Compute minimum semesters to finish courses

You are given n courses labeled 1..n and a list of prerequisite relations prereq, where each element is a pair [a, b] meaning you must complete course a before taking course b.

Part A

Return the minimum number of semesters needed to complete all courses if you may take any number of courses per semester, as long as prerequisites are satisfied.

• If it is impossible to finish all courses (because prerequisites contain a cycle), return -1 .

Input

• Integer n
• List prereq: List[List[int]]

Output

• Integer minimum semesters, or -1

Constraints (reasonable interview constraints)

• 1 <= n <= 10^5
• 0 <= prereq.length <= 2*10^5
• Course labels are in 1..n

Part B (follow-up)

Now you may take at most k courses per semester.

Return the minimum number of semesters needed to complete all courses under this constraint, or -1 if impossible.

Additional input

• Integer k with 1 <= k <= n

Notes

• You may choose which available (prerequisites-satisfied) courses to take each semester.