207. Course Schedule - https://leetcode.com/problems/course-schedule/

courseSchedule.py

from collections import defaultdict

class Solution:
    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
        
        gra = Graph(len(prerequisites))
        for preReq in prerequisites:
            gra.addEdge(preReq[0], preReq[1])
            
            
        for j in range(1, gra.V):
            if gra.dfsUtil(j) == False:
                return False
        
        return True
        
        
        
class Graph:
    def __init__(self, verticies):
        self.V = verticies + 1
        self.graph = defaultdict(list)
        self.time = 0
        self.parent = [-1] * self.V
        self.low = [float("Inf")] * self.V
        self.disc = [float("Inf")] * self.V
        self.visited = [False] * self.V
        
        
    def addEdge(self, u, v):
        self.graph[u].append(v)
        self.graph[v].append(u)
        
    def dfsUtil(self, u):
        self.visited[u] = True
        self.low[u] = self.time
        self.disc[u] = self.time
        self.time += 1
        
        for v in self.graph[u]:
            
            if self.visited[v] == True:
                return False
            
            if self.visited[v] == False:
                
                self.parent[v] = u
                self.dfsUtil(v)
                
                self.low[u] = min(self.low[u], self.low[v])
                
            elif v != self.parent[u]:
                self.low[u] = min(self.low[u], self.disc[v])