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

We want to understand how the time needed to create a circular singly linked list changes as we add more nodes.

How does the work grow when the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

Node* createCircularList(int n) {
    if (n == 0) return nullptr;
    Node* head = new Node{1, nullptr};
    Node* curr = head;
    for (int i = 2; i <= n; i++) {
        curr->next = new Node{i, nullptr};
        curr = curr->next;
    }
    curr->next = head; // Make it circular
    return head;
}
    

This code creates a circular singly linked list with n nodes, linking the last node back to the first.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

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

How Execution Grows With Input

Each new node requires one step to create and link, so the total steps grow directly with n.

Input Size (n)	Approx. Operations
10	About 9 steps to add nodes + 1 step to link last to first = 10
100	About 99 steps + 1 linking step = 100
1000	About 999 steps + 1 linking step = 1000

Pattern observation: The work grows evenly as the list size grows; doubling n roughly doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to create the list grows in a straight line with the number of nodes.

Common Mistake

[X] Wrong: "Creating a circular list is faster than a normal list because of the circle link."

[OK] Correct: The extra step to link the last node back to the head is just one operation and does not reduce the overall linear growth of creating all nodes.

Interview Connect

Understanding how list creation scales helps you explain your code clearly and shows you know how data grows in memory.

Self-Check

"What if we added nodes at the end one by one instead of all at once? 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. It uses an array internally to store nodes.

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

C. It cannot be traversed starting from the head node.

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

Solution

1. Step 1: Understand the structure of a 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 other linked lists

   Unlike doubly linked lists (which have two pointers) or arrays, circular singly linked lists have a single pointer per node and form a circle.

3. Final Answer:

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

4. Quick Check:

   Circular list = last node points to first node [OK]

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

Common Mistakes:

• Thinking circular means two pointers per node
• Confusing with doubly linked list
• Assuming it uses arrays internally

2. Which of the following is the correct way to declare a node structure for a circular singly linked list in C++?

easy

A. struct Node { int data; int next; }; // Incorrect pointer type

B. struct Node { int data; Node* prev; Node* next; }; // Doubly linked list node

C. struct Node { int data; Node* next; }; // Correct declaration

D. struct Node { int data; Node next; }; // Incorrect pointer usage

Solution

1. Step 1: Identify the correct node structure for singly linked list

   A singly linked list node has data and a pointer to the next node. The pointer type must be Node*.

2. Step 2: Check each option

   struct Node { int data; Node* next; }; // Correct declaration correctly declares Node* next. struct Node { int data; Node* prev; Node* next; }; // Doubly linked list node has an extra prev pointer (doubly linked list). struct Node { int data; int next; }; // Incorrect pointer type uses int next which is wrong type. struct Node { int data; Node next; }; // Incorrect pointer usage uses Node next which is not a pointer.

3. Final Answer:

   struct Node { int data; Node* next; }; -> Option C

4. Quick Check:

   Single pointer to next node = correct node structure [OK]

Hint: Node must have pointer to next node only [OK]

Common Mistakes:

• Using non-pointer type for next
• Adding prev pointer for singly linked list
• Declaring next as object instead of pointer

3. What will be the output of the following code snippet that creates a circular singly linked list with 3 nodes and prints their data?

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

int main() {
    Node* head = new Node{1, nullptr};
    Node* second = new Node{2, nullptr};
    Node* third = new Node{3, nullptr};

    head->next = second;
    second->next = third;
    third->next = head; // circular link

    Node* temp = head;
    for (int i = 0; i < 5; i++) {
        std::cout << temp->data << " ";
        temp = temp->next;
    }
    return 0;
}

medium

A. 1 2 3 1 2

B. 1 2 3 3 3

C. 1 2 3 4 5

D. 1 2 3 1 1

Solution

1. Step 1: Understand the circular link setup

   The last node (third) points back to head, so the list loops: 1 -> 2 -> 3 -> 1 -> ...

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

   Starting at head (1), print 1, move to 2, print 2, move to 3, print 3, move to 1, print 1, move to 2, print 2.

3. Final Answer:

   1 2 3 1 2 -> Option A

4. Quick Check:

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

Hint: Circular list repeats nodes after last one [OK]

Common Mistakes:

• Assuming list ends after 3 nodes
• Printing wrong data due to pointer errors
• Confusing circular with linear list output

4. Identify the error in the following code that attempts to create a circular singly linked list with one node:

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

int main() {
    Node* head = new Node{10, nullptr};
    head->next = nullptr; // Intended to make circular
    return 0;
}

medium

A. Memory leak due to missing delete statement.

B. head->next should point to head, not nullptr, to form a circular list.

C. Using nullptr for next is correct for circular list.

D. Node declaration is missing a constructor.

Solution

1. Step 1: Check how circular link is formed

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

2. Step 2: Identify the mistake in the code

   The code sets head->next = nullptr, which breaks the circular property.

3. Final Answer:

   head->next should point to head, not nullptr, to form a circular list. -> Option B

4. Quick Check:

   One node circular list: next points to itself [OK]

Hint: One node circular list points next to itself [OK]

Common Mistakes:

• Setting next to nullptr instead of self
• Confusing circular with linear list
• Ignoring memory management issues (not relevant here)

5. You want to insert a new node with value 4 at the end of an existing circular singly linked list with nodes 1 -> 2 -> 3 -> back to 1. Which of the following code snippets correctly performs this insertion?

hard

A. Node* newNode = new Node{4, head};
Node* temp = head;
while (temp->next != head) temp = temp->next;
temp->next = newNode;

B. Node* newNode = new Node{4, nullptr};
Node* temp = head;
while (temp->next != nullptr) temp = temp->next;
temp->next = newNode;
newNode->next = head;

C. Node* newNode = new Node{4, head};
head->next = newNode;

D. Node* newNode = new Node{4, nullptr};
newNode->next = head;
head = newNode;

Solution

1. Step 1: Understand insertion at end in circular singly linked list

   To insert at end, find last node (whose next points to head), then link new node to head and last node to new node.

2. Step 2: Analyze each option

   Node* newNode = new Node{4, head}; Node* temp = head; while (temp->next != head) temp = temp->next; temp->next = newNode; correctly creates new node pointing to head, finds last node by looping until temp->next == head, then sets last node's next to new node. Node* newNode = new Node{4, nullptr}; Node* temp = head; while (temp->next != nullptr) temp = temp->next; temp->next = newNode; newNode->next = head; incorrectly checks for nullptr which does not exist in circular list. Node* newNode = new Node{4, head}; head->next = newNode; incorrectly sets head->next to new node, breaking list. Node* newNode = new Node{4, nullptr}; newNode->next = head; head = newNode; changes head pointer incorrectly and does not update last node's next.

3. Final Answer:

   Node* newNode = new Node{4, head}; Node* temp = head; while (temp->next != head) temp = temp->next; temp->next = newNode; -> Option A

4. Quick Check:

   Find last node by next == head, link new node to head, last node to new node [OK]

Hint: Loop until next points to head to find last node [OK]

Common Mistakes:

• Checking for nullptr in circular list
• Not updating last node's next pointer
• Incorrectly changing head pointer