Find All Strict Local Maxima in an Integer Array
Company: Pinterest
Role: Machine Learning Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Online Assessment
Given an integer array, return the indices of all of its local maxima. The report says only that the task was to find a local maximum in an array; this version asks for every local maximum so that the answer is unique.
### Function Signature
```python
def local_maxima(nums: list[int]) -> list[int]:
```
### Rules
- Index `i` is a local maximum when `nums[i]` is strictly greater than each of its neighbours that exist: `nums[i - 1]` when `i > 0`, and `nums[i + 1]` when `i < len(nums) - 1`.
- The first and last elements have one neighbour each. In a one-element array, the only element is a local maximum.
- Equal neighbours do not count: in `[4, 4]`, neither element is a local maximum.
- Return the indices in increasing order, or an empty list if there are none.
### Constraints
- `1 <= len(nums) <= 10^5`
- `-10^9 <= nums[i] <= 10^9`
### Examples
**Example 1**
```text
Input: nums = [1, 3, 2, 4, 1]
Output: [1, 3]
```
`3` is greater than `1` and `2`, and `4` is greater than `2` and `1`.
**Example 2**
```text
Input: nums = [5, 5, 4, 6]
Output: [3]
```
The two `5`s are equal neighbours, so neither is a local maximum. The last element, `6`, has one neighbour, `4`, and is greater than it.
**Example 3**
```text
Input: nums = [7]
Output: [0]
```
A single element has no neighbours, so it is a local maximum.
Overview: A coding question asking for the indices of every strict local maximum in an integer array, where boundary elements compare only with their single neighbour and equal neighbours never count. It tests careful handling of array boundaries, plateaus of equal values and single-element input.
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