Started with the naive linear scan and they seemed fine with it, but then asked about doing it faster.
Clarify the problem constraints (e.g., array size, whether multiple peaks exist, edge cases) and then propose an efficient solution. A binary search approach can find a peak in O(log n) time by comparing the middle element with its neighbors and moving towards the side with the larger neighbor. If the array is small or unsorted, a linear scan is acceptable, but emphasize the optimal solution.
Pro tip: Mention that the binary search approach works because if an element is not a peak, there must be a peak on the side of the larger neighbor. This demonstrates deep understanding of the problem's properties.
Ask about edge cases: What if the array is empty? What if there are multiple peaks? Are the boundaries considered peaks if they are greater than their single neighbor? Confirm that any peak is acceptable.
Mention that a linear scan checking each element against its neighbors takes O(n) time. This is simple but not optimal for large arrays.
Explain that we can use binary search to find a peak in O(log n) time. At each step, compare the middle element with its neighbors; if it's a peak, return it; otherwise, move towards the side with the larger neighbor.
Discuss how to handle boundaries: treat out-of-bounds as negative infinity, so the first or last element can be a peak if it's greater than its only neighbor.
State that the binary search approach runs in O(log n) time and O(1) space. Walk through a small example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.