## Introduction to Circular Linked Lists

In the world of data structures, linked lists have always been a fundamental concept. Linked lists are a sequence of elements called nodes, which are connected through pointers, thereby creating a chain of nodes where each node contains two fields: data and a pointer to the next node.

The data can be of any type, such as integer, character, string, etc., and the pointer points to the next node in the sequence. A common variation of the linked list is the Circular Linked List.

It is similar to a standard linked list, except that the last node of the list points to the first node, thereby creating a loop. This article will delve deeper into the concept of Circular Linked Lists, their definition, characteristics, and implementation in Python.

## Understanding of Linked Lists

Before we get into specifics, let us first understand the concept of Linked Lists. Linked lists are a dynamic data structure, meaning that nodes can be added or removed from the list without affecting the rest of the list.

Each node holds a data field and a pointer field. The data field stores the actual data, and the pointer field points to the next node in the list.

Linked lists are an efficient data structure for dynamic data, where we do not know the size of the data beforehand. Linked lists have better insertion and deletion time complexity than arrays, making them ideal for dynamic data.

However, arrays exhibit better performance than linked lists for accessing data since arrays use contiguous memory locations.

## Circular Linked Lists in Python

Similar to standard linked lists, a circular linked list can also be implemented in Python. In a circular linked list, the last node points to the first node, creating a loop.

### Consider the following example:

We have three nodes – Node 1, Node 2, and Node 3. Node 1 points to Node 2, Node 2 points to Node 3, and Node 3 points to Node 1, thereby creating a loop.

## Definition and characteristics of Circular Linked Lists

As the name suggests, a circular linked list is a type of linked list where the last node points to the first node, forming a loop. This loop allows for easy traversal of the list, since we can always start at the first node and continue until we reach the first node again, traversing the entire list.

One of the primary characteristics of circular linked lists is that they have no beginning or endpoint. Each node in the list has two fields – a data field and a pointer field.

The data field holds the actual data, and the pointer field points to the next node in the list. Circular linked lists can be used in scenarios where we need to access data in a circular manner.

For example, we could use a circular linked list to simulate a round-robin scheduling algorithm, where each process takes a turn to execute.

## Visualization of Circular Linked Lists

Visualizing circular linked lists can help us understand the concept better. Consider the following example of a circular linked list of three nodes – Node 1, Node 2, and Node 3.

______ _______

| | | |

| |————>| | |

| 1 | | 2 |

|______|______________| ______|

| |

| 3 |

|______|

In the above example, Node 1 is connected to Node 2, which is connected to Node 3. Node 3 is connected back to Node 1, thereby creating a loop.

The loop represents the end of the linked list, and we can traverse through the entire list by starting at any node and following the next node until we reach the starting node.

## Conclusion

Circular linked lists are a vital data structure in computer science, and their applications are widespread. In scenarios where we need to access data in a circular manner, circular linked lists can be an excellent choice.

Python provides a simple and intuitive way of implementing circular linked lists. By understanding the basics of linked lists and their variation – circular linked lists, we can create efficient solutions for a wide range of problems.

## Implementing Circular Linked Lists in Python

Now that we understand how Circular Linked Lists work and their characteristics, we can move on to implementing them in Python. In this section, we will cover the implementation of the Node class and the Circular Linked List class, along with their methods.

### Implementation of Node class

The Node class represents a single node in the Circular Linked List. Each node has two fields – data and the next node.

The data field stores the actual data, and the next node field is a pointer to the next node in the list. Here is an example of a Node class implementation in Python:

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

In the above code, we have defined the constructor for the Node class.

It takes two parameters – the data to store in the node, and the pointer to the next node. If no data or next node is specified, the default value is None.

### Implementation of Circular Linked List class

The Circular Linked List class is the primary data structure we will work with. It represents the entire circular linked list and provides methods to manipulate the list.

The class contains a head node to represent the starting node of the list, and a count member to store the size of the list. Here is an example of a Circular Linked List class definition:

```
class CircularLinkedList:
def __init__(self):
self.head = Node()
self.count = 0
```

In the above code, we have defined the constructor for the Circular Linked List class.

The initializer sets the head node to a default node and sets the count of nodes in the list to zero. **__init__** method

The **__init__** method is responsible for initializing the Circular Linked List class and creating a head node.

It takes no input parameters and is automatically called when a new instance of the class is created. In our example implementation, the **__init__** method sets the head node to a default node with no data and no next node.

It also sets the count of nodes in the list to zero. **__repr__** method

The **__repr__** method is responsible for returning a string representation of the Circular Linked List object and is called when we try to print the object.

In our example implementation, we have defined the **__repr__** method for the Circular Linked List class as follows:

```
def __repr__(self):
nodes = []
node = self.head.next_node
for i in range(self.count):
nodes.append(str(node.data))
node = node.next_node
return "n".join(nodes)
```

In the above code, we iterate through the list and append the data of each node to a list of strings. We then join the strings with a newline character to create a string representation of the list.

### append and insert method

The append method appends a new node to the end of the Circular Linked List. Here is an example implementation of the append method:

```
def append(self, data):
new_node = Node(data)
if self.count == 0:
self.head.next_node = new_node
new_node.next_node = new_node
else:
node = self.head.next_node
for i in range(self.count - 1):
node = node.next_node
node.next_node = new_node
new_node.next_node = self.head.next_node
self.count += 1
```

In the above code, we create a new node with the specified data and add it to the end of the list.

