Check feasibility of AI course schedule

You are designing a learning path for n AI-related courses, labeled from 0 to n - 1.

Some courses have prerequisites. For example, to take course b, you may first need to finish course a. This can be represented as a directed edge a -> b.

You are given:

• An integer n, the number of courses.
• A list prerequisites of pairs [a, b], where each pair means: to take course b, you must first complete course a.

You need to determine whether it is possible to finish all courses.

Formally, model the courses as a directed graph:

• Each course is a node.
• Each prerequisite pair [a, b] is a directed edge from a to b.

If the graph contains a cycle (e.g., 0 -> 1 -> 2 -> 0), then there is no way to complete all courses because each course in the cycle depends on another in the cycle.

Task

Write an algorithm that:

• Returns true if it is possible to complete all n courses given the prerequisites.
• Returns false if it is not possible (i.e., if there is at least one cycle in the prerequisite graph).

Constraints (typical interview constraints; you may assume something like):

• 1 <= n <= 10^5.
• 0 <= prerequisites.length <= 10^5.
• 0 <= a, b < n for every pair [a, b].

Your algorithm should run in O(n + m) time, where m = prerequisites.length, and use O(n + m) extra space.

You may use any standard graph traversal technique (e.g., DFS or BFS/topological sort).

Course Schedule Feasibility

Return true if all courses can be completed, false if prerequisites contain a cycle.

Examples

Example 1

Input: (2, [[0,1]])
Output: True

Explanation: Acyclic.

Example 2

Input: (2, [[0,1],[1,0]])
Output: False

Explanation: Cycle.

Hints

1. Use deterministic tie-breaking for prompts with multiple valid outputs.
2. For design-style APIs, simulate operations with explicit inputs.