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 ^ 1 = 0 and 0 ^ 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 of the variable used to store XOR results when finding the non-repeating element?

The initial value should be 0 because XOR with 0 returns the number itself, so it doesn't affect the result.

beginner

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

The only non-repeating element is 3 because XORing all elements results in 3.

beginner

Write the time complexity of finding the only non-repeating element using XOR in an array of size n.

The time complexity is O(n) because we need to XOR all elements once.

What is the result of XORing a number with 0?

A The number itself

B 0

C 1

D Undefined

XOR of any number with 0 returns the number itself.

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

A Sum of all elements

B Product of all elements

C 0

D The non-repeating element

XOR cancels out pairs of identical elements, leaving the unique element.

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

A 1

B 0

C First element of array

D Array length

Starting with 0 ensures XOR operation works correctly without affecting results.

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

A O(n^2)

B O(n log n)

C O(n)

D O(1)

We XOR all elements once, so time complexity is linear O(n).

Which of the following is true about XOR operation?

A XOR is commutative and associative

B XOR of a number with itself is the number

C XOR of any number with 1 is 0

D XOR always increases the number

XOR is both commutative (order doesn't matter) and associative (grouping doesn't matter).

Explain how XOR operation helps 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 how XOR accumulates the answer.

Practice

1. What does the XOR operation help find in an array where every element except one repeats exactly twice?

easy

A. The smallest element

B. The sum of all elements

C. The largest element

D. The only element that does not repeat

Solution

1. Step 1: Understand XOR properties

   XOR of a number with itself is 0, and XOR with 0 is the number itself.

2. Step 2: Apply XOR on all elements

   XORing all elements cancels out duplicates, leaving only the unique element.

3. Final Answer:

   The only element that does not repeat -> Option D

4. Quick Check:

   XOR cancels duplicates = unique element [OK]

Hint: XOR all elements; duplicates vanish, unique remains [OK]

Common Mistakes:

• Thinking XOR sums elements
• Assuming XOR finds max or min
• Confusing XOR with addition

2. Which of the following is the correct syntax to XOR two integers a and b in C?

easy

A. a | b

B. a & b

C. a ^ b

D. a + b

Solution

1. Step 1: Identify XOR operator in C

   The caret symbol (^) is the XOR operator in C.

2. Step 2: Confirm correct usage

   Using a ^ b performs bitwise XOR between integers a and b.

3. Final Answer:

   a ^ b -> Option C

4. Quick Check:

   ^ is XOR operator in C [OK]

Hint: Use ^ for XOR in C, not & or | [OK]

Common Mistakes:

• Using & instead of ^
• Using | instead of ^
• Using + instead of ^

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

int arr[] = {2, 3, 5, 4, 5, 3, 4};
int result = 0;
for(int i = 0; i < 7; i++) {
    result ^= arr[i];
}
printf("%d", result);

medium

A. 2

B. 5

C. 3

D. 4

Solution

1. Step 1: XOR all elements in the array

   Calculate XOR stepwise: 0^2=2, 2^3=1, 1^5=4, 4^4=0, 0^5=5, 5^3=6, 6^4=2.

2. Step 2: Final XOR result is 2

   After XORing all elements, duplicates cancel out, leaving 2.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   XOR cancels duplicates = 2 [OK]

Hint: XOR all; duplicates vanish, unique stays [OK]

Common Mistakes:

• Not XORing all elements
• Miscomputing XOR steps
• Assuming sum or max instead

4. Identify the error in this C code snippet that tries to find the unique element using XOR:

int arr[] = {1, 2, 1, 3, 2};
int result = arr[0];
for(int i = 1; i <= 5; i++) {
    result ^= arr[i];
}
printf("%d", result);

medium

A. Loop condition should be < 5, not <= 5

B. Initialize result to 0 instead of arr[0]

C. Use & operator instead of ^

D. Array size is incorrect

Solution

1. Step 1: Check loop bounds

   Array has 5 elements indexed 0 to 4; loop runs i from 1 to 5 inclusive, causing out-of-bounds access at i=5.

2. Step 2: Correct loop condition

   Change loop to i < 5 to avoid accessing arr[5] which is invalid.

3. Final Answer:

   Loop condition should be < 5, not <= 5 -> Option A

4. Quick Check:

   Array index out of bounds fixed by i < 5 [OK]

Hint: Loop till i < array size, not <= [OK]

Common Mistakes:

• Using <= instead of < in loop
• Ignoring array bounds
• Wrong operator used

5. Given an array where every element repeats twice except one element which repeats thrice, can XOR alone find the unique element? If not, what is the correct approach?

hard

A. Yes; XOR works for any repetition count

B. No; use bit counting and modulo 3 to find the unique element

C. No; use sum of elements minus sum of unique elements

D. Yes; XOR twice and then XOR thrice elements

Solution

1. Step 1: Understand XOR limitation

   XOR works only when duplicates appear exactly twice; it fails if duplicates appear thrice.

2. Step 2: Use bit counting method

   Count bits in all numbers, take modulo 3 of each bit count to isolate the unique element's bits.

3. Final Answer:

   No; use bit counting and modulo 3 to find the unique element -> Option B

4. Quick Check:

   XOR fails if duplicates appear thrice; bit count works [OK]

Hint: XOR only works for duplicates twice; use bit count mod 3 otherwise [OK]

Common Mistakes:

• Assuming XOR works for any duplicate count
• Trying to XOR thrice duplicates
• Ignoring bit counting approach