What is a circular linked list, and how does it work?

A circular linked list is a type of data structure where the last node points back to the first node, forming a loop.

In more detail, a circular linked list is a variation of the standard linked list. In a standard linked list, each node contains some data and a 'next' reference pointing to the next node in sequence. The last node, instead of having a 'next' reference, has a null reference indicating the end of the list. However, in a circular linked list, the 'next' reference of the last node points back to the first node, creating a circular or looped structure.

This circular structure can be useful in certain situations. For example, it can be used to model problems or systems that are cyclical in nature, such as a round-robin scheduler in an operating system, or a digital media player that loops back to the first song after playing the last one.

In terms of operations, a circular linked list works similarly to a standard linked list. You can add, remove, or search for elements. However, because of the circular nature, you need to be careful to avoid infinite loops. For instance, when traversing the list, you need to remember the starting point and stop when you get back to it.

Another key difference is that in a circular linked list, you can traverse the whole list from any point. In a standard linked list, you can only traverse the list from the first node to the last. This makes circular linked lists more flexible in some scenarios.

In terms of complexity, the operations on a circular linked list have similar time complexities to those on a standard linked list. That is, adding or removing elements is generally an O(1) operation if you're at the correct spot, while searching for an element is an O(n) operation, where n is the number of elements in the list. However, finding the correct spot can take up to O(n) time, especially if you don't have a reference to the node before the one you're interested in.