Find Minimum in Rotated Sorted Array

Find Minimum in Rotated Sorted Array

Suppose an array of length n sorted in ascending order is rotated between 1 and n times. For example, the array [0,1,2,4,5,6,7] might become:

• [4,5,6,7,0,1,2] if it was rotated 4 times.
• [0,1,2,4,5,6,7] if it was rotated 7 times.

Notice that rotating an array [a[0], a[1], a[2], ..., a[n-1]] 1 time results in the array [a[n-1], a[0], a[1], a[2], ..., a[n-2]].

Given the sorted rotated array nums of unique elements, return the minimum element of this array.

You must write an algorithm that runs in O(log n) time.

Examples

Example 1:

Input: nums = [3, 4, 5, 1, 2]
Output: 1
Explanation: The original array was [1, 2, 3, 4, 5] rotated 3 times.

Example 2:

Input: nums = [4, 5, 6, 7, 0, 1, 2]
Output: 0

Example 3:

Input: nums = [11, 13, 15, 17]
Output: 11
Explanation: The array was not rotated (or rotated n times).

Constraints

• n == nums.length
• 1 <= n <= 5000
• -5000 <= nums[i] <= 5000
• All values in nums are unique.
• nums is sorted and rotated between 1 and n times.

Expected Complexity

• Time: O(log n)
• Space: O(1)