Delete Node at Beginning in DSA Typescript - 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 grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class Node {
  value: number;
  next: Node | null;
  constructor(value: number) {
    this.value = value;
    this.next = null;
  }
}

function deleteAtBeginning(head: Node | null): Node | null {
  if (head === null) return null;
  return head.next;
}
    

This code removes the first node from a linked list by returning the second node as the new head.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Accessing the first node and its next pointer.
• How many times: Exactly once, 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	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 a fixed amount of time regardless of list size.

Common Mistake

[X] Wrong: "Deleting the first node takes longer if the list is bigger because there are more nodes."

[OK] Correct: We only change the head pointer to the next node, so the rest of 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 had to delete the last node instead? How would the time complexity change?"

Practice

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

easy

A. The head pointer moves to the second node

B. The last node is deleted

C. The list becomes empty immediately

D. The middle node is removed

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

   Deleting the first node means moving the head pointer to the next node.

3. Final Answer:

   The head pointer moves to the second node -> Option A

4. Quick Check:

   Delete first node = move head to next [OK]

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

Common Mistakes:

• Thinking the last node is deleted
• Assuming list becomes empty always
• Deleting a middle node instead

2. Which of the following is the correct TypeScript 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. delete head;

D. head = null.next;

Solution

1. Step 1: Understand head and next pointers

   head points to first node; head.next points to second node.

2. Step 2: Assign head to head.next to delete first node

   Setting head = head.next moves head to second node, effectively deleting first.

3. Final Answer:

   head = head.next; -> Option A

4. Quick Check:

   Correct syntax to delete first node = head = head.next; [OK]

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

Common Mistakes:

• Using delete keyword incorrectly
• Assigning head.next to head
• Accessing null.next causing error

3. Given the linked list: 1 -> 2 -> 3 -> null and the code snippet:

head = head.next;

What is the resulting linked list?

medium

A. 1 -> 2 -> 3 -> null

B. 2 -> 3 -> null

C. 3 -> null

D. null

Solution

1. Step 1: Initial list and head pointer

   Head points to node with value 1, list is 1 -> 2 -> 3 -> null.

2. Step 2: Move head to head.next

   head = head.next moves head to node with value 2, removing first node.

3. Final Answer:

   2 -> 3 -> null -> Option B

4. Quick Check:

   After deletion, list starts at 2 [OK]

Hint: After head = head.next, list starts from second node [OK]

Common Mistakes:

• Assuming list remains unchanged
• Thinking last node is deleted
• Confusing node values after deletion

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

if (head !== null) {
  head = head.next;
}

What error does this fix compared to just head = head.next;?

medium

A. Prevents deleting the last node

B. Prevents memory leak

C. Prevents runtime error if list is empty

D. Prevents deleting middle node

Solution

1. Step 1: Understand head could be null

   If list is empty, head is null and head.next causes error.

2. Step 2: Check head before accessing next

   Condition ensures head is not null before moving to head.next, avoiding runtime error.

3. Final Answer:

   Prevents runtime error if list is empty -> Option C

4. Quick Check:

   Check head != null before head.next avoids error [OK]

Hint: Check head not null before deleting first node [OK]

Common Mistakes:

• Ignoring null head causing crash
• Thinking it prevents memory leaks
• Confusing node positions deleted

5. You have a singly linked list with nodes: 10 -> 20 -> 30 -> 40 -> null. You want to delete the first two nodes safely. Which code snippet correctly does this?

hard

A. head = null;

B. head = head.next; head = head.next;

C. head.next = head.next.next;

D. if (head && head.next) { head = head.next.next; }

Solution

1. Step 1: Understand deleting two nodes means moving head twice

   Deleting first two nodes means head should point to third node.

2. Step 2: Check head and head.next exist before moving head twice

   Condition ensures no runtime error when accessing head.next.next.

3. Final Answer:

   if (head && head.next) { head = head.next.next; } -> Option D

4. Quick Check:

   Check head and head.next before double move [OK]

Hint: Check head and head.next before skipping two nodes [OK]

Common Mistakes:

• Not checking head.next causing error
• Assigning head.next instead of head
• Setting head to null deletes entire list