Delete from Beginning of Doubly Linked List in DSA C - Time & Space Complexity

Time Complexity: Delete from Beginning of Doubly Linked List

O(1)

Understanding Time Complexity

We want to understand how long it takes to remove the first item from a doubly linked list.

How does the time needed change when the list grows bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Delete node from beginning of doubly linked list
void deleteBeginning(Node** head) {
    if (*head == NULL) return;
    Node* temp = *head;
    *head = (*head)->next;
    if (*head != NULL) {
        (*head)->prev = NULL;
    }
    free(temp);
}
    

This code removes the first node from a doubly linked list and updates pointers accordingly.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Single pointer update and node deletion.
• How many times: Exactly once per call, no loops or recursion.

How Execution Grows With Input

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

Input Size (n)	Approx. Operations
10	5-6 steps
100	5-6 steps
1000	5-6 steps

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

Final Time Complexity

Time Complexity: O(1)

This means deleting the first node takes a constant amount of time no matter how large the list is.

Common Mistake

[X] Wrong: "Deleting from the beginning takes longer as the list grows because we have to move through nodes."

[OK] Correct: We only change a few pointers at the start; we do not traverse the list, so time does not grow with list size.

Interview Connect

Knowing that deleting from the start of a doubly linked list is quick helps you explain efficient list operations clearly in interviews.

Self-Check

"What if we changed this to delete from the end of the doubly linked list? How would the time complexity change?"

Practice

1. What happens to the head pointer when you delete the first node from a doubly linked list?

easy

A. It remains unchanged

B. It becomes NULL immediately

C. It moves to the second node in the list

D. It points to the last node

Solution

1. Step 1: Understand the head pointer role

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

2. Step 2: Effect of deleting the first node

   When the first node is deleted, the head pointer must move to the next node, which becomes the new first node.

3. Final Answer:

   It moves to the second node in the list -> Option C

4. Quick Check:

   Head points to new first node after deletion [OK]

Hint: Head always moves to next node after deleting first [OK]

Common Mistakes:

• Assuming head becomes NULL even if list has more nodes
• Not updating head pointer after deletion
• Pointing head to last node mistakenly

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

easy

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

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

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

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

Solution

1. Step 1: Store current head in temp

   We save the current first 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 second node, free the old first node, and set new head's prev to NULL.

3. Final Answer:

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

4. Quick Check:

   Proper order: save, move, free, update pointers [OK]

Hint: Save old head before freeing, then update pointers [OK]

Common Mistakes:

• Freeing head before moving pointer
• Not setting new head's prev to NULL
• Accessing freed memory after free

3. Given the doubly linked list: 10 <-> 20 <-> 30 <-> NULL, what will be the list after deleting the first node?

medium

A. 20 <-> 30 <-> NULL

B. 10 <-> 30 <-> NULL

C. 30 <-> NULL

D. NULL

Solution

1. Step 1: Identify the first node to delete

   The first node has value 10, which will be removed.

2. Step 2: Update head to second node and adjust pointers

   Head moves to node with value 20, and its prev pointer is set to NULL.

3. Final Answer:

   20 <-> 30 <-> NULL -> Option A

4. Quick Check:

   First node removed, list starts at 20 [OK]

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

Common Mistakes:

• Leaving old head in list
• Not updating prev pointer of new head
• Deleting wrong node

4. What is wrong with this code snippet for deleting the first node of a doubly linked list?

void deleteBegin() {
  if (head == NULL) return;
  free(head);
  head = head->next;
  if (head != NULL) head->prev = NULL;
}

medium

A. It does not free the node

B. It does not check if list is empty

C. It forgets to set head->prev to NULL

D. It frees head before moving pointer, causing invalid access

Solution

1. Step 1: Analyze order of operations

   The code frees head first, then tries to access head->next, which is invalid after free.

2. Step 2: Correct order needed

   We must first save head->next in a temp pointer, move head, then free old node to avoid invalid memory access.

3. Final Answer:

   It frees head before moving pointer, causing invalid access -> Option D

4. Quick Check:

   Free after pointer update to avoid invalid access [OK]

Hint: Always move pointer before freeing old node [OK]

Common Mistakes:

• Freeing node before updating pointers
• Accessing freed memory
• Not handling empty list properly

5. You have a doubly linked list with nodes: 5 <-> 15 <-> 25 <-> 35 <-> NULL. After deleting the first node twice, what will be the 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 node with value 5, head moves to 15.

2. Step 2: Delete first node again

   Second deletion removes node with value 15, head moves to 25.

3. Final Answer:

   25 <-> 35 <-> NULL -> Option B

4. Quick Check:

   Two deletions remove first two nodes [OK]

Hint: Each deletion moves head to next node [OK]

Common Mistakes:

• Deleting only once instead of twice
• Not updating head correctly after second deletion
• Confusing node values after deletion