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

Time Complexity: Insert at End of Circular Linked List

O(n)

Understanding Time Complexity

We want to understand how the time to insert a node at the end 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;
    struct Node* next;
};

void insertEnd(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 inserts a new node at the end of a circular linked list by traversing to the last node.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that moves through the list to find the last node.
• How many times: It runs once for each node until it reaches the last node, so roughly n times for a list of size n.

How Execution Grows With Input

As the list grows, the number of steps to find the last node grows linearly.

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

Pattern observation: The steps increase directly with the number of nodes; doubling nodes doubles the steps.

Final Time Complexity

Time Complexity: O(n)

This means the time to insert at the end grows in direct proportion to the list size.

Common Mistake

[X] Wrong: "Inserting at the end is always quick and takes constant time."

[OK] Correct: Because we must find the last node by moving through the list, which takes longer as the list grows.

Interview Connect

Understanding this helps you explain how linked list operations scale and shows you can analyze code beyond just writing it.

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 a circular linked list that currently has 3 nodes?

easy

A. The new node becomes the head node and points to the second node.

B. The new node becomes the last node and points back to the head node.

C. The new node is inserted in the middle of the list.

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

Solution

1. Step 1: Understand 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 end

   The new node is linked after the current last node, and its next pointer points to the head node, maintaining the circle.

3. Final Answer:

   The new node becomes the last node and points back to the head node. -> Option B

4. Quick Check:

   New node points to head, preserving circular link [OK]

Hint: New end node always points to head in circular list [OK]

Common Mistakes:

• Forgetting to link new node back to head
• Inserting node at wrong position
• Breaking the circular link

2. Which of the following is the correct syntax to create a new node in C for a circular linked list?

easy

A. struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));

B. newNode = malloc(sizeof(Node));

C. struct Node newNode = malloc(sizeof(struct Node));

D. Node* newNode = new Node();

Solution

1. Step 1: Allocate memory for new node

   In C, use malloc with sizeof(struct Node) and cast to (struct Node*).

2. Step 2: Correct pointer declaration

   Declare newNode as a pointer to struct Node to hold the allocated memory address.

3. Final Answer:

   struct Node* newNode = (struct Node*)malloc(sizeof(struct Node)); -> Option A

4. Quick Check:

   Proper malloc and pointer cast in C [OK]

Hint: Use malloc with sizeof(struct Node) and cast to struct Node* [OK]

Common Mistakes:

• Missing (struct Node*) cast
• Declaring newNode as struct Node instead of pointer
• Using C++ style new operator in C

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

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

void printList(struct Node* head) {
  struct Node* temp = head;
  if (head != NULL) {
    do {
      printf("%d -> ", temp->data);
      temp = temp->next;
    } while (temp != head);
  }
  printf("NULL\n");
}

int main() {
  struct Node* head = (struct Node*)malloc(sizeof(struct Node));
  struct Node* second = (struct Node*)malloc(sizeof(struct Node));
  struct Node* third = (struct Node*)malloc(sizeof(struct Node));

  head->data = 1; head->next = second;
  second->data = 2; second->next = third;
  third->data = 3; third->next = head;

  // Insert new node with data 4 at end
  struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
  newNode->data = 4;
  newNode->next = head;
  third->next = newNode;

  printList(head);
  return 0;
}

medium

A. 1 -> 2 -> 3 -> 4 -> 1 -> ... (infinite loop)

B. 1 -> 2 -> 3 -> NULL

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

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

Solution

1. Step 1: Understand list before insertion

   Initial list is 1 -> 2 -> 3 -> back to 1 (circular).

2. Step 2: Insert new node at end

   New node with data 4 points to head; third node points to new node, extending list to 1 -> 2 -> 3 -> 4 -> back to 1.

3. Step 3: Print list

   printList prints nodes until it reaches head again, so output is 1 -> 2 -> 3 -> 4 -> NULL.

4. Final Answer:

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

5. Quick Check:

   New node added at end, circular link maintained [OK]

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

Common Mistakes:

• Printing infinite loop by not stopping at head
• Forgetting to update last node's next pointer
• Incorrect print format

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

void insertEnd(struct Node** head, int data) {
  struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
  newNode->data = data;
  newNode->next = *head;

  struct Node* temp = *head;
  while (temp->next != NULL) {
    temp = temp->next;
  }
  temp->next = newNode;
}

medium

A. The function should not use double pointer for head.

B. newNode->next should be NULL instead of *head.

C. The while loop condition should check for temp->next != *head instead of NULL.

D. Memory allocation for newNode is missing.

Solution

1. Step 1: Analyze loop condition in circular list

   In a circular linked list, last node's next points to head, not NULL.

2. Step 2: Correct loop condition

   Loop should continue until temp->next equals head, not NULL, to find last node.

3. Final Answer:

   The while loop condition should check for temp->next != *head instead of NULL. -> Option C

4. Quick Check:

   Loop must detect circular end by comparing to head [OK]

Hint: In circular list, last node points to head, not NULL [OK]

Common Mistakes:

• Using NULL to detect end in circular list
• Setting newNode->next to NULL
• Not updating last node's next pointer

5. You have a circular linked list with only one node where head points to itself. You want to insert a new node at the end. Which sequence of steps correctly updates the list?

hard

A. Create new node, set newNode->next = head->next, set head->next = newNode.

B. Create new node, set newNode->next = head, set head->next = newNode, then update head to newNode.

C. Create new node, set newNode->next = NULL, set head->next = newNode.

D. Create new node, set newNode->next = newNode, set head = newNode.

Solution

1. Step 1: Understand single node circular list

   The single node has head->next pointing to itself (head).

2. Step 2: Insert at end

   Set newNode->next = head->next (which is head), then head->next = newNode. This makes head -> newNode -> head, maintaining circularity without changing head.

3. Final Answer:

   Create new node, set newNode->next = head->next, set head->next = newNode. -> Option A

4. Quick Check:

   head -> newNode -> head [OK]

Hint: For single node circular: newNode->next = head->next; head->next = newNode [OK]

Common Mistakes:

• Setting newNode->next to NULL breaking circularity
• Unnecessarily updating head to newNode
• Incorrectly linking new node to itself