My first instinct was a hash map and I almost said it out loud before catching myself.
Start by clarifying the problem constraints (e.g., array size, element range, whether elements appear exactly twice or more than twice) and then propose the XOR-based solution that finds the unique element in O(n) time and O(1) extra space. Explain why XOR works: pairs cancel out, leaving the unique element. If the problem allows elements to appear more than twice, discuss alternative approaches like bit manipulation with counters or hash maps, but emphasize the XOR solution as optimal for the common case.
Pro tip: Mention that XOR is both commutative and associative, so the order doesn't matter, and that it's a classic trick for finding the odd-one-out. Also, note that this approach works in-place and is highly efficient, which is crucial for large datasets.
Ask whether all elements appear exactly twice except one, or if they can appear more than twice. Also confirm if the array is mutable and if there are any constraints on time or space.
Explain that XORing all elements together will cancel out duplicates (since x ^ x = 0) and leave the unique element (since x ^ 0 = x). This uses O(1) extra space and O(n) time.
If elements can appear more than twice, XOR alone won't work. Mention alternatives like using a hash map (O(n) space) or bitwise counters (O(1) space but more complex).
Compare the XOR approach with other methods (e.g., sorting, hash map) in terms of time and space complexity, emphasizing the minimal extra space requirement.
Reiterate that for the common case (all elements appear exactly twice except one), XOR is optimal. Provide a quick code snippet or pseudocode to illustrate.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.