PROBLEM 5: (1 point per dot) Fill in the blanks below. Consider worst-case input for any statements involving time. For any statements involving asymptotic complexities, give the bound in simplest form and give the tightest bound you can. Given a list of size n with a tail pointer, adding an item to the beginning of the list takes OL time. Appending an item to the end of the list takes l_ ) time. Given a sorted array of size n, finding an arbitrary item takes ol ) time. When implementing a using a list without a tail pointer, all operations (push/pop or enqueue/dequeue) take constant time. [options: stack or queue] Given a sorted array of size n, inserting an arbitrary item takes o _) time. requires Given a min-heap and an unsorted array, the less time for insert() asymptotically. [options: min-heap, unsorted array] Given an empty min heap, it takes OL time to insert n items. A min heap containing n elements has a depth of C ). Suppose I assign each of n students an index corresponding to their class rank (with no ties). I then give them a number of homework problems equal to their index. The total number of homework problems I give is oL Suppose I assign each of n students an index corresponding to their birth date, with 0 being the index of Jan. 1st and 364 being the index of Dec. 31st. I then give them a number of homework problems equal to their index. The total number of homework problems I give is o