algoadvance

Problem Number: 3158

Find the XOR of Numbers Which Appear Twice

Given an integer array nums where every element appears twice except for one, find that single number which appears twice.

Clarifying Questions

1. Input Size: What is the size of the array nums?
   • Assume the size of the array is within a manageable range for in-memory computation.
2. Values in Array: Are the numbers in the array guaranteed to be integers and within a known range?
   • Assume they are integers and within a reasonable range for XOR operations.
3. Uniqueness: Is there exactly one number that appears twice, and all other numbers appear once?
   • Yes, this is assumed as per the problem statement.

Strategy

Approach:

To solve this problem, we can use the properties of the XOR operation:

1. Properties of XOR:
   • a ^ a = 0 for any integer a
   • a ^ 0 = a for any integer a
   • XOR is both commutative and associative.

Plan:

1. Initialize a variable xor_result to 0.
2. Iterate through each number in the nums array.
3. Take the XOR of each number with xor_result.
4. At the end of the iteration, xor_result will contain the number which appears twice, as all other numbers will cancel themselves out.

Time Complexity:

• Time Complexity: O(n), where n is the length of the nums array since we only need to traverse the array once.
• Space Complexity: O(1), since we are using a constant amount of extra space regardless of the input size.

Code

def find_duplicate_xor(nums):
    xor_result = 0
    for num in nums:
        xor_result ^= num
    return xor_result

# Example usage
nums = [1, 2, 3, 4, 5, 2]  # Expected output: 2
print(find_duplicate_xor(nums))

Explanation:

1. Initialization: We start with xor_result set to 0.
2. Iteration: For each element in nums, we use the XOR operation and update xor_result.
3. Result: After completing the iteration, xor_result will hold the number that appears twice.

This method leverages the properties of the XOR operation to efficiently find the duplicate number in a single pass through the array.

Try our interview co-pilot at AlgoAdvance.com

• Got blindsided by a question you didn’t expect?

• Spend too much time studying?

• Or simply don’t have the time to go over all 3000 questions?