adj[node]:
                        if not visited[course]:
                            q.append([course,node])
                        elif parent != course:
                            return False
        
        # if cc>1:
        #     return False
        # else:
        return True