Schedule prerequisite classes with retakes

Problem

You are building a course-taking engine.

Each course is represented as an object:

• id (unique identifier)
• prevCoursesList : a list of prerequisite course IDs that must be passed before this course can be attempted.

You are given:

• roots : a list of target course IDs the student ultimately wants to complete.
• An API didPass(courseId) -> bool that can be called each time you attempt a course. If it returns false , the student failed that attempt and must retake the course later.

Rules

1. A course can be attempted only after all its prerequisites have been passed .
2. When a course is attempted:
   • If didPass(id) returns true , mark it as passed.
   • If it returns false , the course must be retaken later (i.e., re-queued for another attempt).
3. The input only provides prerequisite pointers ( course -> prerequisites ). You must first discover all involved courses reachable from roots and build any additional relationships you need (e.g., prerequisite → dependent adjacency).

Task

Implement a function that returns the sequence of course IDs in the order they were attempted until:

• all roots have been passed, or
• you detect it is impossible (e.g., a prerequisite cycle), or
• a course exceeds maxRetries failed attempts.

Output

Return:

• attemptOrder : list of attempted course IDs (including retries), if successful.
• Otherwise, return/throw an error indicating the reason (cycle detected or retries exceeded).

Constraints (reasonable assumptions)

• Up to ~1e5 courses and ~2e5 prerequisite edges may be involved after expanding from roots .
• maxRetries is a small integer (e.g., 3–10).

Edge cases to handle

• Shared prerequisites among multiple roots.
• Duplicate IDs in roots .
• Missing prerequisite IDs (treat as invalid input).
• Cycles in prerequisite dependencies.
• Courses that repeatedly fail and exceed maxRetries .