Answer common graph, grid, and array tasks

Problem: Course Dependency Resolver

There are n courses labeled from 0 to n-1. You are given an array of dependencies where dependencies[i] = [a, b] indicates that you must take course b before course a.

Your task is to determine if it is possible to finish all courses. If it is possible, return the valid order (any valid topological sort); otherwise, return an empty list.

Function Signature

def find_order(num_courses: int, dependencies: list[list[int]]) -> list[int]:

Constraints

• 1 <= num_courses <= 2000
• 0 <= len(dependencies) <= 5000
• The graph may contain disconnected components.

Examples

Example 1: Input: num_courses = 2, dependencies = [[1, 0]] Output: [0, 1] Explanation: To take course 1, you must first take course 0.

Example 2: Input: num_courses = 4, dependencies = [[1, 0], [2, 0], [3, 1], [3, 2]] Output: [0, 1, 2, 3] (or [0, 2, 1, 3])

Example 3: Input: num_courses = 2, dependencies = [[1, 0], [0, 1]] Output: [] Explanation: There is a cycle (0 depends on 1, 1 depends on 0), so it is impossible.

Edge Cases

• num_courses with no dependencies.
• Disconnected graph components.
• Self-loops in dependencies.