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

Recall & Review

beginner

What does XOR operation do when applied between two same numbers?

XOR of two same numbers is 0 because each bit cancels out the other.

beginner

Why XOR helps to find the only non-repeating element in an array?

Because XOR of all repeating elements cancels out to 0, leaving only the non-repeating element.

beginner

What is the initial value used when XORing all elements to find the unique element?

The initial value is 0 because XOR with 0 returns the other number unchanged.

beginner

Given array [2, 3, 2, 4, 3], what is the only non-repeating element?

4 is the only non-repeating element because all others appear twice.

beginner

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

The time complexity is O(n) because we scan the array once.

What is the result of XORing a number with 0?

A The number itself

B 0

C 1

D Undefined

XOR with 0 leaves the number unchanged.

If an array has all elements repeated twice except one, what does XOR of all elements give?

A Sum of all elements

B The non-repeating element

C 0

D Product of all elements

XOR cancels out pairs and leaves the unique element.

What initial value should you use when XORing all elements to find the unique one?

A 1

B The first element

C 0

D Any random number

Starting with 0 ensures XOR works correctly.

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

A O(n^2)

B O(log n)

C O(1)

D O(n)

We only scan the array once, so it is linear time.

Which of these is NOT true about XOR operation?

A X XOR X = X

B X XOR X = 0

C X XOR Y = Y XOR X

D X XOR 0 = X

X XOR X equals 0, not X.

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

Think about how pairs disappear when XORed.

Describe the steps and time complexity of the algorithm to find the only non-repeating element using XOR.

Focus on the single pass through the array.

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