81. Search in Rotated Sorted Array II

Follow up for "Search in Rotated Sorted Array":
What if duplicates are allowed?
Would this affect the run-time complexity? How and why?

Suppose an array sorted in ascending order is rotated at some pivot unknown to you beforehand.
(i.e.,0 1 2 4 5 6 7 might become 4 5 6 7 0 1 2).
Write a function to determine if a given target is in the array.
The array may contain duplicates.

class Solution {
public:
    bool search(vector& nums, int target) {
        int n = nums.size();
        int left = 0;
        int right = n-1;
        
        while(left<=right)
        {
            int mid = (left + right)>>1;
            if(target == nums[mid])
               return true;
            if(nums[left]nums[mid])
               if(nums[mid]