# Insert a Node in the Middle of a Doubly Linked List

## Inserting a Node in the Middle

Inserting a node in the middle of a doubly linked list involves finding the middle of the list, traversing to that position, and updating the next and previous references of the surrounding nodes to include the new node. This operation requires careful manipulation of pointers to maintain the integrity of the list.

## Step-by-Step Process

Consider a doubly linked list with the following structure before insertion:

```
Head <-> 1 <-> 2 <-> 4 <-> 5 <-> None
```

We want to insert a new node with the value 3 in the middle of the list. Follow these steps:

**Find the Middle Position**: Use the slow and fast pointer technique to find the middle of the list.**Create a New Node**: Create a new node with the desired value (3).**Set the New Node's Next Reference**: Update the next reference of the new node to point to the node currently at the middle position (node with value 4).**Update the Previous Reference of the Node at the Middle Position**: Update the previous reference of the node at the middle position to point to the new node.**Update the Next Reference of the Node Before the Middle Position**: Set the next reference of the node before the middle position to point to the new node.**Set the Previous Reference of the New Node**: Set the previous reference of the new node to point to the node before the middle position.

After performing these steps, the linked list will have the following structure:

```
Head <-> 1 <-> 2 <-> 3 <-> 4 <-> 5 <-> None
```

## Python Program to Insert a Node in the Middle

```
class Node:
def __init__(self, data):
self.data = data
self.next = None
self.prev = None
class DoublyLinkedList:
def __init__(self):
self.head = None
def append(self, data):
new_node = Node(data)
if self.head is None:
self.head = new_node
else:
current = self.head
while current.next:
current = current.next
current.next = new_node
new_node.prev = current
def insert_at_middle(self, data):
new_node = Node(data)
if self.head is None:
self.head = new_node
return
slow = self.head
fast = self.head
while fast.next and fast.next.next:
slow = slow.next
fast = fast.next.next
new_node.next = slow.next
if slow.next is not None:
slow.next.prev = new_node
slow.next = new_node
new_node.prev = slow
def traverse(self):
current = self.head
while current:
print(current.data, end=" <-> ")
current = current.next
print("None")
# Example usage:
dll = DoublyLinkedList()
dll.append(1)
dll.append(2)
dll.append(4)
dll.append(5)
print("Doubly linked list before insertion in the middle:")
dll.traverse() # Output: 1 <-> 2 <-> 4 <-> 5 <-> None
dll.insert_at_middle(3)
print("Doubly linked list after insertion in the middle:")
dll.traverse() # Output: 1 <-> 2 <-> 3 <-> 4 <-> 5 <-> None
```

This Python program defines a doubly linked list with methods for appending nodes, inserting a node in the middle, and traversing the list. The insert_at_middle method uses the slow and fast pointer technique to find the middle of the list, creates a new node, and updates the next and previous references to include the new node.