Find the Only Non Repeating Element Using XOR in DSA Go - 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 XOR 1 = 0 and 0 XOR 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 to start XORing elements when finding the non-repeating element?

Start with 0 because XOR with 0 returns the other number unchanged, so it does not affect the result.

beginner

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

3 is the only non-repeating element because 2 and 4 appear twice and cancel out when XORed.

beginner

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

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 Undefined

B 0

C 1

D The number itself

XOR with 0 leaves the number unchanged.

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

A The non-repeating element

B Sum of all elements

C 0

D Product of all elements

Repeating elements cancel out, leaving the unique element.

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

A 1

B The first element

C 0

D Any random number

Starting with 0 ensures XOR does not affect the first element.

Which of these arrays has 5 as the only non-repeating element? [2, 5, 2, 3, 3]

A Yes

B No

C Cannot tell

D All repeat

2 and 3 repeat twice, 5 appears once.

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

A O(n^2)

B O(n)

C O(log n)

D O(1)

We XOR all elements once, so time is linear.

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 same numbers behave with XOR.

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

Focus on the process of XORing all elements once.

Practice

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

easy

A. It returns the sum of the numbers

B. It returns 0

C. It returns 1

D. It returns the number itself

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 this property to the question

   Since the two identical numbers cancel out, the result is 0.

3. Final Answer:

   It returns 0 -> Option B

4. Quick Check:

   n XOR n = 0 [OK]

Hint: XOR of 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 Go code snippets correctly initializes a variable to store XOR results for an integer slice named nums?

easy

A. var result int = 0

B. result := []int{}

C. var result string = ""

D. result := make(map[int]int)

Solution

1. Step 1: Identify the correct type for XOR accumulation

   XOR operates on integers, so the variable must be an integer initialized to 0.

2. Step 2: Check each option

   var result int = 0 initializes an integer variable to 0, suitable for XOR operations. Others use wrong types or data structures.

3. Final Answer:

   var result int = 0 -> Option A

4. Quick Check:

   Integer zero initialization for XOR [OK]

Hint: XOR needs an integer variable initialized to zero [OK]

Common Mistakes:

• Using slice or map instead of int
• Initializing with empty string
• Not initializing variable

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

package main
import "fmt"
func main() {
 nums := []int{2, 3, 2, 4, 3}
 result := 0
 for _, num := range nums {
  result ^= num
 }
 fmt.Println(result)
}

medium

A. 2

B. 3

C. 4

D. 0

Solution

1. Step 1: XOR all elements in the slice

   Calculate XOR stepwise: 0^2=2, 2^3=1, 1^2=3, 3^4=7, 7^3=4.

2. Step 2: Identify the non-repeating element

   The final XOR result is 4, which is the only number appearing once.

3. Final Answer:

   4 -> Option C

4. Quick Check:

   XOR cancels duplicates, leaves 4 [OK]

Hint: XOR duplicates cancel, leftover is unique [OK]

Common Mistakes:

• Adding numbers instead of XOR
• Miscomputing XOR steps
• Ignoring duplicates

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

package main
import "fmt"
func main() {
 nums := []int{5, 1, 5, 2, 1}
 var result int
 for i := 0; i <= len(nums); i++ {
  result ^= nums[i]
 }
 fmt.Println(result)
}

medium

A. Loop condition should be i < len(nums), not i <= len(nums)

B. Variable 'result' should be initialized to 1 instead of 0

C. The XOR operator '^=' is invalid in Go

D. The slice 'nums' should be declared as an array

Solution

1. Step 1: Check loop boundary condition

   The loop runs from i=0 to i<=len(nums), which causes out-of-range access at i=len(nums).

2. Step 2: Correct the loop condition

   Change condition to i < len(nums) to avoid index out of range error.

3. Final Answer:

   Loop condition should be i < len(nums), not i <= len(nums) -> Option A

4. Quick Check:

   Index out of range fixed by loop condition [OK]

Hint: Loop index must be less than length, not equal [OK]

Common Mistakes:

• Using <= instead of <
• Initializing result incorrectly
• Misunderstanding XOR operator

5. Given an array where every element appears twice except one element which appears once, how can you find the unique element using XOR in Go? Consider the array nums := []int{7, 9, 7, 8, 9, 10, 10}. What is the unique element?

hard

A. 7

B. 9

C. 10

D. 8

Solution

1. Step 1: XOR all elements in the array

   Calculate XOR stepwise: 0^7=7, 7^9=14, 14^7=9, 9^8=1, 1^9=8, 8^10=2, 2^10=8.

2. Step 2: Identify the unique element

   The final XOR result is 8, which appears only once in the array.

3. Final Answer:

   8 -> Option D

4. Quick Check:

   Duplicates cancel, unique is 8 [OK]

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

Common Mistakes:

• Adding numbers instead of XOR
• Forgetting to initialize result to zero
• Misreading array elements