Schedule prerequisite classes with retakes

Problem Statement

You are building a course scheduling system. Students must complete prerequisite classes before enrolling in advanced ones. Some students may fail a course and need to retake it. You are given a list of courses, their prerequisites, and a list of courses the student has already passed.

A student can only take a course if all its prerequisites are in the 'passed' list. If a course is already in the 'passed' list, it does not need to be taken again. Your task is to return a valid sequence of courses that a student must complete to finish all target courses.

Function Signature

def get_schedule(courses, prerequisites, passed_courses):

• courses: A list of all course IDs (strings).
• prerequisites: A list of pairs (prereq, course), meaning prereq must be completed before course.
• passed_courses: A set of course IDs that the student has already passed.

Return a list of courses in the order they must be taken. If it is impossible to complete the courses due to circular dependencies, return an empty list.

Examples

Example 1:

• courses: ["CS101", "CS102", "CS103"]
• prerequisites: [("CS101", "CS102"), ("CS102", "CS103")]
• passed_courses: ["CS101"]
• Result: ["CS102", "CS103"]

Example 2:

• courses: ["A", "B"]
• prerequisites: [("A", "B"), ("B", "A")]
• passed_courses: []
• Result: [] (Cycle detected)

Constraints

• Number of courses <= 1000.
• passed_courses may contain courses that are not in the current required list.
• The result should only contain courses that have not been passed yet.