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Suppose the problem changes: every element appears k times except one unique element appearing once, where k is unknown and can vary. Which approach best adapts to this variant?

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Bit Manipulation - Single Number II (Three Copies)
Suppose the problem changes: every element appears k times except one unique element appearing once, where k is unknown and can vary. Which approach best adapts to this variant?
AUse the bitwise FSM designed for k=3 without modification
BSort the array and scan for the unique element
CUse bit counting with modulo k, dynamically adjusting modulo based on input
DUse a hash map to count occurrences and find the unique element
Step-by-Step Solution
Solution:
  1. Step 1: Analyze problem variant

    Unknown k means fixed modulo or FSM approaches for k=3 won't work without modification.
  2. Step 2: Identify adaptable approach

    Hash map counting occurrences works regardless of k, though uses extra space.
  3. Step 3: Evaluate other options

    Sorting is O(n log n) and less efficient; bit counting and FSM require known k.
  4. Final Answer:

    Option D -> Option D
  5. Quick Check:

    Hash map works for unknown k variants [OK]
Quick Trick: Unknown k breaks fixed modulo FSM; hash map is flexible [OK]
Common Mistakes:
MISTAKES
  • Assuming FSM works for any k
  • Ignoring hash map as flexible solution
Trap Explanation:
PITFALL
  • Candidates often try to apply fixed k solutions to unknown k problems incorrectly.
Interviewer Note:
CONTEXT
  • Tests adaptability and understanding of approach limitations.
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