Topological Sort (Kahn's & DFS)

from collections import deque, defaultdict

def topological_sort(num_courses: int, prerequisites: list[list[int]]) -> list[int]:
    graph = defaultdict(list)
    indegrees = [0] * num_courses
    
    # Prerequisite [a, b] means: must take b before a (edge: b -> a)
    for course, prereq in prerequisites:
        graph[prereq].append(course)
        indegrees[course] += 1
        
    # Start with all nodes having zero prerequisites
    queue = deque([i for i in range(num_courses) if indegrees[i] == 0])
    order = []
    
    while queue:
        curr = queue.popleft()
        order.append(curr)
        
        for next_course in graph[curr]:
            indegrees[next_course] -= 1
            if indegrees[next_course] == 0:
                queue.append(next_course)
                
    # If order doesn't include all courses, a cycle exists
    return order if len(order) == num_courses else []