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

Find the Only Non Repeating Element Using XOR

📖 Scenario: Imagine you have a list of numbers where every number appears twice except for one number that appears only once. You want to find that unique number quickly.

🎯 Goal: Build a TypeScript program that finds the only number in an array that does not repeat, using the XOR operation.

📋 What You'll Learn

Create an array called numbers with the exact values: [2, 3, 5, 4, 5, 3, 4]

Create a variable called unique and set it to 0

Use a for loop with variable num to iterate over numbers and update unique by XORing it with num

Print the value of unique using console.log

💡 Why This Matters

🌍 Real World

Finding unique elements quickly is useful in error detection, data cleaning, and network packet analysis.

💼 Career

Understanding bitwise operations like XOR helps in systems programming, embedded systems, and performance-critical applications.

1

Create the array of numbers

Create an array called numbers with these exact values: [2, 3, 5, 4, 5, 3, 4]

DSA Typescript

# Your code here

Hint

Use const to create the array numbers with the given values.

2

Initialize the unique variable

Create a variable called unique and set it to 0

DSA Typescript

const numbers = [2, 3, 5, 4, 5, 3, 4];
# Your code here

Hint

Use let to create a variable unique and assign it 0.

3

Use XOR to find the unique number

Use a for loop with variable num to iterate over numbers and update unique by XORing it with num inside the loop

DSA Typescript

const numbers = [2, 3, 5, 4, 5, 3, 4];
let unique = 0;
# Your code here

Hint

Use for (const num of numbers) to loop and update unique with unique ^= num.

4

Print the unique number

Print the value of unique using console.log(unique)

DSA Typescript

const numbers = [2, 3, 5, 4, 5, 3, 4];
let unique = 0;
for (const num of numbers) {
    unique ^= num;
}
# Your code here

Hint

Use console.log(unique) to show the unique number.

Practice

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

easy

A. It returns 1

B. It returns the number itself

C. It returns 0

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 XOR 5 = 0.

3. Final Answer:

   It returns 0 -> Option C

4. Quick Check:

   X XOR X = 0 [OK]

Hint: XOR of same numbers is always zero [OK]

Common Mistakes:

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

2. Which of the following TypeScript code snippets correctly initializes a variable to zero for XOR operation?

easy

A. let result = 1;

B. let result = 0;

C. let result = null;

D. let result = undefined;

Solution

1. Step 1: Identify correct initial value for XOR

   For XOR operations, starting with 0 is correct because 0 XOR any number returns that number.

2. Step 2: Check code snippets

   Only let result = 0; correctly initializes for XOR accumulation.

3. Final Answer:

   let result = 0; -> Option B

4. Quick Check:

   Initial XOR value = 0 [OK]

Hint: Start XOR with zero to keep numbers unchanged [OK]

Common Mistakes:

• Starting XOR with 1 instead of 0
• Using null or undefined which cause errors
• Not initializing the variable

3. What is the output of the following TypeScript code?

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

medium

A. 3

B. 0

C. 2

D. 4

Solution

1. Step 1: XOR all elements in the array

   Calculate stepwise: 0 XOR 2 = 2, 2 XOR 3 = 1, 1 XOR 2 = 3, 3 XOR 4 = 7, 7 XOR 3 = 4.

2. Step 2: Identify the non-repeating element

   All repeating numbers cancel out, leaving 4 as the only non-repeating element.

3. Final Answer:

   4 -> Option D

4. Quick Check:

   Result after XOR = 4 [OK]

Hint: XOR all numbers; duplicates cancel out [OK]

Common Mistakes:

• Not XORing all elements
• Confusing output with last element
• Assuming sum instead of XOR

4. Identify the error in this TypeScript code that tries to find the only 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

B. Loop condition is incorrect

C. XOR operator is used wrongly

D. Array is empty

Solution

1. Step 1: Check variable initialization

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

2. Step 2: Understand XOR with undefined

   XOR with undefined causes NaN or runtime error; it must start at 0.

3. Final Answer:

   Variable 'result' is not initialized -> Option A

4. Quick Check:

   Initialize result = 0 before XOR loop [OK]

Hint: Always initialize XOR accumulator to zero [OK]

Common Mistakes:

• Forgetting to initialize result
• Assuming undefined XOR number works
• Incorrect loop boundaries

5. Given an array where every element repeats twice except one element which repeats thrice, can XOR alone find the unique element? Why?

const arr = [5, 5, 5, 7, 7, 8, 8];

hard

A. No, XOR fails because it only cancels pairs, not triples

B. Yes, XOR works because duplicates cancel out

C. Yes, but only if array is sorted

D. No, XOR works only for arrays with all unique elements

Solution

1. Step 1: Understand XOR behavior with odd counts

   XOR cancels even appearances (like twice) to 0, but leaves the result of odd appearances (like thrice: x ^ x ^ x = 0, not x).

2. Step 2: Analyze the given array

   5 appears thrice (odd), 7 and 8 twice (even); XOR of all yields 0, so XOR alone cannot find the unique element repeated thrice.

3. Final Answer:

   No, XOR fails because it only cancels pairs, not triples -> Option A

4. Quick Check:

   XOR fails to find element repeated thrice [OK]

Hint: XOR cancels pairs, fails for triples [OK]

Common Mistakes:

• Thinking XOR works for triples
• Believing sorting is required for XOR
• Confusing XOR with requiring exactly one unique