Find the Only Non Repeating Element Using XOR in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does XOR operation do when applied between two identical bits?

XOR of two identical bits is 0. For example, 1 XOR 1 = 0 and 0 XOR 0 = 0.

beginner

Why does XOR help find the only non-repeating element in an array where every other element repeats twice?

Because XOR of a number with itself is 0, all repeating elements cancel out, leaving only the non-repeating element after XORing all elements.

beginner

What is the time complexity of finding the only non-repeating element using XOR?

The time complexity is O(n), where n is the number of elements in the array, because we XOR all elements once.

beginner

TypeScript code snippet: How do you initialize the variable to store XOR result before looping through the array?

Initialize with 0 because XOR with 0 returns the other number unchanged. Example: let result = 0;

beginner

What will be the output of XORing all elements in [2, 3, 2, 4, 3]?

4, because 2 XOR 3 XOR 2 XOR 4 XOR 3 = (2 XOR 2) XOR (3 XOR 3) XOR 4 = 0 XOR 0 XOR 4 = 4.

What is the result of XORing a number with 0?

A 1

B 0

C The number itself

D Undefined

XOR with 0 leaves the number unchanged.

If every element except one appears twice in an array, what does XOR of all elements give?

A The non-repeating element

B Sum of all elements

C 0

D Product of all elements

Pairs cancel out to 0, leaving only the unique element.

What is the initial value to start XOR accumulation when finding the unique element?

A 1

B 0

C The first element of the array

D Any random number

Starting with 0 ensures XOR works correctly with all elements.

Which of these is NOT true about XOR operation?

A XOR can be used to find unique elements

B XOR is commutative and associative

C XOR of a number with itself is 0

D XOR of a number with 0 is 0

XOR of a number with 0 is the number itself, not 0.

What is the time complexity of the XOR method to find the unique element?

A O(n)

B O(1)

C O(log n)

D O(n^2)

We iterate once through the array, so time complexity is linear.

Explain how XOR operation helps find the only non-repeating element in an array where all other elements repeat twice.

Think about how pairs of identical numbers behave with XOR.

Write a simple TypeScript function to find the only non-repeating element in an array using XOR.

Use a for loop and XOR operator ^.

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