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Logicmojo - Updated Dec 12, 2023

After arrays, the second most popular data structure is Linked List. A linked list is a linear data structure, made of a chain of nodes in which each node contains a value and a pointer to the next node in the chain. In this article, letโs see how to implement a circular linked list.

### What is Circular Linked List?

A Circular Linked List (CLL) is similar to a singular linked list, except that the next to the last node points to the first node. Simply put, a circular linked list doesnโt have ends. What we must be aware of in traversing the circular linked list is when to terminate, as we might end up in an infinite loop.

Circular linked lists have real-life use cases, like in the famous scheduling algorithm, Round Robin Algorithm, used to make sure no process gets too much CPU time and assure that no process accesses the resources before all other processes.

1. The NULL assignment is not required because a node always points to another node.

2. The starting point can be set to any node.

3. Traversal from the first node to the last node is quick.

Implementing a circular linked list is very easy and almost similar to linear linked list implementation, with the only difference being that, in circular linked list the last Node will have it's next point to the Head of the List. In Linear linked list the last Node simply holds NULL in it's next pointer.

```class Node {
public:
int data;
//pointer to the next node
node* next;

node() {
data = 0;
next = NULL;
}

node(int x) {
data = x;
next = NULL;
}
}
```

1. Any node can be a starting point. We can traverse the whole list by starting from any point. We just need to stop when the first visited node is visited again.

2. Useful for implementation of queue. We donโt need to maintain two pointers for front and rear if we use circular linked list. We can maintain a pointer to the last inserted node and front can always be obtained as next of last.

3. Circular lists are useful in applications to repeatedly go around the list. For example, when multiple applications are running on a PC, it is common for the operating system to put the running applications on a list and then to cycle through them, giving each of them a slice of time to execute, and then making them wait while the CPU is given to another application. It is convenient for the operating system to use a circular list so that when it reaches the end of the list it can cycle around to the front of the list.

1. The real life application where the circular linked list is used is our Personal Computers, where multiple applications are running. All the running applications are kept in a circular linked list and the OS gives a fixed time slot to all for running. The Operating System keeps on iterating over the linked list until all the applications are completed.

2. Another example can be Multiplayer games. All the Players are kept in a Circular Linked List and the pointer keeps on moving forward as a player's chance ends.

3. Circular Linked List can also be used to create Circular Queue. In a Queue we have to keep two pointers, FRONT and REAR in memory all the time, where as in Circular Linked List, only one pointer is required.

Following are the basic operations that are done on any linked list:
โข Insertion
โข Deletion

Insertion

When adding a node to the front of the circular linked list, it also becomes the new head of the CLL. Now after creating our new node, we need to update the next pointer of our head node. After doing this we traverse to the end of the CLL and update the next tail node to our new node.

```void insertAtFront(CLLNode * head, int X) {

CLLNode * ptr, * temp;
ptr = new CLLNode();
if (ptr == NULL)
return;

ptr - > data = X;
ptr - > next = head;
} else {
while (temp - > next != head)
temp = temp - > next;
ptr - > next = head;
temp - > next = ptr;
}
}
```

Insertion at end

Adding at the end is similar to adding at the front. Create a new node and point it next to the head, as it is going to add to the end, which means it becomes the tail and the tail next contains the head pointer.

```void insertAtEnd(CLLNode * head, int X) {

CLLNode * ptr, * temp;
int item;
ptr = new CLLNode();
if (ptr == NULL)
return;

ptr - > data = X;
ptr - > next = head;
} else {
while (temp - > next != head) {
temp = temp - > next;
}

temp - > next = ptr;
ptr - > next = head;
}
}
```

Deleting a Node in a Circular Linked List

AT FRONT: To delete the node at the front we simply replace the next pointer of the tail node with the next field of the first node.

