Create a Circular Singly Linked List in DSA Typescript

Mental Model

A circular singly linked list is like a chain where the last link connects back to the first, forming a circle.

Analogy: Imagine a round table where people sit in a circle; each person points to the next person, and the last person points back to the first, so you can keep going around without stopping.

head -> [1] -> [2] -> [3] -> back to head (1)
          ↑                        ↓
          ← ← ← ← ← ← ← ← ← ← ← ←

Dry Run Walkthrough

Input: Create circular singly linked list with values 1, 2, 3 in order

Goal: Build a circular list where last node points back to the first node

Step 1: Create node with value 1 and set it as head

head -> [1] -> null

Why: We start the list with the first node

Step 2: Create node with value 2 and link it after node 1

head -> [1] -> [2] -> null

Why: Add second node to the list

Step 3: Create node with value 3 and link it after node 2

head -> [1] -> [2] -> [3] -> null

Why: Add third node to the list

Step 4: Link last node (3) back to head (1) to form circle

head -> [1] -> [2] -> [3] -> back to head (1)

Why: Make the list circular by connecting last node to first

Result:

head -> [1] -> [2] -> [3] -> back to head (1)

Annotated Code

DSA Typescript

class Node {
  value: number;
  next: Node | null;
  constructor(value: number) {
    this.value = value;
    this.next = null;
  }
}

class CircularSinglyLinkedList {
  head: Node | null;
  constructor() {
    this.head = null;
  }

  createFromArray(values: number[]): void {
    if (values.length === 0) return;
    this.head = new Node(values[0]);
    let current = this.head;
    for (let i = 1; i < values.length; i++) {
      current.next = new Node(values[i]);
      current = current.next; // advance current to new node
    }
    current.next = this.head; // link last node back to head to form circle
  }

  printList(): void {
    if (!this.head) {
      console.log('List is empty');
      return;
    }
    let current = this.head;
    const values = [];
    do {
      values.push(current.value);
      current = current.next!; // advance current to next node
    } while (current !== this.head);
    console.log(values.join(' -> ') + ' -> back to head (' + this.head.value + ')');
  }
}

// Driver code
const list = new CircularSinglyLinkedList();
list.createFromArray([1, 2, 3]);
list.printList();

this.head = new Node(values[0]);

initialize head with first value

current.next = new Node(values[i]);

link new node after current

current = current.next; // advance current to new node

move current pointer forward to newly added node

current.next = this.head; // link last node back to head to form circle

connect last node to head to make list circular

do { values.push(current.value); current = current.next!; } while (current !== this.head);

traverse circular list once to collect values for printing

Output

1 -> 2 -> 3 -> back to head (1)

Complexity Analysis

Time: O(n) because we create and link n nodes once

Space: O(n) because we store n nodes in memory

vs Alternative: Compared to a linear singly linked list, circular list adds a single extra link from last node to head, no extra traversal cost for creation

Edge Cases

empty input array

list remains empty, no nodes created

DSA Typescript

if (values.length === 0) return;

single element array

one node created that points to itself forming a single-node circle

DSA Typescript

current.next = this.head; // link last node back to head to form circle

When to Use This Pattern

When you need a list that loops back to start for repeated cycling, use circular singly linked list to avoid null ends and enable continuous traversal.

Common Mistakes

Mistake: Forgetting to link the last node back to the head, leaving the list linear
Fix: Add the line that sets last node's next pointer to head after all nodes are created

Mistake: Not handling empty input array, causing errors
Fix: Check if input array is empty and return early to avoid null pointer issues

Summary

Creates a linked list where the last node points back to the first, forming a circle.

Use when you want to cycle through elements repeatedly without stopping.

The key is linking the last node's next pointer back to the head node.

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 always has a fixed size.

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

   Regular singly linked lists end with a null pointer, doubly linked lists have two pointers per node, and arrays are not linked lists.

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 = A [OK]

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

Common Mistakes:

• Thinking circular means doubly linked
• Assuming last node points to null
• Confusing arrays with linked lists

2. Which of the following TypeScript code snippets correctly initializes an empty circular singly linked list?

easy

A. let head: Node = null; head.next = head;

B. let head: Node | null = null;

C. let head: Node | null = new Node(null); head.next = null;

D. let head: Node = new Node(null); head.next = head;

Solution

1. Step 1: Understand initialization of circular singly linked list

   For an empty circular singly linked list with one node, the node's next pointer should point to itself.

2. Step 2: Analyze each option

   let head: Node = new Node(null); head.next = head; creates a node and sets its next to itself, correctly forming a circular list with one node. let head: Node | null = null; sets head to null (empty list, but not circular). let head: Node | null = new Node(null); head.next = null; sets next to null (not circular). let head: Node = null; head.next = head; tries to assign next on null (error).

