Add Two Numbers Represented as Linked List in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does each node in the linked list represent in the 'Add Two Numbers Represented as Linked List' problem?

Each node represents a single digit of a number, stored in reverse order (the head node is the least significant digit).

beginner

Why do we add digits starting from the head node in this problem?

Because the digits are stored in reverse order, the head node contains the least significant digit, so addition starts from the units place.

beginner

What is the role of the carry in adding two numbers represented as linked lists?

The carry stores the overflow digit when the sum of two digits exceeds 9, and it is added to the next pair of digits.

intermediate

How do you handle linked lists of different lengths when adding two numbers?

Continue adding digits until both lists are fully traversed, treating missing digits as zero, and include any remaining carry.

intermediate

What is the time complexity of adding two numbers represented as linked lists?

The time complexity is O(max(m, n)), where m and n are the lengths of the two linked lists, because we traverse both lists once.

In the 'Add Two Numbers Represented as Linked List' problem, what does the head node represent?

A The most significant digit

B The least significant digit

C The sum of all digits

D The carry value

The head node stores the least significant digit because the number is stored in reverse order.

What should you do if one linked list is longer than the other during addition?

A Only add nodes that exist in both lists

B Stop when the shorter list ends

C Treat missing nodes as zero and continue

D Ignore the longer list's extra nodes

You treat missing nodes as zero and continue adding until both lists and carry are processed.

What happens if the final carry after adding all digits is not zero?

A It is added as a new node at the end

B It is discarded

C It causes an error

D It is subtracted from the last digit

If carry remains after processing all nodes, it is added as a new node to represent the extra digit.

What data structure is used to represent the numbers in this problem?

A Linked List

B Stack

C Queue

D Array

The problem uses linked lists where each node stores a digit.

What is the main challenge when adding two numbers represented as linked lists?

A Reversing the linked lists

B Sorting the digits

C Multiplying digits

D Handling carry and different lengths

The main challenge is managing the carry and different lengths of the linked lists.

Explain step-by-step how to add two numbers represented as linked lists.

Think about how you add numbers on paper from right to left.

Describe how carry is used and updated during the addition of two linked lists.

Carry is like the extra you keep for the next addition step.

Practice

1. What does the problem "Add Two Numbers Represented as Linked List" ask you to do?

easy

A. Add two numbers where each digit is a node in a linked list, and return the sum as a linked list.

B. Multiply two numbers stored in arrays and return the product as an array.

C. Sort two linked lists and merge them into one sorted list.

D. Find the difference between two numbers represented as linked lists.

Solution

1. Step 1: Understand the problem statement

   The problem requires adding two numbers where each number is represented by a linked list. Each node contains a single digit, and digits are stored in reverse order.

2. Step 2: Identify the expected output

   The output should be a linked list representing the sum of the two numbers, also in reverse order.

3. Final Answer:

   Add two numbers represented as linked lists and return their sum as a linked list -> Option A

4. Quick Check:

   Adding digits node by node = Add linked lists [OK]

Hint: Remember digits are reversed in linked lists [OK]

Common Mistakes:

• Thinking digits are stored in normal order
• Confusing addition with multiplication
• Returning a number instead of a linked list

2. Which of the following is the correct way to create a node for a singly linked list in JavaScript for this problem?

easy

A. function ListNode(val) { this.val = val; this.next = null; }

B. class ListNode { constructor(val) { this.value = val; this.nextNode = null; } }

C. let node = { value: val, next: null };

D. function Node(val) { this.val = val; this.nextNode = null; }

Solution

1. Step 1: Check the standard node structure

   The node should have a property named 'val' for the digit and 'next' for the next node pointer.

2. Step 2: Verify the syntax correctness

   function ListNode(val) { this.val = val; this.next = null; } correctly defines a function constructor with 'val' and 'next' properties initialized properly.

3. Final Answer:

   function ListNode(val) { this.val = val; this.next = null; } -> Option A

4. Quick Check:

   Node with val and next properties = function ListNode(val) { this.val = val; this.next = null; } [OK]

Hint: Use 'val' and 'next' for node properties [OK]

Common Mistakes:

• Using 'value' instead of 'val'
• Using 'nextNode' instead of 'next'
• Incorrect constructor syntax

