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

Time Complexity: Insert at End of Circular Linked List

O(n)

Understanding Time Complexity

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

Specifically, how does the number of steps grow when the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

func InsertAtEnd(head *Node, data int) *Node {
    newNode := &Node{data: data}
    if head == nil {
        newNode.next = newNode
        return newNode
    }
    current := head
    for current.next != head {
        current = current.next
    }
    current.next = newNode
    newNode.next = head
    return head
}
    

This code inserts a new node at the end of a circular linked list by traversing to the last node and linking the new node after it.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for loop that moves through nodes 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 n nodes.

How Execution Grows With Input

As the list size grows, the loop runs more times because it must check each node to find the end.

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

Pattern observation: The number of steps grows roughly in direct proportion to the list size.

Final Time Complexity

Time Complexity: O(n)

This means the time to insert at the end grows linearly with the number of nodes in the list.

Common Mistake

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

[OK] Correct: Because 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 simple loops clearly.

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 itself, becoming the only node in the list

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

C. The list remains empty because insertion is not possible

D. The new node points to the head, but the list has multiple nodes

Solution

1. Step 1: Understand empty circular linked list

   When the list is empty, there is no node, so the new node must point to itself to maintain circularity.

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 A

4. Quick Check:

   Empty list insertion = single node pointing to itself [OK]

Hint: New node points to itself if list is empty [OK]

Common Mistakes:

• Setting new node's next to null instead of itself
• Not updating head pointer
• Assuming list remains empty after insertion

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

easy

A. newNode.next = nil
last.next = newNode
last = newNode

B. newNode.next = head
last.next = newNode
newNode = last

C. newNode.next = head
last.next = newNode
last = newNode

D. newNode.next = head
newNode.next = last
last = newNode

Solution

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

   In circular linked list, new node's next must point to head to maintain circularity.

2. Step 2: Update last node's next and last pointer

   Last node's next points to new node, and last pointer updates to new node.

3. Final Answer:

   newNode.next = head; last.next = newNode; last = newNode -> Option C

4. Quick Check:

   Correct pointer updates maintain circular list [OK]

Hint: New node next = head; last next = new node; update last [OK]

Common Mistakes:

• Setting newNode.next to nil breaks circularity
• Not updating last pointer to new node
• Incorrect pointer assignments causing runtime errors

3. Given the following Go code for inserting at the end of a circular linked list, what will be the printed list after inserting 4?

type Node struct {
  data int
  next *Node
}

func insertEnd(last *Node, data int) *Node {
  newNode := &Node{data: data}
  if last == nil {
    newNode.next = newNode
    return newNode
  }
  newNode.next = last.next
  last.next = newNode
  return newNode
}

func printList(last *Node) {
  if last == nil {
    fmt.Println("List is empty")
    return
  }
  temp := last.next
  for {
    fmt.Printf("%d -> ", temp.data)
    temp = temp.next
    if temp == last.next {
      break
    }
  }
  fmt.Println("null")
}

func main() {
  var last *Node
  last = insertEnd(last, 1)
  last = insertEnd(last, 2)
  last = insertEnd(last, 3)
  last = insertEnd(last, 4)
  printList(last)
}

medium

A. 1 -> 2 -> 3 -> null

B. 4 -> 1 -> 2 -> 3 -> null

C. 2 -> 3 -> 4 -> 1 -> null

D. 1 -> 2 -> 3 -> 4 -> null

Solution

1. Step 1: Trace insertions in order

   Insert 1: list is empty, new node points to itself. Insert 2: new node added after last, last updated. Insert 3 and 4 similarly.

2. Step 2: Print list starting from last.next

   Printing starts at first node (last.next), so order is 1 -> 2 -> 3 -> 4 -> null.

3. Final Answer:

   1 -> 2 -> 3 -> 4 -> null -> Option D

4. Quick Check:

   Insertion at end maintains order [OK]

Hint: Print starts at last.next, so order is insertion order [OK]

Common Mistakes:

• Assuming last node is printed first
• Not updating last pointer after insertion
• Confusing circular list print start point

4. The following Go function is intended to insert a new node at the end of a circular linked list. What is the bug?

func insertEnd(last *Node, data int) *Node {
  newNode := &Node{data: data}
  if last == nil {
    newNode.next = nil
    return newNode
  }
  newNode.next = last.next
  last.next = newNode
  return newNode
}

medium

A. newNode.next should point to itself when list is empty, not nil

B. last.next should be set to nil instead of newNode

C. Function should return last, not newNode

D. Data field of newNode is not initialized

Solution

1. Step 1: Check empty list insertion

   When list is empty, newNode.next must point to itself to maintain circularity, not nil.

2. Step 2: Identify incorrect pointer assignment

   Setting newNode.next to nil breaks circular linked list property causing runtime errors.

3. Final Answer:

   newNode.next should point to itself when list is empty, not nil -> Option A

4. Quick Check:

   Empty list node next = itself [OK]

Hint: Empty list node next must point to itself, never nil [OK]

Common Mistakes:

• Setting next to nil breaks circularity
• Returning newNode instead of last can confuse list end
• Not initializing data field properly

5. You have a circular linked list with nodes 10 -> 20 -> 30 -> (back to 10). You want to insert 40 at the end. After insertion, which node should the last pointer refer to, and what will be the list order when printed starting from last.next? Choose the correct pair.

hard

A. Last points to node with data 30; list order: 40 -> 10 -> 20 -> 30 -> null

B. Last points to node with data 40; list order: 10 -> 20 -> 30 -> 40 -> null

C. Last points to node with data 40; list order: 40 -> 10 -> 20 -> 30 -> null

D. Last points to node with data 30; list order: 10 -> 20 -> 30 -> 40 -> null

Solution

1. Step 1: Insert new node at end and update last pointer

   New node 40 is added after last (30), so last pointer updates to new node 40.

2. Step 2: Print list starting from last.next

   last.next points to head (10), so printing order is 10 -> 20 -> 30 -> 40 -> null.

3. Final Answer:

   Last points to node with data 40; list order: 10 -> 20 -> 30 -> 40 -> null -> Option B

4. Quick Check:

   Last updated to new end node; print starts at last.next [OK]

Hint: Last always points to newest end node; print starts at last.next [OK]

Common Mistakes:

• Not updating last pointer after insertion
• Printing starting from last instead of last.next
• Confusing list order after insertion