⭕Circular Linked List

What is a Circular Linked List?

💡A circular linked list is a special type of linked list where the last node's "next" pointer points back to the first node, forming a closed loop. A circular linked list can be either a singly circular linked list or a doubly circular linked list.

Here are some key characteristics of circular linked lists:

• No beginning or end: Unlike regular linked lists with distinct "head" and "tail" nodes, circular lists have no clear starting or ending points. Accessing any node and traversing the list can be done from any point.

• Dynamic size: Just like other linked lists, nodes can be added or removed to adjust the list size dynamically.

• Efficient insertion/deletion: Similar to doubly linked lists, insertions and deletions in circular lists can be done in constant time (O(1)) on average, regardless of the location.

• Potential memory benefits: Depending on implementation, circular lists might require slightly less memory than doubly linked lists, as the last node's pointer doesn't need to be set to "null".

However, there are also some trade-offs with circular linked lists:

• Complexity in finding the beginning: Since there's no distinct "head", additional logic might be needed to identify the starting point for traversal or operations like accessing the first element.

• Less intuitive operations: Certain operations like finding the middle element or splitting the list might require additional processing compared to linear linked lists due to the cyclical nature.

Here are some common use cases for circular linked lists:

• Implementing round-robin algorithms: In situations where elements need to take turns, like in a round-robin scheduling system, circular lists offer efficient management.

• Managing buffers: Circular lists can be used to create efficient buffers for data streams, where the oldest data is overwritten when the buffer reaches its capacity.

• Modeling circular structures: They can be helpful in representing data structures related to loops or cycles, like graphs or musical scales.

Big O Notation of Circular Linked List Operations

Operation	Time Complexity	Explanation
Insertion (beginning/end)	$O(1)$	Constant time because you have direct access to these positions.
Insertion (after specific node)	$O(n)$	Needs traversal to find the specific node.
Deletion (beginning/end)	$O(1)$	Similar to insertion.
Deletion (specific node)	$O(n)$	Needs traversal to find the node.
Search	$O(n)$	Requires iterating through the list until the target element is found.
Traversing through the list	$O(n)$	Iterates through each node once.
Minimum/Maximum element	$O(n)$	Requires traversing the list to compare each element.

Important notes:

• Average case: For insertion and deletion after a specific node, the average case complexity is $O(n/2)$ as the target node could be anywhere in the list.

• Doubly linked lists: Generally have the same complexities as circular linked lists, but some operations (e.g., insertion/deletion in the middle) can be faster due to having access to previous nodes.

Implementation of Circular Linked List In JavaScript

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