lazy solutions..... Just skip the duplicates. Then worse case of time is O(n).

 

1 class Solution { 2 public: 3     int findMin(vector
     
       &num) { 4         int start = 0, end = num.size()-1, mid = 0; 5         if (num[start] < num[end]) return num[start]; 6         while (start < end) { 7             while (start < end && num[start] == num[start+1]) start++; 8             while (start < end && num[end] == num[end-1]) end--; 9             mid = (start + end)/2;10             if (num[mid] > num[end]) {11                 start = mid + 1;12             } else {13                 end = mid;14             }15         }16         return num[start];17     }18 };