Insert at Beginning of Circular Linked List in DSA Python - 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

In the insertion at beginning operation, which pointers are changed?

The new node's next pointer is set to the old head. The last node's next pointer is updated to the new node. The head pointer is updated to the new node.

intermediate

What is the time complexity of inserting a node at the beginning of a circular linked list if we keep a pointer to the last node?

O(1) because we can directly access the last node to update its next pointer without traversing the list.

In a circular linked list, what does the last node point to?

A Itself

B Null

C The first node

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 head's previous pointer

B The last node's next pointer

C The second node's next pointer

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 The last node

B Null

C The head

D Itself

The new node points to itself to form a single-node circular linked list.

What is the time complexity of inserting at the beginning if you only have a pointer to the head (not the last node)?

A O(n)

B O(1)

C O(log n)

D O(n^2)

Without a pointer to the last node, you must traverse the list to find it, which takes O(n) time.

Which of these is NOT true about circular linked lists?

A They always have a tail node with next as null

B They can be traversed starting from any node

C They have no null pointers

D Insertion at beginning requires updating last node's next

In circular linked lists, the last node's next is not null; it points to the first node.

Explain step-by-step how to insert a new node at the beginning of a circular linked list.

Think about how the circle is maintained after insertion.

Why is it important to update the last node's next pointer when inserting at the beginning of a circular linked list?

Consider what happens if the last node still points to the old first node.

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 becomes the head and points to the old head, maintaining the circular link.

C. The list breaks and becomes a linear linked list.

D. The new node is added at the end and does not affect the head.

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, last node points to new head [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 linking 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 Python?

easy

A. new_node = Node(data); new_node.next = head; head = new_node

B. new_node = Node(data); last.next = head; head = new_node

C. new_node = Node(data); head.next = new_node; new_node.next = head

D. new_node = Node(data); new_node.next = head; last.next = new_node; head = new_node

Solution

1. Step 1: Create new node and link to current head

   We create a new node and set its next pointer to the current head.

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

   Since it's circular, last node's next must point to new node, then update head to new node.

3. Final Answer:

   new_node = Node(data); new_node.next = head; last.next = new_node; head = new_node -> Option D

4. Quick Check:

   New node points to old head, last points to new node, head updated [OK]

Hint: Update last.next to new node before changing head [OK]

Common Mistakes:

• Not updating last.next to new node
• Changing head before updating last.next
• Linking new node incorrectly

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

class Node:
    def __init__(self, data):
        self.data = data
        self.next = None

def print_list(head):
    temp = head
    if head is not None:
        while True:
            print(temp.data, end=' -> ')
            temp = temp.next
            if temp == head:
                break
    print('null')

# Initial circular linked list: 20 -> 30 -> 40 -> null
head = Node(20)
second = Node(30)
third = Node(40)
head.next = second
second.next = third
third.next = head

# Insert 10 at beginning
new_node = Node(10)
new_node.next = head
third.next = new_node
head = new_node

print_list(head)

medium

A. 10 -> 30 -> 40 -> 20 -> null

B. 20 -> 30 -> 40 -> 10 -> null

C. 10 -> 20 -> 30 -> 40 -> null

D. 30 -> 40 -> 20 -> 10 -> null

Solution

1. Step 1: Understand the initial list and insertion

   The list is 20 -> 30 -> 40 -> back to 20. Inserting 10 at beginning means new_node points to old head (20), and last node (40) points to new_node.

2. Step 2: Trace the print_list function

   Starting from new head (10), it prints 10, then 20, then 30, then 40, then stops when it reaches head again.

3. Final Answer:

   10 -> 20 -> 30 -> 40 -> null -> Option C

4. Quick Check:

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

Hint: New head prints first, then old nodes in order [OK]

Common Mistakes:

• Not updating last node's next pointer
• Printing from old head instead of new head
• Confusing order of nodes after insertion

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

def insert_begin(head, data):
    new_node = Node(data)
    new_node.next = head
    head = new_node
    return head

medium

A. The last node's next pointer is not updated to new_node, breaking the circular link.

B. The new_node.next should point to null instead of head.

C. The head should not be updated to new_node.

D. The function should not return head.

Solution

1. Step 1: Check pointer updates for circular list

   In a circular linked list, the last node's next pointer must point to the head node to maintain the circle.

2. Step 2: Identify missing update

   The code updates new_node.next and head but does not update the last node's next pointer to new_node, breaking the circle.

3. Final Answer:

   The last node's next pointer is not updated to new_node, breaking the circular link. -> Option A

4. Quick Check:

   Last node must point to new head to keep circle [OK]

Hint: Always update last.next to new head in circular list [OK]

Common Mistakes:

• Ignoring last node pointer update
• Setting new_node.next to null
• Not returning updated head

5. Given a circular linked list with nodes 5 -> 15 -> 25 -> back to 5, write the steps to insert a new node with value 1 at the beginning and then print the list. What will be the printed output?

hard

A. 1 -> 5 -> 15 -> 25 -> null

B. 5 -> 15 -> 25 -> 1 -> null

C. 1 -> 15 -> 25 -> 5 -> null

D. 25 -> 5 -> 15 -> 1 -> null

Solution

1. Step 1: Insert new node at beginning

   Create new node with value 1, set its next to current head (5), update last node (25) next to new node, then update head to new node.

2. Step 2: Print the circular linked list

   Start from new head (1), print nodes in order: 1, 5, 15, 25, then stop when back to head.

3. Final Answer:

   1 -> 5 -> 15 -> 25 -> null -> Option A

4. Quick Check:

   New head 1 followed by old nodes in order [OK]

Hint: Update last.next before changing head to new node [OK]

Common Mistakes:

• Not updating last node's next pointer
• Printing from old head instead of new head
• Confusing node order after insertion