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

Time Complexity: Insert at Beginning of Doubly Linked List

O(1)

Understanding Time Complexity

We want to understand how the time needed to insert a node at the start of a doubly linked list changes as the list grows.

How does the number of steps grow when the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public void InsertAtBeginning(int data) {
    Node newNode = new Node(data);
    newNode.Next = Head;
    if (Head != null) {
        Head.Prev = newNode;
    }
    Head = newNode;
}
    

This code adds a new node at the start of a doubly linked list by adjusting pointers.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Creating and linking one new node.
• How many times: Exactly once per insertion, no loops or recursion.

How Execution Grows With Input

Each insertion does the same fixed steps regardless of list size.

Input Size (n)	Approx. Operations
10	4 steps
100	4 steps
1000	4 steps

Pattern observation: The number of steps stays the same no matter how big the list is.

Final Time Complexity

Time Complexity: O(1)

This means inserting at the beginning takes a constant amount of time, no matter how large the list is.

Common Mistake

[X] Wrong: "Inserting at the start takes longer as the list grows because we have to move all nodes."

[OK] Correct: We only change a few pointers at the start; we do not move or touch other nodes.

Interview Connect

Knowing that insertion at the start of a doubly linked list is quick helps you explain efficient data structure operations clearly in interviews.

Self-Check

"What if we changed this to insert at the end of the doubly linked list without a tail pointer? How would the time complexity change?"

Practice

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

easy

A. To add a new node as the first element of the list

B. To remove the last node from the list

C. To search for a node in the list

D. To reverse the entire list

Solution

1. Step 1: Understand the operation

   Inserting at the beginning means adding a new node before the current first node.

2. Step 2: Identify the effect on the list

   The new node becomes the head (first node), shifting others to the right.

3. Final Answer:

   To add a new node as the first element of the list -> Option A

4. Quick Check:

   Insert at beginning = Add first node [OK]

Hint: Insert at beginning means new node becomes the first [OK]

Common Mistakes:

• Confusing insertion with deletion
• Thinking insertion adds at the end
• Mixing up search with insertion

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. newNode = Node(data);

C. Node newNode = Node(data);

D. Node newNode = new Node[];

Solution

1. Step 1: Recall C# object creation syntax

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

2. Step 2: Match syntax with node creation

   Correct syntax is 'Node newNode = new Node(data);' to create a new node with data.

3. Final Answer:

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

4. Quick Check:

   C# new object = new ClassName() [OK]

Hint: Use 'new' keyword to create objects in C# [OK]

Common Mistakes:

• Omitting 'new' keyword
• Using array syntax for single node
• Missing type declaration

3. Consider this code snippet inserting a node with value 10 at the beginning of a doubly linked list:

Node newNode = new Node(10);
newNode.next = head;
if (head != null) {
    head.prev = newNode;
}
head = newNode;

What will be the printed list after insertion if the original list was: 20 <-> 30 <-> null?

medium

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

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

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

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

Solution

1. Step 1: Insert new node at beginning

   New node with 10 points next to old head (20). Old head's prev points back to new node.

2. Step 2: Update head pointer

   Head now points to new node (10), so list starts with 10.

3. Final Answer:

   10 <-> 20 <-> 30 <-> null -> Option D

4. Quick Check:

   New node at front = 10 first [OK]

Hint: New node points to old head; update old head's prev [OK]

Common Mistakes:

• Not updating old head's prev pointer
• Appending new node at end instead of beginning
• Not updating head to new node

4. Identify the error in this code snippet for inserting at the beginning of a doubly linked list:

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

medium

A. Incorrect assignment of newNode.next

B. Missing check if head is null before accessing head.prev

C. head should be assigned before setting newNode.next

D. newNode.prev should be set to head

Solution

1. Step 1: Analyze head.prev assignment

   Code sets head.prev = newNode without checking if head is null, causing error if list is empty.

2. Step 2: Identify missing null check

   Must check if head != null before setting head.prev to avoid null reference error.

3. Final Answer:

   Missing check if head is null before accessing head.prev -> Option B

4. Quick Check:

   Check head != null before head.prev [OK]

Hint: Always check head != null before accessing head.prev [OK]

Common Mistakes:

• Ignoring null check on head
• Setting pointers in wrong order
• Confusing prev and next pointers

5. You have a doubly linked list with nodes: 5 <-> 15 <-> 25 <-> null. You want to insert a new node with value 1 at the beginning. After insertion, which of the following correctly represents the list and the pointers of the new node?

hard

A. 5 <-> 15 <-> 25 <-> 1 <-> null, newNode.prev = 25, newNode.next = null

B. 1 <-> 5 <-> 15 <-> 25 <-> null, newNode.prev = 5, newNode.next = null

C. 1 <-> 5 <-> 15 <-> 25 <-> null, newNode.prev = null, newNode.next = 5

D. 5 <-> 15 <-> 25 <-> 1 <-> null, newNode.prev = null, newNode.next = 5

Solution

1. Step 1: Insert new node at beginning

   New node with value 1 becomes head, points next to old head (5), prev is null.

2. Step 2: Confirm pointers and list order

   List order is 1 <-> 5 <-> 15 <-> 25 <-> null, newNode.prev = null, newNode.next = 5.

3. Final Answer:

   1 <-> 5 <-> 15 <-> 25 <-> null, newNode.prev = null, newNode.next = 5 -> Option C

4. Quick Check:

   New head prev=null, next=old head [OK]

Hint: New head prev=null, next=old head node [OK]

Common Mistakes:

• Setting newNode.prev to old head
• Appending new node at end instead of beginning
• Not updating head pointer