Insert at End of Circular Linked List in DSA Java - Time & Space Complexity

Time Complexity: Insert at End of Circular Linked List

O(n)

Understanding Time Complexity

We want to understand how the time to insert a node at the end of a circular linked list changes as the list grows.

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

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class Node {
    int data;
    Node next;
    Node(int data) { this.data = data; this.next = null; }
}

Node insertEnd(Node head, int value) {
    Node newNode = new Node(value);
    if (head == null) {
        newNode.next = newNode;
        return newNode;
    }
    Node temp = head;
    while (temp.next != head) {
        temp = temp.next;
    }
    temp.next = newNode;
    newNode.next = head;
    return head;
}
    

This code inserts a new node at the end of a circular linked list by traversing the list to find the last node.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that moves through each node until it finds the last node.
• How many times: It runs once for each node in the list until the last node is found, so roughly n times for a list of size n.

How Execution Grows With Input

As the list size grows, the number of steps to find the last node grows roughly the same way.

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 number of nodes, so 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 linearly with the size of the list.

Common Mistake

[X] Wrong: "Inserting at the end is always constant time because we just add the node."

[OK] Correct: We must first find the last node by moving through the list, which takes time proportional to the list size.

Interview Connect

Understanding this helps you explain how linked list operations scale and shows you can analyze code beyond just reading it.

Self-Check

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

Practice

1. What happens when you insert a new node at the end of an empty circular linked list?

easy

A. The new node points to the head, but the list remains empty.

B. The new node points to itself, becoming the only node in the list.

C. The new node is discarded because the list is empty.

D. The new node points to null, ending the list.

Solution

1. Step 1: Understand circular linked list empty state

   When the list is empty, there is no node, so the new node must point to itself to form a circle.

2. Step 2: Insert new node and update pointers

   The new node's next pointer is set to itself, making it the only node and the head of the list.

3. Final Answer:

   The new node points to itself, becoming the only node in the list. -> Option B

4. Quick Check:

   Empty list insertion = node points to itself [OK]

Hint: Empty circular list node points to itself [OK]

Common Mistakes:

• Setting new node's next to null
• Not updating head pointer
• Assuming list remains empty

2. Which of the following Java code snippets correctly inserts a new node at the end of a circular linked list?

easy

A. newNode.next = head; tail.next = newNode; tail = newNode;

B. newNode.next = null; tail.next = newNode; tail = newNode;

C. newNode.next = tail; head.next = newNode; tail = newNode;

D. newNode.next = head; head.next = newNode; tail = newNode;

Solution

1. Step 1: Set new node's next to head

   In a circular linked list, the last node points to the head, so newNode.next = head is correct.

2. Step 2: Update tail's next and tail pointer

   Tail's next should point to newNode, and tail should be updated to newNode to maintain the list.

3. Final Answer:

   newNode.next = head; tail.next = newNode; tail = newNode; -> Option A

4. Quick Check:

   New node points to head, tail updated [OK]

Hint: New node next = head, tail next = new node [OK]

Common Mistakes:

• Setting newNode.next to null
• Updating head.next instead of tail.next
• Not updating tail pointer

3. Given the following circular linked list with nodes 10 -> 20 -> 30 -> back to 10, what will be the list after inserting 40 at the end?

Node head = new Node(10);
Node second = new Node(20);
Node third = new Node(30);
head.next = second;
second.next = third;
third.next = head;

Node newNode = new Node(40);
Node tail = third;
newNode.next = head;
tail.next = newNode;
tail = newNode;

medium

A. 40 -> 10 -> 20 -> 30 -> back to 40

B. 10 -> 20 -> 30 -> back to 10 (unchanged)

C. 10 -> 20 -> 30 -> 40 -> back to 10

D. 10 -> 20 -> 40 -> 30 -> back to 10

Solution

1. Step 1: Understand initial list and insertion

   Initial list is 10 -> 20 -> 30 -> back to 10. Inserting 40 at end means 30's next points to 40, and 40 points to head (10).

2. Step 2: Update tail and next pointers

   After insertion, tail is updated to 40, and list becomes 10 -> 20 -> 30 -> 40 -> back to 10.

3. Final Answer:

   10 -> 20 -> 30 -> 40 -> back to 10 -> Option C

4. Quick Check:

   New node added at end, circular link maintained [OK]

Hint: New node next = head, tail next = new node [OK]

Common Mistakes:

• Not updating tail.next to new node
• Not updating tail pointer
• Breaking circular link

4. Identify the error in the following code snippet that inserts a node at the end of a circular linked list:

Node newNode = new Node(50);
newNode.next = null;
tail.next = newNode;
tail = newNode;
tail.next = head;

medium

A. Setting newNode.next to null breaks the circular link.

B. Not updating tail pointer causes list corruption.

C. tail.next should point to null, not newNode.

D. head pointer is incorrectly updated.

Solution

1. Step 1: Check newNode.next assignment

   Setting newNode.next to null breaks the circular property because last node must point to head.

2. Step 2: Verify tail.next and tail updates

   tail.next is set to newNode and tail updated correctly, but newNode.next should point to head, not null.

3. Final Answer:

   Setting newNode.next to null breaks the circular link. -> Option A

4. Quick Check:

   newNode.next must point to head, not null [OK]

Hint: Last node next must point to head, never null [OK]

Common Mistakes:

• Setting newNode.next to null
• Not maintaining circular link
• Confusing tail and head pointers

5. You have a circular linked list with nodes 5 -> 15 -> 25 -> back to 5. You want to insert a new node with value 35 at the end. After insertion, you want to print the list starting from head. Which code snippet correctly performs insertion and prints the list?

Node head = new Node(5);
Node second = new Node(15);
Node third = new Node(25);
head.next = second;
second.next = third;
third.next = head;

Node newNode = new Node(35);
Node tail = third;
// Insert newNode at end
// Print list starting from head

hard

A. newNode.next = null;
tail.next = newNode;
tail = newNode;
Node temp = head;
while(temp != null) { System.out.print(temp.data + " -> "); temp = temp.next; }
System.out.print("null");

B. newNode.next = head;
tail.next = newNode;
tail = newNode;
Node temp = tail;
do { System.out.print(temp.data + " -> "); temp = temp.next; } while(temp != tail);
System.out.print("null");

C. newNode.next = head;
head.next = newNode;
tail = newNode;
Node temp = head;
do { System.out.print(temp.data + " -> "); temp = temp.next; } while(temp != head);
System.out.print("null");

D. newNode.next = head;
tail.next = newNode;
tail = newNode;
Node temp = head;
do { System.out.print(temp.data + " -> "); temp = temp.next; } while(temp != head);
System.out.print("null");

Solution

1. Step 1: Insert newNode correctly at end

   Set newNode.next to head, update tail.next to newNode, and update tail to newNode to maintain circular list.

2. Step 2: Print list starting from head using do-while

   Use a do-while loop starting at head, printing each node until we return to head, ensuring all nodes are printed once.

3. Final Answer:

   newNode.next = head; tail.next = newNode; tail = newNode; followed by do-while print from head -> Option D

4. Quick Check:

   Insert at end + do-while print from head [OK]

Hint: Use do-while to print circular list once [OK]

Common Mistakes:

• Setting newNode.next to null
• Using while loop with null condition
• Starting print from tail instead of head