I jumped straight to sorting and scanning, which works but they pushed back on the space complexity.
Start by clarifying the problem constraints (e.g., array size, value range, whether modification is allowed). Then propose an O(n) time, O(1) space solution using cyclic sort or in-place hashing to place each positive integer at its correct index, followed by a scan to find the first missing positive. If the interviewer prefers a simpler approach, mention the O(n) time, O(n) space hash set solution as a fallback.
Pro tip: Always discuss edge cases like empty array, all negatives, or all positives in sequence, and explicitly state the time and space complexity of your solution. Showing awareness of trade-offs (e.g., modifying input vs. using extra space) demonstrates maturity.
Ask about array size, value range, whether the array can be modified, and expected time/space complexity. Discuss edge cases such as empty array, all non-positive numbers, and arrays with duplicates.
Briefly mention a simple solution like sorting or using a hash set, and state its time and space complexity. This shows you can start simple and then optimize.
Explain the cyclic sort approach: iterate through the array, and for each positive integer within the range [1, n], swap it to its correct index (value-1). After rearranging, scan the array to find the first index i where nums[i] != i+1; the missing positive is i+1.
State that the algorithm runs in O(n) time and O(1) extra space (if in-place). Discuss the trade-off of modifying the input array and mention that if modification is not allowed, a hash set approach uses O(n) space.
Walk through a few examples, including edge cases, to verify correctness. For instance, [3,4,-1,1] returns 2; [1,2,0] returns 3; [7,8,9,11,12] returns 1.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.