First, we traverse to the tail of the CLL and update the next pointer of the tail with the node next to the first node. Note, we must store the first node in some temp node to delete it at last.

```void deleteAtEnd(CLLNode * head) {
CLLNode * ptr;
return;

} else {
while (ptr - > next != head)
ptr = ptr - > next;
ptr - > next = head - > next;
head = ptr - > next;
}
}
```

Traversal and Displaying:

Traversing a circular linked list can be done in the following steps:

1. The first step is to check whether the list is Empty or not (Head==NULL).
2. If the list is Empty then finish executing the program.
3. If the list is not Empty then define a node pointer called โtempโ and initialize it with the value of the head node.
4. Keep iterating through the list and printing the value of the nodes by setting โthe value of temp to the value of the data of the nodesโ until โtempโ has reached the last node.
Finally print the values by setting โthe value of temp to the value dataโ.

Circular Linked List Code in Python, C++

```# Python code to perform circular linked list operations

class Node:
def __init__(self, data):
self.data = data
self.next = None

def __init__(self):
self.last = None

if self.last != None:
return self.last

# allocate memory to the new node and add data to the node
newNode = Node(data)

# assign last to newNode
self.last = newNode

self.last.next = self.last
return self.last

# add node to the front

# check if the list is empty
if self.last == None:

# allocate memory to the new node and add data to the node
newNode = Node(data)

# store the address of the current first node in the newNode
newNode.next = self.last.next

# make newNode as last
self.last.next = newNode

return self.last

# add node to the end
# check if the node is empty
if self.last == None:

# allocate memory to the new node and add data to the node
newNode = Node(data)

# store the address of the last node to next of newNode
newNode.next = self.last.next

# point the current last node to the newNode
self.last.next = newNode

# make newNode as the last node
self.last = newNode

return self.last

# insert node after a specific node

# check if the list is empty
if self.last == None:
return None

newNode = Node(data)
p = self.last.next
while p:

# if the item is found, place newNode after it
if p.data == item:

# make the next of the current node as the next of newNode
newNode.next = p.next

# put newNode to the next of p
p.next = newNode

if p == self.last:
self.last = newNode
return self.last
else:
return self.last
p = p.next
if p == self.last.next:
print(item, "The given node is not present in the list")
break

# delete a node
def deleteNode(self, last, key):

# If linked list is empty
if last == None:
return

# If the list contains only a single node
if (last).data == key and (last).next == last:

last = None

temp = last
d = None

# if last node is to be deleted
if (last).data == key:

# find the node before the last node
while temp.next != last:
temp = temp.next

# point temp node to the next of last i.e. first node
temp.next = (last).next
last = temp.next

# travel to the node to be deleted
while temp.next != last and temp.next.data != key:
temp = temp.next

# if node to be deleted was found
if temp.next.data == key:
d = temp.next
temp.next = d.next

return last

def traverse(self):
if self.last == None:
print("The list is empty")
return

newNode = self.last.next
while newNode:
print(newNode.data, end=" ")
newNode = newNode.next
if newNode == self.last.next:
break

# Driver Code
if __name__ == "__main__":

cll.traverse()

last = cll.deleteNode(last, 8)
print()
cll.traverse()
```

