A circular linked list is an important data structure used in computer science. It’s a data structure that allows the storage of data in a linked list, where the last node links back to the first node to create a circle. It offers advantages over traditional linked lists in certain applications, and is integral to the functioning of certain systems.

What is a Circular Linked List?

A circular linked list, also known as just a circular list, is a type of linked list where the last node in the list points back to the first node, forming a ‘loop’ or ‘circle’. This is what makes it distinct from the more traditional ‘linear linked list’, where the last node points to a null value. The goal of this circular construction means each element in the sequence can be easily accessed without needing to jump from one end to another each time. An analogy for this can be drawn from an English tenses exercise book.

The main element of this data structure is the Node object. Each Node object has three components: a data field to store the element of interest, a next pointer pointing to the next Node in the list and a previous pointer pointing to the previous Node in the list. The data structure starts with a ‘head’ pointer, pointing to the Node at the start of the list. The first Node points to the second, and so on until the last Node in the list, which points back to the Node at the start. This completes the circle.

Benefits of a Circular Linked List

Circular linked lists offer many advantages over linear linked lists that make them useful in certain situations. Being circular in nature gives them greater flexibility to loop through elements quickly and easily. Additionally, data structures that are designed using this data structure can be determined to be a ‘true’ circular structure by examining the pointers. A classic example of this is a ring buffer, which stores elements in a FIFO (first-in-first-out) structure. It is better to use a circular linked list for this than a linear one, since it removes the need to search for the start of the list when elements are added/deleted.

A circular linked list also makes it easier to execute specific algorithms such as QuickSort or Rotate by quickly moving nodes in one direction instead of visitng each element individually. Additionally, circular linked lists enable fast and efficient searching algorithms that can search through elements quickly and easily.

How to Implement a Circular Linked List

Implementing a circular linked list in Java is relatively straightforward. All that is required is an object class (Node) and a class (List) that contains references to the first and last Nodes. The List class also contains several methods to add/remove nodes from the list, traverse it and print it.

There are two ways to implement a circular linked list in Java:

• Using an array, where each element of an array is a pointer to an array of Node objects.
• Using pointers, where each element of the list is an object of type Node that contains both a ‘data’ field and two pointers: one pointing to the next Node (the one following it in the list) and one pointing to its preceding Node (the one before it).

In both instances, after setting up the head and tail pointers, it is necessary to also set up the last pointer (to which both head and tail point) so that when traversing through the list, it loops all the way around.

Example of a Circular Linked List in Java

Let’s look at a simple example of a circular linked list implemented in Java. This example creates a circular linked list consisting of three nodes each storing an integer value.

To create a circular linked list we first need to create the List class which contains all references to the Nodes.The List class needs three properties: head, tail, and size.

public class List {   Node head;   Node tail;   int size;   ... } 

Then we must create our Node class which will also contain three properties: data, next and previous.

public class Node {   int data;   Node next;    Node previous;   ... } 

To add and remove nodes from our list we will use the append() and remove() methods as follows:

public void append(int data) {   Node node = new Node();    if (size == 0) {      head = node;      tail = node;    } else {      tail.next = node;      node.previous = tail;      tail = node;    }    size++;  } public void remove(Node node) {    if (size == 1) {      head = null;      tail = null;    } else if (node == head) {      node.next.previous = null;      head = node.next;    } else if (node == tail) {      node.previous.next = null;      tail = node.previous;    } else {      node.previous.next = node.next;      node.next.previous = node.previous;    }    size--;  } 

How to Traverse a Circular Linked List

Traversing a circular linked list is similar to traversing any other type of linked list, however it requires an additional step at the end. This additional step takes care of looping through all elements of the list by resetting the start pointer back to its original spot once visiting all elements.

// Traversing a Circular Linked List in Java public void traverseList() {      // Assigning pointer temp with head of list      Node temp = head;      // traversing until it reaches null      while (temp != null) {          System.out.print(temp.data);          // Move pointer towards next Node if next Node is not null          if (temp.next != null) {              temp = temp.next;          } else {              // If tail Node is reached set back temp pointer to head              temp = head;              break;          }      }  }

Common Operations on a Circular Linked List

Most operations performed on a circular linked list will be familiar as they are similar to operations performed on any other type of linked list. These include adding, removing, copying and sorting data.

• Add/Remove Nodes: Adding and removing nodes to/from the linked list is done in a similar fashion to how it is done on any other type of linked list and involves operating on the pointers that connect each node together.
• Copy Nodes: Linked lists can be easily copied by simply pointing all list elements to a new location in memory.
• Sorting Data: Generally sorting data inside a circular linked list involves using existing sorting algorithms such as QuickSort or RadixSort.

Time and Space Complexity of a Circular Linked List

Circular linked lists offer good time performance when compared to linear linked lists as they allow faster traversal. Each operation on a circular linked list takes O(1) (constant) time in most cases, except for sorting which takes O(n log n). On average, most operations take O(n/2) time.

In terms of space complexity, Circular Linked lists require more memory than linear linked lists since they need an extra pointer to point back to the beginning of the list.

Applications of a Circular Linked List

Circular linked lists have various applications in computer science, including applications related to algorithms such as QuickSort or RadixSort which need fast traversal capabilities, as well as applications involving manipulation of database information, for instance searching for data more quickly or efficiently managing items within a data structure.

Conclusion

The Circular Linked List data structure is an important part of computer science due to its ability to store data efficiently while providing fast traversal capabilities. It offers great advantages over traditional linear linked lists in certain situations and applications, making it an important part of many computer algorithms and systems.