Creating a Singly Linked List from Scratch in DSA Javascript - Complexity Walkthrough

Time Complexity: Creating a Singly Linked List from Scratch

O(n^2)

Understanding Time Complexity

When we create a singly linked list from scratch, we add nodes one by one. Understanding time complexity helps us see how the work grows as we add more nodes.

We want to know how the time to build the list changes as the number of nodes increases.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

class SinglyLinkedList {
  constructor() {
    this.head = null;
  }

  append(value) {
    const newNode = new Node(value);
    if (!this.head) {
      this.head = newNode;
      return;
    }
    let current = this.head;
    while (current.next) {
      current = current.next;
    }
    current.next = newNode;
  }
}

const list = new SinglyLinkedList();
const n = 10; // Added definition for n
for (let i = 1; i <= n; i++) {
  list.append(i);
}
    

This code creates a singly linked list by adding nodes at the end one by one.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop inside append that moves through the list to find the last node.
• How many times: For each new node, it traverses from the head to the end, which grows as the list grows.

How Execution Grows With Input

As we add more nodes, each append takes longer because it walks through the list to find the end.

Input Size (n)	Approx. Operations
10	1 + 2 + 3 + ... + 10 = 55 steps
100	1 + 2 + ... + 100 = 5050 steps
1000	1 + 2 + ... + 1000 = 500500 steps

Pattern observation: The total steps grow roughly like the square of the number of nodes.

Final Time Complexity

Time Complexity: O(n2)

This means the time to build the whole list grows very quickly as we add more nodes, because each new node requires walking through the entire list.

Common Mistake

[X] Wrong: "Appending a node always takes the same time, so building the list is O(n)."

[OK] Correct: Each append walks through the list to find the end, so the time grows with the list size, making the total time grow much faster.

Interview Connect

Understanding how linked list operations scale helps you explain trade-offs clearly and shows you know how data structure choices affect performance.

Self-Check

"What if we kept a reference to the tail node to avoid walking the list each time? How would the time complexity change?"

Practice

1. What is the main purpose of a Singly Linked List in data structures?

easy

A. To store elements with random access by index

B. To store elements in a tree-like hierarchy

C. To store elements in a linear order where each element points to the next one

D. To store elements in a fixed-size array

Solution

1. Step 1: Understand the structure of a singly linked list

   A singly linked list stores elements in nodes where each node points to the next node, forming a chain.

2. Step 2: Compare with other data structures

   Unlike arrays or trees, singly linked lists do not support random access or hierarchical storage.

3. Final Answer:

   To store elements in a linear order where each element points to the next one -> Option C

4. Quick Check:

   Singly linked list = linear chain of nodes [OK]

Hint: Remember: singly linked list is a chain of nodes [OK]

Common Mistakes:

• Confusing linked list with arrays
• Thinking linked list supports random access
• Mixing linked list with tree structures

2. Which of the following is the correct way to define a Node class for a singly linked list in JavaScript?

easy

A. class Node { constructor(value) { this.next = value; this.value = null; } }

B. class Node { constructor(value) { this.value = value; this.next = null; } }

C. class Node { constructor() { this.value = null; this.next = null; } }

D. class Node { constructor(value) { this.value = null; this.next = value; } }

Solution

1. Step 1: Identify the correct property assignments for a node

   A node should store the given value and have a pointer to the next node, initially null.

2. Step 2: Check each option's constructor

   class Node { constructor(value) { this.value = value; this.next = null; } } correctly assigns value and sets next to null. Others assign incorrectly or swap properties.

3. Final Answer:

   class Node { constructor(value) { this.value = value; this.next = null; } } -> Option B

4. Quick Check:

   Node stores value and next pointer [OK]

Hint: Node must store value and next=null initially [OK]

Common Mistakes:

• Swapping value and next assignments
• Not initializing next to null
• Leaving value or next undefined

3. What will be the output after running this code?

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

class LinkedList {
  constructor() {
    this.head = null;
  }
  add(value) {
    const newNode = new Node(value);
    if (!this.head) {
      this.head = newNode;
    } else {
      let current = this.head;
      while (current.next) {
        current = current.next;
      }
      current.next = newNode;
    }
  }
  print() {
    let current = this.head;
    let result = '';
    while (current) {
      result += current.value + ' -> ';
      current = current.next;
    }
    result += 'null';
    console.log(result);
  }
}

const list = new LinkedList();
list.add(10);
list.add(20);
list.add(30);
list.print();

medium

A. 10 -> 20 -> 30 -> null

B. 30 -> 20 -> 10 -> null

C. 10 -> 20 -> null

D. null

Solution

1. Step 1: Trace the add method calls

   Adding 10 sets head to node with value 10. Adding 20 and 30 appends nodes at the end.

2. Step 2: Trace the print method

   Print traverses from head: 10, then 20, then 30, then null.

3. Final Answer:

   10 -> 20 -> 30 -> null -> Option A

4. Quick Check:

   Nodes added in order, printed in order [OK]

Hint: Add appends at end; print shows nodes in insertion order [OK]

Common Mistakes:

• Assuming add inserts at head
• Printing nodes in reverse order
• Missing last node in print

4. Identify the error in this linked list add method and select the fix:

add(value) {
  const newNode = new Node(value);
  if (this.head === null) {
    this.head = newNode;
  } else {
    let current = this.head;
    while (current.next !== null) {
      current = current.next;
    }
    current = newNode;
  }
}

medium

A. Replace current = newNode; with current.next = newNode;

B. Replace this.head = newNode; with this.head.next = newNode;

C. Remove the while loop entirely

D. Change if (this.head === null) to if (!this.head.next)

Solution

1. Step 1: Understand the purpose of the while loop

   The loop finds the last node where current.next is null.

2. Step 2: Identify the mistake in assignment

   Assigning current = newNode; only changes the local variable, not the list. It should link the last node's next to newNode.

3. Final Answer:

   Replace current = newNode; with current.next = newNode; -> Option A

4. Quick Check:

   Link last node's next to new node [OK]

Hint: Assign newNode to current.next, not current [OK]

Common Mistakes:

• Assigning newNode to current variable instead of current.next
• Changing head incorrectly
• Removing necessary traversal loop

5. You want to create a method remove(value) in your singly linked list that deletes the first node with the given value. Which approach correctly handles removing the head node and other nodes?

hard

A. Remove node by setting head = null if value matches, else do nothing

B. Always traverse from head and remove node by setting current = current.next without checking head separately

C. Traverse list and remove node by setting current.next = null when value matches

D. Check if head has the value, update head to head.next; else traverse and update previous.next to current.next when found

Solution

1. Step 1: Handle removal of head node

   If the head node contains the value, update head to head.next to remove it.

2. Step 2: Traverse and remove non-head nodes

   Traverse nodes keeping track of previous; when node with value found, set previous.next to current.next to unlink it.

3. Final Answer:

   Check if head has the value, update head to head.next; else traverse and update previous.next to current.next when found -> Option D

4. Quick Check:

   Remove head or unlink node by adjusting pointers [OK]

Hint: Handle head removal separately, then unlink nodes [OK]

Common Mistakes:

• Not updating head when removing first node
• Breaking links incorrectly causing list loss
• Setting current.next = null removes too much