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?

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

public class Solution {
    public boolean search(int[] A, int target) {
		// Start typing your Java solution below
		// DO NOT write main() function
		int len = A.length;
		if (len < 1)
			return false;
		int start = 0, end = len - 1, mid;
		while (start <= end) {
			mid = start + (end - start) / 2;
			if(A[mid] == target)
				return true;
			if(A[start] < A[mid]){// sorted left, unsorted right
				if(target >= A[start] && target <= A[mid])
					end = mid - 1;
				else
					start = mid + 1;
			}
			else if(A[start] > A[mid]){// unsorted left, sorted right
				if(target >= A[mid] && target <= A[end])
					start = mid + 1;
				else
					end = mid - 1;
			}
			else // skip duplicate one, A[start] = A[mid]
				start++;
		}
		return false;
	}
}