Insert at Beginning of Circular Linked List in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a circular linked list?

A circular linked list is a linked list where the last node points back to the first node, forming a circle. There is no NULL at the end.

intermediate

Why do we need to update the last node when inserting at the beginning of a circular linked list?

Because the last node points to the first node, when we insert a new node at the beginning, the last node's next pointer must be updated to point to the new first node.

beginner

What happens if the circular linked list is empty and we insert a node at the beginning?

The new node points to itself, making it both the first and last node, forming a single-node circular linked list.

intermediate

Show the steps to insert a new node at the beginning of a non-empty circular linked list.

1. Create new node with data.
2. Find the last node (node whose next points to head).
3. Set new node's next to head.
4. Set last node's next to new node.
5. Update head to new node.

intermediate

What is the time complexity of inserting at the beginning of a circular linked list if we do not keep a tail pointer?

O(n), because we need to traverse the list to find the last node before updating its next pointer.

In a circular linked list, what does the last node's next pointer point to?

A The first node

B NULL

C Itself

D The second node

In a circular linked list, the last node points back to the first node to form a circle.

When inserting at the beginning of a circular linked list, which pointer must be updated besides the new node's next?

A The last node's next pointer

B The second node's next pointer

C The head pointer only

D No other pointer

The last node's next pointer must point to the new first node to maintain the circular structure.

If the circular linked list is empty, what should the new node's next pointer point to after insertion at beginning?

A NULL

B Itself

C Head

D Last node

For a single node circular linked list, the node points to itself.

What is the time complexity of inserting at the beginning of a circular linked list without a tail pointer?

A O(1)

B O(log n)

C O(n)

D O(n^2)

Finding the last node requires traversing the list, which takes O(n) time.

Which of the following is true about circular linked lists?

A They are the same as doubly linked lists

B They always have a NULL pointer at the end

C They cannot be empty

D They can be traversed starting from any node

Because the list is circular, you can start traversal from any node and visit all nodes.

Explain how to insert a new node at the beginning of a circular linked list and why updating the last node is necessary.

Think about the circular link from last node to first node.

Describe the difference in insertion steps when the circular linked list is empty versus when it has nodes.

Consider the special case of a single node.

Practice

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

easy

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

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

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

D. The list becomes a linear linked list instead of circular.

Solution

1. Step 1: Understand the circular linked list structure

   A circular linked list has its last node pointing 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 B

4. Quick Check:

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

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

Common Mistakes:

• Forgetting to update last node's next pointer
• Breaking the circular link by not connecting last node
• Replacing the 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. head = new_node; new_node->next = head; last->next = head;

B. head = new_node; new_node->next = last; last = head;

C. last->next = new_node; new_node->next = head; head = new_node;

D. new_node->next = NULL; head = new_node; last->next = NULL;

Solution

1. Step 1: Link new node to current head

   Set new_node->next to head so new node points to old first node.

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

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

3. Final Answer:

   last->next = new_node; new_node->next = head; head = new_node; -> Option C

4. Quick Check:

   New node links head and last points to new node [OK]

Hint: Link new node between last and head, then update head [OK]

Common Mistakes:

• Setting new_node->next to NULL breaks circular link
• Updating head before linking last node
• Confusing order of pointer assignments

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;
  struct Node* next;
};

// Existing list: 20 -> 30 -> 40 -> back to 20
struct Node* head = node20;
struct Node* last = node40;

// Insert 10 at beginning
struct Node* new_node = malloc(sizeof(struct Node));
new_node->data = 10;
new_node->next = head;
last->next = new_node;
head = new_node;

// Print list starting from head (print 4 nodes)

medium

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

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

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

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

Solution

1. Step 1: Insert new node at beginning

   New node with data 10 points to old head (20), last node (40) points to new node, head updated to new node.

2. Step 2: Print nodes starting from new head

   Printing 4 nodes from head: 10, 20, 30, 40, then back to 10.

3. Final Answer:

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

4. Quick Check:

   New head 10 followed by old nodes in order [OK]

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

Common Mistakes:

• Not updating last->next to new node
• Printing old head as start
• Mixing node order after insertion

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

void insertAtBeginning(struct Node** head, int data) {
  struct Node* new_node = malloc(sizeof(struct Node));
  new_node->data = data;
  new_node->next = *head;
  *head = new_node;
}

medium

A. The head pointer is not updated to new node.

B. The new node's data is not assigned correctly.

C. Memory allocation is missing for new node.

D. The last node's next pointer is not updated to new head, breaking circular link.

Solution

1. Step 1: Check pointer updates

   The code updates head to new node and new node points to old head, but does not update last node's next pointer.

2. Step 2: Understand circular link maintenance

   In circular linked list, last node must point to new head to keep circle intact; missing here causes broken link.

3. Final Answer:

   The last node's next pointer is not updated to new head, breaking circular link. -> Option D

4. Quick Check:

   Last node must point to new head [OK]

Hint: Always update last node's next to new head [OK]

Common Mistakes:

• Ignoring last node pointer update
• Assuming head update is enough
• Not handling empty list case

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 maintains the circular linked list?

hard

A. Create new node with 1, set last->next = new_node, new_node->next = head, head = new_node.

B. Create new node with 1, set head = new_node, new_node->next = head, update last->next = new_node.

C. Create new node with 1, set new_node->next = NULL, head = new_node, last->next = head.

D. Create new node with 1, set head = new_node, new_node->next = last, last->next = head.

Solution

1. Step 1: Link new node between last and head

   Set last->next to new node, then new_node->next to old head to maintain circle.

2. Step 2: Update head pointer

   Set head to new node so it becomes the first node in the list.

3. Final Answer:

   Create new node with 1, set last->next = new_node, new_node->next = head, head = new_node. -> Option A

4. Quick Check:

   Last points new node, new node points old head, head updated [OK]

Hint: Last points new node, new node points old head, update head last [OK]

Common Mistakes:

• Setting new_node->next to NULL breaks circle
• Updating head before linking last node
• Confusing pointer order causing broken links