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] = [y, x] indicates that you must take course x first if you want to take course y.

Return true if you can finish all courses, or false otherwise.

Function Signature:

from typing import List

def can_finish_courses(numCourses: int, prerequisites: List[List[int]]) -> bool:
    """
    Determine if it is possible to finish all courses based on prerequisites.

    Parameters:
    - numCourses: The total number of courses.
    - prerequisites: A list of prerequisites, where prerequisites[i] = [a, b]
      indicates that you must take course b first if you want to take course a.

    Returns:
    - bool: True if it is possible to finish all courses, False otherwise.
    """
    # Your code here

Example:

# 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.

# 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.

# Input: numCourses = 4, prerequisites = [[1, 0], [2, 1], [2, 3], [3, 0]]
# Output: True
# Explanation: There are a total of 4 courses available. We can start by taking
# course 0, which will then enable us to take courses 1 and 3. 
# Once we have completed courses 1 and 3, we can proceed to take course 2. 
# Therefore, it is indeed possible to complete all the courses.

Note:

  • The input prerequisites are a graph represented by a list of edges, not adjacency matrices.
  • You may assume that there are no duplicate edges in the input prerequisites.

Instructions:

  • Write the can_finish_courses function to solve the problem.
  • Implement your solution in Python.
  • Provide clear comments in your code.
  • Discuss the time and space complexity of your solution.

As always, we’ll share our solution to this problem tomorrow. Stay tuned 😊