12. Course Schedule

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] = [ai, bi] indicates that you must take course bi first if you want to take course ai.

For example, the pair [0, 1], indicates that to take course 0 you have to first take course 1.

Return true if you can finish all courses. Otherwise, return false.

This problem is about detecting cycles in a directed graph. If there's a cycle in the prerequisites (e.g., course A requires course B, and course B requires course A), it's impossible to complete all courses.

Requirements

1. Basic Functionality

• Check if all courses can be completed
• Detect cycles in prerequisite dependencies
• Return true if no cycles exist, false otherwise

Example Usage

canFinish(2, [[1,0]]);           // true - course 1 requires course 0, no cycle
canFinish(2, [[1,0],[0,1]]);     // false - circular dependency
canFinish(3, [[1,0],[2,1]]);     // true - linear chain, no cycle

Real-World Context

This problem models real course scheduling systems:

• University course registration: Students must complete prerequisites before advanced courses
• Task scheduling: Tasks with dependencies must be completed in order
• Build systems: Compilation order for modules with dependencies
• Package managers: Resolving dependency conflicts in software packages