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You are given an array where every element appears exactly twice except for one element that appears only once. Which approach guarantees finding the unique element in linear time and constant space?

easy🔍 Pattern Recognition Q11 of Q15
Bit Manipulation - Single Number (XOR Self-Cancellation)
You are given an array where every element appears exactly twice except for one element that appears only once. Which approach guarantees finding the unique element in linear time and constant space?
AUsing a dynamic programming approach to track element counts
BSorting the array and then scanning to find the unique element
CUsing a brute force nested loop to count occurrences of each element
DUsing XOR operation to cancel out duplicates and find the single element
Step-by-Step Solution

  1. Step 1: Understand problem constraints

    Every element except one appears twice, so duplicates cancel out under XOR.

  2. Step 2: Identify approach that leverages XOR properties

    XOR of a number with itself is zero, and XOR with zero is the number itself, so XORing all elements leaves the unique one.

  3. Final Answer:

    Option D -> Option D

  4. Quick Check:

    XOR approach runs in O(n) time and O(1) space [OK]
Quick Trick: XOR cancels duplicates perfectly [OK]
Common Mistakes:
MISTAKES
  • Sorting is O(n log n), not optimal
  • Brute force is O(n²), inefficient
  • DP is unrelated to this problem
Trap Explanation:
PITFALL
  • Sorting and brute force seem straightforward but are less efficient; DP is unrelated here.
Interviewer Note:
CONTEXT
  • Tests if candidate recognizes XOR self-cancellation pattern for uniqueness detection.
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