3. Final Answer:

   let head: Node = new Node(null); head.next = head; -> Option D

4. Quick Check:

   One node points to itself = A [OK]

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

Common Mistakes:

• Setting next to null instead of self
• Assigning next on null variable
• Not creating a node before linking

3. Given the following TypeScript code for a circular singly linked list, what will be the output after inserting nodes with values 1, 2, and 3 in order?

class Node {
  value: number;
  next: Node | null;
  constructor(value: number) {
    this.value = value;
    this.next = null;
  }
}

class CircularList {
  head: Node | null = null;

  insert(value: number) {
    const newNode = new Node(value);
    if (!this.head) {
      this.head = newNode;
      newNode.next = this.head;
    } else {
      let temp = this.head;
      while (temp.next !== this.head) {
        temp = temp.next!;
      }
      temp.next = newNode;
      newNode.next = this.head;
    }
  }

  print() {
    if (!this.head) return '';
    let result = '';
    let temp = this.head;
    do {
      result += temp.value + ' -> ';
      temp = temp.next!;
    } while (temp !== this.head);
    result += 'null';
    return result;
  }
}

const list = new CircularList();
list.insert(1);
list.insert(2);
list.insert(3);
console.log(list.print());

medium

A. 1 -> 2 -> 3 -> 1 -> null

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

C. 1 -> 2 -> 3 -> null

D. 1 -> 2 -> 3

Solution

1. Step 1: Trace insertions and list structure

   Insert 1: head points to node 1, node 1 next points to itself.
   Insert 2: find last node (1), set last node's next to new node 2, new node 2 next points to head (1).
   Insert 3: find last node (2), set last node's next to new node 3, new node 3 next points to head (1).

2. Step 2: Trace print method output

   Print starts at head (1), prints 1 -> 2 -> 3 -> then stops when it reaches head again, appends 'null'.

3. Final Answer:

   1 -> 2 -> 3 -> null -> Option C

4. Quick Check:

   Print stops at head, adds null = B [OK]

Hint: Print stops when node loops back to head [OK]

Common Mistakes:

• Printing extra head node again
• Missing 'null' at end
• Infinite loop without stopping condition

4. Identify the bug in this TypeScript method for inserting a node into a circular singly linked list:

insert(value: number) {
  const newNode = new Node(value);
  if (!this.head) {
    this.head = newNode;
    newNode.next = null;
  } else {
    let temp = this.head;
    while (temp.next !== this.head) {
      temp = temp.next!;
    }
    temp.next = newNode;
    newNode.next = this.head;
  }
}

medium

A. The method does not create a new node correctly.

B. newNode.next should point to head, not null, when list is empty.

C. The while loop condition should be temp.next === null.

D. The head should be set to null after insertion.

Solution

1. Step 1: Analyze insertion when list is empty

   When the list is empty, newNode.next is set to null, breaking circular property. It should point to head to form a circle.

2. Step 2: Check loop condition and other logic

   The while loop correctly finds the last node by checking temp.next !== head. Other parts are correct.

3. Final Answer:

   newNode.next should point to head, not null, when list is empty. -> Option B

4. Quick Check:

   Empty list node next must point to itself = C [OK]

Hint: Empty list node next must point to itself, not null [OK]

Common Mistakes:

• Setting next to null breaks circular link
• Wrong loop condition causes infinite loop
• Resetting head incorrectly

5. You want to implement a method delete(value: number) to remove a node with a given value from a circular singly linked list. Which approach correctly handles deleting the head node while maintaining the circular structure?

hard

A. Find the last node, set its next to head.next, then update head to head.next.

B. Set head to null directly without updating any other node.

C. Set head.next to null and keep head unchanged.

D. Remove the node by setting head to head.next without updating last node's next.

Solution

1. Step 1: Understand deleting head in circular list

   To delete the head, we must update the last node's next pointer to the new head (head.next) to maintain the circle.

2. Step 2: Analyze each option

   Find the last node, set its next to head.next, then update head to head.next. correctly finds last node, updates its next to head.next, then moves head to head.next.
   Set head to null directly without updating any other node. breaks the list by setting head to null without fixing last node.
   Set head.next to null and keep head unchanged. breaks the circle by setting head.next to null.
   Remove the node by setting head to head.next without updating last node's next. moves head but leaves last node pointing to old head, breaking the circle.

3. Final Answer:

   Find the last node, set its next to head.next, then update head to head.next. -> Option A

4. Quick Check:

   Last node next updated to new head = D [OK]

Hint: Update last node's next when deleting head [OK]

Common Mistakes:

• Not updating last node's next pointer
• Setting head to null without cleanup
• Breaking circular link by null assignments