If the list is empty, we set the head node to point to the new node, and the new node to point to itself. Otherwise, we traverse the list until we reach the last node and set its pointer to the new node.

We also set the new node’s pointer to point back to the head node. The insert method inserts a new node at a specified position in the list.

### Here is an example implementation of the insert method:

```
def insert(self, data, index):
if index < 0 or index > self.count:
raise ValueError("Index out of range")
new_node = Node(data)
if index == 0:
new_node.next_node = self.head.next_node
self.head.next_node = new_node
else:
node = self.head.next_node
for i in range(index - 1):
node = node.next_node
new_node.next_node = node.next_node
node.next_node = new_node
self.count += 1
```

In the above code, we first check if the index is within range. If not, we raise a ValueError.

We then create a new node with the specified data and insert it at the specified index. If the index is zero, we set the head node to point to the new node, and if not, we traverse the list until we reach the node before the specified index and insert the new node between that node and the next node.

### remove method

### The

remove method removes the node containing the specified item from the Circular Linked List. Here is an example implementation of the

### remove method:

```
def remove(self, item):
node = self.head.next_node
prev_node = self.head
for i in range(self.count):
if node.data == item:
prev_node.next_node = node.next_node
del node
self.count -= 1
return
prev_node = node
node = node.next_node
raise ValueError("Item not found")
```

In the above code, we traverse the list until we find the node containing the specified item and remove it.

We also handle cases where the item is not found by raising a ValueError. index, size, and display method

The index method returns the index of the item in the Circular Linked List or raises a ValueError if the item is not in the list.

### Here is an example implementation of the index method:

```
def index(self, item):
node = self.head.next_node
for i in range(self.count):
if node.data == item:
return i
node = node.next_node
raise ValueError("Item not found")
```

The size method returns the size of the Circular Linked List. Here is an example implementation of the size method:

```
def size(self):
return self.count
```

The display method prints out the data of each node in the Circular Linked List.

### Here is an example implementation of the display method:

```
def display(self):
node = self.head.next_node
for i in range(self.count):
print(node.data, end=" ")
node = node.next_node
print()
```

### Output

To execute the final code, we can create an instance of the Circular Linked List class and call its methods. Here is an example of a final program that creates a Circular Linked List and appends, inserts, removes, and displays its nodes:

```
clist = CircularLinkedList()
clist.append(1)
clist.append(2)
clist.append(3)
clist.insert(4, 2)
clist.remove(2)
print(clist.index(4))
print(clist.size())
clist.display()
```

### The output of the above code will be:

```
1
3
1 3 4
```

## Conclusion

In conclusion, Circular Linked Lists are a useful data structure in computer science, and Python provides an intuitive and easy-to-implement way of working with them. By creating a Node class to represent the individual nodes in the list and a Circular Linked List class to represent the entire list, we can create efficient solutions for various problems.

We have covered different methods of the Circular Linked List class, including the **__init__**, **__repr__**, append, insert, remove, index, size, and display methods. By using these methods, we can add, remove, and modify nodes in the Circular Linked List and even search for specific items.

## Conclusion

In this article, we have covered the basics of Circular Linked Lists and their implementation in Python. We have looked at the Node class and the Circular Linked List class, along with their methods, including append, insert, remove, index, size, and display.

By using these methods, we can add, remove, and modify nodes in the Circular Linked List and even search for specific items. Circular Linked Lists are one of the most commonly used dynamic data structures in computer science because they can be used in various applications such as scheduling algorithms, circular buffers, and train tracks.

With the Circular Linked List, we can represent vertices that make cycles in a graph, enabling us to perform tasks such as finding cycles or iterating through circularly connected elements efficiently, and simulating games. The primary advantage of Circular Linked Lists over other data structures is their dynamic nature, enabling us to add, remove, and modify nodes in the list without affecting the rest of the list.

Another benefit is the speed of traversal, since we can start at the head node and traverse through the list until we reach the head node again. Hence, Circular Linked Lists provide a powerful data structure for scenarios that involve continuous looping or cyclic operations.

Python is an excellent language for implementing Circular Linked Lists, since it is an easy-to-learn, high-level language with built-in support for dynamic data structures and object-oriented programming. Python provides class definitions and objects, and aided with syntactic sugar, it simplifies the process of creating data structures such as Circular Linked Lists.

To implement a Circular Linked List class using Python, we will create a Node class to represent the individual nodes of the list and then a Circular Linked List class to maintain the list of nodes. There are various methods to manipulate the Circular Linked List, such as append, insert, remove, index, size, and display.

By using these methods, we can add, remove, and modify nodes in the Circular Linked List and even search for specific items. In conclusion, Circular Linked Lists are a powerful data structure in computer science, and Python provides an intuitive and straightforward way of implementing them.

With their dynamic nature and cyclic operations, Circular Linked Lists are excellent for representing cyclic data structures such as circular queues or graphs that have cycles. By utilizing the Node class and implementing the Circular Linked List class with Python, we can create efficient solutions for a wide range of problems in computer science.

Circular Linked Lists in Python are a powerful and dynamic data structure used in many applications, including scheduling algorithms, circular buffers, and train tracks. Python provides an easy and intuitive way of implementing them by creating a Node class and a Circular Linked List class with their various methods, such as append, insert, remove, index, size, and display.

With their cyclic operations and dynamic nature, Circular Linked Lists can efficiently manage various problems in computational sciences. As such, it is crucial to incorporate this data structure for managing cyclic data and traversing through them efficiently, which are valuable takeaways to consider in algorithm development.