Course Schedule

Problem Statement

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] = [a_i, b_i] indicates that you must take course b_i first if you want to take course a_i.

• 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.

Leetcode link

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 <= a_i, b_i < numCourses
• All the pairs prerequisites[i] are unique.

Code

Python Code

from collections import defaultdict
class Solution(object):
    def canFinish(self, numCourses, prerequisites):
        """
        :type numCourses: int
        :type prerequisites: List[List[int]]
        :rtype: bool
        """
        # Idea is to create topological sort using dependencies given. If we are able to create it then its possible otherwise not possible
        # Maintain two set visited, complete_explore
        # if all of neighbours are explored then add to complete_explore and remove from visited
        # if vertex and its neighbour are in visited (partially visited) that means somehow we reached vertex again as both of them are still partially explored and we have dependenices on each other via some vertices or directly
        # then its a cycle which means we can't create topological order based on given prereq..
        # Here we go
        # stack contains dependecies path just extra thing
        # if visited is not empty that means there is cycle
        adj_matrix = self.create_adj_matrix(prerequisites)
        complete_explore = set()   # To maintain completely explored vertex
        visited = set()     # partially explored vertex
        stack = []          # topological order
        for elem in range(numCourses):
            if elem not in visited and elem not in complete_explore:   # If vertex is not explored completely or partially then explore it
                self.find_topological_order(elem, adj_matrix, visited, stack, complete_explore)
        if not visited:     # if partially visited set is  empty then Voila
            return True
        else:
            return False

    def find_topological_order(self, vertex, adj_matrix, visited, stack, complete_explore):
        visited.add(vertex)     # add to partially visited
        for elem in adj_matrix[vertex]:     # adj vertices
            if elem not in visited and elem not in complete_explore: # if vertex not in partially visited and not in completely explored set
                self.find_topological_order(elem, adj_matrix, visited, stack, complete_explore)
            if elem in visited and vertex in visited:       # if vertex and its neighbour in visited then its cycle
                return False
        complete_explore.add(vertex)    # add to completely explored as we have reached to end and there are no more edges to explore
        visited.remove(vertex)  # remove from partially removed
        stack.append(vertex)    # add to path

    def create_adj_matrix(self, prereq):
        adj_matrix = defaultdict(list)
        for elem in prereq:
            adj_matrix[elem[0]].append(elem[1])

        return adj_matrix