Find the Only Non Repeating Element Using XOR in DSA Javascript - Build from Scratch

Find the Only Non Repeating Element Using XOR

📖 Scenario: Imagine you have a list of product IDs scanned at a store. Every product ID appears twice except one product that was scanned only once by mistake. You want to find that unique product ID quickly.

🎯 Goal: You will write a program to find the only product ID that does not repeat in the list using the XOR operation.

📋 What You'll Learn

Create an array called productIDs with the exact values: [4, 1, 2, 1, 2]

Create a variable called uniqueID and set it to 0

Use a for loop with variable id to iterate over productIDs and update uniqueID by XORing it with id

Print the value of uniqueID to display the only non-repeating product ID

💡 Why This Matters

🌍 Real World

Stores and inventory systems often need to find unique or missing items quickly from large lists.

💼 Career

Understanding bitwise operations like XOR helps in optimizing algorithms for performance-critical applications.

1

Create the product ID list

Create an array called productIDs with these exact values: [4, 1, 2, 1, 2]

DSA Javascript

// Create the array productIDs with the values [4, 1, 2, 1, 2]
// Your code here

Hint

Use const productIDs = [4, 1, 2, 1, 2]; to create the array.

2

Initialize the unique ID variable

Create a variable called uniqueID and set it to 0

DSA Javascript

const productIDs = [4, 1, 2, 1, 2];
// Create a variable uniqueID and set it to 0
// Your code here

Hint

Use let uniqueID = 0; to start with zero.

3

Use XOR to find the unique product ID

Use a for loop with variable id to iterate over productIDs and update uniqueID by XORing it with id

DSA Javascript

const productIDs = [4, 1, 2, 1, 2];
let uniqueID = 0;
// Use a for loop with id to XOR uniqueID with each id in productIDs
// Your code here

Hint

Use for (const id of productIDs) { uniqueID ^= id; } to XOR all IDs.

4

Print the unique product ID

Print the value of uniqueID to display the only non-repeating product ID

DSA Javascript

const productIDs = [4, 1, 2, 1, 2];
let uniqueID = 0;
for (const id of productIDs) {
    uniqueID ^= id;
}
// Print uniqueID
// Your code here

Hint

Use console.log(uniqueID); to print the result.

Practice

1. What does the XOR operation do when applied between two identical numbers?

easy

A. It returns 0

B. It returns the number itself

C. It returns 1

D. It returns the sum of the numbers

Solution

1. Step 1: Understand XOR property for identical numbers

   XOR of a number with itself always results in 0 because bits cancel out.

2. Step 2: Apply XOR to example

   For example, 5 ^ 5 = 0 as each bit is the same and cancels.

3. Final Answer:

   It returns 0 -> Option A

4. Quick Check:

   X ^ X = 0 [OK]

Hint: XOR same numbers always zeroes out [OK]

Common Mistakes:

• Thinking XOR returns the number itself
• Confusing XOR with OR operation
• Assuming XOR sums numbers

2. Which of the following is the correct syntax to XOR two variables a and b in JavaScript?

easy

A. a && b

B. a ^ b

C. a xor b

D. a | b

Solution

1. Step 1: Recall JavaScript bitwise XOR operator

   In JavaScript, the XOR operator is represented by the caret symbol ^.

2. Step 2: Check each option

   a ^ b uses ^ correctly. a xor b uses 'xor' which is not valid syntax. Options A and D are logical AND and bitwise OR respectively.

3. Final Answer:

   a ^ b -> Option B

4. Quick Check:

   Use ^ for XOR in JavaScript [OK]

Hint: Use ^ symbol for XOR in JavaScript [OK]

Common Mistakes:

• Using 'xor' keyword
• Confusing XOR with && or ||
• Using | instead of ^

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

const arr = [2, 3, 2, 4, 3];
let result = 0;
for (const num of arr) {
  result ^= num;
}
console.log(result);

medium

A. 2

B. 0

C. 4

D. 3

Solution

1. Step 1: XOR all elements in the array

   Start with result = 0, then XOR with each element: 0 ^ 2 = 2, 2 ^ 3 = 1, 1 ^ 2 = 3, 3 ^ 4 = 7, 7 ^ 3 = 4.

2. Step 2: Final XOR result is the non-repeating element

   The only element that does not repeat is 4, which is the final XOR result.

3. Final Answer:

   4 -> Option C

4. Quick Check:

   Final XOR = 4 [OK]

Hint: XOR all numbers; result is unique element [OK]

Common Mistakes:

• Not starting XOR from 0
• XORing incorrectly in loop
• Assuming sum instead of XOR

4. Identify the error in the following code that tries to find the non-repeating element using XOR:

const arr = [1, 2, 1, 3, 2];
let result;
for (let i = 0; i < arr.length; i++) {
  result ^= arr[i];
}
console.log(result);

medium

A. Variable 'result' is not initialized to 0

B. Loop condition should be i <= arr.length

C. XOR operator is incorrect, should be &&

D. Array should be sorted before XOR

Solution

1. Step 1: Check initialization of 'result'

   The variable 'result' is declared but not initialized, so it is undefined initially.

2. Step 2: Effect of uninitialized 'result' on XOR

   XOR with undefined results in NaN, so the final output will be incorrect. Initializing 'result' to 0 fixes this.

3. Final Answer:

   Variable 'result' is not initialized to 0 -> Option A

4. Quick Check:

   Initialize result = 0 before XOR loop [OK]

Hint: Always initialize XOR accumulator to 0 [OK]

Common Mistakes:

• Not initializing XOR variable
• Using wrong loop condition
• Misusing XOR operator

5. Given an array where every element appears three times except one element which appears once, can XOR be used directly to find the unique element? Why or why not?

hard

A. Yes, but only if the array length is odd

B. Yes, XOR works for any number of repetitions

C. No, because XOR requires sorted arrays

D. No, because XOR only cancels pairs of identical numbers

Solution

1. Step 1: Understand XOR behavior with repeated elements

   XOR cancels out pairs of identical numbers because x ^ x = 0.

2. Step 2: Analyze effect of triply repeated elements

   Elements repeated thrice do not cancel out with XOR because XOR of three identical numbers is the number itself, not zero.

3. Step 3: Conclusion on XOR usage

   Therefore, XOR alone cannot find the unique element if others repeat thrice; other methods are needed.

4. Final Answer:

   No, because XOR only cancels pairs of identical numbers -> Option D

5. Quick Check:

   XOR cancels pairs, not triples [OK]

Hint: XOR cancels pairs only, not triples [OK]

Common Mistakes:

• Assuming XOR works for any repetition count
• Thinking sorting helps XOR
• Confusing XOR with sum or count