Insert at Beginning of Doubly Linked List in DSA Python - Time & Space Complexity

Time Complexity: Insert at Beginning of Doubly Linked List

O(1)

Understanding Time Complexity

We want to know how the time to insert a new node at the start of a doubly linked list changes as the list grows.

How does the number of steps grow when the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

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

    def insert_at_beginning(self, data):
        new_node = Node(data)
        new_node.next = self.head
        if self.head is not None:
            self.head.prev = new_node
        self.head = new_node

This code adds a new node at the start of a doubly linked list by adjusting pointers.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Assigning pointers to link the new node at the start.
• How many times: These pointer assignments happen once per insertion, no loops or recursion.

How Execution Grows With Input

Each insertion requires the same fixed number of steps, no matter how big the list is.

Input Size (n)	Approx. Operations
10	3-4 pointer assignments
100	3-4 pointer assignments
1000	3-4 pointer assignments

Pattern observation: The number of steps stays the same regardless of list size.

Final Time Complexity

Time Complexity: O(1)

This means inserting at the beginning takes a constant amount of time no matter how large the list is.

Common Mistake

[X] Wrong: "Inserting at the beginning takes longer as the list grows because we have to move all nodes."

[OK] Correct: We only change a few pointers at the start; we do not move or touch the other nodes.

Interview Connect

Knowing that insertion at the start of a doubly linked list is quick helps you explain efficient data structure operations clearly.

Self-Check

"What if we had to insert at the end of the doubly linked list without a tail pointer? How would the time complexity change?"

Practice

1. What is the main purpose of inserting a node at the beginning of a doubly linked list?

easy

A. To add a new node as the first element of the list

B. To remove the last node from the list

C. To reverse the entire list

D. To find the middle node of the list

Solution

1. Step 1: Understand the operation

   Inserting at the beginning means adding a new node before the current first node.

2. Step 2: Identify the purpose

   This operation makes the new node the first element in the doubly linked list.

3. Final Answer:

   To add a new node as the first element of the list -> Option A

4. Quick Check:

   Insert at beginning = Add new first node [OK]

Hint: Insert at beginning means new node becomes the first [OK]

Common Mistakes:

• Confusing insertion at beginning with deletion
• Thinking it reverses the list
• Assuming it finds a node instead of adding

2. Which of the following is the correct syntax to create a new node and insert it at the beginning of a doubly linked list in Python?

easy

A. new_node = Node(data); new_node.prev = head; head.next = new_node; head = new_node

B. new_node = Node(data); head.next = new_node; new_node.prev = head; head = new_node

C. new_node = Node(data); new_node.next = head; head.prev = new_node; head = new_node

D. new_node = Node(data); head.prev = new_node; new_node.next = head.next; head = new_node

Solution

1. Step 1: Create new node and link next pointer

   new_node.next should point to current head to place it before head.

2. Step 2: Update previous head's prev pointer and head reference

   head.prev must point back to new_node, then update head to new_node.

3. Final Answer:

   new_node = Node(data); new_node.next = head; head.prev = new_node; head = new_node -> Option C

4. Quick Check:

   New node next = head, head prev = new node [OK]

Hint: New node next points to head; head prev points back [OK]

Common Mistakes:

• Swapping prev and next pointers
• Not updating head to new node
• Forgetting to update old head's prev pointer

3. What will be the output of the following code after inserting 10 at the beginning of the doubly linked list?

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

head = Node(20)
new_node = Node(10)
new_node.next = head
head.prev = new_node
head = new_node

# Print list forward
current = head
result = []
while current:
    result.append(current.data)
    current = current.next
print(result)

medium

A. [20, 10]

B. [10, 20]

C. [10]

D. [20]

Solution

1. Step 1: Insert 10 before 20

   New node with data 10 points next to old head (20), old head prev points back to new node.

2. Step 2: Traverse from new head and collect data

   Starting at head (10), next is 20, then None. So list is [10, 20].

3. Final Answer:

   [10, 20] -> Option B

4. Quick Check:

   List after insertion = [10, 20] [OK]

Hint: Traverse from head to next to see order [OK]

Common Mistakes:

• Confusing order and printing reversed list
• Not updating head pointer
• Printing only one node

4. Identify the error in the following code snippet that inserts a node at the beginning of a doubly linked list:

new_node = Node(5)
new_node.next = head
head = new_node
head.prev = new_node

medium

A. head.prev should be set before updating head

B. new_node.next should be None

C. head.prev should point to None, not new_node

D. No error, code is correct

Solution

1. Step 1: Analyze pointer assignments

   new_node.next points to old head (correct), but head = new_node happens before head.prev = new_node.

2. Step 2: Identify the error

   By the time head.prev = new_node executes, head is already the new_node, creating a self-loop. The old head's prev is never set. head.prev must be set before updating head to link the old head back correctly.

3. Final Answer:

   head.prev should be set before updating head -> Option A

4. Quick Check:

   Update old head.prev before head = new_node [OK]

Hint: Set head.prev before head = new_node [OK]

Common Mistakes:

• Setting prev pointer after head update incorrectly
• Making first node's prev point to itself
• Ignoring prev pointer for head node

5. Given a doubly linked list with nodes 30 <-> 40 <-> 50, write the sequence of node values after inserting 20 at the beginning and then 10 at the beginning. What is the final list?

hard

A. 10 <-> 30 <-> 20 <-> 40 <-> 50

B. 20 <-> 10 <-> 30 <-> 40 <-> 50

C. 30 <-> 40 <-> 50 <-> 20 <-> 10

D. 10 <-> 20 <-> 30 <-> 40 <-> 50

Solution

1. Step 1: Insert 20 at beginning

   New node 20 points next to 30, 30 prev points to 20. List becomes 20 <-> 30 <-> 40 <-> 50.

2. Step 2: Insert 10 at beginning

   New node 10 points next to 20, 20 prev points to 10. List becomes 10 <-> 20 <-> 30 <-> 40 <-> 50.

3. Final Answer:

   10 <-> 20 <-> 30 <-> 40 <-> 50 -> Option D

4. Quick Check:

   Insertions add nodes at front in order [OK]

Hint: Insertions at beginning stack nodes in reverse order [OK]

Common Mistakes:

• Inserting nodes in wrong order
• Appending instead of prepending
• Not updating prev pointers correctly