Doubly Linked List Structure and Node Design in DSA C# - Time & Space Complexity

Time Complexity: Doubly Linked List Structure and Node Design

O(1)

Understanding Time Complexity

We want to understand how the time to create and link nodes in a doubly linked list grows as we add more nodes.

How does the work change when the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public class Node {
    public int Value;
    public Node Prev;
    public Node Next;

    public Node(int value) {
        Value = value;
        Prev = null;
        Next = null;
    }
}
    

This code defines a node for a doubly linked list with pointers to previous and next nodes.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Creating a single node and setting its pointers.
• How many times: Each node creation is a single operation; no loops or recursion here.

How Execution Grows With Input

Each node creation takes the same small amount of work, so the total work grows directly with the number of nodes.

Input Size (n)	Approx. Operations
10	10 node creations
100	100 node creations
1000	1000 node creations

Pattern observation: The work grows in a straight line as we add more nodes.

Final Time Complexity

Time Complexity: O(1) per node creation

This means creating each node takes a fixed amount of time, no matter how many nodes exist.

Common Mistake

[X] Wrong: "Creating a node takes longer as the list grows because it has to check all other nodes."

[OK] Correct: Creating a node only sets its own pointers; it does not scan or loop through the list.

Interview Connect

Understanding the basic cost of node creation helps you build efficient linked list operations and shows you know how data structures work under the hood.

Self-Check

"What if we added a loop to link multiple nodes at once? How would the time complexity change?"

Practice

1. What is the main advantage of a Doubly Linked List compared to a singly linked list?

easy

A. It allows traversal in both forward and backward directions.

B. It uses less memory than a singly linked list.

C. It does not require a head pointer.

D. It automatically sorts the elements.

Solution

1. Step 1: Understand the structure difference

   A doubly linked list has nodes with two pointers: one to the next node and one to the previous node.

2. Step 2: Identify traversal capabilities

   This allows moving forward and backward through the list, unlike singly linked lists which only move forward.

3. Final Answer:

   It allows traversal in both forward and backward directions. -> Option A

4. Quick Check:

   Doubly linked list = two-way traversal [OK]

Hint: Remember: two pointers mean two directions [OK]

Common Mistakes:

• Thinking it uses less memory than singly linked list
• Assuming it doesn't need a head pointer
• Believing it sorts elements automatically

2. Which of the following is the correct way to declare a node class for a doubly linked list in C#?

easy

A. class Node { public int data; public Node next; }

B. public class Node { public int data; public Node next; public Node prev; }

C. public class Node { int data; Node next; }

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

Solution

1. Step 1: Check for public access and all pointers

   The node must have public fields for data, next, and prev to represent doubly linked list nodes.

2. Step 2: Verify syntax correctness

   public class Node { public int data; public Node next; public Node prev; } declares all required fields with public access, suitable for a doubly linked list node.

3. Final Answer:

   public class Node { public int data; public Node next; public Node prev; } -> Option B

4. Quick Check:

   Node class with data, next, prev = public class Node { public int data; public Node next; public Node prev; } [OK]

Hint: Doubly linked node needs next and prev pointers public [OK]

Common Mistakes:

• Omitting the prev pointer
• Using struct instead of class (less common for linked lists)
• Not making fields public for access

3. What will be the output of the following C# code snippet for a doubly linked list node?

Node node = new Node();
node.data = 10;
node.next = null;
node.prev = null;
Console.WriteLine(node.data);

medium

A. 10

B. null

C. 0

D. Compilation error

Solution

1. Step 1: Analyze node initialization

   The node's data is set to 10 explicitly, and next and prev are set to null.

2. Step 2: Check the printed value

   The Console.WriteLine prints node.data, which is 10.

3. Final Answer:

   10 -> Option A

4. Quick Check:

   node.data = 10 prints 10 [OK]

Hint: Prints the assigned data value, not pointers [OK]

Common Mistakes:

• Confusing null pointers with data value
• Expecting default 0 instead of assigned 10
• Thinking it causes compilation error

4. Identify the error in this doubly linked list node insertion code snippet:

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

medium

A. Missing initialization of newNode.prev to null

B. head.prev should be assigned after head is updated

C. No error, code correctly inserts at the beginning

D. newNode.next should be null

Solution

1. Step 1: Understand insertion at list start

   newNode's next points to current head, head's prev points back to newNode, then head updates to newNode.

2. Step 2: Check pointer assignments

   newNode.prev is null by default or not needed explicitly here; the code correctly links nodes.

3. Final Answer:

   No error, code correctly inserts at the beginning -> Option C

4. Quick Check:

   Insertion at head with correct pointers = No error, code correctly inserts at the beginning [OK]

Hint: Check pointer updates order carefully [OK]

Common Mistakes:

• Assuming prev must be set explicitly to null
• Thinking head.prev must be set after head update
• Confusing next pointer assignment

5. You want to design a method to remove a node from the middle of a doubly linked list. Which pointers must be updated to maintain list integrity?

hard

A. Only the head pointer

B. The tail pointer and the node's prev pointer

C. Only the node's next pointer

D. The previous node's next and the next node's prev pointers

Solution

1. Step 1: Identify nodes around the removed node

   To remove a node, you must link its previous node to its next node directly.

2. Step 2: Update pointers to bypass the removed node

   Set previous node's next to removed node's next, and next node's prev to removed node's prev.

3. Final Answer:

   The previous node's next and the next node's prev pointers -> Option D

4. Quick Check:

   Update prev.next and next.prev to remove node [OK]

Hint: Update both prev and next pointers around removed node [OK]

Common Mistakes:

• Only updating one pointer and breaking the list
• Trying to update head or tail unnecessarily
• Ignoring the prev pointer of the next node