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.
numCourses = course count, prerequisites = prerequisite pairs [course, prerequisite]
true if all courses can be completed
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.