Editorial for Faulty Check-in

At any point in time, Jackson only has 3 options: Check in the first queue student, check in the second queue student, or move the first queue student to the front of the second queue.

Because of the first hint, and because we always know the next student Jackson needs to check in, there is always really only a single choice for Jackson - what should Jackson do in what scenario?

If Jackson sees the next student ID at the front of either queue, he should check them in, always.

Otherwise, he can only take the student in the first queue, and move them to the front of the second queue.

Jackson's second queue is not a queue. What is it?

Jackson's second queue is not a queue - it's a stack! We always place students and check them in from the front.

As was covered in Hint 2, there is only one option Jackson has available at any point in time, so we just need to simulate this second queue current state using a stack, as we read through the input queue.