Inserting a node at the beginning of a doubly linked list involves creating a new node and updating the head reference to point to this new node, as well as updating the previous reference of the old head node to point to the new node. This operation is efficient as it only requires updating a few pointers.

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

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

We want to insert a new node with the value 0 at the beginning. Follow these steps:

**Create a New Node**: Create a new node with the desired value (0).**Set the New Node's Next Reference**: Update the next reference of the new node to point to the current head of the list.**Update the Previous Reference of the Current Head**: If the list is not empty, update the previous reference of the current head to point to the new node.**Update the Head Reference**: Update the head reference to point to the new node.**Set the Previous Reference of the New Node**: Set the previous reference of the new node to None, since it is now the first node in the list.

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

```
Head <-> 0 <-> 1 <-> 2 <-> 3 <-> 4 <-> None
```

```
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_beginning(self, data):
new_node = Node(data)
if self.head is None:
self.head = new_node
else:
new_node.next = self.head
self.head.prev = new_node
self.head = new_node
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(3)
dll.append(4)
print("Doubly linked list before insertion at beginning:")
dll.traverse() # Output: 1 <-> 2 <-> 3 <-> 4 <-> None
dll.insert_at_beginning(0)
print("Doubly linked list after insertion at beginning:")
dll.traverse() # Output: 0 <-> 1 <-> 2 <-> 3 <-> 4 <-> None
```

This Python program defines a doubly linked list with methods for appending nodes, inserting a node at the beginning, and traversing the list. The insert_at_beginning method creates a new node, sets its next reference to the current head, updates the previous reference of the current head, and updates the head reference to the new node.