Search in Rotated Sorted Array II

Question:

Follow up for "Search in Rotated Sorted Array":
What if duplicates are allowed?

Would this affect the run-time complexity? How and why?

Write a function to determine if a given target is in the array.

Solution:

class Solution {
public:
    bool search(vector<int>& nums, int target) 
    {
       int left=0;
    int right=nums.size()-1;
    if(left==right && nums[left]==target)
        return true;
    while(left!=right)
    {
        int mid=(left+right)/2;
        if(nums[mid]==target) return true;
        if(nums[left]<nums[mid])
        {
            if(nums[left]<=target && target<=nums[mid])
                right=mid;
            else
                left=mid+1;
        }
        else if(nums[left]>nums[mid])
        {
            if(nums[mid]<=target && target<=nums[right])
                left=mid+1;
            else
                right=mid;
        }
        else
            left++;
        if(left==right && nums[left]==target)
            return true;
    }
    return false;  
    }
};