Leetcode: Search in Rotated Sorted Array II in C++

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.

bool search(int A[], int n, int target) {
        int start = 0;
        int end = n-1;
        while(start<=end)
        {
            int mid = start+(end-start)/2;
            if(A[mid]==target)
             return true;
            if(A[mid]>A[start])
            {
                if(target>=A[start]&&target<A[mid])
                end = mid-1;
                else 
                start = mid+1;
            }
            else if(A[mid]<A[start])
            {
                if(target>A[mid]&&target<=A[end])
                start = mid + 1;
                else
                end = mid -1;
            }
            else
                start++;
        }
        return false;
    }