Classic binary search variant but my first instinct was just linear scan, which works but they clearly wanted the O(log n) approach.
Clarify the problem constraints (e.g., array size, whether duplicates exist, and if the array is guaranteed to have a local minimum). Then propose an efficient binary search solution that finds a local minimum in O(log n) time by comparing the middle element with its neighbors and deciding which half to search.
Pro tip: Mention that the binary search approach works even if the array has multiple local minima, and that you can handle edge cases by treating out-of-bounds neighbors as positive infinity. This shows you think about robustness and efficiency.
Ask about input size, whether duplicates are allowed, and if the array is guaranteed to have at least one local minimum. Confirm that a local minimum is defined as an element smaller than its immediate neighbors.
Mention that a linear scan checking each element against its neighbors takes O(n) time. This is a valid fallback but not optimal for large arrays.
Explain that you can use binary search: compare the middle element with its neighbors. If it's smaller than both, return it. If the left neighbor is smaller, search the left half; otherwise, search the right half.
Treat out-of-bounds indices as positive infinity so that the first and last elements can be considered local minima if they are smaller than their only neighbor. Also discuss how duplicates might affect the search.
State that the binary search solution runs in O(log n) time and O(1) space. Mention that it's optimal for large arrays and that the problem is well-suited for a divide-and-conquer strategy.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.