LeetCode 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.     

#include <iostream>

using namespace::std;

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

int main()
{
	int A[]={1,1,1,2,2,3};
	bool flag = search(A, 6, 2);
	cout << flag << endl;
	
	return 0;
}