Search in Rotated Sorted Array II - Solution & Explanation

This approach uses a modified binary search to handle the rotated sorted array with duplicates. Normally, in a binary search, you would compare the middle element with the target and adjust your search range accordingly. However, because this array is rotated, the sorted order is disrupted, and duplicates can complicate matters.

The key steps are:

• Ignore duplicate elements by adjusting the left and right pointers when nums[left] == nums[mid] == nums[right].
• Determine the sorted half of the array and decide the search direction.

The time complexity is generally O(log N), but in the worst case with duplicates, it can degrade to O(N).

This Python implementation of the modified binary search accounts for duplicates by checking for duplicate middle elements. If they exist, the algorithm adjusts the search boundaries while maintaining the sorted distinction in either half of the array.

In cases of heavy element duplication, when the above methods become inefficient, a linear search ensures completion of the task. Though not ideal for large-sized arrays, this method provides a simple, guaranteed solution without involving complicated logic.

The complexity for linear search is both time and space O(N).

In this simplistic Python solution, we loop through the entire array, checking each element for equality with the target, making it a reliable brute-force method.