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

Recall & Review

beginner

What does the XOR operator (^) do when applied between two bits?

XOR returns 1 if the two bits are different, and 0 if they are the same.

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, and XOR with 0 is the number itself, XORing all elements cancels out duplicates, leaving the unique element.

beginner

What is the result of XORing a number with 0?

The result is the number itself.

beginner

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

3 is the unique element because XORing all elements results in 3.

beginner

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

The time complexity is O(n), where n is the number of elements in the array.

What is the XOR of a number with itself?

A The number itself

B 0

C 1

D Undefined

XOR of a number with itself is always 0.

If you XOR all elements in an array where every element except one appears twice, what do you get?

A Product of all elements

B Sum of all elements

C 0

D The unique element

Duplicates cancel out, leaving the unique element.

What is the initial value to start XORing elements to find the unique element?

A 1

B The first element

C 0

D Array length

Start with 0 because XOR with 0 returns the number itself.

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

A O(n)

B O(log n)

C O(n^2)

D O(1)

You need to XOR all elements once, so time is linear.

Which of these is NOT true about XOR?

A XOR of two identical numbers is the number itself

B XOR of a number with itself is 0

C XOR is commutative and associative

D XOR of a number with 0 is the number

XOR of two identical numbers is 0, not the number itself.

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

Think about what happens when you XOR a number with itself and with zero.

Describe the steps to find the unique element using XOR in a given array.

Start with zero and combine all elements using XOR.

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 the sum of the numbers

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 to example

   For example, 5 ^ 5 = 0 as each bit is the same and cancels.

3. Final Answer:

   It returns 0 -> Option A

4. Quick Check:

   X ^ X = 0 [OK]

Hint: XOR same numbers always zeroes out [OK]

Common Mistakes:

• Thinking XOR returns the number itself
• Confusing XOR with OR operation
• Assuming XOR sums numbers

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

easy

A. a && b

B. a ^ b

C. a xor b

D. a | b

Solution

1. Step 1: Recall JavaScript bitwise XOR operator

   In JavaScript, the XOR operator is represented by the caret symbol ^.

2. Step 2: Check each option

   a ^ b uses ^ correctly. a xor b uses 'xor' which is not valid syntax. Options A and D are logical AND and bitwise OR respectively.

3. Final Answer:

   a ^ b -> Option B

4. Quick Check:

   Use ^ for XOR in JavaScript [OK]

Hint: Use ^ symbol for XOR in JavaScript [OK]

Common Mistakes:

• Using 'xor' keyword
• Confusing XOR with && or ||
• Using | instead of ^

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

const arr = [2, 3, 2, 4, 3];
let result = 0;
for (const num of arr) {
  result ^= num;
}
console.log(result);

medium

A. 2

B. 0

C. 4

D. 3

Solution

1. Step 1: XOR all elements in the array

   Start with result = 0, then 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 C

4. Quick Check:

   Final XOR = 4 [OK]

Hint: XOR all numbers; result is unique element [OK]

Common Mistakes:

• Not starting XOR from 0
• XORing incorrectly in loop
• Assuming sum instead of XOR

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

const arr = [1, 2, 1, 3, 2];
let result;
for (let i = 0; i < arr.length; i++) {
  result ^= arr[i];
}
console.log(result);

medium

A. Variable 'result' is not initialized to 0

B. Loop condition should be i <= arr.length

C. XOR operator is incorrect, should be &&

D. Array should be sorted before XOR

Solution

1. Step 1: Check initialization of 'result'

   The variable 'result' is declared but not initialized, so it is undefined initially.

2. Step 2: Effect of uninitialized 'result' on XOR

   XOR with undefined results in NaN, so the final output will be incorrect. Initializing 'result' to 0 fixes this.

3. Final Answer:

   Variable 'result' is not initialized to 0 -> Option A

4. Quick Check:

   Initialize result = 0 before XOR loop [OK]

Hint: Always initialize XOR accumulator to 0 [OK]

Common Mistakes:

• Not initializing XOR variable
• Using wrong loop condition
• Misusing XOR operator

5. Given an array where every element appears three times except one element which appears once, can XOR be used directly to find the unique element? Why or why not?

hard

A. Yes, but only if the array length is odd

B. Yes, XOR works for any number of repetitions

C. No, because XOR requires sorted arrays

D. No, because XOR only cancels pairs of identical numbers

Solution

1. Step 1: Understand XOR behavior with repeated elements

   XOR cancels out pairs of identical numbers because x ^ x = 0.

2. Step 2: Analyze effect of triply repeated elements

   Elements repeated thrice do not cancel out with XOR because XOR of three identical numbers is the number itself, not zero.

3. Step 3: Conclusion on XOR usage

   Therefore, XOR alone cannot find the unique element if others repeat thrice; other methods are needed.

4. Final Answer:

   No, because XOR only cancels pairs of identical numbers -> Option D

5. Quick Check:

   XOR cancels pairs, not triples [OK]

Hint: XOR cancels pairs only, not triples [OK]

Common Mistakes:

• Assuming XOR works for any repetition count
• Thinking sorting helps XOR
• Confusing XOR with sum or count