207. Course Schedule

Description

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.

Thoughts

This is a classical topological sorting question. We can use BFS to solve this kind of problems. But we have to build the graph and count the indegree first.
The graph shows the order for 2 courses – prerequisite course: unlocked courses
The indegree list shows the number of prerequsited courses for every course.
We start from the courses with indegree 0 – meaning they have no prerequisite courses. Then we do BFS from these courses. Its neighbor is the unlocked courses in the graph. For all the neighbors, their indegree can be deducted by 1 because there is one less prerequisited course for them. And now, we may some courses that have 0 indegree. We add the into the queue and do the work again until there is no course in the queue.

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Codes

    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
        if not prerequisites:
            return True
        '''
        build graph and indegree list first
        the given input using int to represent each course, so we can use list of list
        list_index(which is prerequisited course): [unlocking courses]
        be sure to cover all the courses
        so we use the numCourses instead of the list prerequisites to build the graph and indegree
        there maybe some courses who have no prerequisites hence not appear in prerequisites
        later we need to add/undate values into the graph/indegree
        '''
        # build adjacent courses list
        adj_course = [[] for _ in range(numCourses)]
        # number of prerequisites of each course
        preres = [0] * numCourses
        
        for unlock, prere in prerequisites:
            adj_course[prere].append(unlock)
            preres[unlock] += 1
            
        queue = collections.deque([])
   		
        for i in range(numCourses):
            if preres[i] == 0:
                queue.append(i)
        '''
        we want to know if we are able to take all the courses
        so we need to take notes on the number of courses taken
        we are not able to take all the courses in order
        if the number is less then numCourses after all the bfs done
        '''        
        taken = 0
        
        while queue:
            current = queue.popleft()  
            taken += 1
            for next_course in adj_course[current]:
                preres[next_course] -= 1
                if preres[next_course] == 0:
                    queue.append(next_course)
                    
        return taken == numCourses

Notes

This problem is asking for if we are able to take all the courses. It has other format like: return the order, if the topological order unique etc.

• return the order
  we need to build a list to store all the courses and return it if the number of courses taken == numCourses

• if the topological order unique
  we need to check if len(queue) == 1 in every round. len(queue) == 2 means we can learn either course in queue hence the order is not unique.