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

Time Complexity: Create a Circular Singly Linked List

O(n)

Understanding Time Complexity

When creating a circular singly linked list, it is important to understand how the time needed grows as we add more nodes.

We want to know how long it takes to build the list as its size increases.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

class CircularSinglyLinkedList:
    def __init__(self):
        self.head = None

    def append(self, data):
        new_node = Node(data)
        if not self.head:
            self.head = new_node
            new_node.next = self.head
        else:
            temp = self.head
            while temp.next != self.head:
                temp = temp.next
            temp.next = new_node
            new_node.next = self.head

This code creates a circular singly linked list by adding nodes one by one, linking the last node back to the head.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that finds the last node before the head.
• How many times: It runs once for each node already in the list when appending a new node.

How Execution Grows With Input

Each time we add a new node, we walk through the list to find the last node.

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

Pattern observation: The number of steps grows roughly in a straight line with the number of nodes.

Final Time Complexity

Time Complexity: O(n)

This means adding a new node takes longer as the list grows, because we must find the last node each time.

Common Mistake

[X] Wrong: "Appending a node always takes the same time, no matter how big the list is."

[OK] Correct: Because we must walk through all existing nodes to find the last one, the time grows with the list size.

Interview Connect

Understanding how adding nodes scales helps you explain trade-offs in linked list operations clearly and confidently.

Self-Check

"What if we kept a reference to the last node? How would the time complexity of appending 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 instead of nodes.

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

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

D. The list has a fixed size and cannot grow.

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 list types

   Unlike doubly linked lists, nodes have only one pointer. Unlike arrays, nodes are linked dynamically. The circular nature is unique to this structure where the last node points back to the first node, forming a circle.

3. Final Answer:

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

4. Quick Check:

   Circular list loops back = C [OK]

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

Common Mistakes:

• Confusing circular with doubly linked list
• Thinking nodes have two pointers
• Assuming fixed size like arrays

2. Which of the following is the correct way to initialize an empty circular singly linked list in Python?

easy

A. head = None

B. head = Node(0); head.next = None

C. head = Node(0); head.next = head

D. head = []

Solution

1. Step 1: Understand empty list initialization

   An empty circular singly linked list has no nodes, so head should be None.

2. Step 2: Analyze other options

   head = Node(0); head.next = None sets next to None, which is not circular. head = Node(0); head.next = head creates a node pointing to itself, which is a single-node circular list, not empty. head = [] uses a list, not a linked list.

3. Final Answer:

   head = None -> Option A

4. Quick Check:

   Empty list head = None [OK]

Hint: Empty list means head points to nothing (None) [OK]

Common Mistakes:

• Setting head.next to None in empty list
• Creating a node when list is empty
• Using Python list [] instead of nodes

3. What will be the output of the following code snippet?

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

head = Node(1)
second = Node(2)
third = Node(3)

head.next = second
second.next = third
third.next = head

current = head
result = []
for _ in range(4):
    result.append(current.data)
    current = current.next
print(result)

medium

A. [1, 2, 3, 3]

B. [1, 2, 3, None]

C. [1, 2, 3, 1]

D. RuntimeError due to infinite loop

Solution

1. Step 1: Understand the circular link setup

   Nodes 1, 2, 3 are linked in a circle: 1->2->3->1.

2. Step 2: Trace the loop for 4 iterations

   Starting at head (1), the loop collects data: 1, then moves to 2, then 3, then back to 1.

3. Final Answer:

   [1, 2, 3, 1] -> Option C

4. Quick Check:

   Loop of 3 nodes repeated once = [1,2,3,1] [OK]

Hint: Follow next pointers carefully for given loop count [OK]

Common Mistakes:

• Assuming last node points to None
• Stopping after 3 elements instead of 4
• Confusing data values with node references

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

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

head = Node(10)
head.next = None  # Intended to point to head for circular list

medium

A. Data value 10 is invalid for circular lists

B. Node class is missing a previous pointer

C. head should be initialized as None

D. head.next should point to head, not None

Solution

1. Step 1: Check the pointer assignment for circularity

   For a circular singly linked list with one node, the node's next must point to itself (head), not None.

2. Step 2: Analyze the given code

   The code sets head.next = None, breaking the circular link.

3. Final Answer:

   head.next should point to head, not None -> Option D

4. Quick Check:

   Single node circular list loops to itself [OK]

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

Common Mistakes:

• Setting next to None instead of head
• Confusing singly with doubly linked list
• Thinking data value affects circularity

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. new_node = Node(4)
current = head
while current.next != head:
current = current.next
current.next = new_node
new_node.next = head

B. new_node = Node(4)
new_node.next = head
head.next = new_node

C. new_node = Node(4)
head.next = new_node
new_node.next = None

D. new_node = Node(4)
current = head
while current.next != None:
current = current.next
current.next = new_node
new_node.next = head

Solution

1. Step 1: Locate the last node in the circular list

   Traverse nodes until current.next points back to head, identifying the last node.

2. Step 2: Insert new node after last node and link it back to head

   Set last node's next to new_node, then new_node's next to head to maintain circularity.

3. Final Answer:

   Traverse until current.next != head, then set current.next = new_node and new_node.next = head -> Option A

4. Quick Check:

   Traverse till last node, link new node, maintain circle [OK]

Hint: Find last node by checking next != head, then insert [OK]

Common Mistakes:

• Setting new_node.next to None breaking circularity
• Not traversing to last node correctly
• Assuming head.next is always last node