Create a Circular Singly Linked List in DSA C - Time & Space Complexity

Time Complexity: Create a Circular Singly Linked List

O(n)

Understanding Time Complexity

When creating a circular singly linked list, we want to know how the time to build it grows as we add more nodes.

We ask: How does the work increase when the list gets longer?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

struct Node* createCircularList(int arr[], int n) {
    if (n == 0) return NULL;
    struct Node* head = malloc(sizeof(struct Node));
    head->data = arr[0];
    struct Node* temp = head;
    for (int i = 1; i < n; i++) {
        temp->next = malloc(sizeof(struct Node));
        temp = temp->next;
        temp->data = arr[i];
    }
    temp->next = head; // Make it circular
    return head;
}
    

This code creates a circular singly linked list from an array of integers.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that creates each new node and links it.
• How many times: It runs once for each element after the first, so (n - 1) times.

How Execution Grows With Input

As the number of elements increases, the loop runs more times, adding one node each time.

Input Size (n)	Approx. Operations
10	About 9 node creations and links
100	About 99 node creations and links
1000	About 999 node creations and links

Pattern observation: The work grows directly with the number of elements; doubling n roughly doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to create the list grows linearly with the number of nodes.

Common Mistake

[X] Wrong: "Creating a circular list takes more time than a normal list because of the circular link."

[OK] Correct: Adding the final link to make the list circular is just one extra step, so it does not change the overall linear time.

Interview Connect

Understanding how list creation scales helps you explain your code clearly and shows you grasp fundamental data structure costs.

Self-Check

"What if we added a step to find the last node each time before linking a new node? How would the time complexity change?"

Practice

1. What is a key characteristic of a circular singly linked list compared to a regular singly linked list?

easy

A. The last node points back to the first node, forming a circle.

B. Each node has two pointers, one to the next and one to the previous node.

C. It uses an array internally to store nodes.

D. The list ends with a null pointer indicating the end.

Solution

1. Step 1: Understand the pointer structure in circular singly linked list

   In a circular singly linked list, the last node's next pointer points back to the first node, creating a loop.

2. Step 2: Compare with regular singly linked list

   Regular singly linked lists end with a null pointer, while circular ones loop back to the start.

3. Final Answer:

   The last node points back to the first node, forming a circle. -> Option A

4. Quick Check:

   Circular list last node points to head = C [OK]

Hint: Remember: circular means last node links back to first [OK]

Common Mistakes:

• Thinking circular list ends with null pointer
• Confusing circular singly linked list with doubly linked list
• Assuming nodes have two pointers in singly linked list

2. Which of the following is the correct way to initialize a circular singly linked list with one node in C?

easy

A. node->next = head->next;

B. node->next = NULL;

C. node->next = node;

D. node->next = 0;

Solution

1. Step 1: Understand initialization of single node circular list

   For a circular singly linked list with one node, the node's next pointer must point to itself to form a circle.

2. Step 2: Check each option

   node->next = node; sets node->next = node, correctly creating a self-loop. Others either set null or incorrect pointers.

3. Final Answer:

   node->next = node; -> Option C

4. Quick Check:

   Single node points to itself = A [OK]

Hint: Single node circular list points to itself [OK]

Common Mistakes:

• Setting next pointer to NULL instead of self
• Using uninitialized pointers
• Confusing NULL with 0 in pointer context

3. Consider the following C code snippet that creates a circular singly linked list with three nodes. What will be the output of the print loop?

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

int main() {
  Node n1 = {1, NULL};
  Node n2 = {2, NULL};
  Node n3 = {3, NULL};

  n1.next = &n2;
  n2.next = &n3;
  n3.next = &n1;  // circular link

  Node* temp = &n1;
  int count = 0;
  while (count < 5) {
    printf("%d ", temp->data);
    temp = temp->next;
    count++;
  }
  return 0;
}

medium

A. 1 2 3 3 3

B. 1 2 3 2 3

C. 1 2 3 1 1

D. 1 2 3 1 2

Solution

1. Step 1: Trace the linked list nodes and their next pointers

   n1 points to n2, n2 points to n3, n3 points back to n1, forming a circle: 1 -> 2 -> 3 -> 1 ...

2. Step 2: Follow the print loop for 5 iterations

   Print order: 1 (n1), 2 (n2), 3 (n3), 1 (n1 again), 2 (n2 again).

3. Final Answer:

   1 2 3 1 2 -> Option D

4. Quick Check:

   Loop prints nodes in circle: 1 2 3 1 2 [OK]

Hint: Follow next pointers in circle for given count [OK]

Common Mistakes:

• Stopping after 3 nodes instead of 5
• Not following circular link back to first node
• Confusing node data values

4. The following code attempts to create a circular singly linked list with two nodes. What is the error?

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

int main() {
  Node* n1 = malloc(sizeof(Node));
  Node* n2 = malloc(sizeof(Node));
  n1->data = 10;
  n2->data = 20;
  n1->next = n2;
  n2->next = NULL;  // mistake here
  return 0;
}

medium

A. Memory allocation is missing for nodes.

B. n2->next should point to n1 to make the list circular.

C. Data values are not initialized correctly.

D. n1->next should be NULL instead of n2.

Solution

1. Step 1: Identify the circular link requirement

   In a circular singly linked list, the last node's next pointer must point back to the first node.

2. Step 2: Check the code's next pointers

   n1->next points to n2, but n2->next is NULL, breaking the circle. It should point to n1.

3. Final Answer:

   n2->next should point to n1 to make the list circular. -> Option B

4. Quick Check:

   Last node next points to head = D [OK]

Hint: Last node's next must link to first node [OK]

Common Mistakes:

• Setting last node next to NULL instead of head
• Forgetting to allocate memory for nodes
• Mixing up which node points where

5. You want to insert a new node with data 5 at the end of an existing circular singly linked list. The list currently has nodes 1 -> 2 -> 3 -> (back to 1). Which steps correctly insert the new node to maintain the circular structure?

hard

A. Create new node; set new_node->next = head; find last node; set last_node->next = new_node;

B. Create new node; set new_node->next = NULL; find last node; set last_node->next = new_node;

C. Create new node; set new_node->next = last_node; set head = new_node;

D. Create new node; set new_node->next = head->next; set head->next = new_node;

Solution

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

   The new node's next pointer must point to the head to keep the circle intact.

2. Step 2: Find the last node and update its next pointer

   Traverse the list to find the last node (which points to head), then set last_node->next to new_node.

3. Final Answer:

   Create new node; set new_node->next = head; find last node; set last_node->next = new_node; -> Option A

4. Quick Check:

   New node next = head, last node next = new node = A [OK]

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

Common Mistakes:

• Setting new node next to NULL breaks circularity
• Not updating last node's next pointer
• Confusing head and last node pointers