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

Time Complexity: Insert at Specific Position in Doubly Linked List

O(n)

Understanding Time Complexity

When inserting a new item at a specific place in a doubly linked list, we want to know how the time to do this changes as the list grows.

We ask: How much work does the computer do as the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

func InsertAtPosition(head *Node, data int, pos int) *Node {
    newNode := &Node{data: data}
    if pos == 1 {
        newNode.next = head
        if head != nil {
            head.prev = newNode
        }
        return newNode
    }
    current := head
    for i := 1; i < pos-1 && current != nil; i++ {
        current = current.next
    }
    if current == nil {
        return head
    }
    newNode.next = current.next
    if current.next != nil {
        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 for-loop that moves through the list nodes to reach the position before insertion.
• How many times: Up to pos - 1 times, which depends on the position where we insert.

How Execution Grows With Input

As the list gets bigger, the time to insert depends on how far we must move to reach the position.

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

Pattern observation: The number of steps grows roughly in direct proportion to the position number, which can be as large as the list size.

Final Time Complexity

Time Complexity: O(n)

This means the time to insert grows linearly with the size of the list because we may need to walk through many nodes to find the insertion point.

Common Mistake

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

[OK] Correct: Even though nodes link both ways, we still must find the position by moving through nodes one by one, which takes time proportional to the position.

Interview Connect

Understanding this helps you explain how linked lists work and why some operations are faster or slower, a key skill in many coding discussions.

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

easy

A. Only changing the head pointer of the list

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

C. Replacing the node at that position without changing pointers

D. Appending 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

   To insert, 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 B

4. Quick Check:

   Pointer updates = A [OK]

Hint: Remember both previous and next pointers must be updated [OK]

Common Mistakes:

• Only updating one pointer and ignoring the other
• Not handling edge cases like insertion at head or tail
• Replacing node data instead of inserting new node

2. Which of the following Go code snippets correctly declares a doubly linked list node struct for insertion?

easy

A. type Node struct { data int; prev *Node; next *Node }

B. type Node struct { data int; next *Node }

C. type Node struct { data int; prev int; next int }

D. type Node struct { data int; prev Node; next Node }

Solution

1. Step 1: Check struct fields for doubly linked list

   A doubly linked list node must have pointers to previous and next nodes, both of type *Node.

2. Step 2: Validate Go syntax

   type Node struct { data int; prev *Node; next *Node } correctly uses pointers (*Node) for prev and next fields, matching doubly linked list requirements.

3. Final Answer:

   type Node struct { data int; prev *Node; next *Node } -> Option A

4. Quick Check:

   Pointers for prev and next = A [OK]

Hint: Use *Node type for prev and next pointers in struct [OK]

Common Mistakes:

• Using non-pointer types for prev and next
• Omitting prev pointer for doubly linked list
• Using incorrect field types like int for pointers

3. What will be the output of the doubly linked list after inserting a node with value 25 at position 3 in the list 10 <-> 20 <-> 30 <-> 40?

medium

A. 10 <-> 20 <-> 25 <-> 30 <-> 40

B. 10 <-> 25 <-> 20 <-> 30 <-> 40

C. 25 <-> 10 <-> 20 <-> 30 <-> 40

D. 10 <-> 20 <-> 30 <-> 40 <-> 25

Solution

1. Step 1: Identify position 3 in the list

   Positions: 1=10, 2=20, 3=30, 4=40. Inserting at position 3 means before node with value 30.

2. Step 2: Insert node with value 25 at position 3

   New node 25 goes between 20 and 30, updating pointers accordingly.

3. Final Answer:

   10 <-> 20 <-> 25 <-> 30 <-> 40 -> Option A

4. Quick Check:

   Insert before 3rd node = D [OK]

Hint: Insert before node currently at that position [OK]

Common Mistakes:

• Inserting after the node at position instead of before
• Appending at end instead of correct position
• Confusing position indexing starting at 0

4. Given the following Go code snippet for insertion, what is the error?

func InsertAtPosition(head *Node, data int, pos int) *Node {
    newNode := &Node{data: data}
    if pos == 1 {
        newNode.next = head
        head.prev = newNode
        head = newNode
        return head
    }
    temp := head
    for i := 1; i < pos-1; i++ {
        temp = temp.next
    }
    newNode.next = temp.next
    temp.next.prev = newNode
    temp.next = newNode
    newNode.prev = temp
    return head
}

medium

A. Incorrect assignment of newNode.prev

B. Missing creation of newNode

C. No check if temp or temp.next is nil before accessing pointers

D. Returning newNode instead of head

Solution

1. Step 1: Analyze pointer usage in loop and insertion

   The loop moves temp to position before insertion. If pos is beyond list length, temp or temp.next can be nil.

2. Step 2: Identify missing nil checks

   Accessing temp.next.prev without checking if temp.next is nil can cause runtime panic.

3. Final Answer:

   No check if temp or temp.next is nil before accessing pointers -> Option C

4. Quick Check:

   Missing nil checks cause runtime errors [OK]

Hint: Always check for nil before accessing next or prev pointers [OK]

Common Mistakes:

• Ignoring nil pointer checks causing crashes
• Incorrect pointer assignments order
• Returning wrong node pointer

5. You have a doubly linked list: 5 <-> 15 <-> 25 <-> 35. You want to insert a node with value 20 at position 3. After insertion, what will be the correct order of nodes and how should pointers be updated?

hard

A. 5 <-> 20 <-> 15 <-> 25 <-> 35; update 5.next to 20, 20.prev to 5, 20.next to 15, 15.prev to 20

B. 5 <-> 15 <-> 25 <-> 20 <-> 35; update 25.next to 20, 20.prev to 25, 20.next to 35, 35.prev to 20

C. 20 <-> 5 <-> 15 <-> 25 <-> 35; update head to 20, 20.next to 5, 5.prev to 20

D. 5 <-> 15 <-> 20 <-> 25 <-> 35; update 15.next to 20, 20.prev to 15, 20.next to 25, 25.prev to 20

Solution

1. Step 1: Determine correct insertion position

   Position 3 means node with value 20 goes between nodes 15 (pos 2) and 25 (pos 3).

2. Step 2: Update pointers for insertion

   Set 15.next to new node 20, 20.prev to 15, 20.next to 25, and 25.prev to 20 to maintain list integrity.

3. Final Answer:

   5 <-> 15 <-> 20 <-> 25 <-> 35; update 15.next to 20, 20.prev to 15, 20.next to 25, 25.prev to 20 -> Option D

4. Quick Check:

   Insert between 15 and 25 with pointer updates = C [OK]

Hint: Insert between nodes and update four pointers correctly [OK]

Common Mistakes:

• Swapping nodes or inserting at wrong position
• Forgetting to update prev pointers
• Incorrectly updating next pointers causing broken links