Delete Node at Beginning in DSA Python - Time & Space Complexity

Time Complexity: Delete Node at Beginning

O(1)

Understanding Time Complexity

When we delete a node at the beginning of a linked list, we want to know how the time it takes changes as the list grows.

We ask: Does deleting the first node take longer if the list is bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

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

    def delete_at_beginning(self):
        if self.head is not None:
            self.head = self.head.next

This code removes the first node by moving the head pointer to the next node.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Updating the head pointer to the next node.
• How many times: This happens only once per deletion, no loops or repeated steps.

How Execution Grows With Input

Deleting the first node always takes the same steps, no matter how big the list is.

Input Size (n)	Approx. Operations
10	1
100	1
1000	1

Pattern observation: The work stays the same even if the list grows larger.

Final Time Complexity

Time Complexity: O(1)

This means deleting the first node takes the same amount of time no matter how big the list is.

Common Mistake

[X] Wrong: "Deleting the first node takes longer if the list is very big because we have to check all nodes."

[OK] Correct: We only change the head pointer once; we do not look at other nodes, so size does not affect the time.

Interview Connect

Understanding this simple operation helps build confidence in working with linked lists and shows you can reason about how changes affect performance.

Self-Check

"What if we changed the code to delete the last node instead? How would the time complexity change?"

Practice

1. What happens to the head pointer when you delete a node at the beginning of a singly linked list?

easy

A. It points to the last node

B. It becomes null immediately

C. It remains unchanged

D. It moves to the next node in the list

Solution

1. Step 1: Understand the head pointer role

   The head pointer points to the first node in the list.

2. Step 2: Effect of deleting the first node

   Deleting the first node means the head must now point to the second node, which becomes the new first node.

3. Final Answer:

   It moves to the next node in the list -> Option D

4. Quick Check:

   Head points to next node after deletion [OK]

Hint: Head always moves to next node when deleting at start [OK]

Common Mistakes:

• Thinking head becomes null even if list has more nodes
• Assuming head points to last node after deletion
• Not updating head pointer at all

2. Which of the following is the correct Python syntax to delete the first node in a singly linked list with head pointer head?

easy

A. head = head.next

B. head.next = head

C. head = null

D. delete head

Solution

1. Step 1: Understand Python linked list node deletion

   To delete the first node, we move the head pointer to the next node.

2. Step 2: Check syntax correctness

   Assigning head = head.next correctly moves head to the next node. Other options are invalid Python or incorrect logic.

3. Final Answer:

   head = head.next -> Option A

4. Quick Check:

   Assign head to head.next to delete first node [OK]

Hint: Use head = head.next to delete first node [OK]

Common Mistakes:

• Using 'null' instead of 'None' in Python
• Trying to delete node with 'delete' keyword (not valid in Python)
• Assigning head.next = head which breaks list

3. What will be the output linked list after deleting the first node from the list: 1 -> 2 -> 3 -> 4 -> null?

medium

A. 3 -> 4 -> null

B. 1 -> 3 -> 4 -> null

C. 2 -> 3 -> 4 -> null

D. 1 -> 2 -> 3 -> 4 -> null

Solution

1. Step 1: Identify the first node to delete

   The first node has value 1.

2. Step 2: Delete first node and update head

   After deletion, head points to node with value 2, so list becomes 2 -> 3 -> 4 -> null.

3. Final Answer:

   2 -> 3 -> 4 -> null -> Option C

4. Quick Check:

   First node removed, list starts at 2 [OK]

Hint: Remove first node value, start list from second node [OK]

Common Mistakes:

• Removing wrong node (like second node)
• Not updating head pointer
• Assuming list becomes empty

4. Given the code below, what is the error when deleting the first node?

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

head = Node(10)
head.next = Node(20)
head = head.next.next  # Delete first node

medium

A. head becomes None causing loss of list

B. SyntaxError due to invalid assignment

C. No error, list updates correctly

D. RuntimeError due to NoneType access

Solution

1. Step 1: Trace the assignment head = head.next.next

   head.next is node with data 20, head.next.next is None (end of list).

2. Step 2: Effect of assignment

   Assigning head to None loses the entire list, effectively emptying it.

3. Final Answer:

   head becomes None causing loss of list -> Option A

4. Quick Check:

   head = head.next.next sets head to None [OK]

Hint: Assign head = head.next to delete first node, not head.next.next [OK]

Common Mistakes:

• Assigning head to head.next.next instead of head.next
• Expecting list to remain intact after wrong assignment
• Ignoring None assignment effect

5. You have a singly linked list with nodes: 5 -> 10 -> 15 -> 20 -> null. Write the steps to delete the first node and then insert a new node with value 25 at the beginning. What will be the final list?

hard

A. 10 -> 15 -> 20 -> 25 -> null

B. 25 -> 10 -> 15 -> 20 -> null

C. 5 -> 10 -> 15 -> 20 -> 25 -> null

D. 25 -> 5 -> 10 -> 15 -> 20 -> null

Solution

1. Step 1: Delete the first node

   Move head pointer from node 5 to node 10, so list becomes 10 -> 15 -> 20 -> null.

2. Step 2: Insert new node with value 25 at beginning

   Create new node with data 25, set its next to current head (node 10), then update head to new node.

3. Step 3: Final list after insertion

   List becomes 25 -> 10 -> 15 -> 20 -> null.

4. Final Answer:

   25 -> 10 -> 15 -> 20 -> null -> Option B

5. Quick Check:

   Delete first, then add new node at head [OK]

Hint: Delete head by moving to next, then add new node before head [OK]

Common Mistakes:

• Not updating head after deletion
• Appending new node at end instead of beginning
• Forgetting to link new node to old head