Insert at Specific Position in Doubly Linked List in DSA Typescript - Time & Space Complexity

Time Complexity: Insert at Specific Position in Doubly Linked List

O(n)

Understanding Time Complexity

We want to know how the time to insert a node at a certain position in a doubly linked list changes as the list grows.

How does the number of steps grow when the list gets longer?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function insertAtPosition(head: Node | null, data: number, position: number): Node | null {
  if (position === 1) {
    const newNode = new Node(data);
    newNode.next = head;
    if (head) head.prev = newNode;
    return newNode;
  }
  let current = head;
  let count = 1;
  while (current && count < position - 1) {
    current = current.next;
    count++;
  }
  if (!current) return head;
  const newNode = new Node(data);
  newNode.next = current.next;
  if (current.next) current.next.prev = newNode;
  current.next = newNode;
  newNode.prev = current;
  return head;
}
    

This code inserts a new node at a given position in a doubly linked list by moving through the list to find the right spot.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that moves through the list nodes to reach the position before insertion.
• How many times: Up to position - 2 times, which depends on the input position.

How Execution Grows With Input

As the list gets longer, the steps to reach the insertion point grow roughly in direct proportion to the position number.

Input Size (n)	Approx. Operations
10	Up to 9 steps to reach position
100	Up to 99 steps to reach position
1000	Up to 999 steps to reach position

Pattern observation: The number of steps grows linearly with the position where we insert.

Final Time Complexity

Time Complexity: O(n)

This means the time to insert grows in a straight line with the size of the list or the position where we insert.

Common Mistake

[X] Wrong: "Inserting at any position in a doubly linked list always takes constant time because we can go backwards and forwards."

[OK] Correct: We still need to move through the list to find the position, which takes time proportional to the position number, so it is not constant time.

Interview Connect

Understanding how insertion time depends on position helps you explain and reason about linked list operations clearly, a skill valued in many coding discussions.

Self-Check

"What if we kept a pointer to the tail and inserted near the end? How would the time complexity change?"

Practice

1. What does inserting a node at a specific position in a doubly linked list involve?

easy

A. Adjusting the previous and next pointers of neighboring nodes to include the new node

B. Only changing the head pointer of the list

C. Replacing the node at that position without changing pointers

D. Adding the node at the end regardless of position

Solution

1. Step 1: Understand doubly linked list structure

   Each node has pointers to both previous and next nodes, so insertion requires updating these pointers.

2. Step 2: Insert node at specific position

   We must update the previous node's next pointer and the next node's previous pointer to point to the new node.

3. Final Answer:

   Adjusting the previous and next pointers of neighboring nodes to include the new node -> Option A

4. Quick Check:

   Pointer updates = Adjust neighbors [OK]

Hint: Remember to update both previous and next pointers [OK]

Common Mistakes:

• Only updating one pointer leads to broken links
• Ignoring the previous pointer in insertion
• Replacing nodes instead of inserting

2. Which of the following TypeScript code snippets correctly declares a node class for a doubly linked list?

easy

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

B. class Node { value: number; next: Node; prev: Node; constructor(value: number) { this.value = value; } }

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

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

Solution

1. Step 1: Check for previous and next pointers

   A doubly linked list node must have both next and prev pointers, which can be null.

2. Step 2: Verify constructor initializes all properties

   class Node { value: number; next: Node | null; prev: Node | null; constructor(value: number) { this.value = value; this.next = null; this.prev = null; } } initializes value, next, and prev correctly with proper types.

3. Final Answer:

   class Node { value: number; next: Node | null; prev: Node | null; constructor(value: number) { this.value = value; this.next = null; this.prev = null; } } -> Option D

4. Quick Check:

   Both pointers initialized = class Node { value: number; next: Node | null; prev: Node | null; constructor(value: number) { this.value = value; this.next = null; this.prev = null; } } [OK]

Hint: Doubly linked nodes need both next and prev pointers [OK]

Common Mistakes:

• Forgetting to initialize prev pointer
• Using wrong property names
• Not allowing null for next or prev

3. Given the doubly linked list 1 <-> 2 <-> 4 and the code below inserting 3 at position 3, what is the list after insertion?

insertAtPosition(head, 3, 3);

Positions start at 1.

medium

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

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

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

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

Solution

1. Step 1: Identify position 3 in the list

   Positions: 1=1, 2=2, 3=4. We want to insert before node with value 4.

2. Step 2: Insert node with value 3 at position 3

   Update pointers so 2 points next to 3, 3 points prev to 2 and next to 4, 4 points prev to 3.

3. Final Answer:

   1 <-> 2 <-> 3 <-> 4 -> Option A

4. Quick Check:

   Insert at position 3 = 1-2-3-4 [OK]

Hint: Count nodes, insert before node at that position [OK]

Common Mistakes:

• Inserting after instead of before position
• Mixing up prev and next pointers
• Off-by-one errors in position counting

4. What is wrong with this TypeScript code snippet for inserting a node at position 2 in a doubly linked list?

function insertAtPosition(head: Node | null, value: number, position: number): Node | null {
  let newNode = new Node(value);
  if (position === 1) {
    newNode.next = head;
    if (head) head.prev = newNode;
    return newNode;
  }
  let current = head;
  for (let i = 1; i < position - 1; i++) {
    if (!current) return head;
    current = current.next;
  }
  newNode.next = current.next;
  current.next = newNode;
  newNode.prev = current;
  return head;
}

medium

A. Not handling insertion at head

B. Incorrect loop range in for loop

C. Missing update of newNode.next.prev to newNode

D. Not creating new node correctly

Solution

1. Step 1: Analyze pointer updates after insertion

   After inserting newNode, newNode.next.prev should point back to newNode to maintain doubly links.

2. Step 2: Identify missing pointer update

   The code misses updating newNode.next.prev = newNode, which breaks backward link from next node.

3. Final Answer:

   Missing update of newNode.next.prev to newNode -> Option C

4. Quick Check:

   Update both next and prev pointers [OK]

Hint: Always update newNode.next.prev after insertion [OK]

Common Mistakes:

• Forgetting to update newNode.next.prev
• Loop off-by-one errors
• Not handling empty list insertion

5. You have a doubly linked list representing train cars: Engine <-> Car1 <-> Car2 <-> Caboose. You want to insert a new CarX at position 2. After insertion, what is the correct order of cars?

hard

A. CarX <-> Engine <-> Car1 <-> Car2 <-> Caboose

B. Engine <-> CarX <-> Car1 <-> Car2 <-> Caboose

C. Engine <-> Car1 <-> CarX <-> Car2 <-> Caboose

D. Engine <-> Car1 <-> Car2 <-> Caboose <-> CarX

Solution

1. Step 1: Identify position 2 in the list

   Positions: 1=Engine, 2=Car1. Insert CarX before Car1 to become new position 2.

2. Step 2: Insert CarX at position 2

   Update pointers so Engine next points to CarX, CarX prev to Engine, CarX next to Car1, Car1 prev to CarX.

3. Final Answer:

   Engine <-> CarX <-> Car1 <-> Car2 <-> Caboose -> Option B

4. Quick Check:

   Insert at position 2 = Engine-CarX-Car1... [OK]

Hint: Insert before node at position to shift others right [OK]

Common Mistakes:

• Inserting after instead of before position
• Not updating prev pointers correctly
• Confusing position indexing starting at 0