Search in Rotated Sorted Array II

There is an integer array nums sorted in non-decreasing order (not necessarily with distinct values).

Before being passed to your function, nums is rotated at an unknown pivot index k (0 <= k < nums.length) such that the resulting array is [nums[k], nums[k+1], ..., nums[n-1], nums[0], nums[1], ..., nums[k-1]] (0-indexed). For example, [0,1,2,4,4,4,5,6,6,7] might be rotated at pivot index 5 and become [4,5,6,6,7,0,1,2,4,4].

Given the array nums after the rotation and an integer target, return true if target is in nums, or false if it is not in nums.

You must decrease the overall operation steps as much as possible.

Example 1:

Input: nums = [2,5,6,0,0,1,2], target = 0
Output: true

Example 2:

Input: nums = [2,5,6,0,0,1,2], target = 3
Output: false

Constraints:

• 1 <= nums.length <= 5000
• -104 <= nums[i] <= 104
• nums is guaranteed to be rotated at some pivot.
• -104 <= target <= 104

Follow up: This problem is similar to Search in Rotated Sorted Array, but nums may contain duplicates. Would this affect the runtime complexity? How and why?

SOLUTION:

class Solution:
    def search(self, nums: List[int], target: int) -> bool:
        # Initilize two pointers
        begin = 0
        end = len(nums) - 1 
        while begin <= end:
            mid = (begin + end)//2
            if nums[mid] == target:
                return True
            if nums[mid] == nums[end]: # Fail to estimate which side is sorted
                end -= 1  # In worst case: O(n)
            elif nums[mid] > nums[end]: # Left side of mid is sorted
                if  nums[begin] <= target and target < nums[mid]: # Target in the left side
                    end = mid - 1
                else: # in right side
                    begin = mid + 1
            else: # Right side is sorted
                if  nums[mid] < target and target <= nums[end]: # Target in the right side
                    begin = mid + 1
                else: # in left side
                    end = mid - 1
        return False