Find the Only Non Repeating Element Using XOR in DSA C# - 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 initial value to start XORing elements to find the unique element?

Start with 0 because XOR with 0 leaves the number unchanged, so it does not affect the result.

beginner

Given the array [2, 3, 2, 4, 4], what is the unique element found using XOR?

The unique element is 3. XORing all elements: 2 XOR 3 XOR 2 XOR 4 XOR 4 = 3.

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, because we XOR all elements once.

What is the result of XORing a number with zero?

A Undefined

B Zero

C The number itself

D One

XOR with zero leaves the number unchanged.

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

A The unique non-repeating element

B Sum of all elements

C Zero

D Product of all elements

Repeating elements cancel out, leaving the unique element.

What is the XOR of 5 and 5?

A 1

B 5

C 10

D 0

XOR of a number with itself is always zero.

Which initial value should you use to start XORing elements to find the unique element?

A 0

B 1

C The first element

D Any random number

Starting with 0 ensures XOR does not change the first element.

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

A O(n)

B O(1)

C O(log n)

D O(n^2)

Only one variable is used to store XOR result, so space is constant.

Explain how XOR operation helps to find the only non-repeating element in an array where every other element repeats twice.

Think about how pairs of numbers behave with XOR.

Describe the steps and code logic to find the only non-repeating element using XOR in C#.

Focus on the loop and XOR operation.

Practice

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

easy

A. It returns the number itself

B. It causes an error

C. It returns 1

D. It returns 0

Solution

1. Step 1: Understand XOR behavior on identical bits

   XOR returns 0 when both bits are the same (0 XOR 0 = 0, 1 XOR 1 = 0).

2. Step 2: Apply XOR on identical numbers

   Since all bits are identical, XOR of a number with itself results in 0.

3. Final Answer:

   It returns 0 -> Option D

4. Quick Check:

   5 XOR 5 = 0 [OK]

Hint: XOR of same numbers always zeroes out [OK]

Common Mistakes:

• Thinking XOR returns the number itself
• Confusing XOR with OR or AND
• Assuming XOR causes errors with identical inputs

2. Which of the following is the correct syntax to initialize an integer variable named result to zero in C#?

easy

A. int result => 0;

B. int result == 0;

C. int result = 0;

D. int result := 0;

Solution

1. Step 1: Recall C# variable initialization syntax

   In C#, variables are initialized using single equals sign (=) for assignment.

2. Step 2: Check each option

   int result = 0; uses correct syntax: int result = 0;. Others use invalid operators.

3. Final Answer:

   int result = 0; -> Option C

4. Quick Check:

   Correct assignment uses = in C# [OK]

Hint: Use single = for assignment in C# [OK]

Common Mistakes:

• Using double equals (==) for assignment
• Using := or => which are invalid here
• Missing semicolon at the end

3. What is the output of the following C# code?

int[] arr = {2, 3, 2, 4, 3};
int result = 0;
foreach (int num in arr) {
    result ^= num;
}
Console.WriteLine(result);

medium

A. 4

B. 3

C. 2

D. 0

Solution

1. Step 1: XOR all elements in the array

   Start with result = 0. XOR with 2 -> 0^2=2, then 3 -> 2^3=1, then 2 -> 1^2=3, then 4 -> 3^4=7, then 3 -> 7^3=4.

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

   The final result after XORing all elements is 4, which is the only non-repeating number.

3. Final Answer:

   4 -> Option A

4. Quick Check:

   Only 4 appears once, XOR result = 4 [OK]

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

Common Mistakes:

• Not XORing all elements correctly
• Confusing XOR with addition
• Assuming first unique number is output

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

int[] arr = {1, 2, 1, 3, 2};
int result;
foreach (int num in arr) {
    result ^= num;
}
Console.WriteLine(result);

medium

A. Variable 'result' is not initialized before XOR operation

B. Using '^=' operator is incorrect for XOR in C#

C. Array syntax is invalid

D. Console.WriteLine cannot print integers

Solution

1. Step 1: Check variable initialization

   The variable 'result' is declared but not initialized before using '^=' operator, which causes a compile-time error.

2. Step 2: Correct initialization needed

   Initialize 'result' to 0 before the loop to correctly accumulate XOR results.

3. Final Answer:

   Variable 'result' is not initialized before XOR operation -> Option A

4. Quick Check:

   Uninitialized variables cause errors in C# [OK]

Hint: Always initialize variables before use [OK]

Common Mistakes:

• Forgetting to initialize variables
• Misunderstanding '^=' operator usage
• Assuming Console.WriteLine can't print ints

5. Given an array where every element appears twice except one element which appears once, how would you modify the XOR approach to find the unique element if the array is very large and you want to optimize memory usage?

hard

A. Sort the array first then scan for unique element

B. Use XOR in a single pass without extra memory

C. Use a dictionary to count occurrences

D. Copy array to a new list and remove duplicates

Solution

1. Step 1: Understand XOR single pass advantage

   XOR operation can be done in one pass over the array without extra memory, as duplicates cancel out.

2. Step 2: Avoid extra memory by not using sorting or dictionaries

   Sorting or dictionaries use extra memory or time, which is inefficient for large arrays.

3. Final Answer:

   Use XOR in a single pass without extra memory -> Option B

4. Quick Check:

   XOR single pass = memory efficient [OK]

Hint: XOR once over array; no extra memory needed [OK]

Common Mistakes:

• Using extra data structures unnecessarily
• Sorting which costs extra time and memory
• Copying arrays wastes memory