23. Course Schedule
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The problem can be found at the following link:
I am using a topological sorting approach to find the order of courses. The idea is to first create a directed graph representing the prerequisite relationships between courses. Then, I calculate the in-degree (number of incoming edges) for each course. Starting with the courses that have no prerequisites (in-degre e = 0), I use a queue to perform a topological sort.
Creating the Graph
I create an array of vectors to represent the graph, where graph[i]
contains the courses that depend on course i
.
I also maintain an array degree
to store the in-degree of each course.
Topological Sort
I initialize a queue with courses having no prerequisites (in-degree = 0).
While the queue is not empty, I dequeue a course, add it to the result, and reduce the in-degree of its dependent courses.
If any dependent course now has in-degree = 0, I enqueue it.
Validating the Result
After the topological sort, I check if all courses have been included in the result. If not, it means there is a cycle, and the schedule is not possible.
Time Complexity: O(n + m)
, where n is the number of courses and m is the number of prerequisites. Building the graph takes O(m) time, and the topological sort takes O(n + m) time.
Auxiliary Space Complexity: O(n)
, where n is the number of courses. This is used for the degree array and the queue.
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