Find a Target's Index in a Rotated Sorted Array of Distinct Integers

An array of distinct integers was sorted in strictly increasing order and then rotated at an unknown pivot: for some `k` with `0 <= k < n`, the array `[a0, a1, ..., a(n-1)]` became `[ak, a(k+1), ..., a(n-1), a0, a1, ..., a(k-1)]`. A rotation with `k = 0` leaves the array unchanged. Given the rotated array `nums` and an integer `target`, return the index of `target` in `nums`, or `-1` if it is not present. The interviewer expects a solution whose running time is logarithmic in the length of the array. ### Function Signature ```python def search_rotated(nums: list[int], target: int) -> int: ``` ### Rules - Indices are 0-based. - All values in `nums` are distinct, so the answer is unique. - `nums` is guaranteed to be a rotation of a strictly increasing array. ### Constraints - `1 <= len(nums) <= 10^5` - `-10^9 <= nums[i] <= 10^9` - `-10^9 <= target <= 10^9` ### Examples **Example 1** - Input: `nums = [15, 18, 22, 3, 7, 11]`, `target = 7` - Output: `4` - Explanation: the array is `[3, 7, 11, 15, 18, 22]` rotated by three positions, and `7` sits at index `4`. **Example 2** - Input: `nums = [15, 18, 22, 3, 7, 11]`, `target = 20` - Output: `-1` **Example 3** - Input: `nums = [1, 4, 9, 12]`, `target = 12` - Output: `3` - Explanation: this array was not rotated (`k = 0`).