Delete by Value in Doubly Linked List in DSA Typescript - Time & Space Complexity

Time Complexity: Delete by Value in Doubly Linked List

O(n)

Understanding Time Complexity

When deleting a value from a doubly linked list, we want to know how long it takes as the list grows.

We ask: How does the time to find and remove a value change with list size?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function deleteByValue(head: Node | null, value: number): Node | null {
  let current = head;
  while (current !== null) {
    if (current.data === value) {
      if (current.prev) current.prev.next = current.next;
      if (current.next) current.next.prev = current.prev;
      if (current === head) head = current.next;
      break;
    }
    current = current.next;
  }
  return head;
}
    

This code searches the list for the first node with the given value and removes it by adjusting links.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Traversing the list nodes one by one to find the value.
• How many times: Up to n times, where n is the number of nodes in the list.

How Execution Grows With Input

As the list grows, the time to find the value grows roughly in a straight line.

Input Size (n)	Approx. Operations
10	Up to 10 checks
100	Up to 100 checks
1000	Up to 1000 checks

Pattern observation: The number of steps grows directly with the list size.

Final Time Complexity

Time Complexity: O(n)

This means the time to delete by value grows linearly as the list gets longer.

Common Mistake

[X] Wrong: "Deleting by value is always fast because we just remove the node."

[OK] Correct: Finding the node takes time because we may need to check many nodes before finding the value.

Interview Connect

Understanding this helps you explain how linked lists work and how operations scale, a key skill in many coding interviews.

Self-Check

"What if the list was sorted? How would that change the time complexity of deleting by value?"

Practice

1. What happens when you delete a node by value in a doubly linked list?

easy

A. All nodes are deleted regardless of value

B. The node with the matching value is removed and links are updated

C. Only the first node is deleted no matter the value

D. The list is reversed instead of deleting

Solution

1. Step 1: Identify the node with the given value

   Traverse the list from head to tail to find the node whose value matches the target.

2. Step 2: Remove the node and update links

   Adjust the previous node's next pointer and the next node's previous pointer to exclude the found node.

3. Final Answer:

   The node with the matching value is removed and links are updated -> Option B

4. Quick Check:

   Deleting by value removes matching node [OK]

Hint: Find node by value, then update previous and next links [OK]

Common Mistakes:

• Not updating previous node's next pointer
• Not updating next node's previous pointer
• Deleting all nodes instead of one

2. Which of the following is the correct TypeScript syntax to delete a node by value in a doubly linked list?

easy

A. function deleteNode(value) { /* code */ }

B. removeNode(value: number) => { /* code */ }

C. deleteNode(value: number): void { /* code */ }

D. delete node(value: number) { /* code */ }

Solution

1. Step 1: Check method declaration syntax in TypeScript class

   Methods inside classes use the syntax methodName(params): returnType { body }.

2. Step 2: Identify correct syntax for deleteNode method

   deleteNode(value: number): void { /* code */ } uses correct TypeScript method syntax with type annotation and void return.

3. Final Answer:

   deleteNode(value: number): void { /* code */ } -> Option C

4. Quick Check:

   TypeScript method syntax = deleteNode(value: number): void { /* code */ } [OK]

Hint: Use methodName(params): returnType { } inside class [OK]

Common Mistakes:

• Using arrow function syntax inside class method
• Missing type annotations
• Using invalid keywords like 'delete node'

3. Given the doubly linked list: 10 <-> 20 <-> 30 <-> 40, what is the list after deleting the node with value 30?

medium

A. 10 <-> 20 <-> 40

B. 10 <-> 30 <-> 40

C. 20 <-> 30 <-> 40

D. 10 <-> 20 <-> 30 <-> 40

Solution

1. Step 1: Locate node with value 30

   Traverse the list: 10 -> 20 -> 30 found at third node.

2. Step 2: Remove node 30 and link 20 to 40

   Update 20's next pointer to 40 and 40's previous pointer to 20.

3. Final Answer:

   10 <-> 20 <-> 40 -> Option A

4. Quick Check:

   Deleted 30, list links updated [OK]

Hint: Remove node, link previous and next nodes directly [OK]

Common Mistakes:

• Not updating previous node's next pointer
• Not updating next node's previous pointer
• Deleting wrong node

4. What is wrong with this delete function snippet for doubly linked list?

deleteNode(value: number): void {
  let current = this.head;
  while (current !== null) {
    if (current.value === value) {
      current.prev.next = current.next;
      current.next.prev = current.prev;
      break;
    }
    current = current.next;
  }
}

medium

A. It does not handle deleting the head node correctly

B. It deletes all nodes with the value instead of one

C. It uses wrong variable names

D. It causes infinite loop

Solution

1. Step 1: Check handling of head node deletion

   If current is head, current.prev is null, so current.prev.next causes error.

2. Step 2: Identify missing head update

   Function does not update this.head when deleting the first node, causing broken list.

3. Final Answer:

   It does not handle deleting the head node correctly -> Option A

4. Quick Check:

   Head deletion needs special handling [OK]

Hint: Check if node is head before updating prev pointers [OK]

Common Mistakes:

• Not checking if current.prev is null
• Not updating head pointer when deleting first node
• Assuming all nodes have prev and next

5. You have a doubly linked list: 5 <-> 10 <-> 15 <-> 20 <-> 25. You want to delete the node with value 5, then delete the node with value 25. What is the final list?

hard

A. 15 <-> 20

B. 5 <-> 10 <-> 15 <-> 20

C. 10 <-> 15 <-> 20 <-> 25

D. 10 <-> 15 <-> 20

Solution

1. Step 1: Delete node with value 5 (head node)

   Update head to 10, set 10.prev to null.

2. Step 2: Delete node with value 25 (tail node)

   Update 20.next to null, removing 25.

3. Final Answer:

   10 <-> 15 <-> 20 -> Option D

4. Quick Check:

   Deleted head and tail nodes correctly [OK]

Hint: Update head or tail pointers when deleting first or last nodes [OK]

Common Mistakes:

• Not updating head when deleting first node
• Not updating tail when deleting last node
• Breaking links between middle nodes