Delete from End of Doubly Linked List in DSA Javascript - Time & Space Complexity

Time Complexity: Delete from End of Doubly Linked List

O(1)

Understanding Time Complexity

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

We ask: How many steps does it take to remove the last node when the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class Node {
  constructor(data) {
    this.data = data;
    this.prev = null;
    this.next = null;
  }
}

class DoublyLinkedList {
  constructor() {
    this.head = null;
    this.tail = null;
  }

  deleteFromEnd() {
    if (!this.tail) return null;
    const removed = this.tail;
    this.tail = this.tail.prev;
    if (this.tail) this.tail.next = null;
    else this.head = null;
    return removed.data;
  }
}
    

This code removes the last node from a doubly linked list by updating pointers.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Accessing the tail node and updating pointers.
• How many times: This happens once per deletion, no loops or recursion involved.

How Execution Grows With Input

Deleting from the end always takes the same number of 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 as the list grows.

Final Time Complexity

Time Complexity: O(1)

This means deleting from the end takes a constant amount of time regardless of list size.

Common Mistake

[X] Wrong: "Deleting from the end takes longer as the list grows because you have to find the last node."

[OK] Correct: The doubly linked list keeps a direct reference to the last node (tail), so no searching is needed.

Interview Connect

Knowing that deleting from the end of a doubly linked list is quick shows you understand how pointers help save time in data structures.

Self-Check

"What if we did not keep a tail pointer? How would the time complexity change when deleting from the end?"

Practice

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

easy

A. It moves to the next node of the deleted node.

B. It becomes null immediately without change.

C. It moves to the previous node of the deleted node.

D. It stays pointing to the deleted node.

Solution

1. Step 1: Understand tail pointer role

   The tail pointer always points to the last node in the list.

2. Step 2: Effect of deleting last node

   When the last node is deleted, tail must move to the previous node to remain correct.

3. Final Answer:

   It moves to the previous node of the deleted node. -> Option C

4. Quick Check:

   Tail updates to previous node [OK]

Hint: Tail always points to last node, update to previous on delete [OK]

Common Mistakes:

• Setting tail to null without checking list emptiness
• Not updating tail pointer after deletion
• Moving tail to next node which doesn't exist

2. Which of the following is the correct syntax to remove the last node from a doubly linked list in JavaScript?

easy

A. tail = tail.prev; tail.next = null;

B. tail = tail.next; tail.prev = null;

C. tail = tail.prev; tail.prev = null;

D. tail = null; head = null;

Solution

1. Step 1: Move tail pointer to previous node

   To delete last node, tail moves to tail.prev.

2. Step 2: Set new tail's next to null

   New tail's next must be null to mark end of list.

3. Final Answer:

   tail = tail.prev; tail.next = null; -> Option A

4. Quick Check:

   Correct tail update and next nullify [OK]

Hint: Tail moves back, next pointer cleared [OK]

Common Mistakes:

• Moving tail forward instead of backward
• Not setting tail.next to null
• Setting tail.prev to null incorrectly

3. Consider the following doubly linked list: 1 <-> 2 <-> 3 <-> 4. After deleting the last node, what will be the new list?

medium

A. 2 <-> 3 <-> 4

B. 1 <-> 2 <-> 3

C. 1 <-> 2 <-> 3 <-> 4

D. 1 <-> 2

Solution

1. Step 1: Identify last node

   Last node is 4, which will be removed.

2. Step 2: Remove last node and update tail

   Tail moves to node 3, and node 3's next becomes null.

3. Final Answer:

   1 <-> 2 <-> 3 -> Option B

4. Quick Check:

   Last node removed, list ends at 3 [OK]

Hint: Remove last node, tail moves back [OK]

Common Mistakes:

• Forgetting to update tail pointer
• Not setting new tail's next to null
• Removing wrong node

4. Given this code snippet to delete the last node from a doubly linked list, what is the error?

if (tail === null) return;
tail = tail.prev;
tail.next = null;

medium

A. It should check if tail.next is null before deleting.

B. It incorrectly sets tail.next to null before moving tail.

C. It should set tail.prev to null instead of tail.next.

D. It does not handle the case when list has only one node.

Solution

1. Step 1: Check single node case

   If list has one node, tail.prev is null, so tail becomes null.

2. Step 2: Problem with tail.next assignment

   After tail becomes null, tail.next causes error because tail is null.

3. Final Answer:

   It does not handle the case when list has only one node. -> Option D

4. Quick Check:

   Single node deletion needs special handling [OK]

Hint: Check single node before updating tail [OK]

Common Mistakes:

• Not checking if tail is null after update
• Accessing properties of null tail
• Ignoring empty list case

5. You have a doubly linked list with nodes: 10 <-> 20 <-> 30. After deleting the last node twice, what will be the state of the list?

hard

A. 10

B. 10 <-> 20

C. 20

D. Empty list

Solution

1. Step 1: Delete last node once

   Last node 30 is removed, list becomes 10 <-> 20.

2. Step 2: Delete last node again

   Now last node 20 is removed, list becomes 10 only.

3. Step 3: Verify final list

   After two deletions, list is just node 10.

4. Final Answer:

   10 -> Option A

5. Quick Check:

   Two deletions remove last two nodes [OK]

Hint: Delete last node repeatedly removes tail nodes [OK]

Common Mistakes:

• Assuming list becomes empty after two deletions
• Not updating tail pointer correctly
• Confusing node values after deletion