Insert at Beginning of Circular Linked List in DSA C++ - Time & Space Complexity

Time Complexity: Insert at Beginning of Circular Linked List

O(1)

Understanding Time Complexity

We want to understand how the time to insert a new node at the start 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.

struct Node {
    int data;
    Node* next;
};

void insertAtBeginning(Node*& tail, int value) {
    Node* newNode = new Node{value, nullptr};
    if (!tail) {
        newNode->next = newNode;
        tail = newNode;
    } else {
        newNode->next = tail->next;
        tail->next = newNode;
    }
}
    

This code inserts a new node at the start of a circular linked list by adjusting pointers.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Pointer updates to insert the new node.
• How many times: These pointer changes happen only once per insertion, no loops or recursion.

How Execution Grows With Input

Since the insertion only changes a few pointers, the number of steps stays the same no matter how big the list is.

Input Size (n)	Approx. Operations
10	3-4 pointer changes
100	3-4 pointer changes
1000	3-4 pointer changes

Pattern observation: The work stays constant regardless of list size.

Final Time Complexity

Time Complexity: O(1)

This means the insertion takes the same amount of time no matter how many nodes are in the list.

Common Mistake

[X] Wrong: "Inserting at the beginning requires going through the whole list to find the start."

[OK] Correct: Because we keep a pointer to the tail, we can access the start directly without walking through the list.

Interview Connect

Knowing this operation is constant time shows you understand how circular linked lists use pointers smartly to avoid extra work.

Self-Check

"What if we did not keep a tail pointer and only had a head pointer? How would the time complexity change?"

Practice

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

easy

A. The new node replaces the last node in the list.

B. The new node is added at the end of the list, breaking the circular link.

C. The new node becomes the head and points to the old head, maintaining the circular link.

D. The list becomes linear instead of circular.

Solution

1. Step 1: Understand the circular linked list structure

   In a circular linked list, the last node points back to the head node, forming a circle.

2. Step 2: Insert new node at beginning

   The new node is linked to the current head, and the last node's next pointer is updated to this new node, making it the new head.

3. Final Answer:

   The new node becomes the head and points to the old head, maintaining the circular link. -> Option C

4. Quick Check:

   New head points to old head, circle intact = A [OK]

Hint: New head points to old head; last node links to new head [OK]

Common Mistakes:

• Forgetting to update last node's next pointer
• Breaking the circular link by not linking last node
• Replacing last node instead of adding new head

2. Which of the following is the correct syntax to create a new node and insert it at the beginning of a circular linked list in C++?

easy

A. Node* newNode = new Node(data); newNode->next = head; last->next = newNode; head = newNode;

B. Node newNode(data); newNode.next = head; head = &newNode;

C. Node* newNode = new Node(data); newNode->next = head; head = newNode;

D. Node newNode = new Node(data); head = newNode; newNode->next = head;

Solution

1. Step 1: Create new node dynamically

   Use 'new' keyword to allocate memory for new node: Node* newNode = new Node(data);

2. Step 2: Link new node and update pointers

   Set newNode->next to current head, update last node's next to newNode, then update head to newNode.

3. Final Answer:

   Node* newNode = new Node(data); newNode->next = head; last->next = newNode; head = newNode; -> Option A

4. Quick Check:

   Dynamic node + last->next update + head change = C [OK]

Hint: Update last node's next before changing head [OK]

Common Mistakes:

• Not updating last node's next pointer
• Using stack allocation for node causing scope issues
• Assigning head before updating last->next

3. What will be the output of the following code snippet after inserting 10 at the beginning of the circular linked list?

struct Node {
  int data;
  Node* next;
};

Node* head = new Node{20, nullptr};
head->next = head;

// Insert 10 at beginning
Node* newNode = new Node{10, nullptr};
Node* temp = head;
while(temp->next != head) {
  temp = temp->next;
}
newNode->next = head;
temp->next = newNode;
head = newNode;

// Print list
Node* curr = head;
do {
  std::cout << curr->data << " -> ";
  curr = curr->next;
} while(curr != head);
std::cout << "null";

medium

A. 20 -> null

B. 20 -> 10 -> null

C. 10 -> null

D. 10 -> 20 -> null

Solution

1. Step 1: Initial list and insertion

   Initially, list has one node with data 20 pointing to itself. New node 10 is inserted before 20, updating last node's next to new node and head to new node.

2. Step 2: Print traversal

   Traversal starts at head (10), prints 10, moves to 20, prints 20, then back to head stops loop.

3. Final Answer:

   10 -> 20 -> null -> Option D

4. Quick Check:

   New head 10 followed by 20 = A [OK]

Hint: Head changes to new node; print starts from new head [OK]

Common Mistakes:

• Not updating last node's next pointer
• Printing stops too early or infinite loop
• Confusing order of nodes after insertion

4. Identify the error in the following code that attempts to insert a node at the beginning of a circular linked list:

void insertAtBeginning(Node*& head, int data) {
  Node* newNode = new Node{data, nullptr};
  newNode->next = head;
  head = newNode;
  Node* temp = head;
  while(temp->next != head) {
    temp = temp->next;
  }
  temp->next = head;
}

medium

A. The last node's next pointer is updated after changing head, causing infinite loop.

B. The new node is not linked to the old head.

C. The while loop condition is incorrect and never executes.

D. The new node is created on stack instead of heap.

Solution

1. Step 1: Analyze pointer updates order

   The code updates head to newNode before finding the last node, so temp starts at newNode, causing the while loop to never find the last node correctly.

2. Step 2: Consequence of wrong order

   Because last node is not found properly, temp->next = head may not update the correct node, breaking the circular link or causing infinite loops.

3. Final Answer:

   The last node's next pointer is updated after changing head, causing infinite loop. -> Option A

4. Quick Check:

   Update last node before changing head to avoid loop [OK]

Hint: Update last node's next before changing head [OK]

Common Mistakes:

• Changing head before updating last node's next
• Not handling empty list case
• Incorrect while loop condition

5. You have a circular linked list with nodes: 5 -> 15 -> 25 -> (back to 5). You want to insert 1 at the beginning. Which sequence of pointer updates correctly inserts the new node and maintains the circular structure?

hard

A. Create new node with data 1; set newNode->next = head; update head = newNode; find last node and set last->next = newNode;

B. Create new node with data 1; find last node; set last->next = newNode; set newNode->next = head; update head = newNode;

C. Create new node with data 1; update head = newNode; set newNode->next = head; find last node and set last->next = newNode;

D. Create new node with data 1; set newNode->next = nullptr; update head = newNode; find last node and set last->next = newNode;

Solution

1. Step 1: Create new node and find last node

   Create new node with data 1. Traverse list to find last node (node pointing back to head).

2. Step 2: Update pointers in correct order

   Set last->next to newNode, newNode->next to head, then update head to newNode to maintain circular link.

3. Final Answer:

   Create new node with data 1; find last node; set last->next = newNode; set newNode->next = head; update head = newNode; -> Option B

4. Quick Check:

   Last node updated before head change = B [OK]

Hint: Update last node's next before changing head [OK]

Common Mistakes:

• Changing head before updating last node's next
• Setting newNode->next to nullptr breaks circular link
• Incorrect order of pointer updates