I jumped straight to binary search because I'd seen similar problems before, then realized mid-explanation that the problem asks for the FIRST local minimum by index, not just any one.
Clarify the definition of local minimum, especially edge cases, then propose a single-pass O(n) scan that checks each element against its neighbors. Walk through the algorithm with examples and discuss time/space complexity.
Pro tip: Explicitly handle edge cases (array length 0, 1, 2) and mention that a local minimum always exists in an array of distinct elements, but with duplicates you may need to define strict inequality carefully.
Ask about array size, duplicates, and whether the first/last elements can be local minima. Confirm the definition of 'immediate neighbors' for edges.
Propose a linear scan: for each index i, compare arr[i] with arr[i-1] (if exists) and arr[i+1] (if exists). Return i if both comparisons satisfy strict inequality.
For i=0, only compare with arr[1]; for i=n-1, only compare with arr[n-2]. Also handle empty array and single-element array (which is trivially a local minimum).
State that the algorithm runs in O(n) time and O(1) space, which is optimal since any element could be the first local minimum.
Walk through a few examples (e.g., [3,2,1,4], [1,2,3], [2,1,2]) to verify correctness and edge case handling.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.