CSSE 230 Fundamentals of Computing Final Exam

Transcription

1 CSSE 230 Fundamentals of Computing Final Exam Winter term, Your name: Instructions: This exam is open book and notes. In addition: All the work you turn in must be your own. You must not use any forms of communication or cooperation. Disable all chat tools (IM, ICQ, etc) before the exam starts! For the first four problems, your computer has to be closed. You may look at all problems of this exam and work on them. However, once you open up your computer, you need to turn in the first four problems. The code you provide should follow good style and should be efficient. Due to time constraints, you do not have to comment your code. Write all answers on these pages. Use the back as necessary. Problem Points available Your score Total 100

2 1) a) [5 points] Insert the following elements: 7-8-3, in the order listed, into the Splay tree below. Use top-down insertion and simplified top-down zig-zag. Show your work b) [5 points] Remove elements 14-13, in the order listed, from the Splay tree below. Use top-down removal and simplified top-down zig-zag. Show your work

3 2) a) [5 points] Insert the following elements: in the order listed, into the AA tree below. Either indicate the level of each node by writing down its level or draw nodes that are on the same level using horizontal links. Show rotations that need to be performed b) [5 points] Remove node 3, followed by node 7 followed by node 5 from the AA tree below. Either indicate the level of each node by writing down its level or draw nodes that are on the same level using horizontal links. Show rotations that need to be performed

4 3) [10 pts] A project showcased at a CSSE Senior Project Expo has as its goal to take photos along a certain route and enable folks to see a composite image of the photos. Imagine you drive down Route 66 from Chicago to L.A. and you take a picture outside of the passenger side window every 1/10 of a second. Each image is automatically tagged with its GPS position. You can then process the images in a way that you could see one large photo of route 66; quite certain that largest photo ever made. Suppose you place those photos on a website and let users navigate this giant photo. Users need to be able to find photos by location and they need to be able to go forward and backwards. For convenience sake, user should be able to fast forward by only looking at each kth image, where k is determined by the speed of the fast forward or rewind. k can range from 1 to n, where n is the number of images along a route. Propose an efficient data structure that enables you to process the images as specified. Justify your choice by stating the expected runtimes of the operations specified above.

5 4) Analyse the best and worst case time complexity of the following algorithm. Assume that the graph is not empty. Let n be the number of nodes in the graph and let m be the number of edges. Count the number of times an edge gets accessed. Show your work. public ArrayList<Edge> somegraphalgorithm(graph g){ LinkedList<Edge> result = new LinkedList<Edge>(); HashSet<String> visitednodes = new HashSet<String>(); Iterator i = g.getnodeiterator(); Node initialnode = i.next(); visitednodes.add(initialnode.getname()); PriorityQueue<Edge> edges = new PriorityQueue<Edge>(); edges.addall(initialnode.getedges()); while (i.hasnext()) { edges.addall(i.next().getedges()); while (!edges.isempty()){ Edge e = edges.remove(); if (!visitednodes.contains(e.getneighbor())){ result.add(e); visitednodes.add(e.getneighbor()); return result; a) [5 pts] Worst case run time, using big-oh: Give an explanation of your answer and describe a case in which the worst case may happen. b) [5 pts] Best case run time, using big-oh: Give an explanation of your answer and describe a case in which the best case may happen.

6 5) [5 points] You are the Vice President of Data Structures (VPODS) at NORAD which monitors threats of Nuclear War. One of your engineers comes to you with a proposal for a better data structure. The engineer proposes to use a Hashtable of AVL trees. In other words, if two elements map to the same bucket of the hash table, they are inserted into an AVL tree, housed at that bucket. This proposed data structure is to supersede the current use of plain Top-Down Red Black trees. Evaluate this proposal. Appeal to the efficiency of common operations and the overall properties of the proposed data structure and the currently used data structure.

7 6) On-the-Computer part Download the FinalExam project from the folder located at: Study the code and modify it as follows. You may extend or implement any methods you would like. All code you write should be correct, efficient, and use good style. However, no documentation is required, because of time constraints. [10 points] Add a Java HashSet to the BinarySearchTree (BST) class. Add each element you insert into the BST also to that HashSet. Similarly, if you successfully remove an element from the BST, also remove it from the HashSet. Furthermore, use the HashSet to improve the performance of the BST insert and remove methods, by first checking whether an element to be inserted or removed is in the BST. [15 points] Implement a method called iscomplete() which checks whether a BST is complete. By complete we mean that the length of each path from the root to a leaf has the same length. [30 points] Modify the given code so that it implements a threaded Binary Search Tree. By a Threaded Binary Search Tree, we mean a tree in which each node has a link to its successor. The last node points to null. This can be accomplished in several ways. In order to get maximum credit, you need to update the successor pointers while inserting and removing a node, i.e. in average log(n) time. Simply put, you may not place all nodes into a sorted ArrayList and update the links in this fashion. If you add pointers to a nodes predecessor, inserting and removing nodes is a little bit easier than if you do not use pointers to predecessors. If you use pointers to the predecessors, the maximum number of points for this problem is 25 points. Below is an example of a Threaded Binary Search Tree. The dashed lines are links to the successors. Please submit your BinarySearchTree.java file to the Final Exam drop box on our Angel site.