Course Schedule (Cycle Detection)

There are n courses numbered 0 … n−1. A prerequisite pair a b means you must finish course b before course a. Can you finish all the courses?

Input:

• line 1: n m
• next m lines: a prerequisite pair a b

Output: true if all courses can be finished, false otherwise.

Constraints: 1 ≤ n ≤ 10⁵, 0 ≤ m ≤ 10⁵, a ≠ b; a pair may appear more than once.

Think about it: you can finish everything exactly when the prerequisite graph has no cycle. Detect it with Kahn's algorithm (repeatedly take courses with no remaining prerequisites) or with a DFS that colours nodes white/grey/black.