Implementation in C++

```// C++ code to perform circular linked list operations

#include <iostream>

using namespace std;

struct Node {
int data;
struct Node* next;
};

struct Node* addToEmpty(struct Node* last, int data) {
if (last != NULL) return last;

// allocate memory to the new node
struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));

// assign data to the new node
newNode->data = data;

// assign last to newNode
last = newNode;

last->next = last;

return last;
}

// add node to the front
struct Node* addFront(struct Node* last, int data) {
// check if the list is empty
if (last == NULL) return addToEmpty(last, data);

// allocate memory to the new node
struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));

// add data to the node
newNode->data = data;

// store the address of the current first node in the newNode
newNode->next = last->next;

last->next = newNode;

return last;
}

// add node to the end
struct Node* addEnd(struct Node* last, int data) {
// check if the node is empty
if (last == NULL) return addToEmpty(last, data);

// allocate memory to the new node
struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));

// add data to the node
newNode->data = data;

// store the address of the head node to next of newNode
newNode->next = last->next;

// point the current last node to the newNode
last->next = newNode;

// make newNode as the last node
last = newNode;

return last;
}

// insert node after a specific node
struct Node* addAfter(struct Node* last, int data, int item) {
// check if the list is empty
if (last == NULL) return NULL;

struct Node *newNode, *p;

p = last->next;
do {
// if the item is found, place newNode after it
if (p->data == item) {
// allocate memory to the new node
newNode = (struct Node*)malloc(sizeof(struct Node));

// add data to the node
newNode->data = data;

// make the next of the current node as the next of newNode
newNode->next = p->next;

// put newNode to the next of p
p->next = newNode;

// if p is the last node, make newNode as the last node
if (p == last) last = newNode;
return last;
}

p = p->next;
} while (p != last->next);

cout << "\nThe given node is not present in the list" << endl;
return last;
}

// delete a node
void deleteNode(Node** last, int key) {
// if linked list is empty
if (*last == NULL) return;

// if the list contains only a single node
if ((*last)->data == key && (*last)->next == *last) {
free(*last);
*last = NULL;
return;
}

Node *temp = *last, *d;

// if last is to be deleted
if ((*last)->data == key) {
// find the node before the last node
while (temp->next != *last) temp = temp->next;

// point temp node to the next of last i.e. first node
temp->next = (*last)->next;
free(*last);
*last = temp->next;
}

// travel to the node to be deleted
while (temp->next != *last && temp->next->data != key) {
temp = temp->next;
}

// if node to be deleted was found
if (temp->next->data == key) {
d = temp->next;
temp->next = d->next;
free(d);
}
}

void traverse(struct Node* last) {
struct Node* p;

if (last == NULL) {
cout << "The list is empty" << endl;
return;
}

p = last->next;

do {
cout << p->data << " ";
p = p->next;

} while (p != last->next);
}

int main() {
struct Node* last = NULL;

traverse(last);

deleteNode(&last, 8);
cout << endl;

traverse(last);

return 0;
}
```

### Time & Space Complexity Analysis

Doubly Linked List Time complexityTime complexitySpace complexity
Insert OperationO(1) or O(n)O(1)
DeletionO(1)O(1)

With this article at Logicmojo, you must have the complete idea of analyzing Circular Linked List and it's operations.

Good Luck & Happy Learning!!

A circular linked list is a type of linked list where the last node of the list points back to the first node, creating a circular structure. In other words, the "next" pointer of the last node in the list points to the first node instead of being NULL, forming a loop. This circular arrangement allows for continuous traversal and iteration of the list.

1. Structure of a Node:

- Each node in a circular linked list contains two components: data and a pointer to the next node.

- The data component stores the value or information associated with the node.

- The pointer component (usually called "next" or "link") points to the next node in the list.

2. Construction of a Circular Linked List:

- The construction of a circular linked list is similar to that of a singly linked list, with the additional step of linking the last node back to the first node.

- When a new node is added to an empty list, its next pointer is set to point to itself, establishing the circular structure.

- When nodes are added to an existing circular linked list, the next pointer of the new node is set to point to the first node, and the next pointer of the last node is updated to

point to the new node, maintaining the circular connectivity.

3. Traversing a Circular Linked List:

- Since a circular linked list forms a loop, traversing the list involves starting at any node and visiting all the nodes until reaching the starting node again.

- To iterate through a circular linked list, we can use a loop that continues until we revisit the starting node or use a do-while loop to ensure that the loop runs at least once.

- The traversal process is similar to that of a singly linked list, where we follow the next pointers from one node to the next.

4. Applications of Circular Linked Lists:

- Circular linked lists are useful in scenarios where continuous iteration or rotation is required.

- They are often used in circular buffer implementations where a fixed-size buffer wraps around itself and operates in a circular manner.

- Circular linked lists are also utilized in round-robin scheduling algorithms and applications that involve cyclic or circular data structures.

