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

Time Complexity: Insert at Specific Position in Doubly Linked List

O(n)

Understanding Time Complexity

We want to understand how long it takes to insert a new item at a certain place in a doubly linked list.

Specifically, how the time changes when the list gets bigger.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public void insertAtPosition(int data, int position) {
    Node newNode = new Node(data);
    if (position == 1) {
        newNode.next = head;
        if (head != null) head.prev = newNode;
        head = newNode;
        return;
    }
    Node current = head;
    for (int i = 1; i < position - 1 && current != null; i++) {
        current = current.next;
    }
    if (current == null) return; // position out of bounds
    newNode.next = current.next;
    if (current.next != null) current.next.prev = newNode;
    current.next = newNode;
    newNode.prev = current;
}

This code inserts a new node at a given position in a doubly linked list by moving to that position and adjusting links.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

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

How Execution Grows With Input

As the list grows, the time to reach the position grows roughly in a straight line with 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 time grows directly with the position number, so doubling the position roughly doubles the steps.

Final Time Complexity

Time Complexity: O(n)

This means the time to insert grows linearly with the position where we insert in the list.

Common Mistake

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

[OK] Correct: We 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

Knowing how insertion time depends on position helps you explain and choose the right data structure for tasks needing fast insertions.

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 insertion

   Inserting at position 1 means adding the node at the start of the list.

2. Step 2: Effect on the list head

   The new node becomes the head, and its next points to the old 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 head's previous pointer
• 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 Java?

easy

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

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

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

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

Solution

1. Step 1: Identify correct pointer updates

   For insertion, newNode's next points to current's next, and prev points to current.

2. Step 2: Update surrounding nodes

   current.next's prev must point to newNode, and current's next must point to newNode.

3. Final Answer:

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

4. Quick Check:

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

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

Common Mistakes:

• Swapping next and prev pointers
• Not updating current.next.prev
• Incorrect order of pointer assignments

3. Given the doubly linked list: 1 <-> 2 <-> 4 <-> null, what will be the list after inserting node with value 3 at position 3?

medium

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

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

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

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

Solution

1. Step 1: Locate position 3 in the list

   Positions: 1=1, 2=2, 3=4 currently. Insert before node with value 4.

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

   New node's next points to node with value 4, prev points to node with value 2. Update pointers accordingly.

3. Final Answer:

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

4. Quick Check:

   Insert at position 3 places 3 before 4 [OK]

Hint: Insert before node currently at position [OK]

Common Mistakes:

• Inserting after position instead of at position
• Not updating prev pointer of next node
• Confusing node values and positions

4. Consider this code snippet to insert at position 2 in a doubly linked list:

Node newNode = new Node(5);
Node current = head;
current = current.next;
newNode.next = current.next;
newNode.prev = current;
current.next = newNode;
newNode.next.prev = newNode;

What is the error in this code?

medium

A. It does not handle insertion at head correctly.

B. It may cause NullPointerException if current.next is null.

C. It forgets to update newNode.prev pointer.

D. It inserts the node at the end always.

Solution

1. Step 1: Analyze newNode.next assignment

   newNode.next = current.next; If current.next is null (inserting at end), newNode.next.prev causes error.

2. Step 2: Identify NullPointerException risk

   Accessing newNode.next.prev without checking null causes NullPointerException.

3. Final Answer:

   It may cause NullPointerException if current.next is null. -> Option B

4. Quick Check:

   Check for null before newNode.next.prev update [OK]

Hint: Always check if next node is null before accessing its prev [OK]

Common Mistakes:

• Not checking for null before pointer updates
• Assuming list has more nodes without validation
• Forgetting to update head or tail pointers

5. You have a doubly linked list: 10 <-> 20 <-> 30 <-> 40 <-> null. You want to insert a node with value 25 at position 3. After insertion, you also want to delete the node at position 4. What will be the final list?

hard

A. 10 <-> 25 <-> 20 <-> 40 <-> null

B. 10 <-> 20 <-> 25 <-> 30 <-> null

C. 10 <-> 20 <-> 25 <-> 40 <-> null

D. 10 <-> 20 <-> 30 <-> 25 <-> null

Solution

1. Step 1: Insert 25 at position 3

   Positions before insertion: 1=10, 2=20, 3=30, 4=40. Insert 25 before 30, so list becomes 10 <-> 20 <-> 25 <-> 30 <-> 40.

2. Step 2: Delete node at position 4

   After insertion, position 4 is node with value 30. Remove it by updating pointers: 25's next points to 40, 40's prev points to 25.

3. Final Answer:

   10 <-> 20 <-> 25 <-> 40 <-> null -> Option C

4. Quick Check:

   Insert then delete correct nodes = 10 <-> 20 <-> 25 <-> 40 <-> null [OK]

Hint: Insert first, then delete at updated position [OK]

Common Mistakes:

• Deleting wrong node after insertion
• Not updating pointers after deletion
• Confusing positions before and after insertion