3. What is the output linked list after adding the two numbers represented by these linked lists? List 1: 2 -> 4 -> 3 -> null (represents 342) List 2: 5 -> 6 -> 4 -> null (represents 465)

function addTwoNumbers(l1, l2) {
  let dummy = new ListNode(0);
  let current = dummy;
  let carry = 0;
  while (l1 || l2 || carry) {
    let sum = carry;
    if (l1) { sum += l1.val; l1 = l1.next; }
    if (l2) { sum += l2.val; l2 = l2.next; }
    carry = Math.floor(sum / 10);
    current.next = new ListNode(sum % 10);
    current = current.next;
  }
  return dummy.next;
}

medium

A. 7 -> 0 -> 7 -> null

B. 7 -> 0 -> 8 -> null

C. 7 -> 1 -> 7 -> null

D. 8 -> 0 -> 7 -> null

Solution

1. Step 1: Add digits node by node with carry

   2+5=7 (carry 0), 4+6=10 (carry 1), 3+4+1=8 (carry 0)

2. Step 2: Form the resulting linked list

   The digits are 7 -> 0 -> 8 representing 807 in reverse order.

3. Final Answer:

   7 -> 0 -> 8 -> null -> Option B

4. Quick Check:

   342 + 465 = 807 = 7->0->8 [OK]

Hint: Add digits with carry, build new nodes [OK]

Common Mistakes:

• Ignoring carry after adding digits
• Mixing digit order in output
• Returning sum as a number, not linked list

4. Identify the bug in the following code snippet for adding two numbers represented as linked lists:

function addTwoNumbers(l1, l2) {
  let dummy = new ListNode(0);
  let current = dummy;
  let carry = 0;
  while (l1 !== null && l2 !== null) {
    let sum = carry + l1.val + l2.val;
    carry = Math.floor(sum / 10);
    current.next = new ListNode(sum % 10);
    current = current.next;
    l1 = l1.next;
    l2 = l2.next;
  }
  return dummy.next;
}

medium

A. The function does not return the dummy node itself.

B. The carry is not calculated correctly using Math.floor.

C. The dummy node should be initialized with value 1 instead of 0.

D. The loop condition should use '||' instead of '&&' to handle lists of different lengths.

Solution

1. Step 1: Analyze the loop condition

   The loop stops when either l1 or l2 becomes null, missing remaining nodes if lists differ in length.

2. Step 2: Correct the loop condition

   Using '||' ensures the loop continues until both lists and carry are fully processed.

3. Final Answer:

   The loop condition should use '||' instead of '&&' to handle lists of different lengths. -> Option D

4. Quick Check:

   Loop condition must cover all nodes = The loop condition should use '||' instead of '&&' to handle lists of different lengths. [OK]

Hint: Use '||' to continue while any list or carry remains [OK]

Common Mistakes:

• Stopping loop too early with '&&'
• Ignoring leftover carry after loop
• Not advancing pointers correctly

5. Given two linked lists representing numbers in reverse order, how would you modify the addition function to handle the case where the input lists have different lengths and the final carry creates a new node? Choose the best approach to ensure correct output for inputs like: List 1: 9 -> 9 -> 9 -> null (represents 999) List 2: 1 -> null (represents 1)

function addTwoNumbers(l1, l2) {
  let dummy = new ListNode(0);
  let current = dummy;
  let carry = 0;
  while (l1 || l2 || carry) {
    let sum = carry;
    if (l1) { sum += l1.val; l1 = l1.next; }
    if (l2) { sum += l2.val; l2 = l2.next; }
    carry = Math.floor(sum / 10);
    current.next = new ListNode(sum % 10);
    current = current.next;
  }
  return dummy.next;
}

hard

A. Add zeros to the shorter list before starting the addition to equalize lengths.

B. Stop the loop when both lists end and ignore carry since it won't affect the sum.

C. Use a loop condition that continues while l1, l2, or carry exists, adding carry as a new node if needed.

D. Only add nodes while both lists have nodes, then append the remaining nodes without addition.

Solution

1. Step 1: Understand the need to handle different lengths and carry

   When lists differ in length, addition must continue until both lists and carry are fully processed.

2. Step 2: Use a loop condition that checks l1, l2, or carry

   This ensures the loop adds all digits and creates a new node if carry remains after lists end.

3. Final Answer:

   Use a loop condition that continues while l1, l2, or carry exists, adding carry as a new node if needed. -> Option C

4. Quick Check:

   Loop until all digits and carry processed = Use a loop condition that continues while l1, l2, or carry exists, adding carry as a new node if needed. [OK]

Hint: Loop while any list or carry remains to add all digits [OK]

Common Mistakes:

• Ignoring carry after lists end
• Trying to pad shorter list manually
• Appending leftover nodes without adding carry