LeetCode 81. 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.

Worst Time Complexity would be O(N).... for example: whole array is [4, 4, 4, 4, 4.....4] then the target is 3.

#include <vector>
#include <iostream>
using namespace std;


bool search(vector<int>& nums, int target) {
    if(nums.size() == 0) return false;
    int low = 0;
    int high = nums.size() - 1;
    while(low <= high) {
        int mid = low + (high - low) / 2;
        if(nums[mid] == target) return true;
        if(nums[mid] < nums[high]) {
            if(target <= nums[high] && target > nums[mid]) {
                low = mid + 1;
            } else high = mid - 1;

        } else if(nums[mid] > nums[high]) {
            if(target >= nums[low] && target < nums[mid]) {
                high = mid - 1;
            } else {
                low = mid + 1;
            }
        } else { high--;}
    }
    return false;
}

// duplicates in rotated sorted array.
// For example: 4, 4, 5, 6, 1, 2, 3, 4, target is 3.
int main(void) {
    vector<int> nums{4, 4, 5, 6, 1, 2, 3, 4};
    int target = 2;
    bool found = search(nums, target);
    cout << found << endl;
}