5. Operations on Circular Linked Lists:

- The operations on circular linked lists are similar to those on singly linked lists, including insertion, deletion, searching, and updating.

- Insertion and deletion operations require special attention to maintain the circular structure by updating the next pointers accordingly.

- Care must be taken when deleting the last node in the list to ensure the proper reconnection of the circular links.

6. Terminating the Circular Linked List:

- To terminate a circular linked list, the next pointer of the last node can be set to NULL or to a special sentinel value indicating the end of the list.

- This breaks the circular structure and converts the list back into a traditional singly linked list.

In summary, a circular linked list is a data structure where the last node points to the first node, creating a circular arrangement. It allows for continuous traversal, rotation, and circular buffer-like behavior. Circular linked lists are used in various applications that require cyclic or continuous data structures. Proper management of the circular links is crucial when performing operations on circular linked lists.

Circular linked list insertion refers to the process of adding a new node to a circular linked list. The insertion can be performed at different positions in the list, such as at the beginning, end, or anywhere in between. The steps for circular linked list insertion depend on the desired position of the new node.

Here's a detailed explanation of the different scenarios for circular linked list insertion:

1. Insertion at the Beginning:

- To insert a new node at the beginning of a circular linked list, the following steps can be followed:

- Create a new node with the desired data.

- If the list is empty (no nodes exist), set the "next" pointer of the new node to point to itself.

- If the list is not empty, find the last node in the list by following the "next" pointers until the last node is reached.

- Set the "next" pointer of the new node to point to the first node in the list.

- Update the "next" pointer of the last node to point to the new node.

- Set the new node as the new first node of the circular linked list.

2. Insertion at the End:

- To insert a new node at the end of a circular linked list, the following steps can be followed:

- Create a new node with the desired data.

- If the list is empty (no nodes exist), set the "next" pointer of the new node to point to itself.

- If the list is not empty, find the last node in the list by following the "next" pointers until the last node is reached.

- Set the "next" pointer of the new node to point to the first node in the list.

- Update the "next" pointer of the last node to point to the new node.

- Set the new node as the new last node of the circular linked list.

3. Insertion in the Middle:

- To insert a new node in the middle of a circular linked list, the following steps can be followed:

- Create a new node with the desired data.

- Locate the node after which the new node should be inserted.

- Set the "next" pointer of the new node to point to the next node.

- Update the "next" pointer of the previous node to point to the new node.

- Set the new node as the new intermediate node in the circular linked list.

It is important to consider edge cases such as inserting the first node, handling an empty list, or inserting the node at a specific position. Properly updating the "next" pointers is crucial to maintain the circular structure of the list.

After performing the circular linked list insertion, the new node becomes part of the list and can be traversed and accessed along with the existing nodes. The specific insertion position depends on the requirements of the application or the desired behavior of the circular linked list.

In C, a circular linked list can be defined using structures and pointers. Here's an example of how a circular linked list can be defined and implemented in C:

```#include
#include

// Define the structure for a node
struct Node {
int data;
struct Node* next;
};

// Function to create a new node
struct Node* createNode(int data) {
struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
newNode->data = data;
newNode->next = NULL;
return newNode;
}

// Function to insert a node at the beginning of the circular linked list
void insertAtBeginning(struct Node** head, int data) {
struct Node* newNode = createNode(data);
// If the list is empty, make the new node point to itself
newNode->next = newNode;
} else {
// Find the last node and update its "next" pointer
last = last->next;
last->next = newNode;
// Make the new node point to the old first node
}
// Update the head to point to the new node
}

// Function to display the circular linked list
return;
}
do {
printf("%d ", temp->data);
temp = temp->next;
printf("\n");
}

// Main function
int main() {

return 0;
}
```

In this example, the circular linked list is defined using a structure called `Node`. Each node contains two components: `data` to store the value and `next` to store the pointer to the next node in the list.

