Given a sequence database, we would like to find all sequential patterns that do not only satisfy a minimum support min_sup, but also start with “{a}” and end with “{b}”, where {a} or {b} is an itemset containing a single item a or b, respectively. How would you modify the PrefixSpan algorithm so that such patterns can be generated efficiently?

We discussed several Linked List Variations, each of which was more complex than the one preceding it, but that was able to do certain things asymptotically faster than the simpler variants could. This is one of many examples we'll see this quarter where we make a classic tradeoff in computing: using more memory (and, correspondingly, more complexity for managing what it's in it) in an effort to spend less time. While it's not always true that we can make things faster by using more memory, it's not at all uncommon to see these two things be on opposite sides of a tradeoff. One of the linked list variants we saw was a singly-linked list with head and tail pointers. Let's consider where this variant fell short and whether there are other ways to improve it besides what we saw. 1. Why isn't the presence of a tail pointer enough to allow us to remove the last node in the list in O(1) time? 2. Suppose that we added a third list-level pointer (i.e., outside of the nodes) called before Tail,…

It is straightforward and efficient to compute the union of two sets using Boolean values. We may create a new union set by Oring the matching items of the two BitArrays since the union of two sets is a combination of the members of both sets. At other words, if the value in the corresponding place of either BitArray is True, a member is added to the new set.Computing the intersection of two sets is analogous to computing the union, except that the And operator is used instead of the Or operator Using the same technique we used to detect the difference, we can determine if one set is a subset of another. For example, if:setA(index) && !(setB(index))evaluates to False then setA is not a subset of setB.The BitArray Set ImplementationWrite The code for a CSet class based on a BitArray.

Array lists and linked lists are both examples of list implementations. Give an example of a case in which an array list might be preferable over a linked list. Justify your actions in each scenario.