leetcode81 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.

class Solution {
public:
    bool search(vector<int>& nums, int target) {
        int a=0,b=nums.size()-1;
        while(a<=b)
        {
            int m=a+(b-a)/2;
            if(nums[m]==target)
                return true;
            if(nums[a]<target&&target<nums[m])
                b=m-1;
            else if(nums[m]<target&&target<nums[b])
                a=m+1;
            else
            {
                if(nums[a]==target)
                    return true;
                else
                    a++;
                if(nums[b]==target)
                    return true;
                else
                    b--;
            }
        }
        return false;
    }
};