Insert at End of Doubly Linked List in DSA C# - Time & Space Complexity

Time Complexity: Insert at End of Doubly Linked List

O(n)

Understanding Time Complexity

We want to understand how the time to insert a new item at the end of a doubly linked list changes as the list grows.

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

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public class Node {
    public int data;
    public Node prev, next;
    public Node(int d) { data = d; prev = next = null; }
}

public class DoublyLinkedList {
    public Node head;

    public void InsertAtEnd(int data) {
        Node newNode = new Node(data);
        if (head == null) {
            head = newNode;
            return;
        }
        Node temp = head;
        while (temp.next != null) {
            temp = temp.next;
        }
        temp.next = newNode;
        newNode.prev = temp;
    }
}

This code inserts a new node at the end of a doubly linked list by traversing from the head to the last node.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that moves through each node from the head to the last node.
• How many times: It runs once for each node in the list until it reaches the end, so roughly n times where n is the number of nodes.

How Execution Grows With Input

As the list gets longer, the number of steps to find the end grows linearly.

Input Size (n)	Approx. Operations
10	About 10 steps to reach the end
100	About 100 steps to reach the end
1000	About 1000 steps to reach the end

Pattern observation: The steps increase directly with the size of the list; doubling the list size roughly doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to insert at the end grows in direct proportion to the number of nodes in the list.

Common Mistake

[X] Wrong: "Inserting at the end of a doubly linked list always takes constant time because we just add a node at the end."

[OK] Correct: Without a pointer to the last node, we must walk through the entire list to find the end, which takes time proportional to the list size.

Interview Connect

Understanding this helps you explain how data structure design affects performance, a key skill in coding interviews and real projects.

Self-Check

"What if we kept a pointer to the last node in the list? How would the time complexity change?"

Practice

1. What is the main purpose of inserting a node at the end of a doubly linked list?

easy

A. To remove the first node

B. To find the middle node

C. To reverse the list

D. To add a new element after the last node

Solution

1. Step 1: Understand the structure of a doubly linked list

   A doubly linked list has nodes connected forward and backward, allowing traversal in both directions.

2. Step 2: Purpose of insertion at the end

   Inserting at the end means adding a new node after the current last node, updating pointers accordingly.

3. Final Answer:

   To add a new element after the last node -> Option D

4. Quick Check:

   Insert at end = add after last node [OK]

Hint: Insert at end means add after last node [OK]

Common Mistakes:

• Confusing insertion at end with deletion
• Thinking insertion reverses the list
• Assuming insertion happens at the start

2. Which of the following is the correct syntax to create a new node in C# for a doubly linked list?

easy

A. Node newNode = new Node(data);

B. Node newNode = Node(data);

C. newNode = Node.new(data);

D. Node newNode = new Node[];

Solution

1. Step 1: Understand object creation in C#

   In C#, objects are created using the 'new' keyword followed by the constructor call.

2. Step 2: Apply to Node creation

   Creating a new node requires calling the Node constructor with data inside parentheses after 'new'.

3. Final Answer:

   Node newNode = new Node(data); -> Option A

4. Quick Check:

   Use 'new' keyword with constructor call [OK]

Hint: Use 'new' keyword with constructor parentheses [OK]

Common Mistakes:

• Omitting 'new' keyword
• Using array syntax incorrectly
• Calling constructor without 'new'

3. Given the following code snippet, what will be the printed output after inserting 30 at the end of the doubly linked list?

class Node {
  public int data;
  public Node next, prev;
  public Node(int d) { data = d; next = prev = null; }
}

class DoublyLinkedList {
  public Node head;
  public void InsertAtEnd(int data) {
    Node newNode = new Node(data);
    if (head == null) {
      head = newNode;
      return;
    }
    Node temp = head;
    while (temp.next != null) {
      temp = temp.next;
    }
    temp.next = newNode;
    newNode.prev = temp;
  }
  public void PrintList() {
    Node temp = head;
    while (temp != null) {
      Console.Write(temp.data + " -> ");
      temp = temp.next;
    }
    Console.WriteLine("null");
  }
}

DoublyLinkedList dll = new DoublyLinkedList();
dll.InsertAtEnd(10);
dll.InsertAtEnd(20);
dll.InsertAtEnd(30);
dll.PrintList();

medium

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

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

C. 10 -> 20 -> null

D. null

Solution

1. Step 1: Trace InsertAtEnd calls

   First insert 10: list is 10 -> null. Then insert 20: list is 10 -> 20 -> null. Then insert 30: list is 10 -> 20 -> 30 -> null.

2. Step 2: PrintList outputs nodes in order

   PrintList prints each node's data followed by '->', ending with 'null'. So output is '10 -> 20 -> 30 -> null'.

3. Final Answer:

   10 -> 20 -> 30 -> null -> Option A

4. Quick Check:

   Insertion at end appends nodes in order [OK]

Hint: Insert at end appends nodes; print shows order [OK]

Common Mistakes:

• Confusing insertion order
• Printing in reverse order
• Missing 'null' at end

4. Identify the error in the following InsertAtEnd method for a doubly linked list:

public void InsertAtEnd(int data) {
  Node newNode = new Node(data);
  if (head == null) {
    head = newNode;
  }
  Node temp = head;
  while (temp.next != null) {
    temp = temp.next;
  }
  temp.next = newNode;
  newNode.prev = temp;
}

medium

A. Loop condition should be temp != null

B. Missing return after setting head when list is empty

C. Incorrect assignment of newNode.prev

D. Node constructor is called incorrectly

Solution

1. Step 1: Analyze empty list case

   If head is null, head is set to newNode but code continues to loop and assign pointers again, causing newNode to link to itself.

2. Step 2: Fix by adding return after setting head

   Adding 'return;' after 'head = newNode;' stops further code execution, preventing incorrect pointer assignments.

3. Final Answer:

   Missing return after setting head when list is empty -> Option B

4. Quick Check:

   Return after empty list insert prevents errors [OK]

Hint: Add return after empty list insertion [OK]

Common Mistakes:

• Not returning after setting head
• Wrong loop condition
• Misassigning prev pointer

5. You have a doubly linked list with nodes: 5 <-> 15 <-> 25. You want to insert 35 at the end. After insertion, which of the following correctly describes the pointers of the new node and the previous last node?

hard

A. newNode.prev points to null; node with 25.next points to newNode

B. newNode.next points to node with 25; node with 25.prev points to newNode

C. newNode.prev points to node with 25; node with 25.next points to newNode

D. newNode.prev and newNode.next both point to null; node with 25.next points to null

Solution

1. Step 1: Understand pointer updates when inserting at end

   The new node's prev pointer should point to the current last node (25), and the current last node's next pointer should point to the new node.

2. Step 2: Confirm new node's next pointer

   The new node's next pointer should be null because it is now the last node.

3. Final Answer:

   newNode.prev points to node with 25; node with 25.next points to newNode -> Option C

4. Quick Check:

   Prev points backward; next points forward [OK]

Hint: New node prev = old last; old last next = new node [OK]

Common Mistakes:

• Swapping prev and next pointers
• Setting newNode.prev to null
• Not updating old last node's next pointer