Clarify the definition of a local minimum (e.g., strictly smaller than neighbors, handling boundaries) and then propose an efficient algorithm. For unsorted arrays, a linear scan works; for sorted or rotated arrays, binary search can achieve O(log n).
Pro tip: Always discuss edge cases and trade-offs; interviewers value candidates who consider boundary conditions and can adapt the solution based on array properties.
Ask questions to define local minimum precisely: strict vs non-strict inequality, handling of first/last elements, and whether the array is sorted or has special properties.
Mention that a linear scan checking each element against its neighbors is O(n) time and O(1) space, which is optimal for unsorted arrays.
If the array is sorted or rotated, use binary search to find a local minimum in O(log n) time by comparing mid with neighbors and deciding which half to search.
Explicitly cover empty array, single element, and boundaries (first/last elements) where only one neighbor exists.
State time and space complexity for each approach and justify why it's optimal given the constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.