The `createNode()` function is used to create a new node by allocating memory dynamically. It initializes the data and sets the `next` pointer to `NULL`.

The `insertAtBeginning()` function is used to insert a new node at the beginning of the circular linked list. It creates a new node, updates the `next` pointers to maintain the circular structure, and updates the head to point to the new node.

The `display()` function is used to display the circular linked list. It starts from the head node and iterates through the list, printing the data of each node until it reaches the head again.

In the `main()` function, a circular linked list is created by calling the `insertAtBeginning()` function to insert nodes at the beginning. Finally, the `display()` function is called to print the elements of the circular linked list.

This implementation provides a basic understanding of how a circular linked list can be defined and used in C. Additional functions can be added to perform other operations such as insertion at the end, deletion, or searching based on specific requirements.

In a circular linked list, the concept of "null" is not applicable in the traditional sense as in other data structures. In a circular linked list, the "null" value is replaced by a circular link that connects the last node of the list back to the first node, creating a loop. This loop allows for continuous traversal and iteration of the list.

Here's a detailed explanation of why a circular linked list does not have a "null" value:

- In a circular linked list, the "next" pointer of the last node does not point to a null value as it does in a traditional singly linked list.

- Instead, the "next" pointer of the last node in the circular linked list is updated to point back to the first node, forming a loop or cycle.

- This circular linking is what differentiates a circular linked list from other types of linked lists.

2. Continuous Traversal:

- The circular link in the last node allows for continuous traversal of the circular linked list without encountering a null value.

- Starting from any node in the list, you can follow the "next" pointers indefinitely until you reach the node from which you started.

- This property of a circular linked list ensures that there is no endpoint or null value encountered during traversal.

3. Termination:

- While a circular linked list does not have a null value within the list structure, it is possible to define a termination condition for the traversal or operation on the list.

- One common approach is to define a sentinel node that serves as a marker for the end of the list.

- The sentinel node acts as a placeholder and is typically distinct from the regular nodes in terms of data or structure.

- When traversing the circular linked list, if you encounter the sentinel node, you can consider it as the termination point.

In summary, a circular linked list does not have a "null" value within the list structure due to the circular linking of nodes. The "next" pointer of the last node points back to the first node, creating a loop that allows for continuous traversal without encountering a null value. While a null value is not present within the list structure, it is possible to define a termination condition or use a sentinel node to mark the end of the list when needed.

A circular linked list is a type of linked list in which the last node of the list points back to the first node, forming a loop or cycle. This means that the "next" pointer of the last node in the list does not point to null but instead points back to the first node. The circular structure allows for continuous traversal and iteration of the list.

1. Continuous traversal: Since the last node points back to the first node, it is possible to traverse the entire list without encountering a null value or reaching the end of the list.

2. Efficient operations: Insertion and deletion at the beginning or end of the list can be performed more efficiently than in singly linked lists.

1. Complexity: The circular structure introduces additional complexity in terms of implementation and maintenance compared to singly linked lists.

2. Termination condition: It can be challenging to determine a termination condition for traversal, as there is no natural end point in the list.

A doubly linked list is a type of linked list in which each node contains two pointers: one pointing to the next node and another pointing to the previous node. This bidirectional linkage allows for traversal in both forward and backward directions.

1. Bi-directional traversal: The presence of previous pointers enables traversal in both forward and backward directions, which can be useful in certain scenarios.

2. Easy removal: Removal of a node from the doubly linked list is more efficient compared to singly linked lists because it does not require traversal from the beginning of the list.

1. Increased memory usage: The inclusion of an additional pointer for each node requires more memory compared to singly linked lists.

2. Complexity: The doubly linked list structure introduces additional complexity in terms of implementation and maintenance compared to singly linked lists.

Comparison:

1. Structure: In a circular linked list, the last node points back to the first node, forming a loop. In a doubly linked list, each node contains both next and previous pointers.

2. Traversal: Circular linked lists allow for continuous traversal without encountering a null value, while doubly linked lists allow for traversal in both forward and backward directions.

