Problem: Search in Rotated Sorted Array

Statement

You are given an integer array nums that was originally sorted in ascending order with all distinct values. This array may have been left rotated at some unknown pivot index k, transforming it into [nums[k], nums[k+1], ..., nums[n-1], nums[0], nums[1], ..., nums[k-1]] (using $0$-based indexing). If no rotation was applied, the array remains in its original sorted order.

Given the array nums after this possible rotation and an integer target, return the index of target in nums if it exists, or return $-1$ if it does not.

Your solution must achieve $O(\log n)$ ...