Course Schedule Feasibility II

Given numCourses and prerequisite pairs, return true if it is possible to finish all courses. Pattern focus: DFS Approach. Use visit states to detect back-edges and prove acyclicity.

Input Format

numCourses = course count, prerequisites = prerequisite pairs [course, prerequisite]

Output Format

true if all courses can be completed

Constraints

  • 1 <= input size <= 10^5
  • -10^9 <= numeric values <= 10^9

Examples

Example 1:

Input:

numCourses = 2
prerequisites = [[1,0]]

Output:

true

Explanation:

A simple dependency chain is valid.

Example 2:

Input:

numCourses = 2
prerequisites = [[1,0],[0,1]]

Output:

false

Explanation:

The DFS will revisit a node currently in the recursion stack.

Example 3:

Input:

numCourses = 4
prerequisites = [[1,0],[2,1],[3,2]]

Output:

true

Explanation:

A chain without a back-edge is valid.

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Course Schedule Feasibility II