Find the Only Non Repeating Element Using XOR in DSA C# - 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 one number that appears only once. You want to find that unique number quickly.

🎯 Goal: Build a program that finds the only number that does not repeat in a list using the XOR operation.

📋 What You'll Learn

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

Create an integer variable called unique and set it to 0

Use a for loop with variable i to iterate over the numbers array

Inside the loop, update unique by XORing it with numbers[i]

Print the value of unique to display the only non-repeating element

💡 Why This Matters

🌍 Real World

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

💼 Career

Understanding bitwise operations like XOR is important for software engineers working on performance-critical applications and embedded systems.

1

Create the array of numbers

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

DSA C#

// Your code here

Hint

Use int[] numbers = { ... }; to create the array with the exact numbers.

2

Create the variable to hold the unique number

Create an integer variable called unique and set it to 0

DSA C#

int[] numbers = {2, 3, 5, 4, 5, 3, 4};
// Your code here

Hint

Use int unique = 0; to start with zero before XOR operations.

3

Use a for loop to XOR all elements

Use a for loop with variable i to iterate over the numbers array. Inside the loop, update unique by XORing it with numbers[i] using unique ^= numbers[i];

DSA C#

int[] numbers = {2, 3, 5, 4, 5, 3, 4};
int unique = 0;
// Your code here

Hint

Use for (int i = 0; i < numbers.Length; i++) and inside the loop write unique ^= numbers[i];

4

Print the unique number

Print the value of unique using Console.WriteLine(unique); to display the only non-repeating element

DSA C#

int[] numbers = {2, 3, 5, 4, 5, 3, 4};
int unique = 0;
for (int i = 0; i < numbers.Length; i++)
{
    unique ^= numbers[i];
}
// Your code here

Hint

Use Console.WriteLine(unique); to print the unique number.

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