Two Non Repeating Elements in Array Using XOR in DSA Javascript - 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. For example, 5 ^ 5 = 0.

beginner

Why XOR all elements in the array to find two non-repeating elements?

XORing all elements cancels out pairs of repeating numbers, leaving XOR of the two unique numbers.

intermediate

How do you find a bit that differs between two unique numbers after XOR?

Find the rightmost set bit (bit with value 1) in the XOR result using 'xor & (-xor)'.

intermediate

How does dividing elements into two groups help find the two unique numbers?

Elements are split by whether they have the set bit or not. Each group XORs to one unique number.

beginner

What is the time complexity of finding two non-repeating elements using XOR?

The time complexity is O(n) because the array is traversed a few times linearly.

What is the XOR of a number with 0?

A The number itself

B 0

C 1

D Undefined

XOR with 0 leaves the number unchanged.

After XORing all elements in the array, what does the result represent?

A Number of unique elements

B Sum of all elements

C Product of unique elements

D XOR of two unique elements

Pairs cancel out, leaving XOR of the two unique numbers.

How do you find the rightmost set bit in a number 'x'?

A x & (-x)

B x & (x - 1)

C x | (-x)

D ~x

x & (-x) isolates the rightmost set bit.

Why split elements into two groups based on a set bit?

A To sort the array

B To find the sum of elements

C To separate unique elements

D To count duplicates

Each group contains one unique element and duplicates cancel out.

What is the space complexity of this XOR method?

A O(log n)

B O(1)

C O(n)

D O(n^2)

Only a few variables are used, so space is constant.

Explain step-by-step how XOR helps find two non-repeating elements in an array where all others repeat twice.

Think about how pairs cancel out and how the set bit helps separate unique numbers.

Describe why the rightmost set bit in the XOR of two unique numbers is important for solving the problem.

Focus on how this bit helps separate the two unique numbers.

Practice

1. What is the main purpose of using XOR operation to find two non-repeating elements in an array?

easy

A. To cancel out all repeating elements and isolate the unique ones

B. To sort the array in ascending order

C. To count the total number of elements in the array

D. To reverse the array elements

Solution

1. Step 1: Understand XOR behavior with duplicates

   XOR of two identical numbers is 0, so repeating elements cancel out.

2. Step 2: Isolate unique elements using XOR

   XOR of all elements leaves XOR of two unique elements, isolating them.

3. Final Answer:

   To cancel out all repeating elements and isolate the unique ones -> Option A

4. Quick Check:

   XOR cancels duplicates = isolate unique elements [OK]

Hint: XOR cancels pairs, leaving only unique elements [OK]

Common Mistakes:

• Thinking XOR sorts the array
• Using XOR to count elements
• Assuming XOR reverses arrays

2. Which of the following JavaScript code snippets correctly initializes the XOR variable to find two non-repeating elements?

easy

A. let xor = null;

B. let xor = 1;

C. let xor = 0;

D. let xor = undefined;

Solution

1. Step 1: Understand XOR identity element

   XOR with 0 returns the other number unchanged, so start with 0.

2. Step 2: Initialize XOR variable correctly

   Initialize xor as 0 to accumulate XOR of all elements properly.

3. Final Answer:

   let xor = 0; -> Option C

4. Quick Check:

   Start XOR with 0 for correct accumulation [OK]

Hint: Initialize XOR with 0, not 1 or null [OK]

Common Mistakes:

• Starting XOR with 1 changes results
• Using null or undefined causes errors
• Not initializing XOR variable

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

const arr = [2, 3, 7, 9, 2, 3];
let xor = 0;
for (const num of arr) {
  xor ^= num;
}
console.log(xor);

medium

A. 7

B. 0

C. 9

D. 14

Solution

1. Step 1: XOR all elements in the array

   Calculate XOR stepwise: 0^2=2, 2^3=1, 1^7=6, 6^9=15, 15^2=13, 13^3=14.

2. Step 2: Final XOR value

   The final XOR value after processing all elements is 14.

3. Final Answer:

   14 -> Option D

4. Quick Check:

   XOR all elements = 14 [OK]

Hint: XOR duplicates cancel; XOR unique pairs remain [OK]

Common Mistakes:

• Miscomputing XOR stepwise
• Assuming output is one unique element
• Confusing XOR with sum

4. Identify the error in the following code snippet that attempts to find two non-repeating elements using XOR:

const arr = [4, 1, 2, 1, 2, 5];
let xor = 0;
for (let i = 0; i <= arr.length; i++) {
  xor ^= arr[i];
}
console.log(xor);

medium

A. Use let xor = null instead of 0

B. Loop condition should be i < arr.length, not i <= arr.length

C. Array elements should be sorted before XOR

D. XOR should start from 1, not 0

Solution

1. Step 1: Check loop boundary condition

   The loop runs from i=0 to i<=arr.length, which accesses arr[arr.length] (undefined).

2. Step 2: Correct loop condition

   Change condition to i < arr.length to avoid accessing undefined and runtime error.

3. Final Answer:

   Loop condition should be i < arr.length, not i <= arr.length -> Option B

4. Quick Check:

   Loop must stay within array bounds [OK]

Hint: Use i < arr.length to avoid out-of-bounds errors [OK]

Common Mistakes:

• Using <= instead of < in loop
• Starting XOR with 1 instead of 0
• Sorting array unnecessarily

5. Given the array [6, 1, 3, 6, 1, 5], which two numbers are the non-repeating elements found using the XOR method? Choose the correct pair.

hard

A. [3, 5]

B. [6, 1]

C. [1, 3]

D. [5, 6]

Solution

1. Step 1: XOR all elements to get xor of two unique numbers

   6^1=7, 7^3=4, 4^6=2, 2^1=3, 3^5=6 (xor = 6).

2. Step 2: Find rightmost set bit and separate elements

   Rightmost set bit in 6 (binary 110) is bit 2 (value 2). Separate elements into two groups based on this bit and XOR each group to find unique numbers 3 and 5.

3. Final Answer:

   [3, 5] -> Option A

4. Quick Check:

   Unique elements are 3 and 5 [OK]

Hint: Use rightmost set bit to split and find unique numbers [OK]

Common Mistakes:

• Mixing up repeating and unique elements
• Not splitting array by set bit
• Incorrect XOR calculations