Given an array of integers, find the index of a local minimum.
A local minimum is defined as an element that is strictly smaller than its neighbors.
Formally:
- For any index
i,A[i] < A[i-1]andA[i] < A[i+1].
You may assume:
- The array has no equal adjacent elements, i.e.,
A[i] != A[i+1]. - A valid local minimum always exists.
- The array is not necessarily sorted.
- You need to find any one local minimum.
Goal:
Return the index of one such local minimum.
Example:
Input: [9, 7, 2, 8, 5, 6]
Output: 2 # A[2] = 2 is a local minimum
You must return the index of any element that is strictly smaller than both neighbors.
Since adjacent duplicates do not exist and a local minimum is guaranteed, you can apply binary search in O(log n) to efficiently find one.
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