1. Introduction

A doubly linked list (DLL) is a type of linked list in which each node contains:

1. Data — the value stored in the node.

2. Prev (previous pointer) — a pointer/reference to the previous node.

3. Next (next pointer) — a pointer/reference to the next node.

Unlike a singly linked list, a doubly linked list allows traversal in both directions: forward and backward.

2. Structure of a Node

+--------+--------+--------+
| Prev   | Data   | Next   |
+--------+--------+--------+

• Prev points to the previous node (or null if it's the first node).

• Next points to the next node (or null if it's the last node).

• Data stores the value (integer, string, object, etc.).

3. Basic Operations

3.1 Create a Doubly Linked List

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

class DoublyLinkedList:
    def __init__(self):
        self.head = None

3.2 Insertion

1. Insert at the beginning

def insert_at_head(self, data):
    new_node = Node(data)
    if self.head:
        new_node.next = self.head
        self.head.prev = new_node
    self.head = new_node

2. Insert at the end

def insert_at_tail(self, data):
    new_node = Node(data)
    if not self.head:
        self.head = new_node
        return
    current = self.head
    while current.next:
        current = current.next
    current.next = new_node
    new_node.prev = current

3. Insert after a given node

def insert_after(self, prev_node, data):
    if not prev_node:
        return
    new_node = Node(data)
    new_node.next = prev_node.next
    new_node.prev = prev_node
    if prev_node.next:
        prev_node.next.prev = new_node
    prev_node.next = new_node

3.3 Deletion

1. Delete a node by value

def delete_node(self, key):
    current = self.head
    while current:
        if current.data == key:
            if current.prev:
                current.prev.next = current.next
            else:
                self.head = current.next
            if current.next:
                current.next.prev = current.prev
            return
        current = current.next

3.4 Traversal

1. Forward traversal

def traverse_forward(self):
    current = self.head
    while current:
        print(current.data, end=" <-> ")
        current = current.next
    print("None")

2. Backward traversal

def traverse_backward(self):
    current = self.head
    if not current:
        return
    # go to last node
    while current.next:
        current = current.next
    # traverse backward
    while current:
        print(current.data, end=" <-> ")
        current = current.prev
    print("None")

4. Advantages of Doubly Linked List

1. Can traverse in both directions.

2. Easier to delete a node if a pointer to it is known.

3. More flexible insertion and deletion compared to singly linked list.

Disadvantages:

• Uses extra memory for the previous pointer.

• Slightly more complex to implement than singly linked list.