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:

 1 class Solution {
 2 public:
 3     bool search(vector<int>& nums, int target) 
 4     {
 5        int left=0;
 6     int right=nums.size()-1;
 7     if(left==right && nums[left]==target)
 8         return true;
 9     while(left!=right)
10     {
11         int mid=(left+right)/2;
12         if(nums[mid]==target) return true;
13         if(nums[left]<nums[mid])
14         {
15             if(nums[left]<=target && target<=nums[mid])
16                 right=mid;
17             else
18                 left=mid+1;
19         }
20         else if(nums[left]>nums[mid])
21         {
22             if(nums[mid]<=target && target<=nums[right])
23                 left=mid+1;
24             else
25                 right=mid;
26         }
27         else
28             left++;
29         if(left==right && nums[left]==target)
30             return true;
31     }
32     return false;  
33     }
34 };