3. Termination: Circular linked lists do not have a natural termination point, whereas doubly linked lists can be terminated by reaching a null pointer.

4. Complexity: Doubly linked lists have more complex implementation and maintenance due to the bidirectional linkage, while circular linked lists introduce complexity in terms of termination conditions.

The choice between a circular linked list and a doubly linked list depends on the specific requirements of the application. Circular linked lists are useful in scenarios where continuous traversal is required, while doubly linked lists are advantageous when bidirectional traversal or efficient removal is needed.

A circular linked list is a type of linked list where the last node of the list points back to the first node, forming a loop or cycle. This circular structure allows for continuous traversal and iteration of the list without encountering a null value. The "next" pointer of the last node in the list does not point to null but instead points back to the first node.

A normal or singly linked list is a linear data structure in which each node contains data and a pointer to the next node. The last node in a normal linked list points to null, indicating the end of the list.

1. Structure:

- In a circular linked list, the last node points back to the first node, creating a loop. This circular structure enables continuous traversal without reaching a null value.

- In a normal linked list, the last node points to null, indicating the end of the list. It does not form a loop, and traversal stops when reaching the null pointer.

2. Termination:

- Circular linked lists do not have a natural termination point or end. The traversal can continue indefinitely, looping through the list.

- Normal linked lists have a natural termination point when the "next" pointer of the last node points to null. Traversal stops at this point.

3. Traversal:

- Circular linked lists allow for continuous traversal by following the "next" pointers from one node to another, eventually reaching the starting point again.

- Normal linked lists are traversed until the last node is reached, which is identified by its "next" pointer pointing to null.

4. Complexity:

- Circular linked lists introduce additional complexity compared to normal linked lists due to their circular structure. The presence of the circular link requires careful management when performing operations on the list.

- Normal linked lists are relatively simpler to implement and maintain because they do not have the circular structure.

5. Use Cases:

- Circular linked lists are useful in scenarios that require continuous traversal, rotation, or circular buffer-like behavior.

- Normal linked lists are commonly used in situations where a linear sequence of elements needs to be stored and traversed, such as maintaining a collection of data.

Overall, the choice between a circular linked list and a normal linked list depends on the specific requirements of the application. Circular linked lists are suitable when continuous traversal or circular behavior is needed, while normal linked lists are appropriate for linear sequences where termination is essential.

Circular linked lists are used in various scenarios where a continuous loop or cyclic behavior is required. Here are some common use cases where circular linked lists are employed:

1. Round-Robin Scheduling:

- Circular linked lists are often used in scheduling algorithms, such as round-robin scheduling.

- In round-robin scheduling, tasks or processes are assigned time slices or quantum in a cyclic manner.

- Each task is represented by a node in the circular linked list, and the scheduler moves from one task to the next in a circular fashion.

2. Circular Buffers:

- Circular linked lists are frequently used to implement circular buffers or ring buffers.

- Circular buffers are data structures that allow continuous storage and retrieval of a fixed-size collection of elements.

- They are used in scenarios where data needs to be processed or buffered in a cyclic manner, such as in audio or video streaming applications.

3. Game Development:

- Circular linked lists find application in game development for implementing circular movement or behavior.

- For example, in a game with a circular path, a circular linked list can be used to represent the path, and game objects can move along the circular path by traversing the list.

4. Cache Replacement Policies:

- Caches in computer systems often use circular linked lists to implement cache replacement policies.

- Cache replacement policies, such as the Clock or Second-Chance algorithm, utilize circular linked lists to keep track of the order of cache entries.

- When a cache miss occurs, the circular linked list helps determine which entry to replace based on the defined replacement policy.

- Circular linked lists are useful in scenarios where circular navigation is required.

- For instance, in a text editor, circular linked lists can be employed to implement the undo-redo functionality, allowing the user to move back and forth in a cyclic manner through the editing history.

6. Sensor Data Processing:

- Circular linked lists are suitable for storing and processing sensor data in a continuous loop.

