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

Time Complexity: Delete Node at Beginning

O(1)

Understanding Time Complexity

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

How does the time needed change as the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void deleteAtBeginning(Node*& head) {
    if (head == nullptr) return;
    Node* temp = head;
    head = head->next;
    delete temp;
}
    

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

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

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

How Execution Grows With Input

The time to delete the first node stays the same no matter how big the list is.

Input Size (n)	Approx. Operations
10	4 operations
100	4 operations
1000	4 operations

Pattern observation: The number of steps does not increase as the list grows.

Final Time Complexity

Time Complexity: O(1)

This means deleting the first node takes the same amount of time no matter how large 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 delete one node, so the list size does not affect the time.

Interview Connect

Knowing that deleting the first node is quick helps you explain efficient list operations clearly and confidently.

Self-Check

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

Practice

1. What happens when you delete the first node of a singly linked list?

easy

A. The head pointer moves to the second node, and the first node is removed.

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

C. The list becomes empty regardless of its size.

D. The second node is deleted, but the head remains the same.

Solution

1. Step 1: Understand the head pointer role

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

2. Step 2: Delete the first node by moving head

   To delete the first node, update head to point to the second node, removing the first node from the list.

3. Final Answer:

   The head pointer moves to the second node, and the first node is removed. -> Option A

4. Quick Check:

   Deleting first node means head moves forward [OK]

Hint: Deleting first node means head points to next node [OK]

Common Mistakes:

• Deleting the wrong node (not the first)
• Not updating the head pointer
• Assuming list becomes empty always
• Confusing first and second nodes

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

easy

A. head->next = head; delete head;

B. head = head->next; delete head;

C. delete head; head = head->next;

D. Node* temp = head; head = head->next; delete temp;

Solution

1. Step 1: Store the current head node

   We save the current head in a temporary pointer to delete it safely later.

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

   Update head to point to the next node, then delete the old head using the temporary pointer.

3. Final Answer:

   Node* temp = head; head = head->next; delete temp; -> Option D

4. Quick Check:

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

Hint: Save old head before deleting to avoid losing access [OK]

Common Mistakes:

• Deleting head before moving pointer
• Not saving old head before deleting
• Assigning head incorrectly
• Deleting head twice

3. What will be the output linked list after executing the following code?

struct Node {
  int data;
  Node* next;
};

Node* head = new Node{10, new Node{20, new Node{30, nullptr}}};

Node* temp = head;
head = head->next;
delete temp;

Node* curr = head;
while(curr != nullptr) {
  std::cout << curr->data << " -> ";
  curr = curr->next;
}
std::cout << "null";

medium

A. 20 -> 30 -> null

B. null

C. 30 -> null

D. 10 -> 20 -> 30 -> null

Solution

1. Step 1: Initial linked list setup

   The list starts as 10 -> 20 -> 30 -> null.

2. Step 2: Delete first node and update head

   We save head (10) in temp, move head to 20, then delete node 10.

3. Step 3: Print remaining list

   Starting from new head (20), we print 20 -> 30 -> null.

4. Final Answer:

   20 -> 30 -> null -> Option A

5. Quick Check:

   First node deleted, list starts at 20 [OK]

Hint: After deleting head, list starts from next node [OK]

Common Mistakes:

• Printing deleted node data
• Not updating head pointer
• Deleting wrong node
• Forgetting to print null at end

4. Identify the error in the following code snippet that deletes the first node of a linked list:

void deleteFirstNode(Node* head) {
  Node* temp = head;
  head = head->next;
  delete temp;
}

medium

A. head->next is not a valid pointer.

B. Deleting temp before moving head causes runtime error.

C. The function does not update the original head pointer outside the function.

D. No error; code works correctly.

Solution

1. Step 1: Understand pointer passing in C++

   Function receives head by value, so changes inside do not affect original head.

2. Step 2: Identify missing update to original head

   Updating local head pointer does not update the caller's head, so list head remains unchanged.

3. Final Answer:

   The function does not update the original head pointer outside the function. -> Option C

4. Quick Check:

   Pointer passed by value, original head unchanged [OK]

Hint: Pass head by reference to update original pointer [OK]

Common Mistakes:

• Assuming head changes outside function
• Deleting node before moving head
• Confusing pointer and value passing
• Ignoring nullptr checks

5. Given a singly linked list, write the correct approach to delete the first node safely and update the head pointer in C++. Which of the following code snippets correctly achieves this?

hard

A. void deleteFirstNode(Node* head) {
Node* temp = head;
head = head->next;
delete temp;
}

B. void deleteFirstNode(Node*& head) {
if (head == nullptr) return;
Node* temp = head;
head = head->next;
delete temp;
}

C. void deleteFirstNode(Node** head) {
Node* temp = *head;
*head = (*head)->next;
delete temp;
}

D. void deleteFirstNode(Node head) {
head = head.next;
delete head;
}

Solution

1. Step 1: Pass head by reference to modify original pointer

   Using Node*& head allows the function to update the caller's head pointer directly.

2. Step 2: Check for empty list and delete first node safely

   Check if head is nullptr to avoid errors, then move head to next node and delete old first node.

3. Final Answer:

   void deleteFirstNode(Node*& head) { if (head == nullptr) return; Node* temp = head; head = head->next; delete temp; } -> Option B

4. Quick Check:

   Reference parameter updates head safely [OK]

Hint: Use reference parameter to update head pointer [OK]

Common Mistakes:

• Passing head by value instead of reference
• Not checking for empty list
• Deleting node without updating head
• Using incorrect pointer syntax