Course Schedule

Course Schedule

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 must first take course 1.

Return true if you can finish all courses. Otherwise, return false.

Examples

Example 1:

Input: numCourses = 2, prerequisites = [[1,0]]
Output: true
Explanation: You can take course 0 first, then course 1.

Example 2:

Input: numCourses = 2, prerequisites = [[1,0],[0,1]]
Output: false
Explanation: Course 0 requires course 1 and course 1
requires course 0. This creates a cycle, making it
impossible to finish both.

Example 3:

Input: numCourses = 3, prerequisites = [[1,0],[2,1]]
Output: true
Explanation: Take course 0, then 1, then 2.

Constraints

• 1 <= numCourses <= 2000
• 0 <= prerequisites.length <= 5000
• prerequisites[i].length == 2
• 0 <= ai, bi < numCourses
• All prerequisite pairs prerequisites[i] are distinct.

Expected Complexity

• Time: O(V + E) where V = numCourses and E = number of prerequisites
• Space: O(V + E) for the adjacency list and tracking arrays