- In systems that collect sensor data, circular linked lists can be used to store a fixed-size buffer of sensor readings.

- The oldest readings are continuously replaced by the newest readings, providing a rolling window of data for analysis or real-time processing.

7. Network Protocol Design:

- Circular linked lists have applications in the design of network protocols.

- For example, in a token ring network, where devices take turns transmitting data in a ring-like topology, a circular linked list can be used to manage the order of device transmission.

These are just a few examples illustrating the use of circular linked lists in different domains. Circular linked lists are employed in situations that require cyclic behavior, continuous traversal, or the ability to loop through a sequence of elements. Their circular structure and inherent looping capability make them a valuable data structure for such scenarios.

In a circular linked list, each node contains one pointer, commonly known as the "next" pointer or the "link" pointer. The purpose of this pointer is to establish the connection between nodes and enable traversal through the list.

Here's a detailed explanation of the pointers in a circular linked list:

1. Next Pointer:

- The most essential pointer in a circular linked list is the "next" pointer.

- Each node in the list contains a "next" pointer that points to the next node in the sequence.

- The "next" pointer is responsible for maintaining the connectivity between nodes, forming the circular structure.

- In the last node of the list, the "next" pointer points back to the first node, completing the loop or cycle.

It's important to note that while a circular linked list only requires one pointer per node, there are additional pointers involved in managing the list, such as the head pointer.

- The head pointer is not specific to a circular linked list but is commonly used to keep track of the first node in the list.

- It points to the beginning of the circular linked list and provides the entry point for accessing or traversing the list.

- The head pointer is essential for operations like insertion, deletion, and traversal.

It's worth mentioning that some circular linked list implementations may incorporate additional pointers or attributes to support specific functionalities or optimizations. For example, a doubly circular linked list would contain an additional "previous" pointer in each node for bidirectional traversal.

In summary, a circular linked list typically consists of one pointer per node, known as the "next" pointer. This pointer establishes the connection between nodes and forms the circular structure. The head pointer, not specific to circular linked lists, is used to reference the first node. While a circular linked list primarily requires one pointer per node, additional pointers or attributes can be included based on the specific requirements or variations of the implementation.

Circular linked lists can be found in various real-life scenarios where cyclic behavior or continuous looping is required. Here's an example to illustrate the use of a circular linked list in a real-life situation:

- A roundabout or traffic circle is a common example where a circular linked list can be applied.

- In a roundabout, vehicles enter and exit at various points, continuously moving in a circular pattern.

- Each entry point in the roundabout can be represented as a node in the circular linked list, and the vehicles move from one node to the next in a cyclic manner.

- The circular structure of the linked list aligns with the physical behavior of vehicles circulating in the roundabout.

For instance, imagine a roundabout with four entry points: A, B, C, and D. Each entry point represents a node in the circular linked list. When a vehicle enters the roundabout at point A, it follows the circular linked list by moving from node A to node B, then from B to C, and so on until it reaches the desired exit point. Once the vehicle exits, the circular linked list continues with other vehicles entering and exiting in a continuous loop.

This real-life example demonstrates how a circular linked list can model the behavior of vehicles in a roundabout, where the circular structure ensures continuous movement without the need for additional control structures.

Circular linked lists find application in various other scenarios as well, such as:

- Cyclic animations in video games or graphical applications.

- Circular buffers used for streaming or buffering data in audio or video applications.

- Continuous data collection or sensor readings in real-time systems.

- Circular navigation through a playlist or media player.

- Cyclic scheduling algorithms in operating systems.

These examples highlight the practical usage of circular linked lists in various domains where continuous looping or cyclic behavior is needed to model or manage real-life processes or data structures.

To identify a circular linked list, you need to detect if there is a loop or cycle within the list. There are a few common approaches to identify a circular linked list:

1. Using Two Pointers (Floyd's Cycle-Finding Algorithm):

- One common technique is to use two pointers, often referred to as the "slow" pointer and the "fast" pointer.

