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

Time Complexity: Insert at Beginning of Circular Linked List

O(n)

Understanding Time Complexity

We want to understand how long it takes to add a new node at the start of a circular linked list.

How does the time needed change as the list grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

void insertAtBeginning(struct Node** head, int value) {
    struct Node* newNode = malloc(sizeof(struct Node));
    newNode->data = value;
    if (*head == NULL) {
        newNode->next = newNode;
        *head = newNode;
        return;
    }
    struct Node* temp = *head;
    while (temp->next != *head) {
        temp = temp->next;
    }
    temp->next = newNode;
    newNode->next = *head;
    *head = newNode;
}
    

This code adds a new node at the start of a circular linked list, updating links to keep the circle intact.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that finds the last node in the list.
• How many times: It runs once for each node until it reaches the last node, so it runs n times if the list has n nodes.

How Execution Grows With Input

As the list gets bigger, the loop runs more times to find the last node.

Input Size (n)	Approx. Operations
10	About 10 steps to find last node
100	About 100 steps to find last node
1000	About 1000 steps to find last node

Pattern observation: The number of steps grows directly with the size of the list.

Final Time Complexity

Time Complexity: O(n)

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

Common Mistake

[X] Wrong: "Inserting at the beginning is always O(1) because we just change the head pointer."

[OK] Correct: In a circular linked list, we must also update the last node's next pointer, which requires finding the last node by traversing the list, taking O(n) time.

Interview Connect

Understanding this helps you explain how linked list operations can vary in cost depending on the structure, showing your grasp of data structure details.

Self-Check

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

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