Classic problem, probably should've nailed it without hesitation but I spent a beat overthinking whether they wanted the sum formula or a sort-based approach.
Start by clarifying the problem constraints: is the array a permutation of numbers from 1 to n with one missing, or from 0 to n? Then present the optimal solution using the sum formula (or XOR) to achieve O(n) time and O(1) space, and discuss trade-offs with alternative approaches like sorting or hashing.
Pro tip: Mention that XOR avoids integer overflow issues that can occur with the sum approach when n is large, showing awareness of edge cases and numerical limits.
Ask questions to confirm the range of numbers (e.g., 1 to n or 0 to n), whether the array is sorted, and if there are any constraints on time or space complexity.
Briefly mention naive solutions like sorting (O(n log n)) or using a hash set (O(n) space), then transition to the optimal approach.
Explain the sum formula: expected sum = n*(n+1)/2, actual sum = sum of array, missing = expected - actual. Alternatively, use XOR: XOR all numbers from 1 to n and XOR all array elements; the result is the missing number.
State time complexity O(n) and space O(1). Discuss edge cases like missing number being the first or last, and potential integer overflow with sum (mitigated by XOR).
Write clean code in a preferred language, handling input validation and explaining each step.
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