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

Time Complexity: Delete Node at Beginning

O(1)

Understanding Time Complexity

We want to know how the time needed changes when we delete the first node in a linked list.

How does the work grow as the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void deleteAtBeginning(Node** head) {
    if (*head == NULL) return;
    Node* temp = *head;
    *head = (*head)->next;
    free(temp);
}
    

This code removes the first node from a linked list by moving the head pointer to the next node and freeing the old first node.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Accessing and updating the head pointer once.
• How many times: Exactly once per deletion.

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	4 steps
100	4 steps
1000	4 steps

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 a fixed amount of time no matter how big the list is.

Common Mistake

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

[OK] Correct: We only change the head pointer and free one node; we do not look at other nodes.

Interview Connect

Understanding this helps you explain how simple operations on linked lists work efficiently, a key skill in many coding tasks.

Self-Check

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

Practice

1. What happens to the linked list when you delete the node at the beginning?

easy

A. All nodes are deleted at once.

B. The last node is deleted instead of the first.

C. The list remains unchanged.

D. The head pointer moves to the next node, removing the first node.

Solution

1. Step 1: Understand the head pointer role

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

2. Step 2: Effect of deleting the first node

   Deleting the first node means moving the head pointer to the second node, effectively removing the first node from the list.

3. Final Answer:

   The head pointer moves to the next node, removing the first node. -> Option D

4. Quick Check:

   Deleting at beginning means head moves forward [OK]

Hint: Deleting at start moves head to next node [OK]

Common Mistakes:

• Thinking the last node is deleted
• Assuming the list stays the same
• Deleting all nodes instead of one

2. Which of the following is the correct syntax to delete the first node in a singly linked list in C?

easy

A. temp = head; head = head->next; free(temp);

B. head = head->next; free(head);

C. free(head); head = head->next;

D. head->next = NULL; free(head);

Solution

1. Step 1: Store current head in temp

   We save the current head node in a temporary pointer to free it later.

2. Step 2: Move head to next node and free old head

   Update head to point to the next node, then free the old head stored in temp.

3. Final Answer:

   temp = head; head = head->next; free(temp); -> Option A

4. Quick Check:

   Save old head, move head, free old [OK]

Hint: Save old head before moving and freeing [OK]

Common Mistakes:

• Freeing head before moving pointer
• Not saving old head before moving
• Setting next to NULL incorrectly

3. What will be the output linked list after deleting the first node from the list: 10 -> 20 -> 30 -> NULL?

medium

A. 10 -> 20 -> 30 -> NULL

B. NULL

C. 20 -> 30 -> NULL

D. 30 -> NULL

Solution

1. Step 1: Identify the first node

   The first node has value 10.

2. Step 2: Delete first node and move head

   After deletion, head points to node with value 20, so list starts from 20.

3. Final Answer:

   20 -> 30 -> NULL -> Option C

4. Quick Check:

   First node removed, next node becomes head [OK]

Hint: After deletion, list starts from second node [OK]

Common Mistakes:

• Not updating head pointer
• Deleting wrong node
• Assuming list becomes empty

4. Consider this code snippet to delete the first node:

struct Node* temp = head;
head = head->next;
free(head);

What is the error in this code?

medium

A. It frees the new head instead of the old head.

B. It does not update the head pointer.

C. It frees the temp pointer instead of head.

D. It causes a syntax error.

Solution

1. Step 1: Analyze pointer usage

   temp stores old head, head moves to next node.

2. Step 2: Identify which node is freed

   free(head) frees the new head, not the old node stored in temp, causing memory error.

3. Final Answer:

   It frees the new head instead of the old head. -> Option A

4. Quick Check:

   Free old node, not new head [OK]

Hint: Free the saved old head pointer, not the updated head [OK]

Common Mistakes:

• Freeing updated head instead of old node
• Not freeing any node causing memory leak
• Confusing temp and head pointers

5. You have a singly linked list with nodes: 5 -> 15 -> 25 -> 35 -> NULL. After deleting the first node twice, what will be the resulting list?

hard

A. 15 -> 25 -> 35 -> NULL

B. 25 -> 35 -> NULL

C. 35 -> NULL

D. NULL

Solution

1. Step 1: Delete first node once

   First deletion removes 5, list becomes 15 -> 25 -> 35 -> NULL.

2. Step 2: Delete first node again

   Second deletion removes 15, list becomes 25 -> 35 -> NULL.

3. Final Answer:

   25 -> 35 -> NULL -> Option B

4. Quick Check:

   Two deletions remove first two nodes [OK]

Hint: Each deletion moves head forward by one node [OK]

Common Mistakes:

• Deleting only once instead of twice
• Confusing node values after deletion
• Assuming list becomes empty too soon