Daily Coding Problem

An array sorted in ascending order is rotated at some pivot unknown to you beforehand. Find the minimum element in O(log N) time. You may assume the array does not contain duplicates. (According to the source this problem was asked by Uber.)

For example, given [5, 7, 10, 3, 4], return 3

The idea is to use binary search to find the pivot element, which is the minimum element in the array. Since the array is sorted in ascending order and then rotated, the pivot element splits the array into two parts: one part is still sorted in ascending order, while the other part is rotated and not sorted.

We start by defining two pointers, left and right, to represent the start and end of the array. In each iteration, we calculate the midpoint of the array and compare nums[mid] it with nums[right]. If nums[mid] > nums[right], it means that the pivot element is in the right half of the array, so we update left to mid + 1. Otherwise, the pivot element is in the left half of the array, so we update right it to mid.

Since the array has no duplicates, each iteration eliminates half of the remaining elements, so the algorithm takes O(log N) time. Finally, the left the pointer will point to the minimum element in the array.

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