In many deletion problems, only a small change occurs in the array/circle. For example, in the problem Playlist, at most three GCD pairs change. This can usually help in either simulating the problem or getting to some other observation.

In deletion problems, there are some common approaches like doubling the array, using a data structure (set, segment tree) to erase and then binary searching or observing minor changes after deleting an element.

I like to use a circular linked list. It is extremely intuitive as it is literally a circle (I feel this makes more sense than for example, doubling the array).

https://www.geeksforgeeks.org/circular-linked-list/