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

Find the Only Non Repeating Element Using XOR

📖 Scenario: Imagine you have a list of product IDs scanned at a store. Every product ID appears twice except one product that was scanned only once by mistake. You want to find that unique product ID quickly.

🎯 Goal: Build a Java program that finds the only non-repeating element in an array using the XOR operation.

📋 What You'll Learn

Create an integer array called productIds with the exact values: {4, 1, 2, 1, 2}

Create an integer variable called uniqueId and initialize it to 0

Use a for loop with variable id to iterate over productIds and update uniqueId by XORing it with id

Print the value of uniqueId to display the only non-repeating product ID

💡 Why This Matters

🌍 Real World

Finding unique items in data streams or logs where duplicates occur is common in fraud detection, error checking, and inventory management.

💼 Career

Understanding XOR and unique element detection is useful for software engineers working on algorithms, embedded systems, and performance-critical applications.

1

Create the product ID array

Create an integer array called productIds with these exact values: {4, 1, 2, 1, 2}

DSA Java

# Your code here

Hint

Use int[] productIds = {4, 1, 2, 1, 2}; to create the array.

2

Initialize the uniqueId variable

Create an integer variable called uniqueId and set it to 0 inside the main method after the productIds array.

DSA Java

public class Main {
    public static void main(String[] args) {
        int[] productIds = {4, 1, 2, 1, 2};
        // Your code here
    }
}

Hint

Use int uniqueId = 0; to start with zero.

3

Use XOR to find the unique product ID

Use a for loop with variable id to iterate over productIds and update uniqueId by XORing it with id inside the loop.

DSA Java

public class Main {
    public static void main(String[] args) {
        int[] productIds = {4, 1, 2, 1, 2};
        int uniqueId = 0;
        // Use a for loop to XOR each id with uniqueId
    }
}

Hint

Use for (int id : productIds) and inside the loop write uniqueId ^= id;.

4

Print the unique product ID

Write System.out.println(uniqueId); to print the only non-repeating product ID after the loop.

DSA Java

public class Main {
    public static void main(String[] args) {
        int[] productIds = {4, 1, 2, 1, 2};
        int uniqueId = 0;
        for (int id : productIds) {
            uniqueId ^= id;
        }
        // Print the uniqueId
    }
}

Hint

Use System.out.println(uniqueId); to show the result.

Practice

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

easy

A. It returns 0

B. It returns the number itself

C. It returns 1

D. It returns -1

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 on example

   For example, 5 XOR 5 = 0.

3. Final Answer:

   It returns 0 -> Option A

4. Quick Check:

   X XOR X = 0 [OK]

Hint: X XOR X always equals zero [OK]

Common Mistakes:

• Thinking XOR returns the number itself
• Confusing XOR with OR
• Assuming XOR returns 1 for identical numbers

2. Which of the following is the correct syntax to initialize an integer variable named result to 0 in Java?

easy

A. int result := 0;

B. int result == 0;

C. int result = 0;

D. int result = zero;

Solution

1. Step 1: Recall Java variable initialization syntax

   In Java, variables are declared with type, name, and assignment using single equals sign.

2. Step 2: Check each option

   int result = 0; uses correct syntax: int result = 0;. Others have syntax errors.

3. Final Answer:

   int result = 0; -> Option C

4. Quick Check:

   Correct Java variable initialization [OK]

Hint: Use single '=' for assignment in Java [OK]

Common Mistakes:

• Using '==' instead of '='
• Using ':=' which is not Java syntax
• Assigning undefined variable 'zero'

3. What will be the output of the following Java code?

int[] arr = {2, 3, 2, 4, 3};
int result = 0;
for (int num : arr) {
    result ^= num;
}
System.out.println(result);

medium

A. 4

B. 3

C. 2

D. 0

Solution

1. Step 1: Apply XOR operation on array elements

   Start with result=0, XOR with each element: 0^2=2, 2^3=1, 1^2=3, 3^4=7, 7^3=4.

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

   The only element that does not repeat is 4, which is the final XOR result.

3. Final Answer:

   4 -> Option A

4. Quick Check:

   Only non-repeating element = 4 [OK]

Hint: XOR all elements; result is unique number [OK]

Common Mistakes:

• Not starting XOR with 0
• Miscomputing XOR steps
• Assuming sum instead of XOR

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

int[] arr = {1, 2, 1, 3, 2};
int result;
for (int num : arr) {
    result ^= num;
}
System.out.println(result);

medium

A. System.out.println syntax is wrong

B. Array 'arr' is not declared properly

C. For-each loop syntax is incorrect

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

Solution

1. Step 1: Check variable initialization

   The variable 'result' is declared but not initialized before XOR operation, causing a compile error.

2. Step 2: Correct initialization needed

   Initialize 'result' to 0 before the loop to avoid error.

3. Final Answer:

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

4. Quick Check:

   Uninitialized variable causes error [OK]

Hint: Always initialize XOR accumulator to 0 [OK]

Common Mistakes:

• Forgetting to initialize result
• Misusing loop syntax
• Incorrect print statement

5. Given an array where every element repeats twice except one element which repeats thrice, can the XOR method find the unique element? What will be the output of this code?

int[] arr = {5, 5, 5, 7, 7, 8, 8};
int result = 0;
for (int num : arr) {
    result ^= num;
}
System.out.println(result);

hard

A. 5

B. Cannot find unique element correctly

C. 0

D. 7

Solution

1. Step 1: Understand XOR property for odd/even counts

   XOR cancels even number of identical elements to 0; odd count leaves the element.

2. Step 2: Analyze given array and XOR result

   5 appears 3 times (odd) -> XOR of three identical numbers is not the number itself; XOR of 5^5=0, 0^5=5, but this pattern does not hold for triple repeats in general.

3. Step 3: Conclusion

   XOR method cannot reliably find the unique element when counts are not exactly twice except one.

4. Final Answer:

   Cannot find unique element correctly -> Option B

5. Quick Check:

   XOR fails for elements repeating thrice [OK]

Hint: XOR only works when all elements except one appear exactly twice [OK]

Common Mistakes:

• Thinking XOR finds unique element with triple repeats
• Miscomputing XOR of three identical numbers as the number itself
• Ignoring that XOR only cancels pairs