Find the Only Non Repeating Element Using XOR in DSA Typescript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this XOR-based function?

Given the array [2, 3, 5, 4, 5, 3, 4], what will the function return?

DSA Typescript

function findUnique(arr: number[]): number {
  let result = 0;
  for (const num of arr) {
    result ^= num;
  }
  return result;
}

console.log(findUnique([2, 3, 5, 4, 5, 3, 4]));

A 3

B 4

C 2

D 5

💡 Hint

XOR of a number with itself is zero, and XOR with zero is the number itself.

The function uses XOR to cancel out all numbers that appear twice. Only the unique number remains.

Here, 5, 3, and 4 appear twice, so they cancel out. The remaining number is 2.

❓ Predict Output

intermediate

What is the output of this code with negative numbers?

What will the function return for the array [-1, -2, -2, -1, -3]?

DSA Typescript

function findUnique(arr: number[]): number {
  let result = 0;
  for (const num of arr) {
    result ^= num;
  }
  return result;
}

console.log(findUnique([-1, -2, -2, -1, -3]));

A 0

B -1

C -2

D -3

💡 Hint

XOR works with negative numbers as well because it operates on binary bits.

Pairs of -1 and -2 cancel out. The only number left is -3.

🔧 Debug

advanced

What error does this code produce?

Identify the error when running this code snippet.

DSA Typescript

function findUnique(arr: number[]): number {
  let result = 0;
  for (let i = 0; i < arr.length; i++) {
    result ^= arr[i];
  }
  return result;
}

console.log(findUnique([1, 2, 2, 1, 3]));

A No error, outputs 3

B SyntaxError: Unexpected token

C TypeError: Cannot read property 'undefined' of undefined

D ReferenceError: result is not defined

💡 Hint

Check the loop boundary condition carefully.

No error occurs. The loop runs from i = 0 to i = arr.length exclusive, so no out-of-bounds access happens.

The output is 3 as expected.

🧠 Conceptual

advanced

Why does XOR help find the unique element?

Which property of XOR makes it useful to find the only non-repeating element in an array?

A XOR adds numbers together without overflow

B XOR of a number with itself is zero, and XOR with zero is the number itself

C XOR sorts the array automatically

D XOR multiplies numbers efficiently

💡 Hint

Think about what happens when you XOR a number twice.

XOR cancels out pairs because n ^ n = 0, and 0 ^ n = n.

This property helps isolate the unique number.

🚀 Application

expert

What is the output after XOR operations on this array?

Given the array [10, 14, 10, 14, 9, 9, 7], what is the unique element found by XOR?

DSA Typescript

function findUnique(arr: number[]): number {
  let result = 0;
  for (const num of arr) {
    result ^= num;
  }
  return result;
}

console.log(findUnique([10, 14, 10, 14, 9, 9, 7]));

A 7

B 9

C 10

D 14

💡 Hint

All numbers except one appear twice.

Pairs 10, 14, and 9 cancel out. The remaining unique number is 7.

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