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

Time Complexity: Insert at Specific Position in Doubly Linked List

O(n)

Understanding Time Complexity

When inserting a new node at a specific position in a doubly linked list, we want to know how the time needed changes as the list grows.

We ask: How many steps does it take to find the right spot and insert the node?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function insertAtPosition(head, position, data) {
  let newNode = { data, prev: null, next: null };
  if (position === 1) {
    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; // position out of bounds
  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 the given position by first moving through the list to find the spot, then adjusting pointers to insert.

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 position increases, the number of steps to reach it grows roughly the same amount.

Input Size (n)	Approx. Operations
10	Up to 8 steps to reach position 10
100	Up to 98 steps to reach position 100
1000	Up to 998 steps to reach position 1000

Pattern observation: The steps grow linearly with the position number, so doubling the position roughly doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to insert grows directly with the position in the list; farther positions take more time.

Common Mistake

[X] Wrong: "Insertion at any position in a doubly linked list always takes constant time O(1)."

[OK] Correct: You must first find the position by moving through the list, which takes time proportional to the position, so it is not always instant.

Interview Connect

Understanding how list traversal affects insertion time helps you explain and write efficient code for linked lists, a common topic in interviews.

Self-Check

"What if we kept a pointer to the tail of the list and wanted to insert near the end? How would the time complexity change?"

Practice

1. What happens when you insert a new node at position 1 in a doubly linked list?

easy

A. The new node becomes the new head of the list.

B. The new node is added at the end of the list.

C. The new node replaces the last node.

D. The list remains unchanged.

Solution

1. Step 1: Understand position 1 in doubly linked list

   Position 1 means the start of the list, so the new node should be the first node.

2. Step 2: Effect of insertion at position 1

   The new node's next pointer points to the old head, and the old head's previous pointer points back to the new node. The new node becomes the head.

3. Final Answer:

   The new node becomes the new head of the list. -> Option A

4. Quick Check:

   Insert at position 1 = new head [OK]

Hint: Position 1 means new head insertion [OK]

Common Mistakes:

• Thinking position 1 means end insertion
• Not updating previous pointer of old head
• Ignoring head pointer update

2. Which of the following is the correct syntax to insert a new node at position pos in a doubly linked list in JavaScript?

easy

A. newNode.next = current.next; current.next.prev = newNode; current.next = newNode; newNode.prev = current;

B. newNode.prev = current.next; current.prev = newNode; newNode.next = current; current.next = newNode;

C. newNode.next = current.prev; current.next = newNode; newNode.prev = current.next;

D. newNode.prev = current; current.next = newNode; newNode.next = current.next; current.next.prev = newNode;

Solution

1. Step 1: Identify correct pointer updates for insertion

   When inserting after current, newNode.next should point to current.next, and current.next.prev should point back to newNode.

2. Step 2: Update current's next and newNode's prev

   Set current.next to newNode and newNode.prev to current to link newNode properly.

3. Final Answer:

   newNode.next = current.next; current.next.prev = newNode; current.next = newNode; newNode.prev = current; -> Option A

4. Quick Check:

   Correct pointer updates = newNode.next = current.next; current.next.prev = newNode; current.next = newNode; newNode.prev = current; [OK]

Hint: Next and prev pointers must be updated symmetrically [OK]

Common Mistakes:

• Mixing prev and next pointers
• Not updating current.next.prev
• Incorrect order of assignments causing broken links

3. Given the doubly linked list: 10 <-> 20 <-> 30 <-> null, what is the list after inserting 15 at position 2 using correct insertion logic?

medium

A. 10 <-> 20 <-> 30 <-> 15 <-> null

B. 15 <-> 10 <-> 20 <-> 30 <-> null

C. 10 <-> 15 <-> 20 <-> 30 <-> null

D. 10 <-> 20 <-> 15 <-> 30 <-> null

Solution

1. Step 1: Identify position 2 in the list

   Position 2 means after the first node (10), so 15 should be inserted between 10 and 20.

2. Step 2: Insert 15 between 10 and 20

   Update pointers so 10 points to 15, 15 points to 20, and 20's prev points to 15.

3. Final Answer:

   10 <-> 15 <-> 20 <-> 30 <-> null -> Option C

4. Quick Check:

   Insert at position 2 = between first and second node [OK]

Hint: Position 2 means after first node [OK]

Common Mistakes:

• Inserting at wrong position
• Not updating prev pointer of next node
• Breaking list links after insertion

4. Consider this code snippet to insert a node at position 3 in a doubly linked list:

let current = head;
for(let i = 1; i < pos - 1; i++) {
  current = current.next;
}
newNode.next = current.next;
current.next.prev = newNode;
current.next = newNode;
newNode.prev = current;

What error might occur if pos is greater than the list length?

medium

A. The new node is inserted at the head incorrectly.

B. Runtime error due to accessing next of null.

C. The list becomes circular causing infinite loop.

D. No error; insertion happens at the end automatically.

Solution

1. Step 1: Analyze loop for position traversal

   The loop moves current forward pos-2 times. If pos is too large, current becomes null.

2. Step 2: Accessing current.next when current is null

   Trying to access current.next.prev causes runtime error because current is null.

3. Final Answer:

   Runtime error due to accessing next of null. -> Option B

4. Quick Check:

   Out-of-range position causes null access error [OK]

Hint: Check list length before insertion [OK]

Common Mistakes:

• Not validating position against list length
• Assuming insertion at end without checks
• Ignoring null pointer exceptions

5. You have a doubly linked list: 5 <-> 10 <-> 15 <-> 20 <-> null. You want to insert a new node with value 12 at position 3. After insertion, you also want to remove the node at position 4. What will be the final list?

hard

A. 5 <-> 12 <-> 10 <-> 20 <-> null

B. 5 <-> 10 <-> 12 <-> 15 <-> 20 <-> null

C. 5 <-> 10 <-> 15 <-> 20 <-> null

D. 5 <-> 10 <-> 12 <-> 20 <-> null

Solution

1. Step 1: Insert 12 at position 3

   Position 3 means between nodes with values 10 and 15. After insertion: 5 <-> 10 <-> 12 <-> 15 <-> 20.

2. Step 2: Remove node at position 4

   Position 4 now points to node with value 15. Removing it links 12 directly to 20.

3. Final Answer:

   5 <-> 10 <-> 12 <-> 20 <-> null -> Option D

4. Quick Check:

   Insert then remove node at position 4 = 5 <-> 10 <-> 12 <-> 20 <-> null [OK]

Hint: Insert first, then remove target node [OK]

Common Mistakes:

• Removing wrong node after insertion
• Not updating pointers after removal
• Confusing positions after insertion