- Move the slow pointer one step at a time and the fast pointer two steps at a time.

- If the linked list contains a loop, the fast pointer will eventually catch up to the slow pointer or overtake it within the loop.

- If at any point during traversal the two pointers meet (i.e., their memory addresses become the same), it indicates the presence of a loop or cycle in the linked list.

This algorithm works because if there is a loop, the fast pointer, which moves faster, will eventually lap the slow pointer and catch up to it within the loop.

2. Using a Hash Set or Hash Table:

- Another approach is to use a hash set or hash table data structure to keep track of visited nodes.

- Traverse the linked list, and for each node encountered, check if it already exists in the hash set.

- If a node is found in the hash set, it indicates the presence of a loop or cycle in the linked list.

- If the traversal reaches the end of the list (i.e., encounters a null pointer), it means there is no loop in the linked list.

This approach relies on the fact that a loop will cause a node to be visited multiple times, which can be detected by the duplicate presence in the hash set.

- A less common approach involves modifying the linked list by temporarily breaking the loop to check for a loop's presence.

- During traversal, keep track of the last visited node.

- When visiting a node, check if its "next" pointer points to the last visited node.

- If such a connection is found, it indicates the presence of a loop or cycle in the linked list.

- After identifying the loop, the linked list can be restored to its original state by reconnecting the "next" pointer of the last visited node.

This method requires temporarily modifying the linked list structure, so it may not be suitable in all scenarios.

These approaches allow you to identify the presence of a loop or cycle in a linked list and confirm if it is a circular linked list. Once a loop is detected, you can determine that the linked list is circular and take appropriate actions based on your requirements.

Using a circular linked list offers several advantages in certain scenarios. Here are some of the advantages of using a circular linked list:

1. Continuous Traversal:

- One of the main advantages of a circular linked list is the ability to traverse the list continuously without encountering a null value or reaching the end of the list.

- Since the last node points back to the first node, it forms a loop, allowing for seamless traversal through all the nodes.

- This continuous traversal is useful in applications where cyclical or periodic behavior is desired, such as rotating through a set of elements or repeatedly processing data in a circular manner.

2. Efficient Operations:

- Circular linked lists can offer more efficient operations in certain cases compared to other types of linked lists.

- Insertion and deletion operations at the beginning or end of the list can be performed more efficiently in a circular linked list than in a singly linked list.

- In a circular linked list, adding a node at the beginning only requires updating a few pointers, making it a constant time operation (O(1)).

- Similarly, removing the first node in a circular linked list involves updating pointers, without the need for traversing the entire list.

3. Cyclic Behavior:

- Circular linked lists are well-suited for modeling cyclic behavior or circular structures in real-world scenarios.

- They can represent processes that repeat in a loop or systems that exhibit circular patterns.

- Examples include round-robin scheduling algorithms, circular buffer implementations, circular navigation through playlists, cyclic animations, or circular data collection and processing.

4. Memory Management:

- Circular linked lists can be beneficial in certain memory management scenarios.

- For instance, in garbage collection systems, a circular linked list can be used to maintain a list of allocated memory blocks or objects that need to be reclaimed.

- The circular structure simplifies the process of iterating through the list of allocated memory blocks without needing additional pointers or bookkeeping.

5. Implementation Simplicity:

- In some cases, implementing certain algorithms or data structures using a circular linked list can be simpler than using other data structures.

- Circular linked lists can provide an elegant solution when cyclical or circular behavior is a fundamental requirement of the problem domain.

- The circular structure aligns more naturally with the problem's characteristics, leading to a more straightforward and intuitive implementation.

While circular linked lists offer these advantages, it's important to note that they are not suitable for every situation. They introduce additional complexity compared to singly linked lists and may not be efficient for scenarios that involve frequent random access or extensive modifications at arbitrary positions. The advantages of a circular linked list become prominent when its cyclic behavior and continuous traversal align with the requirements of the application or problem at hand.