Find Minimum in Rotated Sorted Array II

This problem challenges you to efficiently locate the minimum element within a rotated sorted array. A rotated sorted array is a sorted array that has been shifted by some number of positions. Finding the minimum element is useful in various scenarios, such as searching and data analysis, where identifying the smallest value is crucial.

Problem Description

You are given a sorted array nums that has been rotated at some pivot unknown to you beforehand. This means the array was initially sorted in ascending order, but then a portion of it was moved from one end to the other. The array may also contain duplicate elements. Your task is to find the minimum element in the rotated array.

What needs to be achieved:

• Implement a function that takes a rotated sorted array nums as input.
• The function should return the minimum element present in the array.

Key Requirements:

• The array nums is initially sorted in ascending order.
• The array has been rotated at least once.
• The array may contain duplicate elements.
• The minimum element is guaranteed to be present in the array.

Expected Behavior:

The function should correctly identify the minimum element even when the array is heavily rotated or contains duplicates. It should handle edge cases gracefully.

Edge Cases to Consider:

• Array with a single element.
• Array with all elements being the same (duplicates).
• Array rotated such that the minimum element is at the beginning.
• Array rotated such that the minimum element is at the end.
• Large arrays with many duplicates.

Examples

Example 1:

Input: [4,5,6,7,0,1,2]
Output: 0
Explanation: The array was originally [0,1,2,4,5,6,7] and rotated 4 times. The minimum element is 0.

Example 2:

Input: [2,2,2,0,1]
Output: 0
Explanation: The array contains duplicates. The minimum element is 0.

Example 3:

Input: [1,3,5]
Output: 1
Explanation: The array is already sorted and not rotated. The minimum element is 1.

Example 4:

Input: [11,13,15,17]
Output: 11
Explanation: The array is sorted and not rotated. The minimum element is 11.

Constraints

• 1 <= nums.length <= 5000
• -10^4 <= nums[i] <= 10^4
• All elements in nums are integers.
• nums is rotated at least once.
• The array may contain duplicate elements.
• The time complexity should be O(log n) in the average case. While O(n) is acceptable, strive for a more efficient solution.

Notes

• Consider using a modified binary search approach to efficiently locate the minimum element.
• The presence of duplicates can complicate the binary search process. You may need to adjust your comparison logic to handle cases where nums[left] == nums[mid].
• Think about how the rotation affects the relative ordering of elements in the array. This can help you determine which half of the array to search next.
• Be mindful of edge cases where the minimum element might be at the beginning or end of the array.